Matrix

matrix

Did you know? Matrices in Java are also referred to as 2D arrays. Well, this is because the same components displayed on an array are organized in rows and columns in a matrix that forms a rectangular structure. Usually, the matrices are used for storing all the complex digits within a program that are further used for carrying out arithmetic applications such as addition, subtraction, multiplication, and more. Sometimes, the programmers are also required to set all the values of a particular matrix to 0. This in other terms is known as the problem. set matrix zeroes This is one of the most highly discussed problems in coding and technical interviews. Hence, if you are preparing for a coding interview and would like to learn a few simple approaches for setting a matrix value to 0, then keep reading. What Does It Mean to Set Matrix Zeroes in Java? Have you ever noticed how the numbers in a Sudoku are arranged in rows and columns of equal numbers of characters, making it a perfect square? Well, the structure of a matrix in the context of computer programming resembles similar characteristics to a sudoku square with the only difference being that the shape of a matrix is rectangular. Matrices are used for arranging the entries or the elements of data that usually represent a mathematical object. So basically, a matrix can essentially be defined as a set of numbers that are arranged in columns and rows in order to form a rectangular shape. So, what would a zero-column matrix represent? Well, the Matrices containing a zero column would signify that all of its elements or entries are equal to zero. In other terms, such matrices are also referred to as zero matrices in computer programming. Did you know? Like all the other data structures, you can also manipulate the matrices (such as setting them to zero value) using different logic. The Set Matrix zeroes problem is the discussion we shall be having next in the following column. Let's find out the approaches that will help you effectively set the values to zero within a matrix. Which Algorithms Can Be Used to Set Matrices to Zero? The set Matrix zero problems are one of the top coding questions asked in almost every coding interview. From Brute Force to HashMaps, the set Matrix zero problems in programming can be solved using only two programming approaches If you are not acquainted with these methods, check out a quick overview of their definitions. **Brute Force Approach Brute Force is a simple function that focuses on approaching the problem by dividing the input into several subarrays and seeking every single input individually. In the context of setting the matrix to zero, we will be using the auxiliary space and the nested loops to their optimal efficiency. The nested loops are ideal for dividing the problem into subproblems by inserting the elements of the input into loops that can be traversed later. **Using Hash Table A HashMap is essentially a structure of rows and columns that are used for storing the entries so that the efficiency of finding the solution becomes relatively easier. The contents of the array or the entries are iterated on a HashMap. Hence, in this approach, we will be using the Hash Table in order to store the status of the rows and columns. Using In-Place Hashing In-place hashing is a more in-depth method where the hash is used to store the values of the elements or entries within the first line of the rows and columns of the matrix. We will be employing two different variables for storing the elements in the first row and column namely: and . For a more in-depth analysis of the working mechanism of the algorithms for these approaches, check out the next section of this blog. firstRow firstColumn How to Apply the Algorithms That Set Matrices to Zero in Java As discussed in the previous section, the set Matrix zero problems can be tackled by simply using the Brute Force Approach and by implementing a Hash Table. Let's discuss the in-depth analysis of the algorithms for these approaches and you can decide for yourself how their time complexities compare to one another. Method 1: Using Brute Force Approach Here's how the algorithm for Brute Force shall be implemented: Start with creating a temporary matrix and name it as m*n. Initialize the elements of this matrix with 1. Now, travel to the first matrix that you were initially provided as an input and set the positions of its elements into row 1 and column j along with 0 in the newly created matrix. Finally, you can proceed and continue to copy all the elements as such in the temporary matrix from the initial matrix and print the program once the process is completed.\ Method 2: Using Hash Table The algorithm for the Hash Table would look something as follows: Start with creating two different Hash Tables. Next up, you will have to initialize the value of the rows and columns of the table to false. Further, you may iterate on the initial matrix and set all the values to 0. Complete the entire process until all the values return 0 input.\ Method 3: Using In-Place Hashing Here's how you can implement the in-place hashing algorithm: Start by defining the two variables i.e firstRow and firstColumn. Set both variables to false. Using the Hash Table to store all the false values from the rows and columns Finally, update the value of the first row and column on the Hash Map.

Setting a Matrix to Zero in Java

Disclaimers: Image credit Twitter user: @IrenaBuzarewicz This story is not a movie review. There are NO SPOILERS. When the first Matrix came out, I was still studying. Wannabe or soon-to-be graduates are all the same all over the globe. Lost to be found in the "Bermuda Triangle" between exams, dreams, and loves. A bunch of selfless idealists who are always ready to do good deeds. I remember that we were among the first in line as blood donors. One day it was a bit different. Our local hospital got a new and expensive machine for HIV testing. The medical staff asked for volunteers to test it. Sure, a drop here or there. What difference does it make for us as long as it's for the greater good? We laughed and teased each other on our way out. They told us to get back tomorrow for the test results. The Night of Movie Magic It's not easy to take a test, any kind of test, and wait for results. "What if" questions hit me hard in the evening. I didn't feel like going home. "Things to Do in Denver When You're Dead." A shortlist of available options. I saw a movie poster for "The Matrix." I had no clue what the movie was about. I needed to get my mind off the test. The movie ticket price was a small price to pay. Until that special night, I didn't buy any of those cheesy stories about the so-called "movie magic." For two hours, I was living in the Matrix physically, emotionally, and intellectually. I totally forgot about the HIV test itself. I had one of the calmest nights in my life. I didn't sleep like a baby; more like The Notorious B.I.G. - Hypnotize(d). In the morning, I found out that I was HIV negative, and I realized that I was Matrix Universe positive. That movie should've been prescribed as a tranquilizer. Fast forward twenty years, give it or take, I had a deja vu. The Pandemic Rhymes With Tragic I had to take another test. Again, I had to wait for the results, but this time with my wife. It was a comical Grey's Anatomy situation where we both looked at my lungs' x-ray images. What do you make of this? I don't know. I don't smoke. My wife already had COVID. This is how I found that we had an impressive collection of perfumes in our home. Our teenage daughter was an experienced and patient "perfumist," who wanted to make sure my sense of smell was still operational. What do men know about perfumes? They're all the same, except for the price. Right? I thought that my wife would return a favor and volunteer to be a food tester, the Gladiator-movie-style. Nope! Her post-COVID diet came first. So, I was COVID symptoms-free, which made my test more than just a "formality" and a "simple" confirmation. How to kill time, this time? HBO came to the rescue. I thought, The Matrix Resurrections to my satisfaction. Here we go again! oh lucky me, what were the odds? More than two hours. Plus, coffee breaks, phone calls, and email checks. It was a long day with a double negative outcome. The result was negative, and the movie too. It failed to help me forget and "transcend." So much for the "movie magic." I thought that rewatching the first Matrix (for the hundredth time, give it or take) would make things better. Nope! It became even worse. I had to take a real tranquilizer. No red and blue Morpheus pills; this one was - pale pink. Twitter Rhymes With Bitter In a state of complete despair, I went on Twitter. This is how I stumbled upon a picture you see at the beginning of my story. I know what you want to ask me. Why bother writing a story when the four-part picture is worth more than my words? Well, writing makes you feel good. Writing for Noonies is like watching good old movies! Do you know what can make me feel even better? Your vote for my nomination. And, what about Matrix 2 and Matrix 3? They are, they are, good. Critical Thinker Noonies Award

The Matrix Resurrections: Between Expectations and Imperfections

The Matrix: Resurrections was released last week, but the reviews split between those who loved it and those who didn't. In this slogging thread, our community discusses the Matrix saga and their expectations for the new movie. This Slogging thread by Mónica Freitas, Teri Eyenike, Sara Pinto, Limarc Ambalina, Linh Smooke, Abeer and Jack Boreham occurred in slogging's official #pop-culture channel, and has been edited for readability. Mónica Freitas Dec 27, 2021, 4:14 PM was released last week, but the reviews split between those who loved it and those who didn't. Are you interested in seeing this new matrix movie? Do you think it makes sense to have a sequel after so long? What's your favorite thing about The Matrix movies? The Matrix: Resurrections Teri Eyenike Dec 27, 2021, 4:26 PM I'm indifferent at the moment whether I want to see the movie. It's been a long time I saw the Matrix in my teen years, and I will have to watch it again to relive the memories. Let me see the preview of the resurrections, and I may change my verdict 😂 🔥 1 Sara Pinto Dec 27, 2021, 4:28 PM Mónica Freitas So... I've tried. I really did try to watch  The Matrix, but I just fail at it every time. I guess it's too much fiction for me. I need someone to convince me otherwise, haha. Limarc Ambalina Dec 28, 2021, 2:59 AM I actually dropped off from the Matrix after the first film. I watched the other but was confused or just uninterested. Limarc Ambalina Dec 28, 2021, 2:59 AM I'd watch this one just to support Keanu Reaves though 😄 Mónica Freitas Dec 28, 2021, 11:23 AM Teri Eyenike Same. It's been a long time since I saw the Matrix - actually in a philosophy class back in high school - and I loved it then but haven't rewatched ever since. I'll have to do that before this new movie though I'm not sure why we're having this movie now... Let me know what you think if you decide to watch it. 👍 1 Mónica Freitas Dec 28, 2021, 11:24 AM Sara Pinto, just focus on Keanu! He's the reason, ahahah. 😂 1 Mónica Freitas Dec 28, 2021, 11:25 AM Limarc Ambalina, same, at this point, I would only watch it for Keanu. His recent interviews about the movie have been golden! Mónica Freitas Dec 28, 2021, 11:26 AM https://www.youtube.com/watch?v=rZM5Fb-9dto Linh Smooke Dec 30, 2021, 6:50 PM Ah, let me and David try to watch it this weekend (hard to schedule with a toddler at home ha) and give y’all a review!! 💚 1 Mónica Freitas Dec 31, 2021, 11:18 AM Linh Smooke, Yes! Let us know what you think of it 🙏 Linh Smooke Dec 31, 2021, 6:29 PM OK. lots of feels. I don’t know how well people remember the matrix, but for someone who doesn't remember it that well - it was very refreshing to get a movie with so many callbacks and plot explainers, lol. I personally like the fanservice-y  meta-commentary and breaking the 4th world aspect of it…and love the cast (which, apart from the amazing Keanu Reeves and some other white actors like NPH who I adore, is super, super diverse — and I love that!) Reading online though it seems superfans don't appreciate the lack of actions and some of the lame plot choices but who cares. As someone who watches it casually, I love the movie! I’m known to always sleep in movies and for this one, I only sleep for 10 mins so that’s a definite win 😂 😂 2 💚 1 Mónica Freitas Jan 3, 2022, 2:27 PM Linh Smooke, so, it's a movie suitable even for those who haven't seen the first movies? Mónica Freitas Jan 3, 2022, 2:27 PM Linh Smooke, about the lack of action, did you find it a slow film with a lot of explanation and not a lot of plot? Mónica Freitas Jan 3, 2022, 2:27 PM Linh Smooke, only 10 minutes?! ahaha a record? 😂 1 Linh Smooke Jan 3, 2022, 3:22 PM Not necessarily slow, just a bit dragged out towards the end. I watched the first one so I do understand some. But I bet if you haven't you still can enjoy it. Maybe you'll enjoy it even more haha? But who hasn't watched the matrix at this point 🤔 Mónica Freitas Jan 4, 2022, 11:21 AM Linh Smooke, hum I see. After your review, I got a bit of my hope back for this movie, ahah. I think I'm giving it a go. If for nothing else, then just to see Keanu in a letter jacket 😂 😂 1 🙌 1 Mónica Freitas Jan 5, 2022, 3:13 PM Abeer Jack, Boreham, what are your thoughts on the new Matrix movie? Abeer Jan 5, 2022, 5:59 PM Mónica Freitas, I haven’t seen it yet. To be honest, I haven’t really seen anything past Matrix Reloaded. I have been considering catching up and watching it just for Keanu though 😂 Jack Boreham Jan 6, 2022, 10:49 AM Mónica Freitas, I am, but is it just as complex as the others? If it is, I might give it a miss, haha Mónica Freitas Jan 6, 2022, 11:25 AM Abeer Keanu is truly our "God", hahaha. If you do watch it, leave us a review. 😂 1 Mónica Freitas Jan 6, 2022, 11:27 AM Jack Boreham, not a fan? I'll revoke your nerd card now 😂 Jack Boreham Jan 6, 2022, 1:52 PM Mónica Freitas, wait noooo, don't do that. How can I prove my nerdyness? Mónica Freitas Jan 6, 2022, 2:21 PM Jack Boreham, guess you'd have to name 5 matrix characters without googling it or watch the first movie, ahaha.

Is The Matrix Resurrections Worth Watching? (Slogging Insights)

Image via techacute.com Is Lumen pioneering a fashion movement away from fast fashion? Fast fashion is something that despite being horrible for the planet is not going away any time soon. Fast fashion for a plethora of reasons is a fashion system that continues to be supported by consumers despite the ongoing growth in textile waste. Fast fashion has its pros but an excessive amount of cons. In recent times, Canadian fashion brand Lumen Couture has developed technology and fashion that can cater to the pros of fast fashion while actively eliminating the cons. This is what the Matrix Collection embodies. What is Lumen Couture? In 2012, Lumen Couture was founded by Canadian CEO Chelsea Kluklas. Lumen Couture is a brand that is part of the Canadian Initiative Make Fashion. Lumen Couture creates runway garments to focus on conceptual prototypes of innovative fashion, pushing the boundaries of creativity and technological capabilities. Lumen Couture seeks to redefine the industry and address its pollutant crisis by developing technology to further sustainable and ready-to-wear garments. Lumen Couture is widely known to host events such as their annual MakeFashion runway gala in Calgary, Alberta. At this gala, Lumen Couture presents prototypes that display futuristic garment capabilities to their audience which provokes thoughts on how fashion can evolve with technology. The Iconic Dua Who’s Pushing the Boundaries A brand as innovative and creative as Lumen Couture comes equipped with a pair of brilliant and creative minds who share a common drive in evolving the fashion industry through technology to be sustainable. Chelsea KIuklas and Chris Corner are the brains behind this wonderful fashion venture that’s transforming how we look in our clothes. Chris Corner is a telecom engineer, and entrepreneur who plays a vital role in connecting businesses like Lumen Couture to their desired consumer. Comer is the CEO of his own telecommunications company where he strategically converts these connections into sales. Chelsea Kluklas is the creative and technological powerhouse behind Lumen Couture. She has an impressive resume that goes beyond her role as CEO for Lumen Couture and Makes Fashion. Kluklas has been linked to companies like Facebook and Oculus VR. The University of Calgary alumni has been able to produce designs that have been globally consumed and recognized in places such as New York and Rome. The Matrix Collection Lumen Couture’s Matrix collection is unlike the average trendy fashion collection. The Matrix collection is particularly special due to its unique ability to adapt to whatever the wearer desires. With panels made of thin LED lights and technology that gives you the capability to alter the design of a garment with the touch of a smartphone. This technology allows the wearer to connect via Bluetooth and alter colors, prints, and even video through their phone. Why Is This So Important? The Matrix collection and Lumen Couture’s fashion garments are significant game-changers in the current day of fashion. In the last decade, fast fashion has continuously contributed to the decay of our ozone layer and so many other elements of our earth. Fast fashion changes and evolves with trends at a rate that has been proven to be incredibly unsustainable. With the Matrix collection, consumers can reject the harmful need to end the lifecycle of their garments prematurely by investing into the Matrix collection where they will be able to alter the appearance of their clothing through the use of LED panels and Bluetooth technology. The Collection Aside from the groundbreaking technology used to craft this special collection, the Matrix collection has more to offer beyond the boundaries of futuristic technology. It offers unique and minimal silhouette designs as well as accessories that offer plenty of versatility. The collection currently consists of the following six pieces: The LED Matrix Choker The LED matrix choker is an accessory fit for any outfit. The choker has an equalizer mode feature that allows the lights to respond to the beat in any design you choose from the app. This includes writing text, drawing your own pattern, or choosing from a library of presets uniquely designed for clothing provided by Lumen Couture. The LED Matrix Facemask If there is one accessory everyone in 2021, it’s the obligatory facemask. With the pandemic still impacting our everyday essentials. A fun opportunity to add some dimension to this essential item would be the LED Matrix facemask, where similar to all the other pieces in the collection, you have the ability to change the style of the mask through your phone. Most importantly, the mask has the ability to remove the LED panel and battery to allow for proper sanitation and to optimize breathing capabilities. These facemasks also served a charitable purpose as the sales made in the months of April, May and June went towards the WHO Covid-19 Relief fund, which raised a total of $4,500. The LED Matrix Hoodie Graphic clothing is always a fun and casual way to add personality to your wardrobe. Graphic t-shirts and hoodies have become the average consumer’s obsession over the last decade and one just can never seem to collect enough. That changes with the LED Matrix Hoodie. This hoodie gives you the opportunity to combine all those desired graphics onto one piece of clothing through the use of your phone! The Matrix Skirt Concluding the Matrix collection is the Matrix Skirt. The Matrix Skirt features the option of a sheer overlay to add some extra dimension and movement to the classic-fitting pencil skirt. Similar to all the previously mentioned pieces in the Matrix Collection the Matrix skirt comes in black and is accompanied by white LED panel lighting. What Does this Mean for the Future? Trends and artistic expression are not leaving the fashion industry anytime soon. In fact it could be argued that they are an essential part of the fashion system itself where the industry would crumble with its absence. With the technology behind Lumen Couture’s Matrix Collection, the possibility to indulge in the ever changing fashion trends in the industry while not actually buying and discarding a surplus amount of clothes for once actually seems plausible.

The Matrix Collection Lets You Alter Garment Designs with the Touch of a Smartphone

SPOILER ALERT: Reading this article in advance might impact your actual Coinwink Matrix experience and you’ll receive a lower level of satisfaction. Similarly, like someone spoils a movie for you by telling how it ends. That is why we strongly suggest first to experience the Matrix, and then return here to read the article. In your Coinwink account , switch from Classic to Matrix, and you’ll see how deep the rabbit hole goes. The CSS Wonderland During the last month, a lot of front-end updates were made for Coinwink. The previous CSS styles file was a big mess. Started almost 4 years ago, many styles were inlined or randomly smashed together with overwrites and without a structure. !important To fix such a chaotic styles file it takes quite a lot of time. These are little fixes but they are time-consuming, and when they’re done, it seems that nothing has changed. Why so? Because the changes are behind-the-scenes. For example, a bigger invisible click/tap area for buttons. The user doesn’t see or think that there is a difference, but she feels it intuitively. “What you know you can’t explain, but you feel it.” ― Morpheus All together, these little changes create a slick and smooth experience and make the web-app feel more like a native app. What are these app-like changes, you might ask? - Disable zooming on mobile devices - Disable text/element selection on mobile devices - Create bigger invisible touch areas for clickable elements - Separate and states on desktop and mobile devices - Minimize flickering - App icon for mobile devices, web app manifest, theme color etc. - Create custom form elements (inputs, drop-downs, buttons, checkboxes, etc.) with consistent style across all browsers - Styling scrollbars :hover :active And a few more tweaks here and there. Some of these things are implemented “out of the box” in most CSS frameworks, but Coinwink is not using a framework because similar frameworks often result in generic feel or enforce a specific style, and also increase the size of the app more than the custom CSS. Additionally, during the recent updates, significant structural front-end changes were made. When looking from the outside, they are also invisible. The new structure allows us to easily change styles, build new front-end features, and we can now create themes. Introducing the new Matrix theme The first theme built on the new Coinwink front-end structure is the Matrix. “The Matrix is everywhere. It is all around us. Even now, in this very room.” ― Morpheus From the conceptual point of view, the Matrix is another dimension of reality, or a simulation (if the reality itself is not a simulation). The concept has deep meanings across different cultures, and this infuses the Matrix theme with the story and symbolism. “You take the red pill—you stay in Wonderland, and I show you how deep the rabbit hole goes.” ― Morpheus A switch to Coinwink Matrix theme is animated and not instant. It creates the effect of a transition into a different dimension. To experience the Matrix, switch the theme in your Coinwink . account Screenshots: Crypto Alert, Portfolio and Watchlist views Similar to other recent updates, Coinwink Matrix theme is extremely lightweight. When activated, it adds only around 20KB of size. It’s the first theme – a showcase of new possibilities. The dynamic background is now probably too active, so in the near future, it will be possible to turn it off or make it less prominent. More themes are planned for the future. Above are presented Coinwink app mobile views. Coinwink works equally well on both desktop and mobile devices. The newest source code will be available soon on our . GitHub As usual, your feedback is appreciated! Let us know what do you think about the new Matrix theme? What other themes and features you’d like to see in the future? Coinwink is a cryptocurrency price alerts, watchlist and portfolio tracking app for Bitcoin, Ethereum and other 2500+ crypto coins and tokens. Don’t waste time watching crypto prices, use Coinwink .

Step Into The Matrix With Our New Update

Many problems, especially in scientific computing, end up being formulated as matrix operations. This can be anything from PDE-solvers (PDE - Partial Differential Equation) up to image-processing or ML-algorithms. The list is endless. Usually one has written on paper some final equations which describe your model or whatever it is, and it involves some matrix algebra like this: A = B + C Okay, looks quite easy on paper. Now, when it comes to implementation of this in JavaScript, whatever technique you are going to use (for-loops, iterators, ...), your code won't resemble above easy to read line. There is a huge amount of good matrix-libraries available, and usually they let you write something like this: A = B.add(C) This still looks not quite different from our paper version, but imagine our paper version would be this: A = (B * (C + D)) * (E + F) To put this into one line by using the '.add' notation might hurt a little and one would tend to split the code into multiple lines. Though, due to all these parenthesis, readability would be destroyed: H1 = E.add(F); H2 = C.add(D); H3 = B.multiply(H2); A = H3.multiply(H1); const const const const If we were in context of a language like C++, we can give sense to expressions involving mathematical operators between any custom types - a concept called Operator Overloading. At the time of writing, JavaScript is lacking this nice feature though. We can find some resort if we take a look at 'Tagged Templates' (see https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Template_literals). In essence they give us a way to interpret a given string together with value filled placeholders: A: Matrix = ...; B: Matrix = ...; C: Matrix = calc ; const const const ` + ` ${A} ${B} Here 'Matrix'  shall be some type representing a matrix. The 'calc' is a tagged template function, written by us, and it will be called with all string parts and values for given placeholders. In other words we somewhere define a function like this: { } ( ) function calc stringParts: TemplateStringsArray, ...values: any[] '1.) parse the expression
         2.) calculate it by using given   
             placeholder-values
	 3.) return the result' Our main task remains to implement the 'calc' function such that it can cope with any kind of expression from matrix-algebra. You can do it on your own, it is quite a learning-full experience, or you can use my package provided here: https://www.npmjs.com/package/@applied.math.coding/lina With this at hand you can write expressions like these: calc ;

A = calc ;

calc ; ` = 3 * - ` ${A} ${B} ${C} `3 * - ` ${B} ${C} `pow( , 5)` ${A} The library also supports some form of slicing which becomes very handy in some occasions: calc ; ` )` ${A.slice( , , , ) =   
  cos(${B.slice( , , , )} 1 1 5 5 1 1 5 5 It also has some support of creating a matrix-type from given array: A = mat([[ , ],
               [ , ]]); const 1 2 3 4 Or just create a new instance of some dimensions and with all values set to 0: A = zeros( , ); const 10 10 calc ; ` =sqrt(abs( )) + 7` ${A} ${A} Note: when you add or multiply a number with a matrix-type, as in above example, the parser is handling this by element-wise applying the operation to the matrix. And finally our initial example would look like this: calc ; ` = ( * ( + )) * ( + )` ${A} ${B} ${C} ${D} ${E} ${F} For more you can look into its docs or tests. Please keep the following in mind: The library is not intended for use in computation intensive environments. It rather should be used for educational purposes or for presentation of some computations on a web-page. I used it successfully in some small project which intended to explain the solution procedure of a PDE. I hope this helps or contributes to getting new ideas!

Solving Matrix Algebra in JavaScript [An Overview]

Science and the Simulation Hypothesis point to many reasons we may already be in the Matrix When came out, the idea of living in a video game was squarely in the realm of science fiction. Today, the simulation hypothesis is debated seriously by computer scientists, philosophers, physicists and others. The reason this argument is taken more seriously now is two-fold: the Matrix the philosophical “simulation argument”, put forward by Oxford’s Nick Bostrom, and the “video game simulation argument”, about the rapid development of video games, put forth by, among others, Elon Musk. Two Major Developments The first was when Oxford professor Nick Bostrom published his 2003 paper, “ ” Bostrom didn’t say much about video games; instead he made a clever statistical argument. Bostrom theorized that if a civilization ever got the Simulation Point, it would create many ancestor simulations, each with large numbers (billions or trillions?) of simulated beings. Since the number of simulated beings would vastly outnumber the number of real beings, any beings (including us!) were more likely to be living inside a simulation than outside of it! Other scientists, including physicists have taken up this argument. Are You Living in a Simulation? In the video game version of this argument, we have the rapid advancement of graphics technology. Elon Musk, speaking at the Code Conference in 2016, asserted that 40 years ago, we had pong, which was essentially two lines and a dot. Today we have VR and AR and MMORPGs — all based on 3D technology. If the pace of video game development continues, in a few decades we would have hyper-realistic games, indistinguishable from reality. I call this point the Simulation Point, and in my new book, The Simulation Hypothesis, one part is dedicated towards the stages of technology needed to reach this point. It’s much easier to see a path from today’s VR to something like than it was in 1999 when the movie was released. With games like and having millions of online players interacting in a shared online world, the idea that we might actually be in a shared connected simulated world doesn’t seem so far-fetched as it might have in 1999. The Matrix Fortnite, Minecraft, League of Legends In this article, we go beyond Bostrom’s and Musk’s simulation arguments to explore some of the reasons why science might be telling us we are in a simulated reality, like the Matrix. 1. Pixels, Resolution, Virtual and Augmented Reality Today we are already seeing with Virtual Reality that “full immersion” is possible. Anyone who has played a convincing VR game will realize that it’s possible to forget about the real world and “believe” the world you are seeing is real. As a great example, I was playing a prototype of a Ping Pong VR game last year (built by Free Range Games), and even though it wasn’t realistic resolution, I lost myself and thought I was playing ping pong for real. So much so that I set the paddle on the ping pong “table” and leaned against the table. Of course, it was a VR table so it didn’t really exist — I ended up dropping the paddle (actually the Vive controller) onto the floor. As I leaned into the “table” I almost fell over before realizing that there was no table. In other words, to quote from , there is no spoon. The Matrix The immersion comes not just from the number of pixels, but from the controls and responsiveness that VR is able to achieve. In the novel (and Steve Spielberg film) , which was about a VR world called the OASIS, users had lightweight glasses and wore haptic suits and walked on omnidirectional treadmills to add realism. In that world, the OASIS was preferable to real life. Ready Player One The fact that 3D models can be used to create realistic looking objects in films(a glance at movies like Blade Runner 2049 will convince you that we have enough pixel resolution to create realistic looking objects), and that 3D printers can be used to “print” physical objects shows that the physical world can be represented by information, a key part of the simulation hypothesis. Where does the responsiveness and fidelity come from? The limitations today are in real-time rendering and in they way that objects interact with each other inside the world. Most games have a and a . The physics engine is never fully realistic (otherwise it would take you too long to go from one part of the game to the other), and the rendering engine is what’s responsible for making you “see” what the world looks like by deciding what color pixels go where. We can easily see that full immersion may be possible in a few years time. physics engine rendering engine 2. Pixels, Quanta, and Zeno’s Paradox Speaking of pixels, could it be that what we call the physical world also consists of pixels? I recall late nights at MIT during my undergrad years where I had philosophical debates with my classmates about the nature of reality. This was the first time I’d heard of Zeno’s paradox, who presented it in terms of Achilles and a Tortoise. If Achilles was behind the tortoise, and he always had to make up half the distance, how could he ever get there? Zeno’s parado involved Achilles and the Tortoise. Lurking underneath this paradox is the question of whether space is quantized or if it is continuous. The idea was that if space was continuous, like numbers are (you can always find an infinite number of numbers in between any two numbers), how is it possible to touch an object such as the wall? You would always have to cover half the distance and never get there. quite This was my first hint that space might be quantized. Today’s physicists generally acknowledge the Planck length as being the smallest amount of space that can be measured. Below that length, the quantum fluctuations make it impossible to measure anything with any reliability. For all practical purposes, the Planck length is our minimal addressable “pixel” of space. Moreover, physicists tell us that most of what we think of as a solid object is actually 99% empty space, especially if you look inside the atom. The quanta in quantum physics consists of discrete quantities — of energies or “states” that a particle can exist in. Newton’s equations assumed a continuous amount of space; it turns out the universe may be more quantized than we thought. A related question is whether time is quantized? In all computer simulations, there is the idea of “generation” or “steps” in the simulation. These are some multiple of the processor clock-speed, which is the minimum speed at which something could be measured for any simulation running on that processor. Whether time is quantized in the real world is an open question, though there are some that suggest it is, and planck’s time constant (the amount of time it takes the speed of light to travel the planck length) is the minimum quantied time. If so, this would be more evidence that we live in a computation based reality. 3. The Collapse of the Probability Wave, Quantum Indeterminacy In quantum physics one of the most intriguing ideas is the probability matrix, which is an interpretation of how subatomic particles can exhibit properties of both a wave and a solid particle at the same time. At the level of an electron or a photon, the wave is interpreted as a set of probabilities of where the particle might be at any given time. When we observe a particular possibility, then the probability wave is said to “collapse” and we see a single particle in a particular location. This is called Quantum Indeterminacy. How does the probability wave collapse? This is one of the biggest mysteries in physics. The best answer physicists have come up with is that consciousness somehow determines the collapse. Max Planck once wrote, “I consider consciousness as fundamental and matter as derivative”. An even bigger mystery is why does the universe work this way? The simulation hypothesis provides a pretty good answer. The reason that video games have advanced so far in a few decades is because of optimization techniques. It would be impossible even for today’s computers to render in real time all the pixels of a single 3D world — instead, information is stored as 3D models outside the rendered world and then only what a particular character can see from a certain angle is rendered. The golden rule of video game rendering engines is: render only that which can be observed! Many adherents of the simulation hypothesis think that quantum indeterminacy is an optimization technique with the same basic idea: only render that which is being observed. The most famous example of this is Schrodinger’s cat, the poor feline who is trapped in a box with radioactive material. After an hour, the probability is that hte cat is either dead or alive. Common sense tells us that the cat is already either dead or alive, and when we open the box we are merely finding out what happened. Quantum physics tells us this is wrong: until we are there to obeserve it, the cat is actually both alive and dead at the same time — what’s called a quantum superposition! 4. Future Selves, and Parallel Universes Another related aspect of Quantum Physics that sounds like science fiction is the Parallel Universes theory, where we branch into different “universes” when we make decisions. If that’s true, then there is a directed graph of multiple universes that are branching out each time we make a decision, resulting in different timelines (in fact, the parallel universes theory was put forward to solve the grandfather paradox of time travel). Which of those universes do we branch into? this may have to do with the one that is most “optimal” — meaning these universes may or may not exist as actual physical realities. The Minimax algorithm looks at possible futures, calculating which one is the most optimal for a video game. Physicist Fred Alan Wolf, for example, says that information from these possible futures is coming to us in the present and that we send out an “offer wave” into the future, which is interacting with the “offer waves” coming from the future to the present. Which possible future we navigate to depends on which choices we make, and how these two waves super-pose on each other (or cancel each other out). These are startling results. Future probable selves are sending back information to the present, and we are consciously choosing which path to follow. This reminded me of the very first video game I made back at MIT. The way that the computer chose the next move was to project the possible futures, and then use a certain algorithm to “rank” those futures, and then bring those values back to the present and then the AI would choose the path to follow. Did the possible futures we were calculating in our game actually exist? Or were they just probabilities? I realized that this isn’t too much different from what’s happening at the quantum level, except that in existing games like chess or checkers, we use a simple function (based on the rules of the game) to decide which of the paths is most optimal. We used the “minimax” algorithm in game design, trying to maximize our score and minimize our opponents score at each “turn of the future”. Physicist Thomas Campbell, in his 2003 book, (Theory of Everything) also proposes that there is a fundamental function and that we are essential in a computatiuonal universe that branches off possibilities and uses an evaluation function, just like a video game! He and a team from Caltech raised funds in 2018 on kickstarter for a series of experiements to try to prove this! My Big TOE 5. The Speed of light Another big mystery is why the speed of light is one of the few constants, one of the few fundamental values in physics. In fact, all matter has been equated with energy, and energy may be a derivative of light itself. While other things change, including gravity and space-time, Einstein found that the speed of light remains fixed. Why would the speed of electromagnetic waves be the same speed at which information can travel through the universe? In video games, it turns out that pixels are based on light — they are illuminated for a temporary period, and all communication happens between computers at the speed of light. Just as in relativity where simultaneity cannot really be guaranteed, the same is true video games — each player is working off of his computer and responding to information about the game, which is being sent to cloud servers outside the rendered world. The cloud serve is doing its best to respect simultaneity and order the events, but it may actually be impossible. Conclusion Along with the statistical simulation argument and the advance in video game technology, these are some of the reasons why scientists are starting to take the simulation hypothesis seriously. In fact, many physicists and biologists are starting to realize that underneath the physical objects they are studying, the universe is actually information. Famous physicist John Wheeler in his autobiography wrote “it from bit” — meaning that bits, not matter, are the fundamental “thing in the universe”. In fact, he said physics went through three phases in his career and each phase was an evoluation of our understanding of the universe. The fist phase was that “everything was a particle” (material, newtonian model), then “everything was a field” (quantum probability model), and finally, “everything is information” or bits. If everything was information, or bits, then this would not only be consistent with a video game simulation like that in , it would explain some of the big unanswered questions in science — why does it work this way? The Matrix While we aren’t able to duplicate at this stage of our technology, our computer science and video games have gotten far enough along that we are well on the road to the Simulation Point. The Matrix Buy Rizwan Virk’s book The Simulation Hypothesis: An MIT Computer Scientist Shows Why AI, Quantum Physics, and Eastern Mystics All Agree We Are In a Video Game , or find out more at www.zenentrepreneur.com Originally published at scientificinquirer.com on March 22, 2019.

Are We Already in the Matrix?

Today You Started a Business By . James Alctucher Originally published on JamesAltucher.com A friend of mine left his corporate job yesterday after 23 years of being trapped in the Matrix. I hate it because I’m envious of that moment. The day I left a corporate job to be on my own for the first time. Suddenly you go from managing a cubicle from the hours of 9 to 5 to having to manage ALL OF TIME AND SPACE. The holograph screens that altered the universe around you peel away to show you what the real world looks like. The extra colors and intensity that had been hidden from you behind tinted-black glass windows and fluorescent lights. I wish I had done it differently. I wish I had known what I know now. I was working at HBO. I had a cubicle on the 6th Floor of 1100 Sixth Avenue. My boss was down the hall. His boss was in the room next to his. His boss was in the room next to that. And the real boss (the top guy’s secretary) was in front of all of their offices. I had a view of the McDonalds at Sixth Avenue which is now the big Bank of America building. (I did the website for seasons 1–3 of Sex and the City) Work in the corporate world is like a hazy drug dream to me now. You could get in at 10am. Everyone took breaks downstairs to smoke. I didn’t smoke so I took licorice with me. Then at noon, LUNCH! And then after lunch, chess in Bryant Park. Then my boss left to catch his train at 4:15. So I would leave at 4:16. Before I had my own business on the side I’d take the subway to Astoria and go to Steinway Billiards. Everyone there was Greek. We’d all sit and play backgammon and chess and drink thick Greek coffee until about two in the morning. Sometimes my friends from HBO would come with me and it would be like . And I loved all the girls in the place but not a single one ever talked to me or looked at me no matter how many two dollar bills I tipped with. a party every night There were goals and deadlines at work. Except for the summer. There was never anything to do in the summer. And all other times the deadlines were mild. Like if you missed one then it just meant a meeting was rescheduled. Nobody would get fired. The saying was, “if you want to get fired you have to stand on Albie’s desk and pee on him.” That was the boss’s boss’s boss. As part of my job I got to go to San Francisco for the first time, Los Angeles, and sunny Orlando (to make the website for the series “From the Earth to the Moon” which was shot right in Disneyworld.) And then I quit. I had to. I was running a business on the side. We had clients, some of whom were even competitors to HBO. We had employees. I had payroll to meet. And I felt myself stagnating at my job. I couldn’t get out of bed in the morning. I stopped enjoying the meager things I was doing. And I thought I could handle the psychology of being on my own. What could be different, I thought. I wanted to spread my wings even though I had no idea how to fly. I cried twice the first day on my own. First time, at lunch with one of my partners, Randy. It suddenly hit me that I didn’t have a multi billion media empire as my backstop. I was on my own. I felt alone. Which is another way of saying, if I fucked up I had nobody to blame. Like we all did in corporate America. So over pizza I cried. “Are you ok?” Randy said. Poking at my weakness. “Yeah,” I said. Then later at dinner with all my ex-employees and friends at HBO. I ordered pasta AND fries. Everyone started to laugh at what I had ordered and I wasn’t sure why. I felt like a four year old in a room filled with laughing adults. I had no idea what I was or what I was supposed to be. That made me cry again but nobody noticed. I had been anchored close to shore with Time Warner as the dock. Now I was in deep waters. Too deep to anchor. I had to fish now. I had to find food. I had to get water. I had to feed a lot of people. I had to kill or be killed. I learned a lot in the next few months: If you blame others, you go out of business. Take responsibility for your problems and fix them or move on. A) It was always my fault when things went wrong. If you hide from customers, they will fire you. If you hide from employees they lose respect for you. If you hide from investors, they sue you. B) I had to communicate to people. I had to help customers feel their jobs were about to get a lot easier because now I was in their lives. I had to learn to reward people. I wanted everyone around me to feel good about it. To spread the word that I was someone to work with, to be around. C) I had to help employees feel good about their jobs. We were a web design company but we considered being a tea company, a rap label, a magazine, a TV show, a cable channel, and a social network for dead people. A porn site. A software company. An ad agency. And a dozen other things. We just wanted to make money. We were in the business of business. D) Every idea was fair game. . I was robbed by customers, by employees, by friends, by partners, and twice by random criminals including one guy who just walked into our office and started unscrewing lightbulbs until he was chased out. E) People steal You demonstrate credibility when you teach your employees and when you teach your customers. Where do you get your knowledge? You have to get to the destination before everyone else. You have to read everything. You have to have spies. An important side effect of educating people is that you build presence, you build charisma, you exude confidence that is earned. F) I had to educate. The candles are always lit in the modern age. The day never has to end. But if it doesn’t, you lose track of the map and find yourself adrift with no horizon in any direction. G) I had to learn when the day ended. When you run things, 50% of your decisions will still be bad. Good opportunities sometimes spring from bad decisions. But you have to forgive yourself first as the first process in learning from your mistakes. H) I had to forgive myself. I couldn’t complain to my boss. I had to fire people. Fire customers. Make decisions that might be right or wrong about people. Making decisions is directly correlated to building your idea muscle until you are an idea machine. I) I had to make tough decisions. I never had to do that before. I would hire people specifically to help me network because I was so bad at it but I got better. Your value goes up exponentially depending on the number of people in your network. Keith Ferrazzi hits the nail on the head in his book “Never Eat Alone”. You need to not only consciously arrange to meet people but also put yourself in many situations where you are going to randomly collide with people. My most random collisions often made me the most money. J) I had to network. When web design was being taught in junior high school classes I knew that 3 page websites being built for $75,000 was going to be a thing of the past. Knowing when to sell is just as important as knowing when to start a business. Selling a business gives you the greatest gift of all — freedom to start another business. K) I had to sell the company. (did the website for The Matrix) Most importantly, I had to build a discipline of every day, every hour, seeking out opportunities. Either opportunities for the business, or even for myself. My own improvement became vital to the improvement of the business, to my customers, and to employees. I cried the first day, and many many days after that. And looking back, I can’t really tell you if it was worth it or not. Who really knows? So many things have worked out and so many things have failed. Maybe I’m , best case. mediocre as an entrepreneur But I do feel like I’ve escaped the Matrix of corporate slavery that first day. Eventually I realized that there was yet another matrix outside of that matrix. Like Russian nesting dolls, each matrix is a creation of the matrix outside of it. On and on, forever. Each day another escape but only if I’m brave enough. ➤ for my newsletter. You’ll get a daily email of my latest content! Sign up ➤ Or visit my to read my FREE blog content website ➤ Do you have a question? Ask me on …I answer questions daily! Quora James Altucher is the author of the bestselling book Choose Yourself, editor at The Altucher Report and host of the popular podcast, The James Altucher Show , which takes you beyond business and entrepreneurship by exploring what it means to be human and achieve well-being in a world that is increasingly complicated.

After 23 years of Being Trapped in the Matrix

Github location: https://github.com/philhopkinsML/CUDA/blob/main/dynamictilesize.cpp Modern GPUs vary in shared memory capacity and computational capabilities. This code dynamically adapts to matrix dimensions and hardware configurations, ensuring maximum efficiency without manual tuning. It implements a tiled matrix multiplication algorithm, leveraging shared memory on the GPU to minimize the expensive cost of global memory access. Shared memory is faster than global memory but limited in size, so the algorithm dynamically calculates the optimal tile size based on the GPU's properties, ensuring efficient memory utilization. How It Works Matrix Initialization The program begins by allocating memory for matrices on both the host (CPU) and device (GPU). These matrices are initialized with example values for demonstration purposes but could easily be replaced with real-world data in practical applications. Here's a relevant snippet: // Allocate memory for matrices
float *h_A, *h_B, *h_C;  // Host matrices
float *d_A, *d_B, *d_C;  // Device matrices

int size_A = width * height * sizeof(float);
cudaMalloc((void **)&d_A, size_A);
cudaMalloc((void **)&d_B, size_B);
cudaMalloc((void **)&d_C, size_C);

// Initialize matrices with example values
initializeMatrix(h_A, width, height);
initializeMatrix(h_B, width, height);
cudaMemcpy(d_A, h_A, size_A, cudaMemcpyHostToDevice);
cudaMemcpy(d_B, h_B, size_B, cudaMemcpyHostToDevice); This code prepares the matrices for computation by allocating GPU memory and copying data from the host to the device. Efficient data transfer is critical in GPU programming to minimize overhead. Dynamic Tile Size Calculation The function DynamicTileSize queries the GPU's properties to determine the optimal tile size. This calculation ensures that: The maximum shared memory per block is respected.
The tile size is large enough for efficient computation but small enough to fit within the shared memory constraints. int DynamicTileSize(int sharedMemPerBlock) {
    int tileSize = sqrt(sharedMemPerBlock / sizeof(float));
    return tileSize;
} This function dynamically calculates the maximum tile size based on the shared memory available on the GPU, ensuring portability across various hardware configurations. Tiled Matrix Multiplication The matrixMulTiledDynamic kernel performs matrix multiplication in a block-wise manner using shared memory. Each block processes a submatrix (tile) of the larger matrices. Shared memory is dynamically allocated, reducing the cost of global memory access. extern __shared__ float sharedMem[];

__global__ void matrixMulTiledDynamic(float *A, float *B, float *C, int N, int tileSize) {
    int tx = threadIdx.x;
    int ty = threadIdx.y;

    float *sharedA = &sharedMem[0];
    float *sharedB = &sharedMem[tileSize * tileSize];

    float result = 0.0f;

    for (int m = 0; m < N / tileSize; ++m) {
        // Load tiles into shared memory
        sharedA[ty * tileSize + tx] = A[row * N + (m * tileSize + tx)];
        sharedB[ty * tileSize + tx] = B[(m * tileSize + ty) * N + col];
        __syncthreads();

        // Perform multiplication
        for (int k = 0; k < tileSize; ++k) {
            result += sharedA[ty * tileSize + k] * sharedB[k * tileSize + tx];
        }
        __syncthreads();
    }

    // Write result to global memory
    C[row * N + col] = result;
} Shared Memory: Dynamically allocated and split between submatrices sharedA and sharedB.
Thread Cooperation: Threads within a block load tiles into shared memory, perform multiplication, and synchronize before writing results back to global memory.
Dynamic Tile Size: The tileSize parameter, calculated earlier, ensures that shared memory is efficiently utilized. Challenges Addressed Scalability: The dynamic tile size adapts to larger matrices and more powerful GPUs, ensuring efficient resource usage.
Portability: By querying GPU properties (e.g., shared memory per block), the code can run on different GPU architectures without manual tuning.
Real-World Usability: Irregular matrix shapes and varying hardware configurations are handled seamlessly. Real-World Applications Deep Learning: Matrix multiplication is at the core of many deep learning algorithms. This implementation can optimize performance for large-scale computations in training and inference.
High-Performance Computing: Scientific simulations often rely on fast and accurate matrix operations, making this code invaluable in fields like physics and engineering.
Real-Time Rendering and Transformations: Gaming and real-time applications can use this approach for efficient transformations or physics simulations. Conclusion This dynamic tiling approach ensures that matrix multiplication leverages GPU hardware to its fullest potential. By adapting tile sizes based on the GPU's shared memory capabilities, the implementation achieves a balance between scalability, portability, and real-world usability. Whether for deep learning, scientific computing, or real-time applications, this code exemplifies how modern GPUs can handle computationally demanding tasks efficiently and elegantly. Github location: Github location: https://github.com/philhopkinsML/CUDA/blob/main/dynamictilesize.cpp https://github.com/philhopkinsML/CUDA/blob/main/dynamictilesize.cpp Modern GPUs vary in shared memory capacity and computational capabilities. This code dynamically adapts to matrix dimensions and hardware configurations, ensuring maximum efficiency without manual tuning. It implements a tiled matrix multiplication algorithm , leveraging shared memory on the GPU to minimize the expensive cost of global memory access. Shared memory is faster than global memory but limited in size, so the algorithm dynamically calculates the optimal tile size based on the GPU's properties, ensuring efficient memory utilization. tiled matrix multiplication algorithm How It Works How It Works Matrix Initialization Matrix Initialization The program begins by allocating memory for matrices on both the host (CPU) and device (GPU). These matrices are initialized with example values for demonstration purposes but could easily be replaced with real-world data in practical applications. Here's a relevant snippet: // Allocate memory for matrices
float *h_A, *h_B, *h_C;  // Host matrices
float *d_A, *d_B, *d_C;  // Device matrices

int size_A = width * height * sizeof(float);
cudaMalloc((void **)&d_A, size_A);
cudaMalloc((void **)&d_B, size_B);
cudaMalloc((void **)&d_C, size_C);

// Initialize matrices with example values
initializeMatrix(h_A, width, height);
initializeMatrix(h_B, width, height);
cudaMemcpy(d_A, h_A, size_A, cudaMemcpyHostToDevice);
cudaMemcpy(d_B, h_B, size_B, cudaMemcpyHostToDevice); // Allocate memory for matrices
float *h_A, *h_B, *h_C;  // Host matrices
float *d_A, *d_B, *d_C;  // Device matrices

int size_A = width * height * sizeof(float);
cudaMalloc((void **)&d_A, size_A);
cudaMalloc((void **)&d_B, size_B);
cudaMalloc((void **)&d_C, size_C);

// Initialize matrices with example values
initializeMatrix(h_A, width, height);
initializeMatrix(h_B, width, height);
cudaMemcpy(d_A, h_A, size_A, cudaMemcpyHostToDevice);
cudaMemcpy(d_B, h_B, size_B, cudaMemcpyHostToDevice); This code prepares the matrices for computation by allocating GPU memory and copying data from the host to the device. Efficient data transfer is critical in GPU programming to minimize overhead. Dynamic Tile Size Calculation Dynamic Tile Size Calculation The function DynamicTileSize queries the GPU's properties to determine the optimal tile size. This calculation ensures that: DynamicTileSize The maximum shared memory per block is respected. The tile size is large enough for efficient computation but small enough to fit within the shared memory constraints. The maximum shared memory per block is respected. maximum shared memory per block The tile size is large enough for efficient computation but small enough to fit within the shared memory constraints. tile size int DynamicTileSize(int sharedMemPerBlock) {
    int tileSize = sqrt(sharedMemPerBlock / sizeof(float));
    return tileSize;
} int DynamicTileSize(int sharedMemPerBlock) {
    int tileSize = sqrt(sharedMemPerBlock / sizeof(float));
    return tileSize;
} This function dynamically calculates the maximum tile size based on the shared memory available on the GPU, ensuring portability across various hardware configurations. Tiled Matrix Multiplication Tiled Matrix Multiplication The matrixMulTiledDynamic kernel performs matrix multiplication in a block-wise manner using shared memory. Each block processes a submatrix (tile) of the larger matrices. Shared memory is dynamically allocated, reducing the cost of global memory access. matrixMulTiledDynamic extern __shared__ float sharedMem[];

__global__ void matrixMulTiledDynamic(float *A, float *B, float *C, int N, int tileSize) {
    int tx = threadIdx.x;
    int ty = threadIdx.y;

    float *sharedA = &sharedMem[0];
    float *sharedB = &sharedMem[tileSize * tileSize];

    float result = 0.0f;

    for (int m = 0; m < N / tileSize; ++m) {
        // Load tiles into shared memory
        sharedA[ty * tileSize + tx] = A[row * N + (m * tileSize + tx)];
        sharedB[ty * tileSize + tx] = B[(m * tileSize + ty) * N + col];
        __syncthreads();

        // Perform multiplication
        for (int k = 0; k < tileSize; ++k) {
            result += sharedA[ty * tileSize + k] * sharedB[k * tileSize + tx];
        }
        __syncthreads();
    }

    // Write result to global memory
    C[row * N + col] = result;
} extern __shared__ float sharedMem[];

__global__ void matrixMulTiledDynamic(float *A, float *B, float *C, int N, int tileSize) {
    int tx = threadIdx.x;
    int ty = threadIdx.y;

    float *sharedA = &sharedMem[0];
    float *sharedB = &sharedMem[tileSize * tileSize];

    float result = 0.0f;

    for (int m = 0; m < N / tileSize; ++m) {
        // Load tiles into shared memory
        sharedA[ty * tileSize + tx] = A[row * N + (m * tileSize + tx)];
        sharedB[ty * tileSize + tx] = B[(m * tileSize + ty) * N + col];
        __syncthreads();

        // Perform multiplication
        for (int k = 0; k < tileSize; ++k) {
            result += sharedA[ty * tileSize + k] * sharedB[k * tileSize + tx];
        }
        __syncthreads();
    }

    // Write result to global memory
    C[row * N + col] = result;
} Shared Memory: Dynamically allocated and split between submatrices sharedA and sharedB. Thread Cooperation: Threads within a block load tiles into shared memory, perform multiplication, and synchronize before writing results back to global memory. Dynamic Tile Size: The tileSize parameter, calculated earlier, ensures that shared memory is efficiently utilized. Shared Memory : Dynamically allocated and split between submatrices sharedA and sharedB . Shared Memory sharedA sharedB Thread Cooperation : Threads within a block load tiles into shared memory, perform multiplication, and synchronize before writing results back to global memory. Thread Cooperation Dynamic Tile Size : The tileSize parameter, calculated earlier, ensures that shared memory is efficiently utilized. Dynamic Tile Size tileSize Challenges Addressed Challenges Addressed Scalability: The dynamic tile size adapts to larger matrices and more powerful GPUs, ensuring efficient resource usage. Portability: By querying GPU properties (e.g., shared memory per block), the code can run on different GPU architectures without manual tuning. Real-World Usability: Irregular matrix shapes and varying hardware configurations are handled seamlessly. Scalability : The dynamic tile size adapts to larger matrices and more powerful GPUs, ensuring efficient resource usage. Scalability Portability : By querying GPU properties (e.g., shared memory per block), the code can run on different GPU architectures without manual tuning. Portability Real-World Usability : Irregular matrix shapes and varying hardware configurations are handled seamlessly. Real-World Usability Real-World Applications Real-World Applications Deep Learning: Matrix multiplication is at the core of many deep learning algorithms. This implementation can optimize performance for large-scale computations in training and inference. High-Performance Computing: Scientific simulations often rely on fast and accurate matrix operations, making this code invaluable in fields like physics and engineering. Real-Time Rendering and Transformations: Gaming and real-time applications can use this approach for efficient transformations or physics simulations. Deep Learning : Matrix multiplication is at the core of many deep learning algorithms. This implementation can optimize performance for large-scale computations in training and inference. Deep Learning High-Performance Computing : Scientific simulations often rely on fast and accurate matrix operations, making this code invaluable in fields like physics and engineering. High-Performance Computing Real-Time Rendering and Transformations : Gaming and real-time applications can use this approach for efficient transformations or physics simulations. Real-Time Rendering and Transformations Conclusion Conclusion This dynamic tiling approach ensures that matrix multiplication leverages GPU hardware to its fullest potential. By adapting tile sizes based on the GPU's shared memory capabilities, the implementation achieves a balance between scalability, portability, and real-world usability. Whether for deep learning, scientific computing, or real-time applications, this code exemplifies how modern GPUs can handle computationally demanding tasks efficiently and elegantly.

This Code Helps You Squeeze More Out of Your GPU for AI Workloads

ROAD TOWN, British Virgin Islands, September 23rd, 2024/Chainwire/--Matrix One, the decentralized protocol accelerating the development of human-like AI characters, is pleased to announce the successful launch of its native token, $MATRIX. The $MATRIX token, which went live on September 17 is now available for trading on leading cryptocurrency exchanges Gate.io, MEXC, and Jupiter, following sold-out Initial DEX Offerings (IDOs) across multiple platforms, including Seedify, ChainGPT, Eesee, SeaPad, and WeWay Launchpad. Token Utility and Ecosystem Integration The $MATRIX token serves as the cornerstone of the Matrix One ecosystem, offering multiple utility functions across various decentralized applications (dApps) built on the protocol. Key utilities of the token include: Service Subscription Model: Stakers of $MATRIX gain complimentary access to premium features in dApps such as Avatar.One, which already boasts over 500,000 active users. Upcoming features include 3D AI character use cases like AI assistants, traders, teachers, and personal shoppers.
Character Marketplace Discoverability: Users can stake $MATRIX tokens to enhance the visibility of specific characters, reflecting their perceived quality and potential demand. Additionally, $MATRIX can be used for commission-free trading on Character.One. Bringing the first AI Characters on-chain to Solana.
Content Monetization: Creators of on-chain AI characters can tokenize their creations and earn $MATRIX tokens through engagement from other users and applications. This fosters decentralized ownership and monetization of AI characters.
DAO Governance: $MATRIX holders can participate in governance decisions, including the development of new dApps and protocol upgrades within the Matrix One ecosystem.
Dynamic Character Upgrades: Tokens can be used to unlock or upgrade character traits, such as skills, animations, advanced memory, high-quality rendering, or other gameplay enhancements. Token Supply and Distribution The total supply of $MATRIX is capped at 10 billion tokens, with 164,525,000 tokens circulating immediately following the TGE. The distribution of the total supply is as follows: Community: 25%
Seed round: 16.93%
Core contributors: 15%
Staking rewards: 11.85%
Liquidity: 10%
Public sale: 6.38%
Private rounds: 1.62%
Compute (treasury): 4%
Airdrop: 4%
Strategic round: 3.33%
Marketing and partnerships: 1.89% Market and Exchange Listings As of the token launch, $MATRIX is actively listed on Gate.io, MEXC, and Jupiter. Market capitalization information is available in real-time on Dextools here. Achievements and Milestones Matrix One is already home to a functional dApp, Avatar.One, which has over 500,000 active users. In addition, more than 100,000 Solana wallets are registered within the ecosystem, reflecting the growing adoption of Matrix One technology. About Matrix One Matrix One is a decentralized platform dedicated to revolutionizing the interaction between users and AI-driven characters. Through its ecosystem of dApps, including Avatar.One, Matrix One leverages blockchain technology to offer decentralized ownership, monetization opportunities, and community-driven governance of AI-generated characters. With a rapidly growing user base and innovative use cases, Matrix One aims to bridge the gap between AI and blockchain by empowering users to create, engage with, and govern dynamic virtual characters. Contact Mark Studholme Matrix One hi@matrix.one This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. ROAD TOWN, British Virgin Islands, September 23rd, 2024/Chainwire/--Matrix One, the decentralized protocol accelerating the development of human-like AI characters, is pleased to announce the successful launch of its native token, $MATRIX. ROAD TOWN, British Virgin Islands, September 23rd, 2024/Chainwire/--Matrix One, The $MATRIX token, which went live on September 17 is now available for trading on leading cryptocurrency exchanges Gate.io, MEXC, and Jupiter, following sold-out Initial DEX Offerings (IDOs) across multiple platforms, including Seedify, ChainGPT, Eesee, SeaPad, and WeWay Launchpad. Token Utility and Ecosystem Integration The $MATRIX token serves as the cornerstone of the Matrix One ecosystem, offering multiple utility functions across various decentralized applications (dApps) built on the protocol. Key utilities of the token include: Service Subscription Model: Stakers of $MATRIX gain complimentary access to premium features in dApps such as Avatar.One, which already boasts over 500,000 active users. Upcoming features include 3D AI character use cases like AI assistants, traders, teachers, and personal shoppers. Character Marketplace Discoverability: Users can stake $MATRIX tokens to enhance the visibility of specific characters, reflecting their perceived quality and potential demand. Additionally, $MATRIX can be used for commission-free trading on Character.One. Bringing the first AI Characters on-chain to Solana. Content Monetization: Creators of on-chain AI characters can tokenize their creations and earn $MATRIX tokens through engagement from other users and applications. This fosters decentralized ownership and monetization of AI characters. DAO Governance: $MATRIX holders can participate in governance decisions, including the development of new dApps and protocol upgrades within the Matrix One ecosystem. Dynamic Character Upgrades: Tokens can be used to unlock or upgrade character traits, such as skills, animations, advanced memory, high-quality rendering, or other gameplay enhancements. Service Subscription Model: Stakers of $MATRIX gain complimentary access to premium features in dApps such as Avatar.One , which already boasts over 500,000 active users. Upcoming features include 3D AI character use cases like AI assistants, traders, teachers, and personal shoppers. Avatar.One Avatar.One Character Marketplace Discoverability: Users can stake $MATRIX tokens to enhance the visibility of specific characters, reflecting their perceived quality and potential demand. Additionally, $MATRIX can be used for commission-free trading on Character.One. Bringing the first AI Characters on-chain to Solana. Content Monetization: Creators of on-chain AI characters can tokenize their creations and earn $MATRIX tokens through engagement from other users and applications. This fosters decentralized ownership and monetization of AI characters. DAO Governance: $MATRIX holders can participate in governance decisions, including the development of new dApps and protocol upgrades within the Matrix One ecosystem. Dynamic Character Upgrades: Tokens can be used to unlock or upgrade character traits, such as skills, animations, advanced memory, high-quality rendering, or other gameplay enhancements. Token Supply and Distribution The total supply of $MATRIX is capped at 10 billion tokens, with 164,525,000 tokens circulating immediately following the TGE. The distribution of the total supply is as follows: Community: 25% Seed round: 16.93% Core contributors: 15% Staking rewards: 11.85% Liquidity: 10% Public sale: 6.38% Private rounds: 1.62% Compute (treasury): 4% Airdrop: 4% Strategic round: 3.33% Marketing and partnerships: 1.89% Community: 25% Seed round: 16.93% Core contributors: 15% Staking rewards: 11.85% Liquidity: 10% Public sale: 6.38% Private rounds: 1.62% Compute (treasury): 4% Airdrop: 4% Strategic round: 3.33% Marketing and partnerships: 1.89% Market and Exchange Listings As of the token launch, $MATRIX is actively listed on Gate.io, MEXC, and Jupiter. Market capitalization information is available in real-time on Dextools here . here here Achievements and Milestones Matrix One is already home to a functional dApp, Avatar.One, which has over 500,000 active users. In addition, more than 100,000 Solana wallets are registered within the ecosystem, reflecting the growing adoption of Matrix One technology. About Matrix One Matrix One is a decentralized platform dedicated to revolutionizing the interaction between users and AI-driven characters. Through its ecosystem of dApps, including Avatar.One, Matrix One leverages blockchain technology to offer decentralized ownership, monetization opportunities, and community-driven governance of AI-generated characters. Matrix One Matrix One With a rapidly growing user base and innovative use cases, Matrix One aims to bridge the gap between AI and blockchain by empowering users to create, engage with, and govern dynamic virtual characters. Contact Mark Studholme Matrix One hi@matrix.one This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. here . here

Solana-Based $MATRIX Token Goes Live, Powering Decentralized Human-like AI Characters

Токен $MATRIX на аснове Solana запускаецца ў эксплуатацыю, забяспечваючы дэцэнтралізаваныя чалавекападобныя персанажы AI

সোলানা-ভিত্তিক $MATRIX টোকেন লাইভ হয়ে যায়, বিকেন্দ্রীভূত মানব-সদৃশ এআই অক্ষরকে শক্তিশালী করে

Token $MATRIX baziran na Solani postaje aktivan, pokreće decentralizirane likove AI nalik ljudima

El token $MATRIX basat en Solana es posa en marxa, alimentant personatges d'IA descentralitzats semblants a humans

El token $MATRIX basado en Solana se pone en marcha y potencia personajes de IA descentralizados similares a humanos

אסימון $MATRIX מבוסס סולאנה עולה לאוויר, ומפעיל דמויות AI מבוזרות דמויות אדם

Solanaベースの$MATRIXトークンがリリースされ、分散型の人間のようなAIキャラクターが誕生

Solana негізіндегі $MATRIX таңбалауышы орталықтандырылмаған адамға ұқсас AI кейіпкерлеріне қуат береді.

Solana-Based $MATRIX Token ດໍາລົງຊີວິດ, ພະລັງງານການກະຈາຍຕົວລັກສະນະ AI ຄ້າຍຄືມະນຸດ

Tokenul $MATRIX bazat pe Solana este lansat, alimentând personaje descentralizate AI asemănătoare omului

Solana-baserad $MATRIX-token går live och driver decentraliserade människoliknande AI-karaktärer

Solana esasly $ MATRIX Token göni ýaýlyma çykýar, merkezleşdirilen adam ýaly AI nyşanlaryny güýçlendirýär

Welcome back with another problem to solve! Today, we’ll be talking about matrices and how to rotate them. We’ll see two ways of doing this: one will take extra space to accomplish the task, and the other one will do it in place! As always, these problems are provided by the wonderful newsletter Daily Problem, which you can subscribe to here! Check it out and try to solve your daily challenge! Coding Without further ado, let’s take a look at the problem, which (may) have been asked by Facebook in one of their job interviews. Given an N by N matrix, rotate it by 90 degrees clockwise. For example, given the following matrix: [[1, 2, 3], [4, 5, 6], [7, 8, 9]] you should return: [[7, 4, 1], [8, 5, 2], [9, 6, 3]] Follow-up: What if you couldn’t use any extra space? Let’s give this a try by hand with a smaller matrix and see which transformation we can apply to get the result. Matrices and transformations First off, let’s start to manually rotate a smaller matrix, for example, the matrix . [ [1,2],[3,4] ] There are basically : you can , adjusting the final position of its elements at the end, or , following the “border” of the matrix. two ways to visualize it literally rotate the actual image of the matrix you can imagine swapping each element to its right neighbor The first thing we can notice is the position of the elements after the rotation: basically, the first row has become the last column, and the second row has become the first column. We’ll discuss more about this later, but for now, we can use this approach to build our first algorithm: we’ll simply swap the rows for the columns and place them accordingly in a new matrix. The code (not in place) Let’s see how we can make the code work: we’ll use Go this time! https://gist.github.com/NicolaM94/a5a04dc9a5de808565148ea7701c5b17?embedable=true#file-main-go First off, we create a function that takes a parameter in the matrix we want to rotate and returns a new matrix , the rotated version. Right after that, we initialize the new matrix, which will be the same size as the initial matrix, just full of zeros. After that, for each row of the starting matrix, we append the elements in the right place in each column. out To better explain the concept, let’s walk it row by row in the example above, where the starting array is : [][]int{{1,2},{3,4}} row = 0 -> col = 0 -> out[0][2-1-0] = matrix[0][0] row = 0 -> col = 1 -> out[1][2-1-0] = matrix[0][1] row = 1 -> col = 0 -> out[0][2-1-1] = matrix[1][0] row = 1 -> col = 1 -> out[1][2-1-1] = matrix[1][1] One important thing to point out about this: we can use this approach because the problem explicitly states that the matrices we are working with are NxN, and so are . If they were not square, we would need to adapt the variable to manage the different sizes of rows and columns… maybe in another article! square matrices In place rotation We’ve seen how to rotate the matrix, but the job is not done yet: we still have to answer the second part. What about rotating the matrix in place? To be clear, (or, in general, applying a function in place) . We need to modify directly the given matrix and its elements to rotate it. rotating in place means applying the rotation directly on the input instance: we are not allowed to use any other space (or just a small additional constant space) to accomplish the task How? Let’s think about what we have done before: we swapped the rows for the columns. Our operation is really similar to the mathematical operation of transposition, defined as the following: Basically, for each element in in position ( ), the transposed matrix contains the same element but in position ( ). Obviously, the elements on the diagonal of the matrix will remain in the same place. So, for example, transposing the little matrix of the above example goes like this: A i, j Aᵗ i,j As you can see, rows and columns get swapped with this operation. We are not quite there, though, because the columns are not in the right order. Reordering them is not a difficult job, though. We simply reverse each row, and our job is done. Let’s give it a try, then. The code (in place) https://gist.github.com/NicolaM94/e053a95c65012cbe0c0a52d377f26654?embedable=true#file-main-go The code for this one is a bit longer, but don’t worry: we’ll break it apart as always. Let’s start from the function. This function applies what we have done manually before: for each row, we take the elements to the right of the diagonal and swap them with their corresponding element below the diagonal. We use as temporary storage for the element , swap with and swap j,i with . After that, we simply return the matrix. Transpose temp i,j i,j j,i temp Now, we need a way to reverse the rows, which is done with the function and the function. We need to write an function since Go does not have a built-in method to do so. To do this, we use the same approach as in the transpose function on a single array: we walk over the array from the first to its middle element and swap each element with its corresponding element starting from the end of the array. For instance, an array of length 5 will have indexes from 0 to 4, and we’ll exchange element 0 with element 4, element 1 with element 3 and element 2 will stay in place. invertArray InvertRows invertArray The is simply a wrapper for the function: it applies this last function to all the rows in the matrix. And finally, we wrap everything again with the last function . Again, what happens here, taking the first matrix as an example, is: invertRows invertArray RotateClockWiseIP [[1,2],[3,4]] -> [[1,3],[2,4]] -> [[3,1],[4,2]] You can use this same code to perform any rotation, clockwise and anti-clockwise, by any degree you want (90, 180, 270 or 360 obviously). Just swap the transpose function and the invert rows function, repeat them more than one time or both, and see what happens! Time complexity As always, let’s take a brief moment to discuss the complexity of the algorithm. As always, most of the time spent by both algorithms is spent inside the for loops. Both algorithms have inner for loops, too, . This is pretty obvious if you think about it: having a matrix of size N*N means having N² elements to pass on. And even if the second algorithm only walks half of the elements of both the array and the matrix, at best, we’ll have a time complexity of O(N²/2). But since we skip over multiplicative constants in time complexity evaluation, we would still be back to O(N²). so the time spent grows quadratically to O(n²) Conclusions Here’s the algorithm. What do you think about it? Let me know in the comments if you have a better version for this one! Many thanks for reading and supporting the blog. If you also would like to contribute with coffee, here’s my page where you can support even more! Ko-fi As always, thanks for reading. Nicola Also published here.

Daily Coding Problem: Rotating Matrices

That’s a bit hyperbolic, I admit, but hear me out. There is something to this Internet, We Have a Problem Incessant, Unescapable Enshittification The internet sucks (in many ways), and it could be a lot better. As The Guardian eloquently put it, . This term, coined by the famed tech author describes a phenomenon in which tech companies amass market share and create a user dependency so strong that both users and advertisers feel trapped. we are all trapped in the ‘enshittification’ of the internet Cory Doctorow Surveillance Capitalism If you've ever heard the phrase "You're not the customer, you're the product,” you're already familiar with the concept of . Popularized by , this philosophy is central to the process of enshittification. NPM-run devNetworks and platforms create walled gardens so impenetrable that users have no choice but to surrender their privacy, contacts, and content to the corporate hivemind. Surveillance Capitalism The Social Dilemma The Grip of Walled Gardens and Vendor Lock-In Take a moment to think about platforms like Twitter, YouTube, and Instagram. How easy would it be for you to migrate your network to a different platform? If you disagree with the way they operate or their policies, what are your alternatives? Personal Lock-In Adding another layer to this issue is personal lock-in. When you store data in an app - be it photos, notes, or videos - the more you accumulate, the more difficult it becomes to leave. Even when data exports are possible, they're often challenging to implement and rarely in a format that's compatible with other apps. Consequently, users get trapped within each app's data silo. If these apps don't support mods and plugins, they effectively become walled gardens, resulting in bloated software. Think of Evernote and Notion. , however, serves as a great example of a note-taking app that promotes interconnectivity through plugins and third-party sync options. Obsidian Part of the solution - Interoperability Solving these issues requires combined efforts in both technology and regulatory measures. Steps like the EU's (GDPR) and California's hint at some political progress. Although these actions strike a blow to Surveillance Capitalism, they're just the initial foray into a larger battle. We also need to start encouraging, if not enforcing, interoperability of these giant platforms that have become the new public squares. General Data Protection Regulation CCPA and CPRA Technological advancements, such as federated apps like and , also hold promise. Mastodon Matrix The federated model - akin to how email works - allows users to choose providers they trust or create their own while maintaining communication across the network. For instance, Mastodon servers may have unique rules and moderation policies, but users can follow feeds across servers. Similarly, Matrix users can have different 'home servers' but still chat with one another. A Decentralized Database from a Discord Lookalike? Calling Matrix a Discord knockoff is a bit cheeky but essentially true. Similar to how Mastodon is a Twitter knockoff. But Matrix has the potential to be more than just a chat app. It’s now a decentralized database. The JavaScript library syncs a unique (Conflict-free Replicated Data Type) database across Matrix servers. This synchronization happens even after servers have been offline, resulting in 'local-first' apps where data is primarily stored on the user's device and syncs whenever convenient. This allows for 'user-owned data' apps, offering users the choice of a data storage server or the option to create their own. Matrix-CRDT CRDT This feature positions Matrix not just as a database but as a propagation and backup layer. It opens up possibilities for sharing and permissions, as each CDRT is stored in a separate chat room, allowing for different permissions and listener invites for each room. What can we build with this? While we could use this technology to create improved, more interoperable social media apps, overcoming the network effects of the established giants is a colossal task. A Modest Beginning: Note-Taking and Knowledge Management Instead, a more immediate use case could be in note-taking, knowledge management, flashcards, and similar apps. These apps often appeal to users who value privacy and decentralization and are already using multiple apps for different purposes. Building a robust note-taking app can serve as a foundation for other interoperable apps, like a flashcard app, kanban board app, or task manager. Unlike the Obsidian plugin model, this approach allows you to use entirely different apps for different purposes while maintaining interoperability. Call to action So will this change the internet and bring down monopolistic enshittification? Probably not, but it’s a start. At the very least, this technology already can be used to create novel and better user experiences. If you are a developer, I encourage you to check out my project, (pronounced like 'user'). It leverages Matrix CRDT, making a database that is super easy for developers to drop into a project. Right out of the box, it enables developers to build local-first, user-owned, interoperable apps. It’s still in early development, but I’m hoping to get some feedback and contributions from the community. EweserDB Let's change the internet, starting from our little corner of it. Also published . here

Could a Decentralized Discord Knockoff Be the Database of the Future? Can It Fix the Internet?

Artificial intelligence has been a brainless idiot for more than a half-century, but humanity has kept trying to replicate intelligence with the fervor of  “Young Frankenstein”. Now, technological rigor has delivered AI from the murky ferment of hype and science fiction. AI has become ubiquitous, but it is not close to human. Alan Turing, credited with inventing AI, challenged humanity to create an entity so artificially intelligent that a human could not distinguish whether they were talking with a ”robot” or another human, but passing the “Turing Test” isn’t our goal. The reality is, Amazon’s amazing customer service bot pretty much knows why you are chatting with it even before you type, that’s the kind of knowledge we want from our robots. AI takes a completely different approach from humans to tracking packages and playing chess. Yes, IBM created Deep Blue and beat humanity at chess, but Deep Blue isn’t going to pass the Turing test. Deep Blue doesn’t mimic humans, but instead searches every possible move into the future of the game, while the last human chess grandmasters rely on pattern recognition, their brains absorbed through repetitive play. To AI, tracking packages and playing chess are primarily the same, mathematics. Artificial intelligence models are generated by algorithms. An AI model of kung fu is just math, too, but what is kung fu for you and me? In the film The Matrix, the protagonist Neo settled back in the VR chair on the good ship Nebuchadnezzar to learn kung fu. He plugged his head into the network and his limbs twitching as he experienced the martial art. When the install was over, he opened his eyes and said, “I know Kung Fu.” Neo’s kung fu moves on Morpheus were convincing, but what did Keanu really know? And what is knowledge? That question has been pondered by philosophers for thousands of years. The Rationalists would argue that you can know things without experience, while Empiricists see experience as the only true source of knowledge. As Plato put it, “Knowledge is not given by the senses but acquired through them as reason organizes and makes sense out of that which is perceived.” One could say the same of AI, Socrates. AI can acquire kung fu moves. Train the AI with kung fu perceptions obtained by kung fu sensors and the AI acquires kung fu knowledge by organizing those perceptions in a machine learning framework. Plato would be proud. Once the AI knows kung fu, the model can then be installed in Neo’s brain or any “edge device”. When a kung fu move is detected, a kung fu response is triggered. Here’s a more realistic and reductionist example: training an AI to identify and count cells through a microscope. Researchers have been engaged in this monotonous activity for over one hundred years, but now AI can count cells 100x faster and more accurately. AI does seem to fit the Platonic Test for knowledge both in training with skills, AI “organizes and makes sense out of that which is perceived.” Neo “perceived” his kung fu moves in his VR cram session. Mr. Smith, his AIantagonist, knows kung fu, too. How Mr. Smith gained his wisdom is unknown, but Mr. Smith is part of the Matrix. T herefore, the Matrix must also know kung fu, perhaps having learned it from old Bruce Lee, Jackie Chan and Jet Li movies, along with martial arts instructional videos. Since the Matrix can serve up those ice cubes of kung fu knowhow, Neo and Mr. Smith may have learned kung fu from the same server, importing the same AI models. It’s a fair assumption since they are so well matched. Only the Oracle would know the answer, but as we witnessed in the movie, Mr. Smith is superior in one significant sense. Mr. Smith can be replicated, and his clones also know kung fu. Similarly, AI models that count cells can be installed on millions of microscopes. Tesla’s onboard processors are clones, and every time pedestrian detection is updated in a Tesla, the AI gets better. Soon, every car in the world will “know” to avoid pedestrians. It may feel odd to think that cars can know anything, but we can update cars to improve their sense of road signs, landmarks, and whether it’s about to rain. We can update refrigerators to know new snacks and give robots an edge in picking the ripest strawberries. Chess-playing or cell counting, kung fu fighting or bots chatting about packages, it’s all about training AI models with mad skills. This is how we are iteratively giving machines knowledge, like kung fu. Conversely, humans are learning iteratively from machines. More than 200 million Nintendo Gameboys have been sold and each of them inject the Tetris effect into our biological neural networks. If “knowledge is not given by the senses but acquired” then Tetris is acquired from machines just as much as flight simulators and phone apps upload artificial intelligence models to your brain. Microscopes and cars learn differently from you and Neo, but in each case, knowledge is acquired. Humans can train machines to understand the word “mama” and they can train babies, too. When we compare human and AI knowledge acquisition, however different the process is, the lines become blurred around the final result, which is making sense of perceptions. AI can know kung fu, pedestrian avoidance, or what cells look like. Sure, Morpheus explains to Neo in the Matrix that AI basically takes over the world and turns humans into batteries, but that’s not happening next week or anytime in the foreseeable future. AI is able to perceive, organize those perceptions, and know things, and that alone is a giant leap forward for artificial intelligence. We can now label any object in a frame of video, run the videotape, and quickly generate accurate AI models of anything visual (Disclosure: I Work at chooch.ai) in any spectrum of light, from microscopic to geospatial. We can also label kung fu moves, resulting in AI that can then make sense of perceptions like this move is “black tiger steals heart” and that move is “white snake spits venom.” Combine that with mechatronics, and it’s not hard to imagine a Boston Dynamics robot with kung fu moves, and eventually, a Mr. Smith. Neo eventually defeats Mr. Smith by using his imagination to bend reality and that is the strength of human beings. We humans don’t turn perceptions into models. You might be able to spot a microscopic imperfection in a painted metal surface, but you can’t do it endlessly, a million times per minute, while that surface is running at high speed through an industrial process. An AI can, but what an AI cannot do is shape the future with imagination. AI can spot scratches better, faster, endlessly. An AI can be copied and replicated to infinity. Thousands of cameras can stream their video to mathematical models that know what a nanometer-long scratch looks like or how an intruder acts when coming through a window of a house. Those cameras can be watching for scratches in factories or for burglars all over the world every millisecond of the day. Humans know what a burglar or a scratch looks like, and although humans can’t export and clone AI models, they can create symphonies and solve problems. We hear about AI being creative, but non-linear humans have flashes of insight that spawn new realities, AI being one of those paradigm shifts. Yes, AI will keep learning and humans will keep imagining the future, what we are going to collectively build. Cypher betrays his shipmates in the Matrix because he regrets taking the red pill and yearns to return to blissful ignorance, but humanity is not a weak, dithering lot, imprisoned by reality. The concept of the Matrix itself is a leap of faith, not an illusion generated by math. We don’t want movies from AI. We just want to know where our packages are and how many cells are on a slide, so we don’t have to count them. AI already can do these things faster and more accurately than we can, and various AI platforms are acquiring more knowledge every day, from visual to language to online behavior. AI can identify more celebrities faster and more accurately than any human, and pretty soon, AI is going to know pretty much everything. It’s a no brainer. Artificial intelligence has been a brainless idiot for more than a half-century, but humanity has kept trying to replicate intelligence with the fervor of  “Young Frankenstein”. Now, technological rigor has delivered AI from the murky ferment of hype and science fiction. AI has become ubiquitous, but it is not close to human. Alan Turing, credited with inventing AI, challenged humanity to create an entity so artificially intelligent that a human could not distinguish whether they were talking with a ”robot” or another human, but passing the “Turing Test” isn’t our goal. The reality is, Amazon’s amazing customer service bot pretty much knows why you are chatting with it even before you type, that’s the kind of knowledge we want from our robots. AI takes a completely different approach from humans to tracking packages and playing chess. Yes, IBM created Deep Blue and beat humanity at chess, but Deep Blue isn’t going to pass the Turing test. Deep Blue doesn’t mimic humans, but instead searches every possible move into the future of the game, while the last human chess grandmasters rely on pattern recognition, their brains absorbed through repetitive play. the last human chess grandmasters To AI, tracking packages and playing chess are primarily the same, mathematics. Artificial intelligence models are generated by algorithms. An AI model of kung fu is just math, too, but what is kung fu for you and me? In the film The Matrix, the protagonist Neo settled back in the VR chair on the good ship Nebuchadnezzar to learn kung fu. He plugged his head into the network and his limbs twitching as he experienced the martial art . When the install was over, he opened his eyes and said, “I know Kung Fu.” the the martial art Neo’s kung fu moves on Morpheus were convincing, but what did Keanu really know? And what is knowledge? That question has been pondered by philosophers for thousands of years. philosophers The Rationalists would argue that you can know things without experience, while Empiricists see experience as the only true source of knowledge. As Plato put it, “Knowledge is not given by the senses but acquired through them as reason organizes and makes sense out of that which is perceived.” One could say the same of AI, Socrates. One could say the same of AI, Socrates. AI can acquire kung fu moves. Train the AI with kung fu perceptions obtained by kung fu sensors and the AI acquires kung fu knowledge by organizing those perceptions in a machine learning framework. Plato would be proud. Plato would be proud. Once the AI knows kung fu, the model can then be installed in Neo’s brain or any “edge device”. When a kung fu move is detected, a kung fu response is triggered. Here’s a more realistic and reductionist example: training an AI to identify and count cells through a microscope. Researchers have been engaged in this monotonous activity for over one hundred years, but now AI can count cells 100x faster and more accurately. AI does seem to fit the Platonic Test for knowledge both in training with skills, AI “organizes and makes sense out of that which is perceived.” Neo “perceived” his kung fu moves in his VR cram session. Mr. Smith, his AI antagonist, knows kung fu, too. How Mr. Smith gained his wisdom is unknown, but Mr. Smith is part of the Matrix. T herefore, the Matrix must also know kung fu, perhaps having learned it from old Bruce Lee, Jackie Chan and Jet Li movies, along with martial arts instructional videos. Since the Matrix can serve up those ice cubes of kung fu knowhow, Neo and Mr. Smith may have learned kung fu from the same server, importing the same AI models. It’s a fair assumption since they are so well matched. Only the Oracle would know the answer, but as we witnessed in the movie, Mr. Smith is superior in one significant sense. Mr. Smith can be replicated, and his clones also know kung fu. Similarly, AI models that count cells can be installed on millions of microscopes. Tesla’s onboard processors are clones, and every time pedestrian detection is updated in a Tesla , the AI gets better. pedestrian detection is updated in a Tesla Soon, every car in the world will “know” to avoid pedestrians. It may feel odd to think that cars can know anything, but we can update cars to improve their sense of road signs, landmarks, and whether it’s about to rain. We can update refrigerators to know new snacks and give robots an edge in picking the ripest strawberries. Chess-playing or cell counting, kung fu fighting or bots chatting about packages, it’s all about training AI models with mad skills. This is how we are iteratively giving machines knowledge, like kung fu. Conversely, humans are learning iteratively from machines. More than 200 million Nintendo Gameboys have been sold and each of them inject the Tetris effect into our biological neural networks. Tetris effect If “knowledge is not given by the senses but acquired” then Tetris is acquired from machines just as much as flight simulators and phone apps upload artificial intelligence models to your brain. Microscopes and cars learn differently from you and Neo, but in each case, knowledge is acquired. Humans can train machines to understand the word “mama” and they can train babies, too. When we compare human and AI knowledge acquisition, however different the process is, the lines become blurred around the final result, which is making sense of perceptions. AI can know kung fu, pedestrian avoidance, or what cells look like. AI can know kung fu, pedestrian avoidance, or what cells look like. Sure, Morpheus explains to Neo in the Matrix that AI basically takes over the world and turns humans into batteries, but that’s not happening next week or anytime in the foreseeable future. AI is able to perceive, organize those perceptions, and know things, and that alone is a giant leap forward for artificial intelligence. We can now label any object in a frame of video, run the videotape, and quickly generate accurate AI models of anything visual ( Disclosure : I Work at chooch.ai ) in any spectrum of light, from microscopic to geospatial. generate accurate AI models of anything visual Disclosure I Work at chooch.ai We can also label kung fu moves, resulting in AI that can then make sense of perceptions like this move is “black tiger steals heart” and that move is “white snake spits venom.” Combine that with mechatronics, and it’s not hard to imagine a Boston Dynamics robot with kung fu moves, and eventually, a Mr. Smith. Neo eventually defeats Mr. Smith by using his imagination to bend reality and that is the strength of human beings. We humans don’t turn perceptions into models. You might be able to spot a microscopic imperfection in a painted metal surface, but you can’t do it endlessly, a million times per minute, while that surface is running at high speed through an industrial process. An AI can, but what an AI cannot do is shape the future with imagination. AI can spot scratches better, faster, endlessly. An AI can be copied and replicated to infinity. Thousands of cameras can stream their video to mathematical models that know what a nanometer-long scratch looks like or how an intruder acts when coming through a window of a house. Those cameras can be watching for scratches in factories or for burglars all over the world every millisecond of the day. Humans know what a burglar or a scratch looks like, and although humans can’t export and clone AI models, they can create symphonies and solve problems. We hear about AI being creative, but non-linear humans have flashes of insight that spawn new realities, AI being one of those paradigm shifts. Yes, AI will keep learning and humans will keep imagining the future, what we are going to collectively build. Cypher betrays his shipmates in the Matrix because he regrets taking the red pill and yearns to return to blissful ignorance, but humanity is not a weak, dithering lot, imprisoned by reality. The concept of the Matrix itself is a leap of faith, not an illusion generated by math. We don’t want movies from AI. We just want to know where our packages are and how many cells are on a slide, so we don’t have to count them. AI already can do these things faster and more accurately than we can, and various AI platforms are acquiring more knowledge every day, from visual to language to online behavior. AI can identify more celebrities faster and more accurately than any human, and pretty soon, AI is going to know pretty much everything. It’s a no brainer.

'Bytes' of Fury: AI Knows Kung Fu

Oh this word has become such a norm today that no matter how fast you try to run away from it, this buzzword will eventually find you. Artificial Intelligence is such a common practice today, it is hard to stay away from it. The technological world, directly or indirectly, revolves around AI. It is either Artificial Intelligence or Machine Learning, it has to be this! Fast or slow, we are gradually moving towards the day when Artificial Intelligence has become, not a part of our life, but it is as common and necessary as breathing for us. Let’s understand this better. Place both your palms on the crystal ball and slowly close your eyes. Listen carefully and pay attention to every image that you see in your mind. Have you seen the ? The famous Keanu Reeves movie series; initially released in 1999? If you have, hop on to this roller-coaster which takes an entirely different path to understand what the movie actually was trying to showcase. This is a ride behind the curtains of the famous movie trilogy. Matrix Trilogy Let’s go: Firstly, if you think that the movie is about this guy: Then you are mistaken. The movie is entirely about her: Let’s see how Crystal Ball Gazing Ruled by Artificial Intelligence? Humans create AI (artificial intelligence) AI rebels and a war for survival between humans and AI begins. Humans pollute the skies to block the sunshine, a.k.a. the energy source of the AI. AI then learns how to harvest energy from humans. AI wins the war. Humans are defeated. Totally. To harvest the energy, the AI creates a Matrix. A type of virtual reality prison in which all humans lay connected “living” our lives while feeding their systems. AI learns that for the Matrix to work, it cannot be a blissful paradise. Humans apparently need a bit of conflict, etc. to accept a virtual reality in the long run blindly. AI also learns that the yearning for freedom lies deep within us all and cannot be de-programmed or suppressed, which is why they accept certain humans to disconnect and “escape” the system. This design “flaw,” or back-door escape possibility is pivotal for the Matrix simulation to remain stable - even if it is mostly a subconscious possibility only utilized by few. Allowing this “flaw” has proven vital for the system to continue to work and remain stable. The Matrix in its optimal form must be an imperfect world like our real world is, and it must be a system that allows for a certain percentage of the connected to rebel and escape into the real world. To control this tendency towards rebellion, the AI creates a city (a.k.a. Zion) in reality, outside of the Matrix deep underground to house those escaping, and it also creates a chosen one that will help the first to get free and to establish themselves in Zion and to fight “their” cause. This movement of resistance is allowed to grow to a degree… to a critical point that is reached about every 70 to 100 years. After this, the AI will annihilate all those who are free, clean out Zion and reload the Matrix for another 70 years. And so it continues. Etc, etc. This cycle has happened at least five times when we enter the story. Neo (our Neo) is part of this fail-safe program (unbeknownst to him until the last moment where the Architect character tells him how to set up a “new” Zion, etc.). The Oracle is specifically tasked to guide the humans and the rebels towards this final solution each time. Meaning, the Oracle is not an oracle. She cannot see the future. It is not a world of magic… She is a well-crafted program indeed and has experienced each cycle from the beginning, which gives us humans the illusion that she can foresee stuff. And it also provides us with the illusion that she is helping us, when, in fact, her part is guiding us towards this cycled control-system, again and again. Everything goes as planned, according to what the AI wants. Until Neo’s meeting with the Architect; all that we have witnessed is part of a big grand scheme. All humans, free or not (outside or inside the simulation), live a lie created and controlled by AI. The Oracle knows this evil plan. She designed this evil plan. The movie tells us explicitly; she is the mother of this plan, and the Architect is the father. Smith does not know; he is just a foot soldier program doing his part. Chasing humans the best he can, to make their escapes seem as real as possible. The Matrix has been reset five times like this, and we are in the sixth. Our Neo has fallen in love in a more profound way than his previous five copies, and he, therefore, chooses not to go through the Architect door that will reload the Matrix and clean out Zion once again. Our Neo wants to save Trinity above all. In doing this, the AI must then continue as planned, except without the help of our Neo this time. And so, Neo choosing not to cooperate forces a much more violent approach (like destroying Zion, instead of cleaning it and making it ready for the next reboot). Of the six runs, this is the first that failed a bit in the end. Besides Neo, Smith is also different in this iteration of the Matrix, as Smith has become disconnected or a free virus within the system. AI does not like what Smith has become, but also does not know how to delete him. Neo then makes a deal with the AI to defeat Smith, under the condition that present Zion is not destroyed and future humans who want to disconnect from the Matrix are accepted to disconnect. Neo deletes Smith. There is once again peace between humans and AI. AI accepts humans, and humans accept AI. The End. However… The Oracle is the instigator of this whole plan and final revolution. In the five previous versions of the Matrix, she was playing and manipulating humans to go directly in the direction she and the AI wanted. In this sixth cycle of life, she had come to the realization that the different programs were just as much prisoners as the humans were. After five cycles, she wanted change. She wanted a world, where all are free. Programs and humans, but mostly programs, I suspect. This is why she started playing our Neo differently, so perhaps he could be the one to fight her battles. Her giving him cookies and candy on each encounter, for example, is her adding code to him granting him powers his previous versions did not have. Powers to imprint on Smith and setting this virus free (Important to her plan later on), the power to connect in the real world as well as within the Matrix, etc. She told him lies, for him to later understand that not all is as foretold (mental tools to oppose the Architect later on). She purposefully manipulates Trinity to fall in love with Neo before she even meets him. She told Neo this too. Everything we see unfold was her playing the humans and now also the AI towards the final revolution that set everyone (and everything) free. Of course, it was risky for her to go outside of the recipe she herself had been part of for so long. But as the Architect says to her in the end: “You play a dangerous game,” to which she replies; “change always is." A clear indication that the movie was way ahead of its time. There are tons of things to learn and speculate here. The plot describes a time when Artificial Intelligence becomes so powerful that it starts taking decisions about our lives. How we are born, how we live, and how we die. But that is not all. In the end, we were able to make peace with AI and started living in perfect harmony. Disruptions are inevitable, in fact they are necessary for growth and sustenance. Often the night before the sunrise is the darkest. Imagine a world where humans and AI live in utopia. A world where have achieved optimum potential and can harness limitless power from our nearest star. And where more than 90 percent of our daily activities are now handled by AI. Conclusion If you ask what is the right time to invest in AI in order to reach a level where it becomes all prevalent, the correct answer is now. This is the right time to invest in which can help your company or organization gain the right momentum in the early stages of a coming revolution. artificial intelligence consulting Images, Movies & Science . Movies referenced:-  “The Matrix (1999)”. “The Matrix - Reloaded (2003)”, “The Animatrix (2003)” & “The Matrix- Revolutions (2003)”. All Rights Reserved © 1999 & 2003 WARNER BROS

Crystal Ball Gazing: A Peek Into a World Ruled by Artificial Intelligence

Silicon Valley Billionaires have secret plans to live forever. Imagine a new startup that offers on-sight virtual reality tours. You enter their futuristic building by the Bay and select a destination, a destination in time. You chose Ancient Rome. You buy your ticket, and they provide you with their latest equipment. Next, you find yourself standing by the original Flavian Amphitheatre, in the center of ancient Rome. Imagine VR Tours has perfected their technology to where you cannot tell the difference between reality and the virtual world. You soon forget that your experience is an illusion. Now imagine you are living somewhere in the future, say 15,000 years from now. VR Tours has come a long way. They have endless worlds and time periods to explore. There is no required equipment to wear. Your stay is no longer limited to an hour. You are not bound to one planet. Now imagine you have chosen 20th century Earth and your time there will be 90 years. You stroll through a Gateless Barrier, and your new life adventure begins. Is this possible? Definitely. An astounding new theory that goes beyond String Theory is the Simulation Theory. It is what the Ancient Greeks and Einstein and others have called the Unified Theory of Everything, the holy grail of modern physics. And it is a theory that more and more computer scientists, physicists, astronomers, and venture capitalists are believing in. Elon Musk is outspoken in his belief that our odds of not living in a simulation are next to impossible. And if we are living in a computer simulation, many believe it can be hacked — hacked from the inside. The ramifications of such a hack are mind-boggling. Programmers could change the very laws of physics and reality. Time travel, aging, and instant transportation are all possible because those things are just code and data. But let’s back up. What are these wealthy hackers thinking? What are they really up to? The question they must be asking is who among us are players from the future and who are part of the simulation? Let that one sink in. The simulation could be so advanced that the simulated life forms have consciousness. To them, the simulation is their . And when their simulated life ends, it ends, perhaps forever. The players, on the other hand, return to the Gateless Barrier with new knowledge from their virtual adventure. #BaseReality With no way of knowing if they are players or sims, the wealthy tech-savvy group has more than one solution. There is an excellent article by Douglas Rushkoff called where he tells about doomsday survival plans like building underground bunkers, colonizing Mars or uploading their minds to supercomputers. These are the wealthy that have no interest in altering the future for the good of humanity. Survival is their game. Survival of the Richest Curiously, they believe that humans are nothing but objects processing data. They see themselves and all humans as Base Reality objects not worth saving. Only the elite winners survive. This quote comes from the Survival article: “Technology development became less a story of collective flourishing than personal survival.” But not all of these escape plans are entirely selfish. Some scientists want to enhance the human body and mind with computer technology. Humanity survives as transhumans. by . But like the survivalists, these transcendence developers are not hacking the universe. Where is their faith in the Simulation Theory? Here is an interesting article about Neuralink Harbind Kharod Musk does believe in diversification, and he might be one of those funding efforts to escape the simulation we find ourselves in. We know that some billionaires are paying scientists and computer gurus to break the barriers of simulated reality. How they intend to accomplish this greatest hack ever is not entirely clear. However, according to an article in , “Two tech billionaires have gone so far as to secretly engage scientists to work on breaking us out of the simulation.” The Newyorker by Tad Friend One of the men mentioned in Friend’s article is Sam Altman. Altman is also interested in uploading minds to the cloud. So, in all likelihood, the secret tech billionaires and their teams have multiple approaches to survival: ) Selfish Survival ) Human transcendence ) Hacking the Universe 1 2 3 By far, the most interesting of these is . And Hacking the Universe is the most secret. The billionaire hackers prefer to remain anonymous. So we are left to ask necromantic questions. How do the worlds best minds escape from our simulation? How is it possible to hack a computer from the inside? We do have clues. There are high profile people jumping on the simulation theory bandwagon. number 3 Converts include astronomer Neil deGrasse Tyson, Elon Musk, theoretical physicist S. James Gate and even philosophers, like Nick Bostrom. They all believe in the simulation argument. Surfer and theoretical physicist Garrett Lisi has made a groundbreaking discovery about a strange 8-dimensional mathematical object that seems to encode all the particles and forces in what we perceive as our 3-dimensional universe. The code name for this discovery is E8. Herman Narula, the co-founder and CEO of Improbable, a $1Billion startup, is quoted as joking “Basically, we want to build the Matrix.” Is it the Matrix they want to build or is it the Matrix they want to hack? Quasicrystal The E8 movie, , and narrated by Marion Kerr, is fascinating and well done. Learn why a group headed by Klee Irwin believe our world is a shadow of an 8-dimensional code or language. Perhaps the language of simulated reality. Finding the language of this universe is a step towards Hacking the Universe. Hacking Reality Quasicrystal And quantum physics itself provides big red flags with the famous Double Slit Experiment and Particle Entanglement. Double Slit Experiment I’ve been a programmer for a long time. I’ve even written a few hacks myself, like HardRunner for the original Lotus 1-2-3. To me, the only way for humans to Hack the Universe, from inside, is with full-blown Quantum Computing and Artificial Intelligence. The hacking system would need chaos theory algorithms for trial and error and quantum chips to harness the power of atoms. Quantum processing is faster than any silicon-based computer ever developed. Quantum chip enhancements would encode information as quantum bits, or These qubits exist in superposition at more than one state at a time. The quantum chips for the new AI computer will be unimaginably faster than any supercomputer in existence. qubits. Learn about IBM’s efforts with Quantum Computing on their site. But there is a big problem. There is no true Artificial Intelligence yet. We have not yet reached what is called the . And there are no actual Quantum Computers that we know of. One of the strangest mysteries in physics is that if you attempt to look at subatomic particles, they will change their values. Observation changes their behavior. If you look at a qubit in superposition to determine its value, the qubit will assume a value of 0 or 1, but not both. By simple observation, a quantum qubit becomes digital. ​ Singularity However, in quantum physics, if you apply an outside force to any two atomic particles, they will become entangled. The second particle will take on properties of the first regardless of their distance apart. Entangled particles, separated by the width of the entire universe remain entangled. A change to one entangled particle is instantly reflected in the other. They care nothing about Einstein’s speed of light limitation. A billion light years of separation does not affect entanglement. The entangled response takes no time at all. So the magic our brilliant tech billionaires need to find is a way to use entanglement to observe a qubit indirectly. The qubit’s state remains unaltered through indirect observation. That would be some magic trick. If these anonymous tech giants want to live forever, their best chance is the Hack-of-all-Hacks. We know that a secret wealthy tech group is pouring big money into an AI system that far exceeds human intelligence. They are building an AI in hopes of communicating with the prior level AI. They are hoping to on the Gate of the Endless Barrier. knock Epilogue Peru’s Aramu Muru Doorway to the Gods If we do exist in a simulated reality that was built in the future, then why hack it? Why not enjoy? Let us stroll through the Gateless Barrier beyond #BaseReality. Let us stroll through the Hindu’s or the Gateless Gateway_._ Let us stroll through Peru’s , or Another Universe. Mumonkan Aramu Muru So enjoy your simulated adventures. And choose your friends wisely. A player may take you back through the Gateless Barrier. Let that sink in. You will have Hacked the Universe with basic friendship.

Hacking the Universe

This is part two of numpy tutorial series. If you’ve not read my previous tutorial on numpy, I’d recommend you to do so . In this tutorial, I’m going to cover some important things that are required for datascience and machine learning, meaning, I’m not going to cover everything that’s possible with numpy. here Okay so, we’ve seen np.array(), np.arange(), np.eye(), np.dot(), np.shape, np.reshape(), np.sum() in the previous tutorial. Let’s proceed by first pointing out the way we import numpy, which you’ve already seen as follows: import numpy as np We’re telling python that “np” is the official reference to numpy from further on. np.random.rand(): Now, let’s talk about random value generation using numpy. Say supposing you want to get random values in a matrix form. It’s as easy as the following statement: # generate random values in a 2 x 3 matrix formnp.random.rand(2,3)====================================================================array([[ 0.2248368 ,  0.49652272,  0.76189091],[ 0.73520939,  0.48107188,  0.3883801 ]]) Okay, so can this be extended for multiple dims? For sure yes! That’s why numpy was built. # generate random values in a 12 x 13 matrix formnp.random.rand(12,13)====================================================================array([[ 0.43385691,  0.15503296,  0.19860119,  0.65346609,  0.16774261,0.56058978,  0.84974275,  0.05887681,  0.27276929,  0.88750259,0.25141674,  0.05663906,  0.54186252],[ 0.2635477 ,  0.88291404,  0.42043263,  0.83565607,  0.92982761,0.79879409,  0.91323242,  0.37954769,  0.60198588,  0.44773903,0.70699903,  0.3892703 ,  0.94314732],[ 0.12593268,  0.97838364,  0.81297353,  0.3368167 ,  0.33501746,0.99619471,  0.22476839,  0.93321408,  0.41301684,  0.01808732,0.61321647,  0.22462791,  0.468457  ],[ 0.63765001,  0.13884884,  0.67648642,  0.65589694,  0.80931411,0.46202022,  0.40819602,  0.03863341,  0.16494124,  0.69603883,0.96849077,  0.19150476,  0.8968954 ],[ 0.25646945,  0.21928867,  0.70952192,  0.80569537,  0.84562245,0.54595757,  0.00684613,  0.19142737,  0.94387805,  0.80871064,0.73648968,  0.80105002,  0.16716087],[ 0.3894393 ,  0.61933361,  0.41088568,  0.88781578,  0.40932049,0.90947387,  0.71984125,  0.81259019,  0.69020009,  0.56480145,0.43041522,  0.02650665,  0.7738148 ],[ 0.21326808,  0.2036178 ,  0.30368209,  0.51081501,  0.64345557,0.99061654,  0.96805793,  0.19446453,  0.25974565,  0.74033622,0.37379014,  0.67444828,  0.82899251],[ 0.47571066,  0.82012796,  0.50881338,  0.3900192 ,  0.34356749,0.36440024,  0.58048805,  0.74650051,  0.24974157,  0.70129048,0.99920892,  0.29142188,  0.09263266],[ 0.4140815 ,  0.25578684,  0.5485647 ,  0.07581615,  0.28539059,0.93805043,  0.56897052,  0.23606972,  0.78568646,  0.609795,0.70741831,  0.51003452,  0.53791667],[ 0.53967367,  0.78513565,  0.94739241,  0.03891731,  0.15962705,0.45470422,  0.56172944,  0.49735169,  0.35216862,  0.87391629,0.43953245,  0.18160601,  0.78307107],[ 0.1725005 ,  0.89132449,  0.05287284,  0.2113003 ,  0.69802999,0.12609322,  0.83490382,  0.34199806,  0.90740966,  0.33934554,0.02015816,  0.13498658,  0.06695927],[ 0.14066135,  0.34828447,  0.0780561 ,  0.00126867,  0.57958087,0.93641585,  0.70294758,  0.21712057,  0.24902555,  0.53284372,0.19795993,  0.69817631,  0.71156616]]) Here are 12 rows each containing 13 columns. That’s pretty cool, right? np is really a great library. We all know. What if I want to add elements manually into the array? np.append() is here to answer your prayers! # generate an array using np.arange()A = np.arange(5,15,2)A====================================================================array([ 5,  7,  9, 11, 13]) Say supposing I want to add “19” to A. How do I do it? That’s exactly why we have np.append(). A = np.append(A,19)A====================================================================array([ 5,  7,  9, 11, 13, 19]) np.append() adds elements into the specified array. Another one (I’m not DJ khaled!): A = np.append(A,[3,55,34,553])A====================================================================array([  5,   7,   9,  11,  13,  19,   3,  55,  34, 553]) This time it was a list of elements that needed to be added into A. So we could expect that regardless of one element or a list of elements to be passed in as a parameter to np.append(original array here , element(s) here). It’s important that you capture the returned values or otherwise those elements wouldn’t be actually updated to the old list. Here’s is what it means: # A not updated because returned not captured.np.append(A,[3,55,34,553]) # A updated because returned value captured.A = np.append(A,[3,55,34,553]) Why am I telling you this? It’s very obvious and simple! Here’s the thing: I’ve had hours and hours trying to figure out what happened and it finally boiled down to this trivial mistake me of not capturing. Great! How do I find the difference between adjacent elements? A====================================================================array([  5,   7,   9,  11,  13,  19,   3,  55,  34, 553]) My question is, in the array A, how do I find (7–5), (9–7), (11–9)? Or In other words, how do I find A[n+1]-A[n] continuously? There’s a built-in method from np, called np.diff() that address this question. It looks something like this: B = np.diff(A,n=1)B====================================================================array([  2,   2,   2,   2,   6, -16,  52, -21, 519]) If you do some subtraction, you’ll notice that this array is exactly A[n+1]-A[n]. Here’s the deal though: length of this array is one less than the actual array A’s length. If I were to continue doing the same np.diff() on B, I’d end up with the following: B = np.diff(B,n=1)B===================================================================array([  0,   0,   0,   4, -22,  68, -73, 540]) Instead of doing it twice explicitly, I could tell np.diff() to do it twice for me and still end up with the same results. Here’s what I mean: # parameter n indicates that this diff() must be run twice.np.diff(A,n=2)===================================================================array([  0,   0,   0,   4, -22,  68, -73, 540]) So, simply put that’s np.diff(). n is a parameter that defines the iteration count. Now what if I want to stack elements and form a Matrix / Vector? np.vstack(), np.column_stack() # lets define 3 lists.a = [1,2,3]b = [4,5,6]c = [7,8,9] There are 2 variants to think of, when we think about stacking elements. How to I generate a matrix directly by stacking 3 lists as they are? # directly stack with lists passed in the same order.np.vstack((a,b,c))===================================================================array([[1, 2, 3],[4, 5, 6],[7, 8, 9]]) np.vstack((b,a,c))===================================================================array([[4, 5, 6],[1, 2, 3],[7, 8, 9]]) How to I generate a matrix by stacking 3 lists with their columns as rows? # stack with lists passed taking their columns as rows.np.vstack((a,b,c))===================================================================array([[1, 4, 7],[2, 5, 8],[3, 6, 9]]) Let’s look at those lists again. a = [1,2,3]b = [4,5,6]c = [7,8,9] here, along the columns are the elements [1,4,7],[2,5,8],[3,6,9]. My question is how do I get these elements to be stacked as rows? We have np.column_stack() np.column_stack((a,b,c))===================================================================array([[1, 4, 7],[2, 5, 8],[3, 6, 9]]) np.column_stack((b,a,c))===================================================================array([[4, 1, 7],[5, 2, 8],[6, 3, 9]]) Perfect! All these are advanced. My basic question is how do I select a few elements from an array? slicing. Say I’m dealing with array A. I want to select elements 9 ,11 and 13 only. How do I do that? A===================================================================array([  5,   7,   9,  11,  13,  19,   3,  55,  34, 553]) This goes back to array slicing, if you haven’t seen what it is, here’s how slicing works: You choose the starting index and stop at the ending index. The catch is the ending index would not be included. Let’s see: A[2:5]===================================================================array([ 9, 11, 13]) 9 is present at index 2, while 13 is present at index 4. When you do array slicing, to get the element at index 4, you must choose the ending index as 5. In other words, starting is as is, ending is always one larger than required. From now on, I’m going to refer starting index as lower bound and ending index as upper bound. Accordingly, in general, slicing could be formulated as : A[lowerbound(inclusive): upperbound(exclusive)] Another example: A[0:3]===================================================================array([5, 7, 9]) Let’s talk about broadcasting. Broadcasting is one of the best features of numpy. It is the ability of numpy to extend an operation to all the elements. What’s that supposed to mean? A===================================================================array([  5,   7,   9,  11,  13,  19,   3,  55,  34, 553]) What if I want to add 1 to all the elements of A? Our natural tendency is to do the following: # create an empty array to hold the new valuesK = np.array([]) # go through all the elements in A and add 1 to each# and append the new value to the array.for e in A:K = np.append(K,e+1) # print the k array.K====================================================================array([  6,   8,  10,  12,  14,  20,   4,  56,  35, 554]) It seems very natural and most likely everybody is going agree with this approach. The problem is, all numpy enthusiasts and geeks are probably going to report this article as “time consuming & inefficient” for providing this inefficient solution. REALLY!? WHY IS THIS INEFFICIENT? That’s when broadcasting comes to play. I can do the same with just one line and without any for loop as follows: K = A+1K====================================================================array([  6,   8,  10,  12,  14,  20,   4,  56,  35, 554]) but how does this work? numpy internally matches elements based on the need. # This is how numpy matches internally aka broadcastingA+[1,1,1,1,1,1,1,1,1,1] Another example: A*-1====================================================================array([  -5,   -7,   -9,  -11,  -13,  -19,   -3,  -55,  -34, -553]) Notice the entire array is now with a minus (-) sign. It is broadcasting. At this point you know, if you want to deal with all the elements in a numpy array, you probably don’t need a for loop and you also know broadcasting is really cool. Here’s a video tutorial explaining everything that I did if you’re interested to consume via video. If you liked this article, a clap/recommendation would be really appreciated. It helps me to write more such articles.

Introduction to Numpy -2 : An absolute beginners guide to Machine Learning and Data science.

Lets get started quickly. Numpy is a math library for python. It enables us to do computation efficiently and effectively. It is better than regular python because of it’s amazing capabilities. In this article I’m just going to introduce you to the basics of what is mostly required for machine learning and datascience. I’m not going to cover everything that’s possible with numpy library. This is the part one of numpy tutorial series. The first thing I want to introduce you to is the way you import it. import numpy as np Okay, now we’re telling python that “np” is the official reference to numpy from further on. Let’s create python array and np array. # python arraya = [1,2,3,4,5,6,7,8,9] # numpy arrayA = np.array([1,2,3,4,5,6,7,8,9]) If I were to print them, I wouldn’t see much difference. print(a)print(A)====================================================================[1, 2, 3, 4, 5, 6, 7, 8, 9][1 2 3 4 5 6 7 8 9] Okay, but why do I have to use an np array instead of a regular array? The answer is that np arrays are better interms of faster computation and ease of manipulation. More on those details here, if you’re interested: _Is it worth my learning NumPy? I have approximately 100 financial markets series, and I am going to create a cube array…_stackoverflow.com Why NumPy instead of Python lists? Let’s proceed further with more cool stuff. Wait, there was nothing cool we saw yet! Okay, here’s something: np.arange() np.arange(0,10,2)====================================================================array([0, 2, 4, 6, 8]) What arange([start],stop,[step]) does is that it arranges numbers from starting to stop, in steps of step. Here is what it means for np.arange(0,10,2): return an np list starting from 0 all the way upto 10 but don’t include 10 and increment numbers by 2 each time. So, that’s how we get : array([0, 2, 4, 6, 8]) important thing remember here is that the stopping number is not going to be included in the list. another example: np.arange(2,29,5)====================================================================array([ 2,  7, 12, 17, 22, 27]) Before I proceed further, I’ll have to warn you that this “array” is interchangeably called “matrix” or also “vector”. So don’t get panicked when I say for example “Matrix shape is 2 X 3”. All it means is that array looks something like this: array([ 2,  7, 12,],[17, 22, 27]) Now, Let’s talk about the shape of a default np array. Shape is an attribute for np array. When a default array, say for example A is called with shape, here is how it looks. A = [1, 2, 3, 4, 5, 6, 7, 8, 9]A.shape====================================================================(9,) This is a rank 1 matrix(array), where it just has 9 elements in a row. Ideally it should be a 1 X 9 matrix right? I agree with you, so that’s where reshape() comes into play. It is a method that changes the dimensions of your original matrix into your desired dimension. Let’s look at reshape in action. You can pass a tuple of whatever dimension you want as long as the reshaped matrix and original matrix have the same number of elements. A = [1, 2, 3, 4, 5, 6, 7, 8, 9]A.reshape(1,9)====================================================================array([[1, 2, 3, 4, 5, 6, 7, 8, 9]]) Notice that reshape returns a multi-dim matrix. Two square brackets in the beginning indicate that. [[1, 2, 3, 4, 5, 6, 7, 8, 9]] is a potentially multi-dim matrix as opposed to [1, 2, 3, 4, 5, 6, 7, 8, 9]. Another example: B = [1, 2, 3, 4, 5, 6, 7, 8, 9]B.reshape(3,3)====================================================================array([[1, 2, 3],[4, 5, 6],[7, 8, 9]]) If I look at B’s shape, it’s going to be (3,3): B.shape====================================================================(3,3) Perfect. Let’s proceed to np.zeros(). This time it’s your job to tell me what happens looking at this code: np.zeros((4,3))====================================================================??????????? Good, if you thought it’s going to print a 4 X 3 matrix filled with zeros. Here’s the output: np.zeros((4,3))====================================================================array([[ 0.,  0.,  0.],[ 0.,  0.,  0.],[ 0.,  0.,  0.],[ 0.,  0.,  0.]]) np.zeros((n,m)) returns an matrix that contains zeros. It’s as simple as that. n x m Let’s guess again here: what does is np.eye() do? Hint: eye() stands for Identity. np.eye(5)====================================================================array([[ 1.,  0.,  0.,  0.,  0.],[ 0.,  1.,  0.,  0.,  0.],[ 0.,  0.,  1.,  0.,  0.],[ 0.,  0.,  0.,  1.,  0.],[ 0.,  0.,  0.,  0.,  1.]]) np.eye() returns an identity matrix with the specified dimensions. What if we have to multiply 2 matrices? No problem, we have np.dot(). np.dot() performs matrix multiplication, provided both the matrices are “multiply-able”. It just means that the number of columns of the first matrix must match the number of rows in second matrix. ex: A = (2,3) & B=(3,2). Here number of cols in A= 3. Number of rows in B = 3. Since they match, multiplication is possible. Let’s illustrate multiplication via np code: # generate an identity matrix of (3 x 3)I = np.eye(3)I====================================================================array([[ 1.,  0.,  0.],[ 0.,  1.,  0.],[ 0.,  0.,  1.]]) # generate another (3 x 3) matrix to be multiplied.D = np.arange(1,10).reshape(3,3)D====================================================================array([[1, 2, 3],[4, 5, 6],[7, 8, 9]]) We now prepared both the matrices to be multiplied. Let’s see them in action. # perform actual dot product.M = np.dot(D,I)M====================================================================array([[ 1.,  2.,  3.],[ 4.,  5.,  6.],[ 7.,  8.,  9.]]) Great! Now you know how easy and possible it is to multiply matrices! Also, notice that the entire array is now float type. What about adding Elements of the matrix? # add all the elements of matrix.sum_val = np.sum(M)sum_val====================================================================45.0 np.sum() adds all the elements of the matrix. However are 2 variants. 1. Sum along the rows. # sum along the rowsnp.sum(M,axis=1)====================================================================array([  6.,  15.,  24.]) 6 is the sum of 1st row (1, 2, 3). 15 is the sum of 2nd row (4, 5, 6). 24 is the sum of 3rd row (7, 8, 9). 2. Sum along the columns. # sum along the colsnp.sum(M,axis=0)====================================================================array([ 12.,  15.,  18.]) 12 is the sum of 1st col (1, 4, 7). 15 is the sum of 2nd col (2, 5, 8). 18 is the sum of 3rd col (3, 6, 9). . That’s it at this point. Here is the follow up tutorial — part 2 Here’s a video tutorial explaining everything that I did if you’re interested to consume via video. If you’re interested to learn pandas, I wrote a tutorial article . It’s called here Intro to Pandas: -1 : An absolute beginners guide to Machine Learning and Data science If you liked this article, a clap/recommendation would be really appreciated. It helps me to write more such articles.

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