Best Computation Quotes

"Compute is going to be the most precious commodity in the world."

"You believe that consciousness is in some fundamental sense non-computational."

"It takes an enormous amount of computational horsepower to create an image so subtle, so beautiful, that we believe it's real."

"A quantum computer can pursue all possible computations at the same time simultaneously."

"Time is sort of the progressive doing of computation, the progressive changing of the world by virtue of the application of rules."

"Increasingly, I'm sure you all see this—those of you who are science majors—an increasing reliance on computation rather than traditional experimentation."

"The universe is an enormously big computer that has information going into it and information comes out processed."

"Turing's little machines took on a life of their own by making a definition of computation that was rigorous, people were able to study the nature of computation and its limitations like never before."

"Anything from your desktop to your smartphone to the computers on the International Space Station are based on Turing's model."

"There is currently no working model of computation more powerful than Turing's. This is embodied in the Church-Turing thesis, which states that anything that can be computed, can in principle be done so by a Turing machine."

"Quantum computers, if they work, will definitely bring something new to the table but so far, Turing's simple model, which he dreamed up at age 22, kind of as a by-product to answer a totally different question, is still the most widespread model of computation to date."

"The big question in this class is: what are the capabilities and limitations of a computer?"

"There's something outside computation in human understanding."

"Turing introduced what became known as the Turing machine to formalize computation."

"Underlying all computation, all Turing machines, all artificial intelligent systems perhaps might be a very simple instruction set like RISC 5."

"EC2 provided a way for everyone to perform intensive computations in the cloud."

"Quantum computers calculate things very differently than classical computers do and that makes them good at different things."

"Consciousness is non-computational and there's something other than computation going on." - Dr. Stuart Hammeroff

"The problem with computations with a Turing machine is that a Turing machine can do its computations in one of two ways: deterministic or non-deterministic." - Chris Langan

"Reflex models are models which just require a fixed set of computations."

"It's absolutely fascinating because in terms of the computational expense, it's kind of almost 3D-like."

"I guess we should figure out what's the running time."

"To be a mathematician is not just to compute a formula, but also to ask the right questions."

"What the computer is doing instead is thinking about elliptic curves modulo primes."

"Causality is one of the most important computations that we do."

"Computers are actually very good at very formal systems."

"Simple methods, general methods that leverage computation seem to work well."

"It's going to take some time for those to become more mature and robust, but in the long run, I do think ZK is going to eat everything when it comes to computation over a long enough time Horizon."

"Imagine a super-advanced civilization built a computer with memory storage that operates at the Bekenstein bound. Essentially, they're computing on the surface of a black hole event horizon."

"Utilizing a supercomputer though they Solve the Riddle."

"The function that's being computed by the neural net is getting closer to the function we actually wanted."

"Time is this sort of inexorable computational process of applying rules."

"We are computationally bounded, implies we build a physics/mathematics that we can do."

"We have a good intermediary, and the good intermediary is computers and computation."

"The passage of time is the operation of irreducible computation and it really means something."

"So in digital computation, the whole idea is that you separate the hardware from the software so you can run the same computation on different pieces of hardware. And that means the knowledge that the computer learns or is given is immortal."

"There started to be this kind of robust notion of universal computation that existed."

"It really is computation all the way down."

"Knowing what's actually going to happen is something that's kind of computationally irreducible."

"You can reproduce the behavior of any other Turing machine."

"This is a sign of a feature of combinators that they're capable of doing universal computation."

"...what programs out in the computational universe typically do, the biggest is this thing I call the principle of computational equivalence."

"One of the things we realize is that there's sort of this ocean of computational possibility that exists out there."

"The question for us as humans wanting to use this is how do we take the things that we want to do and map those things into this sort of ocean of computational possibility."

"What does it mean that there's a universal Turing machine?"

"Could our universe be just lying out there in this computational universe of all possible universes?"

"Every program is represented by some natural number."

"This program should output the word yay if the program P finishes when we input D into it and should output whoops if the program P does not finish when we input D into it."

"Our amazing program may never finish on some inputs, defeating its whole purpose."

"No matter how clever we try to be, we can never actually do this."

"The arrows between numbers are simply partial functions on the numbers which can be implemented as programs."

"Our amazing program A is clearly playing the role of this powerful thing here."

"Our main assumption is that this program A is total and it correctly finishes on all of its inputs."

"Such a powerful total program like A could not have existed."

"Simple programs can produce great complexity."

"It has automatically calculated the totals for all your rows for these three columns."

"We can always do simpler computations here by converting our data into table format."

"The richness or infinite potential that language offers is why many experts in linguistics and computation strongly believed computers would never come close to understanding human language."

"Homomorphic encryption allows users to run calculation on data while it is still encrypted."

"Once you have a computational language to express things, you can expect to kind of weave this complicated kind of computational web."

"The carpet of a million computations."

"The wedge product will distinguish if it's to the right or to the left."

"Reversing a quaternion is just a swizzle; you just shuffle the components. It's a free operation in terms of computational power."

"If the sequence is generated in a regular language, then there exists a DFA that will generate that sequence."

"The structure of space in a Turing machine."

"That sum over all trajectories is what's called the Feynman path integral."

"What Post had seen was an example of what's probably universal computation in the wild."

"Aggregate functions in SQL allow us to do computations on top of a single column through every single row of a table."

"The backward pass of a matrix multiply is a matrix multiply."

"The only way to achieve that is to take the delogits and matrix multiply it with W2 transpose, and it's the only way to make these two pieces to make the shapes work out."

"Matrix multiplication and a few transposes—that's the only way to make the dimensions work out."

"We backpropagated through a linear layer."

"And we are going to do for batch normalization exactly what we did for cross entropy loss in exercise number two."

"So previously we've broken up batch normalization into all of the little intermediate pieces and all the atomic operations inside it and then we back propagated through it one by one."

"The empty string can always be generated."

"A single neuron is basically a function that takes in a vector and outputs a scalar."

"As you get to 86 billion neurons, you can now compute the truth or at least the parts of the truth that we need."

"I think the real thing to understand about what's happening is the great democratization of access to computation."

"The goal is to have made as much as possible of the world computable."

"Using analytic continuation we can just compute directly that zeta of minus 1 happens to be exactly minus a 12."

"The architecture of the brain supports executing computational languages. That's obvious."

"Compute these different values on these different spatial and temporal scales and see where it peaks."

"Turing complete is not measured in gigabytes or teraflops, but in which class of problems you can solve."

"How the heck do all these abstract rules mean anything in terms like numbers or strings or anything that computers do?"

"Computational essays are a way to present one's thinking in a mixture of text, formulas, graphics, and computational language."

"Computational language is an integrated part of communicating ideas, not just something you feed to the computer."

"The future of pretty much every field is computational."

"Mathematica is kind of the thing that the brand that is the strong one for for mathematical kinds of things but Wolfram Language as a whole is really more about this General computational language story."

"The beauty with this code is that it's strictly equivalent to the one that we've seen before, which means that if any of those functions fail, it's going to bypass the whole computation and just returns optional empty."

"The internet being a psychedelic substance... people having these psychedelic experiences where they realize that computation can be embodied in analog carbon-based systems—it's all kind of connected."

"So instead of doubling per year, which is the MS law Trend, we're increasing the amount of compute by 10 times per year because in this case, we don't need the compute to be smaller."

"Every program can be written using combinatory logic using only the combinators s, k, i, b, and c."

"We want people doing research to just be academically oriented but because in the last few years all the development of AIS is actually happening now in these huge AI Labs because those are the only ones that can afford these billion dollar compute clusters right."

"What happens when you can compute for a million times cheaper than today? Then there are many new ways of doing something you're willing to do."

"Turing's brilliant mind saw that any calculation had two aspects: the data and the instructions."

"It's worth noting that there's just not enough computation available in the world to try out all the possible examples."

"...there's nothing else that's even close to this right now in computation."

"Amazing... you can think of it as an entirely new model of computation in a way."

"Consciousness is something different from computation."

"What evolution does is it uses bioelectricity to get meaning and computation out of physics."

"So this is just a layer where each point has a shortest distance, so I can just sum up the total distance and that will be my cumulative distance."

"There really isn't a bright line between the intelligent and the merely computational."

"...intelligence is at some level just computation but for us intelligence is defined to be computation that is doing things we care about."

"Computation is the process of systematically following rules."

"Straight line distance is quick and easy and very fast to compute."

"Quantum computers enlarge what is computable in polynomial time."

"P is contained in BQP, meaning everything a classical computer can do, so can a quantum computer."

"The internal nature of thought was a mystery until mathematical theories of computation were developed in the 20th century. Now, we've been able to capture the essence of this system."

"What we need, what is somehow coded in our brains, is a finite procedure, kind of like a program in your laptop, which generates an infinite number of hierarchically structured expressions, each of which is an expression of thought."

"...a complete algorithm for computing the 3D Vector corresponding to a triplet of spherical coordinates is given by this tight little expression."

"You'd like to be able to say hey we're going to get a solution Bam Bam Bam it's easy it's easy to explain but actually it's something where it rides on top of a bunch of ideas that that you know it's sort of interesting to me like the idea of computational irreducibility."

"The bulk of what's there altogether in the computational universe is all possible computations."

"How to compute area of polygon? That's easy."

"Their cross product is, let's remember, area of the triangle, and sine will tell you automatically if it's left or right."

"If it says compute area of polygon, area of this polygon is 8.8 point zero, let's say, then I not rightly, I got 16. And now to really print the area, I should divide by two, and now my program prints the area. It's 8."

"They say print twice the area because this ensures that the result is integer."

"...there's interesting things about these... not a very productive way to compute but a lot got done."

"An algorithm is a set of steps to complete a task or to solve a problem."

"We need a nonlinearity to introduce nonlinearities in our neural networks."

"Logical functions, at its core, ask a question. Is this number greater than the other? You'll get an answer of true or false."

"Monads abstract away accumulation of log data during computation, as well as the possibility of missing data and asynchronous operations."

"Now, you can do anything that you could have done in a regular for loop, such as if you want the sum of all these numbers, you can do so like this."

"One of the big results: Turing machines and lambda calculus are equivalent."

"This model is sufficient for all of computation; anything that can be computed can be computed with just these primitives."

"An axiom tower that's sort of different than the Turing machine is called Turing complete if and only if it can be used to emulate our Turing machine."

"Conway's Game of Life is turning complete."

"...this task itself is... only 5% parallelizable."

"To me, anchoring meaning is about turning natural language into computational constructs."

"The practical version of meaning is the ability to do computation."

"We want this to compute the sum of the list of floats."

"The trick is to have just enough computational flexibility to describe constraints for layer twos without injecting arbitrary computation into the base layer."

"Can computation occur at zero temperature? It has nothing to do with temperature."

"We're doing it the learning way, making one small change at a time in a very high dimensional space of computations."

"Scale is important because many problems require doing computation that is intractable if you want to really get the right answer."

"It makes thousands of calculations every second."

"So now we can use the new function we've created here to extract the coordinates of the pixel that has the smallest depth of all the pixels of the kernel."

"Large language models provide a path to making programming and computation as easy as asking a computer what you want in natural language."

"The power of ZK is that I can prove a full-blown computation. I will just give you a proof, and you are 100% sure that everything was executed correctly."

"This is the function we need and how to do those computations quickly."

"The bottleneck of this algorithm is not the memory access, it is actually the number of computations."

"Multi-head attention computes different representations simultaneously."

"So, as you remember, when we calculated the attention using this formula, softmax of Q multiplied by K, divided by square root of DK..."

"Dynamic quantization calculates alpha and beta on the fly for each input to quantize the input matrix."

"The ruad may be defined as the entangled limit of everything is computationally possible, i.e., the result of following all possible computational rules in all possible ways."

"Computers also just take inputs in the form of 0s and 1s, and then they transform them in some way."

"Part of being a mathematician: making the most of the computational power."

"Why does cheap and deep learning work so well? I think Darwinian evolution gave us this particular kind of neural network based computer precisely because it's really well tuned for tapping into the kind of computational needs that our cosmos has dished out to us."

"That's the general rule that we're working with, that anytime that we provide multiple scalars, that that formula will spill."

"The answer is yes. The most powerful computer in the world today does 36 trillion operations a second."

"But you can see we didn't bother to expand C or L or even consider I and J, many fewer nodes got put in the stack...In both terms of the amount of computation we did and the memory footprint was reduced and we still obtained the same result."

"If you want to tell it's a double precision, put the number sign after, and it still works, but it's not double precision, obviously. Interesting."

"What do the arguments mean? It's a computation. Whose line are we dealing with? Where are we right now?"

"Super computes the next one in the line."

"We're realizing that the human brain is not very good at doing computation in the sense of just thinking many times, many steps ahead for chess or go."

"Let's take a look at our program and let's see what we need to add to start Computing these numbers."

"So the first number that you're adding together is comprised of this bit, this bit, this bit, and that bit in that order."

"Human beings have been performing computations for thousands of years."

"The largest publicly known training run to date is GPT-4, estimated to use nearly eight orders of magnitude more compute than AlexNet."

"And those gradients are going to be used as weights for the attention matrices to average across them."

"Dynamic programming is a method for solving complex problems by breaking them down into simpler overlapping subproblems and storing solutions to these subproblems to avoid redundant computations."

"With fuzzy logic, crisp inputs with precise values--like we have with a very specific credit rating--these are converted to fuzzy variables in a process called fuzzification."

"The finite element method is one of the most powerful numerical methods."

"The real cost of computation is the cost of programmers."

"With something like that, I think that actually allows you to do pretty hefty computation."

"I can use this any number of times I can use it the same thing a bazillion times with different M's and that doesn't give any help on how to factor n or how to compute D."

"The most sophisticated have been more about massive compute than massive data."

"Every new wave of computation at the very beginning started off looking like a toy."

"I see it being direct natural language to computation, nothing in between."

"Different use cases will require different methods and are going to drive different amounts of compute."

"If you type in pytorch a times B plus c uh what this is going to do is it's going to first multiply Adam B A and B and store that result into memory and then it is going to add C by reading that result from memory."

"Ultimately, P versus NP is about peace of mind and a good night's sleep."

"You could think of it as the function of this particular machine is to double your input and then add 1."

"If we really got quantum computers to work, they would accelerate certain types of computation."

"The amount of compute being devoted to artificial intelligence applications has been growing a lot faster than Moore's Law over the past years."

"You only need to kind of zoom in and think about this local picture of little computational graph nodes that compute outputs and then multiply the local gradients to compute downstream gradients."

"You can model your own computational processes, but it's an illusion."

"...and in the hidden layer here I have put 4 neurons and these 4 neurons are the size of my embedding vector."

"We're now turning the world of biology into a computational search exercise."

"Under the hood is a 2D boundary element field solver that calculates all the couplings between every single leg and all the signals in them."

"Even with today's technology, checking a Mersenne number that has millions of digits can take a modern computer from a week to an entire month or even more."

"So let's print and we're going to use the math library."

"Anything that can be computed can be computed by the brain."

"Neural networks could implement any sort of computation."

"So we can compute the median of big R by taking the transformation of the median of the binomial distribution, then median can be approximated by np."

"Looking at algorithmic development that can really perform very efficiently given the computational constraints."

"With the power of the lazy evaluation that pausing each time that we call next gives us, we can actually create really expensive computations, infinite sequences, things that would otherwise crash our computers."

"At the core, we're doing research and really asking social science questions, but using computation and statistics to help distill information from data, to be able to answer those questions."

"It has to calculate the coordinates of everything, it has to calculate the size of everything and place it on the screen, and then when all that is done, it actually renders every pixel on the screen."

"So there's a lot of work involved if you want to do it by hand even though you can do it you have to find igen values find igen vectors in this case you have to find three of them and then you have to do more work and more work but it can be done and we are done now."

"So the bottom line is V1, V2 is equal to the inverse of Matrix A times Matrix B."

"You're saying divide by three, but how could we make this so that it's extensible to any number of elements in the array? We could do sum divided by nums.length."

"...we can actually easily approximate the option value using Monte Carlo and this is less computationally expensive than having to solve high dimensional PDEs."

"The magic of the Monad is not in what a Monad is, but in why are these Kleisli arrows so useful and what kind of problems do they solve?"

"The Monad is just composition. It lets you split your big computation into smaller computations and glue them together."

"The Monad is all about composing stuff. It replaces this dot with the Kleisli arrow."

"Everything that can be computed using non-pure functions can be converted into pure calculations as long as you replace regular functions with functions that return embellished results."

"Impure computations can be transformed into pure computations in functional programming, but they return embellished results."

"Computers are capable of organizing raw data and performing calculations that are truly impossible for human beings."

"SGX is the right technology for Suave's credible computation."

"This also allows you to use a 64 to work with more than 32 2 to the 30 year second power on the side of the array."