Best Approximation Quotes

"As the number of rectangles increases, as the distance H shrinks, we've got a pattern of approximations."

"Names are like a game of horseshoes for me; close is good enough."

"Science creates models that are the best approximations of the universe we live in."

"I obviously couldn't do an exact replica but I still feel like we got some thin fairly close."

"One of the pillars of AI is that it does not need to be true. It only needs to be an approximation, a guess, but it is treated as absolute truth."

"Maybe it's not exactly two, but if it's in the ballpark of two, that's going to be sufficient."

"Let's just make it simple and round that down to 80. 80 divided by 3 is like 26 point something."

"Question for you: How could you use this expression to calculate better and better approximations for pi?"

"Fermi estimation baby, we can get close to the actual value basically."

"If you aim at something, you may not hit it dead on, but you'll get within the parameters of it."

"Think of it as a conceptual shorthand for 'the best constant approximation for the rate of change'."

"Let's call it 95, just for the sake of argument."

"The total number of lattice points inside a big circle with radius R should be about pi*R^2."

"I just made that number up, but it's probably somewhere around there."

"I think this is the closest we're gonna get to purple."

"Approximate answers are likely just as good, if not better, in the presence of noisy data."

"You take your diameter... multiply by 8 over 9, you square that, and that gives you a pretty good approximation of the area of that circle."

"It's better to be approximately right than exactly wrong."

"Thirty-four, thirty-five, almost three dozen."

"There's a lot more to tailor series and approximating functions than first meets the eye."

"it's not an accurate statement but it's close enough for argument's sake."

"Calculus teaches us that if you zoom in on something enough, no matter how curvy it was, it begins to look straight."

"Our sense of flowing time is not fundamental; it's in the approximation."

"But I want to say roughly around 100,000."

"That's pretty good I think we're in the ballpark there."

"A vague approximation is still an approximation."

"Better to be roughly right than exactly wrong."

"These numbers aren't going to be perfect or exact."

"It's not the Gibson version, but plugged in it's going to be close enough."

"Science is about approximation, a gradual reduction of uncertainty."

"If you have numbers where you don't care about the exact value of the number, you just kind of want to know roughly how big things are, then the logarithm is a perfect thing."

"It doesn't have to be exact, but something in that general vicinity will work out."

"I would have said twenty-two to three hundred."

"He was in his late 30s to mid-40s."

"...so if that's if that were the world in which we were in to start then classical mechanics would not be a good approximation..."

"That's what we have, the approximation. Anytime you have an exact answer in math like X is equal to 2, that's the precise, exact total answer."

"The goal is to keep in mind what the perfect is, and then try and get there through successive approximations."

"Close is all you need, boys. Horseshoes and hand grenades."

"Approximate nearest neighbor basically takes an approach to finding the nearest neighbors just like K-nearest neighbors does but it does it in an approximate manner obviously which prioritizes speed over accuracy."

"We just basically say, 'Hey, this number is really small, we're just going to call it one.'"

"It's not going to go over the entire range, but it's going to be pretty close."

"All of electronics is approximation. We're trying to minimize all the bad stuff."

"So, just, it's never, almost never an even five and five. It's almost always a five and a three or a six and a two or, you know."

"It's important to note that 10 to 15 years is not set in stone."

"Every individual beautiful phenomenon is a mere approximation of true beauty itself."

"You aren't trying to be exact of course either."

"The main ideas here are that you can use the linearization to estimate the change of a function if you change the inputs by a small amount, and that this can be represented using differential notation."

"Judging by the color here, we're going to call it 80 or so."

"Look, this is not a Neapolitan pizza but it sure is pretty adjacent. It's definitely Neapolitan-ish and it's plenty good for you and your friends drinking wine, having fun at your house whenever that happens again."

"For linear shape functions, we get a piecewise linear approximation for U."

"Circa means approximately 1750, could be a little older, could be a little younger, so you're safe if you say circa."

"You just need to kind of eyeball it and if it's in a comfortable 30-70 ratio or something close to that, I think you're in business."

"It's supposed to be fun, don't stress out about things like the exact color, just get it close as you can."

"Kind of coming, get it close, and call it good enough."

"This is as close as you're going to get to an exotic."

"I'm just going to mostly eyeball the whole thing."

"There's only three and I've been told them that's probably almost true."

"If I did this infinitely and filled the entire space, I would get closer and closer and closer to a better approximation of the number pi."

"It probably will be around an hour or so."

"That's kind of approaching your numbers."

"Usually in most cars on most junctions like this around about three quarters of a turn of the wheel should do it but that is a very rough guide."

"Sometimes we only know their radius not their mass, though we can make decent approximations of the latter from the former."

"It's like 768 Square feet so just say 800 square foot, you know?"

"This looks like it's probably a 40 45 in screen TV, something along those lines, somewhere close to there."

"So now let's figure out how to deal with the current term this is when we make one of the biggest approximations here."

"Let's say it's right about in the middle."

"Other than that if it was a silhouette it would be pretty close."

"That's pretty close, it's not as perfect as I had it yesterday, but you get the idea."

"One therefore has to make approximations."

"I suspect that somewhere in between there is probably about where the right."

"The Taylor series lets us linearize the differential equation to turn it into a problem we can solve much more easily."

"The key point here is that when x is small, like say 0.1, then the higher powers of x in the successive terms in the Taylor series get even smaller."

"Very, very close to 13 months either way."

"Well, looks pretty darn close to me. I got lucky this time."

"They don't have to be exact. It'll still taste great."

"You will save about 17, I think it was."

"That might be just a little bit more than half but it's close enough."

"There are these classical ways of thinking, and it's amazing what people did before computations and simulations. But at some point, you're gonna find an approximation, and they're brilliant approximations, but they're probably a little bit wrong, and we can do better now."

"I just know it's useful and hey, it gets pretty close."

"Every time this has happened to us before in the history of physics, that some concept we can't even in principle give operational meaning to, it's meant that that concept is approximate and somehow arises in an approximate way from more fundamental ideas."

"I didn't even measure it's about a yard I guess."

"So, we're gonna say eight inches."

"When you estimate you make a really good guess so even if you don't know the exact answer you can still get close enough."

"It's probably not right, but it's going to be close."

"You just want to build something that is good enough approximation locally that you can say, 'I trust it enough to know that the age here in this locality is important or not.'"

"It's approximate like six foot by six foot square maybe."

"Paraphrasing never produces a hundred percent match; the meaning should be close enough."

"Life is more complicated than that, and so the CAPM is really just an approximation to a much more complex reality."

"We get pretty close to Euler's number itself, to the number e = 2.718."

"Proto-languages are just models and are just approximations. Proto-languages are very unlikely to ever be precise because there are always features like sounds, words ending, sentence patterns that are lost without a trace forever."

"If something looks like 1 + x raised to a power, and if you're not going too far from the point 1, namely if your x is very small, then don't bother with doing the whole 1 + x times 1 + xn times, it's approximately equal to 1 + nx."

"You cannot beat the exact formula; it's the exact truth but if you're interested in that exact function for small values of v/c, it's much more useful to use this approximation."

"Maybe there is some dynamical reason why the universe that we live in is so well approximated by local hamiltonian."

"If Δx is very, very small and it's your intention in the end to make very, very tiny Δxs then we say we will use this approximation."

"Therefore we're going to make use of approximate models."

"It's like the sixty to one rule, which is based off of basic geometry, but we kind of round it off."

"It is meant to count primes or it's meant at least to find some simple curve or some simple function that's a reasonable approximation for the count of primes up to any number X."

"It's approximated to PI of X is approximated by lye of X with essentially square root accuracy."

"The universal approximation theorem... states that a feed-forward neural network with just a single neural layer is absolutely sufficient to approximate any arbitrary function."

"The first harmonic approximation is just saying let's ignore all the upper harmonics and only consider the first harmonic."

"Pi is approximately equal to 21 times 80,504 minus 29,973 times the square root of three all over one nine one one zero five."

"That's a really good approximation."

"The truth is an approximation of what the data presents us right now."

"Language is always of course approximate... when people are striving for what they think of as precision, they are advising a process which inevitably involves approximation."

"All we can ever do is approximate."

"Deep learning doesn't exactly implement the optimal functions you want, but it generally approximates the functions we're interested in really, really well."

"A single hidden layer MLP can approximate any function to arbitrary precision."

"The truth is you can't calculate it exactly right because the decimals never really end."

"We did a pretty good job; this curve follows the curve pretty well, it has like little jumps on it, bins they don't quite match up, but it's pretty darn close."

"The more particles you have, the better you approximate the true distribution."

"The scientist explains the world by successive approximations."

"Deep neural networks can be used to approximate just about any continuous function."

"In practice, they tend to get very close to the right answer."

"The idea was if I start with some function like maybe this discontinuous function, the square wave that's one and then minus one, I can try and approximate that function with a sum of trigonometric terms."

"It's never about exact values, it's always just about the rough feeling of it."

"...this is an odd British folk tradition going back hundreds of years, but it is also a mathematically legitimate way to approximate the digits of pi."

"Pi is approximately equal to 3.14."

"The philosophy of the Taylor series is the following: That if some function f(x)... you can only zero-in on a tiny region around here."

"The RBF kernel is so popular for various reasons, number one, you can prove that it's a universal approximator."

"I don't have 20/20 vision, but it's pretty close."

"String theory certainly has compelling features... because to first approximation it did some things dramatically well."

"If f(x) converges for all the x or some interval I, then how accurately do the functions or the Taylor polynomial approximate the given function on this interval?"

"We're going to first approximate the region asked by rectangles and then we're going to take the limit of the areas of these rectangles as we increase the number of rectangles."

"In order to find the area under some curve, we're going to just approximate it by drawing rectangles underneath."

"The mathematics will play roles in defining how to measure how well we've done in approximating our original data."

"Euler's constant... e is approximately equal to 2.718."

"We're at a starting point where, in leading approximation, these ideas that we're talking about actually describe the real world."

"The key ideas are approximation and parametrization and there's different things that one can approximate or parametrize and that gives different types of methods."

"Any approximate method as the approximations become better and better, it should give you a sound exact algorithm."

"If the universe is doing real valued computation, then real value computations can only be approximated on finite computers."

"We're going to talk about variational inference, which is how do we actually find the approximate questions when we can't do analytic inference."

"This is what is called a first order approximation."

"Floating point numbers are an approximation to the set of real numbers."

"Sampling is approximate but faster, and the more time you spend, the more accurate your answer will become."

"This model is only an approximation to the true dynamics in that system, so you're probably missing some physics."

"A variational principle is just a family of methods that allows you to approximate something difficult with something simple."

"The universal approximation theorem... for any epsilon accuracy that we wish, if your neural network is large enough, it can approximate any nice function within epsilon accuracy."

"We assume that this is an ideal system highly idealized; we only consider motion with small angle approximation, only small displacement."

"With enough hidden units, we can use a neural network to approximate anything."

"It's not about exacto measurement, it's about approximating things but quite accurately."

"We need approximate solutions because in all but the most simple of problems, we won't be able to find an exact solution."

"The rule of mixtures can be applied to approximate the modulus and strength of a fiber reinforced composite."

"This is actually a pretty close approximation to what the 90s and early 2000s kind of portrayed VR to look like in the future."

"Science doesn't make proclamations about truth; it creates models that are the best approximations of the most consistently reliable and accurate models about the universe."

"Truth is something that we have access to, and it may be the case that all we ever have are continuing increasing approximations of truth."

"Slater's rules are used to get a better approximation of the screening or shielding constant when calculating effective nuclear charge."

"The quality of the policy after K iterations is bounded by the approximation errors we've incurred up to that point."

"Algorithms that give up on absolute correctness and achieve bounded approximations... can calibrate and guarantee how much they diverge from the optimal solution."

"There's been a shift away from thinking of theories as being true to thinking of theories as being approximately true."

"The vast majority of the claims that we make about the world in natural language are only going to be approximately true."

"All of the claims we make about the world are at best approximately true."

"For small angles, $ \sin(\theta) $ is roughly $ \theta $, $ \tan(\theta) $ is roughly $ \theta $, and $ \cos(\theta) $ is roughly $ 1 - \frac{\theta^2}{2} $."

"The cosine of A equals minus zero point two seven four approximately."

"For small values of theta, sine theta is approximately the same as theta."

"The tangent line is a good approximation to the curve for values near the solution."

"It's both beautiful and useful, says that n factorial is approximately square root of 2pi n times n over e to the n."

"Any digital simulation is only an approximation of the real world."

"Every function can be approximately locally by a polynomial of some degree as long as it's not discontinuous."

"This is a really good approximation of the correct number."

"It turns out that this gives a very good approximation of the PMF of the binomial."

"In factorial is approximately $$ n^n \times \sqrt{2\pi n} \times \text{some constant} $$."

"This is approximately four to the n over the square root of pi n."

"An approximate answer is a whole lot better than no answer."

"In machine learning language, we can write a discrete approximation of the Langevin dynamics."

"Solving this problem exactly is NP-hard, therefore we have to resort to an approximation method."

"The least squares solution will propose an approximate solution that minimizes the sum of the errors squared."

"The big idea of Taylor's theorem is to take a function and approximate it by a polynomial with more and more and more terms."

"It's far better to have an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise."

"It's a very good object that describes that approximates things that you do see in the real world, like stock prices."

"It's not a hundred percent, but it's pretty accurate."

"Higher order systems can be approximated by first or second order models."

"We're going to move beyond those limitations and look at sampling based approximations."

"It's not going to be 100% accurate because that wind loading will be changing over time in reality, but it's a good way of speeding up your simulation."

"The most important approximation was that we have neglected the fluctuations of the magnetization with respect to the saddle point value."

"The Ginsburg criterion tells us how justified the saddle point approximation in the Landau-Ginzburg Hamiltonian was."

"None of this needs to be a hundred percent accurate; it's just got to look good."

"We can draw a picture like this in 30 seconds, maybe it's not exactly correct, but it gives us a rough idea of how qualitatively changing our parameter affects the location of the poles and in turn affects the transient response of our system."

"I think that looks actually pretty close to the design, without measuring anything out."

"It would be a miracle if science were able to support such successes if its theories were not even approximately correct."

"We can use an approximation given by the Trotter-Suzuki formula."

"No circle is really a circle, but only a polygon with a very large number of very small sides."

"Taylor series is the foundation for all of the numerical approximations we'll do in this class."

"This is an extremely useful form for approximating smooth functions in a neighborhood of a point if I know something about the smoothness at that point."

"We might call it an approximately awesome auction."

"Every numerical approximation method always begins with a guess, and then we hope we make the best better."

"The human can only perceive an approximation of the external world."

"But with the approximations that I've made, I get an answer which is consistent with what is observed."

"Next time, we're going to look at an approximate way of computing answers to probabilistic inference queries."

"The power series of a function allows us to approximate values of the function easily computationally."

"And it's noteworthy that regardless of theta, we're always guaranteed to draw either the best approximation or one of the two best approximations when there's a tie, with probability that appears to be just above 40%."

"It is also possible to approximate the quantum Fourier transform with very shallow circuits, meaning ones with small depth, in case that's something that we wish to do."

"If the approximation is good enough, we'll get R when we round, which is what we're looking for."

"This isn't a perfect way of calculating this, but it's good enough."

"DFT suggests an amazing approximation to the Schrödinger equation."

"The simplest functional that you might imagine is the so-called local spin density approximation."

"Pi does not equal 3.14, it is approximately 3.14."

"E is not going to repeat, it just goes on forever and it's going to be approximately 2.718."

"The exchange correlation is a crucial approximation, and that's where you have to be careful when you do DFT."

"Most of the convex sets that come up through natural causes can actually be approximated by ellipsoids stunningly well."

"The level sets near the analytic center are ellipsoids that are a pretty good approximator of the shape of this set."