> Exploits will always be able to chained, and everything will always be exploitable. Including AI systems. Good point. Also, discovering exploits is also equivalent to the halting problem. So both things are impossible…
This is a good question that doesn't have a short answer. There are some different philosophical opinions about this. One way to look at this is to note that even with forward mode autodiff, there have generally…
So does Pytorch: https://pytorch.org/tutorials/intermediate/forward_ad_usage....
Sure, right here: https://github.com/pytorch/pytorch/blob/main/torch/autograd/... Here's the documentation: https://pytorch.org/tutorials/intermediate/forward_ad_usage.... > When an input, which we call “primal”, is…
It isn't true for all ordered rings, and the dual numbers are in fact a counterexample to the claim that it is true. Beyond that I'm not sure what to tell you, other than it's fairly easy to see that the dual numbers do…
That isn't what an ordered ring is. Your property of a < b → a² < b² doesn't even hold true in the integers. For instance, let a = -2 and b = -1. The correct property is that if a ≤ b, a + c ≤ b + c, and if a ≥ 0 and b…
These things are different and I did mean dual numbers. The dual numbers do form an ordered ring. When you complain about certain elements being non-invertible, I think you are probably complaining that they aren't a…
Thank you for repeating yourself three times. It seems like you think that the dual number algebra involves "magic woo numbers." It seems like you haven't really worked through this stuff too much. I would suggest…
At the end of the day, if you are storing inputs and outputs to a function as a pair of numbers - one for the actual value, and one for the derivative - and if addition and multiplication work the way you expect and…
There are a few good resources. Here is a good blog post with some introduction: https://towardsdatascience.com/forward-mode-automatic-differ... Some thorough notes from MIT:…
One very interesting thing about automatic differentiation is that you can think of it as involving a new algebra, similar to the complex numbers, where we adjoin an extra element to the reals to form a plane. This new…
XKCD should solve the problem the same way Tetris randomizers do. In Tetris, they don't use naive memoryless uniform randomizers for pretty much the same reasons that people are complaining about in this article: you…
He points out that the YouTube video "uses mediants" to compute rational approximations to real numbers. He then says that the continued fraction expansion is better. However, the mediant-based method is totally…
We'll know if an AI is conscious same way we know if a cat is consciousness, and it has nothing to do with language.
Unrelated rant: The Unicode people have missed a lot more than that. There are an enormous amount of, for instance, musical accidentals that are missing, including ones that have been in use for at least a hundred…
There are some pretty clear indications that the derivative of civilization is strongly negative at the moment, particularly if you live in Europe. Actually, the fact that people are supposed to pretend things are OK,…
For jazz it's also the composer. People like Wayne Shorter, Herbie Hancock, Billy Strayhorn, Thelonious Monk, etc - all incredible composers
I'm not sure much of the stuff really needs to be "debunked" at all. Let's look, for instance, at Gobekli Tepe. Is it really the position of mainstream archaeology that something like Gobekli Tepe was built by nomadic…
This article is bizarre. It reads like they've unearthed some long lost Rosetta Stone artifact from thousands of years ago. In reality, these people have "discovered" that everyone right around them writes using this…
I can't comment regarding how you think is best to teach your students. This is now a popular blog post that has gone viral on HackerNews to a much wider audience of well-educated people, so you should expect people…
You are correct. For instance, traditionally, in barbershop vocal music, singers are trained to deliberately deviate from 12 equal, towards an ever-shifting kind of just intonation, in order to maximize the extent to…
There is some basic information that is very wrong in this article. For example: "My track is tuned in a system called five-limit just intonation via the magic of MTS-ESP. It’s the basis for all the tuning systems used…
> Exploits will always be able to chained, and everything will always be exploitable. Including AI systems. Good point. Also, discovering exploits is also equivalent to the halting problem. So both things are impossible…
This is a good question that doesn't have a short answer. There are some different philosophical opinions about this. One way to look at this is to note that even with forward mode autodiff, there have generally…
So does Pytorch: https://pytorch.org/tutorials/intermediate/forward_ad_usage....
Sure, right here: https://github.com/pytorch/pytorch/blob/main/torch/autograd/... Here's the documentation: https://pytorch.org/tutorials/intermediate/forward_ad_usage.... > When an input, which we call “primal”, is…
It isn't true for all ordered rings, and the dual numbers are in fact a counterexample to the claim that it is true. Beyond that I'm not sure what to tell you, other than it's fairly easy to see that the dual numbers do…
That isn't what an ordered ring is. Your property of a < b → a² < b² doesn't even hold true in the integers. For instance, let a = -2 and b = -1. The correct property is that if a ≤ b, a + c ≤ b + c, and if a ≥ 0 and b…
These things are different and I did mean dual numbers. The dual numbers do form an ordered ring. When you complain about certain elements being non-invertible, I think you are probably complaining that they aren't a…
Thank you for repeating yourself three times. It seems like you think that the dual number algebra involves "magic woo numbers." It seems like you haven't really worked through this stuff too much. I would suggest…
At the end of the day, if you are storing inputs and outputs to a function as a pair of numbers - one for the actual value, and one for the derivative - and if addition and multiplication work the way you expect and…
There are a few good resources. Here is a good blog post with some introduction: https://towardsdatascience.com/forward-mode-automatic-differ... Some thorough notes from MIT:…
One very interesting thing about automatic differentiation is that you can think of it as involving a new algebra, similar to the complex numbers, where we adjoin an extra element to the reals to form a plane. This new…
XKCD should solve the problem the same way Tetris randomizers do. In Tetris, they don't use naive memoryless uniform randomizers for pretty much the same reasons that people are complaining about in this article: you…
He points out that the YouTube video "uses mediants" to compute rational approximations to real numbers. He then says that the continued fraction expansion is better. However, the mediant-based method is totally…
We'll know if an AI is conscious same way we know if a cat is consciousness, and it has nothing to do with language.
Unrelated rant: The Unicode people have missed a lot more than that. There are an enormous amount of, for instance, musical accidentals that are missing, including ones that have been in use for at least a hundred…
There are some pretty clear indications that the derivative of civilization is strongly negative at the moment, particularly if you live in Europe. Actually, the fact that people are supposed to pretend things are OK,…
For jazz it's also the composer. People like Wayne Shorter, Herbie Hancock, Billy Strayhorn, Thelonious Monk, etc - all incredible composers
I'm not sure much of the stuff really needs to be "debunked" at all. Let's look, for instance, at Gobekli Tepe. Is it really the position of mainstream archaeology that something like Gobekli Tepe was built by nomadic…
This article is bizarre. It reads like they've unearthed some long lost Rosetta Stone artifact from thousands of years ago. In reality, these people have "discovered" that everyone right around them writes using this…
I can't comment regarding how you think is best to teach your students. This is now a popular blog post that has gone viral on HackerNews to a much wider audience of well-educated people, so you should expect people…
You are correct. For instance, traditionally, in barbershop vocal music, singers are trained to deliberately deviate from 12 equal, towards an ever-shifting kind of just intonation, in order to maximize the extent to…
There is some basic information that is very wrong in this article. For example: "My track is tuned in a system called five-limit just intonation via the magic of MTS-ESP. It’s the basis for all the tuning systems used…