Zeilberger's Opinion 123 is an April Fool's Day joke.
Firstly, Kalman filtering is optimal, that is, it produces exactly the correct posterior distribution. As you mention, particle filters cannot achieve this. It's a rough heuristic that to achieve a certain accuracy for…
Yep, this is what I meant to allude to, and you've worded it much better than I could have. Perhaps a nice way to say it is that the mathematical objects necessary for physics that I can think of are separable (such as…
ihm's response to you I think did a great job explaining what I meant to say, but let me elaborate further. Just like you might define computable real numbers, you may similarly describe the "definable" real numbers,…
They're usually used synonymously. Yes, Cantor's diagonal argument can still be used to show the uncountability of real numbers in a constructive setting.
It seems misleading to say that intuitionistic logic assigns statements to one of the two values, True or False. There's no symmetry between the notions of truth and falsity as there is in boolean logic. You need to be…
This video is somewhat misleading. I appreciate the attempt at making Banach-Tarski accessible to a general audience, but it dwells on the wrong aspects of what makes Banach-Tarski interesting, making the construction…
To define variance as E[x^2] - E[x]^2 and not ever allude to the far more meaningful version, E[ (x - E[x])^2 ] is just criminal. This is not at all a good explanation of variance, covariance, and correlation.
The treatment of Big O notation is not only misleading (and poorly conveyed) but wrong in several ways. Big O is an upper bound that does not need to be tight. The table displaying the "limit of N for 1 second (standard…
In the type theory literature, it is rather the other way: Void is synonymous with the bottom type. I don't know who has first claim to the name "void", but from the type theory perspective, it is C, Java, et. al. who…
It is in fact Markov; Markov just means that the probability distribution of the future depends only on the present, and so the past adds no additional information in conjunction with the present. That's certainly the…
Oh, I didn't realize that. Well, the book is Probability Theory: The Logic of Science ET Jaynes 2003 I highly suggest buying it or finding it from your library!
ET Jaynes is the best! Read the whole book! http://bayes.wustl.edu/etj/prob/book.pdf
I don't think this is a great idea, for several reasons: Arithmetic is a very small part of mathematics, and perhaps the least important. But even as far as arithmetic goes, I don't see this game giving children a good…
> The concept of "compactness" is the technical solution that lets you formulate calculus without them -- it's typically only taught to math majors because infinitesimals are less awkward to do algebra with: we can now…
Absolutely not. I'm actually very frustrated that they give that code as an example. First of all, it misses the most important of quicksort - the fact that it can be implemented in place (and yes, you can write an pure…
Let's not blow this out of proportion. They scraped private data (that required a Yale login) without permission and accidentally made it available to a wider audience than intended. Yale has historically been very…
It is sad that Taleb does not see the value in the standard deviation; standard deviation is far more natural, and more useful, than MAD. For example, if X has a standard deviation of s, and Y has a standard deviation…
The mean would certainly be n! (note that it is possible, and even likely, that you may create the same sorting multiple times by random chance). The median, which I don't think you're referring to, is something else (I…
Perhaps the more interesting question is why do most programming languages allow several input values? I'll make the argument that in Haskell, functions BOTH support only a single input value and a single output value.…
For those who aren't aware of it, I think Lockhart's Lament [1] is definitely worth a read. Here's an excerpt: "How many people actually use any of this “practical math” they supposedly learn in school? Do you think…
Think of it like this: Let's say that Apple sees the price of its stock drop to something that it thinks is unreasonably low. They may choose to spend some of their cash on hand to buy back some of their stock. This is…
There is plenty of gold in Fort Knox! Our currency has not been pinned to gold for 40 years (when the Bretton Woods system collapse), but the Federal Reserve still maintains the holdings. Before the Bretton Woods system…
Yes, what I described is not actually how the Federal Reserve works. I was trying to give the essence of what it does in a single sentence. The USD is not literally backed by gold, but part of the Federal Reserve's…
I pretty much agree - taxation could be the only non-circular source of demand for the USD. But there is also the fact that the Federal Reserve generates demand by offering to buy USDs for other things when the exchange…
Zeilberger's Opinion 123 is an April Fool's Day joke.
Firstly, Kalman filtering is optimal, that is, it produces exactly the correct posterior distribution. As you mention, particle filters cannot achieve this. It's a rough heuristic that to achieve a certain accuracy for…
Yep, this is what I meant to allude to, and you've worded it much better than I could have. Perhaps a nice way to say it is that the mathematical objects necessary for physics that I can think of are separable (such as…
ihm's response to you I think did a great job explaining what I meant to say, but let me elaborate further. Just like you might define computable real numbers, you may similarly describe the "definable" real numbers,…
They're usually used synonymously. Yes, Cantor's diagonal argument can still be used to show the uncountability of real numbers in a constructive setting.
It seems misleading to say that intuitionistic logic assigns statements to one of the two values, True or False. There's no symmetry between the notions of truth and falsity as there is in boolean logic. You need to be…
This video is somewhat misleading. I appreciate the attempt at making Banach-Tarski accessible to a general audience, but it dwells on the wrong aspects of what makes Banach-Tarski interesting, making the construction…
To define variance as E[x^2] - E[x]^2 and not ever allude to the far more meaningful version, E[ (x - E[x])^2 ] is just criminal. This is not at all a good explanation of variance, covariance, and correlation.
The treatment of Big O notation is not only misleading (and poorly conveyed) but wrong in several ways. Big O is an upper bound that does not need to be tight. The table displaying the "limit of N for 1 second (standard…
In the type theory literature, it is rather the other way: Void is synonymous with the bottom type. I don't know who has first claim to the name "void", but from the type theory perspective, it is C, Java, et. al. who…
It is in fact Markov; Markov just means that the probability distribution of the future depends only on the present, and so the past adds no additional information in conjunction with the present. That's certainly the…
Oh, I didn't realize that. Well, the book is Probability Theory: The Logic of Science ET Jaynes 2003 I highly suggest buying it or finding it from your library!
ET Jaynes is the best! Read the whole book! http://bayes.wustl.edu/etj/prob/book.pdf
I don't think this is a great idea, for several reasons: Arithmetic is a very small part of mathematics, and perhaps the least important. But even as far as arithmetic goes, I don't see this game giving children a good…
> The concept of "compactness" is the technical solution that lets you formulate calculus without them -- it's typically only taught to math majors because infinitesimals are less awkward to do algebra with: we can now…
Absolutely not. I'm actually very frustrated that they give that code as an example. First of all, it misses the most important of quicksort - the fact that it can be implemented in place (and yes, you can write an pure…
Let's not blow this out of proportion. They scraped private data (that required a Yale login) without permission and accidentally made it available to a wider audience than intended. Yale has historically been very…
It is sad that Taleb does not see the value in the standard deviation; standard deviation is far more natural, and more useful, than MAD. For example, if X has a standard deviation of s, and Y has a standard deviation…
The mean would certainly be n! (note that it is possible, and even likely, that you may create the same sorting multiple times by random chance). The median, which I don't think you're referring to, is something else (I…
Perhaps the more interesting question is why do most programming languages allow several input values? I'll make the argument that in Haskell, functions BOTH support only a single input value and a single output value.…
For those who aren't aware of it, I think Lockhart's Lament [1] is definitely worth a read. Here's an excerpt: "How many people actually use any of this “practical math” they supposedly learn in school? Do you think…
Think of it like this: Let's say that Apple sees the price of its stock drop to something that it thinks is unreasonably low. They may choose to spend some of their cash on hand to buy back some of their stock. This is…
There is plenty of gold in Fort Knox! Our currency has not been pinned to gold for 40 years (when the Bretton Woods system collapse), but the Federal Reserve still maintains the holdings. Before the Bretton Woods system…
Yes, what I described is not actually how the Federal Reserve works. I was trying to give the essence of what it does in a single sentence. The USD is not literally backed by gold, but part of the Federal Reserve's…
I pretty much agree - taxation could be the only non-circular source of demand for the USD. But there is also the fact that the Federal Reserve generates demand by offering to buy USDs for other things when the exchange…