thetwiceler

6 ms·

1.
by thetwiceler 9y ago
Zeilberger's Opinion 123 is an April Fool's Day joke.
2.
by thetwiceler 11y ago
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 a linear/Ga
3.
by thetwiceler 11y ago
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 the real numbers
4.
by thetwiceler 11y ago
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, that is,
5.
by thetwiceler 11y ago
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.
6.
by thetwiceler 11y ago
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 very, very caref
7.
by thetwiceler 11y ago
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 look more like a magi
8.
by thetwiceler 12y ago
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.
9.
by thetwiceler 12y ago
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 processor)&quot
10.
by thetwiceler 12y ago
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 have it
11.
by thetwiceler 12y ago
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 case here. This i
12.
by thetwiceler 12y ago
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!
13.
by thetwiceler 12y ago
ET Jaynes is the best! Read the whole book! http://bayes.wustl.edu/etj/prob/book.pdf
14.
by thetwiceler 12y ago
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 "numbe
15.
by thetwiceler 12y ago
> 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 pro
16.
by thetwiceler 13y ago
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 in-place quicks
17.
by thetwiceler 13y ago
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 supportive of these
18.
by thetwiceler 13y ago
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 of t, then the standar
19.
by thetwiceler 13y ago
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 imagine it
20.
by thetwiceler 13y ago
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 example, con
21.
by thetwiceler 13y ago
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 car
22.
by thetwiceler 13y ago
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 a wise investmen
23.
by thetwiceler 13y ago
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 collapsed, the US
24.
by thetwiceler 13y ago
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 mission is to modera
25.
by thetwiceler 13y ago
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 rate of the USD ge
26.
by thetwiceler 13y ago
> A currency only has value because we, as a society, decide that it does. For some reason, many people believe that this is true. I believe that it is not. Technically, yes, if people all decide the currency has value, then it will ha
27.
by thetwiceler 13y ago
Take a look at this [1], particularly the second answer, which links to a Github Gist for "ghc-pkg-clean." I tend to use that when I run into trouble. [1] http://stackoverflow.com/questions/7961604/fixing
28.
by thetwiceler 13y ago
Because monads are abstract, and very general, there turn out to be many different ways to think of monads, and each of the perspectives is enlightening in its own way. In fact, really the ONLY thing that monads provide is an abstraction fo
29.
by thetwiceler 13y ago
Yep. And I'd feel equally confident making a similar remark if someone presented me with a perpetual motion machine as well!
30.
by thetwiceler 13y ago
I hate to break it to you, especially since I don't exactly understand the scheme you're describing, but "virtually unlimited compression" is impossible [1]. [1] http://en.wikipedia.org/wiki/Shannon&

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