vladsotirov

7 ms·

1.
by vladsotirov 11mo ago
A simpler explanation of the technique in the article that I believe matches the C standard more closely is the following. Ideally the result of processing a macro ("macro-replacement") would contain no further macros. But in orde
2.
by vladsotirov 4y ago
The second Q needs no input because it is not executed: its source code is used as input for the first Q.
3.
by vladsotirov 4y ago
> The Halting Problem is famously only undecidable if the code you're analyzing is being modeled on a "Turing machine" or something equally "powerful" to it. The Halting Problem applies as long as you're abl
4.
by vladsotirov 4y ago
> It does not. That only means that you if you, say, want to analyze how a program behaves when ran in a computer with 16 GB of state, you need to analyze it on a computer that has more than 16 GB of state. Then we must differ on what th
5.
by vladsotirov 4y ago
> Now, I'm not a computer scientist nor a mathematician or logician. So I could be wrong. If so, I would be interested in knowing how I'm wrong, as I've never seen this issue being discussed in a thorough way. Rice's
6.
by vladsotirov 8y ago
> Some numbers in a set called the "smooth reals" square to 0... without being zero. This seems to create a universe in which every geometric object is "infinitesimally straight". I haven't fully grasped why this
7.
by vladsotirov 8y ago
One "application" (in quotes because honestly for all the fanfare I haven't come across something that was worked out to be usable by non-specialists) is automatic differentiation, see http://blog.sigfpe.com/2
8.
by vladsotirov 8y ago
The remarks on computable and continuous functions can also be thought about as follows. The law of the excluded middle is only one non-constructive aspect of classical mathematics. Dropping it leaves you with what is usually called "i
9.
by vladsotirov 9y ago
Originally, categories arose as (mathematical) descriptions of various universes of functions. For example, there is universe of functions that are given linear functions (i.e. matrices), which is contained in the universe of functions give
10.
by vladsotirov 9y ago
> without the abstractions we take for granted as superior, such as money. That's only true if by "money" you mean coinage, which is a definition so narrow that it also excludes the modern notion of money (you think that&#
11.
by vladsotirov 10y ago
History is a convenient and readily available proxy for shifting content focus away from mathematical facts and toward mathematical processes such as problem-solving, proof-writing, problem-posing, abstraction, theorizing. History's ap
12.
by vladsotirov 10y ago
The UI confuses me to the point of frustration. 1. A "Previous" button would help since otherwise you have to go loop through the whole thing to see what actually happened (e.g. how exactly the first step lifts and rotates the mat
13.
by vladsotirov 10y ago
I'm puzzled by your comment, especially the first few sentences. What did you not understand from her blog post? What kind of evidence would help you understand? What would you ask her to clarify, what would you like to know, if you we
14.
by vladsotirov 10y ago
It's not enough to like the work for it to be easy: it's also important that your work be appreciated and encouraged. Scholze happens to be interested in a popular/prestigious subfield of mathematics, but my experience sugges
15.
by vladsotirov 10y ago
I think it's pretty good evidence that Gowers' blog post fails miserably to either persuade or explain why the fundamental theorem of arithmetic isn't obviously true. Garbage in, garbage out, irrelevant of how good the machin
16.
by vladsotirov 10y ago
This blog post illustrates well the infuriating tendency of academics to teach by calling people stupid. The substance of his answers are: 1. " If you think it’s obvious, then you’re probably assuming what you need to prove" i.e.
17.
by vladsotirov 10y ago
You've correctly shown that "f2 does not contain p". However, the subtle bit of reasoning "f2 cannot be evenly divisible by p as that would require it to have a prime factor of p" is not justified by any of your ass