chess93

Almost all fields of pure math use a much stronger set of axioms called ZF and essentially everyone also accepts the axiom of choice (making it ZFC). The axioms in ZF are reasonable but the axiom of choice is surprisingly controversial for an axiom. There are some unintuitive consequences of the axiom but even more unintuitive consequences without it or with the negation of it.

Number theory uses a much smaller set of axioms.

It should be stated that most mathematicians don't really mind the logical foundations of their work when they are actually working in the same way that most programmers don't worry about assembly language or transistors.

Benford's law works in any base.

I have no php experience so I have absolutely zero conception of what the language used to be like, just what it looks like now. I can't help but see it as some kind of frankenlanguage put together with pieces of java/python/javascript and a ton of dollar signs.

In other words, it seems too similar to languages that I already know to be worth learning. Lisp was fun to learn because it is an alien language. C was worth learning because of its usability and centrality to modern computing. The only benefit I can see from learning php is being able to understand more of software history. Cool but I'd rather learn another lisp.

Does anyone disagree with my analysis? I wish the language well but I don't see what it offers me. Obviously it offers a lot to the people who see JS as franken-php and so forth.

Union types are cool though.

Hopefully this helps make video gaming a more community oriented activity instead of something done at home alone.

My belief is that people believe whatever they want to believe. If you are liberal it is because you want to be liberal. Alternatively you might just not want to be conservative. Same for the other direction. Naturally formed beliefs are just an afterthought. It goes without saying that this might not apply to everyone or to every belief.

For the record, I recognize that perhaps I believe this belief strictly because I want to believe it. I also think many people don't want to believe it.

I was wondering why these worked everywhere. I had no idea it was a mac feature.

"In the game of chess, you can never let your adversary see your pieces." - Zapp Brannigan

I, for one, would love to see professional players attempt to play this game. It does seem extremely frustrating to play, however.

I'm glad the label worked for you but it did not work at all for me. It kind of shoehorned me in to a personality type and limited my social options.

In all honesty I look back at my "smartness" as a kind of attention-seeking behavior where all I really wanted was the attention you got from getting the highest grade in the class or being the only one from your school to go to the ivy league.

To me, the smart label just means you are willing to sacrifice more than others to study/learn/build. Everything I have learned about people since starting college has told me that this is a net negative.

What is everyone’s favorite translation of Meditations? I bought a cheap copy and the translation is unsurprisingly hard to read and distracts from the text’s content.

I've noticed several side effects such as decreased attention span, decreased sociability, decreased desire to do anything other than your preferred method of attention capturing.

Frankly I just think that many of these things are simply addictive and, with an appeal to naturalism, I don't think it is what humans were meant to do. Increased smartphone use or TV watching or video games probably almost never results in increased happiness over the long term.

Not to mention the ability to use attention capturing as a way to hide from one's own emotions.

Note for any college students (especially undergrad): Do your STEM presentations in Beamer to get extra brownie points.

No denominators for zero divisors in the localization of any ring!!! [English: No denominators where you can multiply the denominator by anything nonzero to get zero.]

Technically, many definitions of localization do allow for zero/zero divisors to be included (we can use any multiplicatively closed set) however by the definition of localization all of the elements in our localized ring become equal to each other.

The mathematical meaning of a/b = c/d in a general ring is that there exists some value s in the set of legal denominators where s(ad - c*b) = 0. If 0 is an allowable denominator then a/b = c/d for every a,b,c,d.

Smartphones are what I think of as "attention capturers" which are able to completely capture almost anyone's attention span for a significant amount of time. Other attention capturers include computers[0], video games, TV, books, chess. Each of these has varying capability as attention capturers but it is safe to say that smartphones are the strongest attention capturer for most people.

I believe that using any attention capturer for long periods is not healthy and should be avoided. The hard part for me is actually finding anything else to do in a new city without family/friends. Especially on a Tuesday night after work where it is less possible to go to a bar and talk to strangers.

[0] Smartphones can be included here.

https://en.wikipedia.org/wiki/Lattice-based_cryptography

My current favorite is

1.e4 c6 2. d4 d5 3. e5 Bf5 4. Nc3 e6 5. g4 :)

There is also a "Red Book" in mathematics. It is David Mumford's Algebraic Geometry book.

Are there any other fields with a "Red Book"? I am mildly curious.

I simply don't understand what is going to happen to all of the PhD students that I saw when I was in university. I managed to escape the PhD trap and find software engineering but I was extremely lucky. Had I gone to any other school I probably would not be anywhere near as fortunate.

That being said, I worry about the people who go to PhD programs just because that's what they are "supposed to do" or because they just don't know what else to do. Especially the ones who lack social skills or lack "connections". Many of my friends from college fall in to this category.

I don't even want to think about the people in the above category who get a PhD at a "non-target" school.

Its not really "what we perceive as mental illness", it's just a mental illness. It doesn't have to have an innate biological component to be a mental illness.

I am a big fan of the "humans are social creatures" mantra. In that regard, if something is more stimulating than social interaction it is likely to be harmful but if something is less stimulating than social interaction it is probably fine. [1]

In this simple model, I would probably say books are definitely less stimulation, TV is probably about equal (I have no idea), and modern videogames and social media are definitely much more stimulating. So, books would only become a problem in the presence of other factors but social media can become a problem for anyone.

In highschool I would play high stimulation PC games while browsing the internet on another monitor while listening to music while using voice chat. I also had almost no desire to socialize while in highschool.

[1] It goes without saying that we probably can't reduce activities to a single metric like "amount of stimulation" but I think this is a useful thought experiment.

I can't help but think I would be much happier if I had never seen a computer or cell phone in my life. Maybe its just my personality type. Maybe its because I started at a very young age. It could be anything but I am fairly certain that the constant stream of stimulation to my brain has done plenty of damage.

This article seems analogous [1] to an article that states "I use hard drugs and I'm not ashamed" authored by someone who manages to keep their use under control. Sure, it works for them. Great, but they are not the failure mode of drug use.

Can someone explain how it is physically possible for them to eat a monkey whole? That's probably the craziest video I've seen in a while.

One feature that would be useful for me would be the ability to convert a video to a PGN of the game. This could, for example, be used to strip game data from streamed chess en masse and then analyze the chess games in aggregate.

What's the difference between someone getting in because their parents bought a building and someone getting in because their parents spent 50k/year on a highschool?

Brexit might have more of an influence than it seems. However, the effect is probably because no one is paying attention to anything else other than Brexit [1].

[1] I read a few sentences of a newspaper suggesting this.

I've only ever been impressed with mass transit in megacities like NYC. SF public transit left a lot to be desired. The muni was not worth the hassle and I did not have a bart station near my rented room in a house.

On the other hand, in practice, log log n is basically constant so we have had a practical n log n algorithm for a while :)

Perhaps a neural network that detects politically charged posts?

Sounds like a fun side project.

:%s/Asbergers/Aspergers/g

Sorry I was up all night and didn't even consider that I was spelling it wrong. My track pad is broken and so I can't right click to spell check. (I am waiting to start my new job to get a new laptop.)

Its not really relevant but the list seems to not actually describe Asbergers but some other collection of symptoms that results from being socially deprived. (However, this probably matches up with popular conception of Asbergers individuals.)

I think the "key" is finding people who deal with their problems by diving deep in to technical tasks and becoming absorbed in minutiae. An unnaturally small interest set combined with a lack of interest in people.