The argument isn't saying that arithmetic is random. It's saying that a lot of properties of number systems behave as if they are random.
A good example is finding arithmetic sequences of length K in the prime numbers (for example, the sequence 3, 5, 7 is an arithmetic sequence of length 3, as is 17, 23, 29). It can be shown that random sets that have a density similar to the primes (i.e. the chance that N is in the set is proportional to 1 / log(N)) have arbitrarily long arithmetic sequences - as, in fact, do the prime numbers.
This looks like an interesting perspective. Do you have any pointers to discussions of topics that become more intuitive/clearer when thought about in other bases ?
Kind of off topic, but your comment reminded me of something that I've wondered about for a couple of months.
I was in the US (NYC) last year and went to a music event at a bar. My girlfriend and I were there an hour early, so we grabbed a table of four near the front (we were meeting two other friends). When our friends arrived and sat down, we noticed that someone had left a jacket on one of the chairs at our table while we were sitting there (it wasn't there when we took the table).
We were a little confused but our friends sat down anyway. Right as the show was starting, an older guy came up and said that we were in "his" seat, as it had his jacket on it. He was pretty angry that we'd taken "his" seat, and we didn't feel like an argument, so we let him drag the chair off somewhere else, but it felt like he was being a bit of an asshole.
Is this a social thing in the US that I just don't get (I'm British) or was the guy just being an asshole?
Probably cultural. Where I'm from (NZ) chairs sorta belong to the table; you wouldn't take a chair from a table or hang your jacket on it if there's someone else sitting there, at least not without asking first.
I had a similar experience in a food court in Bangkok. My wife and I bought our food and sat down at a table that had some bagged food on it (since there weren't any clean tables available). Assuming it was someone's leftovers that they neglected to trash, we just moved the food to the side since there wasn't a rubbish bin nearby.
A few minutes later someone came up and angrily told us that was his table and it was his food, and he demanded we find another table.
Really confused but not yet learning our lesson we moved to another table and moved some more food aside. Another man yelled at us, this time even angrier.
Seems it's pretty common for people to buy one thing, take it to the nearest empty table to 'reserve' it, and go elsewhere and get more food.
I guess when you're in someone else's country you just have to realise that you probably are the asshole and apologise, even though it doesn't make much sense :S
Maybe he was alone, he went to buy a drink and came back to find his seat taken? I wouldn't be too surprised if leaving your jacket to claim a seat is a common practice among older generations. If I imagine the setting to be 50's/60's, and watched it in a movie, it would seem you were the assholes. At least offer him a space in the table to join you. Alas, this is the modern times, so my critique does not apply, it's only a suggestion why the older man might be angry.
TIL I am part of the "older generation". Kids today don't know to leave a jacket on a chair or movie theater seat to claim your territory?
Regarding the original question, the couple that arrived early should have "claimed" the two empty chairs by placing jackets or some other items on them. Failing that, they should have been alert to the "older" man who put his jacket down on it and immediately stated that the seat was already taken.
I agree with you - but I've done that myself and still had my seat taken before, even with my stuff on the table, it only got moved to the corner! I only went to the bathroom and back. I told him to get up, he refused, and I only got it back after insisted he give me 10 minutes to finish my work - and then I gave it back to him (he was with his friends so he didn't want to be humiliated). My description of modern "etiquette" was descriptive, not prescriptive.
P.S. I specified older generation because the parent specified "older man".
Well, I don't know about the "older generation", but I grew up being taught all throughout life to not leave any of my belongings anywhere unless I want them to get stolen.
Whenever I'm out somewhere with someone else and they set anything down on a table (jacket, hat, notes, wallet, anything) and get up to use the restroom, they say, "Make sure no one takes anything." I say the same.
I'm not sure if this is just a generational thing that follows from "stranger danger" or what.
On the other hand, it sucks when you can't get a seat in a half empty venue because everything is 'reserved'. Often myself and my girlfriend can spend a couple of hours somewhere standing, only to leave without these seats ever getting filled.
It's painfully obvious to me that I have this linguistic quirk, because my fiancé (who is not a computer geek) interjects with "buttons!" every time I start a sentence with "So...".
This is annoying, but possibly not as annoying as listening to someone who starts half their sentences with the same word.
--
Thinking about it a little more, this habit is not specific to the computer / programming geek communities. I noticed others doing it around 2009-10, when I did almost no programming and didn't hang around with programmers. I mostly hung around with math and physics grad students. I suspect it is more generally a geek phenomenon, not specifically computer / programming geeks. Or possibly it's an even wider phenomenon than that - hard to say, since most of my friends are geeks of one sort or another.
It would be interesting to see if male and female geeks do it with similar frequencies. My guess would be that male geeks do it more often (based on the interpretation that starting a sentence with "So..." is a way of saying "I have given this topic serious thought" and the assumption that this is more likely something that a male geek will want to indicate than a female geek).
I know some non-geek Canadians who use this particle: "So, how was your day?". There are similar or even equivalent particles in other dialects and languages, for example "Also .." in German and "Look, .." in Australian English. However, in my experience, the purpose of that particle is to introduce a new topic or to indicate a context switch, rather than signaling that 'I've given the following serious thought'.
Almost entirely unrelated but another good/incredibly annoying interjection is to say '-tish' when hearing someone pause mid-sentence with 'but um'. It's an excellent way to lose friends and get socked on the nose.
Everyone has a personal tolerance for risk. If you are diversified, then you decrease the risks that you are exposed to - possibly below your personal risk tolerance. That allows you to use leverage to increase your risk back up to your tolerance, which also increased your expected return.
So yes, diversification (plus leverage) absolutely increases expected value, if you hold risk a constant.
I think it's something that's worth pointing out occasionally. Male programmers tend to assume that all other programmers are male. Even if they don't actually think that, it slips out in their language (as in this case).
In this case the error is a little perplexing since the OP's name is "Lexi" which is almost never used as a male name!
Not a lie: I have never encountered the name Lexi before. I would have assumed it to be a made-up pseudonym. Or a reference to a post-modern sci-fi / futuristic book.
If it's short for "Alexis," which is a claim you edited out of your comment, then I'm even more confused, as that name seems to be male preferred within the US.
This conversation got really out of hand really quickly, so I've stayed out of it, but is Alexis really male-preferred? That's an honest question; I don't know. Wolfram Alpha seems to find the opposite.
No - I just use a throwaway account by default (actually, several of them on different machines) because (a) sometimes I do want to comment on something without having my name attached to it, and (b) it's too much effort to switch between accounts depending on what I want to say.
> It feels a little redundant to have to manually list out all the elements when the information is known statically, and updating the list will be necessary if the Peg type changes. In Racket, writing a macro for this would be trivial, but alas, this is Haskell. Perhaps there is a way, I’m just not aware of it.
A reasonably clean way would be to define
data Color = Red | Green | Blue | Yellow | Orange | Purple
deriving (Enum, Bounded, Show)
Yep, I posted this on r/haskell and someone pointed this out, which is cool. The provided type for Peg didn't derive Enum or Bounded, but it's a good trick to know.
I'm kind of surprised that `enumerate` isn't defined in any standard libraries (as far as I know) since I need it pretty often.
After a while spent programming in Haskell you would probably develop your own mini-library of functions that make your life easier. Another one I often find useful is
(.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
(.:) f g = \x y -> f (g x y)
which e.g. allows you to define the absolute distance function
dist :: (Num a) => a -> a -> a
dist = abs .: (-)
A fun challenge is figuring out why the definition of (.:) is equivalent to
> A fun challenge is figuring out why the definition of (.:) is equivalent to
> (.:) = fmap . fmap
> !
Of course it's not really equivalent, since the most general type of the LHS is as you have said, whereas that of the RHS involves functor constraints; but inlining the definition of `fmap` for arrows gives the amusing definition:
(.:) = (.) . (.)
I tend to figure this sort of thing out by successive eta conversion:
\f g x y -> f (g x y)
\f g x y -> (f . g x) y
\f g x -> f . g x
\f g x -> ((f .) . g) x
\f g -> (f .) . g
\f g -> ((f .) .) g
\f -> ((f .) .)
\f -> (.) (f .)
\f -> (.) ((.) f)
\f -> ((.) . (.)) f
(.) . (.)
The downside of using (.:) is that it is used heavily in other libraries (Aeson for instance) in a very different context (field accessors, similar in look to json's `:`).
I can't speak for other teams, obviously. But almost everything we do would fall under the heading of "Bayesian methods". It's such a broad term that it would be hard to write a trading algorithm that couldn't be described as Bayesian.
What Virtu does to make money (market making and latency arbitrage on a milli- and microsecond timescale) is very, very far away from recognizing chart patterns and trading on them!
What is being discussed in those links is commonly called complex systems theory[0] which is a mathematical/scientific/philosophical field concerned with how complexity (in the natural language sense of the world) arises from what appear to be simple natural laws. For example, how chaotic dynamics arise from deterministic systems, how biology arises from chemistry, or how consciousness arises from neural activity. It is connected to chaos theory, nonlinear dynamics and systems theory.
It is completely different to computational complexity[1] which is what is being discussed in Aaronson's article.
My mistake, I meant it as a basis for incorporating computational complexity. The original article posted shows how computational complexity is applicable to non-linear systems, which I think are philosophically more interesting. Deleuze's work would provide some good groundwork for seeing how those kinds of ideas can be applied in a philosophical context.
A good example is finding arithmetic sequences of length K in the prime numbers (for example, the sequence 3, 5, 7 is an arithmetic sequence of length 3, as is 17, 23, 29). It can be shown that random sets that have a density similar to the primes (i.e. the chance that N is in the set is proportional to 1 / log(N)) have arbitrarily long arithmetic sequences - as, in fact, do the prime numbers.