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tell me what languages you know
2017-06-12, 1:27 AM #81
Originally posted by Jon`C:
I'm not sure what that would mean. The output of every function is disjoint subsets of the input set, defined using some predicate and a goal quantity (= cardinality, if the input has unit quantities). It's like a way of converting an input set into a bunch of disjoint subsets, such that the desired predicates and cardinalities of those disjoint sets are satisfied.


The function that maps a set to its cardinality is actually a measure on *some collections of sets that satisfy certain axioms. Those axioms being it's closed under set union and set minus (intersection follows as a theorem from these two). Usually we desire countable unions, which is fine on a collection of finite sets because countable unions of finite sets is just a finite union**. So in a sense your language already meets the axioms. You could define other measures, in a sense giving more "weight" to some set. We just established that it does have an additive set function, thus we have a measure of your sets, the "cardinality-measure" for lack of a better term. Which means there's probably others.

Originally posted by Jon`C:
I'm talking about programming language theory, but only to the extent that it is a programming language, and it's usefulness is theoretical. I wouldn't pretend to be competent at the actual theory of programming language design.

I more or less designed this language on a lark (and for a bunch of undergrad credit). I'm not sure I really "get" the language anymore, assuming I ever did. Probably running out of steam explaining it though.


Ah, gotcha. I guess this stuff is for the academics.

*as long as infinity = infinity for all infinity

**as long as the union of all sets in the collection is finite
2017-06-12, 1:41 AM #82
The second part of Jon's post looks interesting and I look forward to reading it, but let me respond to this:

Quote:
Why wouldn't computer science be math? The Curry-Howard isomorphism shows that both computer programmers and mathematicians share an elementary kind of reasoning. It's just as valid to say that computer programming is math, as it is to say that math is computer programming, or that both are special cases of something more fundamental that we haven't yet discovered.


I am sure you are right about this and from what I understand, I agree with the sentiment too.

But what I mostly meant was that Reid's suggestion that we "define an additive set function and turn the space of tables into a measure space" reminded me of the flavor of very old writings of mathematicians from the 40's and '50's, before the right mathematical abstractions for computer science were obvious enough that one could define crazy things like this willy-nilly and expect a positive probability that they'd at all be useful.

Like, there's a very old paper by Kleene, where he invents regular expressions, but the paper was about neural nets.

Edit: "define", not "definitely"
2017-06-12, 1:56 AM #83
Quote:
The best static analysis checkers are the ones that automatically enforce some badly specified contract, like catching when code fails to check the return value from a standard library function that can return null. Those kinds of things are easily enforced through a competent type system, as long as you take the time to do it, but most don't.


I will keep this in mind, since I had planned to look into TLA+, which I have heard good things about.
2017-06-12, 2:11 AM #84
Actually, this same fellow Ron Pressler seems to have just spoken to this matter in his third installment of his TLA+ series of blog posts:

Quote:
Some programming languages that include specification mechanisms (like Eiffel, SPARK and Clojure) also allow you to specify what an algorithm does in some language-specific level of detail, and those specifications also denote the set of all possible implementations, but they still make a very clear distinction between a specification and a program, the latter being the only thing that’s executable. The same is true in sophisticated research programming languages (like Agda and Idris) that make use of dependent types as a specification language. Even though the type definitions (like specification contracts) allow full use of the language’s syntax, there is a clear-cut, binary distinction between a specification — a type — which can be at some relatively flexible level of detail, and a program or a subroutine — a type inhabitant — whose level of detail is predetermined by the language’s particular semantics. Types and their inhabitants, even in dependently-typed languages, are two distinct semantic categories. You cannot execute a type, nor can a subroutine directly serve as a specification for another subroutine. TLA makes no such distinction; one algorithm can implement another, and “running” an algorithm means examining all of its possible behaviors, whether there are very few of them (as in a program) or very many (as in a non-detailed algorithm).


So the tl;dr for me, if I understand this properly, is that TLA+ can very well be a vehicle for model checking used in a way that heeds Jon's advice to enforce the correctness of the specifications themselves, since TLA+ makes no distinction between type and program anyway.
2017-06-12, 2:12 AM #85
Originally posted by Reverend Jones:
The second part of Jon's post looks interesting and I look forward to reading it, but let me respond to this:



I am sure you are right about this and from what I understand, I agree with the sentiment too.

But what I mostly meant was that Reid's suggestion that we "define an additive set function and turn the space of tables into a measure space" reminded me of the flavor of very old writings of mathematicians from the 40's and '50's, before the right mathematical abstractions for computer science were obvious enough that one could define crazy things like this willy-nilly and expect a positive probability that they'd at all be useful.

Like, there's a very old paper by Kleene, where he invents regular expressions, but the paper was about neural nets.

Edit: "define", not "definitely"


Hey, I never said it would be useful, just that it would be cool. It does seem like Jon stumbled upon measure theory a bit though.
2017-06-12, 2:18 AM #86
As for the uses, you could probably define measures that let you do cool things with the language beyond just taking the cardinality of a set. Extend its uses. For instance, probabilties, and so forth. Though I don't know how that'd look on the computer science end of things.

Also, I think you could probably get integration out of it.
2017-06-12, 2:19 AM #87
What's more interesting to me than measure theory is topology. Wikipedia tells us that "each Boolean algebra B has an associated topological space, denoted here S(B), called its Stone space".

And if you follow the thread between topology and types far enough, you can get to wild things using category theory and topoi, or even algebraic topology, where you have people like Vladimir Voevodsky and his work in Homotopy Type Theory and Univalent Foundations:

Quote:
After Goedel’s famous results there developed a ”schism” in mathematics when abstract mathematics and constructive mathematics became largely isolated from each other with the ”abstract” steam growing into what we call ”pure mathematics” and the ”constructive stream” into what we call theory of computation and theory of programming languages.

Univalent Foundations is a new area of research which aims to help to reconnect these streams with a particular focus on the development of software for building rigorously verified constructive proofs and models using abstract mathematical concepts.

This is of course a very long term project and we can not see today how its end points will look like. I will concentrate instead its recent history, current stage and some of the short term future plans.


But I can see how adding mathematical information to a programming language would be useful to mathematicians who already use said formalism (in your case, measure theory).
2017-06-12, 2:23 AM #88
Originally posted by Reverend Jones:
But what I mostly meant was that Reid's suggestion that we "define an additive set function and turn the space of tables into a measure space" reminded me of the flavor of very old writings of mathematicians from the 40's and '50's, before the right mathematical abstractions for computer science were obvious enough that one could define crazy things like this willy-nilly and expect a positive probability that they'd at all be useful.


Wait, isn't Kolmogorov complexity still an important topic in CS? I mean, I'm not well-versed in 1950's CS articles, so I guess only the useful was taken out?
2017-06-12, 2:26 AM #89
I would actually hazard to guess that Kolmogorov complexity is more useful in applications of computer science, especially to complex systems theory.

Also, Kolmogorov introduced it roughly half a century ago, which is not exactly recent. But like I said, people like Wolfram are still at at and it is certainly a hot topic to try to expand the purview of C.S. It's just that the basics of the theory have been around long enough (and measure theory even longer), that I would have expected the sort of thing you dreamed up to have been discovered by now (and maybe it has been).
2017-06-12, 2:31 AM #90
But to be fair, I see that you are right about it being fundamental, even if it was discovered a bit later than the earliest stuff. From Wikipedia:

Quote:
The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem.
2017-06-12, 2:34 AM #91
(It looks like I was pretty wrong when I guessed about Komogorov complexity being used mostly outside C.S. itself, seeing that the Wikipedia article is chock full of applications within C.S.)
2017-06-12, 2:42 AM #92
Originally posted by Reverend Jones:
What's more interesting to me than measure theory is topology. Wikipedia tells us that "each Boolean algebra B has an associated topological space, denoted here S(B), called its Stone space".

And if you follow the thread between topology and types far enough, you can get to wild things using category theory and topoi, or even algebraic topology, where you have people like Vladimir Voevodsky and his work in Homotopy Type Theory and Univalent Foundations:


I don't know much about Boolean algebra, though I proved some stuff about Boolean rings yea months ago. I've brain rotted out of topology though. At this point I want to get back in. I'll probably have to get a copy of a text on smooth manifolds soon and do differential topology.

But the question you should be asking about Stone spaces is what they are useful for.

Originally posted by Reverend Jones:
But I can see how adding mathematical information to a programming language would be useful to mathematicians who already use said formalism (in your case, measure theory).


Well, proving that it's a measure space wouldn't be useful to just mathematicians, measure theory is a well-developed field, and you can pull quite a bit out of the theory.
2017-06-12, 2:43 AM #93
Originally posted by Reverend Jones:
I would actually hazard to guess that Kolmogorov complexity is more useful in applications of computer science, especially to complex systems theory.

Also, Kolmogorov introduced it roughly half a century ago, which is not exactly recent. But like I said, people like Wolfram are still at at and it is certainly a hot topic to try to expand the purview of C.S. It's just that the basics of the theory have been around long enough (and measure theory even longer), that I would have expected the sort of thing you dreamed up to have been discovered by now (and maybe it has been).


I would expect someone much cleverer than me has done quite a bit of programming related to measure theory, so yeah, I just got excited because he basically said his statements were a sigma-ring.
2017-06-12, 2:47 AM #94
Actually, Reid, for overlap between probability theory and programming, you can check out probabilistic programming. It's full of theoretical connections to machine learning, prolog, or statistical relational learning (which is somewhere in between the first two).
2017-06-12, 2:52 AM #95
Quote:
But the question you should be asking about Stone spaces is what they are useful for.


Quite a bit, if you are interested in algebraic approaches to formal methods.

To the presume the same about measure theory will most likely imply a probabilistic programming model (follow the link in my post above), although I admit there could be other applications.
2017-06-12, 2:56 AM #96
Just be careful, though. Richard Hamming once said:

Quote:
Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether, say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.
2017-06-12, 3:00 AM #97
...and I think you and I have just lost the interest of literally everyone else in this forum.
2017-06-12, 3:16 AM #98
oooph.
former entrepreneur
2017-06-12, 11:35 AM #99
ani lo yodea eykh ledaber anglit
2017-06-12, 12:36 PM #100
bo shuda... my pee kasa Grismath. dolpee kikyuna! ohhhhhh
Cordially,
Lord Tiberius Grismath
1473 for '1337' posts.
2017-06-12, 12:37 PM #101
UTTINI
2017-06-12, 1:02 PM #102
Originally posted by 'Thrawn[numbarz:
;1201083']ani lo yodea eykh ledaber anglit


[RIGHT]?אבל למשעה אתה מדבר עברית? אתה גר בארץ[/RIGHT]
former entrepreneur
2017-06-12, 1:18 PM #103
Originally posted by Reid:
Yeah, in every STEM department, but in my experience it's more common in engineering and physics, are those total "that guys" who have not even a smidge of social comprehension. Usually the sorts of people who dog on math when their last course was calc 3, and love to condescend to people about how smart they are and tell anecdotes about people they never met and will never be as important as, like Feynman. And I can't generalize too much but I don't get the sense anyone here would be highly involved in Greek life, if you get what I mean.


I am the humanities version of this (though the degree I am working on is 'science') and I mostly tell anecdotes about Diogenes (and Feynman actually soooooo) so I guess I am involved with greek life lolololol. But no, you will not find me at frat parties. Theatre department parties and drag shows definitely yes though.

Quote:
I'm not in any way trying to justify my use because it was wrong. But holy ****, society has come a long way in our thousands of years.


Yes but some (some) of their slaves were treated better than the way we treat our slaves now for example. I'm not one for golden age thinking in either direction, but while in general things are better I can't really get with the 'it is a better time to be alive than ever in every way be grateful and don't criticize anything' that the techno optimists and priests of progress seem to think I have to believe to not be a dirt eating moron.
Epstein didn't kill himself.
2017-06-14, 6:47 AM #104
Originally posted by Spook:
I am the humanities version of this (though the degree I am working on is 'science') and I mostly tell anecdotes about Diogenes (and Feynman actually soooooo) so I guess I am involved with greek life lolololol. But no, you will not find me at frat parties. Theatre department parties and drag shows definitely yes though.

Yes but some (some) of their slaves were treated better than the way we treat our slaves now for example. I'm not one for golden age thinking in either direction, but while in general things are better I can't really get with the 'it is a better time to be alive than ever in every way be grateful and don't criticize anything' that the techno optimists and priests of progress seem to think I have to believe to not be a dirt eating moron.


I'm definitely not advocating we don't complain today, I mean I'm a pretty big whiner about the state of things myself. But I think it's clear from reading the texts that Greek society was still far more cruel than ours. We don't have so much literal slavery (?) proportionately but we do have a worldwide proletariat that's treated terribly. Maybe the Greek slaves were treated better than black slaves in America, probably so in fact. So you have a point.

The thing with pharmakos sacrifice is that it's something of an incomparable event. I maybe left out too many details. For one, the entire town would be forced, literally, to participate so that nobody could build sympathy with the victim. It's like a serious, adult version of muckle. I don't see anything comparable to that in modern society.
2017-06-14, 6:49 AM #105
Also, I think the Greek word sophrosyne needs to re-enter our vocabulary. And all people need a bit more of it.
2017-06-14, 9:43 AM #106
Originally posted by Reid:
I'm definitely not advocating we don't complain today, I mean I'm a pretty big whiner about the state of things myself. But I think it's clear from reading the texts that Greek society was still far more cruel than ours. We don't have so much literal slavery (?) proportionately but we do have a worldwide proletariat that's treated terribly. Maybe the Greek slaves were treated better than black slaves in America, probably so in fact. So you have a point.


אם אתם רוצים לדבר על עבדות בבקשה בשפות אחרות

הנושא הזה לא בשביל אנגלית
2017-06-14, 10:44 AM #107
Originally posted by Reid:
I'm definitely not advocating we don't complain today, I mean I'm a pretty big whiner about the state of things myself. But I think it's clear from reading the texts that Greek society was still far more cruel than ours. We don't have so much literal slavery (?) proportionately but we do have a worldwide proletariat that's treated terribly. Maybe the Greek slaves were treated better than black slaves in America, probably so in fact. So you have a point.

The thing with pharmakos sacrifice is that it's something of an incomparable event. I maybe left out too many details. For one, the entire town would be forced, literally, to participate so that nobody could build sympathy with the victim. It's like a serious, adult version of muckle. I don't see anything comparable to that in modern society.


Yeah that was my general point re:slaves as the 1800s was like ten minutes ago in my mind. Though the general treatment of the global proletariat (which doesn't include anyone here, and can definitely be portrayed as 'slavery' without too many gymnastics) is definitely an unprecedented flavor (though perhaps not degree) of cruel, so I'm not sure where it actually ranks in the oppression olympics. Regardless, all of us including those greeks are prisoners in the black iron prison that corrals us into participating in things along these lines, to whatever extent we do.

I have not read very much about this weird greek kind of sacrifice, I will have to look into it more, thanks for telling me about it.
Epstein didn't kill himself.
2017-06-14, 10:48 AM #108
This thread does not deliver.
Star Wars: TODOA | DXN - Deus Ex: Nihilum
2017-06-14, 10:50 AM #109
I thought it was going ok until the cliquish academic elitism stuff
2017-06-14, 10:52 AM #110
the social sciences are for retards who don't understand statistics. ugh. but at least they aren't too autistic to understand math, like those rapey engineering students.
2017-06-14, 11:26 AM #111
Originally posted by Spook:
Yeah that was my general point re:slaves as the 1800s was like ten minutes ago in my mind. Though the general treatment of the global proletariat (which doesn't include anyone here, and can definitely be portrayed as 'slavery' without too many gymnastics) is definitely an unprecedented flavor (though perhaps not degree) of cruel, so I'm not sure where it actually ranks in the oppression olympics. Regardless, all of us including those greeks are prisoners in the black iron prison that corrals us into participating in things along these lines, to whatever extent we do.

Ah, yeah, I think the main difference is westerners have a comedy of innocence trying to put distance between us and the cruelty of our economic system, we normally don't have to face it directly. But it's nonetheless there.

Originally posted by Spook:
I have not read very much about this weird greek kind of sacrifice, I will have to look into it more, thanks for telling me about it.


It's called pharmakos and there's a great journal article, "Scapegoat Rituals in Ancient Greece" by Jan Bremmer which gives it a good treatment.

Ironically pharmakos is pretty close to pharmakon, which means either "cure" "poison" or "purify", and is the word used to describe what happened to Socrates, some philosophers make a few nudge nudge suggestions but academics hate this.
2017-06-14, 11:27 AM #112
They (we?) probably don't hate it as much they hate Derrida.
former entrepreneur
2017-06-14, 11:29 AM #113
^ also there's little "normal" in any Greek sacrifice.. even the normal versions are pretty weird by our standards

Originally posted by Jon`C:
I thought it was going ok until the cliquish academic elitism stuff


Lol my mistake. Reverend Jones and I are to blame for the math talk.

Originally posted by Jon`C:
the social sciences are for retards who don't understand statistics. ugh. but at least they aren't too autistic to understand math, like those rapey engineering students.


Uh...
2017-06-14, 11:30 AM #114
Originally posted by Eversor:
They (we?) probably don't hate it as much they hate Derrida.


That's probably true.
2017-06-14, 11:33 AM #115
Dutch
English
French
German
Spanish
Latin
Ancient Greek
(some) Japanese, studied it for one year, a long time ago. Most of it has sunk away in the mists of time.
ORJ / My Level: ORJ Temple Tournament I
2017-06-14, 11:33 AM #116
Originally posted by Jon`C:
the social sciences are for retards who don't understand statistics. ugh. but at least they aren't too autistic to understand math, like those rapey engineering students.


You're right. Those comments I made were really ****ty. I'm sorry about that.
2017-06-14, 11:35 AM #117
It's not just you
2017-06-14, 11:40 AM #118
I know, I did my part in saying/normalizing the activity though.
2017-06-14, 12:55 PM #119
The S.F. knows I've said my share of ****ty things on this board. On the other hand, I don't like to emphasize the penance aspect of rectifying these sins, because while saying privilagy stuff that scapegoats some outgroup makes us all cringe, I've always felt that the potential for negative social consequences that this kind of darkness revealed within ourselves could engender--if we don't put a mirror up to it (which we absolutely ought to do!) before we let ourselves do real harm down the road-- is in some ways secondary to another problem.

Namely, that explaining away something neutral to negative about ourselves by scapegoating an outgroup is lazy, and more importantly, usually flat out wrong.

This board could be different, but I imagine that only 1% or less of people called autistic are actually autistic at all. And while it's a ****ty thing to say--especially if it becomes normalized (stop to think about where the word "dumb" comes from)--the most damaging consequence of being this lazy is that that the actual problems you have go totally unacknowledged, just because it's amusing enough to indulge for a moment in a humorous fantasy that you in fact have a genetic and therefore immutable problem, which you can laugh at because it's a fantasy after all, and also use to hide your actual shortcomings, because genetics are immutable.

"He's pretty stupid." Oh, that's just because he's "dumb". Case closed.

"He's socially awkward." Easy, he's "autistic".

See, it makes you a dick, but more importantly, you are hurting yourself because you justify a lack of introspection hiding behind humor.

Which, I believe, is a pretty good description of 4chan, so perhaps this is a juncture to bannish the meme and cast it back from whence it came.
2017-06-14, 12:59 PM #120
(I just scapegoated 4chan as a way of hiding my real problems. ;) )
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