upquark
That's mine too, but nowadays teams and especially managers last about 6 months in one place. What is one supposed to do?
> In January 1920, Mustafa Kemal advanced his troops into Marash where the Battle of Marash ensued against the French Armenian Legion. The battle resulted in a Turkish victory alongside the massacres of 5,000–12,000 Armenians spelling the end of the remaining Armenian population in the region.
He finished off the Cilician Armenians from Anatolia, whoever was left under French protection and had escaped the Genocide.
I'm saying that ^ sentence makes no sense to me, I don't know how to parse it formally. If you start talking about the set of "definable" numbers (not computable, but specifically "definable"), I believe you're gonna run into paradoxes as it's an ill-defined concept, similar (in spirit) to "all integers described under 100 words". In fact, the linked article actually talks about it in 2.3.
> For any given language, like for instance ZFC, we can say that definable numbers are a countable subset. Hence measure zero.
If I can describe a set of objects, then we're all set as far as I'm concerned (mathematically speaking). Being able to efficiently construct individual elements of this set using Turing machines or other computational devices is an orthogonal problem.
Also, I don't think having only countable number of utterances in ZFC precludes you from having well-defined uncountable sets described in that system (quite obviously, for any set S take 2^S which is very well-defined).
I am leaving out any linguistic or Turing-computability aspects out of this, and people try to bring it back in, mixing computability with definability.
For instance, Chaitin's constant is a perfectly well-defined number, albeit uncomputable by construction: https://en.wikipedia.org/wiki/Chaitin%27s_constant
Either way, my point above was that this entire branch is not "mainstream math" by any means, AFAIK
The way you defined that number makes it a perfectly valid element of the set R, as described by, say, the axiomatic definition here:
https://en.wikipedia.org/wiki/Real_number#Axiomatic_approach
Whether it's easy or hard or computationally intractable to compare it to other numbers, that's a totally different question unrelated to its definition.
Plus, you can actually empirically compute a finite set of initial digits (a specific Turing machine can be analyzed to see if it terminates or not), so you can compare this number with one that's constructed by flipping its digits, or with pi, etc.
See, I claim that this set is ill-defined, so I can't know its properties like whether or not it's dense, open, closed, Borel-measurable, etc. etc.
You have to tell me what its properties are, and I will come up with a concrete proof that the set in question is ill-defined.
EDIT: After I RTFA'd, this is actually the paradox in section 2.3 of the linked article
In my view, every real number is well-defined and there's nothing controversial about the set of real numbers. If the infinite aspect of it causes some researchers to call it a "mathematical fantasy", so be it, so is literally every other mathematical model we use in our lives.
If I make 350k+, and a startup is telling me I should take their 150k base + worthless options deal, or else I've "pigeonholed myself in the current role" (actual quote), I think they're just being stupid and unrealistic.
As for ML methods, I know for a fact that modern Bayesian inference techniques have been successfully applied in comparative linguistics and proto-language reconstruction.
As someone who self-selected the name 'bayesian_horse', can you please cite the evidence you're basing this on?
> ...the class hierarchy: as an example, in Pharo Smalltalk you have the following hierarchy: ProtoObject -> Object -> Collection -> SequencableCollection -> ArrayedCollection -> String
Seems ridiculously over-engineered to me, but whatever, let's keep going..
> with the "reduce" method being declared on Collection class (reduce being the easiest way to implement "join").
'reduce' and 'join' are very different things. one is a generic function (aka fold, also exists in python as 'reduce'), the other is a string concatenation method that takes an iterable and produces a string. the latter can be implemented via the former, but they're not the same thing. no one's stopping you from using 'reduce' in Python instead of the built-in string member function 'join', btw.
> So in short: no. There are many interesting languages which implement various interesting techniques which solve various problems
Ugh, i give up :)
Also, doesn't seem like you read the actual argument following the first sentence :)
Seems like a minor point to me, really. Sure, join could've been a member function of the list class, but that would prevent applying it to arbitrary iterables, no? In other words, delimiter.join(items) is more general than items.join(delimiter), because in the latter join must be a member function of the class of items or its ancestor class, and you won't be able to apply it to other iterable objects.
I haven't had much interaction with Ruby, but from my limited experience the syntax felt strictly less intuitive than Python. The only other languages where syntax felt more intuitive to me than Python is the ML family (with derivatives like OCaml, etc).
Hmm, i've always felt the exact opposite, that Python feels just right syntax-wise (this after years of C/C++, Perl, bash, JavaScript, etc).
What would be your example of a language residing in "euclidean space"?