upquark's comments

> Nowadays, my primary criteria for joining a team is the quality of the people and of the manager.

That's mine too, but nowadays teams and especially managers last about 6 months in one place. What is one supposed to do?

Totally a preference thing. I strongly prefer pandas to dplyr having worked with both.

How much of success is luck? I honestly don't know. It feels like another feel-good mantra coming out of SV culture. Most successful people I know or have heard of do not fit the profile of an average Joe (including qualities that are pre-set at birth and cannot change with success).

> bilateral clash

https://en.wikipedia.org/wiki/Warsaw_Ghetto_Uprising

What makes reddit and now HN think Ataturk was some sort of beacon of democracy?

> 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.

> Defining the set of real numbers is very different from defining all real numbers.

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).

Then we mean different things by define. I am saying the set R (with all its elements) is an uncontroversial, well-defined construction within ZFC.

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

I said "and other groups that reject all infinite constructions". Some schools of thought within that general intuitionist/constructivist/etc branch of mathematical logic do reject all infinite constructions: https://en.wikipedia.org/wiki/Finitism

Either way, my point above was that this entire branch is not "mainstream math" by any means, AFAIK

Oh it's definitely more real, as in it belongs to R and not to any of its extensions. You guys realize that the definition of R is non-controversial in modern math, right? There are fringe theories like constructivist logic and other groups that reject all infinite constructions, but this is not the consensus view among practicing mathematicians...

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.

No, my "ill-defined" means "will lead to contradictions if you look too closely", not "I haven't exactly specified what it means".

Yes but you defined the number just fine, right? "Compute" is a separate issue from "define", you can't compute a lot of things. Is this going in the intuitionistic logic direction?

Still not sure I follow. Set of non-kings is not ill-defined, not in the same way as set of numbers non-describable by any formal system is.

My example is incomplete, not faulty. I left it as a question (does the inf belong to the set?). If the answer is yes, we reached a contradiction. If the answer is no, we have to continue further zooming in to this interval (or some other construction along those lines).

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

Wait, you're agreeing with me that the set in question is ill-defined, but still somehow comparable to other sets? I am not sure I follow. My statement is that you cannot meaningfully talk about "all the numbers that cannot be described with language". If you could, I'd ask you if this set intersected with [0, 1] has a lower bound / 'inf' that's contained in it, and if so, did I just describe that lower bound with language? I'm sure some sort of paradox similar to the one with integers can be constructed here...

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.

"Real numbers that cannot be defined with language" is not a well-defined set though. Just like "integers that cannot be described in less than 100 words" is not well-defined (I could reach a contradiction by pointing to the "smallest integer that cannot be described in less than 100 words").

$25 - two sandwiches from Toasties baby :o

Do the esteemed downvoters care to substantiate their position with anything other than "my daddy said so" anecdotes?

Is this slave mentality or what?

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.

This whole discussion is setting off my BS detectors (your comments specifically, dad with HS degree vs 'the Chinese', etc), and to be honest, the whole tribal knowledge thing may be much more wishful thinking than an actual true effect...

It's just that the answer to the question posed in the headline is a definite 'no'. This type of silly inquiry into "is Azeri related to Sumerian", "is Georgian related to Chinese" etc. is very common in that part of the world, and is largely pseudo-scientific at its core.

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.