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).
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.
>What makes reddit and now HN think Ataturk was some sort of beacon of democracy?
I haven't seen anyone say that. People are specifically saying he would be disgusted with how non secular Turkey has become since secularizing Turkey was one of his biggest things.
Read more on what lead to banishment of Armenians. If you attack unprotected Turkish villages with the help of foreign powers and betray your neighbours, you face the consequences, this is war.
Also there was no such thing as hating Armenians til aforementioned betrayal. At the time there were even couple of high ranking statesman like Gabriel Noradunkyan
from Armenians.
You are calling Genocide of 1.5 million of their own citizens "banishment". And then you advice people to go and read on the subject.
Your lack of education on the topic of Armenian Genocide is astonishing.
I am calling the relocation of troublesome Armenians to Syria as banishment. Armenians perished along the way, it wasn't a systematic killing. Death toll of Armenians were only 500.000 while it was 1 million on Turkish side.
After living 600 years peacefully Armenians got greedy and betrayed Turkish people with the help of Russians.
Check my first comment there was even Armenian ministers in the government that time, did you see any Jew ministers during Hitler regime? Why would they allow such thing if they were about to commit some horrible genocide. Makes no sense.
While some Armenian independence organisations did use terrorism as a means, and indeed the question of the Armenian genocide is not that of the Ottoman Empire's momentary caprice to remove Armenians as a worse people like it was in the Holocaust (Holocaust and Medz Yeghern are incredibly different events, the former was head hunting against completely peaceful people for stupid racial ideals), the genocide happened, and words like betrayal and greed in what amounts to a global war of greed and massacres sound childish. If as Turks we have the right to indipendence as a people, so does ever other peoples.
It started out as exile. The Ottomans basically rounded up large numbers of Armenian civilians and forcefully marched them from Eastern Anatolia to today's Syria, in the hopes that separating them from their Turkish neighbors (with whom they were fighting violently) would put an end to what was seen as a civil distraction during war. Countless Armenians perished along the way as a result of gross incompetence and negligence on the part of the soldiers in charge.
If genocide is defined as "systematic and deliberate extermination of a group of people" then it wasn't genocide, because the intention was not to exterminate, but to relocate. Turkey absolutely needs to own up to what happened and pay reparations (even though it is a different country than the Ottoman Empire under which the events occurred), but in my opinion calling it genocide is inaccurate.
Word "Genocide" was introduced by Raphael Lemkin to describe systematic extermination of Armenians and Jews by Young Turks in Ottoman Empire and by Nazis in Europe.
Genocide was thoroughly planned and executed by Ottoman Government which was run by Young Turks. Archives of multiple countries have documented evidence of the fact that it was Planned Systematic Extermination of Armenians - Genocide.
There are archives from US embassy in Turkey, German archives, French Archives and press archives from that period that all confirm that.
Genocide did not start with marching people to deserts in Syria. It started with arrests and massacre of around 250 political and cultural leaders of Armenian origin, to prevent any organized resistance. [1]
Entire civilized world recognizes these events as a Genocide. One of the latest recognitions came from German government (in 2015). They were allies of Ottoman Empire by that time and did not do much to prevent the Genocide. [2]
Please do not spread misinformation and mislead people.
Atatürk was not a beacon of democracy, he never pretended to be. As a military man, he did resort to heavy handed methods at times. The republic he left behind as his legacy is however one when you consider the circumstances. He created a secular, Muslim majority country that was aligned with the Western ideals and was even ahead of Europe in some aspects (women's suffrage). This is truly impressive considering no country in the region has been close to that level in the last century.
The important word should be "was". If you try to remove it from the past, by arguing semantics or by any other means, you make it stick into the present. A past genocide would be much easier to live with than a permanently unsettled question of genocide or war event or war atrocity or paranoid fantasy of everybody else conspiring to sully a history they actually don't even care that much about as if they had nothing better to do.
The thing is, history is full of ugly things and arguing them creates a much stronger link between the uglyness and the one arguing than ancestry could ever do.
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?
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:
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.
In constructive mathematics, we don't reject "all infinite constructions". The only axiom which we don't generally assume is the axiom which says "any statement is either true or not true". (Note that we also do not use the counterfactual axiom "there is a statement which is neither true nor false". In fact, we're just agnostic on some truth values.)
In constructive mathematics, there is a perfectly well-defined set of real numbers. The usual diagonalization proof that this set is not a countable set applies.
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
I totally agree that mainstream mathematics doesn't have any problem whatsoever with infinite constructions and in fact embraces them.
I just wanted to clarify that intuitionistic and constructive mathematics don't have any problems with infinite constructions either. Finitism and ultrafinitism do, but they're not what's usually called "constructive mathematics".
There are at least three orthogonal axes which you can classify mathematical schools of thought in:
* Is the law of excluded middle accepted? ("Any statement is either true or not true.")
* Are infinite sets accepted? (They are not in finitism, but they are in constructive mathematics and of course in ordinary mathematics.)
* Can constructions implicitly refer to the result of what is being constructed? Is the powerclass of a set again a set? (Yes in ordinary mathematics and in constructive mathematics, no in predicative mathematics.)
> 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).
Well, the fact that the number is not computable means that there will exist an index i, for which you will not be able to compute a_i (no matter how hard you try). In other words, you will not be able to analyze the Turing Machine i, i.e. it will not be possible to prove the termination or non-termination of the Turing Machine i.
So this specific digit will be a mystery forever, and you would not be able to compare it to anything.
"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").
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.
> 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?
The "indescribable numbers" are dense in [0,1], and so (if the set exists) the inf of the set of indescribable numbers which are between 0 and 1 is 0. Perfectly describable.
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
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.
Defining the set of real numbers is very different from defining all real numbers. Yes, Chaitin's constant is defined(with a computable system as a parameter).
But that's the point - we cant produce such a definition for almost all reals.
> 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).
The point is straightforward - the fact that you have defined a country on a map, doesnt mean you have defined all its cities and towns. Especially if the number of markers you have are less than the number of towns.
Also, we can talk about definable numbers as long as we choose some specific system which we assume is consistent. So we are talking about numbers which are definable by predicates using the language of ZFC or Peano Axioms.
There is no need to invoke computability, just definability is sufficient. There are lots of definable numbers which are not computable(like Chaitins constant or the real number whose digits encode information about halting of Turing Machines).
But even with this more relaxed constraint, we still dont have enough definable numbers.
If you can describe a set of objects thats fine. But by itself that would be nearly useless. The problem is that ZFC and the like add an axiom that you can identify an element of any described set, and use that to prove further theorems. That makes no sense; its an elimination rule with no corresponding introduction, materializing members of a set from nothing.
There are more people on earth than, say, kings. That's true, even though I can't enumerate all non-kings, and even if the set of non-kings is somehow ill-defined.
A sentence which fails to specify a real uniquely… fails to specify a real uniquely. Borel's talking about numbers which can be defined uniquely: that is, picked out, identified. Your Berry-paradox description doesn't identify an integer.
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.
>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.
I should have made this clearer, but the 'question' I had in mind was not whether Basque is related to Georgian, but the more general one of whether it's related to anything at all.
That's mine too, but nowadays teams and especially managers last about 6 months in one place. What is one supposed to do?