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Dec
22
comment Is Euclid dead?
@quid: The critical thought existed in USSR, otherwise the Gorbachov reforms wouldn't have support at their beginning. And I would say, it was based on technical education (rested upon logic, without Latin, Philosophy and Linguistics). Quid, do you have time for a little chat? I forsee accusations in off-topic.
Dec
22
comment Is Euclid dead?
@quid, this is indeed intriguing. Are you saying that this is taught at schools in the West? Latin, Philosophy, Logic?
Dec
22
comment Is Euclid dead?
Maybe this explains everything... In Russia nothing of this exists at school. I even hardly imagine this. In particular, Latin and Greek authors were almost inavailable in USSR, they were published rarely and with little circulation. I read Herodotus only in 1990ies...
Dec
22
comment Is Euclid dead?
@quid: Blow out... I must say, I don't see how training in langauge and philosophy could be useful here. As to logic do you know a way to train logic outside of mathematics?
Dec
21
comment Is Euclid dead?
Unfortunately, I was born in USSR, where those stupidities were presented without hesitation in school education as "great truth of modern science", and "modern logic" (since the author, G.W.F.Hegel suggested his own understanding of logic in his great masterpieces marxists.org/reference/archive/hegel/works/hl/hlconten.htm). Fortunately, we had been also taught geometry, where we could understand what actually logic is, and this saved us from total intellectual degradation.
Dec
21
comment Is Euclid dead?
Or: "That the line does not consist of points, nor the plane of lines, follows from their concepts, for the line is the point existing outside of itself relating itself to space, and suspending itself and the plane is just as much the suspended line existing outside of itself.-Here the point is represented as the first and positive entity, and taken as the starting point. The converse, though, is also true: in as far as space is positive, the plane is the first negation and the line is the second, which, however, is in its truth the negation relating self to self the point."
Dec
21
comment Is Euclid dead?
For example marxists.org/reference/archive/hegel/works/na/nature1.htm: "Negativity, which as point relates itself to space and in space develops its determinations as line and plane, is, however, in the sphere of self-externality equally for itself and appearing indifferent to the motionless coexistence of space. Negativity, thus posited for itself is time."
Dec
21
comment Is Euclid dead?
Gil, when children at school are taught religion or military training, is it doubtful for you as well? Wouldn't it be better to explain them that when a "great intellectual leader" tells something strange there is a possibility to verify whether what he says is indeed wise, or on the contrary stupid? :)
Dec
20
comment Is Euclid dead?
It is clear for me that the attitude of different people to this subject depends exactly on the culture of teaching geometry in their countries. As far as I see, Russians are more satisfied with the way of how EG is taught at school, than Americans and Chinese. The solution I believe is sharing the experience: translating textbooks, teaching school teachers, and so on.
Dec
20
comment Is Euclid dead?
@Zhen Lin: I don't understand your point. It is desirable to have illustrations when you explain something, that's why visualization is important. If there is a possibility to explain logic WITH illustrations, it is better than explaining it WITHOUT them. Or what are you talking about? Again, I feel that this will be a long discussion, will it be better to chat?
Dec
20
comment Is Euclid dead?
Ah, yes! Thank you! I'll add this to my armoury. :)
Dec
20
comment Is Euclid dead?
I forgot to add that in my opinion so far there are no other effective tools to teach people logic at school but giving them Euclidean Geometry. You (and other people) mentioned combinatrics, projective geometry, etc., but first, there must be good textbooks for children (I do not know them), and second I don't believe that one can think up something that can compete with the visuality of EG.
Dec
20
comment Is Euclid dead?
@Qiaochu Yuan: my thesis is opposite. I disagreee that it is possible to explain which arguments are good and which are bad, if the listener has no idea of what logic is. There are many examples when people followed false arguments of intellectual pilferers (with horrible results) just because they looked "attractive". Hegel's filosophy is one of these examples. if you want. But I am afraid, this will be a long dispute, we can chat if you want.
Dec
20
comment Is Euclid dead?
@Qiaochu Yuan, I can explain this: "why do most people need to understand what a proof, a theorem, or an axiom are..." Because in human society there must be a critical mass of those who understand what logic is, and as a corollary who can estimate the reasonableness of what different other people say among those who pretend to be leaders ("political, economical, intellectual", etc.) This is very important. I dare to say that all the main horrors of social life of 20 century were results of the underestimation of this need. :)
Dec
20
comment Is Euclid dead?
@Anton Petrunin: your quotation of Sharygin is interesting, where is it from?
Dec
20
comment Is Euclid dead?
To avoid international dipute I think one should give references to good textbooks. My generation had been taught geometry (in Russia of 1970es) by Kolmogorov's books: twirpx.com/file/489992. As far as I understand, they were not translated into English. Later a lot of reproaches to these textbooks appeared (and it was impossible to understand what the authors of these reproaches had in mind), but for me these textbooks are examples of well-done work.
Dec
19
comment Is Euclid dead?
This sounds as if you used bad textbooks in your school. Andreas, was that in USA? :)
Nov
29
answered Banach algebra for measures induced by Haar measures
Nov
1
awarded  Yearling
Oct
28
comment A Hausdorff abelian group with no character?
I thought that each Banach space has enough linear continuous functionals (by the Hahn-Banach theorem). :)