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So, I was an undergrad mathematician, and planned to become an academic, but bailed out of my PhD and became a programmer instead. I made notes as I was reading the various articles.
My strong suit in maths was analysis. I just never 'got' algebra at all and didn't touch it after the first year.
Weirdly I was very good at linear algebra/matrices/spectral theory/fourier analysis. But all that seemed like a geometrical, intuitive theory about high-dimensional spaces to me. I had very strong reliable intuition there, but I never had any intuition, or idea about how one might go about acquiring one, for rings/fields/groups or mathematical logic.
I never liked any sort of symbol-manipulation. I felt I understood things if and only if I could make mental pictures of what was going on that would imply the answers 'as if by magic'.
M. Meray's endeavours seem unappealing. I appreciate them in the abstract but cannot imagine getting interested. Prof. Klein's conducting sphere seems a fascinating masterstroke.
Feynman/Einstein are definitely 'what I'd be if I was twenty times better'. I recognise their ways of thinking, at least as they explained them.
I agree wholeheartedly with Arnold's rant.
I'm ambivalent on the problem-solver/theorizer distinction. I think I'm more of a theorizer, but problem-solving is important and they both matter. I'd have been proud to have contributed in either way.
Maths is very visual for me. The symbols mean nothing without the pictures.
As a programmer, I:
loathe OO
love lisp, and found it mind blowing when I first found it. By default I use a lisp variant called Clojure both personally and professionally, although I've tried almost everything. I avoid java and c++ if I can.
have occasionally tried Haskell, and feel that I ought to understand it, but it feels like programming with one hand tied behind my back. An awful lot of extra effort for no gain.
am quite fond of python, although I use it as a watered-down lisp and avoid all its OO facilities.
adored "Why Arc isn't especially Object Oriented"
have never tried template metaprogramming, C++ is just too dirty for me, although I love C itself.
like both vi and emacs, and was originally a vi user, but these days I use emacs almost exclusively, and have done ever since I discovered what a joy it is as a lisp editor.
I think that all, with the exception of emacs, puts me strongly on the analysis/intuition side of things and weakly confirms the suggested dichotomy and its relationship to programming styles.
But it's been a long time since I ate corn-on-the-cob. When I try to visualise it I see myself eating it in rows rather than spirals. But I don't want to go out and find some, because then I'd bias the result. Somehow I have to catch myself in the act of eating it unconsciously. Any suggestions?
Suppose that in the recent referendum, Scotland had voted to leave the UK. Does anyone think that the situation would have been more stable if England had attempted to keep Scotland by force?
To let subgroups defy this system of property and take possession of themselves and the land on which they reside would greatly destabilize the current world system.
Even speaking historically, this is not clear. The pre-twentieth century transition of the various territories of the British Empire to Dominion status stabilised the system greatly.
Essentially peaceful transitions from centrally controlled colony -> self-government for Canada, Australia, South Africa, Rhodesia and New Zealand, and the resulting states remained tightly allied.
The two places where dominion status wasn't given freely by the Empire, America and Ireland, were the two where there was "destabilization". If those two had been given their own governments peacefully when they demanded it, we might today be part of one vast friendly Commonwealth, and a large amount of unpleasantness might have been avoided.
And that in a world where everyone quite reasonably expected their neighbours to attack at any time, and splitting a state was seen as a disaster from a defensive point of view.
I have missed your clarity of mind Eliezer, it is very good to hear your voice again.
I'm not sure it would be a good thing for anyone if states and counties seceded into ever-smaller units and elected the usual run of even more nitwit governments, especially if it was only the democracies that started doing that.
I'm not sure of this either, but democracies don't seem to fight much, or even want to, and it's not clear that small countries are more prone to electing nitwits, so what are we worried about?
I'd be just as worried by the thought of the world's democracies unifying.
It seems to me that democracy is even more appalling than usual as a form of government for states that have two distinct tribes. The majority tribe ends up imposing a one-party state on the minority, with all the injustice and corruption that that implies.
Consider e.g. Zimbabwe. But also England and Ireland. Unity was very bad for the Irish, and separation has been unambiguously good for both countries.
I highly recommend this book, but then it's currently my introduction to both Information Theory and Bayesian Statistics, and I haven't read any others to compare it to. I find it difficult to imagine a better one though.
Clear, logical, rigorous, readable, and lots of well chosen excellent exercises that illuminate the text.
The link is well worth following. Wow! Stereo vision with one eye closed!
I'll be there. Someone should make a sign with a paperclip on it, or at least have a laptop open and displaying one.
I believe this one is becoming traditional.