earthicus

12 ms·

61.
by earthicus 7y ago
Very nice article! Also of interest, 1 not being prime can be viewed as a particular example of a more general phenomenon that occurs throughout mathematics, known as the 'Too simple to be simple' principle: https://nca
62.
Number Crunching vs. Number Theory: Computers and Fermats Last Theorem 1850-1960(tau.ac.il)
30 points by earthicus 8y ago|3 comments
63.
by earthicus 8y ago
I've linked [1] to another example of exploiting an invariant that you might find more compelling. The presenter takes a multi-page mess of UI code from Chrome containing something like 8 loops, then solves an even harder version of th
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by earthicus 8y ago
I don't think the utility of invariants is restricted to proving program correctness, as is suggested by a number of commenters in this thread. Instead, they identify some underlying structure in your problem, and that structure can
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by earthicus 8y ago
According to an amazon reviewer [1], Sammet's book Programming Languages: History and Fundamentals (from 1969) already discusses ~120 different languages! And gives code examples in 30 of them. [1] https://www.amazon.com&#x2
66.
by earthicus 8y ago
The book has an appendix, labeled 'background' which lays out more precisely the formal prerequisites from point-set topology and algebra which you should review. The algebra is surely going to be a bigger obstacle than differenti
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Ask HN: Improving the Notation of APL/J (and Other Languages)
5 points by earthicus 8y ago|0 comments
68.
by earthicus 8y ago
How are you interpreting this experiment with DeBroglie-Bohm? This is bumping up into the area where the theory gets into trouble, as photons aren't described by the Schrodinger equation or Dirac equation, and don't have wave func
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by earthicus 8y ago
For those of you who haven't yet read the article, the cool thing about this new technology is that the material is not a solid plane, but an empty ring that allows air to pass through: https://www.bu.edu/research/
70.
by earthicus 8y ago
I know nothing about acoustics and its units - the abstract of actual paper says more precisely that it reduces the 'acoustic energy' by 94%, not the power. Can you convert this to a decibel figure? Would you mind explaining what
71.
by earthicus 8y ago
According to [1], the question Goedel raises is equivalent to P vs NP, although clearly not phrased in the same language. The author claimes Goedel's phi(n) is polynomially bounded if and only if P=NP. Do you disagree with that statem
72.
by earthicus 8y ago
Here's a nice article that discusses the historical importance of the letter and the problem Goedel raises: https://ecommons.cornell.edu/bitstream/handle/1813/6910/89-9...
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by earthicus 8y ago
My source for learning about the exchange was a biography of von Neumann by Macrae, but i double-checked it and it appears you are correct. I was mis-remembering how much of the correspondence von Neumann was able to contribute at that poi
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by earthicus 8y ago
These letters contain some of the first discussions of computational complexity theory, and von Neumann immediately identifies P vs NP as a central problem in the field. The work was unpublished and undeveloped, as von Neumann became ill an
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by earthicus 8y ago
Thanks for the link, everything written by Baez is interesting! Grothendieck's algebraic geometry is, I lament, a bit too intimidating for me at this point & I suspect that will be true for pretty much everyone who reads this websi
76.
by earthicus 8y ago
I don't see it on that list, but there's apparently an implementation of Algol 60 baked into dr racket, so you need not limit yourself to lisps if you want to put in the work to do something more far-reaching. https://d
77.
by earthicus 8y ago
It's (sort of) discussing the work of Nima Arkani-Hamed and his Colleagues, and their attempt to reformulate quantum field theory so that it doesn't refer explicitely to space-time, in analogy to how the principle of least action
78.
by earthicus 8y ago
Here's an interesting article which gives some response to the accusations made of Churchill's actions during the Bengal famine. It's short and well worth reading, although it clearly is papering over Churchill's racism.
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by earthicus 8y ago
Warning: These books are kind of all over the place as far as technical prerequisites go, but they all satisify being heavier than pop-sci and lighter than a textbook. :) ------- Aleksandrov et al - Mathematics: Its content, Methods, ad Mea
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by earthicus 8y ago
> From very private conversations with others, many labs are abusive, fraudulent, 'me-too' landmines, and generally lying to grant funders, donors, and potential/enrolled students I have a friend who worked in a neurology
81.
by earthicus 8y ago
I'm hesitant to take an anonymous and unsourced internet comment at face value, but assuming it's true, that is quite damning for American academia! It occurs to me that the claimed effect, if it exists, might also be due in part
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by earthicus 8y ago
The spectacular knot homology theories such as Khovanov Homology and Heegaard Floer Homology can detect the unknot 'on the blackboard' as well. Wow!!! Actually it can detect the genus of the knot: that's an amazing theorem! I
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by earthicus 8y ago
That's not at all an accurate description of the book. Goedel is not just used as an example of a strange loop, he bases his entire model of mind on it. This is developed in chapter 20. Particularly noteworthy are the sections of that
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by earthicus 8y ago
GEB not just a popular exposition of mathematical logic, the book is quite explicitly about philosophy of mind. In particular, he develops the self-reference stuff so he can draw an analogy to brains and tell us his theory of consciousness.
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by earthicus 8y ago
Does anyone here have any experience using semi-formal methods, like 'cleanroom' techniques? The commentaries I've heard (e.g. [1]) tend to be very enthusiastic, but I don't have enough experience to judge their credibil
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by earthicus 8y ago
If you managed to survive high school algebra, you might be able to 'redo' your basic math education with a geometric bent from Stillwell's book 'Numbers and Geometry', which teaches the classical link between the t
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by earthicus 8y ago
An interesting response to the explanation video from u/functor7 on reddit: https://www.reddit.com/r/math/comments/ahz8k3/so_why_do_coll...
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by earthicus 8y ago
I snapped a few photos from Russo's book 'The Forgotten Revolution' that show the logical structure of the mechanism, and also the pump of Ctesibus mentioned in the article: https://imgur.com/a/BnaGIvW T
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by earthicus 8y ago
There was a discussion about this issue last month, where i wrote out a fairly detailed reply and gave a good reference to learn more: https://news.ycombinator.com/item?id=18644880
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by earthicus 8y ago
The first genralization is in section 1.3.3 and 1.3.4 https://mitpress.mit.edu/sites/default/files/sicp/full-text/... Unfortunately I couldn't find the material about interpreters - my memory o

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