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I was extremely fascinated by bacterial resistance growth mechanisms (DNA exchange). It was the first time I realized how immensely complicated the biosystem is

by atmosx 9y ago

I was extremely fascinated by bacterial resistance growth mechanisms (DNA exchange). It was the first time I realized how immensely complicated the biosystem is at lower level. The 2nd time I had this feeling was when introduced to space of possible protein structures & the futility of prediction strategies. Suddenly the “known universe” and things like “number of known stars” started looking “reasonably sized” or even small. Fascinating stuff. People can read more about it here: https://en.m.wikipedia.org/wiki/Protein_structure_prediction https://en.m.wikipedia.org/wiki/Protein_structure_prediction

chriswarbo 9y ago
> The 2nd time I had this feeling was when introduced to space of possible protein structures & the futility of prediction strategies. Suddenly the “known universe” and things like “number of known stars” started looking “reasonably sized” or even small. This is a common experience in combinatorics ( https://en.wikipedia.org/wiki/Combinatorics https://en.wikipedia.org/wiki/Combinatorics ). Similar things happen when beginner programmers (like me!) try to solve chess by recursing/looping through possible moves (there are about 10^123 separate paths, if duplicate configurations are merged together), or brute-force a cryptographic hash/key (2^k possibilities for keys of length k; keys of length 2048 and above are common). The "standard big number" that gets thrown around when pop-sci articles talk about this stuff is the number of atoms in the observable universe, which is estimated at around 10^80. It irks me that this is used so much for comparison, since combinations of things are so overwhelmingly larger than collections of things that it feels like a category error to compare them. After all, "the number of atoms in the observable universe" isn't a particularly intuitive quantity; unlike, say, "football field" as a unit of length or "bag of sugar" as a unit of mass/weight (UK media loves to use the latter; since a bag of sugar is 1kg, it shows off both their laziness and lack of faith in their audience...). Also, picking "the number of atoms in the universe" is really trying hard; yet these combinatorial numbers (protein foldings, chess positions, etc.) are actually small, everyday examples! People have no problems (either conceptually or practically) with playing board games, choosing passwords, etc. despite these large numbers lurking in there. The "atoms in the universe" number would be a hopeless comparison if we really tried to make a big combinatorial number. For example, "the number of binary sequences that can be represented by all the world's computer storage"; a quick Google search estimates the world's data storage as 295 exabytes, so that makes this number around 256^(295 * 10^18)
- taneq 9y ago
  > It irks me that this is used so much for comparison, since combinations of things are so overwhelmingly larger than collections of things that it feels like a category error to compare them. I think this is the core of the issue. "Atoms in the universe" is only such a relatively 'small' number if you assume that the way they're arranged is unimportant.
- wk2jkhkjdfglsl 9y ago
  one thing, if you were talking keys of length 2048, your talking RSA, and to break it you are applying GNFS, not trying all the numbers up to 2^2048. 2^2048 is so astronomically large a number it has no universe sized meaning, its likely way way more than any discrete chunking you can do of stuff in the whole universe. Something like 2^128 or 2^256 are more common 'brute' force type numbers, which would correspond to trying every key in a symmetric cipher like AES or a public key signature in ECDSA 2^256 is similarly quite large, but we can practically estimate this to be about the number of atoms in tens of thousands of galaxies.

by atmosx 9y ago

chriswarbo 9y ago

> The 2nd time I had this feeling was when introduced to space of possible protein structures & the futility of prediction strategies. Suddenly the “known universe” and things like “number of known stars” started looking “reasonably sized” or even small. This is a common experience in combinatorics ( https://en.wikipedia.org/wiki/Combinatorics https://en.wikipedia.org/wiki/Combinatorics ). Similar things happen when beginner programmers (like me!) try to solve chess by recursing/looping through possible moves (there are about 10^123 separate paths, if duplicate configurations are merged together), or brute-force a cryptographic hash/key (2^k possibilities for keys of length k; keys of length 2048 and above are common). The "standard big number" that gets thrown around when pop-sci articles talk about this stuff is the number of atoms in the observable universe, which is estimated at around 10^80. It irks me that this is used so much for comparison, since combinations of things are so overwhelmingly larger than collections of things that it feels like a category error to compare them. After all, "the number of atoms in the observable universe" isn't a particularly intuitive quantity; unlike, say, "football field" as a unit of length or "bag of sugar" as a unit of mass/weight (UK media loves to use the latter; since a bag of sugar is 1kg, it shows off both their laziness and lack of faith in their audience...). Also, picking "the number of atoms in the universe" is really trying hard; yet these combinatorial numbers (protein foldings, chess positions, etc.) are actually small, everyday examples! People have no problems (either conceptually or practically) with playing board games, choosing passwords, etc. despite these large numbers lurking in there. The "atoms in the universe" number would be a hopeless comparison if we really tried to make a big combinatorial number. For example, "the number of binary sequences that can be represented by all the world's computer storage"; a quick Google search estimates the world's data storage as 295 exabytes, so that makes this number around 256^(295 * 10^18)

taneq 9y ago
> It irks me that this is used so much for comparison, since combinations of things are so overwhelmingly larger than collections of things that it feels like a category error to compare them. I think this is the core of the issue. "Atoms in the universe" is only such a relatively 'small' number if you assume that the way they're arranged is unimportant.
wk2jkhkjdfglsl 9y ago
one thing, if you were talking keys of length 2048, your talking RSA, and to break it you are applying GNFS, not trying all the numbers up to 2^2048. 2^2048 is so astronomically large a number it has no universe sized meaning, its likely way way more than any discrete chunking you can do of stuff in the whole universe. Something like 2^128 or 2^256 are more common 'brute' force type numbers, which would correspond to trying every key in a symmetric cipher like AES or a public key signature in ECDSA 2^256 is similarly quite large, but we can practically estimate this to be about the number of atoms in tens of thousands of galaxies.