Yeah, the messaging got a little muddled, but the relation was purely analogical.
I was trying to point to a situation where you have a clear problem: a generating function for the prime number sequence; and a solution that identifies a small subset of the intended sequence without addressing, or even informing in any substantial way, the full breadth of the original problem.
> At the time of writing the longest known arithmetic progression of primes is of length 23, and was found in 2004 by Markus Frind, Paul Underwood, and Paul Jobling: 56211383760397 + 44546738095860 · k; k = 0, 1, . . ., 22.'.
The triviality was overloaded to both imply that calculating this subset is trivial, it is a simple arithmetic progression, and that subset of the full prime number sequence is now trivial to produce.
In the same way that the Green-Tao theorem has yet to lead to a complete solution to the prime number sequence, I feel, the machine learning techniques will fail to lead to a complete solution to protein folding.
It would be very hard to make a good analogy with this since the problem of "finding" arithmetic progressions is, as far as I know, of negligible interest compared to the structural knowledge of their existence. The situation is perfectly reversed in both computational biology and machine learning. But maybe I misunderstand what you mean by "a complete solution to the prime number sequence."
I was trying to point to a situation where you have a clear problem: a generating function for the prime number sequence; and a solution that identifies a small subset of the intended sequence without addressing, or even informing in any substantial way, the full breadth of the original problem.
> At the time of writing the longest known arithmetic progression of primes is of length 23, and was found in 2004 by Markus Frind, Paul Underwood, and Paul Jobling: 56211383760397 + 44546738095860 · k; k = 0, 1, . . ., 22.'.
The triviality was overloaded to both imply that calculating this subset is trivial, it is a simple arithmetic progression, and that subset of the full prime number sequence is now trivial to produce.
In the same way that the Green-Tao theorem has yet to lead to a complete solution to the prime number sequence, I feel, the machine learning techniques will fail to lead to a complete solution to protein folding.