3 ms·

Yeah - divergence would be a far better term rather than the analogy. They go apart but specifically don't interact. Instead it gets people to overlook it as m

Yeah - divergence would be a far better term rather than the analogy. They go apart but specifically don't interact. Instead it gets people to overlook it as more new age nonsense woo that abuses appropeiated quantum physics terminology.

LolWolf 6y ago
> that abuses appropeiated quantum physics terminology I would certainly not only specifically not say this is borrowed from quantum physics (perhaps classical EM?), but in fact the whole point of the theorem is to show that such roots do interact in a specific way. From Theorem 1 of the paper: > Let P ∈ Z[X] be a monic integer irreducible polynomial of degree n > 1. If P is not cyclotomic, then [the largest root of P is bounded away from 0 with norm at least 2^(1/4n)]. In particular, it is a statement about a specific root (the largest one) lying outside of the unit disk, whereas the remaining roots could potentially lie within it (and specific examples of this 'tightness' condition are given in applications in section 5).
pas 6y ago
From the article: """ Schinzel and Zassenhaus predicted that every non-cyclotomic polynomial must have at least one root that’s outside the unit circle and at least some minimum distance away. Or, to put the Schinzel-Zassenhaus conjecture in terms of repulsion, it predicted that the smallest roots of a non-cyclotomic polynomial — which might fall within the unit circle — effectively push other roots outside the unit circle, like magnets pushing each other away. You can think of the roots of a polynomial as negatively charged particles that repel each other with a force that decays when the distance increases, """ So if they can write a formula for distance between these roots, and it's always positive and has a similar dynamic to Newton's (or Maxwell's, or Ampere's) force, then why not call it repulsive force?

LolWolf 6y ago

> that abuses appropeiated quantum physics terminology I would certainly not only specifically not say this is borrowed from quantum physics (perhaps classical EM?), but in fact the whole point of the theorem is to show that such roots do interact in a specific way. From Theorem 1 of the paper: > Let P ∈ Z[X] be a monic integer irreducible polynomial of degree n > 1. If P is not cyclotomic, then [the largest root of P is bounded away from 0 with norm at least 2^(1/4n)]. In particular, it is a statement about a specific root (the largest one) lying outside of the unit disk, whereas the remaining roots could potentially lie within it (and specific examples of this 'tightness' condition are given in applications in section 5).

pas 6y ago

From the article: """ Schinzel and Zassenhaus predicted that every non-cyclotomic polynomial must have at least one root that’s outside the unit circle and at least some minimum distance away. Or, to put the Schinzel-Zassenhaus conjecture in terms of repulsion, it predicted that the smallest roots of a non-cyclotomic polynomial — which might fall within the unit circle — effectively push other roots outside the unit circle, like magnets pushing each other away. You can think of the roots of a polynomial as negatively charged particles that repel each other with a force that decays when the distance increases, """ So if they can write a formula for distance between these roots, and it's always positive and has a similar dynamic to Newton's (or Maxwell's, or Ampere's) force, then why not call it repulsive force?