Well, that's a bunch of ignorant baloney.

If Russia and China have these capabilities today, then opponents we DO engage will have them tomorrow... unless, you know, someone fixes the problem.

Not to say that we have nuclear assurances against a direct conflict between the US and Russia, we don't have such assurances for US proxies engaging Russian or Chinese proxies. The US needs to have enough conventional deterrence to prevent major proxy wars - which, by the way, destabilize the world economy and make the world a crappier place for everyone, including the "third-world-lives-don't-matter" isolationists such as yourself.

As someone who was born in the crappy part of communist Yugoslavia, I can confirm: slowly starving to death in a dark, abandoned nuclear bunker is an apt metaphor.

Invariants are useful because they allow you to distinguish equivalent knots, which is otherwise really hard to do. If two knots have different invariants, then they are surely different.

Dually, you would want the following: if two knots have identical dinvariants, then they are surely the same. Since "if the knots are equivalent, the assigned values might not be equal", dinvariants cannot accomplish this function, and that makes them mostly useless.

(full disclosure: lawyer who did his undergraduate degree in math, not a topologist)

> Invariants are useful because they allow you to distinguish equivalent knots, which is otherwise really hard to do. If two knots have different invariants, then they are surely different.

> if two knots have identical dinvariants, then they are surely the same. Since "if the knots are equivalent, the assigned values might not be equal", dinvariants cannot accomplish this function, and that makes them mostly useless.

That doesn't make them useless. Dinvariants just serve a different purpose:

- invariants serve the purpose of distinguishing knots that are different

- dinvariants serve the purpose of detecting that knots that look very different are actually the same

Scala 0.98

    #define def int
    
    def main(def x) {
     return x;
   }

Oh man, that's a dirty trick. I like it.