/sci/ - Science & Math

He has a point but at face value the statement is misleading or useless because the word "hard" is used in various ways.

>The subject X is hard because out of 100 people learning it, only 5 people will pass the test
The quantum mechanics is much harder than psychology

>The subject X is hard because to come up with something genuinely innovative is difficult
The quantum mechanics is harder than psychology

>The subject X is hard because to come up with something novel and useful is difficult
This is similar to the above, except in a field like quantum mechanics where experiments itself is difficult to obtain, and where only view people make progress, it becomes very fuzzy to compare it with a field where there's in-principle-simple studies that might still get hard to get by.

It's conceptually trivial to come up with a routine and questionaire of 100,000 people on a subject and do the statistical evaluation - but if you look at e.g. nutrition papers, it's evident that even those researchers usually only ever manage to run their study on 50 people.

Is it "hard" to do a nutrition experiment with 100,000 people?
It's BOTH basically trivial as well as basically impossible to do.

>The subject X is hard because it's hard to make a case for something that will not be overhauled in a decade
This is where he tries to make a point - if the ontology of a subject is variable and dependencies of results are highly multi-dimensional, it's basically impossible to make universal cases. So the subject is "hard" in the sense of coming up with the perfect theory (in the sense that Newton's theory is perfectly effective on its scale) is not feasible.

cont.

and sure, you could argue that a lot of overhead is left implicit there.
But a lot of overhead is left implicit always.
E.g. you can't prove
[math] \sum_{k=2}^\infty (1/k) = 1 [/math]
from Peano arithmetic, since for that infinite sum people use a limit, defined in terms of the norm on the reals, defined as equivalent classes of infinite sequences of rationals, which are themselves defined as equivalent class of pairs of naturals, which are need large cardinal axioms (if you want to call Inf one) as well as collection axioms in set theory

Algebraically closed fields were a mistake.