# Been AFK

I have not been well so I wan't able to blog or do much work on math recently.

Today I got sad because I desperately want to do programming and be involved in coding stuff but my RSI problem stops me. I had to stop programming to stop being in pain. I feel like I can't do programming again or I'll hurt again and being in pain caused me a lot of anguish that I'm not able to cope with.

Games too. A couple of days ago I tried playing a game for just about an hour maybe - pain for 2 days after. It just makes me feel terrible that I can't enjoy myself.

So I searched around a bit (again) for more information about resolving RSI. I've been doing weights a little bit recently. Now I've started doing reverse-flights which seem like a good idea. Strengthening and shoulder related stuff is promising.

In particular the mental aspect of it. It seems like stress can result in physical deprivation of oxygen to muscles, this can atrophy the muscles and result in pain. That is the theory, I hope this isn't just a seductive idea and will really help me out.

# Bigger mites

the book mites have gotten bigger, maybe it's a different type of creature entirely. Anyway they're horrible and I don't want them there so I've got a dehumidifier now. It's pulling a lot of moisture out of the air which I find fascinating. Hopefully this will put an end to the bug problem.

# Random math stuff

I learned a cool fact about constructive math. There is a thing where you double negative a constructive logic formula to get a classical logic one - what I learned was that this actually only applies to propositional statements. ~~(forall P, P \/ ~P) is in fact not provable.

You can show that propositional logic formula such as Pierces law are not constructively provable using semantics arguments, but this only applies to first order logic. I wonder how to prove that the ~~LEM formula above is not provable?

Really nice bit about monogenic/power basis' for rings of integers or math overflow:

Oh yeah so where was I in Reid, I did Noether normalization which I would say shows that a f.g. ring ext. has the structure of a trancendental ext. followed by an integral one.

After that I struggled with some good problems, the most important one is: Let $A \subset B$ be a ring extension and $P$ a maximal prime ideal of $A$. Then we can show there is a prime ideal $Q$ of $B$ satisfying "aboveness" $Q \cap A = P$.

This was a nice application of Nakayama's lemma. You also don't need maximality, but I do - too hard to prove without out. More is true: There are a finitely amount of these $Q$ under general conditions.

After this chapter 5 is some algebraic geometry stuff, I'm skipping that but then I got a bit disinterested in the book. Next is localization, primary decomposition and then DVRs. So I think I will just keep on with it. Let's do the last 3 chapters and I can be pleased with my accomplishment and continue algebraic number theory.

I certainly have been learning good material from it and it's an enjoyable book. I just needed a break. Brushed up on modules more too, I also got some practice with short exact sequences. It's been good.