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Thank you for writing up your insights.

You cannot change and yet remain the same, though this is what most people want.

--Patrick J. MacDonald

I'm studying K-theory using Atiyah's book. A partner would be welcome. Required background is some familiarity with vector spaces and vector bundles, some familiarity with topology, and very basic knowledge of groups. It is a very good introduction for universal properties.

Attractiveness: Health and fitness are effective at getting the attention of others.

In Newcomb's problem, the affect on your behavior doesn't come from Omega's simulation function. Your behavior is modified by the information that Omega is simulating you. This information is either independent or dependent on the simulation function. If it is independent, this is not a side effect of the simulation function. If it is dependent, we can model this as an explicit effect of the simulation function.

While we can view the change in your behavior as a side effect, we don't need to. This article does not convince me that there is a benefit to viewing it as a side effect.

Of my two friends who I talk the most math with, I explain to one of them with examples and the other with general statements. I don't know why it helps, I just know from experience that I have to give examples to one and general statements to the other.

It reminds me of the witch powers from Alicorn's Twilight fanfic. Some witches have power over the same thing, experienced through different senses.

Such witches were especially powerful working in pairs. I wonder if there's anything special about collaborations between example thinkers and general thinkers? I'm an example thinker, and with my general thinker friend, a common pattern is that he'll conjecture, and I'll search for counterexamples.

Another example is that Saharon Shelah, perhaps the most accomplished living set theorist/logician, is known to disdain examples. Here's one expression of his view:

I have always felt that examples usually just confuse you (though not always), having always specific properties that are traps as they do not hold in general.

My opinion is that Grothendieck, Kontsevich and Shelah are not fooling themselves, but their advice is wrong for most people who are not them. Personally, I'm annoyed at myself at not remembering more often to approach unfamiliar claims through small and simple examples. Whenever I do, I end up understanding the general claim more clearly, nonwithstanding the warning about the specific properties of examples. When I do not, I often end up feeling as if I'm in a fog, grasping perhaps the literal meaning of the claim but not being able to see its significance or what it implies.

Perhaps those exceptional people who dislike examples (and I don't think that this view is typical among even the most accomplished mathematicians) get that clarity of understanding from the claim itself, and don't need to unfog their brain through looking at examples. I could believe that in the case of Shelah, anyhow. I took his advanced course in set theory once, a long time ago. It was the closest I've ever come in my life to feeling that I've encountered not just someone much smarter than me, but a truly superior intellect from a whole different level. His atomic inferential step was unbelievably wide - that is, he (genuinely and humbly, without any attempt at showing-off) saw as an immediate consequence something it took a hard effort of several minutes for others to work through, again and again. It was incredible to watch, and I've never seen anything like that with any other mathematician.

Read.

Read everything, even if you don't understand it. Read the words and symbols until that item is boring, them read another. At this stage, it barely even matters what you are reading. There is no teacher that can show you everything that there is to know, but strong reading skills will help you discover anything.

The most charitable interpretation would just be that there happened to be a convincing technical theory which said you should two-box, because it took an even more technical theory to explain why you should one-box and this was not constructed, along with the rest of the edifice to explain what one-boxing means in terms of epistemic models, concepts of instrumental rationality, the relation to traditional philosophy's 'free will problem', etcetera. In other words, they simply bad-lucked onto an edifice of persuasive, technical, but ultimately incorrect argument.

We could guess other motives for people to two-box, like memetic pressure for partial counterintuitiveness, but why go to that effort now? Better TDT writeups are on the way, and eventually we'll get to see what the field says about the improved TDT writeups. If it's important to know what other hidden motives might be at work, we'll have a better idea after we negate the usually-stated motive of, "The only good technical theory we have says you should two-box." Perhaps the field will experience a large conversion once presented with a good enough writeup and then we'll know there weren't any other significant motives.

There is an ambiguity in your question. Do you want to learn mathematical techniques or do you wish to learn mathematics? If it is the former, Badger's comment has some good recommendations. If it is the latter, then you just need to examine the patterns that interest you. There is an unfortunate gap between courses in mathematical techniques and the process of mathematics.

While there are many ways of approaching mathematics. I am a big fan of asking "why" of every assumption. Why must the pattern be like this? What happens if it is NOT like this? This method is great practice for identifying conclusions.