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This was a useful article. Consider making it easier to find by submitting it to the main blog.

Thank you for writing up your insights.

Changing while remaining the same is what Algebra is all about. Identify the quality you wish to hold invariant, then find the transformations that do so. Changing things while leaving them the same in important ways is how problems are solved.

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.

Speaking as a abstract thinker, examples itch. I can't work with someone throwing out examples on an idea I'm not fully clear about. The examples are too irritating for me to maintain my attention on the problem and I get stuck shooting down the parts of the examples that are too specific. I've learned to tolerate examples as a check, but I am not be able to work too deeply with example oriented thinkers.

Be careful about using these wide inferential steps as an example. It is much easier to see certain consequences from a model than it is to prove consequences generated by a different model. It is a much better idea to practice deriving a (possibly different) set of consequences from a result you are comfortable with. This will give you a better idea of his intellect. Leading mathematicians often seem so much farther ahead than others because they are less constrained by the paths of other people.


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.

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