How about:

Specialization of Labor vs. Transaction/Communication costs: a trade off between having a task split between multiple people/organizations vs. done by a single person. Generalism vs.Specialization might be a more succinct way to put it.

Also, another pair that has a close connection is 3 and 7. Exploration is flexible strategy, since it leaves open resources to exploit better opportunities that turn up, while exploitation gains in commitment.

I have a question for anyone who spends a fair amount of their time thinking about math: how exactly do you do it, and why?

To specify, I've tried thinking about math in two rather distinct ways. One is verbal and involves stating terms, definitions, and the logical steps of inference I'm making in my head or out loud, as I frequently talk to myself during this process. This type of thinking is slow, but it tends to work better for actually writing proofs and when I don't yet have an intuitive understanding of the concepts involved.

The other is nonverbal and based on understanding terms, definitions, theorems, and the ways they connect to each other on an intuitive level (note: this takes a while to achieve, and I haven't always managed it) and letting my mind think it out, making logical steps of inference in my head, somewhat less consciously. This type of thinking is much faster, though it has a tendency to get derailed or stuck and produces good results less reliably.

Which of those, if any, sounds closer to the way you think about math? (Note: most of the people I've talked to about this don't polarize it quite so much and tend to do a bit of both, i.e. thinking through a proof consciously but solving potential problems that come up while writing it more intuitively. Do you also divide different types of thinking into separate processes, or use them together?)

The reason I'm asking is that I'm trying to transition to spending more of my time thinking about math not in a classroom setting and I need to figure out how I should go about it. The fast kind of thinking would be much more convenient, but it appears to have downsides that I haven't been able to study properly due to insufficient data.

The most important professions in the modern world may be the most reviled: advertiser, salesperson, lawyer, and financial trader. What these professions have in common is extending useful social interactions far beyond the tribe-sized groups we were evolved to inhabit (most often characterized by the Dunbar number). This commonly involves activities that fly in the face of our tribal moral instincts.

Nick Szabo

The theme of this book, then, must be the coming to consciousness of uncertain inference. The topic may be compared to, say, the history of visual perspective. Everyone can see in perspective, but it has been a difficult and long-drawn-out effort of humankind to become aware of the principles of perspective in order to take advantage of them and imitate nature. So it is with probability. Everyone can act so as to take a rough account of risk, but understanding the principles of probability and using them to improve performance is an immense task.

James Franklin, The Science of Conjecture: Evidence and Probability before Pascal

Yes, creating this arbitrary dichotomy keeps lieutenants from fraternizing with enlisted men. But it doesn't keep Chief Master Sergeants from fraternizing with privates or generals from fraternizing with lieutenants. So, taken merely as a way to prevent fraternization across ranks, the dichotomy is of little value.

I think that in the military, the "no fraternizing with enlisted personnel" rule might be one reason why a hard separation is useful. This kind of rule requires a cutoff and can't easily be replaced with a rule like "no fraternizing with people of a rank three or more below your own." For instance, how would you set up the housing arrangements? Also, promotions would be awkward under this system, since you would always have a group of people you previously could fraternize with but no longer can.

I think the containment of the SARS epidemic in 2003 is a under-appreciated success story. SARS spread fairly easily and had a 9% mortality rate, so it could well have killed millions, but it was contained thanks to the WHO and to the quarantine efforts of various governments. Their wasn't much coverage in the vein of "hooray! one of the worst catastrophes in human history has been averted!" afterwards.

Is there any situation that humanity could face that would make us collectively say "Yeah doing Y is right, even though it seems bad for us. But the sacrifice is too great, we aren't going to do it"

This is still probably not the question that you want to ask. Humans do incorrect things all the time, with excellent rationalizations, so "But the sacrifice is too great, we aren't going to do it" is not a particularly interesting specimen. To the extent that you think that "But the sacrifice is too great" is a relevant argument, you think that "Yeah doing Y is right" is potentially mistaken.

I guess the motivation for this post is in asking whether it is actually possible for a conclusion like that to be correct. I expect it might be, mainly because humans are not particularly optimized thingies, so it might be more valuable to use the atoms to make something else that's not significantly related to the individual humans. But again to emphasize the consequentialist issue: to the extent such judgment is correct, it's incorrect to oppose it; and to the extent it's correct to oppose it, the judgment is incorrect.

This is yet another poorly phrased, factually inaccurate post containing some unorthodox viewpoints that are unlikely to be taken seriously because people around here are vastly better at deconstructing others' arguments than fixing them for them.

Ignoring any formal and otherwise irrelevant errors such as what utilitarianism actually is, I'll try to address the crucial questions; both to make Bundle_Gerbe's viewpoints more accessible to LW members and also to make it more clear to him why they're not as obvious as he seems to think.

1: How does creating new life compare to preserving existing life in terms of utility or value?

Bundle_Gerbe seems to be of the view that they are of identical value. That's not a view I share, mostly because I don't assign any value to the creation of new life, but I must admit that I am somewhat confused (or undecided) about the value of existing human life, both in general and as a function of parameters such as remaining life expectancy. Maybe there's some kind of LW consensus I'm not aware of, but the whole issue seems like a matter of axioms to me rather than anything that could objectively be inferred from some sort of basic truth.

2: If creation of life has some positive value, does this value increase if creation is preponed?

Not a question relevant to me, but it seems that this would partly depend on whether earlier creation implied higher total amount of lives, or just earlier saturation, for example because humans live forever and ultimately the only constraints will be space. I'm not entirely certain I correctly understand Bundle_Gerbe's position on this, but it seems that his utility function is actually based on total lifetime as opposed to actual number of human lives, meaning that two humans existing for one second each would be equivalent to one human existing for two seconds. That's kind of an interesting approach with lots of implied questions, such as whether travelling at high speeds would reduce value because of relativistic effects.

3: Is sacrificing personal lifetime to increase total humanity lifetime value a good idea?

If your utility function is based on total humanity lifetime value, and you're completely altruistic, sure. Most people don't seem to be all that altruistic, though. If I had to choose between saving one or two human beings, I would choose the latter option, but I'd never sacrifice myself to save a measly two humans. I would be very suprised if CEV turned out to require my death after 20 years, and in fact I would immediately reclassify the FAI in question as UFAI. Sounds like an interesting setup for an SF story, though.

For what it's worth, I upvoted the post. Not because the case was particularly well presented, obviously, but because I think it's not completely uninteresting and because I perceived some of the comments such as Vladimir_Nesov's which got quite some upvotes as rather unfair.

That being said, the title is badly phrased while not being very relevant, either.

To the extent your question is, "Suppose X is the correct answer. Is X the correct answer?", X is the correct answer. Outside of that supposition it probably isn't.