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Apr
8
revised Expected Value of Flips Until HT Consecutively
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Apr
8
revised Expected Value of Flips Until HT Consecutively
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Mar
18
comment How to study math to really understand it and have a healthy lifestyle with free time?
@user21820 But if that's the standard we want to use, then the same is true for mathematics or statistics as well. Most of that work takes place in companies, defense labs, and R&D consulting firms who are notorious for only going after low-risk demo-ware. As a machine learning professional, I've seen this both with software and with formal math time and again, especially in mathematical finance. Why try fancier learning algorithms if simple OLS will get something (crappy) out the door right now? So if that is the criticism, then it applies just as well to math too.
Mar
14
awarded  Yearling
Feb
23
comment Examples of non-Riemann integrable functions that appear “in nature”?
@JohnDonn Yeah, that's too bad. Once you do have enough points you should click on my user name to see other questions that I have answered and down vote those too, much as you seem to have followed me from the question about whether software abstraction is "mathematical" to this. If you follow me and downvote more, I may have to report it to a moderator. On this question though, I welcome a downvote. After reading your comment, which is correct, I still don't believe it applies at all to my answer or the original question. When you can, you should signal your disagreement with a down vote.
Feb
23
comment Examples of non-Riemann integrable functions that appear “in nature”?
Well then it depends on what you mean. If you mean that because Brownian motion is continuous w.p. 1, and can derive a technical definition of the random-variable-valued "thing" that "is equal" to its "integral" ... then sure, that pedantic definition satisfies. That's clearly a very different thing than what the question is asking about, which is for examples where an attempt to do a naive Riemann integration leads to an unusual outcome that doesn't have the same properties of a conventional integral. Brownian motion certainly counts for that: what's the derivative of the integral of B_t?
Feb
23
comment Examples of non-Riemann integrable functions that appear “in nature”?
Which type of integrability are you talking about? Riemann? Lebesgue? Lebesgue-Stieltjes? Ito? Stratanovich? Henstock-Kurzweil? ... be specific.
Feb
21
comment How to study math to really understand it and have a healthy lifestyle with free time?
@JohnDonn You've clearly never done software engineering. One of the core concepts in all of software engineering is to create abstractions that explicitly prevent manual implementation. Even apart from that, you've got things like functional programming with e.g. Haskell, which is essentially a manifestation of category theory and how to solve practical problems with it.
Dec
24
comment Easy example why complex numbers are cool
What definition of "cool" are we using here?
Dec
19
awarded  Caucus
Dec
19
awarded  Constituent
Oct
23
awarded  Quorum
Sep
26
answered Expected Value of Flips Until HT Consecutively
Sep
24
awarded  Autobiographer
Mar
14
awarded  Yearling
Jan
27
revised Examples of non-Riemann integrable functions that appear “in nature”?
added 86 characters in body
Jan
27
revised Examples of non-Riemann integrable functions that appear “in nature”?
added 86 characters in body
Jan
27
answered Examples of non-Riemann integrable functions that appear “in nature”?
Jan
14
comment Splitting a sandwich and not feeling deceived
Thus, anyone cutting pieces has an incentive to make sure the worst off piece is at least good enough that whoever randomly draws it will decide to keep it, so that everyone gets to keep theirs too. My guess is this leads to some Nash equilibrium kind of thing where making equal cuts leads to the highest expected value.
Jan
14
comment Splitting a sandwich and not feeling deceived
I wonder if anyone has ever looked into a Dictator Game-based stochastic variation. In experiments with things like Dictator Game, people tend to reject unfair offers, even if it makes them uniformly worse off. That is, they are usually willing to pay some "fairness premium" and simply deny any form of splitting the resources unless they are equal to or better than all of the other players. If we assume humans will use this heuristic, then we could take any N pieces of a divided sandwich and randomly assign them to people in a Dictator Game, where the "worst-off" person is the dictator.