June 2016 - mathfun@mailman.xmission.com

[math-fun] A problem about finite sets
by Victor Miller 10 Sep '16

10 Sep '16

Say that a finite set of integers, A, has *property P* is there are two non-empty disjoint subsets S and T of A, such that sum(S) = sum(T) (where sum(X) is the sum of the elements of X). 1) Show that every 10 element subset of {1,...,100} has property P (this is fairly easy). 2) Is it true that every 9 element subset of {1,...,100} has property P? Victor

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[math-fun] Congruent number question
by David Wilson 30 Jun '16

30 Jun '16

Suppose that n == 5*4^k or 6*4^k or 7*4^k (mod 8*4^k) for some k >= 0. Is it then true that n is a congruent number (n in A003273)?

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[math-fun] Instant Insanity
by James Propp 30 Jun '16

30 Jun '16

Does anyone understand the solution presented at https://en.wikipedia.org/wiki/Instant_Insanity ? (I don't.) More broadly, does anyone know of SOME way of solving the puzzle that doesn't involve a goodly amount of trial-and-error? Jim Propp

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[math-fun] Boston Polymath Society
by James Propp 29 Jun '16

29 Jun '16

Does anyone know anything about this group? Does it still exist? I may have the name slightly wrong. Jim Propp

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[math-fun] Illustrating Mathematics
by James Propp 28 Jun '16

28 Jun '16

I'll be attending an ICERM workshop on "Illustrating Mathematics" next week (https://icerm.brown.edu/topical_workshops/tw16-1-im/) though I'm not sure its aims match my needs. In writing articles and essays I spend a lot of not-very-enjoyable time handcrafting illustrations using tikz when I'd rather be using something more interactive and wysiwyg. (Anyone remember a drafting program from the 1980s called idraw, not to be confused with a newer and more famous program by that name? I still miss it.) Sometimes I use pictex, or Mathematica, but it's always a chore. Do any of you use mathematical drawing software that you actually find fun? Jim Propp

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Re: [math-fun] GBP/USD exchange rate made 12-sigma move last Friday
by Dan Asimov 28 Jun '16

28 Jun '16

What's the connection? -----Original Message----- >From: Henry Baker <hbaker1(a)pipeline.com> >Sent: Jun 27, 2016 4:10 PM >To: math-fun <math-fun(a)mailman.xmission.com> >Subject: Re: [math-fun] GBP/USD exchange rate made 12-sigma move last Friday > >I realize that the situations are very different, but construction & zoning standards rely on the concept of "100 year floods". > >https://en.wikipedia.org/wiki/100-year_flood > >I thought it was a little strange that the *probability* of the exchange >rate move would be so low when simply reaching a pre-existing *30 year low*! > >Wouldn't the zero-th order statistic indicate that a 30 year low would >likely be reached every O(30 years) ?? Jez sayin' ... > >At 02:32 PM 6/27/2016, Charles Greathouse wrote: >>Was anyone actually using the standard deviation of the previous 100 days' >>daily returns (or similar) as a risk model? I agree that this would be a >>silly model, and it's it hard to imagine that it would misrepresent the >>odds of such an event, but unless someone is using it this is just a >>strawman. >> >>On Monday, June 27, 2016, Henry Baker <hbaker1(a)pipeline.com> wrote: >> >>> FYI -- Such an event is expected to happen every 2.2516410228987967E+30 >>> YEARS, or about phi*10^20 times the current age of the universe. (Thanks, >>> Maxima). >>> >>> Oops! Time to fire some more bank regulators & helicopter some more $$$$$ >>> onto Wall Street. >>> >>> Some models may be useful, but not these. >>> >>> I'd say that the following announcement may be greeted with raspberries: >>> >>> http://www.cnbc.com/2016/06/27/us-banks-stress-tests-may-offer-comfort-in-b… >>> >>> "The stress tests created for banks by U.S. regulators after the 2008 >>> financial crisis may prove their worth this week, providing a timely >>> message on banks' hardiness in the midst of turbulence over last week's >>> vote by Britain to leave the European Union." >>> >>> "The Federal Reserve will release the second set of results from stress >>> tests it has conducted annually on large banks since 2009 on Wednesday. >>> The tests look at how strong banks would be in the event of an unforeseen >>> crisis, with economies in freefall, stock markets dropping precipitously >>> and market counterparties at risk of failure." >>> >>> "And while the stresses that the Fed is testing for in this case are >>> imagined, analysts say *the results should be reassuring to investors* >>> worried about banks' exposure to Brexit, an outcome that took the world and >>> markets by surprise." >>> >>> https://en.wikipedia.org/wiki/Age_of_the_universe >>> >>> ---- >>> >>> http://www.zerohedge.com/news/2016-06-27/these-brexit-market-moves-were-big… >>> >>> "However, on Friday various markets saw volatile moves that put 2008 in >>> the dust: in fact, the historic collapse in GBPUSD was not only far greater >>> than any such move seen in history, but was an unprecedented 12-sigma move." >>> >>> "A Ten Sigma event happens in one day out of 524,900,000,000,000,000,000 >>> YEARS >>> >>> "A Fifteen Sigma event happens in one day out of >>> 3,671,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 YEARS >>> >>> "A Twelve Sigma Event is somewhere in between. >>> >>> https://arxiv.org/ftp/arxiv/papers/1103/1103.5672.pdf >>> >>> "The Universe is supposedly 15,000,000,000 YEARS old for comparison's >>> sake." >> >>-- >>Charles Greathouse >>Case Western Reserve University > > >_______________________________________________ >math-fun mailing list >math-fun(a)mailman.xmission.com >https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Re: [math-fun] GBP/USD exchange rate made 12-sigma move last Friday
by Henry Baker 27 Jun '16

27 Jun '16

I realize that the situations are very different, but construction & zoning standards rely on the concept of "100 year floods". https://en.wikipedia.org/wiki/100-year_flood I thought it was a little strange that the *probability* of the exchange rate move would be so low when simply reaching a pre-existing *30 year low*! Wouldn't the zero-th order statistic indicate that a 30 year low would likely be reached every O(30 years) ?? Jez sayin' ... At 02:32 PM 6/27/2016, Charles Greathouse wrote: >Was anyone actually using the standard deviation of the previous 100 days' >daily returns (or similar) as a risk model? I agree that this would be a >silly model, and it's it hard to imagine that it would misrepresent the >odds of such an event, but unless someone is using it this is just a >strawman. > >On Monday, June 27, 2016, Henry Baker <hbaker1(a)pipeline.com> wrote: > >> FYI -- Such an event is expected to happen every 2.2516410228987967E+30 >> YEARS, or about phi*10^20 times the current age of the universe. (Thanks, >> Maxima). >> >> Oops! Time to fire some more bank regulators & helicopter some more $$$$$ >> onto Wall Street. >> >> Some models may be useful, but not these. >> >> I'd say that the following announcement may be greeted with raspberries: >> >> http://www.cnbc.com/2016/06/27/us-banks-stress-tests-may-offer-comfort-in-b… >> >> "The stress tests created for banks by U.S. regulators after the 2008 >> financial crisis may prove their worth this week, providing a timely >> message on banks' hardiness in the midst of turbulence over last week's >> vote by Britain to leave the European Union." >> >> "The Federal Reserve will release the second set of results from stress >> tests it has conducted annually on large banks since 2009 on Wednesday. >> The tests look at how strong banks would be in the event of an unforeseen >> crisis, with economies in freefall, stock markets dropping precipitously >> and market counterparties at risk of failure." >> >> "And while the stresses that the Fed is testing for in this case are >> imagined, analysts say *the results should be reassuring to investors* >> worried about banks' exposure to Brexit, an outcome that took the world and >> markets by surprise." >> >> https://en.wikipedia.org/wiki/Age_of_the_universe >> >> ---- >> >> http://www.zerohedge.com/news/2016-06-27/these-brexit-market-moves-were-big… >> >> "However, on Friday various markets saw volatile moves that put 2008 in >> the dust: in fact, the historic collapse in GBPUSD was not only far greater >> than any such move seen in history, but was an unprecedented 12-sigma move." >> >> "A Ten Sigma event happens in one day out of 524,900,000,000,000,000,000 >> YEARS >> >> "A Fifteen Sigma event happens in one day out of >> 3,671,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 YEARS >> >> "A Twelve Sigma Event is somewhere in between. >> >> https://arxiv.org/ftp/arxiv/papers/1103/1103.5672.pdf >> >> "The Universe is supposedly 15,000,000,000 YEARS old for comparison's >> sake." > >-- >Charles Greathouse >Case Western Reserve University

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Re: [math-fun] GBP/USD exchange rate made 12-sigma move last Friday
by Dan Asimov 27 Jun '16

27 Jun '16

There is no fully satisfactory way to apply probability theory to the real world, because our estimate of probabilities depends on assumptions that are often likely to be untrue in the real world. So we cannot say that an incredibly unlikely event just happened; all we can say is that we misunderestimated the probability. —Dan -----Original Message----- >From: Charles Greathouse <charles.greathouse(a)case.edu> >Sent: Jun 27, 2016 2:32 PM >To: math-fun <math-fun(a)mailman.xmission.com> >Subject: Re: [math-fun] GBP/USD exchange rate made 12-sigma move last Friday > >Was anyone actually using the standard deviation of the previous 100 days' >daily returns (or similar) as a risk model? I agree that this would be a >silly model, and it's it hard to imagine that it would misrepresent the >odds of such an event, but unless someone is using it this is just a >strawman. > >On Monday, June 27, 2016, Henry Baker <hbaker1(a)pipeline.com> wrote: > >> FYI -- Such an event is expected to happen every 2.2516410228987967E+30 >> YEARS, or about phi*10^20 times the current age of the universe. (Thanks, >> Maxima). >> >> Oops! Time to fire some more bank regulators & helicopter some more $$$$$ >> onto Wall Street. >> >> Some models may be useful, but not these. >> >> I'd say that the following announcement may be greeted with raspberries: >> >> >> http://www.cnbc.com/2016/06/27/us-banks-stress-tests-may-offer-comfort-in-b… >> >> "The stress tests created for banks by U.S. regulators after the 2008 >> financial crisis may prove their worth this week, providing a timely >> message on banks' hardiness in the midst of turbulence over last week's >> vote by Britain to leave the European Union." >> >> "The Federal Reserve will release the second set of results from stress >> tests it has conducted annually on large banks since 2009 on Wednesday. >> The tests look at how strong banks would be in the event of an unforeseen >> crisis, with economies in freefall, stock markets dropping precipitously >> and market counterparties at risk of failure." >> >> "And while the stresses that the Fed is testing for in this case are >> imagined, analysts say *the results should be reassuring to investors* >> worried about banks' exposure to Brexit, an outcome that took the world and >> markets by surprise." >> >> https://en.wikipedia.org/wiki/Age_of_the_universe >> >> ---- >> >> http://www.zerohedge.com/news/2016-06-27/these-brexit-market-moves-were-big… >> >> "However, on Friday various markets saw volatile moves that put 2008 in >> the dust: in fact, the historic collapse in GBPUSD was not only far greater >> than any such move seen in history, but was an unprecedented 12-sigma move." >> >> "A Ten Sigma event happens in one day out of 524,900,000,000,000,000,000 >> YEARS >> >> "A Fifteen Sigma event happens in one day out of >> 3,671,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 YEARS >> >> "A Twelve Sigma Event is somewhere in between. >> >> https://arxiv.org/ftp/arxiv/papers/1103/1103.5672.pdf >> >> "The Universe is supposedly 15,000,000,000 YEARS old for comparison's >> sake." >> >> >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com <javascript:;> >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> > > >-- >Charles Greathouse >Case Western Reserve University >_______________________________________________ >math-fun mailing list >math-fun(a)mailman.xmission.com >https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] GBP/USD exchange rate made 12-sigma move last Friday
by Henry Baker 27 Jun '16

27 Jun '16

FYI -- Such an event is expected to happen every 2.2516410228987967E+30 YEARS, or about phi*10^20 times the current age of the universe. (Thanks, Maxima). Oops! Time to fire some more bank regulators & helicopter some more $$$$$ onto Wall Street. Some models may be useful, but not these. I'd say that the following announcement may be greeted with raspberries: http://www.cnbc.com/2016/06/27/us-banks-stress-tests-may-offer-comfort-in-b… "The stress tests created for banks by U.S. regulators after the 2008 financial crisis may prove their worth this week, providing a timely message on banks' hardiness in the midst of turbulence over last week's vote by Britain to leave the European Union." "The Federal Reserve will release the second set of results from stress tests it has conducted annually on large banks since 2009 on Wednesday. The tests look at how strong banks would be in the event of an unforeseen crisis, with economies in freefall, stock markets dropping precipitously and market counterparties at risk of failure." "And while the stresses that the Fed is testing for in this case are imagined, analysts say *the results should be reassuring to investors* worried about banks' exposure to Brexit, an outcome that took the world and markets by surprise." https://en.wikipedia.org/wiki/Age_of_the_universe ---- http://www.zerohedge.com/news/2016-06-27/these-brexit-market-moves-were-big… "However, on Friday various markets saw volatile moves that put 2008 in the dust: in fact, the historic collapse in GBPUSD was not only far greater than any such move seen in history, but was an unprecedented 12-sigma move." "A Ten Sigma event happens in one day out of 524,900,000,000,000,000,000 YEARS "A Fifteen Sigma event happens in one day out of 3,671,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 YEARS "A Twelve Sigma Event is somewhere in between. https://arxiv.org/ftp/arxiv/papers/1103/1103.5672.pdf "The Universe is supposedly 15,000,000,000 YEARS old for comparison's sake."

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[math-fun] Erase, rebuild
by Eric Angelini 26 Jun '16

26 Jun '16

Hello MathFun, Do you like numbers? If two terms hereunder, placed one after the other, sum up to a prime, erase them. The non-erased terms will rebuild the starting sequence: Two, three, six, seven, two, seven, six, three, six, three, two, seven, two, seven, two, three, six, three, six, three, six, seven, two, seven, two, seven, two, seven, six, three, six, three, six, three, six, three, two, seven, two, seven, two, seven, two, seven, two, three, six, three, six, three, six, three, six, three, six, seven, two, seven, two, seven, two, seven, two, seven, two, seven, six, three, six, three, six, three, six, three, six, three, six, three, two, ... (Two, three), (six, seven), two, (seven, six), three, six, (three, two), seven, two, seven, (two, three), six, three, six, three, (six, seven), two, seven, two, seven, two, (seven, six), three, six, three, six, three, six, (three, two), seven, two, seven, two, seven, two, seven, (two, three), six, three, six, three, six, three, six, three, (six, seven), two, seven, two, seven, two, seven, two, seven, two, (seven, six), three, six, three, six, three, six, three, six, three, six, (three, two), ... Do you prefer letters? If two terms above, placed one after the other, share a letter, erase them. The non-erased terms will rebuild the starting sequence. Question: is this the lexicographically first such sequence? Best, É.

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