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Re: [math-fun] Deep learning v deep positions
by Guy Haworth 27 Jul '18

27 Jul '18

I didn't see the start of this thread so don't know if it's just about Go or just about Alpha<x>. However, we have the advent of chess engines which rely more (than traditionally) on intelligent rather than deep search. Neural networks are challenging traditional 'alpha-beta cut-off' search, not just with AlphaZero but with LeelaChess and one other engine, making its first appearance in TCEC, Season 13. TCEC13, http://tcec.chessdom.com/live.php , should have kicked off on or before August 3rd according to my latest advice. The two engines above will be using 2x GTX 1080ti GPUs but not Google's TPUs. The improving LeelaChess may arguably be 'better than human' at chess but has not yet been competitive with TCEC engines in its lowest division. g

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Re: [math-fun] Is zero “weakly positive”?
by Dan Asimov 27 Jul '18

27 Jul '18

"We" *who* says that? I don't recall hearing it. ----- we sometimes say that a is strictly positive as a way of saying a>0 ----- —Dan

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Re: [math-fun] Equation plotter
by Dan Asimov 26 Jul '18

26 Jul '18

So little time, so many solutions. —Dan ----- ... but x = x throws it for a loop. -----

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[math-fun] Equation plotter
by David Wilson 26 Jul '18

26 Jul '18

Just so you knows, I get a lot of mileage out of this on-line equation plotter: http://www.cs.cornell.edu/w8/~andru/relplot/

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[math-fun] Machinoid π formulas
by Bill Gosper 26 Jul '18

26 Jul '18

Fooling with pslq (again) In[1209]:= 3 ArcTan[1/7] + 2 ArcTan[2/11] // FullSimplify (or ArcTan[1/5.5]) Out[1209]=π/4 Holy cow! Isn't that slightly better (at least for a true binary computation) than In[1208]:= 4 ArcTan[1/5] - ArcTan[1/239] // FullSimplify Out[1208]= π/4 with which all the old decimalization records were set? Then I stumbled upon In[1210]:= 5 ArcTan[1/7] + 2 ArcTan[3/79] // FullSimplify Out[1210]=π/4 (in http://www.cs.utsa.edu/~wagner/pi/ruby/pi_atan.html ) Euler was inhuman. I suspect the adherence to Machin was because, even on binary machines, people did the whole computation base 10^10 to avoid a big conversion later. Decimal. Feh. --rwg

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[math-fun] photomath
by Thane Plambeck 25 Jul '18

25 Jul '18

i suppose i'm last person to know about this, but .... i wrote this on an index card https://www.flickr.com/photos/thane/28755638457/in/dateposted-public/ then took a photo of it using an iphone app i just installed called photomath and got this (fragment of a) detailed solution in less than a second https://www.flickr.com/photos/thane/41835897350/in/dateposted-public/ don't ask me what this thing can do....i just heard about it just now. -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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[math-fun] was: 3D printers & musical instruments; now is: formerly 3D printers & musical instruments
by Dan Asimov 25 Jul '18

25 Jul '18

----- Airplanes don't have feathers. ----- It's interesting that, mathematically, this is just the dual of ----- Down pillows don't fly. ----- —Dan

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Re: [math-fun] 3D printers & musical instruments
by hbaker1 25 Jul '18

25 Jul '18

I like your idea of a "smart string"! The three lower strings of a violin are typically "wound" with metal, while the highest string ("E") is typically a single wire. It would be easy to incorporate a fiber optic fiber into the core of a string, and utilize this to sense various aspects of the string, and also provide a communications medium to transmit this information to a controller at either the peg or the "tail" attachments. As long as you have control over the tension of the string, one could change this tension on a second-by-second basis, or even within a cycle of the vibration of the string itself. Current rock guitars have a lever to change the tension of *all* of the strings simultaneously, but a more sophisticated system would provide individualized control of each string. If you're ever in L.A., be sure to visit the top floor of the Nethercutt auto museum in Sylmar; it has the most amazing collection of mechanical musical instruments. (It's also a great collection of interesting cars, unlike the Peterson museum which is a collection of so-so cars previously owned by interesting people.) http://www.nethercuttcollection.org/ -----Original Message----- >From: Hilarie Orman <ho(a)alum.mit.edu> >Sent: Jul 24, 2018 11:10 PM >To: math-fun(a)mailman.xmission.com >Subject: Re: [math-fun] 3D printers & musical instruments > >Interesting idea. It is necessary for the adjustment mechanism to be fairly >small and lightweight. How about a "smart string"? > >The sensing of the tone has to be done some distance from the instrument, >so I foresee a phone app for that. Bluetooth comms to the string molecules. >On command from the conductor (the orchestra leader, not the electrical wiring). >Imagine tuning the entire string section in one second! > >Hilarie > >Harmoniously, on Tue, 24 Jul 2018 at 20:51:53 -0700 (GMT-07:00) hbaker1 intoned: > >> It also occurred to me that one could build a "smart" >> tuning "peg" for stringed instruments that would measure the >> tuning of that particular string and adjust itself to always >> be in proper tune. > >> While tuning for 4 strings isn't that much work, keeping a >> piano constantly in tune might be a significant advantage. > >> I don't know the going rate for piano tuning, but it isn't >> cheap, but it is amazingly difficult to schedule if you've >> got an upcoming concert. > >> -----Original Message----- >> >From: Hilarie Orman <ho(a)alum.mit.edu> >> >Sent: Jul 24, 2018 4:30 PM >> >To: math-fun(a)mailman.xmission.com >> >Subject: Re: [math-fun] 3D printers & musical instruments >> > >> >There are 3D printed violins, but they are indeed too heavy. There >> >are electric violins with lovely 3D printed pieces, and there is some >> >hope for customizing such instruments to the anatomy of the artist, >> >and that might be worth the cost of the instrument (for jazz or >> >country musicians). >> > >> >Let me note (a 441 A) in passing that the mystique of a Strad is >> >largely due to marketing hype from a couple of hundred years ago. >> >Yes, they are generally very good instruments, but they have been >> >modified from their original construction to meet modern demands (and >> >to repair them from sometimes awful injuries!). Newly minted >> >instruments from a master luthier can sound equally good. >> > >> >In considering design alternatives based on "aesthetics", it is >> >important to consider the artist as part of that. The instrument must >> >respond to control by the artist, it must be predictable, it must have >> >a range of dimensions and an intuitive interface with tactile >> >feedback. I think that this might be achieved with nanomaterials and >> >active control. I've no idea how to do this, nor if it amounts to >> >"reinvent wood." >> > >> >Hilarie >> > >> >On Mon, 16 Jul 2018 at 09:22:19 -0400 Richard Howard contended: >> > >> >> Airplanes don't have feathers. >> >> Given 3D printing and full acoustic simulation, why would you make a >> >> "violin". >> >> That design came from another set of constraints (properties of wood, >> >> available configuration tools, etc.). >> >> New instrument would be based on other constraints, which could use >> >> principles of aesthetics. >> > >> >> --R >> > >> >> On Mon, Jul 16, 2018 at 3:34 AM, Simon Plouffe <simon.plouffe(a)gmail.com> wrote: >> > >> >> > Ã¢ÂÂHello, >> >> > >> >> > they made one experiment once to make a violin >> >> > from scratch using a design based on acoustic and >> >> > physics only, they actually Ã¢ÂÂsucceeded in making one, >> >> > the sound was good, even comparable to a Stradivarius, >> >> > it worked, the only thing is that the violin was ugly. >> >> > The article was on Scientific American a long time ago. >> >> > >> >> > I think that 3D printing is about the same, we probably >> >> > could print a violin, it could also sound pretty good, >> >> > but it won't replace the look and feel and lightness of >> >> > a wooden real model. Does anybody ever saw the film >> >> > : The Red Violin ? >> >> > >> >> > Best regards, >> >> > Simon Plouffe

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Re: [math-fun] 3D printers & musical instruments
by hbaker1 25 Jul '18

25 Jul '18

It also occurred to me that one could build a "smart" tuning "peg" for stringed instruments that would measure the tuning of that particular string and adjust itself to always be in proper tune. While tuning for 4 strings isn't that much work, keeping a piano constantly in tune might be a significant advantage. I don't know the going rate for piano tuning, but it isn't cheap, but it is amazingly difficult to schedule if you've got an upcoming concert. -----Original Message----- >From: Hilarie Orman <ho(a)alum.mit.edu> >Sent: Jul 24, 2018 4:30 PM >To: math-fun(a)mailman.xmission.com >Subject: Re: [math-fun] 3D printers & musical instruments > >There are 3D printed violins, but they are indeed too heavy. There >are electric violins with lovely 3D printed pieces, and there is some >hope for customizing such instruments to the anatomy of the artist, >and that might be worth the cost of the instrument (for jazz or >country musicians). > >Let me note (a 441 A) in passing that the mystique of a Strad is >largely due to marketing hype from a couple of hundred years ago. >Yes, they are generally very good instruments, but they have been >modified from their original construction to meet modern demands (and >to repair them from sometimes awful injuries!). Newly minted >instruments from a master luthier can sound equally good. > >In considering design alternatives based on "aesthetics", it is >important to consider the artist as part of that. The instrument must >respond to control by the artist, it must be predictable, it must have >a range of dimensions and an intuitive interface with tactile >feedback. I think that this might be achieved with nanomaterials and >active control. I've no idea how to do this, nor if it amounts to >"reinvent wood." > >Hilarie > >On Mon, 16 Jul 2018 at 09:22:19 -0400 Richard Howard contended: > >> Airplanes don't have feathers. >> Given 3D printing and full acoustic simulation, why would you make a >> "violin". >> That design came from another set of constraints (properties of wood, >> available configuration tools, etc.). >> New instrument would be based on other constraints, which could use >> principles of aesthetics. > >> --R > >> On Mon, Jul 16, 2018 at 3:34 AM, Simon Plouffe <simon.plouffe(a)gmail.com> wrote: > >> > âHello, >> > >> > they made one experiment once to make a violin >> > from scratch using a design based on acoustic and >> > physics only, they actually âsucceeded in making one, >> > the sound was good, even comparable to a Stradivarius, >> > it worked, the only thing is that the violin was ugly. >> > The article was on Scientific American a long time ago. >> > >> > I think that 3D printing is about the same, we probably >> > could print a violin, it could also sound pretty good, >> > but it won't replace the look and feel and lightness of >> > a wooden real model. Does anybody ever saw the film >> > : The Red Violin ? >> > >> > Best regards, >> > Simon Plouffe

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[math-fun] Setting records
by Keith F. Lynch 24 Jul '18

24 Jul '18

Dan Asimov <dasimov(a)earthlink.net> wrote: > E.g., is this asking what the expected number of records will be, > before record-keeping began and assuming no knowledge of new records > after they are made? Looks that way. Sorry if I was unclear. There are lots of records, such as hottest recorded July 24th in <your city>. If you look forwards from the beginning of record keeping, there's a 100% chance that the first July 24th will be the hottest ever officially recorded (and the coldest), a 50% chance that the second year's July 24th will be the hottest ever recorded, a 33.3% chance that the third year's July 24th will be the hottest ever recorded, etc. So after N years you'd expect to have set about log(N) such records. (I can never remember whether you're supposed to add or subtract Euler's Constant to get the harmonic sum, so I round that constant to zero. :-) ) If, by contrast, you look backwards from the present, there's always just one hottest July 24th ever recorded, and, assuming no climate change, it's equally likely to be on any of the years since record keeping began. Since there are more days in a year than there are years since record keeping began, it's unusual for the current year not to contain at least one hottest recorded <some date>, and at least one coldest recorded <some other date>. Eventually, of course, weather records will have been kept for eons, and it will be very rare to set a new record. (Assuming, even less plausibly over geological time scales, that there's no climate change. Record cold days will probably be especially unusual after the sun enters its red giant stage.) > Many real-world records, like fastest marathon > (https://en.wikipedia.org/wiki/Marathon_world_record_progression#Men) > show periods of steady, almost differentiable growth over the years, > but also have plenty of what look like discontinuities. I suspect the discontinuities in marathon records are due to sudden improvements in technique and equipment. Similarly with all other human accomplishments. On the other hand, the literally exponential improvements in the number of known decimal digits of pi have been fairly smooth over the past 70 years or so: 10^1 1400 10^2 1706 306 10^3 1949 243 10^4 1958 9 10^5 1961 3 10^6 1973 12 10^7 1983 10 10^8 1987 4 10^9 1989 2 10^10 1997 8 10^11 1999 2 10^12 2002 3 10^13 2011 9

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