June 2014 - mathfun@mailman.xmission.com

[math-fun] about the space shuttle and gliding of a large aircraft
by Simon Plouffe 11 Jun '14

11 Jun '14

Hello, as every body knows, the space shuttle is gliding its way down to the earth (well is used to be), it goes at a speed of thousands of kilometres per hour and what baffles me is the fact that despite the tremendous speed it touches the ground very gently, like 'tip toes in the tulips' as tiny tim used to say. Then : why is it that modern airplanes are not using the same trick to get to the airport ??? without using any gas, Is there something I am missing here ? I know that an airplane can glide a little and also that if it is the case has little manoeuvring (spelling) power , but still , why does airplanes uses a lot of airplane fuel when actually they just have to glide to the airport ??? If you know the answer to this profound aerodynamic puzzle I will be glad to ear it. Best regards and bonne soirÃ©e, Simon plouffe

3 2

[math-fun] Holy cow, I found the equation for melanoma.
by Bill Gosper 11 Jun '14

11 Jun '14

gosper.org/melanoma.png Plot3D[-Log[Abs[-((I EllipticTheta[2, 0, I E^(I t) r])/Sqrt[2]) + EllipticTheta[2, 0, E^(I t) r]]], {r, .99, .9999}, {t, .78, .79}, PlotRange -> {0, 239}, PlotPoints -> 69] --rwg

2 1

Re: [math-fun] Subset-lex: did we miss an order?
by Henry Baker 11 Jun '14

11 Jun '14

"Iterators" -- at least as currently envisioned -- is one of the worst ideas to ever hit computer science. The biggest problem with iterators is that they are _stateful_, which means that formal reasoning about them is at least 10x harder than reasoning about _stateless_ constructs like recursion. The earliest use of iterators that I can find was in Doug Ross's "AED-0" (Algol Extended for Design) language. Briefly, AED's "strings" (AED name for abstract sequences) allowed for looping/iterating over various types of sequences in an sequence-independent way. AED's iterators used callback mechanisms to allow what was then known as "co-routining", but is now simply called "call-backs". AED's implementation of strings was quite similar to C++, in that each type of string had a vector of subroutine addresses to string operations. Recursion, on the other hand, keeps all of its "state" in its arguments, even when that state is in the form of an abstract data type. If your compiler understands _tail recursion_, it can trivially convert simple tail-recursive loops into traditional C/Fortran loops, so there is NO overhead for expressing yourself recursively instead of iteratively. The major problem with doing tail recursions these days is the exceedingly bad idea of forcing the compiler to keep the useless stack frames around to support a very heavyweight exception mechanism in languages like C and even Common Lisp. (This heavyweight exception mechanism for C is now the target of hacking, because the gcc exception handler has a _Turing-complete_ programming language for walking the stack ! Hackers can easily take over this mechanism to do dastardly deeds.) Iterators can be trivially emulated using function _closures_. Since function closures are far more interesting than iterators, it was silly to waste all of that research horsepower for 25-30 years on iterators, instead of going directly to the big hammer: function closures. My entire 50-year career in computer science has been spent scratching my head about the silliness involved in the design of programming languages. Every computer language starts out as "simple", but is forced to add certain features in order to support reasonable programming. Fortran didn't think recursion was necessary. Oops! C didn't implement even "downward" closures, because the Bell Labs folks thought that Algol & PL/I's lexical scoping were too complicated. Oops! C/C++ didn't implement automatic garbage collection because they thought that the programmer knew better. We now know that most programmers haven't a clue about how hard memory management is, and we've now spent in excess of $1 trillion on memory management-related bugs, including the entire computer security field. Fortran, C/C++, etc., didn't bother with array bounds checking. Perhaps 90% of software bugs have to do with array bounds violations. (I may have been the only person to actually utilize PL/I's array bounds checking code; it found innumerable bugs.) Oops! The more you study programming languages, the more you appreciate the power and elegance of the lambda-calculus. Entire decades of computer science research has gone into the understanding of the power inherent in this extremely elegant system: * lexical scoping of variables * function closures * partial application of functions * lazy evaluation of argument expressions * arbitrary recursion via the Y combinator * tail recursion via the eta rule About the only feature of the lambda calculus not normally found in modern computer languages is the lazy evaluation of argument expressions. While this feature can be partially emulated using function closures, it can still provide exceedingly elegant implementation of algorithms like "spigot" algorithms, where the print function decides how many digits of precision to output, and "sucks" these digits out of the rest of the program. At 07:37 AM 6/10/2014, Fred Lunnon wrote: > I scratched my head over this, but now I think these "iterators" must be >the same thing as loopless generators --- see > http://en.wikipedia.org/wiki/Loopless_algorithm >This topic has surfaced previously on math-fun, with respect to various >combinatorial problems; two insights have arisen during my investigations. > > Firstly, that a decent object-oriented / ADT programming environment >greatly facilitates the implementation and useability of such tools. > > Secondly, recursion -- hoary standby of so many programming courses >-- and looplessness seem mutually incompatible. Converting one type of >algorithm into the other is a process which somehow should be mechanical, >but in practice always proves next to impossible in nontrivial situations. > >Fred Lunnon > >On 6/10/14, Joerg Arndt <arndt(a)jjj.de> wrote: >> I missed this message... >> >> I agree that a project "iterators" as suggested >> below appears worthwhile. The chances of adoption >> in other programs (say, Sage) appear low, however. >> >> This is way I concentrate an finding new orders >> with interesting properties instead. >> "interesting properties" would be "changes >> only at end and of bounded length" for >> these subset-lex and SL-Gray orders. >> >> It seems hard to believe that the Gray code for >> compositions isn't already known; I tried hard >> to find it in the literature, to no avail. >> >> Best regards, jj >> >> * rcs(a)xmission.com <rcs(a)xmission.com> [May 28. 2014 12:13]: >>> Once upon a time, I worked at a Lisp-based company. >>> The main technical guru had built a package of >>> "iterators" that fit into the Lisp loop sub-language. >>> Simple iterators were to count through a range, >>> to march down a list or array, and to run through >>> special sets relevant to the company. >>> >>> I later wrote a long list of iterator-combiners >>> that would take cross-products of iterations in >>> various orders, and handle instructions like >>> "next", and perhaps "previous", "skip to next row", >>> "goto position N", and so on. I never wrote any >>> actual code. >>> >>> I think this might be a worthwhile activity, >>> at least as an intellectual exercise. >>> >>> Rich

4 8

[math-fun] To express EllipticTheta[1, (2 n - 1) π/4 , q]
by Bill Gosper 10 Jun '14

10 Jun '14

(integer n) as a 𝜗 constant, I worked all morning. Out[1208]= EllipticTheta[1, 1/4 (2 n - 1) \[Pi], q] == ((-1)^(7/8) I^(n (1 + n)) EllipticTheta[2, 0, I q])/Sqrt[2] Try it: In[1209]:= Table[% /. q -> 1/2, {n, 4}] Out[1209]= {EllipticTheta[1, \[Pi]/4, 1/ 2] == -(((-1)^(7/8) EllipticTheta[2, 0, I/2])/Sqrt[2]), EllipticTheta[1, (3 \[Pi])/4, 1/ 2] == -(((-1)^(7/8) EllipticTheta[2, 0, I/2])/Sqrt[2]), EllipticTheta[1, (5 \[Pi])/4, 1/2] == ((-1)^(7/8) EllipticTheta[2, 0, I/2])/Sqrt[2], EllipticTheta[1, (7 \[Pi])/4, 1/2] == ((-1)^(7/8) EllipticTheta[2, 0, I/2])/Sqrt[2]} Mma knows squat about 𝜗. Try numbers. In[1229]:= N[%1209] Out[1229]= {False, False, False, False} AARRGGHH!! Maybe it's just a sign or something easy to fix. Change equations to lists: In[1211]:= N[%% /. Equal -> List] Out[1211]= {{0.873615, 0.873615 - 1.11022*10^-16 I}, {0.873615, 0.873615 - 1.11022*10^-16 I}, {-0.873615, -0.873615 + 1.11022*10^-16 I}, {-0.873615, -0.873615 + 1.11022*10^-16 I}} In[1230]:= Chop[%1211] Out[1230]= {{0.873615, 0.873615}, {0.873615, 0.873615}, {-0.873615, -0.873615}, {-0.873615, -0.873615}} In[1231]:= Equal @@ # & /@ % Out[1231]= {True, True, True, True} AARRGGHH!! I was right all along! Braindead Mathematica introduced spurious imaginary errors, and then screamed False before it would have been possible to Chop them! --rwg

1 0

Re: [math-fun] Subset-lex: did we miss an order?
by Fred Lunnon 10 Jun '14

10 Jun '14

I scratched my head over this, but now I think these "iterators" must be the same thing as loopless generators --- see http://en.wikipedia.org/wiki/Loopless_algorithm This topic has surfaced previously on math-fun, with respect to various combinatorial problems; two insights have arisen during my investigations. Firstly, that a decent object-oriented / ADT programming environment greatly facilitates the implementation and useability of such tools. Secondly, recursion -- hoary standby of so many programming courses -- and looplessness seem mutually incompatible. Converting one type of algorithm into the other is a process which somehow should be mechanical, but in practice always proves next to impossible in nontrivial situations. Fred Lunnon On 6/10/14, Joerg Arndt <arndt(a)jjj.de> wrote: > I missed this message... > > I agree that a project "iterators" as suggested > below appears worthwhile. The chances of adoption > in other programs (say, Sage) appear low, however. > > This is way I concentrate an finding new orders > with interesting properties instead. > "interesting properties" would be "changes > only at end and of bounded length" for > these subset-lex and SL-Gray orders. > > It seems hard to believe that the Gray code for > compositions isn't already known; I tried hard > to find it in the literature, to no avail. > > Best regards, jj > > > > * rcs(a)xmission.com <rcs(a)xmission.com> [May 28. 2014 12:13]: >> Once upon a time, I worked at a Lisp-based company. >> The main technical guru had built a package of >> "iterators" that fit into the Lisp loop sub-language. >> Simple iterators were to count through a range, >> to march down a list or array, and to run through >> special sets relevant to the company. >> >> I later wrote a long list of iterator-combiners >> that would take cross-products of iterations in >> various orders, and handle instructions like >> "next", and perhaps "previous", "skip to next row", >> "goto position N", and so on. I never wrote any >> actual code. >> >> I think this might be a worthwhile activity, >> at least as an intellectual exercise. >> >> Rich >>

3 3

[math-fun] Turing test passed? Another sucker born every minute
by Warren D Smith 10 Jun '14

10 Jun '14

Stuart Anderson: http://www.smh.com.au/digital-life/computers/super-computer-first-to-pass-t… --software emulates a 13 year old Ukrainian boy named Eugene Goostman, supposedly convinced 33% of judges he was human. Did not say how many judges interviewed him, but at most 30. I tried clicking the "try Goostman yourself" link at the bottom of the page, leading to http://www.princetonai.com/bot/ and/or http://www.princetonai.com/bot/bot.jsp and/or http://default-environment-sdqm3mrmp4.elasticbeanstalk.com/bot/ and the result was nothing, all three just hung. It was unclear from the story whether the judges spoke Ukrainian, or whether Goostman supposedly semi-knew English, or what. Somewhat more illuminating: https://en.wikipedia.org/wiki/Eugene_Goostman http://www.independent.co.uk/life-style/gadgets-and-tech/computer-becomes-f… I'm pretty sure a goodly number of the judges (maybe all) did not speak Ukrainian. Wikipedia also mentions some previous examples of "passing Turing tests" such as 2011 where Cleverbot tricked 59% of judges and 1991 where "PC Therapist" tricked 5 out of 10 judges. https://en.wikipedia.org/wiki/Cleverbot You can converse with cleverbot here: http://www.cleverbot.com/ I typed: Which is more important, death or a yellow clay brick? The answer came back: Truth. For confirmation I tried: Which is larger, a star or the statue of liberty? Answer: They are both about the same size. Game over... total elapsed time, about 15 seconds. I don't care what the newspapers say, I'm not going to believe any computer can fool me for 5 minutes until I actually experience it. Also it says Google has technology that can solve "CAPTCHA" so-called turing tests (image recognition for disguised alphanumeric characters) and also that blind people are infuriated at CAPTCHA anyhow since they have to rely on automated screen-reading software which is blocked by that.

5 5

[math-fun] Turing Test ....
by Guy Haworth 10 Jun '14

10 Jun '14

I think there's a scientific way to appraise an experiment prior to reflecting on the significance of its results. I'm not really the best person for this, but in this case: 1) Were the organisers of the experiment 'professionally neutral' about the result they wanted from the experiment, or were they hoping for one result rather than the other? If the latter, did this bias the arrangements for the experiment? 2) Which people were used as 'perceivers' and which as 'humans responding in the dialogues' and what, if any, connection did they have with the organisers? 3) were the 'humans responding in the dialogues' asked to distinguish themselves as humans as best they could, dialogue normally, or try to disguise their human nature?, 4) what was the independent invigilator actually invigilating? 5) was the successful computer program hiding behind a claimed 'junior, naïve, in second language' persona in order to max its probability of being seen as a human, albeit a limited one? The laboratory notebooks should be made available - and not in a year's time after we've all forgotten the circumstances of this experiment. And, even if the claimed result was as it appears, what is the significance of it. The Turing Test is not reckoned to be Turing's best work by any means. Guy Haworth

2 1

[math-fun] turing test passed, well sort of
by Simon Plouffe 10 Jun '14

10 Jun '14

Hello, they just announced that someone successfuly programmed a computer to pass the Turing Test, but : well, sort of : https://www.google.fr/search?q=turing+test&noj=1&source=univ&tbm=nws&tbo=u&… as far as I can tell , it did NOT passed the test. close but no cigars. Best regards, Simon Plouffe

1 0

[math-fun] Subset-lex: did we miss an order?
by Joerg Arndt 10 Jun '14

10 Jun '14

Remember those combinatorial listings I used to annoy math-funsters with? Finally I managed to write things down: http://jjj.de/tmp-subset-lex/ If anyone wants to comment, I'd be grateful. Simple, loopfree, and fast algorithms for the generation of various combinatorial objects are given. Great care has been taken to keep things accessible as much as possible. Best, jj

3 4

[math-fun] types in languages
by Warren D Smith 09 Jun '14

09 Jun '14

Well, what is wrong with just declaring the types of all the variables, dammit? Sure, maybe many of the types could be "deduced" without you declaring them, but I think forcing you to declare them clarifies thinking and makes the code easier to understand when reading it, at little cost, so this is a feature not a bug. It is like the "cast of characters" at the beginning of the script of a play. Sure, you could deduce it. Hah. And if it is really turing undecidable, then at least sometimes, it is damned hard to make the deductions, proving the necessity of My Way.

4 5