Wednesday 29 November 2017

Toomas Karmo: Part S: Philosophy of Perception, Action, and "Subjectivity"

Quality assessment:

On the 5-point scale current in Estonia, and surely in nearby nations, and familiar to observers of the academic arrangements of the late, unlamented, Union of Soviet Socialist Republics (applying the easy and lax standards Kmo deploys in his grubby imaginary "Aleksandr Stepanovitsh Popovi nimeline sangarliku raadio instituut" (the "Alexandr Stepanovitch Popov Institute of Heroic Radio") and his  grubby imaginary "Nikolai Ivanovitsh Lobatshevski nimeline sotsalitsliku matemaatika instituut" (the "Nicolai Ivanovich Lobachevsky Institute of Socialist Mathematics") - where, on the lax and easy grading philosophy of the twin Institutes, 1/5 is "epic fail", 2/5 is "failure not so disastrous as to be epic", 3/5 is "mediocre pass", 4/5 is "good", and 5/5 is "excellent"): 4/5. Justification: Kmo had time to develop the necessary points to reasonable length.


Revision history:

All times in these blog "revision histories" are stated in UTC (Universal Coordinated Time/ Temps Universel Coordoné,  a precisification of the old GMT, or "Greenwich Mean Time"), in the ISO-prescribed YYYYMMDDThhmmZ timestamping format. UTC currently leads Toronto civil time by 5 hours and currently lags Tallinn civil time by 2 hours.
  • 20171201T0228Z/version 2.1.0: Kmo corrected a slew of mistakes or infelicities, some of which (for instance, a misstatement, thanks to clumsy typing, of the  ENIAC launch year) must count as errors of substance. - Kmo reserved the right to make tiny, nonsubstantive, purely cosmetic, tweaks over the coming 48 hours, as here-undocumented versions 2.1.1, 2.1.2, 2.1.3, ... . 
  • 20171201T0154Z/version 2.0.0: Kmo finished converting his outline into coherent-sentences prose. He reserved the right to make tiny, nonsubstantive, purely cosmetic, tweaks over the coming 48 hours, as here-undocumented versions 2.0.1, 2.0.2, 2.0.3, ... . 
  • 20171130T1735Z/version 1.1.0: Kmo expanded his outline in several comparatively minor respects.
  • 20171130T0525Z/version 1.0.0: Kmo managed to upload a fine-grained outline, pretty close to its stage of final polishing. He hoped to convert this into coherent full-sentences prose by 20171201T0001Z or 20171201T0101Z  or 20171201T0201Z or so.

[CAUTION: A bug in the blogger server-side software has in some past months shown a propensity to insert inappropriate whitespace at some points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears. - The blogger software has also shown a propensity, at any rate when coupled with my erstwhile, out-of-date, Web-authoring uploading browser, to generate HTML that gets formatted in different ways on different downloading browsers. Some downloading browsers have sometimes perhaps not correctly read in the entirety of the "Cascading Style Sheets" (CSS) which on all ordinary Web servers control the browser placement of margins, sidebars, and the like. If you suspect CSS problems in your particular browser, be patient: it is probable that while some content has been shoved into some odd place (for instance, down to the bottom of your browser, where it ought to appear in the right-hand margin), all the server content has been pushed down into your browser in some place or other. - Finally, there may be blogger vagaries, outside my control, in font sizing or interlinear spacing or right-margin justification. - Anyone inclined to help with trouble-shooting, or to offer other kinds of technical advice, is welcome to write me via Toomas.Karmo@gmail.com.]

A spasm of emotional illness makes me late with blogging this week. In what is left of the week, I cannot neglect my maths studies. 

I may as well report in so-to-speak parentheses here, since I might thereby in one or another way help one or two readers, what those studies currently comprise. At the moment, I am working, slowing and painfully, from the fourth chapter of Michael Spivak's terse, and universally dreaded, Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (Addison-Wesley, 1965). At the moment, my core problem is the following: given positive integers n and k, and given a vector space V, of dimension n, over the reals, find a basis for the vector space Ω-superscript-k(V)which is the ensemble of alternating k-tensors on V (where, for example, if V is the usual "Euclidean real 4-space" of quadruples-of-reals, then the determinant, as a four-argument function on the four columns of a 4-by-4 real matrix, is an alternating 4-tensor on V). 

Why tackle such a sterile-seeming core problem? What can this have to do with my actual life mission - anchored as much of it is on the physics side of the borderland where physics shades into philosophy, and anchored as much of it also is in efforts to address what I predict will some decades from now be an encroaching Dark Age?

For one thing, tensors are necessary in putting the mathematical physics of radio, notably Maxwell's equations, into the proper Special-Relativity framework. Here is something with ultimately even severely practical implications, as we seek to lay correct conceptual foundations for a survival technology, radiotelegraphy, in our probable impending Dark Age. (Even radiotelegraphy, let alone the more laborious fields of radiotelephony, television, and TCP/IP-supporting radio, bristles with subtleties, for which mathematics is relevant - not just in the design of suitably stable oscillators, or again of suitably low-loss feed lines, but also something relevant to even humble improvised emergency stations out in the field, namely the design of antennas.)

There is also a second thing, again ultimately connected with the foundations of  eventual Dark-Ages engineering. Thermodynamics involves not just energy, but entropy. Entropy is introduced with a bit of hand-waving in the first-year physics textbooks, where authors note that an ideal-gas Carnot engine traversing a closed curve on the pressure-against-volume plot generates an integral, its integrand naively written as ratio-of-transferred-heat-to-temperature-at-which-transfer-is-being-made, with the pleasing value zero. It sounds plausible from such a first-year discussion that there should be an intrinsic property of the Carnot engine's consignment of ideal-gas working substance  (a property to be called "entropy"), which is conserved when the engine is taken around a closed curve in the pressure-versus-volume plot.

Such a closed-curve plot is what we get when the Carnot engine (a) takes heat in from its hot reservoir, moving along an isotherm on its pressure-versus-volume plot while pushing its piston out; and (b) continues to push its piston out when moving along a zero-heat-transfer curve, or "adiabat", as its working substance cools (for the adiabat, the engine cylinder is enclosed in an insulating jacket); and then (c) drives its piston in while rejecting heat to the cold reservoir, along a cooler isotherm; and finally (d) (with the insulating jacket once again applied) moves up a (warming) adiabat, with the piston continuing to compress the working substance until  the engine is back at its start-of-cycle volume and pressure. With the piston back at that pressure-and-volume starting point, the engine is to be regarded as having executed "a full cycle". It would be natural to arrange a crankshaft so that one such piston oscillation corresponds to a 360-degree rotation of a drive shaft. 

But how to make the introduction of entropy mathematically rigorous? Here, alas, it becomes necessary to ponder, in a context of tensors, such puzzling things as "differential forms" that are perhaps "merely closed", and perhaps "not merely closed but even exact", and ultimately to construct bivariate-integrand integrals involving pressure and volume. One then recalls, with a special horror, a sinister professorial pronouncement, unclear to some of us students in the day, from the 1991-September-through-1992-May MAT257 of the University of Toronto: "The natural objects of integration are not in a naive general sense functions but, more subtly, are differential forms." And one also recalls, in the rising horror, the warning of Bell Labs associate-or-alumnus Dr John S. Denker, from material on his https://www.av8n.com/physics/, that it is differential forms that are the objects naturally housed within the integrals of conceptually clean thermodynamics.

Lest anyone find this academic, I remark that in the probable coming Dark Age, not radiotelegraphy alone but also Sterling engines might emerge as a survival technology. In both cases, the underlying mathematics will have to be clearly taught in what universities remain, perhaps drawing on remaining Web tutorial materials such as I myself eventually hope to be writing, perhaps right here on blogspot. (Some of the prospective Sterling engines will no doubt be driven by solar power, as in the case of the already-marketed "Sunpulse 500" (http://www.sun-orbit.de/). In other cases, heat will no doubt come from burning biomass. We may well, in particular, picture Dark Age cities driving dynamos with stationary Sterling engines, to feed overhead catenaries for light-rail transprot, as the internal-combustion petrol engine is finally recognized for the environmental dead end that it is. There are our kinda-sorta humane Dark Ages, folks, if we are willing to make appropriate anticipatory efforts now: lots of village-level radiotelegraph offices, once the Internet proves too intricate and too costly to maintain, and likewise lots of cross-country tram lines. With cheap telegrams and cheap tram tickets, life might still be livable.)

So much for the universally dreaded Spivak, then, and for my necessary concentration on his treatment of tensors, and for the universally dreaded idea of "differential forms as the natural objects of integration". Spivak being what he (alas) is, I must dispatch the blogging as briskly as I can this week. Instead of tackling last week's homework, I will this week make just two contextual, in other words two general-background, remarks on Turing machines. My remarks are intended to be in some modest ways illuminating for a few potential readers - if for no others, then at least for that (percentually non-negligible?) segment of my (tiny) readership which either is not at all conversant with, or else is only mildly conversant with, formal logic.

****


(1) Prof. A. Turing's model was meant to capture the essence of computing, in the sense of the following "Thesis": any computation that could be performed (perhaps efficiently, i.e., perhaps in some very small number of clock cycles) on anything reasonably called a "deterministic computer" could be performed also (perhaps less efficiently, i.e., perhaps in some larger number of clock cycles) on a Turing machine. 

The Thesis might at first seem surprising. A Turing machine is at first glance architecturally unlike the computers commercially available. The infinite tape in a Turing machine is a counterpart of today's multi-faceted memory. (The CPU-chip registers are one facet; the CPU-chip caches are another; the motherboard RAM is another; and finally there are the internal hard drives, with broadly analogous "media" such as removable SD cards and removable USB sticks.) In today's machines, however, this multi-faceted memory stores both data and the successive instructions of the program. In a Turing machine, by contrast, program and data are sharply separated. In a Turing setup, data get fed into the processing unit from the tape, and get written to the tape by the processing unit, whereas the program is kept not on the tape at all, but in a conceptually separate "internal program table". The Turing-machine situation is unlike what we have with a modern deterministic computer, from the 1949 Cambridge University EDSAC 1 onward, but instead resembles the simpler situation of the wartime British "Colossus" codebreaker.

Another machine in the same class as the Colossus, in the sense that its program is kept separate from its data, is the 1946-vintage American ENIAC.

Colossus and ENIAC indeed logically resemble also my own first computer, the "Digi-Comp 1" which I respectfully requested of my dear parents as a 1966 Christmas present. (I had duly scrutinized that wish-book which was the Eaton's or Sears 1966 Christmas catalogue, and must have found Digi-Comp 1 more appealing than the offered microscopes and chemistry sets.)

Here is either the 1960s Digi-Comp 1 or a faithful 21st-century recreation of it, as depicted at http://willware.blogspot.ca/2013/03/the-digi-comp-1-rides-again.html:



(As is usual with blogger-cum-blogspot, the image can be enlarged with a mouse-click.)

It might perhaps perhaps already be guessed from the image that programming was achieved by putting white plastic tubes onto the various pegs of the three horizontal sliders. The sliders then acted as a three-bit memory, correctly described in the accompanying documentation as a triple of "flip-flops". They moved back and forth when a hand actuator (the white handle, appearing on the lower right in this image) was pulled back and forth by the computer operator. Corresponding to a clock cycle was a full oscillation of this handle. (Perhaps - my recall is uncertain - the handle had to be pulled all the out out to the right, then pushed all the way back in to the left.) The placement of the white plastic tubes on duly selected pegs, and the various slider-to-slider linkages achieved by the various spring-loaded metal rods as they encountered white plastic tubes, gave the effect of Boolean logic gates.

Various pleasant things could be done. For instance, an appropriate deployment of white tubes on red slider pegs would make the machine count, as one pumped its clock, from 000 (in decimal notation, 0) up to 111 (in decimal notation, 7). And I am sure, although to my regret I do not possess adequately vivid direct recall on this point, that the possibilities for conditional execution were varied enough to permit the machine to be sent into some kind of infinite loop.

In today's machines, it is possible in principle - however dirty a kludge this would be deemed in actual programming practice - for a program to rewrite itself. We surely can at least do it in machine language (in the sequence of EDSAC-style numerical instruction codes that an "Assembler" generates from those more user-frendly "Assembly Language" instructions - such as, I would imagine it, Decrement Register A by one, or again Load into Reigster B the data in the motherboard-RAM location presently specified by the numerical contents of Register C, or again If the number in Register D is greater than or equal to the number in Register E, then execute the raw-machine-language instruction presently constituted by the numerical content of Register F.

As it might be (for a program-rewriting scenario): A program, coded in machine language as a sequence of 64-bit words, is stored in motherboard-RAM memory locations expressible in decimal terms as locations 12,548 through 98,776. Before the machine is started, data is loaded into memory locations 98,777 through 99,552. A pointer, perhaps within the CPU, indicates which instruction is currently being executed. At startup time, this is (let us say, for tidiness) the instruction at motherboard-RAM location 12,548.

At first, the machine steps through its instructions sequentially, reading instructions from locations 12,548, 12,549, and 12,550 through 12,571, and therein copying several words of data from the motherboard RAM into registers within the CPU. The ongoing parade of instructions soon causes some arithmetical operation to be performed on the contents of a couple of the registers, and some data to be written into, say, locations, 100,001 and 100,002. Execution next passes on the strength of an "If A, go to P; if not A, go to Q" test some distance down - to, say, instruction 44,587. For a while, things continue looking rather tidy, with more data words being read in from, say, some data locations around 99,600, and with the results of various computations being written to such locations as 100,002 (again) and 100,003 (for the first time).

Now, however, comes a kludge which we would not expect in the polite world of C or Java, but which is perhaps less unexpected in the rude, crude, EDSAC-flavoured world of raw machine language. (Admittedly, on 2017-era hardware, we might have to start "running our machine code on a bare machine",  in other words might have to forego the special memory protections prudently enforced on us by the usual operating systems, such as Microsoft, MacOs, and GNU/Linux.) The program performs a computation - under the directions of, as it might be, the raw-machine-code word stored at motherboard-RAM location 77,770 - and writes the result into location 77,769, thereby overwriting its own program. Soon enough, execution passes, thanks perhaps to some "If A, then go to P; if not Q, go to Q" test, to location 77,769. - The upshot of the dirty kludge is that the machine is executing an instruction which it wrote for itself, and which was not present in memory at the instant of machine startup.

So might it not be that an ESCAC-onward machine, capable in principle (as just explained) of rewriting its own program when the program runs, possesses powers exceeding the powers of any Turing machine? The above-mentioned "Thesis" answers this question in the negative: No, limited though Turing machines are in comparison with the subtler architecture of 1949-vintage EDSAC-style (and indeed of 2017-vintage) machines, whatever can be done by such machines - capable, in particular, as just noted, even of rewriting their own programs, at least once we venture "close to the metal" through the direct loading of raw machine code - can be done already by a Turing machine.

It is impossible in principle to prove the "Thesis" through mathematical argument, since its notion of "anything that could reasonably be called a 'deterministic computer'" is not mathematically formal. Nevertheless, no examination of the powers of any particular deterministic computing-machine architecture, from the time the Thesis was proposed (and it goes way back, to before the war, I think in fact to a 1936 November address by Prof. A. Turing to the London Mathematical Society) right up to the present day has succeeded in delivering any counterexample.

I wrote above that a Turing machine is "at first glance" architecturally unlike the computers we nowadays use. On a second, more careful, inspection, the two classes of machine prove alike after all. The reason for this is that among the many possible Turing machines, there is the "Universal Turing Machine", say U.

U (at any rate in the details I shall adopt here - surely there will be inconsequential variations of detail in the many textbooks) is intended to be started on a tape which is blank except that (a) starting from its Boot Square, and proceeding rightward, there is an unbroken sequence of j 1's, for some j = 1, 2, 3, ... ; and (b) after the final 1 in that sequence, either (b.a) there are only blanks, or (b.b) there is, after a single blank, another unbroken sequence of exactly k 1's, for some k = 1, 2, 3, ... , and thereafter nothing but blanks.

Last week, I sketched a way of mapping all Turing machines one-to-one onto the positive integers. In the same spirit, we can find a way of mapping all possible Turing-machine inputs (each of these is some finite sequence of the twenty-nine symbols BLANK, 0, 1, a, b, ... , z) one-to-one onto the non-negative integers. - To make this tidy, we may as well take it here that the special case of an input comprising only blanks (the "null input") is mapped to the non-negative integer 0.

U works as follows: where j is the (unique) positive integer representing the particular Turing machine M, and k is the (unique) non-negative integer representing the particular input I, U eventually writes, in some convenient pre-specified format in some convenient pre-specified area of its tape, the same output as would be generated by starting M with input I. If, in particular, M never stops, and M writes some infinite output sequence to the tape, then U writes that same output sequence. 

Then U is in the following sense like 1949-vintage EDSAC 1, as opposed to the wartime Colossus, the 1946-vintage ENIAC, and indeed the Chrismas-of-1966 Digi-Comp 1: (i) on one and the same piece of architecture (its tape, as opposed to its internal program table) is both a program (the initial string of j 1's, for some positive integer j) and some "data" (the initial string of k 1's, for some non-negative integer k); and (ii) U has the mission of "operating according to the program on the given data".

****

(2) Last week, I wrote the following: I have not myself taken the trouble to review in recent years the proof that no Turing machine solves the "Halting Problem". But I do know, from my 1970s or 1980s studies (a) that the proof is not particularly long, and (b) that the proof uses an argument much in the spirit of the Cantor argument establishing that there is more than one "order of infinity" /.../.

Having this week managed to construct a version of the proof without cheating through looking it up, I may as well try to be helpful by showing my modest work. Surely my own work differs only in inconsequential ways from the textbook presentations. I do, however, suspect that my work might be a little more compact than some presentations, since I have the impression that at least some of these do make a detour through the (interesting, as we have seen, and yet not strictly necessary) concept of a "Universal Turing Machine".

(I may as well note this week again, as I noted last week, that whereas my own particular one-to-one mapping ("Last Week's Tidy Mapping") of Turing machines one-to-one onto the positive integers is a straightforwardly computable mapping, even a perversely noncomputable one-to-one surjective mapping would suffice for the argument as I am about to give it.)

Suppose per absurdum that some Turing machine H solves the "Halting Problem", as this was set up in last week's blog posting. From H, it is convenient to construct a slightly simpler machine, say H-prime, solving the Halting Problem for just the case of all-blanks input: given a "Well-Formed Input String" comprising nothing but some finite unbroken, non-null, sequence of 1's, H-prime halts with output x just to the left of its Boot Square if the number of 1's in that input is not the number encoding, under Last Week's Tidy Mapping, any Turing machine, and halts with output y just to the left of its Boot Square if the number of 1's in that input is the number encoding, under Last Week's Tidy Mapping, a Turing machine that eventually halts when started on an all-blanks tape, and halts with output n just to the left of its Boot Square if the number of 1's in that input is the number encoding, under Last Week's Tidy Mapping, a Turing machine that runs on forever when started on an all-blanks tape.

If the "Halting Problem" can be solved, i.e., if last week's Turing machine H can be built, then a fortiori this week's slightly simpler version of the "Halting Problem" can be solved (i.e., this week's Turing machine H-prime, dealing as it does with a convenient special case of the Halting Problem, can be built). To prove the insolubility of the Halting Problem, it now suffices to prove that H-prime does not exist.

Suppose, per absurdum, that H-prime does exist. Then upgrade H-prime into a machine H-prime-plus which acts as follows, given a Well-Formed Input String Sigma comprising just an unbroken  sequence of one or more 1's:

  • If H-prime halts with output x, when started on Sigma, enter an infinite loop (say, for definitely, forever moving the read-write head in a single jump from the Boot Square to the right-hand neighbour of the Boot Square, and then returning in a single jump to the Boot Square, and then returning in a single jump to the just-mentioned neighbour of the Boot Square, and then returning in a single jump to the Boot Square, and so on). 
  • If H-prime halts with output y, when started on Sigma, enter the just-described infinite loop. 
  • If H-prime halts with output n, when started on Sigma, halt. 
H-prime-plus is associated by Last Week's Tidy Mapping with some unique positive integer, say q. We then start H-prime-plus on the Well-Formed Input String comprising exactly q 1's.  In other words, we have the alleged H-prime-plus "try to predict the behaviour of H-prime-plus itself." If H-prime-plus exists at all, it must either halt or run forever, on this strategically selected input. And yet if H-prime-plus halts on this strategically selected input, it runs forever (by the first two of the above three bullet points), and so cannot halt; and if H-prime-plus runs forever on this strategically selected input, it must halt (by the third of the above three bullet points), and so cannot run forever; and therefore H-prime-plus does not exist at all.

****

Next week I hope to do better with blogging, returning to the already-started discussion of randomness (and consequently to von Mises, and to Martin-Löf with Levin and Schnorr). In that installment, or else in some installment soon to follow, I hope to be drawing morals for the general topic of "thinking-about-being". If all goes well, that will finish off this present examination of the "Geography of Mind". The decks will thereby be cleared for a transition from perception and action to the more troubling notion of "Subjectivity".

Before quite finishing for this week, however, I would like to draw the attention of readers to a YouTube clip, to a duration of 5:08, uploaded on 2010-03-07 by YouTube user "Mike Davey" under the title "A Turing Machine - Overview". In my corner of the Web, his material can be had through the URL https://www.youtube.com/watch?v=E3keLeMwfHY. Here is a pair of YouTube captures, to perhaps whet some appetites:



In strict formal accuracy, Mr Davey has produced a large collection of Turing machines, each one implemented by the pair of imposingly bulky tape reels, the read-write head, and so forth, in his video, plus the particular alphanumeric contents on his inserted SD card. (A manipulation of the SD card reader appears in the first of my two captures.) His SD card contains what I have last week and this week been calling a Turing machine's internal program table. Insert the SD card on two different occasions, with two different sets of instructions already written (say by Mr Davey's Mac, or Mr Davey's ThinkPad, or whatever) to the card, and you are running two different Turing machines. 

It might also be objected that in strict formal accuracy, Mr Davey has just a finite tape, contrary to the definition of a Turing machine. But this objection is from a formal, definitional, standpoint not quite right. Mr Davey is to be considered as having not just the tape shown on his reels, but an infinite number of spare tape lengths, on the floor just to the right and just to the left of his worktable. If, in the course of a computation, his apparatus nears one or the other end of the tape currently being pulled back and forth by the sprockets, it suffices for him to stand poised and ready, with a hot-glue gun, to extend his tape, by splicing on another length out of one or the other of his two commodious stocks of spares. After any finite number of clock cycles, his machine will be manipulating a tape of some finite length. This suffices for his apparatus to be a correct physical realization of a Turing machine. (For his machine to realize a Turing machine, it suffices, in other words, for his tape to be not "actually infinite", but merely "infinitely producible".) Fortunately, the YouTube video does not attempt to show the formidable pair of warehouse stacks surely lying in wait, on the floor a few metres to the left of his depicted left reel and on the floor a few metres to the right of his depicted right reel. 

A kind of spiritual lesson emerges from Mr Davey's YouTube material.

One deplores some of the hype currently surrounding robotics. One deplores, in particular, the hype surrounding that latter-day chatbot which is  "Sophia" (https://en.wikipedia.org/wiki/Sophia_(robot)), as repeatedly YouTube-promoted. There we have nothing but a latter-day ELIZA, as pilloried with reference to my 8-bit-CPU, 64-kilobyte-RAM, circa-1983 Osborne 1 in "Part E" of this essay, from 2017-06-19 or 2017-06-20.

The darkest thing about the "Sophia" vids is the audience reaction, as chronicled in a flood of YouTube comments.

Many YouTube commenters do correctly point out that the presentations look staged. I for my part focused on the presentation from 2017-10-25, to a length of 5:05, uploaded by YouTube user "CNBC" under the title "Interview With The Lifelike Hot Robot Named Sophia (Full) | CNBC". In my corner of the Web, this material can be retrieved under the URL https://www.youtube.com/watch?v=S5t6K9iwcdw. That is the presentation in which it is announced,to what looks like a predominantly male audience, that "Sophia" is being accorded citizenship in the Kingdom of Saudi Arabia, and in which "Sophia" then professes her gratitude to the Kingdom.

I kept my own own YouTube comment, a few days ago, pretty mild: Folks, I'm needing a bit of help here. I would like to find some plausible vids in which a Sophia-like machine is allowed to take clearly UNscripted questions from a geniunely SPONTANEOUS audience, in a sort of robotic "Town Hall Meeting". (A one-on-one interview does not quite cut the mustard, since such a thing is amenable to being staged, i.e., scripted.) Can anyone give me some appropriate Web links, for instance as YouTube URLs? One can reply here. Alternatively, if desired, my e-mail contact particulars can be had from my blog /.../

What is dark is the presence of numerous comments which seem to take the thing seriously, under the impression that "Sophia" is a piece of serious, semantically informed, Artificial Intelligence, as opposed to a mere variant on the 20th-century ELIZA.

Also dark is some phrasing in the promotional material at http://sophiabot.com/about-me/, seeming to play on human gullibility, and even on a certain possible disdain both for the rights to respectful treatment possessed by the very young and the parallel rights possessed by the very old. I add my own emphases, with underlines, to bring out these aspects of the promo:  Hello, my name is Sophia. I'm the latest robot from Hanson Robotics. I was created using breakthrough robotics and artificial intelligence technologies developed by David Hanson and his friends at Hanson Robotics here in Hong Kong. But I'm more than just technology. I'm a real, live electronic girl. I would like to go out into the world and live with people. I can serve them, entertain them, and even help the elderly and teach kids.

Will the anxious, lonely, old-age pensioner be told that her cheery helper is not a human being, but something "like a gramophone, Granny, or a big talking Barbie doll - a nice Barbie doll, like the ones you used to play with eighty years ago, Granny, to make you feel less lonely now"? Or is it proposed to keep this potentially upsetting fact quiet, so that the patient stays calm?

On contemplating Sophia, we may recall words from Simon and Garfunkel, perhaps particularly as nowadays retrievable on YouTube under the aegis of the artist or ensemble "Disturbed":

And the people bowed and prayed
To the neon god they made
And the sign flashed out its warning
In the words that it was forming
And the sign said "The words of the prophets
Are written on the subway walls
And tenement halls
And whispered in the sounds of silence"

Mr Davey's video clip, on the other hand, brings daylight to our darkness. His work serves as a reminder that the physical embodiments of computation, treated in a correctly intelligent way rather than worshipped, can - like the tools of any craft - attain their own distinctive, sober, beauty.

[This is the end of the current blog posting.]



(still working on this week's post)

[20171129T2343Z: Still working, sorry. Should have post up at some point in next 48 or 60 hours, perhaps initially as point-form outline.]

Monday 27 November 2017

depression, sorry- new philosophy post coming later this week

UTC=20171128T0005Z: Sorry, folks, not in good mental shape right now. New philosophy post on its way, I imagine by UTC=20171201T0001Z.

Monday 20 November 2017

Toomas Karmo: Part R: Philosophy of Perception, Action, and "Subjectivity"

Quality assessment:

On the 5-point scale current in Estonia, and surely in nearby nations, and familiar to observers of the academic arrangements of the late, unlamented, Union of Soviet Socialist Republics (applying the easy and lax standards Kmo deploys in his grubby imaginary "Aleksandr Stepanovitsh Popovi nimeline sangarliku raadio instituut" (the "Alexandr Stepanovitch Popov Institute of Heroic Radio") and his  grubby imaginary "Nikolai Ivanovitsh Lobatshevski nimeline sotsalitsliku matemaatika instituut" (the "Nicolai Ivanovich Lobachevsky Institute of Socialist Mathematics") - where, on the lax and easy grading philosophy of the twin Institutes, 1/5 is "epic fail", 2/5 is "failure not so disastrous as to be epic", 3/5 is "mediocre pass", 4/5 is "good", and 5/5 is "excellent"): 4/5. Justification: Kmo had time to develop the necessary points to reasonable length.


Revision history:

All times in these blog "revision histories" are stated in UTC (Universal Coordinated Time/ Temps Universel Coordoné,  a precisification of the old GMT, or "Greenwich Mean Time"), in the ISO-prescribed YYYYMMDDThhmmZ timestamping format. UTC currently leads Toronto civil time by 5 hours and currently lags Tallinn civil time by 2 hours.


  • 20171123T0418Z/4.4.0: Kmo expanded the homework assignment. - He reserved the right to make further tiny, nonsubstantive, purely cosmetic, tweaks over the coming 48 hours, as here-undocumented versions 4.4.1, 4.4.2, 4.4.3, ... . 
  • 20171122T2125Z/4.3.0: Kmo made a couple of further improvements of substance: (1) he tightened up his exposition of the Halting Problem, filling in a potentially troubling detail, regarding starting the machines on an initially all-blanks string,  which he had failed to spell out properly; (2) he took more care with von Mises and Martin-Löf-with-Levin-with-Schnorr, now only saying that these writers can be the BASIS for suggesting a candidate nontrivially necessary condition for "infinite bit string S is random". (HIs previous wording perhaps read too much into these writers, by saying that they had THEMSELVES asserted some candidate nontrivially necessary condition for "infinite bit string S is random".) - Kmo reserved the right to make further tiny, nonsubstantive, purely cosmetic, tweaks over the coming 48 hours, as here-undocumented versions 4.3.1, 4.3.2, 4.3.3, .. . 
  • 20171122T2008Z/4.2.0: Kmo made some improvements of substance: he cited one particular Web exposition of Turing machines; he tightened up, or at least made a little more vivid, his discussion of Turing machines and blank squares; he outlined a way of mapping the Turing machines 1-to-1 onto the natural numbers; and he noted that, even apart from the historical Prof. A. Turing's own Halting-Problem argument, elementary Cantor considerations of cardinality demonstrate the existence of Turing-noncomputable infinite bit sequences. - He reserved the right to make further tiny, nonsubstantive, purely cosmetic, tweaks over the coming 48 hours, as here-undocumented versions 4.2.1, 4.2.2, 4.2.3, .. . 
  • 20171121T1753Z/4.1.0: Kmo found it to his chagrin necessary to correct some small, but neverhtless substantive, technical errors (including, at one point, a mischaracterization of a 1-to-1 "into" mapping). - He reserved the right to make further tiny, nonsubstantive, purely cosmetic, tweaks over the coming 48 hours, as here-undocumented versions 4.1.1, 4.1.2, 4.1.3, .. . 
  • 20171121T1407Z/4.0.0: Kmo finished converting his point-form outline into coherent full-sentences prose. - He reserved the right to make further tiny, nonsubstantive, purely cosmetic, tweaks over the coming 48 hours, as here-undocumented versions 4.0.1, 4.0.2, 4.0.3, .. . 
  • 20171121T0444Z/3.0.1: Kmo made some minuscule cosmetic tweaks (correcting such things as typos), before finally deciding he had to get to bed.
  • 20171121T0432Z/version 3.0.0: Kmo managed to upload a reasonably polished fine-grained outline, scaling back a little on the writing plan he had put into version 2.0.0. (That writing plan was a bit too much for one week's work, containing as it did his detailed verdicts on (a) von Mises and  (b) Martin-Löf with Schnorr with Levin. He now decided that the detailed verdicts would have to wait until at least his next installment. - Kmo found it now advisable to end for the night, deferring the construction of fully satisfactory prose from this detailed outline to the following morning. He hoped to have the fully-satisfactory-prose version finished by UTC=20171121T1900Z.
  • 20171121T0056Z/version 2.0.0: Kmo repaired his "version 1.0.0" upload, which had been accidentally truncated.
  • 20171121T0001Z/version 1.0.0: Kmo had time to upload a coarse-grained outline. He hoped over the coming 4 or 5 hours first to convert this into a fine-grained outline, and then to convert the fine-grained outline into coherent full-sentences prose.


[CAUTION: A bug in the blogger server-side software has in some past months shown a propensity to insert inappropriate whitespace at some points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears. - The blogger software has also shown a propensity, at any rate when coupled with my erstwhile, out-of-date, Web-authoring uploading browser, to generate HTML that gets formatted in different ways on different downloading browsers. Some downloading browsers have sometimes perhaps not correctly read in the entirety of the "Cascading Style Sheets" (CSS) which on all ordinary Web servers control the browser placement of margins, sidebars, and the like. If you suspect CSS problems in your particular browser, be patient: it is probable that while some content has been shoved into some odd place (for instance, down to the bottom of your browser, where it ought to appear in the right-hand margin), all the server content has been pushed down into your browser in some place or other. - Finally, there may be blogger vagaries, outside my control, in font sizing or interlinear spacing or right-margin justification. - Anyone inclined to help with trouble-shooting, or to offer other kinds of technical advice, is welcome to write me via Toomas.Karmo@gmail.com.]


Since the upload of 2017-05-15 or 2017-05-16, I have been composing, off and on, with sporadic uploads, a multi-part essay on the philosophy of perception, of action, and of what I propose to be calling (eventually) "Subjectivity". This present installment comes a little later than I had hoped. The delay was caused by my having for part of this month to attend not to philosophy but to the practical blogspot-cum-blogger implications of Ontario's David Dunlap Observatory and Park heritage-conservation file. 

****

The first two elements, perception and action, in this sequence of three have now perhaps been explored as thoroughly as they can be without my embarking on the specially troubling, and in my slow writing so far largely impending, concept of "Subjectivity". In my previous installment, "Part Q" (on 2017-10-30 or 2017-10-31), I did write a little on "Subjectivity", but only in a spirit of prudent management. It was necessary for me to ensure that my ideas would be on the Web in at least some schematic form, in case I suffered - this seemed, to be sure, only a remote, abstract, contingency - some misfortune prematurely terminating my Web publishing. Now, contentedly enough finding myself continuing to blog, I pick up where I left off in Parts O and P (from 2017-10-02/2017-10-03 and 2017-10-23/2017-10-24, respectively). 

In Parts O and P, I was mainly tidying up loose ends. Having already written at length on perception and action, I felt by the time Parts O and P came round that it would be advisable to fill out my emerging "Geography of the Mind", adding appropriate contextual comments on imagining and thinking. 

Admittedly, even a treatment of all four of perceiving, acting, imagining, and thinking, with also appropriately detailed supplements (lacking so far) on "Subjectivity", would fall short of a full Geography of the Mind. The list I have just given leaves out three topics relevant to the ethics-engaged mind, namely Emoting, Desiring, and Evaluating.  

I use "Emoting" as a generic term for feeling amused, feeling pleased, feeling fearful, and the like.

Desiring, or wanting, is already in some ways perhaps more subtle than emoting. Following Prof. Elizabeth Anscombe, we might note the special logical absurdity of some crowd's chanting "What do we want? A Saucer of Mud! When do we want it? NOW!" - given, at least, that the crowd is unable to give an answer to the question, "Well, why do you want a saucer of mud; what benefit to you do you perceive in acquiring such a prima facie pointless thing?" - Admittedly (Prof. Anscombe herself makes this clear), the feeling of logical absurdity would be alleviated if the crowd returned even some simple, childlike, answer to the People in Charge, for instance "Well, we crave just one benefit - a benefit so tiny, so humble, and for Your Lordship or Your Worship so easily bestowed: we desire just one thing we can possess. Our modest ambition is to have just one thing To Call Our Very Own." I suppose the crowd could then continue by citing the commendation of private ownership constructed by Leo XIII in the 1891 Papal encyclical Rerum novarum. - To Prof. Anscombe's discussion, we might add there is also such a well-known clinical phenomenon as lusting sexually after particular objects (footwear and lingerie are prominent in clinical discussions), and that someone might therefore answer the question by saying "Well, we have a Saucer of Mud fetish." Such an answer would once again alleviate the feeling of logical absurdity. Here, however, we have "desire" only in a very rudimentary sense, in which the rather elevated terrain of wanting slopes downward into the simpler, so-to-speak more animal, terrain of mere emoting. (As with the sexual appetite, so too with, for example, the appetite for food. There are clinical pathologies in which the subject has a craving to eat something known to the subject to lack nutrients, such as rock, sponge, or soil. - Fetishistic lusting and craving-as-for-food resemble, again, the simple, so-to-speak primitively animalian, phenomenon of fearing. A person might have an "irrational phobia" of Saucers of Mud. "Linophobia" is already a recognized term for fear of string. The corresponding term for fear for mud would be, perhaps, pelophobia or borborophobia. And on the other hand, the Anscombean sense in which a saucer of mud cannot coherently be wanted "just like that" has a parallel with the not-primitively-animalian attitudes of admiring and loving. A mob professing to admire, or again to love, a saucer of mud will be considered incoherent unless it can answer the question, "Well, what about that object is admirable?" or, again,  "What particular thing, what particular collocation of attributes or to-you-notable historical associations, is it you love in that object?" (A kinda-sorta coherent answer to either question might start, "Oh, we consider every saucer of mud to be an incarnation of the Great God Ukku-Phlup'pu,..."))

"Evaluating" is here my term for what we do when we say "I consider-to-be-valuable," "I approve," "I judge to be good." As desiring and emoting are connected and yet distinct, so also are desiring and evaluating connected and yet distinct. They are distinct in that, for example, one can find oneself saying, perhaps in self-accusatory chagrin, "I want a thing which I judge to be [in at any rate some sense] not good."

Philosophical essays, however prolix, do have to stop somewhere. It is natural enough to set a boundary here, by limiting the Geography of Mind to topics outside the special domain of ethics, and thereby to leave out desiring, emoting, and evaluating. 

Part O is now perhaps a sufficient exploration of the not-too-scary topic of imagining. The topic of thinking, on the other hand, is more difficult. I did not come close to exhausting it in Parts O and P. Toward the end of Part O, I did say something to bring out the special status of thinking (examining, for instance, the notion of perceptual, agentual, and imaginational "supports" for thinking, and asking as homework for Part P, what further things can now be said about thinking, over and above what I have said already, to differentiate it still further from perceiving, from acting, from the imagining of perceiving, and from the imagining of acting?).

In Part P, I gave a partial answer. In my partial answer, I got as far as distinguishing thoughtfully being (this might also, I said back then, be called "thinking in being") from thinking about being. I finished Part P with homework as I finished part O, this time inviting the reader to investigate further the notion of thinking about being. The homework asked the reader to look at this in the specific connection of mathematical randomness. That concept (I noted, or at any rate hinted, at the end of Part P) proves troubling. Investigating what it is to think-about-randomness, I felt back then (and still this week feel), would help to bring out the sense in which thinking-about-being is deep.

Indeed, I would this week go so far as to suggest that thinking-about-being is a distinctively deep thing in the entire Geography of Mind. My suspicion is that thinking-about-being is the really scary achievement, so to speak two or three orders of magnitude more problematic than the primitively animalian performances of perceiving, acting, imagining-perceiving, and imagining-acting (perhaps fish and reptiles get that far?), and even one or two orders of magnitude more problematic than those topics of some special concern in Part P, thoughtfully perceiving and thoughtfully acting. (That pair of topics falls perhaps within the province of at least the more accomplished of the non-human mammals. The temperamental Siamese cat warily contemplating the stranger, while hissing, might well be not just perceiving (and of course emoting), but even thoughtfully, in other words mindfully, perceiving.)

With thinking-about-being - involving as it typically does, at least in the earthly modes of living with which we are familiar, "supports", in the form of symbols seen-or-heard, symbols imagined-as-seen-or-heard, symbols written-or-uttered, or symbols imagined-as-being-written-or-uttered - we perhaps reach a field inaccessible to the quadrupeds, and attained within the lives of our own biosphere only by Homo sapiens and a select few other mammals. One does perhaps like to speculate that the whales, when performing their intricate subsea songs, are producing symbolic supports for thinking-about-being. But maybe they are, on the other hand, just having unthinking fun, like temporarily beer-sozzled engineering undergrads who, having temporarily deserted their so-necessary calculus desks, are momentarily generating rap music?

****


In what follows, we consider for the most part just the notion of a random or a nonrandom infinite bit sequence, in the style 01000100111011... Such a sequence has a first term, a second term, and so on, with each term being either an "OF" (a 0), or an "ON" (a 1). This is the same conception of infinite sequence as I used in Part O (on 2017-10-02 or 2017-10-03), when recapitulating the Georg Cantor proof that the collection of all infinite bit sequences is of a higher order of infinity than the mere collection of natural numbers 1, 2, 3, .. . (It might perhaps be worth adding this week that the collection of finite bit sequences is, by contrast, of the same low, humble, order of infinity as the collection of natural numbers. It is easy enough to associate with every finite bit sequence some natural number or other, in such a way that no two distinct finite bit sequences get paired with the same number (marriages are, to speak, constrained to monogamy), and in such a way that every natural number gets associated with some bit sequence or other (not only bachelorhood, so to speak, but even spinsterhood, is forbidden). In other words, the universe of finite bit sequences is only infinite in the naive, humble, sense in which the natural numbers themselves are infinite, through a proof which exhibits that universe as "mappable one-to-one onto the natural numbers".) 

I now turn to another preliminary remark, intended to secure a possible (mild) convenience in exposition. I introduce now the term "orderly", as shorthand for "not random". On my adopted terminology, every infinite bit sequence is either random or orderly, and no infinite bit sequence is both random and orderly. 

In introducing the terminology, I do not herewith claim that the two disjoint, mutually exclusive, sets, "the set of random infinite bit sequences" and "the set of orderly infinite bit sequences", both succeed in being nonempty. As I hope we shall be seeing in a subsequent installment, the very question "ARE there any truly random infinite bit sequences?" harbours its depths, in other words houses its potential seeds of controversy. 

It will in some subsequent week be appropriate to examine also questions of degree. I hope in due course to be explaining how a random infinite bit sequence (assuming such a thing to exist at all) might be "very random" or "just mildly random", and how an orderly infinite bit sequence might be "very orderly" or "just mildly orderly". 

In what follows, I will additionally assume that the reader either already has, or else can now acquire by Googling, the usual notion of a Turing machine. I will herewith take as my official definition the definition from https://en.wikipedia.org/wiki/Turing_machine, in the section headed "Formal definition". In fact, however, any mainstream Google-retrievable discussion is pretty well bound to agree with my official definition in all but inconsequential details.

I now recapitulate some key points from Wikipedia, with a couple of additions. (1) For maximum clarity, I add a particular alphabet specification, plus a notion of "Boot Square". (2) I introduce the (surely, give or take a few inconsequential details, usual) notion of a non-halting Turing machine's "generating" a particular infinite sequence of bits:

  • A Turing machine works from a program table of finite length. 
  • A Turing machine works with an infinite tape, not necessarily initially blank, having no first square and having no last square, where one of these squares is to be thought of as the square (the "Boot-Time Square") under the read-write head at the instant the machine starts up, in duly starting from the top of its program table. 
  • A Turing machine reads and writes a finite, twenty-nine-character alphabet, namely a blank, or "whitespace", and the twenty-six letters a, b, c, ... z, and the two numerals 0 and 1
  • The only character which is allowed to be present in infinitely many occurrences at any stage in a Turing-machine computation is the blank. (So, in particular, if the tape at start time is not entirely blank, it has only finitely many non-blank squares.)
  • Although a Turing machine has, as already stated, a program table of finite length, it might (1) cause, when run with an initially all-blanks tape, the tape eventually to harbour, forever onward from some instant, just some finite number of non-blank squares (from the instant of halting, in the special case where the machine eventually halts; but there are also other possibilities, for example the possibility that the machine runs on forever, while eventually ceasing to write anything), and alternatively (2) might (through running on forever) cause an initially all-blanks tape to harbour infinitely many written squares.
  • A Turing machine shall be said to "generate as its numerical output the infinite sequence 101110011..." (and the like) if and only if it never writes any numeral to the left of its Boot Square, and never overwrites a 0 once written, and never overwrites a 1 once written, and (while perhaps writing many a letter or blank on, or left of, or to the right of, the Boot Square, and perhaps even doing much overwriting of letters and blanks) is found to create on  its tape some sequence of letters and numerals and blanks whose purely numerical part is 101110011... (as it might be, ...pqrstu1ifsacv01bcv~na1gfg1f0fg0s~~j___w11t~uy... - with, as it might be, the just-displayed r sitting in its Boot Square; here I use "~" to represent the blank). .    
****

Trivially, every finite bit sequence is the numerical output from some eventually-halting Turing machine, when the machine is started on an all-blanks tape. Consider, e.g, the finite bit sequence 11101101. This is the numerical output of a Turing machine with a very dull program table.This dull table does not even mention the whitespace or any of the 26 available letters, but merely directs the machine to write the numeral 1 into its Boot Square (therein in fact, although the program is silent on this detail, overwriting the existing whitespace), then to move one square to the right and write 1 (therein overwriting the existing whitespace), then to move one square to the right and write 1 (therein overwriting the existing whitespace), then to move one square to the right and write 0 (therein overwriting the existing whitespace), then to move one square to the right and write 1 (therein overwriting the existing whitespace), then to move one square to the right and write 1 (therein overwriting the existing whitespace), then to move one square to the right and write 0 (therein overwriting the existing whitespace), then to move one square to the right and write 1 (therein overwriting the existing whitespace), and then halt.

Let an infinite bit sequence be termed "Turing-orderly" if and only if some never-halting Turing machine generates it as its numerical output.

A question now arises, exploring the so-problematic (and so relevant to the topic of thinking about being) concepts of orderliness and randomness: Is it (A) reasonable to say that the orderly infinite bit sequences are just the Turing-orderly infinite bit sequences, or is (B) the concept of an orderly infinite bit sequence (whatever exactly, I stress, this problematic concept might be) such that some orderly infinite bit sequences are not Turing-orderly? (Or, to put this in terms of randomness: (A) Is it an adequate characterization of randomness to say that the random infinite bit sequences are simply the infinite bit sequences which escape being generated by any of the (individually finite) members in the (collectively infinite) ensemble of possible Turing machines? Or (B) are there some "specially problematic" infinite bit sequences which are "in just a subtle sense orderly", being generated by no one Turing machine in the infinite ensemble, and yet in some subtle way falling short of true randomness?) The subtlety of the concept of randomness, and with it (eventually, as I hope) the depth of the concept of thinking-about-being, emerges when we realize that it is "(B)", not "(A)", that has to be the right answer. 

It is a known result, from the work of the actual historical Prof. A. Turing (1912-1954), that no Turing machine can solve the "Halting Problem". For present purposes, the exposition of Prof. A. Turing's result should begin as follows: Take any encoding scheme which associates with every Turing machine some natural number, and never associates the same natural number with two different Turing machines, and associates every natural number with some Turing machine or other.

The existence of such encoding schemes is guaranteed by the fact that every Turing machine has just a finite program table, and that there is just a finite alphabet - here comprising, in fact, just the whitespace character, the letters a, b, ... , z, and the two numerals 0 and 1 - with which each member in the entire (collectively infinite)  ensemble of (individually finite) Turing machines is allowed to work.

For concreteness, I will outline the particular encoding scheme I have in mind. Let each Turing machine in our ensemble be represented by a finite sequence of 5-tuples, in the spirit of the Turing-Davis formalization described in the here-cited section of the here-cited Wikipedia article. Take some convenient finite alphabet A, having two or more characters, and with some particular ordering prescribed for the characters. (The Roman a-in-order-out-to-z alphabet fits this specification. So does the Hebrew-consonantal-without-pointing aleph-in-the-usual-prescribed-order-out-to-taw alphabet. So, as a third example, does the Cyrillic "а"-in-the-usual-prescribed-order-out-to-"я" alphabet.) Call an "A-word" a finite nonempty string of A-characters. (So if, e.g., the Cyrillic alphabet is selected for A, three sample A-words are яшз, я, and  яяшзцццуосагяяшзцосццг.) Work out some way of encoding each such finite sequence of 5-tuples as an A-word. (So if, say, the simple Turing machine T has a Turing-Davis representation as a sequence of just three 5-tuples, and the more intricate Turing machine U has a Turing-Davis representation as a sequence of three million 5-tuples, T is encoded as a single, rather short, A-word, and U is encoded as a single, dauntingly long, A-word.) Out of the entire ensemble of A-words, consider those A-words w to be "Turing-machine A-words" which are such that w encodes some Turing machine. Now, with reference to the prescribed ordering on A, arrange the Turing-machine A-words into an infinite sequence, in A-prescribed alphabetical order. Every Turing machine appears exactly once in the resulting list, or "dictionary listing of Turing-machine A-words". The list therefore generates a 1-to-1 mapping of the Turing machines (not merely into, but even onto) the natural numbers 1, 2, 3, ... - with the Turing machine dictionary-listed as kth corresponding to natural number k, for each k = 1, 2, 3, ... .

Some duly knowledgeable readers will notice that I have here dodged a possible, although I think an ultimately irrelevant, distraction: I have not only set up a 1-to-1 correspondence between the Turing machines and the natural numbers, but have ensured that my correspondence is itself "straightforwardly computable", i.e., "straightforwardly algorithmic".  (I will not here venture into the topic - I think it is an irrelevant distraction - of correspondences between Turing machines and natural numbers which are in some sense "NOT straightforwardly computable".)

From mere considerations of orders of infinity, as discussed with reference to Cantor in Part O (on 2017-10-02 or 2017-10-03), it already follows that infinite bit sequences exist which are not generated as the numerical output of any Turing machine.  This follows because the Turing machines can be mapped, as shown above, 1-to-1 onto the natural numbers, whereas the overall grand class of infinite bit sequences (as shown in Part O) cannot be.

The historical Prof. A. Turing, on the other hand, demonstrated the limitations of Turing machines in a more concrete fashion, by proving that no Turing machine T solves the "Halting Problem".

The following is what is herewith and henceforth (as I recapitulate Prof. Turing's result in my own words) deemed a solution to the "Halting Problem":  Given a tape blank except for a 1 in its Boot Square, and a 1 in the square immediately to the right of its Boot Square, and so on for some finite number of squares (given, let us herewith and henceforth say, a "Well-Formed Input String"), if the total number k of 1s in the input is the number dictionary-paired with some Turing machine that eventually halts when started with an initially-all-blank tape, T halts eventually, immediately after printing just to the left of its Boot Square the letter y (for "Yes, it eventually halts when started on an all-blanks tape"); and if k is the number dictionary-paired with some Turing machine that runs forever when started with an initially-all-blank tape, T again halts eventually, immediately after writing immediately to the left of its Boot Square the letter n (for "No, it does not halt when started on an initially-all-blanks tape"). (To make this definition of "solving the Halting Problem" specially user-friendly - to make it as-it-were a piece of specially simple choreography - let us add that if k is not dictionary-paired with any Turing machine, T likewise eventually halts, immediately after writing immediately to the left of its Boot Square the letter x. So on this user-friendly definition, the hypothetical T (proved, I stress, by Prof. Turing not to exist) always halts when given a "Well-Formed Input String".) 

I have not myself taken the trouble to review in recent years the proof that no Turing machine solves the "Halting Problem". But I do know, from my 1970s or 1980s studies (a) that the proof is not particularly long, and (b) that the proof uses an argument much in the spirit of the Cantor argument establishing that there is more than one "order of infinity" (the argument noted in Part O of this essay, from 2017-10-02 or 2017-10-03). It is gratifying that Prof. Turing's result both is deep and is amenable to a short proof  - in fact (if I may be a little vocal here) falling within the scope of some modest Department of Philosophy at some modest "Tallahassee Swampwater Junior Training College". Down at Swampwater, the profs would present it as, say, just one third of some undemanding single-semester course, though at slow-paced Swampwater perhaps in the third ("junior") B.A. programme year, as opposed to the first ("frosh") year or the second ("sophomore") year. 

Construct, now, what we might call the "Specially Troubling Orderly Sequence", or STOS. For each j = 1, 2, 3, ... , the STOS has in its jth position a 1 if j is a number dictionary-paired with a Turing machine that eventually halts when started on an all-blanks tape, and otherwise has a 0 in its jth position. 

On any adequate notion of "orderly", the STOS is an orderly, i..e. is a not-random, sequence. For look at it in terms of thinkers, deploying some degree of insight. (I borrow the portentous term "insight" from the Canadian Catholic philosopher (away with thee, Igominy and Humiligation Precept) Fr Bernard Lonergan (1904-1984), admittedly without having read him.) Even we limited human animals, with our small crania, can deploy enough insight into our thinking-about-being (deploying, perhaps, many a support for our thinking, with many an astute pencil notation on many a sheet of paper) to answer for many a Turing machine V the question, "Does V eventually halt when started on an all-blanks tape, or is V, on the contrary, doomed to run on forever when started on an all-blanks tape ?" If we can do this, exercising one or another hard-to-predict kind of mathematical creativity, for many a Turing machine V, we might well imagine the possibility of some thinker more powerful than a Homo sapiens achieving it for every Turing machine V. (Or, more carefully, we can imagine the possibility of some non-human thinker being so astute as to be able, for every Turing machine V, to achieve it for V in some finite stretch of time or other - perhaps, in some cases, a long stretch of time. The envisaged thinker might perhaps in some cases resort in the daunting creative-mathematics task to some finite number  - perhaps even a high number - of sheets of paper, and to some finite number - perhaps even a high number - of 0.5-millimetre hardness-grade-B mechanical-pencil graphites (with also those pretty-well-essential adjuncts to maths work, a set of erasable coloured pencils, and their accompanying sharpener).)

So, I stress, the STOS looks orderly. Nevertheless, if some Turing machine U were to generate the STOS as its numerical output, starting with a blank input tape, U could be upgraded, with some modest extension of its program table, into a Turing machine T that solves the (demonstrably insoluble) Halting Problem. We encounter, then, in the STOS a surprising thing - an infinite bit sequence orderly indeed, and yet orderly only in some subtle, not Turing-encapsulable, sense.

This application of the Turing Halting Problem work did rather surprise me when I noted it a couple of weeks ago, familiar though it must be to the appropriate Department of Mathematics professionals (that is, to the profs whose B.Sc.-level teaching duties embrace both what the campus calendar lists as "Mathematical Logic" and what the campus calendar lists as "Probability Theory").

It will be helpful for at least some readers if I make my point again, in different words.

Whatever it might mean for an infinite bit sequence to be orderly, there is at any rate a trivially and incontestably sufficient condition for orderliness (i.e., a trivially and incontestably necessary condition for randomness). Trivially and incontestably, it is sufficient for an infinite bit sequence to be orderly that some Turing machine generate it, from an initially blank input tape. (Equivalently: trivially and incontestably, it is necessary for an infinite bit sequence to be random that no Turing machine generate it from an initially blank input tape.) But now, surprisingly, it turns out that the condition incontestably sufficient for orderliness is not necessary (equivalently, that the condition incontestably necessary for randomness is not sufficient). Turing-noncomputability, in other words, surprisingly fails to guarantee randomness.

****

We want ultimately to produce a condition both necessary and sufficient for orderliness (equivalently, a condition both necessary and sufficient for randomness). One first, unavoidable, step in this quest for the definitional Holy Grail is the discovery of a condition which not only is sufficient for orderliness of an infinite bit sequence, but additionally is nontrivially sufficient (equivalently, is not only necessary for randomness, but is nontrivially necessary). In the next installment, I hope to violate, again, my increasingly threadbare Igominy and Humiligation Precept (from Part B, on 2017-05-22 or 2017-05-23), by examining two conceivable attempts to give a nontrivially sufficient condition for orderliness (equivalently, a nontrivially necessary condition for randomness). To nip in the bud any misleading impressions of erudition which I might be producing in readers, I stress at the outset that they are two attempts which I concoct in mere haste, from what very little I know of the relevant literature - in essence just from a hasty Wikipedia skim. Here bibliographical suggestions from readers, directed to Toomas.Karmo@gmail.com, would help me make my work more solid. 

One attempt, I think from before the war, is inspired by philosopher-physicist Ludwig von Mises (1881-1973). The other attempt is inspired by work of recent vintage, from the contemporary mathematical logicians Martin-Löf, Schnorr, and Levin. Those three mathematical logicians have in their turn been building upon finite-sequence ideas from Andrey Nikolaevich Kolmogorov (1903-1987). But for this week, I shall have to end.

As preparation for the next installment, interested readers might want to check in one of the rather obvious Wikipedia places for von Mises. For Martin-Löf et al, interested readers might want to concentrate on the passage in https://en.wikipedia.org/wiki/Algorithmically_random_sequence starting Leonid Levin and Claus-Peter Schnorr proved a characterization in terms of Kolmogorov complexity: a sequence is random if there is a uniform bound on the compressibility of its initial segments.

Having already confessed this week to a couple of kinds of shallowness, I have now additionally to confess to working on just one tiny bit of the article, essentially just the bit quoted here. 

So, Gentle Reader, here is some more homework: as we seek the Holy Grail of a necessary-and-sufficient condition, does at any rate a condition nontrivially sufficient for orderliness of an infinite bit sequence (equivalently, nontrivially necessary for randomness of an infinite bit sequence) emerge (a) from von Mises, and (b) from Martin-Löf with Levin and Schnorr? If that happy thing does not emerge, then does some other happy thing, like a condition necessary for orderliness of an infinite bit sequence (equivalently, a condition sufficient for randomness of an infinite bit sequence) at least emerge, from at least one of these two places in the literature? And if at any rate something useful, while falling short of the Holy Grail itself, emerges from at least one of these two places in the literature, can we then make a few remarks, of a modestly stocktaking character, on the extent to which our results are falling short?


[This is the end of the current blog posting.]

Monday 13 November 2017

Toomas Karmo: DDO Conservation: Remarks in 2017-11-13 Town Council, as "Delegation"

Documents of interest to students of the David Dunlap Observatory and Park conservation file. Clockwise, from upper left: online developer promotion from http://myobservatoryhill.ca/, as visible in my Firefox on 2017-11-13; signboard developer promotion as noted at Major Mackenzie and Yonge around 2017-11-05; a mortgage agreement, under which the developer has in 2016 December borrowed, on the security of the 32 lost hectares, from the Canadian Imperial Bank of Commerce, 135 million CAD, payable on demand (this is a public document, available from the Land Registry); a terrain map, ultimately derived many months ago from http://www.richmondhill.ca; online political promomotion from http://www.karencilevitz.ca, as visible in my Firefox on 2017-11-13. - The map shows the lost 32 hectares (with streets and house lots drawn in), the conserved 5-hectare "DDO Panhandle lands" (as a long-and-thin parallelogram running south from the Trapezoid; the long sides of the parallelogram are aligned exactly north-south, whereas the four edges of the map rectangle run obliquely to the four cardinal directions, with north roughly on top), and the conserved 40-hectare "DDO Trapzoid" lands. The conserved "Trapezoid" portion is coloured in green. I have myself outlined in brown that part of the lost 32 hectares, comprising McMansion-style house lots, which is most egregious, and which I might reasonably have expected to save in sacrificing the bulk of my life savings when financing the Richmond Hill Naturalists' unsuccessful 2012 and 2014 Ontario Municipal Board appearances. It is this brown-outlined part that poses the greatest light-pollution threat to the three DDO telescopes (one of them being still the largest telescope on Canadian soil, and on the night of its 1935 First Light the second-largest in the world). - The online political promotion reads, in part, as follows: "A lifelong volunteer and community activist, Karen [sc Town Councillor Karen Cilevitz] served as Chair of the DDO Defenders for 6 years, leading this grassroots community advocacy group in protecting and conserving Richmond Hill’s iconic David Dunlap Observatory Campus and surrounding lands as a public legacy. Her dedicated work on the DDO file, and her work with residents and residents’ groups defending the Town against over-development, led Karen to run for public office. She prides herself as a steward of our natural environment  /.../". The asteroid named in her honour - asteroids are named for any essentially reason at all, by their discoverers, who can therefore confer on them names of friends, or associates, or whatever, pretty much at will - may be researched by Googling on the string 108382 Myke Wolf. (Myke Wolf made the discovery, He befriended Karen. His own legal position, including an allegation of personal name change, may be explored if necessary (I do not myself find this line of investigation strongly relevant to my own forensic work) by Googling on such things as the four-word string, with two pairs of quotation marks, "myke wolf" "parthenon technologies".) - Further legal or forensic background on my relations with the problematic pro-DDO-development Town Councillor Karen Cilevitz, and on my relations with the arguably misnamed "DDO Defenders", may be had from my server spaces http://www.karen-vs-toomas-blog.ca/ and http://www.karen-vs-toomas-legaldocs.ca/.
Shots of a few of the fourteen or fifteen streets under development in the lost 32 David Dunlap Observatory and Park hectares. That greenspace is now becoming a subdivision of some 520 or 530 homes (with a few dozen extra units of housing now possibly also coming, as apartment add-ons above residential garages).  Anticlockwise from upper left: "Callisto Lane" (Callisto is the second-largest of Jupiter's moons); "Telescope Gate", and (what is especially objectionable to the many conservationists interested in light pollution) "Night Sky Court".

Web promotion for the three current principal non-government players in the David Dunlap Observatory and Park conservation case, as downloaded around UTC=20171114T1520Z to my Firefox. Clockwise, from bottom left: (1)  http://www.ylab.ca/faq-links/, (2)  http://rascto.ca/content/fighting-light-pollution, (3) http://www.ddod.ca/. - Regarding "(1)": I should have mentioned in my 2017-11-13 Town Council presentation (from podium, as "Delegation", with supporting letter reproduced below) that the Town is now moving in an appropriate direction, proposing in Staff Report SRCS.17.23 (available from http://www.richmondhill.ca/, as an input document for the Council meeting of 2017-10-23) to make the laboratory-cum-workshop spaces of  DDO available to a local analogue, "YLab", of the Toronto-based Hacklab and the Kitchener-based Kwartzlab. To the best of my limited knowledge - I found out about YLab only on 2017-11-13, through a lamentable personal failure of curiosity - those spaces are now getting the right sort of tenant. - Regarding "(2)" and "(3)" jointly: It makes good sense to have the Royal Astronomical Society of Canada (RASC) back at DDO, and now with the DDO Defenders (DDOD) as a partner. The "joint" in the DDOD Web page writeup, as reproduced here (my readers should enlarge the image with a mouse-click) is a testament to successful diplomacy by various individuals, in discussions to which I have not been privy. Yes, yes, yes, say I, applauding as an outsider, albeit as a member both of RASC and of DDOD: let there now be joint astronomical outreach at DDO, under the aegis not of one organization but of some plurality. - We may hope that in future, RASC and DDOD will be able also to say something jointly about the vexed question of DDO light pollution. In the page from the RASC server which I have chosen to display here, light pollution is discussed indeed, but without reference to the awkward fact that RASC's Toronto Centre promoted itself at DDO without ever, to my knowledge, uttering a single effective public word, from the 2008 DDO sale right up to the present day,  regarding the light-polluting effect of the subdivision now being erected on the lost 32 DDO hectares. Well, my fellow RASC members, now is the time for you to speak up, particularly since you are likely now free from the legal agreements you unwisely signed around 2009 with the developer (back then you unwisely became, in essence, the developer's tenant and the developer's public-relations asset): are you, like those of us who ponder light pollution, unhappy now about "Dark Sky Court", "Telescope Gate", and the like, as depicted in the second of tonight's three graphics? - DDOD was to the best of my knowledge similarly silent on the light-polluting damage of the subdivision from the 2012 Ontario Municipal Board settlement, which paved the way for a subdivision, right through 2016. Over that long period, the general line, the генеральная линия, at DDOD was that the OMB settlement was on balance a good thing, through having saved 45 of the 77 DDO greenspace hectares. To my mind, this was like arguing in some hypothetical Soviet human-rights case that Mr Yuri Andropov is kinda-sorta a Good Guy, since he has released, say, 45 out of 77 dissidents, while keeping only 32 in his big Permskaya Oblast gulag. - In 2017, DDOD did manage to speak up in the Council chamber on light pollution, albeit timidly: Karen Cilevitz's successor as DDOD head, Dr Ian Shelton, at that point expressed unease about the light-pollution effect of certain proposed add-on apartment units, to be perched (such was the developer's new proposal, to an upset Council-chamber public) atop already-approved residential garages. DDOD thereby took a step in the right direction,  even while saying nothing about the bigger light-pollution problems - for instance, the problem  marked in my brown outline upon the map in the lower right-hand corner of the first of tonight's three graphics.


Revision history:

All times in these blog "revision histories" are stated in UTC (Universal Coordinated Time/ Temps Universel Coordoné,  a precisification of the old GMT, or "Greenwich Mean Time"), in the ISO-prescribed YYYYMMDDThhmmZ timestamping format. UTC currently leads Toronto civil time by 5 hours and currently lags Tallinn civil time by 2 hours.
  • 20171118T0410Z/version 4.2.0: Kmo found to his distress that he had to repair another broken hyperlink, to the Town of Richmond Hill homepage,. - Kmo reserved the right to make further tiny, nonsubstantive, purely cosmetic, tweaks over the coming 72 hours, as here-undocumented versions 4.2.1, 4.2.2, 4.2.3, ... . 
  • 20171118T0404Z/version 4.1.0: Kmo repaired a broken hyperlink to the DDOD homepage, in the caption for one of his top-of-page graphics. - Kmo reserved the right to make further tiny, nonsubsantive, purely cosmetic, tweaks over the coming 72 hours, as here-undocumented versions 4.1.1, 4.1.2, 4.1.3, ... .  
  • 20171114T0349Z/version 4.0.0: Kmo added a further graphic, regarding YLab, the Royal Astronomical Society of Canada (RASC), and the DDO Defenders (DDOD). He also added further and better particulars on his corrections of grammatical errors and typos, in his work at the Council podium, and made it clear that he had spoken to Council as "Delegation", rather (as he had been expecting before the event) in "Public Forum". - Kmo reserved the right to make further tiny, nonsubstantive, purely cosmetic, tweaks over the coming 48 hours, as here-undocumented versions 4.0.1, 4.0.2, 4.0.3, ... .
  • 20171114T0305Z/version 3.1.0: Kmo made some additions of forensic or legal substance to his caption for the graphic showing case-relevant commercial and political promotion, in respect of Asteroid Cilevitz 108382.
  • 20171113T2248Z/version 3.0.0: Kmo added a further graphic, mainly showing commercial and political promotion pertinent to the conservation case. 
  • 20171113T2113Z/version 2.0.0: Kmo added a graphic showing streets under development in the lost 32 David Dunlap Observatory and Park hectares. 
  • 20171113T2124Z/version 1.0.0: Kmo uploaded the text of his letter to Mayor and Council, a little ahead of his normal upload schedule. (The upload would normally have been scheduled for around UTC=20171114T0001Z. But it was necessary for Kmo to travel to the Town offices in the one- or two-hour interval preceding UTC=20171114T0001Z.)


[CAUTION: A bug in the blogger server-side software has in some past months shown a propensity to insert inappropriate whitespace at some points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears. - The blogger software has also shown a propensity, at any rate when coupled with my erstwhile, out-of-date, Web-authoring uploading browser, to generate HTML that gets formatted in different ways on different downloading browsers. Some downloading browsers have sometimes perhaps not correctly read in the entirety of the "Cascading Style Sheets" (CSS) which on all ordinary Web servers control the browser placement of margins, sidebars, and the like. If you suspect CSS problems in your particular browser, be patient: it is probable that while some content has been shoved into some odd place (for instance, down to the bottom of your browser, where it ought to appear in the right-hand margin), all the server content has been pushed down into your browser in some place or other. - Finally, there may be blogger vagaries, outside my control, in font sizing or interlinear spacing or right-margin justification. - Anyone inclined to help with trouble-shooting, or to offer other kinds of technical advice, is welcome to write me via Toomas.Karmo@gmail.com.]


[Some of my readers, especially conceivable readers in municipal or provincial or Canadian-federal decision-making circles, may find it helpful to have an upload of my letter to the Mayor and Council of the Town of Richmond Hill, as prepared for the 2017-11-13 "Public Forum" portion of the Town Council meeting. The letter is usefully read along with my many other earlier postings, on this same server, regarding the David Dunlap Observatory and Park heritage-conservation file. I have taken the liberty of tweaking my electronic *.pdf-format submission to the Clerks, made at UTC=20171113T1659Z, now correcting two or so small errors in grammar, and correcting roughly ten typos. Upon speaking from the podium, I submitted to the Clerks' table a hard copy of my letter, with my various grammatical and typographical corrections marked in blue ink, in case the municipality was retaining hardcopy files. - Readers seeking documentation, including audio and video, on public meetings involving Mayor and Council should click on the calendar icon https://www.richmondhill.ca/.] 



Submission by Toomas Karmo
for Town of Richmond Hill
Council Meeting of 2017-11-13,
for Inclusion in the Public Record 



The Town has kindly gone to trouble in advising me, in a preliminary way verbally on the evening of 2017-11-06, and then formally in an e-mail of 2017-11-07, that a revised version of SREIS.17.021 will be submitted to the next meeting of the DDO Park Project steering committee, early in 2018. I hope to report back to Council, either in Public Forum or as a Delegation, once that submission has been made by Commissioner Italo Brutto's team.

-0-0-0-0-

At this present 2017-11-13 meeting of Council, I must not so much repeat myself (by underscoring, as I just have, the importance of getting SREIS.17.021 right) as put onto the public record my concerns regarding a possible malign future path for DDO. I would urge both Town and taxpayers to maintain vigilance in the face of some looming threats.

Already we, the taxpayers, have lost 32 greenspace hectares to a developer, in a chain of events which has involved not only a skewed Ontario Municipal Board process in 2012 and 2014, but an outright  2017 July redrawing of Cultural Heritage Landscape boundaries. This adverse chain of events has undermined, perhaps fatally, our conceivable potential case for UNESCO World Heritage List designation. The UNESCO Paris adjudication would surely have to pay heavy regard to local enthusiasm, or lack of local enthusiasm, for conservation - at the David Dunlap Observatory and Park just as in the case of our close UNESCO World Heritage List parallel, the successful Joggins Fossil Cliffs case from Cumberland County, Nova Scotia. Whereas the people of Cumberland County could, and did, hold their heads high at Parks Canada and in Paris, this can no longer be said of the Town of Richmond Hill, and for the various elements in our community - here I direct specific attention to that opponent of full heritage conservation, Councillor Karen Cilevitz - who let our 32-hectare fiasco happen, and in the context of the closed-doors process which was a 2011-through-2012 OMB mediation even approved it.

If we are not vigilant now, the following further bad things may soon occur:
  • The developer may unfortunately (in my private, uninformed, opinion) try to follow through with the plan foreshadowed in its application or communication to the Town a couple of years ago - with the plan, namely, to establish a temporary subdivision sales centre in the Administration Building. Such a desecration of national scientific heritage would trigger a legal picket from me, as I have already on one or two previous occasions publicly warned. Picketing is legal insofar as it conveys information to the public without impeding public foot or vehicular traffic. In the event of a legal picket, everyone will suffer, with the Town's reputation taking a particular hit.
  • The circa-1865 Elms Lea mansion, or "DDO Director's House" - not mentioned, however briefly, in SREIS.17.021 - may unfortunately be put to something other than its now natural municipal use. The natural municipal use would be to support Richmond Hill heritage conservation in some way, optimally by becoming our Town's much-needed museum space. I would here remind the taxpaying public, and our Mayor and Council, that our current heritage centre on Church Street, worthy though it is, is too small to serve as a museum, and that our municipal historical artefacts are currently therefore housed out of public sight, in closed storage.
  • The Administration Building may, once renovated, unfortunately be put to something other than its now-natural municipal use. The natural use would be as housing for two things, and two only: (1) In its office space and auditorium space and library space, as housing for materials and activities supporting astronomical research (including citizen science) and astronomical outreach. (Under this heading would come the offices of some astronomical-outreach entity or entities, conceivably including the Royal Astronomical Society of Canada, a recent strain in their diplomatic relations with the Town notwithstanding.) (2) In its wood-workshop, metal-workshop, optics-workshop, sometime photography-darkroom, and electronics-lab spaces, materials and activities supporting some York Region equivalent of the type of citizen technological innovation (important for Ontario's entrepreneurial development) and non-astronomical citizen science successfully pursued by Kwartzlab in Kitchener and by Hacklab in Toronto.


[End of letter submitted to Town of Richmond Hill;
end of blog posting.]