August 2013 - mathfun@mailman.xmission.com

Re: [math-fun] INSTRUCTION SUMMARY CARD
by Henry Baker 07 Aug '13

07 Aug '13

Are you sure this isn't the instruction set for those 'round' computers that someone was giving away in the 1960's at MIT? (The circuit boards were _round_, so they would fit in the nose cone of a (not so ballistic?) missle.) At 06:07 PM 8/7/2013, Bill Gosper wrote: >Oops, those were both side 1. Try these: http://gosper.org/inscard1-lg.jpg http://gosper.org/inscard2-lg.jpg Sorry, --rwg > >On Wed, Aug 7, 2013 at 4:30 PM, Bill Gosper <billgosper(a)gmail.com> wrote: >> >> On 2013-08-03 23:39, Joerg Arndt wrote: >> >> Sounds well worth to take a photo (or better, scan) and put that online? Computer museum people might hugely appreciate. Being born only 1964, I do not recall the instruction set :^) You could ask about the machine on stack-overflow if it remains unknown. Best, jj >> >> Thanks to NeilB >> http://gosper.org/inscard2-lg.jpg >> http://gosper.org/inscard2-lg.jpg >> (16M each!) >> Maybe this was some dream machine that was never built? --rwg >> > * Bill Gosper <billgosper(a)gmail.com> [Aug 04. 2013 08:25]: >> > A bunch of boxes of my stuff fell off the shelves in the basement. > >On the floor was this laminated card, in improbably good condition, and of which I have no recollection. > >It lists three-letter mnemonics, about thirty per side, along with their TIME, plus eight other columns labeled LAR, RAR, LAC, RAC, LBR, RBR, LX, and RX, apparently active registers. > >Typical rows: 6+ ASL U U CH CH U U U U 51 DVD C(LX) C(RX) CH CH C(LAC) C(RAC) U U Presumably Accumulator(?) Shift Left and DiViDe. > >The bottom corners read MCF 105 and APRIL 27, 1959 > >This looks like an improbably rich (and fast) instruction set for 1959. > >51 Ã¬sec was the Divide speed of the 1963 Univac 1206 (Cray's design). > >Pre Cray Univac? RCA? Probably not IBM. > >It must have been the only computer in some large context, given no name on the card. > >(I doubt there was an "MCF 105"!) > >I was a high school sophomore in 1959. > >I wonder if I got it from the "giant brain" in the basement of the Franklin Institute. > >Or maybe it's a souvenir replica from some later exhibit? > >--rwg >> > Does anybody know how to prevent line-break destruction when copying from >> Roundcube to GMail? (Short of switching from Firefox to Safari).

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Re: [math-fun] INSTRUCTION SUMMARY CARD
by Bill Gosper 07 Aug '13

07 Aug '13

Oops, those were both side 1. Try these: http://gosper.org/inscard1-lg.jpg http://gosper.org/inscard2-lg.jpg Sorry, --rwg On Wed, Aug 7, 2013 at 4:30 PM, Bill Gosper <billgosper(a)gmail.com> wrote: > > On 2013-08-03 23:39, Joerg Arndt wrote: > > Sounds well worth to take a photo (or better, scan) and put that online? Computer museum people might hugely appreciate. Being born only 1964, I do not recall the instruction set :^) You could ask about the machine on stack-overflow if it remains unknown. Best, jj > > Thanks to NeilB > http://gosper.org/inscard2-lg.jpg > http://gosper.org/inscard2-lg.jpg > (16M each!) > Maybe this was some dream machine that was never built? --rwg > > * Bill Gosper <billgosper(a)gmail.com> [Aug 04. 2013 08:25]: > > A bunch of boxes of my stuff fell off the shelves in the basement. On the floor was this laminated card, in improbably good condition, and of which I have no recollection. It lists three-letter mnemonics, about thirty per side, along with their TIME, plus eight other columns labeled LAR, RAR, LAC, RAC, LBR, RBR, LX, and RX, apparently active registers. Typical rows: 6+ ASL U U CH CH U U U U 51 DVD C(LX) C(RX) CH CH C(LAC) C(RAC) U U Presumably Accumulator(?) Shift Left and DiViDe. The bottom corners read MCF 105 and APRIL 27, 1959 This looks like an improbably rich (and fast) instruction set for 1959. 51 μsec was the Divide speed of the 1963 Univac 1206 (Cray's design). Pre Cray Univac? RCA? Probably not IBM. It must have been the only computer in some large context, given no name on the card. (I doubt there was an "MCF 105"!) I was a high school sophomore in 1959. I wonder if I got it from the "giant brain" in the basement of the Franklin Institute. Or maybe it's a souvenir replica from some later exhibit? --rwg > > Does anybody know how to prevent line-break destruction when copying from > Roundcube to GMail? (Short of switching from Firefox to Safari).

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[math-fun] INSTRUCTION SUMMARY CARD
by Bill Gosper 07 Aug '13

07 Aug '13

A bunch of boxes of my stuff fell off the shelves in the basement. On the floor was this laminated card, in improbably good condition, and of which I have no recollection. It lists three-letter mnemonics, about thirty per side, along with their TIME, plus eight other columns labeled LAR, RAR, LAC, RAC, LBR, RBR, LX, and RX, apparently active registers. Typical rows: 6+ ASL U U CH CH U U U U 51 DVD C(LX) C(RX) CH CH C(LAC) C(RAC) U U Presumably Accumulator(?) Shift Left and DiViDe. The bottom corners read MCF 105 and APRIL 27, 1959 This looks like an improbably rich (and fast) instruction set for 1959. 51 μsec was the Divide speed of the 1963 Univac 1206 (Cray's design). Pre Cray Univac? RCA? Probably not IBM. It must have been the only computer in some large context, given no name on the card. (I doubt there was an "MCF 105"!) I was a high school sophomore in 1959. I wonder if I got it from the "giant brain" in the basement of the Franklin Institute. Or maybe it's a souvenir replica from some later exhibit? --rwg

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[math-fun] Fwd: "The" q-Fibonacci numbers
by Bill Gosper 06 Aug '13

06 Aug '13

George Andrews privately replied A variety of problems arise in trying to work out q-analogs of various aspects of the Fibonacci numbers using Schur's q-Fibonacci numbers. A description of some of these is given in Fibonacci numbers and the Rogers-Ramanujan identities. Fibonacci Quarterly 42(1):3-19 (2004) George [...] This interesting paper, by somebody-or-other, can be found at http://www.fq.math.ca/Papers1/42-1/quartgranville01_2004.pdf --rwg

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[math-fun] quantum determinism
by Warren D Smith 06 Aug '13

06 Aug '13

--Von Neumann QM is deterministic except during "measurements." Modern view/hope is measurements really do not exist. If so then as a result, everything is completely deterministic. However it sure seems like there are measurements and nondeterminism, e.g. radioactive decay. That allegedly is an illusion. (So Asimov had it exactly wrong, QM excludes the possibility of NONdeterminism.) What happens is, you only perceive part of the universe. The whole ball of wax is deterministic, but since you only perceive part it seems nondeterministic and seems to involve "measurements." > From: Dan Asimov <dasimov(a)earthlink.net> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: Re: [math-fun] free will > Message-ID: <70F0E5F5-28AB-467D-91F3-5CDC403859DE(a)earthlink.net> > Content-Type: text/plain; charset=us-ascii > > These two things ("free will" and "determined by causes I can't perceive") > are not almost the same, but instead are almost opposites. Of course, > "determined by causes I can perceive" would also exclude free will. > Ultimately, "free will" per se is precisely the opposite of "determinism". > > Speaking of determinism, can someone please clarify a confusion I've had > about the consequences of quantum mechanics: > > 1) I used to believe in determinism, but then learned that QM implied some > things happened ultimately by chance with no underlying mechanism. > > 2) Then I believed there must be hidden variables until I heard of Bell's > Theorem, which is said to prove the non-existence of hidden variables in > QM. > > 3) Then I heard that Bell's Theorem is valid only if non-locality is > excluded. > > QUESTION: Does QM exclude the possibility of determinism? Is some kind of > non-locality consistent with known physics? > > --Dan

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Re: [math-fun] quantum theory foundational issues, my theory of how they should be resolved
by Adam P. Goucher 06 Aug '13

06 Aug '13

> So you think we could eventually build a robot that exhibited behavior which we would > consider human-like and indicative of consciousness - but the robot wouldn't be conscious. > What if we replace neurons in your brain, one-by-one, with input-output, functionally > identical artificial components so that your behavior was unchanged? Do you think you > would gradually lose consciousness? Possibly. I can't really speculate until this experiment has been performed (on my brain, since consciousness cannot be measured externally). What happens if someone creates an exact copy of you (impossible by Pauli exclusion, but never mind)? Which one of those (the original or the replica) is `you'? > Whenever anyone writes "obviously" my B.S. meter quivers. I don't think either of your > last two paragraphs is right. First, whether a Turing machine is conscious would depend > on what program it is running. Assuming that Turing machines can be conscious, then (say) a universal machine simultaneously dovetailing all Turing machines would necessarily be conscious. > Does it have enough self-reflection to prove Godel's > incompleteness theorem? Plausibly, yes. > Does it create a narrative memory? I'm not sure exactly what > program instantiates consciousness, but I very much doubt it's just a matter of > "complexity" however that's measured. The reason that we haven't come to a definite conclusion is that people haven't unanimously agreed on a good definition of consciousness. Sincerely, Adam P. Goucher

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Re: [math-fun] quantum theory foundational issues, my theory of how they should be resolved
by Adam P. Goucher 06 Aug '13

06 Aug '13

> > It is unlike anything whatsoever that is covered by physics. As far as physics is concerned (and I am not blaming physics for this), the world could just be a totally insensate machine that follows physical laws but feels nothing. > > Could it? Is philosopher's zombie possible? It seems to me unlikely that one could > construct, grow, or otherwise have something that looks and acts and is physically like a > human being but has no subjective experience. Making something look like a human is not difficult. Nor is making something `physically like' a human being. The only one of those things that is actually hard to replicate is human behaviour. We can simulate neural networks on computers, and they're becoming gradually more intelligent as time progresses. For instance, I think they've been able to design electronic circuits and produce art, amongst other things. Together with natural language processing and database accessing (such as Wolfram Alpha), and knowledge acquisition (such as IBM Watson), it wouldn't surprise me if a machine passes the Turing test within the next decade or so. Also, computers are provably not conscious, since they can be emulated by Turing machines, which are obviously not conscious*. * If they were conscious, then _everything_ of sufficient complexity would have the capability of consciousness. And as Geoff Xia showed us, the n-body problem enables particles to be projected to infinity in finite time, one corollary of which is Turing-completeness, so `sufficient complexity' means `a few elementary particles'. Sincerely, Adam P. Goucher http://cp4space.wordpress.com

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[math-fun] Consciousness vs the mysterious AP Goucher entity... the route to progress
by Warren D Smith 05 Aug '13

05 Aug '13

[Gmail deleted my previous post attempts!?] AP Goucher's "proof" that Turing machines cannot be conscious i.e. "tons of simple systems have Turing universal power", is wrong since Turing machines need infinite memory and providing a system with Turing universal power with an infinite uncorrupted-by-external-noise memory, seems impossible in our universe. So argument based on impossible premise. You can get pretty far with a large finite memory but it seems by far the most probable way a universal-Turing-like machine with large finite memory could arise naturallly is via what we call "life"... Other arguments might include "Turing machine is made of unconscious components" -- but so is allegedly-conscious-entity AP Goucher. Or "self awareness," whatever that is. It seems clear to me a Turing machine which can fully examine (and emulate arbitry bits of!) its entire program is far more self-aware than AP Goucher will ever be. Albeit I must admit this: a Turing machine via introspection is not really capable of deducing its full internal workings (transition table, program) with full confidence since maybe those things had been evilly designed by machine's creator to mislead it. Think can prove this deduction task is undecidable. To break out of this quagmire and make progress we need to begin with a DEFINITION of "consciousness." And I would prefer it be "scientific." I am not sure what definition APG had in mind but it seems clear his notion was not scientific since he agrees it is not externally measurable and I presume also not even internally measurable (how does APG know he is not a program running on a TM?) hence fails Popperian criteria for being "scientific." Consult my paper Mathematical definition of 'intelligence' (and consequences) http://rangevoting.org/WarrenSmithPages/homepage/iq.pdf and section 21 provides an inadequate preliminary discussion of "consciousness." It contains this definition: Tentative Proposal: A consciousness is "an intelligent entity which interacts with some law-obeying randomized external environment in an effort to increase some kind of numerical reward." The paper defines "intelligence" and proves theorems about it, albeit essentially the same definitions and same theorems were also found independently by Marcus Hutter. Now the hackers in the audience might be interested in creating (for the first time?) an intelligent computer program. This is not difficult, I believe it could be done in 1 week of programming. Maybe even 1 day if you are really good. The paper explains how and proves such programs exist. Unfortunately the easy-to-create intelligent programs will be very slow. Another valuable task would be creating an intelligence testing framework and ongoing intelligence competition. Paper also explains how to do that. The fact the so-called "AI community" has not done these things is a severe indictment of it. If this Tentative Proposal can be made more precise we will have a mathematical definition of consciousness and will be able to prove theorems about it; it will become fairly clear AP Goucher really is conscious; we will know conscious computer programs exist and be able to create them; and we'll hopefully be able to prove theorems about what certain conscious entities "experience" when in quantum superpositions.

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[math-fun] Consciousness vs the mysterious "Goucher" entity
by Warren D Smith 05 Aug '13

05 Aug '13

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[math-fun] quantum theory foundational issues, my theory of how they should be resolved
by Warren D Smith 05 Aug '13

05 Aug '13

> 1. Re: NYTimes: quantum theory w/o observers (meekerdb) > There's a good paper by Schlosshauer and Camilleri that discusses the > historical debate > over the Heisenberg cut and how the question has mostly been answered by the > idea of > decoherence. > > http://arxiv.org/pdf/0804.1609v1.pdf > > I say 'mostly' because pushing the Heisenberg cut all the way to include > conscious > observers, as in Everett's interpretation of QM, is still a little > controversial because > we lack a good theory of consciousness. > You won't learn anything useful from the NYT discussion (Callendar's essay > is good, but > it's short and assumes a lot of background). The best current ideas are > decoherence and > Everett's many worlds. Read Schlosshauer's review papers: > > http://arxiv.org/pdf/0804.1609v1.pdf > > or for more depth > > http://arxiv.org/pdf/quant-ph/0312059.pdf > > Brent Meeker --ok. First of all, the "decoherence program" seemed to me inadequate. This is that every physical system is contained in an "environment" and since it interacts with environment it effectively is being "measured" (no real measurement is needed though, that concept is claimed really not to exist). So for example, why do you not experience being in a superposition of living in Paris and Tokyo? Because some cosmic ray, or air molecule, or whatever (environment) interacts with you in Tokyo only, thus "measuring" the fact you are in Tokyo or not. Sounds great... except why wasn't the cosmic ray in a superposition of being in Paris & Tokyo? This doesn't solve the problem of why the world is not weird; it merely pretends to solve the problem by already assuming the answer. ("It's turtles all the way down.") I once wrote a short paper on "why quantum computers won't work" whose argument rested on 4 axioms about the nature of decoherence, which may or may not be true. Read it: "Argument against quantum computers (or against certain decoherence models)" http://rangevoting.org/WarrenSmithPages/homepage/whywontwork2.ps Recently Scott Aaronson read this paper and pointed out things are not as simple as my paper made it appear... for example, some of the axioms are not really well defined. (What is the "location" of a "qubit"?) Second. What if the physical system is "the whole universe"? I have an idea about that, but it is only very slightly mentioned in the papers Meeker cited. It is this. There is a part of the universe we can perceive, and there is a part we cannot. For example, we have a hard time perceiving dark matter and gravitons. Nevertheless, there are interactions between parts A and B. So my proposal is, since we can only see part A, part B acts as the external environment from our point of view. Now what is needed to make this work, is that almost always (or at least, "often"), when parts A and B interact, they never do so again. Similarly to, if you interact with that cosmic ray, it flies off into outer space, never to interact with you again. This causes it to carry away "measured information" permanently. If you could keep interacting over & over again with that cosmic ray, it'd get entangled with your position, and hence would no longer be "measuring" your position in the sense of Von Neumann measurement. (There is an interpretation of Von Neumann measurement involving randomization of the phase angles of off-diagonal terms in density matrix; this randoms need to be independent.) So with the cosmic ray, the problem is, the whole universe might get entangled with your position, so the whole damn universe would not be capable of "measuring" it, so the whole argument would become doubtful. That's why the cosmic ray explanation is inadequate. Now, to return to my "parts A & B" explanation, I have proven, that gravitons after they are created almost never interact with anything. Ever. For the rest of time. See this paper by me: "From time-irreversibility in gravity to measurement in quantum mechanics" http://rangevoting.org/WarrenSmithPages/homepage/absorber.pdf http://rangevoting.org/WarrenSmithPages/homepage/absorber.ps "Almost never" means the interactions occur for less than any fixed positive constant fraction of gravitons. "Anything" means matter. My point is this. The gravitons form a second, shadow universe, or external environment, for the parts of the universe we can see. There is no issue that this external environment might get entangled with our part and hence unable to "measure" our part, because of my "almost never interacts again" theorem -- the first time our part interacts with a graviton, it is a virgin, and that graviton (now entangled), never comes back to haunt us (re-interact, non-independent randomness). So effectively via gravitons, there is an inexhaustible resource of new, non-entangled, random qubits in part B of the universe, which is able to keep decohering our part A. If you examine the numbers, this effect alone is large enough (even though gravity is an extremely weak interaction) to explain why the world appears classical to a human observer. So that is my theory.

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