I've been using LaTeX with subversion for collaboration for years. The LaTeX learning curve is much more an issue than the subversion learning curve.
But if the issue arises at all -- that means you are collaborating, and hopefully somebody in the group knows how to use LaTeX. And that's the best way to learn LaTeX.
You are thinking about the inclination relative to the sun's equator - however, Pluto's orbital inclination to the Earth's plane is more than that: A bit over 17 degrees.
Earth's own axis is tilted 23.5 degrees, and as there's no obvious integer resonance between their orbital periods, Pluto will at some time be visible overhead at as
high as +/- ~40.5 degrees (17+23.5) - which is surprisingly close to Chicago's latitude of ~41 degrees. So either they got lucky, or someone actually thought about that.
No, not quite. You're assuming that the ascending node of Pluto lines up perfectly with the current axis of the Earth, so that when Pluto is 17 degrees above the ecliptic, it's also at its most northerly. But that isn't actually the case.
Pluto's highest declination (angle above the plane of the Earth's equator) is actually only about 24 degrees. So, in fact Pluto does *not* ever pass directly overhead in Illinois.
Unless you want to wait for the Earth's axis to precess to the right alignment. That cycle takes about 17,000 years.
" this discovery alone is worth the cost of the machine in some ways."
Well it certainly would be if it were true. However, the energies the LHC will reach are already reached every day when cosmic rays hit our atmosphere, so this accelerator, at least, can't test many-worlds theories.
This makes me think of the great SF story "Doomsday Device", by John Gribbin (Analog, Feb. 1985 -- unfortunately not available online, AFAIK). In that story a powerful particle accelerator seemingly fails to operate, for no good reason. Then a physicist realizes that if it were to work, it would effectively destroy the entire universe, by initiating a transition from a cosmological false vacuum state to a lower-energy vacuum state. In fact, the accelerator *has* worked; the only realities the characters experience involve highly unlikely equipment failures. (Thus, a many-worlds physics is shown to be correct.) It's further revealed that the world has been "anthropically steered" in the past by arranging for it to be destroyed when things are not going well.
As others have mentioned, Moore's law is relevant because the Monte Carlo approach is highly parallelizable. For other game-play algorithms, indeed, Moore's law might not be relevant.
To elaborate, the MoGo programmers say that when the computing power (number of cores, or time) is doubled, the program beats the baseline version 63% of the time, and so far this seems to hold true no matter how large you scale it. A 63% victory rate corresponds to about a half-stone advantage in go. So, you need a computer roughly four times as fast to improve by one handicap stone. At the current rate of Moore's law (doubling every 2 years) that means about 4 years per stone.
Kim estimated that the game with MoGo would be tough even at 8 stones. That suggests we need roughly 32 years before the current approach is strong enough to beat the best humans on a midrange supercomputer. However, improvements are still being made to applying Monte Carlo techniques to go, so it could happen much sooner. On the other hand, it's conceivable that the 63% rule only operates so far, and the last few stones are the hardest.
The above is just my own back-of-the-envelope calculation; others in attendance felt that about 10 years was the expected timeframe. And actually I feel that way too; I was surprised when I ran the numbers and got 32.
Incidentally, Myungwan Kim expressed the view, before the match, that computers would never be as strong as pros at go. But for most of the programmers in the audience, at least, it was never a question of whether, just when.
Conway's Life was mentioned, but that is still a deterministic computer.
Many puzzles have been shown to effectively be nondeterministic computers. E.g., you can make a sliding-block puzzle that is solvable if and only if a given traditional computation succeeds.
Erickson takes a great approach by admitting that the common perception of hacking is rather negative, and unfortunately accurate in some cases. However, he smoothly counters this antagonistic misunderstanding...
Not having seen the book, I think I can still say he would do a much better job countering this misunderstanding by picking a more appropriate title.
Hmm. I thought the bad hobbit casting and portrayal was one of the most annoying things about the movies, almost as bad as the story changes. Ian Holm as Bilbo was about the least believable. It has nothing to do with how fine an actor he is. He just isn't Bilbo, by any stretch of the imagination.
And of course, it would be even more ridiculous to cast an older Holm as a much younger Bilbo.
This is fun and all, but you're equivocating so fast my head is spinning. I'm not equivocating at all. I'm sorry if you don't find the term "resource" appropriate. Both computability theory and complexity theory (which together broadly constitute "theory of computation") can be thought of in terms of what functions machines of various sorts can compute, or, equivalently, what formal languages they recognize. As well as in many other equivalent terms.
Also, believe it or not, there are some models of computation which are universal even though they only use finite resources! I have no idea what you're talking about. Is the statement not clear enough, or do you simply disbelieve it? There are many notions of computation. For example, there is nondeterministic computation. Of course, a nondeterministic Turing machine still cannot compute all recursive functions using only a (say) polynomially-bounded tape length. However, there are generalizations of Turing machines which can! Whether such machines are "reasonable" is a matter of interpretation. See
Perhaps because they both have to do with what a machine with a given set of resources can compute? No -- computability theory is concerned with what a machine with unlimited resources can compute. An infinite tape is still a resource. Also, believe it or not, there are some models of computation which are universal even though they only use finite resources!
Then, you complain that his use of the term "smallest" is unfair.
Which is it? Both. His use of the term "smallest" seems unfair because it is in relation to what seems to me to a definition of universality which is at best nonstandard and at worst ill-defined.
Again -- "this would be a fun problem to tackle if it were well defined".
It is well defined. And, it concerns whether a machine, which he has introduced, is universal, in a clear, meaningful sense. Well, I must admit that the precise sense escapes me, as it seems to escape Wolfram, from my quote above. I think Wolfram would probably be satisfied with a solution along the lines you propose. But why waste my time working on that, when it is all only for the greater glory of Wolfram's world view?
By the way, when you start to defend yourself by reminding people that you went to MIT, and had a famous advisor, you start to sound a bit like Wol.. oh, now I'm just being cruel. Yeah, you got me there.
Nobody decides 'plausibility' (at least not recursion theorists or researchers in computability). They investigate relative computability. It seems to me that where matters of choice of definition are concerned, questions of appropriateness (perhaps a better word than plausibility) apply.
You see, the functions computable by Turing machines whose "halting" is defined as some pre-specified infinite loop, identical for all outputs, are the same as the functions computable by regular Turing machines with a privileged halting state. That is why, from the point of computability theory, it doesn't matter that Wolfram's possible universal machine doesn't have a privileged halting state. Yes, of course. In other words, what you have done, informally, is specify a Turing machine W', which, when given an arbitrary Turing machine M and input w, will simulate Wolfram's machine on an encoding of M and w, and halt if Wolfram's machine trivially loops. Presumably you would also need to specify different kinds of such loops that should represent accepting and rejecting. But, I believe you will find that any such machine W' will have far more than two states and three symbols. In effect, he's cheated, by redefining universality. Actually I don't believe he gives a precise definition:
(Wolfram) In most cases, it should nevertheless be fairly obvious whether something should be considered a valid encoding for a universal system. What I object to here is Wolfram's taking it on himself to be arbiter of such notions as "universality" (let alone "science").
By contrast, Minsky's 7-state, 4-symbol Turing machine is universal in the standard sense. Now, in a certain sense, perhaps all "reasonable" definition of universal computation are equivalent. But when you are discussing the "smallest universal Turing machine" I believe it is incumbent upon you to not change the definitions of those words to suit your purposes.
Incidentally, you might want to tell Minsky that I don't understand computability theory. He might want to take back my Ph.D.
I don't know why you think that a result in computability theory would be of interest to a researcher in computational complexity (beyond both having 'something to do with computers'). Perhaps because they both have to do with what a machine with a given set of resources can compute?
Yes, that would be one approach. But my point is that this is not the normal definition of a universal Turing machine. It's misleading to use that terminology; also, the real problem he is asking for a solution for seems to be somewhat less well defined than the appropriate, corresponding question would be for an ordinary Turing machine. The decision question should be simply and formally specified. You came up with one that would seem plausible. But who decides what's plausible?
As a result, the result, positive or negative, would seem less interesting to me, as a researcher in computational complexity.
... if it were well defined. Instead Wolfram seems to be using a nonstandard, unclear notion of "universality". By any standard definition, no Turing machine without a halting state can be universal. Thus, coming up with a satisfactory proof of "universality" or "non-universality" would seem to serve no purpose besides promoting Wolfram's nonstandard definitions. At the least, he should not describe this gadget as a Turing machine, which definitely implies a particular notion of universality.
I agree with much of what you say. Yes, the brain was not manufactured based on any model or draft. Yes, the fact that we can't all agree on anything is, at least, a discouraging sign.
However, neuroscience is different from philosphy, because there is a real, physical object there to study. New experimental techniques appear every year. Eventually, we will know how brains work.
Neuroscience is different from physics, precisely because, as you have pointed out, brains are very messy things. Physicists are lucky that the laws of physics are orderly, that there is something simple and elegant like quantum mechanics there. Understanding how brains work is a completely different kind of challenge.
Yes, that's a big part of it. The basal ganliga form a giant reinforcement-learning system in the brain. Cortex on its own can perhaps learn to build hierarchical representations of sensory data, as Hawkins argues. But it can't learn how to perform actions that achieve goals without the basal ganglia. And in fact, there is a lot of evidence that suggests that sensory representation are refined and developed based on what is relevant to the brain's behavioal goals -- that the cortico-basal-ganglia loop contributes to sensory representation as well as motor, planning, intention, etc.
Like a lot of neuroscience, that can be argued either way at present. Clearly there are some differences between the cortical regions, some of which are genetically determined, and others of which might arise through experience. Primary visual cortex, for example, is highly specialized. Anterior (frontal) cortex integrally involves basal ganglia for its function; posterior cortex does so only indirectly. But does all of cortex do essentially the same thing? We'd all love to know the answer to that one. A lot of people would say yes.
Hawkins' book On Intelligence is interesting reading. There are a lot of good ideas in there. From my perspective as an AI / neuroscience researcher, the main weakness in his approach is that he only thinks about the cortex, whereas many other brain structures, notably the basal ganglia, are increasingly becoming implicated as having a fundamental role in intelligence.
This quote from the article is telling:
HTM is not a model of a full brain or even the entire neo-cortex. Our system doesn't have desires, motives, or intentions of any kind. Indeed, we do not even want to make machines that are humanlike. Rather, we want to exploit a mechanism that we believe to underlie much of human thought and perception. This operating principle can be applied to many problems of pattern recognition, pattern discovery, prediction and, ultimately, robotics. But striving to build machines that pass the Turing Test is not our mission. Well, my goal is to build machines that pass the Turing Test, so I have to think about more than cortex. But more generally, one might wonder how much of intelligence it is possible to capture with a system that "doesn't have desires, motives, or intentions of any kind".
out of dominoes. That is, if I give you a sliding-block puzzle, where the blocks are all dominoes laid flat in a box, and to goal is to slide one a certain way, that puzzle is a kind of nondeterministic computer.
... this sounds extremely similar to an experiment I came up with about 13 years ago, that completely convinced me I could send signals back in time. I even bought and assembled enough components to test large portions of the experiment in my garage. Everything except the generation of entangled photons; that takes more of a budget. I was still convinced it would work, until I went back to school and actually took some quantum mechanics courses.
Then I finally understood the elementary mistake I had been making. I find it difficult to believe a respected physics professor could make the same mistake. OTOH, I have shown my proposed experiment to very many extremely smart people, including physics professors, and very few have found the error.
Basically it seems like Cramer's idea is to send one photon on a pathway in which it intereferes with itself or not, as the experimenter chooses, which will then affect whether the entangled photon will have earlier interfered with itself. This doesn't work. You have to write out the QM to really see why. The actual math will depend on the specific experimental setup, but it sounds very likely to me that this is essentially the same experiment.
Anyone have a more technical description of the proposed experiment? (Or should I RTWFT)?
Slashdot Mirror
The current (legal) ones really tie your hands.
I've been using LaTeX with subversion for collaboration for years. The LaTeX learning curve is much more an issue than the subversion learning curve.
But if the issue arises at all -- that means you are collaborating, and hopefully somebody in the group knows how to use LaTeX. And that's the best way to learn LaTeX.
You are thinking about the inclination relative to the sun's equator - however, Pluto's orbital inclination to the Earth's plane is more than that: A bit over 17 degrees.
Earth's own axis is tilted 23.5 degrees, and as there's no obvious integer resonance between their orbital periods, Pluto will at some time be visible overhead at as
high as +/- ~40.5 degrees (17+23.5) - which is surprisingly close to Chicago's latitude of ~41 degrees. So either they got lucky, or someone actually thought about that.
No, not quite. You're assuming that the ascending node of Pluto lines up perfectly with the current axis of the Earth, so that when Pluto is 17 degrees above the ecliptic, it's also at its most northerly. But that isn't actually the case.
Pluto's highest declination (angle above the plane of the Earth's equator) is actually only about 24 degrees. So, in fact Pluto does *not* ever pass directly overhead in Illinois.
Unless you want to wait for the Earth's axis to precess to the right alignment. That cycle takes about 17,000 years.
" this discovery alone is worth the cost of the machine in some ways."
Well it certainly would be if it were true. However, the energies the LHC will reach are already reached every day when cosmic rays hit our atmosphere, so this accelerator, at least, can't test many-worlds theories.
This makes me think of the great SF story "Doomsday Device", by John Gribbin (Analog, Feb. 1985 -- unfortunately not available online, AFAIK). In that story a powerful particle accelerator seemingly fails to operate, for no good reason. Then a physicist realizes that if it were to work, it would effectively destroy the entire universe, by initiating a transition from a cosmological false vacuum state to a lower-energy vacuum state. In fact, the accelerator *has* worked; the only realities the characters experience involve highly unlikely equipment failures. (Thus, a many-worlds physics is shown to be correct.) It's further revealed that the world has been "anthropically steered" in the past by arranging for it to be destroyed when things are not going well.
As others have mentioned, Moore's law is relevant because the Monte Carlo approach is highly parallelizable. For other game-play algorithms, indeed, Moore's law might not be relevant.
To elaborate, the MoGo programmers say that when the computing power (number of cores, or time) is doubled, the program beats the baseline version 63% of the time, and so far this seems to hold true no matter how large you scale it. A 63% victory rate corresponds to about a half-stone advantage in go. So, you need a computer roughly four times as fast to improve by one handicap stone. At the current rate of Moore's law (doubling every 2 years) that means about 4 years per stone.
Kim estimated that the game with MoGo would be tough even at 8 stones. That suggests we need roughly 32 years before the current approach is strong enough to beat the best humans on a midrange supercomputer. However, improvements are still being made to applying Monte Carlo techniques to go, so it could happen much sooner. On the other hand, it's conceivable that the 63% rule only operates so far, and the last few stones are the hardest.
The above is just my own back-of-the-envelope calculation; others in attendance felt that about 10 years was the expected timeframe. And actually I feel that way too; I was surprised when I ran the numbers and got 32.
Incidentally, Myungwan Kim expressed the view, before the match, that computers would never be as strong as pros at go. But for most of the programmers in the audience, at least, it was never a question of whether, just when.
Many puzzles have been shown to effectively be nondeterministic computers. E.g., you can make a sliding-block puzzle that is solvable if and only if a given traditional computation succeeds.
Science News story:
http://www.sciencenews.org/articles/20020817/bob10.asp
Personal plug:
Games, Puzzles, and Computation
How many squares are there on a go board?
Digital devices reaching consumers with malware already installed?
Computers have been shipping with Microsoft products preinstalled for some time, I believe.
Hmm. I thought the bad hobbit casting and portrayal was one of the most annoying things about the movies, almost as bad as the story changes. Ian Holm as Bilbo was about the least believable. It has nothing to do with how fine an actor he is. He just isn't Bilbo, by any stretch of the imagination.
And of course, it would be even more ridiculous to cast an older Holm as a much younger Bilbo.
It says there that for the prize, the notion of universality is to be judged
acceptable by the Prize Committee.
I clicked on Prize Committee:
http://www.wolframscience.com/prizes/tm23/committee.html
And found these members:
Lenore Blum
Greg Chaitin
Martin Davis
Ron Graham
Yuri Matiyasevich
Marvin Minsky
Dana Scott
Stephen Wolfram
Since the prize was awarded, what definition of universality was used during
the deliberations?
In particular, Martin Davis, Ron Graham, and Dana Scott are subscribers to
the FOM list. What definition of universality are they using?
Harvey Friedman followed by:
...But, as I said in an earlier message, although the committee was kept
informed, we were never polled.
Martin
Martin Davis
Visiting Scholar UC Berkeley
Professor Emeritus, NYU Let's see Wolfram explain that.
http://www.subwayshuffle.com/
to the iPhone. With the touch screen, you could literally drag the trains between the stations. It would be the perfect platform.
Oh well.
http://www.cs.duke.edu/~reif/paper/games/bounds/p
or
http://www.swiss.ai.mit.edu/~bob/hearn-thesis-fin
Which is it? Both. His use of the term "smallest" seems unfair because it is in relation to what seems to me to a definition of universality which is at best nonstandard and at worst ill-defined. Again -- "this would be a fun problem to tackle if it were well defined".
It is well defined. And, it concerns whether a machine, which he has introduced, is universal, in a clear, meaningful sense. Well, I must admit that the precise sense escapes me, as it seems to escape Wolfram, from my quote above. I think Wolfram would probably be satisfied with a solution along the lines you propose. But why waste my time working on that, when it is all only for the greater glory of Wolfram's world view? By the way, when you start to defend yourself by reminding people that you went to MIT, and had a famous advisor, you start to sound a bit like Wol.. oh, now I'm just being cruel. Yeah, you got me there.
By contrast, Minsky's 7-state, 4-symbol Turing machine is universal in the standard sense. Now, in a certain sense, perhaps all "reasonable" definition of universal computation are equivalent. But when you are discussing the "smallest universal Turing machine" I believe it is incumbent upon you to not change the definitions of those words to suit your purposes.
Incidentally, you might want to tell Minsky that I don't understand computability theory. He might want to take back my Ph.D. I don't know why you think that a result in computability theory would be of interest to a researcher in computational complexity (beyond both having 'something to do with computers'). Perhaps because they both have to do with what a machine with a given set of resources can compute?
Yes, that would be one approach. But my point is that this is not the normal definition of a universal Turing machine. It's misleading to use that terminology; also, the real problem he is asking for a solution for seems to be somewhat less well defined than the appropriate, corresponding question would be for an ordinary Turing machine. The decision question should be simply and formally specified. You came up with one that would seem plausible. But who decides what's plausible?
As a result, the result, positive or negative, would seem less interesting to me, as a researcher in computational complexity.
... if it were well defined. Instead Wolfram seems to be using a nonstandard, unclear notion of "universality". By any standard definition, no Turing machine without a halting state can be universal. Thus, coming up with a satisfactory proof of "universality" or "non-universality" would seem to serve no purpose besides promoting Wolfram's nonstandard definitions. At the least, he should not describe this gadget as a Turing machine, which definitely implies a particular notion of universality.
I agree with much of what you say. Yes, the brain was not manufactured based on any model or draft. Yes, the fact that we can't all agree on anything is, at least, a discouraging sign.
However, neuroscience is different from philosphy, because there is a real, physical object there to study. New experimental techniques appear every year. Eventually, we will know how brains work.
Neuroscience is different from physics, precisely because, as you have pointed out, brains are very messy things. Physicists are lucky that the laws of physics are orderly, that there is something simple and elegant like quantum mechanics there. Understanding how brains work is a completely different kind of challenge.
Yes, that's a big part of it. The basal ganliga form a giant reinforcement-learning system in the brain. Cortex on its own can perhaps learn to build hierarchical representations of sensory data, as Hawkins argues. But it can't learn how to perform actions that achieve goals without the basal ganglia. And in fact, there is a lot of evidence that suggests that sensory representation are refined and developed based on what is relevant to the brain's behavioal goals -- that the cortico-basal-ganglia loop contributes to sensory representation as well as motor, planning, intention, etc.
Like a lot of neuroscience, that can be argued either way at present. Clearly there are some differences between the cortical regions, some of which are genetically determined, and others of which might arise through experience. Primary visual cortex, for example, is highly specialized. Anterior (frontal) cortex integrally involves basal ganglia for its function; posterior cortex does so only indirectly. But does all of cortex do essentially the same thing? We'd all love to know the answer to that one. A lot of people would say yes.
This quote from the article is telling: HTM is not a model of a full brain or even the entire neo-cortex. Our system doesn't have desires, motives, or intentions of any kind. Indeed, we do not even want to make machines that are humanlike. Rather, we want to exploit a mechanism that we believe to underlie much of human thought and perception. This operating principle can be applied to many problems of pattern recognition, pattern discovery, prediction and, ultimately, robotics. But striving to build machines that pass the Turing Test is not our mission. Well, my goal is to build machines that pass the Turing Test, so I have to think about more than cortex. But more generally, one might wonder how much of intelligence it is possible to capture with a system that "doesn't have desires, motives, or intentions of any kind".
out of dominoes. That is, if I give you a sliding-block puzzle, where the blocks are all dominoes laid flat in a box, and to goal is to slide one a certain way, that puzzle is a kind of nondeterministic computer.
Details: http://www.dartmouth.edu/~rah/ncl-tcs.pdf
... this sounds extremely similar to an experiment I came up with about 13 years ago, that completely convinced me I could send signals back in time. I even bought and assembled enough components to test large portions of the experiment in my garage. Everything except the generation of entangled photons; that takes more of a budget. I was still convinced it would work, until I went back to school and actually took some quantum mechanics courses.
Then I finally understood the elementary mistake I had been making. I find it difficult to believe a respected physics professor could make the same mistake. OTOH, I have shown my proposed experiment to very many extremely smart people, including physics professors, and very few have found the error.
Basically it seems like Cramer's idea is to send one photon on a pathway in which it intereferes with itself or not, as the experimenter chooses, which will then affect whether the entangled photon will have earlier interfered with itself. This doesn't work. You have to write out the QM to really see why. The actual math will depend on the specific experimental setup, but it sounds very likely to me that this is essentially the same experiment.
Anyone have a more technical description of the proposed experiment? (Or should I RTWFT)?