The relativity of originality
An anonymous commenter asked for my opinion of The Free Will Theorem, a much-discussed recent paper by John Conway and Simon Kochen. I’ve been putting it off, but I’ll finally will myself to say something.
I read The Free Will Theorem mostly as an amusing romp through the well-travelled philosophical terrain of quantum mechanics, relativity, and entanglement. I’ve always enjoyed Conway’s writing style, so it was a treat to see his usual jokes and puns out in full force.
Of course, the reason the paper has attracted attention is the Free Will Theorem itself, which I’ll paraphrase as follows:
Suppose that (1) the laws of physics allow something like a Bell or GHZ experiment, (2) the people doing the experiment can set their detectors any way they want (i.e., in a way not determined by the previous history of the universe), and (3) something like Lorentz invariance holds (i.e. there’s one reference frame where experimenter A measures first, and another where experimenter B measures first). Then the results of the experiment are also not determined by the previous history of the universe.
Or as the authors colorfully put it: “if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity.”
(Note that by “free will,” all Conway and Kochen mean is the property of not being determined by the previous history of the universe. So even events with known probability distributions, like coin flips and quantum measurements, can have “free will” according to their definition.)
My reaction to the Free Will Theorem is threefold:
- It’s a very important, even if mathematically trivial, consequence of the Bell/GHZ/Kochen-Specker-type theorems.
- It will be new to many physicists.
- It was folklore among those who think about entanglement and nonlocality.
I’ll be grateful for any references in support of the last point. Right now, all I can offer is that I gave almost the same argument four years ago, in my review of Stephen Wolfram’s A New Kind of Science (see pages 9-11). My goal there was to show that no deterministic cellular-automaton model of physics, of the sort Wolfram was advocating, could possibly explain the Bell inequality violations while respecting relativistic invariance. I didn’t think I was saying anything terribly new.
Conway and Kochen try to preempt such criticism as follows:
Physicists who feel that they already knew our main result are cautioned that it cannot be proved by arguments involving symbols such as , Ψ, ⊗, since these presuppose a large and indefinite amount of physical theory.
I find this unpersuasive. For me, the whole point of the Bell, GHZ, and Kochen-Specker type theorems has always been that they don’t presuppose quantum mechanics. Instead they show that any physical theory compatible with certain experimental results has to have certain properties (such as nonlocality or contextuality).
I should admit that the Free Will Theorem improves on the argument in my book review in at least three ways:
- It gets rid of probabilities, by going through a two-party version of the Kochen-Specker Theorem instead of through Bell’s inequality. (I mentioned in my review that the argument could be redone using the GHZ paradox, which involves three parties but is deterministic. I didn’t mention that it could also be done using two-party Kochen-Specker.)
- It gives a cute, memorable name — “free will” — to something that I referred to only by convoluted phrases like “randomness that’s more fundamental than the sort Wolfram allows” (by which I meant, that’s not reducible to Alice and Bob’s subjective uncertainty about the initial state of the universe).
- It makes the assumptions more explicit. For example, I never talked about Alice and Bob’s “free will” in choosing the detector settings, since I thought that was just assumed in talking about Bell’s inequality in the first place! (In other words, if Wolfram denied that Alice and Bob could choose the detector settings independently of each other, then he could have dispensed with Bell’s inequality in a much simpler way than he actually did.)
I should also admit that I like Conway and Kochen’s paper. Indeed, the main question it raises for me is not “how could they possibly pass this off as original?” but rather “do we, as scientists, sometimes put too high a premium on originality?”
In all the reading I’ve done in philosophy, I don’t know that I’ve ever once encountered an original idea — in the sense that, say, general relativity and NP-completeness were original ideas. Indeed, whenever I read about a priority dispute between philosophers (like the infamous one between Saul Kripke and Ruth Barcan Marcus), it strikes me as absurd: all the ideas under dispute seem obvious!
But does it follow that philosophy is a waste of time? No, I don’t think it does. The same “obvious” idea can be expressed clumsily or eloquently, sketched in a sentence or developed into a book, brought out explicitly or left beneath the surface. Now, I’m well aware that that’s not an original sentiment — nor, for that matter, is anything in this post, or probably this entire blog. Yet here I am writing it, and here you are reading it.
You might respond that Wolfram can (and does) mount a similar defense of A New Kind of Science: that sure, lesser mortals might have realized decades ago that simple programs can produce complex behavior, but they didn’t grasp the true, Earth-shattering significance of that fact. Compared to Wolfram, though, I think Conway and Kochen have at least two things going for them: (1) they don’t spend 1,200 pages denigrating the work of other people, and (2) they accept quantum mechanics.
From Ecclesiastes:
All streams run to the sea,
but the sea is not full;
to the place where the streams flow,
there they continue to flow.All things are wearisome;
more than one can express;
the eye is not satisfied with seeing,
or the ear filled with hearing.What has been is what will be,
and what has been done is what will be done;
there is nothing new under the sun.
Follow
Comment #1 May 11th, 2006 at 8:09 am
How do you reconcile your smugly arrogant description (I’m sure you’ll object to my characterization of it as such, but that’s how I read it) of all of philosophy as “obvious” with the fact that philosophers disagree so vehemently on so many key issues? Two contradictory ideas cannot both be obvious, can they? If you mean that in any such case, one of them is obviously true and the other is obviously false, then you’re making quite a strong claim: that not only do you know the answer to all philosophical problems, but that the answers are all obvious!
Even if we restrict ourselves to something like the Kripke-Barcan dispute, not everyone believes those ideas are correct either. Are you claiming to be able to settle the matter?
Comment #2 May 11th, 2006 at 8:54 am
Two contradictory ideas cannot both be obvious, can they?
Yes, they can. “If water weren’t H2O, it would still be water” is obvious. “If it water weren’t H2O, it would be something other than water” is also obvious.
What I mean is that, if you spent an hour writing down all the arguments for and against these propositions you could think of, then nothing any philosopher had said about them over the centuries would come as a huge surprise to you. (Contrast with “There are no intermediate cardinalities between the integers and the reals.”)
I don’t mean that I can answer the question of whether water would still be water if it weren’t H2O. 🙂
Let me stress, again, that I’m not using the word “obvious” in a pejorative sense. If nothing obvious were ever worth saying, I wouldn’t have started a blog.
Comment #3 May 11th, 2006 at 9:04 am
I’ll be grateful for any references in support of the last point. S.A.
Maybe this one:
Asher Peres, ‘Existence of “free will” as a problem of physics, Foundations of Physics’, vol. 16, no. 6 (1986), pp. 573-584.
and …
“It has been argued that quantum mechanics is not locally causal and
cannot be embedded in a locally causal theory. That conclusion depends on treating certain experimental parameters, typically the orientations of polarization filters, as free variables. But it might be that this apparent freedom is illusory. Perhaps experimental parameters and experimental results are both consequences, or partially so, of some common hidden mechanism. Then the apparent non-locality could be simulated.”
-John Bell, “Free Variables and Local Causality”, Epistemological
Letters, 15, (1977)
Comment #4 May 11th, 2006 at 9:08 am
I’ll check out the Asher Peres paper — thanks!
Comment #5 May 11th, 2006 at 9:16 am
What I mean is that, if you spent an hour writing down all the arguments for and against these propositions you could think of, then nothing any philosopher had said about them over the centuries would come as a huge surprise to you.
Instead of trying to argue the non-obviousness of some philosophical arguments and positions at a general level I’ll just take an example.
Russell is one of your intellectual heroes (I remember reading that in some strange pseudo-autobiographical essay you wrote), right? Well, Russell would in all likelihood have considered the new theory of reference startingly fresh, full of arguments and propositions he had never thought of. And, believe me, he had spent more than an hour trying to write down all the arguments against and in favor of his own descriptive theory of reference; probably what amounts to several years of his life.
What I would agree with is this: philosophical positions and arguments often seem incredibly obvious in hindsight. Everyone who reads about the causal theory of reference for the first time slaps themselves on the head and says “duh! I could have come up with that!” But the fact of the matter is that they didn’t, and I’m willing to bet my copy of “On denoting” on the fact they wouldn’t have if they had spent an hour trying either.
Don’t get me wrong here. I see what you’re getting at, and to some extent I agree. I just think that a) you overstate your case greatly, and b) there’s no reason to be a troll about it. If you use the word “obvious” in anything resembling the ordinary usage of the word, it’s pejorative in the context of describing other people’s ideas as such. No two ways about it.
Comment #6 May 11th, 2006 at 9:35 am
Anonymous: Alright, you win. Indeed, your counterargument involving Russell is completely obvious. 😉
Comment #7 May 11th, 2006 at 10:50 am
“do we, as scientists, sometimes put too high a premium on originality?”
I’ve seen cases of a researcher bringing attention to a new field and the discussion getting bogged on “exactly how new is the new field” instead of “is this new field the next big thing” which was the real point. I.e. the whole argument placed originality above relevance.
Comment #8 May 11th, 2006 at 11:38 am
There is a paper by some philosophers, which is the first occurrance of the type of argument presented in the “Free Will” paper. It was the first “deterministic” proof of the Bell theorem, in the sense of not using inequalities and probabilities in the argument, and uses the bipartite Kochen Specker construction. It even predates the GHZ paper, and the fact that almost no-one in qinfo has heard of it is further evidence that physicists never bother to look at relevant literature published in philosophy journals.
There are a couple of well-kown ideas in qinfo to do with nonlocality that have a similar history. If you are bored then you can try to figure out what they are.
Anyway, I am away, so I can’t look up the reference. Jon Barrett knows it, so you can ask him.
Comment #9 May 11th, 2006 at 1:29 pm
So even events with known probability distributions, like coin flips and quantum measurements, can have “free will” according to their definition.
But the outcome of a coin flip is completely dependent on the previous history of the universe. So would this “theorem” only apply to phenomena where QM is relevant?
(Note: I have not read the paper)
Comment #10 May 11th, 2006 at 2:06 pm
Scott, In one of your previous talks I remember you saying that you started off with a philosophical question and ended up with 7 or 8 results.
Does philosophy still inspire your research or personality?
Comment #11 May 11th, 2006 at 2:07 pm
And please say more than Yes or No.
Comment #12 May 11th, 2006 at 2:34 pm
weichi:
But the outcome of a coin flip is completely dependent on the previous history of the universe.
I meant an idealized coin flip. (If you like, one where the decision of how to toss the coin is based on some quantum event.)
Comment #13 May 11th, 2006 at 3:46 pm
NP-completeness is an original idea? Now, that is an original idea 🙂
Comment #14 May 11th, 2006 at 4:11 pm
Nagesh: That must have been my “postselection” talk, the one where I was trying to sell philosophy to physicists. 7 or 8 is admittedly an exaggeration. 🙂
In general, the results that I admire most in any field are the ones that start with a philosophical question and end with a non-obvious technical result. Cantor’s Theorem, Gödel’s Theorem, the unsolvability of the halting problem, Einstein’s derivation of the Lorentz transforms, Aumann’s Theorem on common knowledge, Arrow’s voting theorem, the PCP Theorem, the Bell and Kochen-Specker theorems, and many results in quantum computing and information are all examples of what I’m talking about. (This is not an exhaustive or representative list.)
Comment #15 May 11th, 2006 at 4:16 pm
To the anonymous philosopher who took me to task earlier:
Out of curiosity, are there “open problems” in the causal theory of reference? I.e. questions that no one has an answer to today, but to which one might expect a surprising answer in the future?
Comment #16 May 11th, 2006 at 5:42 pm
Scott, your list is nonsensical. Can you differentiate the work that started with a philosophical question, from that which arose out of “non-philosophical” mathematical study, and then was later imbued with philosophical import?
Comment #17 May 11th, 2006 at 7:30 pm
Scott, I don’t take much interest in the kind of language philosophy that kripke and his ilk concern themselves with, so I don’t know the answer to your question. Most likely, though, the answer is No. Philosophy tends not to have “open questions” in that way (other than the same perennial questions that never get answered).
“Advances” on questions in philosophy often work by demonstrating in some manner that the original question was ill-formed and should be replaced by another, which can then be answered. I guess this is the prime reason why answering philosophical questions might sometimes seem “obvious” as well — the question which has an obvious answer wasn’t the one that was originally asked.
To the anonymous poster: I think you misunderstood what Scott said (or I am misunderstanding it now). He didn’t say that the result had to have philosophical consequences, but that it was motivated by such concerns. I don’t think any of the results he listed has any philosophical consequences at all, save for Godel’s theorem (alright, and the halting problem). The admiration concerned the starting and end point, not the interpretation of the result.
Comment #18 May 11th, 2006 at 8:05 pm
I think you misunderstood what Scott said (or I am misunderstanding it now). He didn’t say that the result had to have philosophical consequences, but that it was motivated by such concerns … The admiration concerned the starting and end point, not the interpretation of the result.
Thanks! I hadn’t even thought about that distinction, but you’re entirely right.
(One reason I enjoy reading philosophy is all those careful distinctions… 🙂 )
Can you differentiate the work that started with a philosophical question, from that which arose out of “non-philosophical” mathematical study, and then was later imbued with philosophical import?
Well, I know that Cantor, Gödel, Turing, Einstein, and David Deutsch were directly motivated by what I would consider philosophical concerns, usually in addition to technical ones.
(In Cantor’s case, the concerns were actually theological — he believed his work proved that God’s greatness transcends even infinity, and tried to interest the Catholic Church in it!)
For the others I’m just guessing. Someday I should ask Arora et al. whether they were motivated more by proving MAX-CUT and so on NP-hard to approximate, or by clarifying the notion of proof itself.
Comment #19 May 11th, 2006 at 9:05 pm
Thanks Scott. I too like results that have philosophical insights but I am not too technical. But now I see that technicality of a result is very important in giving value to the philosophical insight. Both make a result a complete ice-cream.
Comment #20 May 11th, 2006 at 9:17 pm
Both make a result a complete ice-cream.
🙂
Maybe a better analogy is a cannoli — a creamy technical center surrounded by a flaky philosophical crust.
Comment #21 May 11th, 2006 at 9:41 pm
For the others I’m just guessing. Someday I should ask Arora et al. whether they were motivated more by proving MAX-CUT and so on NP-hard to approximate, or by clarifying the notion of proof itself.
uhh…no, more than likely Sanjeev was trying to get his PhD, and was following up on work of LFKN and FGLSS. then in the second PCP paper, a bunch of authors decided to work on some promising results of arora and safra and got the PCP theorem as we know it.
the same thing is true of einstein, of course–the writing for the special theory of relativity was on the wall. this isn’t to take away from its brilliance, only to say that the mathematical evidence was emerging at the time of einstein’s discoveries. general relativity was a far more heroic accomplishment, and einstein was looking directly for a theory of gravity, not pondering the philosophy of 4-tensors.
Comment #22 May 11th, 2006 at 9:44 pm
Yes:) Again, you are a good writer:)
Comment #23 May 11th, 2006 at 10:22 pm
Anonymous: I certainly agree that GR was a more heroic accomplishment than SR. So let’s consider GR. Einstein was motivated, on the one hand, by the observed equivalence of gravitational and inertial mass, by the perihelion problem, and by the obvious (to him) need for a local description of gravity.
On the other hand, he was clearly also motivated by the writings of Ernst Mach, by Newton’s bucket argument, and by his revulsion at a description of spacetime that depends on a choice of coordinates, or in which “space can affect matter but not vice versa.” (Lee Smolin and Carlo Rovelli have some very interesting essays about this latter strain of Einstein’s thought.)
You might respond that even the latter strain is more science than philosophy. But I think the very fact that we see it that way is mostly due to Einstein!
This brings up a general point that I wanted to make earlier. I think philosophy has made huge contributions to human knowledge, but whenever it does so, neither the philosophers nor anyone else seem willing to call the result philosophy! (AI suffers from a similar problem…)
Comment #24 May 11th, 2006 at 11:11 pm
scott, if you are saying that einstein was driven by intuition and aesthetic, then I would argue that this is a fundamental part of the creative process throughout all of mathematics.
Comment #25 May 11th, 2006 at 11:39 pm
No, I think it goes further than that. Andrew Wiles was motivated by intuition and aesthetic of the highest order, but not by philosophy. Einstein, Cantor, Gödel, and Turing, if their own writings are to be believed, were motivated by philosophy.
Comment #26 May 12th, 2006 at 1:12 am
Incidentally, I’m proud to have staked out what seems like a perfect middle ground between science and philosophy: one that angers and alienates the supporters of both. 🙂
Comment #27 May 12th, 2006 at 7:06 am
Just wondering why it should surprise anyone that questions starting out in philosophy would be answered by science – in other words, that our reasoning would lead us to the factual investigations that (at least one one hopes) at some point will provide an acceptable level of proof/disproof.
Perhaps a difference between Wiles’ “intuition” and the “philosophy” of, e.g., Gödel, is the type or “size” of the problems each was working on. The status of Fermat’s Last Theorem as one of the great unsolved problems of mathematics had more to do with Fermat’s reputation, the length of time it had remained unsolved, and particularly the infamous marginal note on the eve of Fermat’s death as an incredible tease, it seems to me, than with implications for the world-at-large. OTOH, when Gödel showed that one can’t have a provably self-consistent system (of logic, mathematics, or whatever else), it could hardly have had greater implications – how can we finally “know” or “prove” *anything*? Of course this has everything to do with the types of problems Wiles and Gödel were interested in and chose to work on.
Comment #28 May 12th, 2006 at 7:15 am
Scott, that last coment is a shameless paraphrase of Russell’s definition of philosophy as the No Man’s Land between Science and Seligion which is under fire from both sides.
If someone now devises in turn an intellectual position between yours and Science which both you and scientists can attack… we have a model for Zeno’s paradox in our hands.
Comment #29 May 12th, 2006 at 1:44 pm
Here’s a somewhat different point about the obsession of science with originality. Science ought to be aimed at increasing collective knowlege, which is why publication is necessary for credit. (And not just as proof of priority–encrypted publications are no longer acceptable.)
But people should get credit for actually bring an idea to general attention, rather than quietly publishing it. That is the real measure of their contribution. Being famous gives one an unfair advantage in this test. But it also credits people who (successfully) promote their ideas, as Conway and Kochen do by making it the center of the article, rather than burying it in a book review.
I’m ambivalent on the subject of physicists not reading the philosophy literature. Mainly I blame the physicists, but the philosophers ought to figure out that the physicists are interested, and tell them.
On another note,
I think people these days underestimate the heroism of special relativity. It looks obvious in today’s hindsight, but it had trouble convincing people at the time. I find that inexplicable.
Comment #30 May 12th, 2006 at 6:57 pm
From a review on PhysicsWeb:
Gullstrand had no trouble blocking Einstein in the committee. No member approved of relativity theory. As Hasselberg wrote from his sick bed in 1921: “It is highly improbable that [Alfred] Nobel considered speculations such as these to be the object of his prizes.” Most committee members simply could not accept such work as being true physics. Einstein’s manner of revising fundamental assumptions and of seeking unifying theories seemed to them to be the work of a metaphysician rather than a member of their scientific tribe.
Comment #31 May 12th, 2006 at 7:25 pm
For an extended meditation on the value and dangers of originality, see this excerpt from James Gleick’s biography of Feynman. It includes these remarks of Sidney Coleman:
“I suspect that Einstein had some of the same character. I’m sure Dick thought of that as a virtue, as noble. I don’t think it’s so. I think it’s kidding yourself. Those other guys are not all a collection of yo-yos. Sometimes it would be better to take the recent machinery they have built and not try to rebuild it, like reinventing the wheel.
I know people who are in fact very original and not cranky but have not done as good physics as they could have done because they were more concerned at a certain juncture with being original than with being right. Dick could get away with a lot because he was so goddamn smart. He really could climb Mont Blanc barefoot.”
Comment #32 May 13th, 2006 at 4:54 am
Scott: ‘Note that by “free will,” all Conway and Kochen mean is the property of not being determined by the previous history of the universe.’
What if we reverse time? If Bell stuff (if not Kochen-Specker stuff) remains valid under time reversal (de Beauregard, but also Zelinger, Vaidman, Dolev, etc., wrote papers about ‘EPR vs RPE’; and there are also delayed choice effects, like the delayed choice entanglement swapping) would it mean that ‘free will’ is also the property of not being determined by the ‘future’ history of the universe?
s.
ps: the above might be another side of “the obsession of science with originality” 🙂
Comment #33 May 13th, 2006 at 5:40 am
No — having free will in Conway and Kochen’s sense doesn’t preclude your actions being determined by the future history of the universe. This is related to the fact that measurements destroy the symmetry between future and past.
Comment #34 May 13th, 2006 at 8:56 pm
This is the sort of post and thread that I come here for. Thanks!
By the way, it seems to me that
a) the philosophy under discussion here is pretty much limited to analytical philosophy and the intellectual tradition that lead to it
and
b) if the conclusions of this field are obvious in retrospect, isn’t that just what you would expect from an intellectual field more-or-less intentionally built in the image of mathematics?
Comment #35 May 14th, 2006 at 12:12 am
if the conclusions of this field are obvious in retrospect, isn’t that just what you would expect from an intellectual field more-or-less intentionally built in the image of mathematics?
I could give you plenty of mathematical conclusions that aren’t obvious in retrospect.
Comment #36 May 14th, 2006 at 4:52 am
I know for sure that art puts too high a premium on originality, and this has all but destroyed art since World War II. Too many people in painting, music, and writing have disowned the mandatory prerequisite of art — craftsmanship — mistakenly believing that the key to art is a sharp break with the past. Thus poetry is all but dead, and the great composers are in pop and jazz, not orchestral or chamber music. The pop musicians are better because they think about pleasing themselves rather than immortality (though we’ve lost counterpoint and much of harmony in the pop-classical split). I think art (and originality) arises unbeckoned where genius pursues craftsmanship.
Math and science are not in such dire shape, because it’s hard even to fake originality in them without the technical prerequisites. But I think great originality is overrated compared to great exposition. Gian-Carlo Rota believed, “You are more likely to be remembered by your expository work.”
Comment #37 May 14th, 2006 at 8:52 am
yo scott, what’s up dude?
Comment #38 May 14th, 2006 at 11:26 am
Just chillin’, dude.
Comment #39 May 14th, 2006 at 12:16 pm
Jonathan Shewchuk, you missed an important point though. Originality, discovery in art is free, and subjective (who could reinvent Michelangelo’s David? Or the Garden of Earthly Delights by Bosch?). Originality in science is bounded, and more or less objective (Jordan, Dirac, Schroedinger discovered the same things, independently).
-serafino
Comment #40 May 16th, 2006 at 10:03 am
What about the part where they claim that they rule out hidden variable theories of relativistic quantum mechanics? Do you agree with their interpretation and is that part new?
Comment #41 May 16th, 2006 at 10:48 am
I agree with it and I don’t think it’s new.
Comment #42 May 16th, 2006 at 3:24 pm
Here is how we explain, to our engtineering students, the relevance of the Conway-Kochem proof to model order reduction (MOR) in quantum system engineering.
Options for simplifying quantum simulation algorithms
In seeking to simplify [quantum simulations], experts in model order reduction (MOR) naturally ask three questions: Is the state space necessarily complex? Is its time evolution necessarily stochastic? Is the dimensionality of the state space necessarily exponentially large?
The general answer to all three questions is “yes,” for reasons we will now review—these reasons tightly constrain the engineering options for implementing general quantum MOR.
The state space is necessarily complex because otherwise it could not simulate interferometric measurements; the Feynman Lectures discuss this reasoning.
Quantum simulations are necessarily stochastic because the data produced by stochastic simulations has properties that cannot be reproduced by any deterministic simulation, and these properties are found to agree with experiment. This has been known since the 1960’s, when the Bell Inequalities and the Kochen-Specker theorem were derived.
That the dimensionality of the simulation state space is necessarily exponentially large is shown by the following inductive argument. We add a single spin-1/2 particle to the system, and ask, how many new [weak] measurement operators can be constructed? From each measurement operator of the prior simulation, we can construct two new (linearly independent) measurement operators in the new simulation, by scattering (or not) the measurement photon off the new spin. For these new operators to maintain their linear independence, the dimensionality of the state space must double.
What makes quantum MOR feasible is that almost all of the new measurement operators so constructed (i.e. all but an exponentially small fraction) probe high-order quantum correlations, that is, they are physically equivalent to the measurement of photons that have scattered from multiple spins.
Our general strategy for quantum MOR, therefore, is to apply low-order measurement operators that quench these high-order correlations. We are then able to algorithmically compress the simulation states, such that even though their dimensionality formally remains exponentially large, they do not require exponential space to store.
Building on the Kochen-Specker theorem, Conway and Kochen have recently proved that an mathematical relationship exists between the simulation invariance associated with measurement choice (as discussed in Section 2) and the human experience of free will (as cleverly defined in informatic terms by Conway and Specker).
The Conway-Kochen proof is recommended reading because it helps us appreciate that our three “yes” answers—asserting that the state space of quantum simulations is necessarily complex, stochastic, and exponentially large—are essential to the reconciliation of physical causality with our everyday experience of free will.
That is why quantum MOR seeks to work with these features, rather than work around them, and why engineers beginning research in quantum MOR must respect them, despite the computational challenges they pose.
Comment #43 May 16th, 2006 at 4:58 pm
Scott can you give a list of books on philosophy that you read?
Comment #44 May 16th, 2006 at 8:19 pm
Scott, can you tell me what tv shows you watch, your favorite food, and your pants size?
Comment #45 May 16th, 2006 at 10:32 pm
Scott, can you tell me what tv shows you watch, your favorite food, and your pants size?
Some body seems to be even a bigger fan of Scott than I seem to be:)
Comment #46 May 16th, 2006 at 10:57 pm
John–Thanks for the careful explanation. But, how many engineers are really concerned with reconciling the science they use with free will? What does the Conway paper offer to those who could care less? Does it help MOR in a more direct way?
Comment #47 May 17th, 2006 at 5:03 am
Nagesh, why all this worshipping? You ask him these questions in every thread. He’s just a complexity theorist, one out of many (no offense meant, Scott). And I certainly don’t believe he knows more about philosophy than just about any run-of-the-mill philosopher, even an undergraduate (again, no offense meant).
Scott’s a nice guy, and he knows his own area well enough to post interesting and informed stuff about it. But let’s try to keep things in perspective, eh? The other anonymous post about pants size was right on target. If you want to know about philosophy, just check the reading list for Philosophy 101 at some decent college, don’t ask some random guy with a blog about computer science.
Comment #48 May 17th, 2006 at 9:28 am
John–Thanks for the careful explanation. But, how many engineers are really concerned with reconciling the science they use with free will?
Ouch, that hurts!
The way your question is phrased implies that it is surprising for engineers to take a philosophical interest in their work. Young students should be aware that people like Wittgenstein, Dirac, von Neumann, and Shannon were all trained engineers, and that Feynman, Schwinger, and Dyson worked as engineers during WWII.
In fact, isn’t it the case that the present generation of physicists and mathematicians is historically unique mainly in its lack of formal engineering training and/or work experience?
What does the Conway paper offer to those who could care less?
Even hard-nosed engineers who completely disdain philosophical inquiry—and admittedly there are plenty of them—are confronted with the daily professional necessity of designing and emulate complex systems.
Emulating an open quantum system is particularly challenging, because these systems are both stochastic and nonlinear. Heuristically, the only hope of offsetting this complexity is to apply a mathematical invariance principle; the only such general principle we engineers know is the one indexed under “theorem / unitary freedom in the operator-sum representation, p. 372” in Nielsen and Chuang.
Just to be provocative, we engineers think this invariance principle is the most fundamental in all of physics. To us, it seems much more fundamental and useful than gauge invariance or relativistic invariance, for example. So it is a bit shocking to us engineers that physicists have seeming never given this invariance a short name … perhaps readers of Shtetl-Optimized can suggest one for us?
What the Conway-Kochen paper offers, from this engineering perspective, is an exceptionally clear discussion of the informatic consequences of the “no-name” invariance. Even engineers who “couldn’t care less” have to acccept, as a consequence of this fundamental invariance, the necessity of emulating systems whose state space is complex, stochastic, and exponentially large.
Does it help MOR in a more direct way?
To guide her quantum system designs, a young engineer needs a more physical and integrative explanation of the “no-name” invariance than is offered even in Nielsen and Chuang’s wonderful “Mike and Ike” textbook, or in the Conway-Kochen article. Our quantum system engineering group has written a four-page white paper on this topic: Mathematics at the interface of cryptography, quantum physics, and engineering simulations.
Obviously, much more could be said. In particular, we think the “no-name” invariance is mathematically deep, for reasons that the white paper explains.
To summarize, and speaking broadly, our perspective on quantum system engineering is the same as John Bardeen’s: “There is really no sharp dividing line between basic and applied research. Invention does not occur in a vacuum … [most advances] are made in response to a need, so that it is necessary to have some sort of practical goal in mind while the basic research is being done; otherwise it may be of little value.”
As engineers, it is our job to specify design paths and performance metrics for Bardeen’s “practical goals,” and to prove our competence by building hardware that works.
In doing so, we always hope that we will not discover new physics and mathematics (which unpredictably disrupts our engineering development effort) but regrettably this sometimes happens, mainly because Mother Nature is such a good project manager.
Comment #49 May 17th, 2006 at 10:06 am
Anonymous: I don’t worship him and why can’t I be his fan? After all I am not hurting anybody (including my self in the long run hopefully). Philosophy and such stuff is a recreational activity for me, not professional. I live mostly by programming. His views and clarity of expression impressed me and that does not mean I will not be impressed by any body else. I am impressed by Sanjeev Arora’s work, Oded Goldreich’s views, Richard Beigel’s perspectives etc. It just happened that I met him at a conference and came to know about his great work he did, that too early in his life and that he has more public presense than others.
I am curious to know as to why you followed my comments on his blog and spent time thinking about it.
Comment #50 May 17th, 2006 at 3:46 pm
Nagesh, I don’t “follow your comments and spend time thinking about them”. However, I do read and post in the threads on this blog, and since you only seem to post slight variations of the same comment in most of them it would be hard not to notice.
Of course you can be his fan, and of course you can have him tell you what to read. I’m just suggesting that in areas where Scott doesn’t have any particular expertise it doesn’t make much sense. I can’t see any reason at all why one would expect Scott to recommend better books than what’s on some random Philosophy 101 reading list, no matter how you define “better”. (Now that I think about it, I too would like to see what Scott’s recommended philosophy books look like, though probably for different reasons.)
Comment #51 May 17th, 2006 at 3:52 pm
The way your question is phrased implies that it is surprising for engineers to take a philosophical interest in their work. Young students should be aware that people like Wittgenstein, Dirac, von Neumann, and Shannon were all trained engineers, and that Feynman, Schwinger, and Dyson worked as engineers during WWII.
It is surprising. All the people you mention are very much exceptions, and even of them I wouldn’t say many were particuarly prone to philosophy. The only exception is, of course, Wittgenstein, but he didn’t take any philosophical interest in his engineering work at all. It wasn’t until he got bogged down in the fundamentals of mathematics that he got interested in philosophy, and even after that he never wrote anything which had a direct link to engineering in the way you imply. Wittgenstein thought of science and philosophy as two mutually exclusive domains.
Comment #52 May 17th, 2006 at 4:19 pm
Nagesh: Some philosophers I enjoyed reading were Russell (my favorite), Hume, Frege, and Kripke. Some philosopers I don’t recommend to anyone with high blood pressure are Plato, Nietzsche, and Wittgenstein. But my reading has been extremely selective — I haven’t tackled Aristotle, Descartes, Spinoza, Leibniz, or Kant. So I agree with the anonymous commenter who said that if you want a real reading list, you should get it from a real philosopher.
Comment #53 May 17th, 2006 at 5:31 pm
Thanks Scott. And anonymous as I said my activities on the blog are recreational and not very objective. I am not looking for philosophy reading to make fame or fortune among philosophy majors. I just want to read some based on what I subjectively feel are worth reading. I think, people anyway do things to ultimately satisfy subjective needs.
Comment #54 May 17th, 2006 at 5:34 pm
All the [engineers] you mention are very much exceptions …
No person whose creative work defines a whole field of study is an exception!
And I could have added Linus Pauling, George Marshall, and President Hu Jintao of China (as well as all nine members of the China’s CCP Politburo!) as modern engineers who show outstanding creativity and leadership ability.
… and even of them I wouldn’t say many were particuarly prone to philosophy.
Let’s see … Norbert Wiener trained in both zoology and philosophy. Admittedly, this doesn’t mean Wiener was a very good philospher, but at least he tried!
For amusement, I will remark that Wiener was also a (extremely bad) novelist: he wrote The Tempter, a copy of which we keep in our QSE Lab’s “Library of Forbidden Literature.” Do not waste your time reading it — the main character seems to be a blend of Helmholtz and Minorsky.
A better example of engineer-philosopher is John Roebling, the designer of the Brookly Bridge, who studied philosophy under Hegel, conceived himself to be a philosopher, and was so regarded by Walt Whitman.
Perhaps because the Brooklyn Bridge was such a gigantic, graceful, enduring, and wholly beneficial creation, Roebling’s ideas were not widely embraced by academic philosophers. After all, who could hope to top the Brooklyn Bridge as a work of philosophy-realized-in-steel?
Roebling was a builder-philospher more in the ancient Greek tradition than the modern analytic tradition.
The point of this rambling reply (if it has one) is that the pendulum of history swings back-and-forth between specialization and technofederalism.
Since we have just passed through a generation of specialization, maybe the next generation of scientists and engineers will be more federative?
Comment #55 May 17th, 2006 at 8:11 pm
So as not to be a pest, this will be my final post on the very interesting (to me) thread of engineer-philosopher-scientist.
Scott’s mention of Spinoza made me smite my forehead and say “Doh”, Homer Spimson-style!
Of course, Spinoza is the archetypal engineer-philosopher (we are considering Spinoza’s livelihood as a lens-grinder as engineering). And to repay the kindness of all the readers of Scott’s excellent blog, I will insert here a strong recommendation of Jonathan Israel’s Radical Enlightenment, which is a wonderfully-written history of the impact of Spinoza’s philosophy on political thought.
Unfortunately for me, Israel’s history stops before Thomas Jefferson (another engineer-scientist-philosopher). And yet, I knew from the catalog of Jefferson’s library that he had read Spinoza’s works. So last week, while I was in Washington DC, I went to the Library of Congress, identified myself as a researcher, was granted admittance to the rare book room, where librarians placed before me Jefferson’s Spinoza volumes.
I was hoping to find marginalia in Jefferson’s hand. Alas, there were none — the project was a bust. Still, it was a pretty considerable thrill to turn the pages of these 317-year-old first-edition Spinoza volumes (which were printed in 1690), inscribed on the frontspage by Thomas Jefferson himself.
So next time you’re in Washington, prepare yourself with a historical research project, and go to the Jefferson Library. That’s what its for, and you will have a wonderful time, just visiting the reading room and consulting the librarians.
Comment #56 May 18th, 2006 at 8:39 am
No person whose creative work defines a whole field of study is an exception!
Of course they are! Almost by definition. How common do you think it is for people to define a whole field of study?
… and even of them I wouldn’t say many were particuarly prone to philosophy.
Let’s see … Norbert Wiener trained in both zoology and philosophy. Admittedly, this doesn’t mean Wiener was a very good philospher, but at least he tried!
Well, tou didn’t mention Wiener in your original post, did you? There are now two discussions here: the first concerning whether the people you originally brought up where philosophically minded, and the second whether engineers tend to be in general. The first point cannot be made by bringing up new examples.
But, let’s turn to the second discussion. Wiener had a philosophical approach at times, yes. I actually think he did some good work in that vein.
As for John Roebling, he was a philosopher too. But to say that there is some philosophical underpinning to his work is, IMHO, a little silly. The Brooklyn Bridge is a nice bridge, but it has nothing to do with philosophy no matter how you slice it. Roebling was a philosopher as well as an engineer, but they were two separate domains, just as for Wittgenstein.
Maybe you can find a couple of examples, but I’m not sure what that would prove. The fact of the matter is that most engineers don’t take a philosophical stance towards their work. I base this opinion on personal experience. I acknowledge the possibility that the engineers I’ve ever met are all exceptions, and that it is in fact common for engineers to view their work philosophically, but I would say that it is so unlikely as to not be worth discussing.
Comment #57 May 23rd, 2006 at 8:12 am
“…it strikes me as absurd: all the ideas under dispute seem obvious!”
I haven’t read any philosophy, but I have read a certain “anonymous” referee report on one of my papers; thus, I take no issue with the above excerpt :>)
Comment #58 June 6th, 2006 at 5:16 pm
Hi Scott, another paper with ideas similar to Kochen&Conway is this one by Ulvi Yurtsever.