Edge question for 2006 (Lee Smolin's answer)

[marcus]

http://www.edge.org/q2006/q06_4.html#smolin

every year Edge magazine chooses the Question of the Year and asks 100-some smart original-minded people and they get all different answers

this year the question is what do you think is a dangerous idea?
this is Smolin's answer
http://www.edge.org/q2006/q06_4.html#smolinthis is Carlo Rovelli's answer
http://www.edge.org/q2006/q06_9.html#rovelli

this is Lenny Susskind's answer
http://www.edge.org/q2006/q06_6.html#susskind

 

[marcus]

BTW what do YOU personally think is a dangerous idea?
especially in physics, cosmology, intellectual history, mankind's relation to the universe.

I don't mean dangerous like the idea of the all-powerful State is a dangerous idea, or some other totalitarian ideal, or Racial Purity, or God, or whatever. I would call those things not dangerous ideas but dangerous fairytale bullsh*t.

What I mean is, can you come up with some idea that is more of an intellectual earthquake (but in the same ballpark) compared to the ideas of Smolin, Rovelli, Susskind?

 

[Kea]

What I mean is, can you come up with some idea that is more of an intellectual earthquake (but in the same ballpark) compared to the ideas of Smolin, Rovelli, Susskind?

Hi Marcus

Wonderful short article by Smolin. But I'm afraid Susskind definitely wins the contest for having come up with the most dangerous idea. Of course, people have interpreted the word dangerous differently. Smolin has cleverly taken it to mean any truly revolutionary idea which has the potential to radically change science. But this isn't really a fair definition of the word in the current climate of ideas, where such things as the Landscape exist: namely, ideas that are dangerous in the most literal minded sense of the word.

Rovelli's article is a nice short rebuttal to ideas like the Landscape. It's a pity he wasn't a little more explicit.

 

[marcus]

Hi Marcus

Wonderful short article by Smolin...
Rovelli's article is a nice short rebuttal to ideas like the Landscape. It's a pity he wasn't a little more explicit.

I agree with you, you honeyblond category-bird, all the way.
what you say is what I think too. But I was expecting something more from you. Your own favorite interests have some potentially revolutionary ideas in them, n'est-ce-pas?
wouldnt it be a bit dangerous to transcend set theory and take a wild leap into the realm of abstract [***]sense?
this is a friendly challenge. suppose Edge had asked you? or John Baez?

 

[Kea]

Your own favorite interests have some potentially revolutionary ideas in them, n'est-ce-pas? Suppose Edge had asked you? or John Baez?

Well, I could take the cop out that Smolin has done a pretty good job of standing up for Category Theory. Quoting Peirce? Personally, if I had been asked I would have said something about the Landscape, but I would have been much more blunt and bloody minded than Rovelli. The thing about this contest is: if a number of people come up with the same idea (although of course they may have different viewpoints), people get the message that there actually is a pretty amazingly dangerous idea out there right now.

 

[Kea]

Marcus

Note that Woit is now into this game:

http://www.math.columbia.edu/~woit/blog/

Oh! I see now that quite a few people did in fact write about the Landscape. Also: the question was actually: What is your Dangerous Idea? That means, to be fair, one should write about one's own ideas. Well then, I would have to write about the Categorical Landscape, wouldn't I? But how to make this Dangerous? You see, I don't understand how radical ideas can be thought of as dangerous in the way that Smolin does. Hmmm...

From the Edge blurb on the question:
"The history of science is replete with discoveries that were considered socially, morally, or emotionally dangerous in their time; the Copernican and Darwinian revolutions are the most obvious. What is your dangerous idea? An idea you think about (not necessarily one you originated) that is dangerous not because it is assumed to be false, but because it might be true?"

Ok, then. They are defining dangerous to mean correct revolutionary ideas. Sigh. That rules out the Landscape. One should read the instructions first!

 

[marcus]

Ok, then. They are defining dangerous to mean correct revolutionary ideas. Sigh. That rules out the Landscape. One should read the instructions first!

I don't want to get sidetracked worrying about the right interpretation of danger---I think it was a poor (sensationalist) choice of word by Edge;

what they really meant (I tell myself) is what is for you the most EARTHQUAKE idea, the most tectonic. radical.

tectonic ideas are both constructive and destructive, scary and hopeful

but they had to dramatize it in a single short sentence, so they said dangerous----which can also mean "attractive"

close your eyes and visualize all the ideas and tell me which one glows most brightly-----the one outlined in fire (forget whether it is good or bad)

HAH we beat Woit by 40 minutes! he posted at 4:30 PM EST

 

[Kea]

Well, I could take the cop out that Smolin has done a pretty good job of standing up for Category Theory. Quoting Peirce?

Perhaps I should clarify this a bit. Smolin talks about applying Darwinian ideas to the Laws of Physics themselves. He quotes Peirce, but I guess Peirce was heavily influenced by Hegel on this point: the evolution of ideas creates new worlds itself. Now, by new worlds one does not mean any sort of silly multiverse; one is talking about the world's way of viewing itself. At the core of this is the very simple idea that we should understand something about metaphysics, that is, the language in which laws themselves are written.

But we know how to do this with Category Theory. This kind of mathematics is hugely revolutionary. It takes Relationalism to a new level, and in some sense the history of physics is all about an ever increasing envelopment of diverse arenas by a mathematics of Relationalism. (Rovelli says this much better than I can, although apparently he doesn't like categories, which I find more and more astounding every time I think about it).

The unbelievable (for most) point of this is that it will help us calculate things, as any (mathematically minded) computer scientist will readily admit. If it can be measured, it can be computed.

 

[Careful]

But we know how to do this with Category Theory. This kind of mathematics is hugely revolutionary. It takes Relationalism to a new level, and in some sense the history of physics is all about an ever increasing envelopment of diverse arenas by a mathematics of Relationalism. (Rovelli says this much better than I can, although apparently he doesn't like categories, which I find more and more astounding every time I think about it).

It is not so astounding as you might think you know. There is a saying that if you start introducing categorical ideas into your area of research then you should have left the field already for a long time.
I think one should not wonder about what is the wildest, most daring or shocking idea. One should look for (a) the number of degrees of freedom involved (local as well as global), that is the complexity of the idea (b) the chance it has to make a new fasifiable prediction in a real physical situation (c) how it relates to well known physics and hence is not falsfified yet by known (bare) experiments. I am no expert in the landscape, but I once heard a lecture about it by a distinguished string theorist. I was simply astounded by the fact that
such an intelligent person could come up with a fairy tale which clearly defies all common sense.

Perhaps Kea could explain us why category theory takes up relationism at a higher level (that would be of some interest). However, it seems to me that it would be better to first understand at a deeper level the relationism involved in GR (it is my experience that this still defies many physicists).

 

[Kea]

There is a saying that if you start introducing categorical ideas into your area of research then you should have left the field already for a long time.

Dear me. I wouldn't have heard that one before, would I?

I will come back later and say some more.

 

[marcus]

...
But we know how to do this with Category Theory. This kind of mathematics is hugely revolutionary. It takes Relationalism to a new level, and in some sense the history of physics is all about an ever increasing envelopment of diverse arenas by a mathematics of Relationalism. (Rovelli says this much better than I can, although apparently he doesn't like categories, which I find more and more astounding every time I think about it).

this is exciting

but I wish you would not express surprise that Rovelli puts things in his own (simple to him) terms instead of the language of categories. all the better if an idea can be expressed primitively and also translated into some elegant alternative form

 

[Vast]

Excellent reading material!

Although Paul Davies dangerous idea what about environmental concerns, it reminded me of a short http://www.stnews.org/articles.php?category=guide&guide=The%20Multiverse&article_id=146" he wrote earlier this year:

The multiverse is not an idle speculation, but a natural consequence of developments in fundamental physics and cosmology, such as the fashionable string theory and the so-called inflationary universe scenario. It has the backing of many eminent cosmologists, such as Martin Rees, Britain’s Astronomer Royal, and the Nobel Laureate Steven Weinberg. Nevertheless, some distinguished scientists vehemently oppose the idea, believing it to be a cop-out in the race for the holy grail of physics: a final, unified theory of all physical existence. The issue looks set to split the cosmology community as deeply and acrimoniously as the old steady-state versus big bang controversy.

I wonder why he didn’t use this? Maybe he anticipated other physicists bringing up the same issue and decided to say something else instead?

It seems to me that the community of theoretical physicists is already split on this issue. I would have to agree with him.

 

[Kea]

Perhaps Kea could explain us why category theory takes up relationism at a higher level...

There are many ways to answer this question. Mathematically speaking, the question is moot. Category Theory is the mathematics of relationalism, by definition. What did you think all those arrows were for?

In the early days of Category Theory some of its proponents were a little sad to realize that categories appeared to be no more than an organisational tool, albeit a powerful one. They concluded, for technical reasons, that in practice one needed to select a specific category with nice properties in which to set up the structures that one wished to use. Then, in the 1960s, Gray came along and said: "All right, then. I choose Cat, the category of all categories." This no doubt appeared to be more like the behaviour of a petulant two year old than a sensible decision for a practical mathematician. However, after much hard work, Gray (and others) demonstrated that the study of relations between relations could be fruitful because it uncovered combinatorial structures that were previously unknown.

Eventually it was understood that even numbers themselves have contexts, and the contexts affect their type. Why shouldn't quantum numbers, for instance, be like that? Of course they should! Because it is a relational principle.

But this is just mathematics, and it remains to be seen whether or not it has anything to do with the real world. No one (sensible) doubts that GR is a relational theory. A few people have worried about how to think of QM more relationally. Rovelli is one. I guess Careful is another. Most of these people believe that this can be done without resorting to categories. Maybe that is true. It has occurred to me that I might even largely agree with this approach to a rigorous formulation of the SM if it wasn't for the fact that some aspects of the SM are already understood non-trivially in category theoretic terms. But we should want much, much more from a unified theory! And we won't get that without categories because there is no metaphysical mathematics without them.

 

[Chronos]

Kea struck a chord with me there. Can you have a viable theory of most things [not to mention everything] that does submit to category theory? Does it not neatly avoid avoid paradoxes, like the ultra violet catastrophe and absurdly high vacuum energy? The problem with category theory is it's difficult to make falsifiable predictions. The question is, at least IMO, must it be falsifiable to be useful? Like the anthropic principle, it's ability to rule out the impossible is it's virtue. It is certainly preferable to the landscape, which fails to require or forbid hardly anything. If CAT is something close to a 'first principle', must it bootstrap itself into existence to be credible? IMO human logic has it's own Planck wall. At some point it must be suspended to make further progress. I think this is strikingly similar to the struggles classical physicists had coming to grips with quantum theory? To paraphrase Sherlock Holmes . . . . the truth is what remains after eliminating the impossible.

 

[Careful]

**There are many ways to answer this question. Mathematically speaking, the question is moot. Category Theory is the mathematics of relationalism, by definition. What did you think all those arrows were for? **

In this way I can even draw an arrow for the relation ``does agree with´´ between Kea an Careful, but I am afraid that will not be confirmed in practice.

** Gray (and others) demonstrated that the study of relations between relations could be fruitful because it uncovered combinatorial structures that were previously unknown. **

Fine, but you must realize how terribly hard it is to characterize an event in GR, and apart from the relation ``x is in the past of y or not´´, there is really no other canonical relation one can figure out generically. So, this relation between relations seems to far fetched for GR at least.

**
Eventually it was understood that even numbers themselves have contexts, and the contexts affect their type. **

You mean here for example that 5 does not make sense without specifying that it is a natural number (and not one of the prime field defined by 7 - say)?

**
Why shouldn't quantum numbers, for instance, be like that? Of course they should! Because it is a relational principle. **

I do not get that, the numbers in quantum theory are the complex ones, so there is no ambiguity.

**But this is just mathematics, and it remains to be seen whether or not it has anything to do with the real world. **

Here the inverse of our first relation applies

** No one (sensible) doubts that GR is a relational theory. **

I did not say that, I said that many people do not understand relationism properly yet...

**
A few people have worried about how to think of QM more relationally. Rovelli is one. I guess Careful is another.**

But Careful's and Rovelli's strategies are diametrically opposite to each other.

There is only one thing I will still add: start out more humble. We do not even know the boundaries of QM, how can we without this even make a suitable ansatz about what QG should be.

Cheers,

Careful

 

[selfAdjoint]

Fine, but you must realize how terribly hard it is to characterize an event in GR, and apart from the relation ``x is in the past of y or not´´, there is really no other canonical relation one can figure out generically. So, this relation between relations seems to far fetched for GR at least.

Here's a dangerous idea for you. "There is no such thing as a geometrical point, or an event. Only equivalence classes of light cones."

 

[Careful]

Here's a dangerous idea for you. "There is no such thing as a geometrical point, or an event. Only equivalence classes of light cones."

Eeuuh with respect to which equivalence relation ? It seems to me that what you want to imply is trivially equivalent to what we call points for classical spacetimes.

 

[selfAdjoint]

I should have put in a smiley. I suppose we could start with diffeomorphism equivalence and go on from there depending on what we requite for quantization. Or causal sets if you prefer.

 

[Careful]

I should have put in a smiley. I suppose we could start with diffeomorphism equivalence and go on from there depending on what we requite for quantization. Or causal sets if you prefer.

Ah, but causal sets contain mathematical points and require more than just the lightcones in order to recover geometry: the counting measure is needed to compensate for the conformal degree of freedom. But anyway, all this is all just kinematics. You would make a really daring statement if you could propose a quantum dynamics (whatever that means ) -actually you would be the first one to do so

 

[marcus]

...Rovelli's article is a nice short rebuttal to ideas like the Landscape. It's a pity he wasn't a little more explicit...

...Personally, if I had been asked I would have said something about the Landscape, but I would have been much more blunt and bloody minded than Rovelli...

Rovelli was, it turns out, not quite blunt enough, and he was misunderstood by commenters at Woit's blog. So Smolin added a remark (almost an hour ago) to make his message plainer.

-----quote from Not Even Wrong----
Lee Smolin Says:
January 3rd, 2006 at 11:58 am
HI everyone.

Carlo Rovelli did not say or imply that “Physics moved ahead too quickly in the last century, without properly understanding the mathematics of quantum mechanics.” Kasper, this comment was made by Adrian. Please read what he actually said, http://www.edge.org/q2006/q06_9.html#rovelli. Rovelli’s point was entirely different.

What Rovelli is complaining about is clear from his last sentence. It has nothing to do with the math, it is the extent to which string theory has become a study of cataloguing solutions to classical or at best semiclassical equations, ignoring both the background independence of general relativity and the challenges of understanding what a spacetime is within quantum mechanics. His point, with which I sadly have to agree, is that those who think of themselves as doing fundamental physics but have avoided wrestling with the implications of combining the principles of GR and QM have not appreciated the radical conceptual and technical innovations imposed on us just by those principles.

Best wishes to everyone for the new year, Lee

ps To avoid the inevitable misunderstanding, I do NOT imply here that the Einstein equations are fundamental, only that the principles of GR are.
----end quote---

http://www.math.columbia.edu/~woit/wordpress/?p=319#comment-7124

 

[Careful]

This message of Smolin is just incredible , not only is the mathematics behind QFT far from understood but also the *physics* behind quantum mechanics itself : (a) locality versus non-locality (b) the Schroedinger cat problem (c) sub Planckian physics, etc...

He is for the rest blaming the so called short sightedness of string theorists for ignoring the issue of background independence in QG. But what does background independence mean in the first place at the quantum level? ``A theory of quantum gravity is background independent if its basic quantities and concepts do not presuppose the existence of a given background metric´´ (see http://www.arxiv.org/PS_cache/gr-qc/pdf/0510/0510052.pdf ) seems a plausible definition.
However, this statement requires great care IMO in case the background metric (and the appropriate Gaussian coordinate system wrt some hypersurface \Sigma) can be derived dynamically from a plausible covariant action principle (as is the case for Minkowski and the inertial observers orthogonal to a flat spatial hypersurface \Sigma). In this spirit, one can even argue that standard perturbation theory is background independent in the first sense Their second, inequivalent, criterion does not save the day in this respect: ``A theory of quantum gravity is background independent if there is no fixed theoretical structure´´ since - again - the ``background´´ is derived dynamically. However, this second principle is definitely too liberal in another sense since one could interpret a fixed topology as a background structure and that even invalidates GR

This makes his final comments

**
ps To avoid the inevitable misunderstanding, I do NOT imply here that the Einstein equations are fundamental, only that the principles of GR are.
**

even stranger...

Cheers,

Careful

 

[Kea]

So, this relation between relations seems too far fetched for GR at least.

On the face of it, yes, no doubt. The real argument is in the details.

I do not get that, the numbers in quantum theory are the complex ones, so there is no ambiguity.

You seem to agree that QM is 'incomplete', at least in the sense of not being framed in the right language. Hence, the setting of the complex numbers might well be a very relevant question. If one allows extensions of logic, as we do, one comes up against the problem of even defining the complex numbers uniquely.

We do not even know the boundaries of QM, how can we without this even make a suitable ansatz about what QG should be?

I agree with you here. It is not clear that anybody is in a position to make ansatzes about QG.

 

[marcus]

-----quote from Not Even Wrong----
Lee Smolin Says:
January 3rd, 2006 at 11:58 am
HI everyone.

Carlo Rovelli did not say or imply... Please read what he actually said, http://www.edge.org/q2006/q06_9.html#rovelli. ...

... has become a study of cataloguing solutions to classical or at best semiclassical equations, ignoring both the background independence of general relativity and the challenges of understanding what a spacetime is within quantum mechanics.

... think of themselves as doing fundamental physics but have avoided wrestling with the implications of combining the principles of GR and QM have not appreciated the radical conceptual and technical innovations imposed on us just by those principles...

----end quote---

http://www.math.columbia.edu/~woit/wordpress/?p=319#comment-7124

it was interesting to see the heated responses this drew. A half hour ago, responding to several people's reactions, Smolin posted this followup

---more from Woit's blog---
Lee Smolin Says:
January 3rd, 2006 at 4:20 pm
Aaron and Anonymous,

Let’s lower the temperature and discuss the substance of what we disagree about. You say, “People are quite capable of understanding the metaphysics and still rejecting Rovelli’s favorite theory.” But, as Carlo makes clear, his favorite theories are general relativity and quantum mechanics. He claims that the principles of these are ignored by approaches to unification that study only semiclasical effects in fixed classical spacetime backgrounds.

You make it clear that you disagree, i.e. you reject the view that a quantum theory of gravity should be background independent. This is a substantial disagreement. So let's discuss why we disagree.

Certainly, no insult is intended. But it is hard to avoid the impression that some people who reject the case for background independence have not thought carefully through the issues in the interpretation of general relativity that lead us to adopt it. Perhaps this is not true of Aaron, but it is true of many who confuse the methodology used to interpret very symmetric solutions to GR with the very different issue of describing observables for the generic solution.

The issue is not about knowing how to write the Einstein’s equations down or find simple solutions. It is about the interpretation of observables on the space of solutions. until one has struggled through the issues raised by the hole argument, or the problem of specifying diffeomorphism invariant observables, you cannot have absorbed the full meaning of general relativity. My impression is that once people have absorbed this it changes their taste as to what kinds of solutions to the problem of quantum gravity they are willing to entertain. Specifically it seems impossible to have understood these things and still to believe in the possible viability of any background dependent approach to quantum gravity.

Of course the equations of general relativity are used in Kaluza-Klein inspired higher dimensional unifications. But, because of these subtle interpretational issues, this is not the same thing as taking the principles of the theory seriously.

A related issue is that all the higher dimensional unifications require that some degrees of freedom be frozen. Otherwise, as Penrose argues in his recent book, there are instabilities that lead quickly to collapse to singularities. These are to some extent avoided by the flux compactifications but, as we know, the cost is the need to appeal to anthropic arguments.

But the point is that from a background independent point of view, any result that requires the specification of a specific solution rather than a generic prediction of the theory seems unreliable exactly because the symmetric solutions are in many ways non-generic.

Even Einstein saw this was a potential trap, when he commented, ““It is anomalous to replace the four dimensional continuum by a five dimensional one and then subsequently to tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself”

Thanks,

Lee
------endquote----

 

[Kea]

It was interesting to see the heated responses this drew.

Isn't it nice to know that we are so much more civilised!

A colonialist

 

[marcus]

Isn't it nice to know that we are so much more civilised!
A colonialist

yes, and frankly I think we are
besides I have no objection to colonialists as long as they have good manners and can be reasonably charming about it

 

[Careful]

The point I tried to make before it that the notion of background independence is not a clear cut one and Smolin just uses his intuition in labelling some theory as background independent and the other not. Actually, my construction is the Kretchmann comment to the importance of the idea of general covariance in GR (even the Newton Laws can be derived from a contrived covariant theory). So, Smolins arguments are more based on his intuition for naturalness than anything else. I don't say I do not ``have the same measurestick´´ but I prefer to refrain from such useless comments.

Cheers,

Careful

 

[Kea]

I have been browsing the Edge essays. Quite a number of non-physicists are saying something about physics. Have a look at the essay by Donald Hoffman, a cognitive scientist, entitled
A spoon is like a headache

http://www.edge.org/q2006/q06_3.html

 

[MathematicalPhysicist]

BTW what do YOU personally think is a dangerous idea?
especially in physics, cosmology, intellectual history, mankind's relation to the universe.

I don't mean dangerous like the idea of the all-powerful State is a dangerous idea, or some other totalitarian ideal, or Racial Purity, or God, or whatever. I would call those things not dangerous ideas but dangerous fairytale bullsh*t.

What I mean is, can you come up with some idea that is more of an intellectual earthquake (but in the same ballpark) compared to the ideas of Smolin, Rovelli, Susskind?

i think that the dangerous ideas are like: time travel possible, the question of to clone or not to clone human beings, and other ideas of the younger mathematicians/physicists filled with harry potter's and sci-fi films crave for unrealistic perspective of nature. (or if you want, an odd notion of what is real and what not).

i'm at the moment really satisfied as of yet with calculus,set theory, classical mechanics with sr, but there are some youngsters who at a young age want to know it all, even if it's not possibly, humanly possible.

something like this, i think.
what do you think folks?

 

[Careful]

i'm at the moment really satisfied as of yet with calculus,set theory, classical mechanics with sr, but there are some youngsters who at a young age want to know it all, even if it's not possibly, humanly possible.
something like this, i think.
what do you think folks?

Good for you ! You do not need to know it ``all´´ at a young age, important is that you *understand* it deeply, that you always keep your eyes wide open and realize that theories are just models such that in case some of them would defy your common sense: you remain critical and actively look for better. Of course - take this from me - it is wise to withdraw your objections at the appropriate moments in time. Moreover, listen carefully to those who are close to becoming professor emeritus. These people usually tend (on average) to convey more spontaneously what the *real* problems in phyisics are as opposed to the fashionable ones.

Cheers,

Careful

 

[MathematicalPhysicist]

thank you for the advice careful, and cheers too you as well. (-;