# Edge question for 2006 (Lee Smolin's answer)

1. Jan 2, 2006

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

http://www.edge.org/q2006/q06_9.html#rovelli

http://www.edge.org/q2006/q06_6.html#susskind

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2. Jan 2, 2006

### 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?

3. Jan 2, 2006

### Kea

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.

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4. Jan 2, 2006

### marcus

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?

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5. Jan 2, 2006

### Kea

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.

6. Jan 2, 2006

### 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!

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7. Jan 2, 2006

### marcus

I dont 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

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8. Jan 2, 2006

### Kea

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.

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9. Jan 2, 2006

### Careful

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).

10. Jan 2, 2006

### Kea

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

I will come back later and say some more.

11. Jan 2, 2006

### marcus

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

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12. Jan 2, 2006

### Vast

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" [Broken] he wrote earlier this year:

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.

Last edited by a moderator: May 2, 2017
13. Jan 2, 2006

### Kea

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 realise 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.

14. Jan 3, 2006

### 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.

15. Jan 3, 2006

### 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? **

:rofl: :rofl: 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. :tongue2:

** 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

16. Jan 3, 2006

Staff Emeritus
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."

17. Jan 3, 2006

### Careful

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.

18. Jan 3, 2006

Staff Emeritus
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.

19. Jan 3, 2006

### Careful

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

20. Jan 3, 2006

### marcus

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

Last edited: Jan 3, 2006