Sunday, September 23, 2007

The Imaginary Part

Max Tegmark says the whole universe is a mathematical structure...

So he must believe he is a mathematical structure as well...

And I am a mathematical structure too...

I wonder what it feels like being a mathematical structure...

?

Id

I think my brain is invariant under action of this thought.

Up to a face factor.


Update Oct. 11th: See also The Mathematical Universe

42 comments:

Arun said...

LOL!

One of the best things ever that you've posted!

stefan said...

Wonderful photos,
great story :-)

Cheers, Stefan

Santo D'Agostino said...

Bee,

This post is fantastic!

My compliments to you and Stefan on a very interesting and informative blog.

All the best wishes,
Santo

Flip said...

Brava! You're giving Calvin and Hobbes a run for their money. :-)

amaragraps said...

Hilarious!! Thanks, Bee.

Kea said...

Yes, excellent post! LOL.

Eric Gisse said...

I laughed way too hard at that.

Yea, I think I found my occupational home. It uses math.

Uncle Al said...

Is Stefan hoping for a Coolidge Effect with 10^1000 acceptable solutions? Boundary conditions must be imposed!

Bee said...

Hi All:

Thanks for the kind words. PI currently hosts the Many Words - err - Many Worlds at 50 conference, which is pretty mindboggling. Max Tegmark talked yesterday about his Many World worries, and (unsurprisingly) used the occasion to bring up MUH. I still don't really know what to make out of this. As much as I'd hope that the human brain is able to grasp the fundamental concepts that our universe is build on, I can't see no reason for this to necessarily be the case - The Principle of Finite Imagination ;-).

But then, why should we assume that maths is the fundamental 'reality' if there might be a structure underlying it that is as difficult to grasp for us as abstract maths might be for a squirrel?

The whole event is recorded, I will let you know if it goes online. Some of the talks are as entertaining as interesting, and definitely worth the time. Best,

B.

Doug said...

Hi Bee and Stefan,

I think there should be a PI in the exponent of e?

Have you considered posting this to Nature or Science?

Serious journals could use some levity. [A publication is a publication.]

Kea said...

But then, why should we assume that maths is the fundamental 'reality' ...

Theory never describes the 'fundamental' reality: it can merely improve on the understanding that preceded it.

femmeanna said...

LOL!
I really enjoyed that.
Thanks

Moshe said...

My brain is invariant under the action of this thought...just a perfect expression, will definitely become a classic (and also perfectly summarizes my own attitude to that particular thought).

Christophe de Dinechin said...

Very funny post. I remember being very puzzled by Dr Tegmark's ideas myself (my observation being that he was giving his mathematical universe the very same attributes that the Bible gave to God).

Tumbledried said...

Very amusing post. I guess you could say that Tegmark's ideas are more of a sort of general framework for doing philosophy that anything particularly constructive. I do agree with him on a number of his points. That mathematical truth is discovered rather than invented, that seems obvious. It is then an easy step to simply say that the world we live in, assuming that it obeys logical laws, should be described completely by some underlying Platonic framework. This sort of thinking goes back to the ancient Greeks ie Plato. But one has to be careful when saying that mathematics IS the universe, or one runs into problems of things being poorly defined ie which mathematics? All of mathematics? If so, what part of mathematics are we living in? Is this even a useful avenue of thought to pursue? etc etc

Arun said...

Doug,
No pie on the face; this is not slapstick humor!

cecil kirksey said...

Hi Bee:
This maybe a little off topic but here goes. One reason I find your blog so great is that you explain complex theoretical ideas so any lay person with some technical background can understand them.

Back in June you wrote about higher dimensions > 4. But one thing that has really bothered me, I read several books and axiv papers to help me understand, is the following. Prior to inflation is the (our) universe described by what laws of physics? If it is string theory is the universe already compacted to four large dimensions. If so how did this happen?

Another thing that is really totally unclear is: When people discuss the bubble universe concept exactly what are these bubbles in? A larger space? What laws govern this larger space?

You probably will not answer all my concerns but perhaps you might feel like responing since these questions are somewhat related to Max's ideas.

Thanks. A great blog!!!

Bee said...

Hi Cecil:

Space is a fairly abstract 'mathematical structure'. It must not necessarily describe a space-time manifold which seems to be the picture you have in mind. E.g. the possible solutions to an equation form a space as well. Think of us as living in one such possible solution, then the question is where are the other ones? But 'where' doesn't have to mean elsewhere in space-time. Faced with that question, it seems there are two ways out. Either you look for a reason why we live 'where' we live, then you run into the problem you mention What laws govern this larger space?, which is a game you can iterate if you like. Or you go with Tegmark, Many Worlds (or other alterations of this philosophy) and say basically to avoid picking one 'real' solution, all are 'real'. My problem with that reasoning is what Tegmark in his talk called the 'word worry' (no, really ;-) ). I.e. I have the impression there are several concepts of 'reality' around here. Mine seems to be fairly closely attached to human consciousness, which tends to cause a lot of further problems. So, I find all this very interesting, it goes nicely with a glass of wine and works fairly well to convince your seat neighbor on the plane that you're totally nuts, but I wouldn't want to seriously work on it. I leave that to the, oohm, more ambitious people. Best,

B.

PS: Prior to inflation is the (our) universe described by what laws of physics? Good question, let me know if you find an answer.

Bee said...

Hi Tumbledried:

That mathematical truth is discovered rather than invented, that seems obvious.

Aah, sounds good, sounds quite obvious. I'd be tempted to agree, but sentences like this are the reason why I have a problem with philosophy. To begin with what do you mean with 'truth'? What is the difference between 'discovering' and 'inventing'? If the whole universe including us is 'mathematical truth' then what sense does it make to say that part of it (aka us, including our brains, thoughts etc) invents some other part? If you've occasionally read an interview with fiction writers, you'll find some of them say they don't 'invent' a story, but they just discover it as if it's been lying around waiting to be written down. Invention? Discovery? Fact or Fiction? Truth? Statues or Shadows?

It is then an easy step to simply say that the world we live in, assuming that it obeys logical laws, should be described completely by some underlying Platonic framework. This sort of thinking goes back to the ancient Greeks ie Plato. But one has to be careful when saying that mathematics IS the universe,

Sure, it's definitely interesting. But given that we don't have a full understanding of maths either I am not sure whether it's particularly useful to do so.


Best,

B.

Rae Ann said...

That was awesome! Very cute and creative!

Garrett said...

I mostly agree with Max, but think the universe is only the prettiest math (up to a random phrase shift).

Arun said...

That mathematical truth is discovered rather than invented.

Given axioms it is discovered, but the axioms, however well-motivated, are inventions.

Luis Sanchez said...

Very creative and funny, this is the kind of post that makes your blog what I want my blog to be.

Neil' said...

Bee,

This is cool, you have truly discovered the mystique of "modal realism", but it really isn't "funny" (? ; - ) - it's a dead-serious metaphysical concept (and I do like the funny straining look on your face, that makes sense when wondering about stuff like modal realism.) Many thinkers (see for example Wikipedia)
have made the cogent argument that “all logically possible” universes should “exist”, since no clear logical reason can be given for selection and reification of some and not others. Indeed, they make a cogent case that the idea of “existing” as some special material state other than the platonic mathematical world description is circular, indefinable, and not logically coherent - I dare anyone to define it clearly, without circularity, in pure logical terms!

If so, then the problem of explaining why our universe has the traits it has is even worse than in "landscape" theories, because then all possible worlds really means all possible descriptions. If so, one has a vanishing Bayesian probability of finding oneself in a world that continues to be lawful instead of one of the infinitely more that were like this up to this point and then begin to diverge. Why? Because of all the changes from then on to different laws and variations and distortions of laws that can be described, and indeed the entirety of what behavior can be described after that point which certainly includes a gigantic set of chaotic futures, etc.

Hence, I think there really needs to be a manager of some sort, to ensure placement in effect of observers like us in a world that really has laws, since logical possibility is just too inclusive. Think of that as you wish. (Not to mention, our having experiences etc., but that gets into consciousness issues and I am just making the argument relating to physical conditions and our being here.)

But is modal realism true? I don't think so, first because of consciousness, but also because I don't think the "physical world" can really be fully modeled by maths anyway! Just to summarize some of that for now: the collapse of the wave function can't really be modeled coherently (what about simultaneity, sloppy or negative Renninger style measurements too?), nor can even raw probability like decay of muons (we can define ad hoc "random variables", but they aren't actual mechanisms for produced true randomness. We have to use pseudorandom but actually deterministic things like the digits of pi and etc. So then, what models the picking of different such generators for every new nucleus, particle etc, so they don't all decay at the same time? Another, grand pseudorandom generator to pick the other generators? And then how to handle entanglement etc. and other things that can't be classically modeled - what a mess, and how ironic.

Anonymous said...

LOL, very nice!

changcho

Arun said...

Neil,

If you could understand something about our world in purely logical terms, it would mean a priori knowledge of our world is possible.

Given the battles over "existence" (most notably "existence of God") knowledge of existence is not possible a priori.

We even run into problems about the simultaneous "existence" of position and momentum of a particle.

If the truth of modal realism depends on a purely logical definition of existence, then I'd simply not even reject it, but not even **waste** any time thinking about it.

Bee said...

Hi Neil,

argument that “all logically possible” universes should “exist”, since no clear logical reason can be given for selection and reification of some and not others.

Then show me some logically possible universes, but before you do so, define 'logic' without using anything from the universe you live in, like, say human brains.

What I find funny about Tegmark's proposal (and likewise your emphasis of mathematical logic and truth) is that he starts with telling us we should take Darwin seriously, and accept that our brains were made to hunt for food and not to understand the universe, so whatever the fundamental description looks like, it ought to appear weird. Yet he assumes that everything there is can be described by maths, and not possibly by something that our brains simply haven't even been able to remotely grasp. See, the human language was useful to describe nature as long as we were dealing with stories of Gods getting upset and throwing lightnings etc. Without doubt, maths is significantly more powerful and accurate than that. But what if there is another level (levels) beyond that?

What is really funny to me (and Olaf Dreyer asked a similar question at the end of Tegmark's talk that I think however was misunderstood), is our ability to deal with mathematical 'structures' intuitively, and without actually writing down each single equation, definition, property etc. and to make these matters increasingly more abstract. E.g. to take the concept of orthogonality from what we can see with our eyes, and generalize it to something like wave-functions - and then take these and sandwich them or to argue with them (sure sure, I talk to my equations, but then I also talk to my laptop and my car). What I am trying to say is it's not the maths itself that I find stunning but the process in which it connects to us (sorry, I am unable to find a better word). I always wonder why neuroscientists examine human language so extensively. I wish they would take some mathematicians and figure out what pattern the idea of non-commutativity resembles.

Best,

B.

Kea said...

If so, then the problem of explaining why our universe has the traits it has is even worse than in landscape theories...

These are good points, and supportive of the view that an expression of observables in (relative) logic, rather than conventional mathematics, would be a useful step. This would require some concrete 'numerical' interpretation of statements, but fortunately this is one thing that category theory may be able to do. Philosophically, perhaps, such a shift in computational tools opens a much larger can of worms again, but such is progress.

Neil' said...

Bee, you have some good points, as do others. BTW, reminder that I don't believe in MR anyway, I'm just throwing it up as a challenge to which I have my own objections.

BTW, some of you might want to see the premier of “Big Bang Theory” tonight, 8:30 PM EDT on CBS. It’s about a couple of physics students who can “... tell their quarks from their quantum physics, but have no clue how women add up. Leave it to their pretty new neighbor, just off a messy breakup, to teach them a thing or two.” Well, let’s hope she’s bright too.

Anonymous said...

Hi Bee,

I got reminded by cecil's question:

from what moment in time is the theories of relativity valid?

when was "c"= 300000000 m/s defined?

It seems, that in the earliest times things moved considerably faster!

Best
Klaus

Tumbledried said...

Thanks Bee,

If you've occasionally read an interview with fiction writers, you'll find some of them say they don't 'invent' a story, but they just discover it as if it's been lying around waiting to be written down.

A very good point. I guess I didn't think of that.

[Saying the universe is mathematics]... is definitely interesting. But given that we don't have a full understanding of maths either I am not sure whether it's particularly useful to do so.

I very much agree with you here. There is not much point replacing one thing one doesn't fully understand with something else equivalently incomplete.

Alejandro said...

Loved it! I can't wait for an oportunity to use that put-downer. Giving you the full credit, of course.

Plato said...

On another note, and not to take away from the good humour of this sequence of frames, I could not help but think philosophically about the very nature of the title.

It got me to thinking of my previous thoughts in regards to Max Tegmark, Pascal, and the current research into string theory.

People like to jest, but there is a serious side to our endeavours as well.

I only skimmed the surface and did not go beyond the frames of reference, so now, I will have to do this, judging peoples comments.:)

QUASAR9 said...

So we are not "just a number"
we are a complex equation
does that mean all we need is the formula for inmortality, or does such a formula not exist. Or has it simply decayed and being lost.

But hold on if no information gets lost, will I remember who I am (was) when I become a different configuration of symbols.

The funny thing is that if we watch a video (or set if images) digitally generated - we know it is not us but an image of us travelling thru spacetime - but can we remember what we were thinking when the photo was taken.

And we can go back in our mind to where we were three minutes ago, three days ago or even three decades ago - but our body is still going forward thru TIME.

Doug said...

Hi Bee and Stefan,

Yoky Matsuoka, Department of Computer Science and Engineering, has been awarded a 2007 MacArthur fellowship for her work in neurorobotics.

http://www.macfound.org/site/
c.lkLXJ8MQKrH/b.2913817/k.3EC5/
2007_Overview.htm

Much of the work in this area involves mathematical game theory modeling of neurophysiology.

A Tegmark variant?

Christophe de Dinechin said...

Bee wrote: I have the impression there are several concepts of 'reality' around here. Mine seems to be fairly closely attached to human consciousness, which tends to cause a lot of further problems.

So let's drop the confusing term "reality" and leave consciousness out of the picture then :-)

Isn't physics simply about building mathematical laws relating the result of measurements? I don't need consciousness here. A Roomba does not need to be conscious to avoid the walls. It needs, however, a capability to perform measurements on its surroundings, and a mathematical model of what should happen to these measurements if it sends this or that current to this or that motor.

What I am trying to say is that if you write F=ma, there is no "reality" to the equation itself. This is where I strongly disagree with Max Tegmark. There is any truth to it only if F represents a force, m a mass and a an acceleration. And it does not even work for all measurements of force, mass or acceleration. A dynamometer can be calibrated in arbitrary ways, the majority of which would make Newton's second law completely false. So F=ma corresponds to a relation between measurements which is true only after we have made some specific choices (of calibration, type, ...) about these measurements. I do not know of any physics law that is true without "baggage" (as Max Tegmark calls these extra choices).

General relativity followed from the desire to get rid of some baggage, by observing that the laws of physics should apply irrespective of one's state of motion. But that same revolution still remains to be done for other types of measurements. The laws of physics should apply irrespective of how I measure not just an acceleration, but a force, a mass, and so on.

Here is another observation. If we know something about a system, how do we represent that knowledge? One belief that was held until about 1900 was that what we knew would allow us to predict the result of any future experiment to an accuracy only limited by the measurement. But the predictions you can make are, in the most general case, only probabilistic. It can be because you don't have enough information, or it can be because all the information in the world will not allow you to predict the outcome with certainty. If you accept that notion that the most general description is probabilistic, then you get quantum mechanics or something pretty darn similar to it.

There is nothing magical here. I certainly don't need level IV multiverses or conscious observers to make the statements above. So I would refrain from adding them to the theory until we really need them.

Christine said...

And the OSCAR goes to Sabine! :) Very nice post indeed!

The question about the 'mathematical reality', whether there is an ultimate one at all and our capacity of probing it is a fascinating one of course. I am just about to finish an exceptionally well-written and amazing book by Henri Bergson,Creative Evolution. Well in the beginning he writes:

”(…) the human intellect feels at home among inanimate objects, more especially among solids, where our action finds its fulcrum and our industry its tools; that our concepts have been formed on the model of solids; that our logic is, pre-eminently, the logic of solids; that, consequently, our intellect triumphs in geometry, wherein is revealed the kinship of logical thought with unorganized matter, and where the intellect has only to follow its natural movement, after the lightest possible contact with experience, in order to go from discovery to discovery, sure that experience is following behind it and will justify it invariably.”

Yes, our logic is the logic of solids. And hence all the mathematics that we know follow this trend. And the physics modeled after it. Movement is like a sequence of snapshots. This may be the root for our difficulties in dealing with time.

Best,
Christine

Anonymous said...

Reality is that which actually exists. ~ Webster

Christine said...

Reality is that which actually exists. ~ Webster

And existence is that which is actually real.

mollishka said...

I'm a little late to the party, but oh god my sides hurt now.

The Land of Intellect said...

Whole universe a mathematical structure? Yeah, it sure is. ;-] Maths and dancing go together.

fercook said...

Geez, it's a great joke !!