June 27, 2010

Marcelo Gleiser Has a Point

This post is based on my comment at Backreaction, under Marcelo Gleiser's guest post explaining it may be a mistake to pursue a final theory of "the" universe (or at least, to think it must be simple/beautiful etc.)  I think Marcelo has a good point.  Here I delve into the relevant and deep philosophical problems about "why is there something instead of nothing" and "why is it like this and not otherwise."  (We should add: is "something" even clearly defined - a point well made by the modal realists.)

We don't have any a priori notion of why "reality" should be like this or otherwise. For deep logical reason I've noted before, I don't see how we can. There is nothing in logical analysis that can "bless" some mathematical constructs with a "right to life" over others - ie, to be incarnate in the special manner we feel that we are. To be, as Madonna put it, "living in a material world." (I like to say, it's like number 23 specially existing also as brass numerals "just because", despite being just another number ...)

Many thinkers cogently argue we can't even make that distinction. I think that collides with our basic feeling of being alive etc. but it is near impregnable as a strict logical critique of material realism being coherently distinct from abstractly descriptive and totally unselective modal realism.

Hence some believe in MUH: that all structures in the Platonic mindscape exist (logically wide-open, a far bigger set than even the wildest string-theory landscape etc.) If so there is little point in looking for a fundamental theory that makes sense or is beautiful etc, because we are just in a possible world that allows us to exist.

However, that presents deep Bayesian expectation problems. If that were true, our greatest expectation would be living in a universe just orderly enough to get us in this condition and to this point, and no more so (because there are so many more ways to do that than to be very neatly consistent, with identical electrons and laws that don't change over time etc. in various odd ways.)

So no one knows what's going on or why it should be or be like this. I think there's some "management" in the sense some ultimate reality has some intrinsic goals or even purposes like beauty and life-friendliness, but it would be wrong to impose that as a working assumption.  BTW that would not have to be like a person, FWIW.  So: find a TOE that works if you want, but be aware of the logical problem of justifying it existentially.

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Anonymous Anonymous said...

What are your thoughts on many-worlds interpretations?

28/6/10 05:58  
Blogger Neil B said...

I started a whole new post to deal with your question! Please share your thoughts.

28/6/10 11:20  
Anonymous Allen said...

"However, that presents deep Bayesian expectation problems."

It seems to me that probability can lead you astray when it comes to infinities - since the cardinality of infinite sets doesn't satisfy Kolmogorov's probability axioms.

Thus, if you're going to talk about probabilities of infinite sets you
have to introduce some measure other than cardinality.

HOWEVER, as you mentioned in your "Many-Worlds Incoherence" post, it's not clear to me that introducing a new "measure" is legitimate.

At some point, you're no longer talking about the original infinite set...instead you're only talking about your new measure, which is an entirely different thing.

This post, from a philosophy professor with a PhD in mathematics at Baylor University, discusses the kind of problems that arise with probability and infinite sets.

It would seem to me that you can't apply probabilistic reasoning to situations involving *actual* infinities.


Also, for what it's worth, I think Kant is a better guide to grasping the underlying nature of reality than Plato.

29/6/10 14:27  
Blogger Neil B said...

Allen, Pruss's post ranges beyond the simple infinite-set probability problem, so let's review the typical basics of the latter:
We can't compare the size of say, the integers and the odd numbers since both can be Cantor-matched as equivalent cardinality. So you're tempted to say, there's no way to talk about probabilities if there are infinite sets involved.

However, consider a coin-toss exercise. You expect 50/50 from a fair coin over time, and whatever appropriate results from doing other things like cards, dice. But suppose the universe is infinite (and it seems flat, so it supposedly really is.) Now there are Aleph-null people tossing coins, Aleph-null tossings, etc. all over this infinite universe. Aleph null head-landings and Aleph null tails ... Do you really want to say that this exotic boundary condition makes it impossible for you to "expect" normal outcomes?

Somehow, the proportions for probability are based on intrinsic tendencies of the finite limit and not the idealized set properties. If you "fill it in" by making it infinite, that doesn't change the proportion (almost like taking dy/dx in reverse.) So suppose I looked at integers between one and ten and the chance of hitting two, we'd say"1/10". If it's numbers made into tenths like 1, 1.1, ... 9.9, 10 then the chance of hitting from say 1.6 through 2.5 is again 1/10. We can keep making it finer, and the ratio holds. Indeed, we can take a range "1.5-2.5" of the continuum (Aleph = ?!) and it's still intelligible despite there being infinitely many targets.

That's how I look at the problem of constants and features of possible universes. Imagine it being grainy to some fine degree (like 0.001 increments to each spec.), and there's various chances of this or that. Then cut the grain to 1/10, and so on ... The proportionality should hold. That's what matters, not the limit infinities. Think of it more like the chance a dart would hit one colored region rather than another on a picture.

(I want to say more about this later, it's a good topic for posting.)

29/6/10 14:51  
Blogger Neil B said...

Oh, almost forgot how this relates to MWI: Well, their main flaw isn't the trouble of comparing infinite number of worlds to get various probabilities. Reflect on my post: if there are two superposed states A + B, MWI says they diverge (somehow) and there are two separate ("non-interacting") states now. So to get real probability like 64:36 they have to posit some mysterious and non-rigorous "measure" or dimension to the branches. But their measure is not like my above attempt to reconcile actual infinities. It's arm-waving, they just can't explain how that extra property would work. No rigor AFAIK. That link from my top post is really harsh on all that.

But if they did post an actual bundle, they could maybe get away with in like vein to what I said above.

29/6/10 15:01  
Blogger Neil B said...

(I meant, the chance of hitting the number two if we consider picking at random.)

29/6/10 15:05  
Anonymous Allen said...

I think your examples with the number ranges and ratios establish a measure which makes the question of infinity irrelevant.

Your example of the dart and the picture for instance. You can divide the picture up into regions, each of which is finite in size, and then ask which region a dart is most likely to hit. Which makes the fact that each region contains an infinite number of points irrelevant.

But for anthropic reasoning involving infinite populations, I don't think there is an equivalent sort of measure.

So, for instance, lets assume we have an infinitely long array of squares. And a fair 6-sided dice.

We roll the dice an infinite number of times and write each roll's number into a square.

When we finish, how many squares have a "1" written in them? An infinite number, right?

How many squares have an even number written in them? Also an infinite number.

How many squares have a number OTHER than "1" written in them? Again, an infinite number.

Therefore, the squares with "1" can be put into a one-to-one correspondence with the "not-1" squares...correct?

Now, while we have this one-to-one correspondence between "1" and "not-1" squares set up, let's put a sticker with an "A" on it in the "1" squares. And a sticker with a "B" on it in the "not-1" squares. We'll need the same number of "A" and "B" stickers, obviously.

So, if we throw a dart at a random location on the array of squares, what is the probability of hitting a square with a "1" in it?

What is the probability of hitting a square with a "A" sticker?

The two questions don't have a compatible answers, right? So, in this scenario, probability is useless. You should have no expectations about either outcome.

BUT. NOW. Let's erase the numbers and remove the stickers and start over.

This time, let's just fill in the squares with a repeating sequence of 1,2,3,4,5,6,1,2,3,...

And then, let's do our same trick about putting the "1" squares into a one-to-one mapping with the "not-1" squares, and putting an "A" sticker on the "1" squares, and a "B" sticker on the "not-1" squares.

Now, let's throw a dart at a random location on the array of squares. What is the probability of hitting a square with a "1" in it?

What is the probability of hitting a square with a "A" sticker on it?

THIS time we have some extra information! There is a repeating pattern to the numbers and the stickers. No matter where the dart hits, we know the layout of the area. This is our "measure" that allows us to ignore the infinite aspect of the problem and apply probability.

For any finite area the dart hits, there will always be an equal probability of hitting a 1, 2, 3, 4, 5, *or* 6. As you'd expect. So the probability of hitting a square with a "1" in it is ~16.67%.

Any finite area where the dart hits will have a repeating pattern of one "A" sticker followed by five "B" stickers. So the probability of hitting an "A" sticker is ~16.67%.

The answers are now compatible, thanks to the extra "structural" information that gave us a measure allowing us to ignore the infinity.

Oops, out of room...see next comment.

30/6/10 00:31  
Anonymous Allen said...


NOW - going back to your original post, you say:

"...our greatest expectation would be living in a universe just orderly enough to get us in this condition..."

IF all that we know is that there are infinitely many "minimal-order" universes *and* infinitely many "neat-universes"...then nothing can be said about what our expectation should be, regardless of any sort of relative frequency you might expect from considering the relative frequency of production of each type of universe.

We have to have some *extra* structural information that will give us a measure that lets us ignore the infinity. The relative frequency isn't enough.


30/6/10 00:32  
Anonymous Anonymous said...

Hi, I am from Australia.

Please check out an essay re Reality & the Middle via this reference


Plus a related reference


10/8/10 05:52  
Blogger Neil B said...

tx Anonymous. I note with approval, that AADS criticizes "scientism" back in 1979 (if that term used in first draft), before AFAICT the term was fashionable.
BTW pasting URLs into Blogger comments w/o HTML can leave them truncated, so here is that second link:

10/8/10 15:25  

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