To: Alpan Rawal

Subject: Re: The Universe as a Simulation (NY Times) + more

From: Arjun Janah

CC:

Date: Tue, 18 Feb 2014 09:23:34 -0500

Dear Alpan,

Thanks for the response. I was thinking of just two events, A and B -- with A being, say, an electron present at a "fuzzy space-time point" x, y, z, t, with fuzziness dx,dy, dz, dt., and B another such event.

Then P(A, B) would be the probability of A occurring, given that B is true. This is what I meant by relative probability. P(B, A) would be the converse.

For the benefit of some of the others:

P(a,b), being a probability, has a range from 1 (certain) to 0 (impossible).

If we take d(a,b) = - ln (p(a,b)) where ln(x) is the logarithm to the base e (actually any base will do):

then this quantity has the range:

- ln(1) = 0 to - ln(0) = - (- infinity) = + infinity

(if you will excuse the crudities).

In order for this to be a proper distance measure (a true metric) between any two (fuzzy) space-time points a, b, the following should be satisfied:

1. d(a,b) >= 0 (positivity)

2. d(a,b) = 0 if and only if a=b

3. d(a,b) = d(b,a) (symmetry)

4. d(a,b) + d(b,c) >= d(a,c) (triangle inequality)

Alpan is pointing out that the last two may not be satisfied by this simple measure (which Alpan refers to as the relative entropy), but that another, more complicated measure exists for which these are satisfied. I am not familiar with that one. But many thanks, Alpan! (I may have paraphrased Alpan too simply or incorrectly.)

In any case, my earlier statement that this simple measure satisfies "nearly all (but not all) of the mathematical requirements for a distance measure" appears to be incorrect, from what Alpan writes. It has been over forty years, but I recall working things out and finding that only one of the requirements was invalid. But I could be quite wrong.

-- Arjun

In any case, my earlier statement that this simple measure satisfies "nearly all (but not all) of the mathematical requirements for a distance measure" appears to be incorrect, from what Alpan writes. It has been over forty years, but I recall working things out and finding that only one of the requirements was invalid. But I could be quite wrong.

-- Arjun

-----Original Message-----

From: Alpan Rawal

From: Alpan Rawal

To: Arjun Janah

Cc: blank01 ; P. B. ; V. K. ; E. D. ; N. D. ; A. B. ; J. V. ; S. B.

Sent: Tue, Feb 18, 2014 1:46 am

Subject: Re: The Universe as a Simulation (NYT) + more

Sent: Tue, Feb 18, 2014 1:46 am

Subject: Re: The Universe as a Simulation (NYT) + more

Dear Arjunda,

I think you need to define what you mean by "relative probability".
Ordinarily the relative entropy between two probability distributions
is not a true metric (does not satisfy symmetry and triangle
inequality), so I am not sure if that is problematic for your notion of
distance. On the other hand, the square root of the Jensen-Shannon
divergence between two distributions is a metric, but I do not know if
that works for your argument.

Alpan

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Note added: See the next two posts ("A Solitary Pawn" and correspondence on that) for a follow-up on this.************************************************

On Tue, Feb 18, 2014 at 12:25 AM, Arjun Janah wrote:

I am skeptical of the assertion (hypothesis) that the universe might be a computer simulation.

http://www.nytimes.com/2014/02/16/opinion/sunday/is-the-universe-a-simulation.html

But the prefacing description, in the article, about the reality of theholos(the virtual space in which mathematical realities exist) is worth reading about. I once read an interesting imaginary travelog by a writer whose name I forget. In that travelog, the writer met with imaginary mathematicians and physicists in various countries to explore this concept.

Also, the idea that we were reared upon in our schooling -- that the universe "consists of" space, time, and momentum-energy -- with each of the pair-members being transmutablea laEinstein-Minkowski-Poincare, needs expansion and modification to:

(a) include at least one more measurable quantity -- information;

and

(b) acknowledge that there is also (the perhaps unmeasureable thing called) consciousness -- not just the preserve of humans and "higher" animals, but an elemental constituent or "dimension" of the universe as we know it.

Let us first consider (a).

Probability enters into quantum mechanics in a fundamental way -- and probability and information are different measures of the same beast. The universe, every space-time point, every elementary particle, processes information and communicates with other parts of the universe, with information "moving" back and forth. This is true for electrons, atoms, cells, humans, trees, planets and stars. The concepts of fields and forces may be translatable into that of language. Of course, the language of communication between electrons is quantum electrodynamics, not English, that between cells is mainly chemical and electrical, and so on.

The uncertainty principle of Heisenberg and the probabilistic nature of quantum mechanical calculations (which after all simulate what an electron does to "decide" where to go) may perhaps be a consequence of the limitation of processing power of a sufficiently small section of the (phase-space) continuum -- in other words, not just the physicist with his/her equations, but the electron itself does not have the ability to decide for sure.

That is one way of looking at it. Another is to view the negative log of the relative probability of two space-time events (a quantity directly related to information and with a range from zero to positive infinity) as a measure of "distance" between those two events.

This would be a distance in a virtual "possibility" space in which there can be different frames of reference and a sort of "movement" -- corresponding to alternate realities and communication. Two parts of the universe that communicate with each other, and so gain knowledge about each other, move closer together in this virtual space, as measured in this way. The measure itself obeys nearly all the mathematical rules of conventional distance measures -- but not all.

Just as (long before Einstein et al) English (and surely other languages) frequently used the same words for temporal and spatial intervals and separations -- as in "a long/short time", "vowel length (duration)", "near future", "distant past", etc., acknowledging the similarity between these two measures, so also English used spatial-distance terms for probability, as in "a remote chance", "a close call", "far-fetched", "nearly correct", "almost true" and spatial-location terms for possibility/state -- "This is where we're at.", "We will try to reach that goal.", etc.

So, while the probability dimension [or u= - ln (P)] has not yet been put on the same footing as x, y, z, and t, I believe it will, although perhaps not so simply.

Let us look next at (b).

The idea of a conscious universe goes back to Jagadish Chandra Bose as a modern exponent but is actually at least as old as humankind. By defining the "physical universe" to exclude such things as consciousness we could try to save the old framework, but when we look at elementary quantum mechanics and the problems that it has with observation and wave-function collapse, we see that the old framework has already crumbled.

If consciousness is thought of as elemental, pre-existent, much as space-time is, then we see it forms an "orthogonal dimension" to the old "physical universe", but one in which measure (which is a method of comparison by repeated mapping of a standard and a counter) is not applicable. "Physical" quantities, such as wavelengths, have their shadows or correspondences in this "dimension" as qualities -- colors, tones, etc.

The two modifications (a) and (b) to classical ideas may of course be related. Naively speaking, how can one part of the universe communicate with other parts and "know" about them, without being conscious? There could of course be objections to this -- what if they just communicate like network routers do, processing information, surely, but not consciously? But perhaps routers, being parts of a conscious universe, are in asense conscious after all, and could not do their jobs (tunneling down to the electron level, where electrons are pushing and pulling or "speaking" to one another via e-m fields, with all of quantum theory at play) without this?

Well, that's my two-cents worth on (a) and (b). My ignorance and my limitations in this, being away from physics now for three decades, will be evident. These are thoughts I had while a student in India over forty years back, doing my Physcs B.Sc. with Niloy and Arindam who are on this mailing list -- and there (virtually speaking) those thoughts still remain. Not even teaching physics at the high-school level for the past twelve years, things are fading fast, and the fuzziness of the microcosm appears to be manifesting itself more and more in my thoughts and attempts at communication.

More practically, however, the article mentions a paper which purports to offer a measurable means (by measuring asymmetries) of deciding whether indeed the universe is a simulation.

Is the fuzziness of quantum mechanics the by-product the limitations of a simulation on a classical computer? I very much doubt that. The computer itself must be quantum mechanical, I believe -- in which case, it is the universe itself, the physical part and almost surely also the non-physical, in interaction.

Metaphysically speaking,

Orjun

P.S. N. D., my last (more practical) communication with you, regarding your query about V. S., bounced back. This has happened before. Methinks that U. Conn's and AOL's routers have distanced themselves from one another in the virtual manifold. I will try to resend it.

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Note added: See the next two post ( "A Solitary Pawn" and correspondence on that) for a follow-up on this.**********************************************

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