On Thursday, July 4, 2002, at 07:21  AM, Bruno Marchal wrote:
>> (This gets into Tegmark territory, about "actual" (whatever that 
>> means!) physical universes with different mathematics and then, 
>> obviously, different physical laws. Egan, in "Distress," calls this 
>> the "all topology  model.")
> If we are machines I bet the physical laws emerge from all consistent
> possible Universes/Histories) and are necessarily unique! (more in my 
> URL).
> I will search for "Distress". I have read and appreciate "Permutation 
> City" by Egan. "All topology model"?  nice!  Especially because I begin 
> to suspect
> a "many world interpretation" of knots and links!

I happen to have the e-text/online versions of some of Egan's novels, 
including "Distress." I'll include below an excerpt describing the 
fictional ATM (which I found inspirational enough to trigger my recent 
interests!). This is not the only description of ATMs and MWI issues in 
"Distress," but it's one of the most succinct.

By the way, the book is copyrighted "1995," so I repeat my claim that in 
many ways Egan preceeded Tegmark, at least in terms of copyright. 
(Likewise, I am disappointed to see Marcus Chown and other writers 
giving Tegmark credit for the "stand in front of a machine gun and if 
you survive then MWI is real" gedankenexperiment. Hans Moravec wrote at 
length about how to win in a gambling casino by committing suicide if 
one loses in any universe. I, myself, described a way to factor large 
numbers by "guessing" the factors and then detonating the world's 
nuclear arsenal if the guesses don't multiply together to the right 
number. Moravec wrote in the late 80s on this and my own RSA spoof was 
circa 1993.)

Anyway, here is a "fair use" excerpt from "Distress." I recommend people 
find the book. In this excerpt, the main character, a science 
journalist, is flying to an artificial island in the South Pacific where 
a conference on Theories of Everything is about to occur. He is planning 
to interview a mathematical physicist and cosmologist who has developed 
an "all topology model" of the multiverse. The time is around 2050.

--begin excerpt from Greg Egan's "Distress," copyright 1995--

  I forced my attention back to the subject of All-Topology Models.

The concept of ATMs was simple enough to state: the universe was 
considered to possess, at the deepest level, a mixture of every single 
mathematically possible topology.

Even in the oldest quantum theories of gravity, the "vacuum" of empty 
space-time had been viewed as a seething mass of virtual worm-holes, and 
other more exotic topological distortions, popping in and out of 
existence. The smooth appearance at macroscopic lengths and human 
timescales was just the visible average of a hidden riot of complexity. 
In a way, it was like ordinary matter: a sheet of flexible plastic 
betrayed nothing to the naked eye of its microstructureómolecules, 
atoms, electrons, and quarks but knowledge of those constituents allowed 
the bulk substance's physical properties to be computed: its modulus of 
elasticity, for example. Space-time wasn't made of atoms, but its 
properties could be understood by viewing it as being "built" from a 
hierarchy of ever more convoluted deviations from its apparent state of 
continuity and mild curvature. Quantum gravity had explained why 
observable space-time, underpinned by an infinite number of invisible 
knots and detours, behaved as it did in the presence of mass (or 
energy): curving in exactly the fashion required to produce the 
gravitational force.

ATM theorists were striving to generalize this result: to explain the 
(relatively) smooth ten-dimensional "total space" of the Standard 
Unified Field Theory whose properties accounted for all four forces: 
strong, weak, gravitational, and electromagnetic as the net result of an 
infinite number of elaborate geometrical structures.


Nine spatial dimensions (six rolled up tight), and one time, was only 
what total space appeared to be if it wasn't examined too closely. 
Whenever two subatomic particles interacted, there was always a chance 
that the total space they occupied would behave, instead, like part of a 
twelve-dimensional hypersphere, or a thirteen-dimensional doughnut, or a 
fourteen-dimensional figure eight, or just about anything else. In fact 
just as a single photon could travel along two different paths at once 
any number of these possibilities could take effect simultaneously, and 
"interfere with each other" to produce the final outcome. Nine space, 
one time, was nothing but an average.

There were two main questions still in dispute among ATM theorists:

What, exactly, was meant by "all" topologies? Just how bizarre could the 
possibilities contributing to the average total space become? Did they 
have to be, merely, those which could be formed with a twisted, knotted 
sheet of higher-dimensional plastic or could they include states more 
like a (possibly infinite) handful of scattered grains of sand where 
notions like "number of dimensions" and "space-time curvature" ceased to 
exist altogether?

And: how, exactly, should the average effect of all these different 
structures be computed? How should the sum over the infinite number of 
possibilities be written down and added up when the time came to test 
the theory: to make a prediction, and calculate some tangible, physical 
quantity which an experiment could actually measure?

On one level, the obvious response to both questions was: "Use whatever 
gives the right answers" but choices which did that were hard to 
find . . . and some of them smacked of contrivance. Infinite sums were 
notorious for being either intractable, or too pliable by far. I jotted 
down an example remote from the actual tensor equations of ATMs, but 
good enough to illustrate the point:

Let S=l-l+l-l+l-l+l-...
Then S= (1-1)+(1-1)+(1-1)+...
=0+0+0. ..
But S=l +(-1+1)+(-1+1)+(-1+1)...
= 1


It was a mathematically naive "paradox"; the correct answer was, simply, 
that this particular infinite sequence didn't add up to any definite sum 
at all. Mathematicians would always be perfectly happy with such a 
verdict, and would know all the rules for avoiding the pitfalls and 
software could assess even the most difficult cases. When a physicist's 
hard-won theory starred generating similarly ambiguous equations, 
though, and the choice came down to strict mathematical rigor and a 
theory with no predictive power at all ... or, a bit of pragmatic 
side-stepping of the rules, and a theory which churned out beautiful 
results in perfect agreement with every experiment ... it was no 
surprise that people were tempted. After all, most of what Newton had 
done to calculate planetary orbits had left contemporary mathematicians 
apoplectic with rage.

Violet Mosala's approach was controversial for a very different reason. 
She'd been awarded the Nobel prize for rigorously proving a dozen key 
theorems in general topology theorems which had rapidly come to comprise 
a standard mathematical toolbox for ATM physicists, obliterating 
stumbling blocks and resolving ambiguities. She'd done more than anyone 
else to provide the field with solid foundations, and the means of 
making careful, measured progress. Even her fiercest critics agreed that 
her mathematics was meticulous, beyond reproach.

The trouble was, she told her equations too much about the world.

The ultimate test of a TOE was to answer questions like: "What is the 
probability of a ten-gigaelectronvolt neutrino fired at a stationary 
proton scattering off a down quark and emerging at a certain angle?" ... 
or even just: "What is the mass of an electron?" Essentially, Mosala 
prefixed all such questions with the condition: "Given that we know that 
space-time is roughly four-dimensional, and total space is roughly 
ten-dimensional, and the apparatus used to perform the experiment 
consists, approximately, of the following..."

Her supporters said she was merely setting everything in context. No 
experiment happened in isolation; quantum mechanics had been hammering 
that point home for the last hundred and twenty years. Asking a Theory 
of Everything to predict the chance of observing some microscopic event 
without adding the proviso that "there is a universe, and it contains, 
among other things, equipment for detecting the event in question" would 
be as nonsensical as asking: "If you pick a marble out of a bag, what 
are the odds that it will be green?"

Her critics said she used circular reasoning, assuming from the very


beginning all the results she was trying to prove. The details she fed 
into her computations included 50 much about the known physics of the 
experimental apparatus that indirectly, but inevitably they gave the 
whole game away.

I was hardly qualified to come down on either side . . . but it seemed 
to me that Mosala's opponents were being hypocritical, because they were 
pulling the same trick under a different guise: the alternatives they 
offered all invoked a cosmological fix. They declared that "before" the 
Big Bang and the creation of time (or "adjoining" the event, to avoid 
the oxymoron), there had been nothing but a perfectly symmetrical 
"pre-space," in which all topologies carried equal weight. . . and the 
"average result" of most familiar physical quantities would have been 
infinite. Pre-space was sometimes called "infinitely hot"; it could be 
thought of as the kind of perfectly balanced chaos which space-time 
would become if so much energy was poured into it that literally 
everything became equally possible. Everything and its opposite; the net 
result was that nothing happened at all.

But some local fluctuation had disturbed the balance in such a way as to 
give rise to the Big Bang. From that tiny accident, our universe had 
burst into existence. Once that had happened, the original "infinitely 
hot," infinitely even-handed mixture of topologies had been forced to 
become ever more biased, because "temperature" and "energy" now had a 
meaning and in an expanding, cooling universe, most of the "hot" old 
symmetries would have been as unstable as molten metal thrown into a 
lake. And when they'd cooled, the shapes into which they'd frozen had 
just happened to favor topologies close to a certain ten-dimensional 
total space one which gave rise to particles like quarks and electrons, 
and forces like gravity and electromagnetism.
By this logic, the only correct way to sum over all the topologies was 
to incorporate the fact that our universe had by chance emerged from 
pre-space in a certain way. Details of the broken symmetry had to be fed 
into the equations "by hand" because there was no reason why they 
couldn't have been utterly different. And if the physics resulting from 
this accident seemed improbably conducive to the formation of stars, 
planets, and life . . . then this universe was just one of a vast number 
which had frozen out of pre-space, each with a different set of 
particles and forces. If every possible set had been tried, it was 
hardly surprising that at least one of them had turned out to be 
favorable to life.


It was the old anthropic principle, the fudge which had saved a thousand 
cosmologies. And I had no real argument with it even if all the other 
universes were destined to be forever hypothetical.

--end excerpt--

--Tim May
(.sig for Everything list background)
Corralitos, CA. Born in 1951. Retired from Intel in 1986.
Current main interest: category and topos theory, math, quantum reality, 
Background: physics, Intel, crypto, Cypherpunks

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