[ExI] QT and SR
thespike at satx.rr.com
Sat Sep 6 20:23:34 UTC 2008
At 12:25 PM 9/6/2008 -0700, Lee wrote:
>> I really wish it were easier to convey complex
>>ideas, written English is such a narrow bandwidth...
>Ah yes, that would be nice.
>>Do you know of any discussions of this [communication]
>>problem, or proposed solutions?
>Not really. Even Skype or the telephone conferences or
>even if we had perfect video conferencing, two problems
>remain. (1) this kind of forum is great because (excuse
>me a moment while I go get something to eat) allows for
>total freedom of time and opportunity to participate, and
>(2) we simply cannot convey our ideas in any possible
>way to others I reckon, short of mind-melding.
<cough> One can attempt analogies:
Toby opened a Schwelle, took us back into clear
daylight. The trees were gone. I heard chickens
clucking in the dell below, children's voices,
saw a group of huts. Not five meters away a goat
grazed; when it saw me suddenly standing there,
it leaped straight up with all four hooves in the
air. I knew there was a word for that, but
couldn't think of it, because I burst out
laughing at the silly thing. I could have sworn
it shook its head in disbelief before it headed
ambling off downhill, neck bell clanging.
Stotting, that was it. Some African beast was
given to the practice. An adult human came out
from one of the huts. She was naked to the waist,
tall and scrawny, and when she opened her mouth
to scream at us I saw that all her teeth were
filed to points. Half a dozen little angry guys
rushed out of the other huts and ran straight up the hill at us.
`Let's not loiter,' Toby said, and we
went through to a world without huts, but
something immensely tall and pale blue stood
kilometers away on red concrete, soaring up
through light cirrus, bulging out like a turnip.
Windows caught the morning sun from a dozen
directions. The turnip, I saw, shading my eyes,
was slowly turning on its axis. In the low
purple-leaved bushes around us, large lacy
butterflies came and went. The place was
hauntingly beautiful and incredibly strange, like
a dream of impossible architecture.
`It's... wonderful,' I said.
`Yes,' Lune said. She put her hand in
mine. `These are all cognates of Toby's base
universe, you understand. Like the cardinal
numbers. There is a countable infinity of them.'
`Parallel universes,' I said.
`No,' Toby told me. `Well, if you
like. It's a gross simplification. Each of them
is actually in the same universe you've always
lived inside, the same multiverse, but rather a long way as the crow flies.'
`Ten to the 10^29 meters distant from
each other, on average,' Lune said, seesawing her
flat hand to show that the average varied a bit
from place to place, as you'd probably expect if
you had the faintest idea what she was saying.
`That's as the light beam flies too. Luckily, we
can get there faster by redescribing the ontology.'
`Oh, of course. Don't know why I
didn't see it immediately.' I shut my eyes,
calculating. Ten to the thirteen light years,
roughly. The radius of the whole goddamned
universe, wasn't it? It numbed the imagination.
No, wait. There couldn't be that many planets
like Toby's version of Earth, not in the whole
universe. `Actually, I still can't see it. Ten to
the twenty-nine doesn't seem enough--'
`No, no,' Lune said. `It's true that
ten to the twenty-ninth power is a truly enormous
number, there's roughly that many atoms in your
body. A hundred thousand trillion trillion. But
see, that's just the exponent. The whole
multiverse is ever so much bigger, unthinkably
large. You need to raise 10 to that power...'
`Not just one followed by twenty-nine
zeroes, you see, August,' Toby added. `Ten to the
ten to the twenty nine is so big that if you
tried to write it down you'd have to follow the
first one with a hundred thousand trillion
trillion zeros. I computed that once over a cup
of hot chocolate, and it stuck in my mind for a curious reason.'
I felt suitably crushed, and shrugged. `That's plenty of nothing.'
`It's plenty of plenty, my boy. At ten
numerals to the inch, the number you need to
describe how far the distinct universes extend in
the multiverse would itself stretch some twenty
seven billion light years.' Toby smiled
cheerfully and swung his arms wide. `From one
side of the local cosmos all the way to the other, scribble scribble scribble.'
`Yeah, and you'd use up a whole
shitload of ink and paper, right.' I don't think
they were fooled by my feigned nonchalance. What
they were saying beggared the imagination
utterly. My eyes drifted away to the right as I
tried to picture it. A universe of universes. But
that was just the first step. Then do it again: a
universe of universes of universes. And again,
and again, and again, almost endlessly... It was
too much to take in. Okay, yeah, I'd accept it.
You could have as many worlds like Earth as you
liked in a place that big, each of them
resembling the Earth we knew as closely as you
wishedthe planet Lune and Toby and I knew, even
if our worlds were a little dissimilar. I drew in
a staggering breath, looked back to Lune. She was nodding.
`I know,' she said. `It hit me hard
too. All right, my darling,' she added briskly,
`we're shown you the faintest hint of T level
one, where we usually live. Now let's move on toward the larger scales.'
A Schwelle opened as she spoke a
deixis code. We went into a place horribly bent
and twisted into absurd directions.
`A T-prime sample. Tegmark level two,'
she told me, somehow, and I heard her, somehow.
Her voice rattled like old rusted iron on a roof.
`Don't be alarmed. Our senses and our brains are
not designed for this. Aren't evolved to cope with it.'
Was there air in my lungs? I felt
myself choke and gasp. Was there heat enough to
warm the chilled core of my belly? I clutched my
arms around myself, then looked to Lune to make
sure she was okay. She'd turned into an El Greco
witch, elongated and hood-eyed. No, not like that
at all, more a deformed stick figure by Dali, or
Picasso around the time he started deconstructing
the human figure into oblongs with both eyes on
the same side of the face. My brother stalked
beside her, an insect thing with a ruff of indigo
hair. I glanced down at my own hands, recoiled.
Wire and corroded, patched leather.
`God,' I groaned. `Edward Scissorhands.'
`Your grammar is doing its best,' Toby
assured me. He sounded like a whale, very like a
whale. `In this place there are...' He paused,
cast about like a hunting hound. `...Maybe two
spatial dimensions and I'd estimate two temporal directions.'
`Two directions to move in time? You
mean we can walk backwards to the past while we're here?'
`Yes, but only while we're here,' Lune
said. Have you ever heard a peacock's squawk? I
was outraged at the travesty this evil domain had made of her music.
`It's lovely to visit,' I rasped,
`but I don't think I'd want to live here.'
`Moving on, then,' Toby said, and we
passed into somewhere far more disconcerting.
`You're mixing up the sticks,' I said,
witlessly. But what I meant was... I struggled to
hold on to something distinct and knowable.
`These T-prime worlds embody every
conceivable mix of physical dimensions and
constants comprising the multiverse,' Lune told
me. It made me laugh, because that's what I'd just said.
We went into places where surely
nothing solid, regular, persistent could exist,
sustain itself. For one terrifying endless moment
we crossed a vast space with more directions than
seemed possible but without the ticking of a
clock. An odor of incense. Timeless everywhere,
ground to a halt, seized. My Vorpal implants
blazed with light. I felt a cramp, a convulsion.
I was thrown out of that eternal silence, and
Lune murmured, as if in recognition, `Elliptical
partial differential equations.'
Onward we went, ever onward. In a
crushed place of echoes where nothing stood
still, where improbable forces built up and tore
down, Toby told me, `You see? With one dimension
of space but more than four of time, the worlds
are unstable.' We stepped away into places where
time returned to normal but space spread out once
more in directions I could not fathom with my
poor limited brain. He said, `With only one or
two dimensions of either space or time, universes
are too simple to build or sustain atoms, so we must evade those.'
In this inconceivable archipelago we
skittered through cosmos after cosmos in disarray
and flux. Somehow the Vorpal implants held our
bodies and brains, or their semblance in some
safe computational enclosure, from collapse or
dispersal. Lune told us, `Ultrahyperbolic
equations, no stability here.' We did all this
again and again. I will not try to describe those
places of dimensional confusion, it would be as
tedious and contrived as recounting a dream next
morning. The brain can't hold on to it, so it
concocts a bunch of mysticism about colors beyond
the visible spectrum, `ulfire' and `jale' in that
old David Lindsay novel my mother admired, A
Voyage to Arcturus, but that's not it at all. I
got the point, though, I really did. It
frightened me down to the bone, realizing the
truth of it. These were worlds, probably an
infinity of them, where the three familiar
parameters of height, depth and width, and the
one-way stream of time, were thrown heedlessly
into the trash. Dimensions and constants were
remixed and renumbered, the neat domestic floral
display of spacetime was barbarously pruned,
re-sorted, juggled. Roses were jammed in next to
strawberries and stinking weeds, and it made you
sneeze and then tore your nose off. As an
experience it was baroque, I'll give it that. It
was nightmarish in what you might call a bad way.
At the end of it, we stepped through on to a
railway platform and I sagged with relief,
drawing in the sinus-clogging fumes of the steam
engine smoke (so my nose hadn't been torn off
after all, which was a comfort), the heavy tang
of great greased steel locomotive wheels, the
sweat and dirty clothes of early morning
passengers in some kind of traditional Japanese
costume, carrying briefcases and listening to
Walkmen clamped over their high lacquered
hairdos. The men nearby gave us sidelong
scrutiny, but shoved forward with determination
into the open doors. The women kept their eyes on
the ground, shuffling sedately but with a turn of speed.
`Third Tegmark level,' Toby said
cheerfully. `Hold on to your hat, or not, or all three.'
Oh. Oh. Oh.
Was I having a seizure? An epileptic
fit, maybe, with those auras you hear about from
people afflicted with migraine, jittery streaks
of light and the feeling that your eyes are
jumping wildly between the frames of reality.
Everything peeled apart while remaining rock
solid. All the colorful folk on the station got
on the train and stayed off it, changing their
minds. They climbed hastily into the carriage in
front of them, and raced down and up the station
to force themselves belatedly into a different
doorway, or in some cases through the open and
the shut windows, and fell with a cry of dismay
on to the empty tracks where no train stood, and
boarded the sleek helicopter that waited on the elevated pad, and--
--I did all that too, that sort of
thing, my viewpoint jumping like a maddened
kangaroo from one part of the station to another,
with Lune's hand tightly in mine, and torn away
from her, and Toby lost to view, and, horribly,
Toby lying bleeding and surely dead, his abdomen
crushed by the wheels of the departed train, and
Voices chattering in overlap, coming
together into sense, skidding apart into blurred
cacophony: `The quantum view of the multiverse,
August. The all-at-once unfolding of the wave
function. Every possibility realized, all the
options accepted. Schrödinger with no collapse. Like in Sag-A star.'
`Get us the fuck out of here!' I
screamed, and hands tugged at mine and let mine
go and stroked my fingers languorously and
slashed at my skin, and my lurching legs carried me...
...across the Schwelle and jerked up
against my belly in the big bed. The house was
perfectly silent as I awoke in my darkened,
smelly bedroom. I lay still with my eyes closed
for several minutes, percolating upwards,
breathing night odors through my dry, open mouth.
My erection slowly ebbed; I knew I must have been
dreaming of Lune again. I reached behind me
without turning over, prodded under the covers,
but her side of the bed was cold and empty. At
first muzzily, then more sharply, I understood
that it really was completely quiet downstairs.
Odd. Where was her soft buzz of classic rock, her
humming clatter, toaster, muesli bowl, coffee
maker? The skin of my upper body was cool, and I
drew the sheet and blanket more tightly about
myself, hunkering into the pillow, eyes
determinedly shut. She's gone, I told myself with
gloomy dread. She's left me, the bitch. A moment
later, I thought: the Tau Ceti wongles have come
for her. They'll be here for me, next. I started
to weep behind my closed lids. Slow tears soaked
into my pillow. Pull yourself together, man, I
thought at last. With a weary effort, I pushed
back the covers and let my bare feet rest on the
cold floor boards. My bladder was swollen and
urgent. I took a step toward the door, toward the toilet down the hall...
...flipped open the ringing phone and
said in my deepest chocolaty voice, `"Madame Bovary, c'est moi".'
After the smallest hesitation, Toby said: `Gustav?'
How could you not smile? `Monsieur
Flaubert,' I told him, `is not available. This is the parrot.'
A deep, sickening panic invaded me. My
pulse jumped almost instantly to twice its
resting state. I stared in disbelief at the
screen, wondering if I were about to die.
Toby, I keyed, trying to control my
hyperventilation. Is that you hacking my bot?
At the third Tegmark unitarity level,
the screen told me, we've jumped up to 10^118
universes, each maxing at temperatures of 10^8
Kelvin. Every possible alternative quantum choice
is realized simultaneously somewhere when
I jumped out of my chair and kicked
the flat monitor over. Its lightweight nanotube
structure fell with dreamy slowness, bounced once
without breaking, sent me a hot pink blinking
message that I caught from the corner of my eye.
The next and final level is the big
one, August. Take a deep breath, bend over, and kiss your ass goodbye.
Terrified, I ran toward the...
I thought I heard Toby cry out, `Give
me Room 101.' A Schwelle opened in front of me. I plunged through.
Craziness. Disorientation, everything
falling away into a draining, stuttering echo of
itself. This was so much worse than the second
level distortions, or the simultaneous superposed
overlaps of level three. This was Cartesian doubt
so bottomless, so corrosive, that nothing
persisted beyond vertigo and pain. I tried to
squeeze my eyes shut but I had no eyelids, no
eyes. My whole visceral body, sense of awareness,
contracted to two mangled lumps of hieroglyphic
gold and silver linked by a thin shriek,
fingernails on a blackboard. I tried to scream,
and had no voice. Yet somehow I heard Toby
speaking to us, desperate, clinging to his own
sanity by a thread. There he was, in the chaos,
and there was Lune: two infinitely distant,
gruesomely intimate chains of golden hieroglyphs
I could not read. Was it his voice, or were the
hieroglyphs morphing, twisting into meaning? He said:
A man in many Earths wrote a very great book.
Some fragment of memory tore through me, gave utterance:
Echoing mad laughter? Yes, he is a
great Eric as well. I was thinking of Eric Blair.
`Never heard of the bastard.' Nothing
stayed in place. We were plunging like soap
bubbles in a gale through one Schwelle after
another, like mice gnawing their way through an
infinite stack of Stockhausen scores.
Never never never never heard of Nineteen Eighty-Four?
`You mean George Orwell.'
He took that name in some worlds. Do you remember Winston Smith?
`He hated rats. Shit, are rats waiting to claw my face?'
Not rats, August. Dragons, perhaps,
off the edges of all the maps you know. Winston
was shown four fingers and told to see five, do you remember?
I did. I held out four and saw five,
and ten, and one, and none at all. Not fingers. I
was watching the primal order of the cosmos.
And he did see five. That was Blair's
horror story. I always found it absurdly
abstract. Until I came here, into level four. Or
do I mean five? Hollow laughter banging and clanging at the edges of dementia.
`You're saying there are no rules here?'
No fixed rules, Lune told me. She was
formed hot metal in shapes that spoke to me. This
is the manifold. It's so beautiful. I had no idea
what she meant. She said: I stand in the center
of a web of mathematical functions, all in
motion, and I'm part of them, I guess I'm
creating them as well. They are wavelengths of
energy, perceived directly rather than through
eyes and brain, graphs of functions growing,
intertwining, unfolding. Music, sharply defined
and immediate, can't you hear it, August? And
then, cruelly, she was dragged away from me, and
the music and rainbow beauty with her, and once
more I was drowning in noise and terror.
Build it up, something told me. Play
it again, Mr. Peano man. That seemed wrongly
twisted, but somehow righter than wrong. I
scrambled for sensation, sense, sensibility. I could grasp nothing.
Nothing, said Lune's Vorpal hieroglyph display. The empty set. Zero.
I clutching at that nothing. I could
do that much. Emptiness at the heart of the noise
and terror. Emptiness that was the terror, or part of it.
Every natural number a has a successor, denoted by a + 1.
That seemed reasonable, although
everything in this flickering horror of fourth
level worlds denied it, mutated that simple
creed, added and subtracted and transformed in
dizzying confusion. I held to the axiom by brute force.
`All right. What next?'
The set zero is never the successor of any natural number.
No void hidden in the bowels of the
rush of numbers 1 2 3 4 5 6 7 8 9 10 11 12... to
infinity? No swallowing pit at the core of those
things we can count? I hoped it were true. I
assented, fearing its denial. No, wait... wait...
I found another solution lurking in there,
branching out into a permissible loop: 0 1 2 3 4 3 4 3 4...
I shook my head, started again.
0 1 2 3 4 5 6 7 8 9...
B ¥Qø ñ YÐ ...
The simple numbering of the world is pitted with
Chaitin pathologies, a voice told me, unexpected
and random. Yes, all right, I could see that, no
way around it. But it was the best I could do. Press on, then:
Each distinct natural number has a
distinct successor. If a succeeds b, then a + 1 succeeds b + 1.
I had to think about that, but I
grabbed with relief at the very difficulty of the
task with all my two, four, five, billion
handless hands, and felt reality solidify about
me, the endless cascade closing down, the
fecundity extinguishing itself, transfinite
options closing away, not gone, not lost,
merely... pinched off. Or rather: our world was
pinching itself free of that radiant abundance.
If a property is possessed by zero and
also by the successor of every natural number it
is possessed by, then it is possessed by all natural numbers.
If a-- Well, yes, obviously. An
instant earlier it had not been obvious. Now it
seemed both true and self-evident. I hung in a
blue place, and Lune sang to me. Her notes and
chords were filaments and jewels of logic. I
watched, dazzled, as she built an ascending Babel
city whose towers glistened with fractal
complexity, each chamber replete, gorged,
enameled, each linked to others by exquisite
cables of implication and ever higher
abstraction. It was beautiful, an orchid that
opened at the speed of light and made the world in its own image.
Formal systems, she said.
The globe of light branched, adding
axioms in one pathway: Boolean algebra. And,
launching an alternative road: Models.
Links multiplied at dizzying speed:
Lower predicate calculus leaped upward
in a blizzard of subsets, unions, intersections,
to Numbers and Semi-groups, commutativity
operations which spawned Rings, while by another
linkage came Sets, Relations, Abstract
geometries, and Space. All of this, in its
wonderful richness, was rudimentary, I saw, as it
elaborated and grew a world, a cosmos, of
mathematical order: on one side Abelian fields
and Vector spaces, by another path Topological,
Metrical and Banach spaces. Still the flowering
stormed upward and outward, through infinite
hordes of number, relation, ordering, bounds,
completeness, into Tensor and Hilbert spaces, and
Real and Complex manifolds. Finally, at its
sunlit capstone, in a torrent of immense
generativity, loomed twin rainbowed icy mountain peaks.
Lune told me: Here linear vector
mapping births operators that support the panoply
of Quantum field theory, fields on R^4 act on
Hilbert n-dimensional fields while... watch
keenly now, August... by this different but
intricately related pathway General relativity's
3+1 dimensional pseudo-Riemannian is warped by tensor fields.
Somehow I did understand what she was
telling me. The grammar download from the
X-caliber device unfolded, unpacked, in my mind.
I looked in awe, ravished by crystalline
loveliness. And as if I witnessed the collision
of two immense glacial ice shelves in the white
heart of Antarctica, those impossibly abstract
glories, their vast doubled structures, merged
into the computational unity of--
`Too bright!' I screamed. I tasted
lemon in my mouth, sharp and fragrant.
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