From: Eugene Leitl (Eugene.Leitl@lrz.uni-muenchen.de)
Date: Sun May 04 1997 - 07:44:42 MDT
routing in the low transcend
Risking Anders' axe-swinging berserkergang, I hazard to
(briefly) venture into his private domain: Jupiter Brains.
(Since my current shell account at the Leibniz-local Sun
cluster can only lynx, AmiTCP is still not installed, and
I don't like imposing large binaries/high-overhead
applications on a decade-old hardware with just 7-odd MHZ,
7 MB RAM, no virtual memory and a 120 MByte SCSI drive, and
the new 64 MByte/K6/Chaintech/Matrox Millenium/L4 Linux box
is getting delayed, and delayed and delayed, I never can
browse on the great Aleph server too much) </apology>. So:
How much bang can we squeeze from _conventional_ lunatic fringe
tech -- no spacetime engineering, no femtotechnology -- plain
old-fashioned stellar-scale autoreplicating molecular circuitry
clusters, lazily swinging themselves around their own gravity
centers, or solar-sailing fleet of line-of-sight laser-linked
hardware boxes, on light-minute wide (lest their circuitry fry
to black crisp in solproximal infernal heat) stellar orbits?
We already know the outer limits of it, as defined by the
Bekenstein bound. Actual constraints are much more pronounced,
however. Using excited states of organic molecules for doing
logics, obviously limits switching speeds to bond dissotiation
energies (twirling dipoles emit/absorb EM radiation, and
electron density is changed at excitation, geometry as well).
Much lower, even, since thermal vibration will destroy the
circuitry (I think defect introduction rate vs. temperature
will be markedly nonlinear, showing a catastrophic threshold
at few hundred K), and operating many switches at high
frequencies at extremely high integration densities achievable
by three-dimensional macromolecular crystals (I don't think
the respite, if any, granted by reversible logics will amount
to much), will dissipate a lot of heat.
Best implementation for these would be fractal cooling fluid
channels with integrated pumps, in a solid diamond matrix,
encasing, and containing the hyperactively wiggly molecular
switches. Notice that by engineering excited state species -
containing cavities we can control their lifetimes, energy
level spacing, and, most importantly, relaxation trajectories.
However, I am still unsure whether drextech (aka machine-phase
chemistry) is actually viable outside of post-cyberpunk SF
novels, in the real world.
Now autoassembly of linear polymers - macromolecular cluster
complexes, initially going through a solvated, wet stage,
automagically crosslinking to dry, relatively rigid macroscopic
circuitry crystals, instantly inflates the atomic cell edge by
at least one of order of magnitude, dropping integration density
by three. Due to matrix bloating, necessary for kinetical fold
guidance (as we lack the machine-phase reactive-moiety Gatling
guns), and a large density of (mated, in the assembled cell)
complementary surfaces essential in the hierarchical autoassembly
process, structures will be much coarser, and since the crosslink
concentration must be low, mechanical properties drastically
worse than that of a diamodoid solid. Isotopically pure CVD
diamond wafers are the best heat conductors known to man (people
like to slice ice cubes with them for a demo, using merely the
heat of your fingers), while linear polymers, even if dry and
crosslinked, do not conduct at all well, nor would they withstand
much higher operation temperatures than 400 K, or so, before
denaturating irreversibly, while diamondoid matrix might survive
at up to 800 K for prolonged periods of time.
(It is interesting to speculate, whether low-K temperature range
quantum dot (not qubits) arrays can achieve radically new kind of
high-density, high-speed, low-power-dissipation computational
devices, but here I am entirely out of my depth. Likewise in
solid-state qubit devices (which I deem unusable, but then that's
just meek me). Resident physicists please step forth to enlighten
us).
Anyway, the maximal concentration of circuitry in the embedding
matrix, and the limiting amount of dissipated power per volume,
as signal travel delay threshold for a given propagating distance,
(as imposed upon us by that pretty unpopular piece of relativistic
physics), seem to imply there are indeed tight limits to bit
integration density and their kinetics both, even though I am
currently somewhat at loss of giving even ballpark figures.
I guess, that without resorting to yet hypothetical machine-phase
chemistry, one could implement a molecular CAM with an elementary
cell with a 0.1-1 um edge (this gives us a integration density
uncertainty bandwidth of merely three orders of magnitude), and
absolute upper limits to switching speed of roughly 10^14, or
10 THz (visible light photons, of roughly 0.4-0.8 um wavelength
(at least the green/blue ones), bear enough energy to lyse bonds
en masse, obviously a strong no-no in a computer, even a
fault-tolerat one, since defect rate must remain below a
certain threshold to be able to operate the circuitry for a
sufficient time span for it to be useful, before it has to be
replaced by a freshly synthesized module).
As EM radiation in vacuum (in matter significantly slower, the
slower the higher the refractive index and vice versa) travels
roughly 30 cm in 1 ns (1 GHz clock, coming soon to a desktop near
you, e.g. as Merced, though I'd rather like a PIM (processor-in-
memory design) instead), 0.3 mm (300 um) in 1 ps (1 THz clock,
which is unattainable with semiconductor technology), and 0.3 um
(300 nm) in 0.1 fs (1 pHz clock), whereas EM of 1 um wavelength
(still NIR) has a frequency of about 3*10^14 Hz, or theoretical
maximal switching time in fs range, we have discovered our outer
limits at the individual molecular switch model (please notice
that we have not adressed the very thorny issue of maximal switch
concentration yet, which is a function of both the assembly
process, and cooling system efficiency). We know that the
transfer of energy by direct electromagnetic interaction between
chlorophylls is considered to be pretty rapid, while happening
in 10^12 s (ps) range.
Hence it seems to be realistic to assume maximal switching speeds
achievable with physical structures to lie somewhere in the ps..fs
range, 1 THz - 1 pHz, the lower bound to be more probable. Perhaps
my earlier mentioning of "clock" was somewhat misleading: it is
quite clear that, due to relavistic constraints, assuming
synchronized action by a global clock appear unfeasible. Rather,
a system of locally-coupled, externally pumped oscillators, where
synchronization emerges at a higher operational plain appears more
feasible.
Personally, I like laser pumping, where a system of dyes funnels
the energy into an orthogonal 1d metal grid, crisscrossing the
crystal, and acting as a transient energy storage (as photon
absorption is a stochastic event, we cannot count on cell-local
dye assembly to provide cell-local juice at any time) system,
which then feeds the individual cells. A pulsed operation can
be envisioned, with each pulse pumping up the energy cache, until
it discharges spontaneously, or triggered by a second laser pulse.
If we assume 1 ps for 1 um CAM cell switching time, we can expect
a information light cone propagation velocity of roughly 2 um/1 ps,
or 2 Mm/s, almost 1% of c.
(Anyway, as we now have arrived at the very heart of Never-Never
Land, and I am notorious for goofing up my math this numbers should
be taken cum grano salis. If your bogosity detector notices a
supercritical bozon flux, please let the list know).
Let us leap up to the next integration level: energy dissipation
will impose a tight limit onto volume/surface ratio. Whereas
diamondoid systems can directly radiate power into few-K space,
molecular CAMs must be fluid-cooled. I guess one could engineer
proteins the resulting crystals to feature orthogonally aligned
mesopores/channels for the cooling fluid to seep through
(this opens the opportunity for chemical energy pumping), but
this will make the crystal much more brittle, and further dilute
the circuitry concentration.
On the module cluster level, we have a mechanical gravitation/
tidal/resonance problem. If we assume the computational nodes to
be mounted on a stiff truss structure, sooner or later tidal
forces, own gravity, and vibration resonance (a problem already
plaguing today's satellite photovoltaics arrays).
So sooner, or later, we must resort to freely orbiting computational
nodes. If we consider them to be orbiting around their own center of
gravity, orbit perturbations both require the need for active position
control, and limit the maximal module/space voxel. Since their
relative velocities might be considerable, collisions may trigger
release of debris, the so-called fragmentation catastrophe. The need
for active position control requires reactive mass, which must be
sometimes replenished. If solar sails are utilized, this will
dilute the circuitry even further. All in all, a nontrivial
multidimensional optimization problem, as the optimal grain
size of each hierarchy must be chosen.
Furthermore, it is instrumental to realize, that gravitation tends
to create circular, wrap-around structures. Whether nodes on a
planetary surface, nodes orbiting around their common gravity
center, or a star, the node grid is subtly distorted, with node
neighbourhood relation in constant flux. If we assume geodesic
(a quite inappropriate term for an orbiting node cluster) routing
scheme, where a data packet emerged somewhere deep within the
individual molecular circuitry piece has to worm its way towards
surface, being beamed node along node, unless finding the right
node, the right target metaCAM subcell, we must assume each node
to bear an identity which is not a function of relative position.
Instead, node IDs could be derived from a global position,
requiring beakon nodes. As node orbits are deterministic on
the short (a few revolutions) run, perhaps this information
can be used.
As mankind's machines are going to spin off into interplanetary
space, we need a GPS++, which is also handy for node ID derivation.
The natural coordinate system for the solar system seems to be
obviously a heliocentric one.
ciao,
'gene
P.S. This is a pretty old post sketch, expanded on the fly --
sorry if I rehash trivialities.
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