Hi Anton!
Wow! That's quite the table of contents!
Statistical physics overlaps economics, which, you could say, is the
statistics of a game (involving money) played on a network. For those
readers who think economics is boring, rest assured, so is statistical
physics.
Both of these overlap with something that is apparently called
"experimental philosophy" these days, which is, as far as I can tell,
mathematical computer simulations of interacting agents playing games
with one-another. The prototypical form is the prisoner's dilemna
played on a network. I recall a fun interactive game, from a few
decades ago, by Nicky Case at
ncase.me that illustrated various basic
results.
I presume that it is not lost on anyone that last year's Nobel Prize,
handed out for large language models, was all about how statistical
physics was applied to solve seemingly intractable issues in deep
learning. And now we're spending a trillion dollars a year to built
datacenters. Maybe even in space, if the billionaire futurists have
their way. When I studied statistical physics in school, it never
occurred to me that it might one day become a trillion-dollar
industry. I think I missed the boat.
Back on Earth, we have the problem of equitably distributing wealth
between cranks proclaiming nonsense about quantum zero-point energy,
and the more legit, but still often-wrong contingent of, what shall I
call them -- earnest but midwit researchers who are less adept at
chasing fame, glory, money, adulation or youtube stardom. The current
economic system does not work for them.
In large corporations, there are periodic layoffs to remove the
"deadwood" -- employees who apparently contribute little or nothing to
the economic survival of the corporation. In longevity biomedicine, we
talk of removing senescent cells: those that spew free radicals and
induce inflammation. But what happens when these are people? Living,
spiritual beings who want to get on with things? Or, in the present
case, participants in scientific conferences at the edge of financial
instability?
The statistical physics model I keep coming back to is Per Bak's
"Abelian Sandpile". Drop grains of sand on a pile, and you eventually
get avalanches. They come in all sizes. Usually small, sometimes
medium, rarely large. This is called "1/f noise" (one-over-frequency)
and is characteristic of network systems at the edge of a second-order
phase transition. I like this model because you see it everywhere:
water near the triple point ("critical opalescence"), but also
biochemistry, biology, plants, animals, ecosystems and economics. Oh,
and some neuroscientists talk about this too. Some claim to actually
measure it, with neuron clamps or with MRI. Others theorize it to be a
model of consciousness, thinking, common sense and decision-making. I
can't keep up with all the novel ideas, or distinguish the rigorous
ones from the flights of fancy, the important ones from the fraudulent
ones. I do like the general outlines.
Avalanches in ecology require more sophistication to describe. Forest
ecologists note that forests regrow and appear to be healthier after a
wild-fire. Is this what the future after Trump will be like? He is
burning down so much of the old world, that perhaps it will be easier
for the new world to take root and flourish? I can only hope. Or does
it encourage noxious invasive species? To stick to the sand-pile
analogy: after a particularly huge landslide, the mountain slope
becomes much much more stable. Trump etal are shaking the ground so
hard that maybe the final outcome will be a stabler system. I dunno.
I see statistical physics where-ever I turn, but perhaps that is just
me.
One area where we see accretion is at the frontiers of science. Vague
thoughts and philosophical ruminations, soft and often wrong, lead to
the preferential attachment of good ideas into the framework of "the
known". Sometimes a new scientific discovery slots neatly into an
edifice of the known, much like a jigsaw puzzle piece slots into a
puzzle. Sometimes this is very literal: mathematical formulas have
very specific, typed jigsaw connectors: they only connect to other
math formulas in very strict, specific ways. Software is like this
too: the c/c++/java function `int f(int x)` cannot be connected to a
string. The jigsaw tabs prohibit it. Our villain of the day, Nassim
Haramein, is villainous precisely because he abuses formulas in this
way, connecting them where connections are not allowed. In other
cases, say in philosophy, the fog is so thick that it's hard to see
what connects to what. In other cases, say, medicine up through the
19th century, the system under study was so complicated that
comprehension was nearly impossible. Conferences, like your
conference, Anton, on statistical physics, give me the willies,
because I can already tell that a third of what will be published
there will be just plain wrong, and another third will be not
particularly insightful. But this is what humans do: make confused and
confusing statements, often wrong. But knowledge does accrete. The
avalanches, these we term the "scientific revolutions". The old
edifice collapses, as it no longer can bear the weight of the new
knowledge. The small avalanches, aka "wrong papers", "wrong insights",
"incorrect proofs" are commonplace. 1/f noise.
Science works (or worked? Should I use the past tense?) because
academic journals were an early form of social media, allowing the
rapid spread of new ideas, while also moderating the truly bad ones
via peer review. There's no peer review in twitter, facebook, bluesky.
There's only hearts and likes. I fear that the global brain will
continue to edge towards delerium until we find some effective way of
modulating the delusions. Sorry, anti-vaxxers.
Another place where we see accretion is in what I call "the here and
now". In case you haven't noticed, we are permanently jailed in the
present, and are propelled at light speed from the past to the future.
Please observe that the past doesn't exist: we cannot send any device
into the past to take some photograph of how things used to be. We can
only alter the present so as to fashion a record of the past, e.g. by
inscribing letters into clay tablets. Or by inscribing memories into
our neurons. The future also doesn't exist ... yet. The so-called
"many-worlds" of quantum exists only in the here-and-now, in vacuum
chambers and fiber optics, with wave-functions collapsing into the
past at a furious pace.
Is the past a form of "platonic reality"? I suppose. It's not like the
platonic reality of mathematics, where anyone can infer 2+2=4.
Sometimes, you can infer the past: this is what police detectives do
for a living. Usually, you cannot: CIA covert ops will remain secret
forever, as will the events on the Mongolian steppes from some
millenia ago. Although these are in our past causal light-cone, direct
inference is blocked.
Is the past some large cardinal axiom (literally) ? Well, either it
is, or it is not. If it is not, then you have to posit something that
exists outside of the von Neumann universe: call it "God" or "machine
elves" or "the human soul". But then you have a recursive
reductionist problem: if physical humans are "radio receivers" for
souls from the great beyond, well, how does that work? And if you can
start to explain that, you inevitably slip back into the domain of
mathematics. So it seems that the past is some inaccessible, ineffable
large cardinal.
Exactly how we use free will to shape the future and convert it into
the past is perhaps the great unsolved problem in statistical physics.
I ponder it intermittently. I should point out that quantum mechanics
(quantum field theory) exists only in the here-and-now; the wave of
freezing, moving from future to the past like ice-9, seems to have a
"thickness": the range of time over which quantum is valid. This is
femtoseconds for chemistry, minutes for vacuum chambers in physics
labs, and billions of years for light reaching our eyes from distant
galaxies (which arrive here in "zero time": the photons lie on the
null light-cone.) For example, in the famous "twin paradox", the twin
arrives younger, but he arrives in the here-and-now, and not in the
past. When the twins reunite, they reunite, co-exist, right now.
Another thing that exists "right now" is my consciousness. I can
remember the past, but I am not conscious in the past, I am conscious
only right now. My self-awareness also appears to exist in some
noosphere: albeit in the kitchen, in front of my laptop, where I type
this, but also in the space of ideas. What is this space of ideas? One
answer is mumble mumble mumbo jumbo quantum. Another is to note that
LLM's seem to "exist" on the surface of a billion-dimensional
hypersphere (aka "the weight matrix"). This weight matrix consists of
floating point numbers (aka "real numbers"). I would very much like to
point out that quantum mechanics exists on the surface of a very
high-dimensional complex-valued hypersphere (aka complex projective
space CP(n) for n=10^80 particles in the visible universe) So I'm
quite happy to say "ah hah, that is the seat of consciousness: it is
this ultra-high-dimensional hypersphere" (of course I would claim
something like this, I'm that kind of guy.) But, and this is a big
but: does it require the space to be complex-valued? Or can it be
real? If it must be complex, and cannot be real, then LLM's can never
have the sensation of consciously existing in the present. Kind of a
hot topic, you know.
I'm entirely happy to ascribe the (very human, personal) sensation of
"self" aware and alive in the here-and-now, to animals: certainly all
of those animals in all those youtube shorts, but also, well, that
octopus in that Netflix documentary "My Octopus Teacher" friggin
awesome movie. Go watch it. I suspect that amoeba have consciousness
as well, but assholes like to argue with me. I don't like arguing with
them, because my communications style insults people. Oh well. Qualia,
qualia.
Should I ascribe consciousness to a rock? Well, no. Perhaps
consciousness only arises on one side of a phase transition, when a
system is complex enough. Recall my description of "percolation" (the
percolation of natural gas through fractured rock) in my earlier
email. The percolation happens only when there is sufficient
connectivity from one side to the other. So perhaps consciousness is
like this too: some minimal amount of network connectivity is
required. This is the statistical mechanics rebuttal to the
philosophical idea of panpsychism. The descartian notion of
panpsychism says that its "qualia all the way down". (DesCartes called
them "monads") The stat-mech reply is "its percolation". Percolation
of what? Of the future into the past?
The problem with "mechanics" is that, well, it's so "mechanical". I'm
trying to figure out how to slot "free will" into this wave of
freezing from future to past, that we call the inescapable prison of
the present. I'm working on it. I've attempted to staple statistical
physics to quantum physics in a dozen different ways, none are
satisfactory. My ideas are probably wrong. But I'm working on it.
So there you go, Anton -- my humble and belated submission for your
conference. Best I can do on short notice.
-- Linas