Thank you. I don't accept your apology because the tangent was necessary. That
"rolling up" of a finer grained model in order to estimate the finite
parameters of a coarser model is what I was missing. It seems like we're denying the
*soundness* of our decoupling formalism(s), the math of the rolling up. If that's the
case, I'd agree. I'm a fan of the 80/20 posture ... pragmatic if not pragmaticismic. 8^D
I don't yet grok "infinite order". But I will do my homework ... maybe.
On 12/3/25 9:07 AM, Santafe wrote:
I certainly mean the second set of things: scoped, bounded, etc.
But I think I also want to mean aspects of the first as well. Here, it is
clear that I am using templates from within things we (think we) have solved in
physics, and maybe biology, as models for what I expect scientific progress to
look like more generally. At the least, because it has to contain the physics
that has these aspects, but also because there seems every reason to expect
them elsewhere.
To be less vague and cryptic (I hope):
If I ask what we can do correctly within some domain of physics, it often
amounts to predictions that come from the collected action and interaction of a
fairly small collection of coded laws. And in some cases, some parameters that
we just take as inputs, but don’t have “explanations” for.
Even within the Standard Model, though, what we have are finite-dimensional
effective theories at a few energy scales down in the observable range. Even
if you think it will just be quantum field theory with renormalization all the
way down (which there is good reason to distrust would be enough), there is
still a vast range of scales we have no good current ways to probe, which can
be filled with a large number of parameters that get aggregated at low energy
and that we have no way, from low-energy observations alone, to disaggregate.
But it could be worse than that, it seems to me: Consider what we would have
tried to do with only classical physics, if we had (put aside the wrong
ordering of the experimental timing), known the existence and masses of
protons, neutrons, and electrons. We would have had no alternative to
supposing that the masses of nuclei were the sums of the masses of their
components, and that the masses of atoms were the sums of masses of their
nuclei plus some electron masses.
Quantitatively, the above prediction would have been only modestly wrong.
Indeed, the whole masses of the electrons would have been smaller than the
errors in the mass-predictions for the nuclei.
But look what we had to do to improve those predictions: Everything that had
been a number in classical physics became a distribution in quantum mechanics,
and all interactions had to go to infinite order and get renormalized, and on
and on. There was this vast machinery of underlying structure, most of which
vanished into a few aggregate parameters at the low scale, but which we had to
model correctly to get the right values for those parameters.
Apologies for the last few paragraphs; they didn’t address your actual
question, and went off on a tangent about the structures in physics that impact
my thinking.
Back, then, to us and the state of our science: What are we doing at any given
stage? We use these few tokens, with whatever math we have for them, to
calibrate the whole system to some collection of observations. It’s always
very limited. In the case of the discovery of QM, we got a lesson that we were
omitting infinite-dimensional spaces of structured things that we turned out to
need.
If I am right, to use that one past learning event as a model for future
expected reformulations, then I expect that whatever it will take to deal with
QM and gravity is likely to reveal a whole mess of unexpected new
infrastructure, to calibrate to the current (still finite) set of parameters we
use.
If we think about more complex sciences, like biology, and we think of each new
“scientific law” as some kind of compressed description of regularities in an
aggregated system, it seems likely that the potential for distinct and
irreducible new patterns to be characterized will be infinite, kind of like the
eligible patterns in number theory are presumably infinite. At any given time,
we know about and try to use a collection of them that is finite and usually
small.
So that was what I intended in saying that, in science as in everyday behavior,
we act like small finite-state machines, which coarse-grain our momentary
involvements in the world in ways that leave real differences unresolved and
unsensed. Then, to that I attach my own prejudice that the dimension of the
real details we don’t notice is probably infinite. But each stage of our
progress will always be by some finite increment, so presumably the unknown
will remain infinite.
On Dec 3, 2025, at 11:38, glen <[email protected]> wrote:
Dense and and flat at the same time. Well done. I know you meant this for Nick. But I have 1 question that
would help me understand. When you say "finiteness", "finite beings in an infinite
world", and "been infinite forever", do you mean it in the mystico-pop culture sense? Or are
you using it in a technical sense, like the difference between {1,2,3} versus {1,2,3,…}?
Because if I swap out your use of "finiteness" with scoped, bounded, separate,
disjoint, or such ... that 1 thing can be distinct from another thing, then almost all of
what you write snaps into place. But I'm afraid of preemptive registration.
On 12/3/25 3:37 AM, Santafe wrote:
[snip]
4. It is ultimately the problem of finiteness, and of carrying out inductive
behavior, that leads me from the above claims, to the “as if” characterization
of the role of an “objective posture” in our discourse and our behavior. I
acknowledge that Glen didn’t want to sign off on a notion of the “real world”.
But speaking just for myself, I obviously go through the day acting as if there
“is” a “real world” “out there” all the time. And I assume that the reason our
common language gave me a discourse to refer to such things is that
most-everybody else goes through life feeling much like I do about it, and
acting much like I do. Indeed, I would argue that we cannot do otherwise,
because for practical purposes we are induction-committers: finite beings in an
infinite world, who cannot help but coarse-grain endlessly variable
circumstances into limited categories, and then use the limited categories as
indices for our responses. I settle on that act of performing an inductive
continuation as the central feature of us that, if we want to refer to it, will
lead to language about the real world, more or less like the language we find
ourselves having inherited, and using.
4a. On the (still inductive) belief that the moments of my life actually flow
in a sequence roughly like I think they do, and that the wakeful moments of my
life aren't all a grand hallucination, which only those on LSD recognize in its
true nature, and the rest of us are blind to — mea culpa here for my stance on
the matter — I take a certain Darwinian (or reinforcement-learning) view that
there is only some stability to any of these inductions, enough that we ever
have a reason to need to refer to them, because the structure in the events
that happen likewise has elements of stability that we can sync onto,
metaphorically like a phase-locked loop (from electrical engineering) uses its
tendency to synchronize to find the periodicity in a signal that it can lock
onto. My reasoning here is clearly circular: in refusing to reject the premise
of a “real world”, I am using patterns of structure I form within my discourse
about that world, to refer to myself within it, and assign commonalities to me
and to the rest of it that warrant my referring to the rest of it. This is
what the mystics regard as error on my part: that we have all been infinite
forever, and that we therefore never needed to settle for induction. Oh well;
I don’t know what to do with them.
4b. But at last I at least have a language in which to say how objectivity
attached to the earlier discourse about the stability of assertion and
activity. This “source of stabilization” for my inductive behaviors is
effectively what I tag with the name of “the objectively real”. Then, my own
nature as an induction-committer is the thing I tag with this notion of an
“objective frame” that I take on w.r.t. all the dimensions of variation I
effectively regard as ignorable while I am doing my finite-state
induction-committing thing. I suppose that the two different tags have
something to do with each other, to the extent that my inductions are stable
and present to me as having some structure to refer to, and not just being a
structureless random walk.
Anyway, sorry to pile more onto the last. Whenever your current project lets
go of you, if you aren’t sick of (my version of) all this, it can be added to
the silage.
Eric
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