Yes, agreed fully on the overall picture of models versus the reality we
understand is out there.
On convexity, I guess I would put this into the category of error (Bhuddist)
but not sin (Christian). The convex models are the simplest category.
Everything else that isn’t convex occupies a big taxonomy, and even what the
categories should be is probably mostly not understood. For each valid “kind”
of non-convexity, we only make progress on it when we can get some idea that
demonstrably solves problems of analysis for that class. Of course, I don’t
aspire even to make arguments about the whole shebang, but there are a few
small cases in which I can see how the non-convexity works, what mistakes are
made by settling for a convex-hull dimensional reduction, and what other tools
exist for handling the fuller problem. (So as not to be cryptic, I am
referring to uses of Hamilton-Jacobi theory and related dynamical-systems
approximations — also severe severe and information-losing approximations — to
handle a class of nonlinear rate equations for stoichiometric processes in
which the dimensionally-reduced generating functions are not complex.)
On hypergraphs versus other representations, also strongly agree.
Stoichiometry is one very particular aspect in which one can assign types to
events. Even within the tiny world of rule-based stochastic processes, we have
well-developed other representations that capture different information than a
stoichiometric representation could capture, and the two are not
interconvertible. In particular, as I read much of what you describe, it
brings to my mind the many kinds of programmatic organization that I think of
as “computational” or “algorithmic” in one or another sense. I understand that
there is much more in the world, and probably much more you have in mind, than
this second small category too. But for me, a really interesting question is
when less-structured classes like stoichiometric ones can include models whose
dynamics create algorithmic organization as well. My own application is to get
from chemistry to things like biological information flow, lifecycles, and
such.
On mapping from economy to systems biology. Certainly I would not want to
approach the effort as one of mapping, for reasons that I suspect are very much
like yours. One should try to justify a formal representation from the whole
cloth of the phenomena, not by analogy or appeal to authority. But in this
case, once one is using a hypergraph for whatever reason, there is a repository
of tools and experience accumulated by the systems biologists that apply at the
level of the math, and no longer depend on the struts that must be tested
separately to validate that representation.
Pre-registered apologies for whatever incoherence is in the above paragraphs.
I am writing under heavy incoming fire.
Eric
> On Jun 27, 2023, at 12:08 AM, glen <geprope...@gmail.com> wrote:
>
> Being completely ignorant of everything mentioned, here, I can't help but
> wonder whether there is a path from not-even-wrong to schema-for-the-data.
> Going back to EricS' prior comment regarding when a (time/speed) difference
> of scale becomes a difference of kind, I have trouble accepting the convexity
> (or even closure) of any of the referent spaces. (I have no trouble accepting
> the convexity and closure of the models, as defined/abstracted from the
> referent, just the fidelity of the assumptions.) Like Farrell & Shalizi imply
> in their comment, such models work well for description. The problems arise
> when the description is fed *back* into the control. LLMs currently have a
> sticky re-training hurdle, requiring hybridization in order to complete the
> loop. And that's also been the case with economic models. Rather than map to
> systems biology, I'd prefer to map to progress in cyber-physical systems,
> where the models are more tightly and granularly coupled with the systems
> they control.
>
> It feels idealistic ("rationalist"?) to think that these models-in-a-vat
> (will?, can?, do?) capture the "tacit knowledge" adequately, faithfully. I'm
> reminded of the relationship between idealized neurons and neuronal networks,
> including neurotransmitters, hormones, glial cells, etc. Add to that long
> distance signals like proprioception, nociception, etc. and it seems clear
> that a monolithic LLM cannot be as good at "on the fly" model building as an
> organism can be.
>
> Maybe it's obviously modeled as [a] hypergraph[s]. And that might be the only
> way it can be built to dynamically/appropriately adjust fine to coarse
> granularity and tight to loose coupling for any given subset of covariates
> ... *as* the data is extruded through the model[s] into the data[base|lake].
> But for each node and edge in such a graph, it seems like it needs a
> complementary, shadow node and edge of parameters that regulate the graph. I
> guess the graph "plus" its complementing shadow is also a (larger?) graph.
> But are they different things? Or the same thing? And if they're different
> things, meta-things, is there an infinite regress lying about? (e.g. the
> parameter graph also needs its own parameter graph, etc.)
>
> I know I shouldn't hit Send on this one....
>
> On 6/24/23 20:03, David Eric Smith wrote:
>> Stephen, thank you for these,
>> Continuous your paragraphs at the bottom, there is a project I have wanted
>> to pursue off and on for 25 years, and which gets cheaper each year. I
>> probably described it before on the list (maybe more than once), in which
>> case apologies for the repeat.
>> The neoclassical paradigm from much of the past century turned on finding
>> price systems as the separating hyperplanes that separated convex models of
>> consumer preference and producer technology. Besides the fact that those
>> models are often not-even-wrong, lots else, like ecosystems, the polity,
>> etc., are left out of the account altogether.
>> A conceptually easy piece of low-hanging fruit, though laborious to populate
>> with data, would be to make an underlying model of the system you are trying
>> to analyze economically as a real-goods input-output problem. Then you
>> could find the separating hyperplanes that are price systems relating it to
>> whatever-other model you want to make of decision priorities.
>> Real-goods input-output analysis, with price systems as the separating
>> hyperplanes, is ancient; it is called the von Neumann growth model. Like
>> many other things von Neumann, it was picked up, demonstrated, played with
>> for a bit, and largely abandoned as people went wherever-else.
>> Today, of course, input-output models become far more useful than they ever
>> could have been in von Neumann’s time, because big computation allows us to
>> aggregate patchwork descriptions into larger models, which track the
>> stoichiometric dependencies between the sectors. This is some part of the
>> information that the separating hyperplanes discard (by their nature and
>> construction). The models are of course hypergraphs, which means we know
>> things about their topological analysis, and can study correlation of
>> fluctuations as well as constraints on average behavior. Systems biology
>> now does this sort of thing routinely with models big enough that they are
>> no longer just illustrative “toys”, where the separating hyperplanes are
>> biological molecule inventories needed for cells to reproduce, and outputs
>> of wastes to the surroundings can be tracked and their consequences computed
>> as well. All the usual stuff.
>> Most importantly, since ecology is already stoichiometric (in terms of much
>> more than just chemical elements), we can put the Venn diagram in the right
>> order, with the economy < polity < society < ecosphere, and at least
>> represent ecological inputs and outputs as the containers for transient
>> economic activity.
>> Another thing that would be a good use for the capacity of organizations
>> like google to vacuum up data would be to embed lifecycle analysis of things
>> like energy systems, water systems, or other factors impacted by human
>> demography into whole-system cost analyses, where “costs” are first and
>> foremost represented by real materials and embodied free energy, and we can
>> later project them onto smaller decision variables (such as money prices) if
>> those address particular problems.
>> I have a recently-graduated student who is enthusiastic about hypergraphs
>> and looking for general things to do with them, and we might have some EU
>> collaborators who will put in a proposal to do bits on this if they can get
>> their time protected. I don’t know if this goes anywhere, but the idea
>> seems obvious, and it would be nice for somebody to have time and interest
>> to work on it. There must be some class of decision variables that could be
>> served by such tools.
>> Anyway,
>> Eric
>>> On Jun 25, 2023, at 7:27 AM, Stephen Guerin <stephen.gue...@simtable.com>
>>> wrote:
>>>
>>> Thanks, Roger.
>>>
>>> I put a copy of Shalizi and Farrell's paper for discussion here:
>>> https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpapers%2ftemp20230624%2fshaliziFarrell_AI_Economist.pdf&c=E,1,m2nJFtd7iFa86CuE9FCY9CQkVkfHrpw3839u8WWk4epQ9Dy3EVib3NC_DBECSVK5UNlHjlG0hLEjQ23rhXmE6__0NPrgc3IACXkSzuHeXbiorKv-NQ,,&typo=1
>>>
>>> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpapers%2ftemp20230624%2fshaliziFarrell_AI_Economist.pdf&c=E,1,CJ3-rgYB-8TdQWaNu1p0AhBUqcXO0pO9dqRXDZBzKWVQ12oAlh1KuQzt_EhLnMxueuQiwhIBjLiSzOM8G39x-1OEu7gdvP8_MD3TlZkmo2oq5_yoDcKiXA,,&typo=1>
>>>
>>> (As this is a not a public email list, I think it's fair use to post a link
>>> to the article for discussion. I will delete the file tomorrow so the
>>> public archive will have a dead link)
>>>
>>> Also, here's a link to Weitzman's Hyperplane Theory referenced in the
>>> article.
>>> https://scholar.harvard.edu/files/weitzman/files/economicsproofseparating.pdf
>>>
>>> <https://scholar.harvard.edu/files/weitzman/files/economicsproofseparating.pdf>
>>>
>>> In some ways Bill Macready and Mohammed El-Beltagy (cc'd) were trying to
>>> build a version of Weitzman's Hyperplane for economic allocation with
>>> BiosGroup's Prowess Software 20 years ago extending price only auctions to
>>> the hyperplanes of price, time, quality and other multidimensional metrics.
>>>
>>> Mohammed and I have been talking off list these last couple months of the
>>> same points as the article that modern corporations and governments were
>>> some fo the first AIs that we're struggling to understand proper governance
>>> and how the challenge of what AI governance may look like.
>>>
>>> -Stephen
>>>
>>> _______________________________________________________________________
>>> stephen.gue...@simtable.com <mailto:stephen.gue...@simtable.com>
>>> CEO,
>>> https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.simtable.com&c=E,1,pVk4DGbH5fEdQ2LpSYoeT5BoCQgBjjM9XNtADImpKSq2g5UkyUjeAxa4zsVp4us_u14kfuY5Ck6dJbYXD8NHmrDPOyXcn97uTiDDNlMOAw,,&typo=1
>>>
>>> <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fwww.simtable.com%2f&c=E,1,4XrPURB_FCp-WXaQMvTLTW1xqvMkkKCTBaK7-Ku8lkt8BMYtA_py3VocBDX-We9fkc0hgOHqz0PdKUueGHWw0JWwVK86BBIPFP-ULgqi75TH&typo=1>
>>> 1600 Lena St #D1, Santa Fe, NM 87505
>>> office: (505)995-0206 mobile: (505)577-5828
>>>
>>>
>>> On Sat, Jun 24, 2023 at 2:55 PM Roger Critchlow <r...@elf.org
>>> <mailto:r...@elf.org>> wrote:
>>>
>>> I was trawling through my saved bookmarks looking for insights into
>>> Prigozhin's mutiny, when I stumbled to
>>> https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fbactra.org%2fweblog%2f&c=E,1,pzBCdWkUg8FesWYsgrTBa-l6T_PZZb3AZO9YfWUO-i3D-JWipI0OiXspifzHImB9BAGLjoYy9h9lhAx-U6mt6dcRi9c1lLQLtzPn31ANoIS2f2I31774&typo=1
>>>
>>> <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fbactra.org%2fweblog%2f&c=E,1,pE742UlOItFx5PPLUwST8PMDa8MKcLa5OUqvojIZKT-gGjoxhOOXLn5tNOUcOOWdnwn1tVtxHmRAw0repRi6-LwnW0g1Nl8b1Rr1jSJojFC2qrOv0GvEnA,,&typo=1>
>>> and found that Henry Farrell and Cosma Shalizi have just published an
>>> essay in The Economist,
>>> https://www.economist.com/by-invitation/2023/06/21/artificial-intelligence-is-a-familiar-looking-monster-say-henry-farrell-and-cosma-shalizi
>>>
>>> <https://www.economist.com/by-invitation/2023/06/21/artificial-intelligence-is-a-familiar-looking-monster-say-henry-farrell-and-cosma-shalizi>,
>>> paywalled of course, but there is a twitter listicle version at
>>> https://twitter.com/henryfarrell/status/1671547591262191618
>>> <https://twitter.com/henryfarrell/status/1671547591262191618>
>>>
>>> -- rec --
>
> --
> ꙮ Mɥǝu ǝlǝdɥɐuʇs ɟᴉƃɥʇ' ʇɥǝ ƃɹɐss snɟɟǝɹs˙ ꙮ
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