[FRIAM] utility of linguistic interpolation (was Entropy RE-redux)

Thu Jun 19 11:25:24 EDT 2025

 I am a child in this universe.  Delegate someone to set me straight.

Am I not correct that we cannot have the calculus without interpolation?
 Ok,  so the problem is with linguistic interpolation  ?  So, let us
compare two interpolations.

Let us toss a dead  pigeon off the Leaning Tower and predict that it will
arrive on the surface  of  the  Plaza  in N seconds.   We are
interpolating,   right ?    Or  extrapolating.     Whichever.

If  I  said,    "It will fall like a  stone ",   that would  be a
linguistic interpolation,   right ?

  Both  lead  to  concrete  expectations.      Well ,  at least  to
marble  ones.    In  one case we  need  a  stopwatch  to con firm; in   the
other case  we  need a  stone.

Nick

On Thu, Jun 19, 2025 at 9:32 AM glen <gepropella at gmail.com> wrote:

> Sorry. It's my fault the thread was lost. What I was trying to respond to
> was your positive spin on Eric's salvo against interpolation. Eric said:
>
> On 6/17/25 9:19 PM, Santafe wrote:
> > ... they have the greatest thing in the world but they aren’t going to
> tell you what it is (and _you’ll_ never understand; thats for sure!).
> > ...
> > The difference between good and bad presentation of the empirics is that
> at least the good kind has a comprehensible unpacking.
>
> Then you said, apparently in defense of interpolation:
>
> On 6/18/25 10:35 AM, steve smith wrote:
> > trying to regurgitate that to students in a digestible form, and along
> the way, we develop our intuition about which of the
> interpolations/extrapolations/combinatorics that come up in that work might
> be useful/interesting/valid?
>
> My response was intended to suggest that such interpolation is the
> antithesis of useful/interesting/valid. My tack on this might be described
> in terms of explainable versus interpretable algorithms. Explainability
> (and simulation, writ large) is often touted as a good thing. But my claim,
> here at least, is that it's a bit fideistic. It's like the Homeric sirens,
> calling us to our death. We should tie ourselves to the mast of
> "interpretability", or better stated, the ability to *behave* effectively
> rather than *think* abstractly. (The scare quotes around "interpretability"
> indicate that I think it's a horrible abuse of the word. What it means,
> here, is formality ... *not* interpretation/semantics so much as the
> ability to execute *without* or regardless of one's interpretation of it.
> "Explainability" is similarly used opposite to some of its natural meaning.)
>
> Despite Eric's repackaging the transmission of a cultural artifact via his
> 7 tasks (an inherently explanation-oriented activity), it focuses on saying
> what one is doing ... more like Ikea assembly instructions than some
> high-falutin' "modeling".
>
> There's a lot more to respond to in your post. But I'm going to stop here
> to see if we can stay a bit focused. That usually kills the thread. But
> sometimes not. 8^D
>
> p.s. For those who may be enthralled by the opposite-land words xAI and
> iAI, Perplexity does a decent job of ... uh ... explaining the difference:
> https://www.perplexity.ai/search/interpretable-versus-explainab-7AUdfa8tRLmvgIcV4V7mvQ
>
> On 6/18/25 6:24 PM, steve smith wrote:
> > glen wrote:
> >> It prolly won't surprise you that I disagree (I think). Those
> intuitions that we develop may be a) interesting to like-minded people, b)
> valid to those who hold the same value/logic systems [⛧], and c) useful for
> sussing out us-vs-them [in|out]groups.
> > I appreciate (and depend on?) this disagreement
> >> But they don't necessarily track reality.
> > There is /Reality/ and there is /Intersubjective Reality/ (similar but
> different to KellyAnne's "alternate facts")...  I don't think they track
> reality *any better* than the collective corpus of human expression they
> were trained on?
> >> You might even say (ala the Interface Theory of Perception) those
> intuitions are inversely proportional to one's ability to track reality,
> the stronger they are, the less they track. This is adjacent to Eric's full
> tea cup.
> > My only (intended) claim is that machine and human intuitions are
> similar in that they nominally interpolate and extapolate the
> high-dimensional space of all the linguistic/symbolic artifacts they have
> been exposed to.  In deference to my partial agreement  with DaveW, I
> recognize that written/linguistic "symbolic artifacts" are a tiny subset of
> the world even if we acknowledge the linguistic artifacts (writing) about
> the world.
> >> E.g. someone like Denis Noble, whose had a fantastic career in science.
> But now that he's old and out of his lane, his confidence puts him out in
> front of his skis:
> https://en.wikipedia.org/wiki/Denis_Noble#The_Third_Way_of_Evolution
> > I'm definitely old and out of any lane I might have ever held or been in
> for more than a few wild slaps of my arms.
> >> If we allow something like an intuition in LLMs, it should be clear
> that in order for them to track reality, they need "online" learning (as
> Marcus has proposed) and/or robotic embodiment to be able to interact with
> the reality we expect/want those intuitions to be about.
> > Agreed, their "intuition"  is currently limited to intuition about the
> things they have "heard" us talking about... they are the ultimate
> gossip-mongers, listening and passing on and making up new juicy bits from
> the old bits.   I find most pre-enlightenment "science" to be the same:
> rumours and gossip about "how rigid bodies in motion act" without the
> empirical grounding of say "dropping a couple of items off the tower of
> pisa and seeing which one hits  the jerk staring up at them first" or <pick
> your favorite story from alchemy, etc>.
> >> But where you could argue with me might be on something like "muscle
> memory". Turns of phrases in a language should probabilistically constrain
> the response from the LLM. This might be similar to the way some words and
> phrases roll off the tongue. But in that sort of case, it's not *intuition*
> as we might normally think of it ... it's more like habit or practice.
> Again the emphasis is more on the doing than the thinking.
> > Just a facility for the glib?  A propensity for riffing without
> comprehension?  Like me. here. now? (sorta)
> >>
> >> [⛧] Indeed, the only way "valid" has any meaning at all is in the
> context of a language system ... if you fail to say what logic you're
> working with, the use of "valid" is invalid. 8^D ... sorry for the poetic
> license.
> >
> > I'm not sure this impugnes language models (or other ML/AI systems) as
> much as it does the human capabilities they purport to emulate?   My point
> isn't that LLMs do "really cool and meaningful things" but rather that what
> they do *might* not be that dissimilar from what *we* do in many contexts
> soe of which we want to claim is cool and/or meaningful).
> >
> > <anecdote about hand-grinding lenses to make a point about embodied
> learning>
> >
> >     I was trained in my physics classes to believe that the actual
> hands-on-practice in the lab was important, that there were things I could
> learn (ways my intuition could be informed) by that embodied experience
> that no amount of reading and/or simple observation could achieve.   I'm
> still not clear on whether grinding my own objective reflector and silver
> sputtering it in a vacuum chamber improved my understanding of the things
> in the sky I then observed with it, but it did do something for me in terms
> of an "embodied appreciation" for the statistics and geometry of spherical
> and parabolic cross-sections and the implications of different levels of
> vacuum, boiling of elemental silver, thin-films, etc.
> >
> >     My lab-professor wasn't interested in my questions about the
> geometric implications (as I saw them) of the "figuring" techniques which
> best I could tell took the basic shape of a very large radius spherical
> section and added (central deepening and edge flattening) two more
> spherical sectionings such that the final mirror was a piecewise
> combination of 3 spherical sections with "maybe" a little feathering or
> blending between them.  I also worried the question of whether the distance
> and *angle* from the boiling silver (strip?) and the lens) mattered for the
> thickness/shape of the surface layer.  He (understandably) held that all
> that maundering and mentating was masturbatory and "all that mattered" was
> "that it works".
> >
> >     I'm glad I did those things and even though "george" can talk me
> through and around and up one side and down the other about DIY reflector
> construction and be more patient with me about whether the off-axis
> silver-sputter layer is "good enough and nuances of various methods of
> "figuring" the psuedo-sphere the primary grinding yields?
> >
> > </anecdote>
> >
>
>
> --
> ¡sıɹƎ ןıɐH ⊥ ɐןןǝdoɹ ǝ uǝןƃ
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>
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-- 
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology
Clark University
nthompson at clarku.edu
https://wordpress.clarku.edu/nthompson
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