Brilliant, Eric. I think I have strong attraction to Platonism. I had a
thought a few years ago that every right triangle in the plane has the
Pythagorean property regardless of humans or their awareness. Then I
wondered where a perfect right triangle exists in nature. My answer to
myself was {(0, 0), (1,0), (0, 1)}. But that's a "mathematical
confabulation" according to Nick I suppose.
People who haven't studied limits carefully, say elementary calculus
students, think they're mysterious when they aren't. As you know lim(f(x))
as x goes to 0 just means some number, if it exists, which f(x) approaches
arbitrarily closely as x gets arbitrarily close to zero. f(0) may or may
not exist. If Zeno had understood that I don't think he would have felt
there was a paradox.
But I don't know that obviously.
Frank
---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505
505 670-9918
Santa Fe, NM
On Sat, Oct 2, 2021, 7:47 PM David Eric Smith <desm...@santafe.edu> wrote:
> I feel in this, Frank, like your comments will fall on deaf ears, for an
> interesting reason. The thing you summarize for Nick is precisely the
> thing he wants to object to.
>
> It seems to me that Nick believes that Zeno’s arrow paradox,
> https://plato.stanford.edu/entries/paradox-zeno/
> or something close to it, defines in some Platonic way the “right rules of
> thought”. Whatever Zeno’s rules of argument make ill-defined, we should
> somehow believe isn’t really properly conceived, and _cannot be_.
>
> If I were to tell Nick (replace “momentum” where he has “acceleration” in
> the sentences below), that in 1833, Hamilton took us beyond all the things
> Zeno can’t do, by writing the states of objects in a 2-coordinate space,
> where one coordinate is position and the other is momentum, and the two
> coordinates are _independent of one another_, and in some important sense
> _symmetric_ and _peer_ attributes of the object, I would not be addressing
> his objection to calculus (which does define these things in limits as you
> say below), but I would be arguing that physics may suggest the
> limit-definition from calculus is not the most fundamental one. If I were
> then to tell Nick that the duality between being at a place (all position)
> and being in a state of motion (all momentum) became in quantum mechanics
> the duality between standing and traveling waves, and that we understand
> their independence and peer status even more thoroughly in quantum
> mechanics than in Hamilton’s classical mechanics, I would still not be
> addressing the unquiet about calculus, but would perhaps be asserting that
> physical reality is even further from needing its in-the-limit definitions.
>
> But the part of this that is interesting (to me) is: why is this
> Nick-as-I-perceive-him (which the real Nick may or may not be) convinced
> that Zeno’s rules of argument are somehow the defined “right rules of
> thought”? Why is anyone convinced that he knows ahead of time what rules
> are the right rules of thought for anything? Why are we not somehow always
> aware that all these words and rules come up together somehow as parts of a
> mutually-interdependent system, really “pulled up by their own bootstraps”
> in a much more perfect way than the way that metaphor is used for the
> startup of an operating system in a computer? And if we were thus aware of
> the somehow out-of-nowhere character of the bootstrapped systems within
> which all the terms and rules take their meaning, how would it then change
> the way we think about choosing which one to use? The Platonists in their
> own words b believe that truth somehow comes to them through the divine
> channel of thought from a reality beyond experience. I think they are more
> fond (in the original sense of “crazy”) of their own preconceived notions
> than they are of the complexity of experience, and mistake their
> preconceived notions for a more ultimate and perfect, but in any case
> preferable “reality”. If we get out of that habit, how does our style of
> argument for what constitutes right thought change?
>
> Neither here nor there to this thread, I did want to mention some weeks
> ago that I really liked Glen’s formulation of The Will to Simulation. I
> think Nietzsche would have appreciated its irreverence, though he would
> have been too vain and obstreperous to contribute anything to it.
>
> Eric
>
> p.s. On the above, I could have stayed with Nick’s original query about
> acceleration, and gone to physics. I could have spoken of his very
> physical self, standing here on the surface of the Earth, and accelerated
> away from the world-line of an inertial observer in general relativity by
> the fact that the Earth is in the way of his free fall. The gravity that
> he feels in the seat of his pants is the acceleration that is a property of
> his state. But it was simpler to refer to momentum and to go back to
> Hamiltonian mechanics, which has an additional century behind it, and which
> really marked the turn away from Zeno and a definition of velocities in
> terms of derivatives by Lagrange, and toward a recognition of momentum as
> an inherent property. If one can see that clearly and with familiarity, it
> is then a straightforward next step to say that Mach’s principle just said
> “if frame-independence applies to velocity, then why not also to rotational
> velocity, and what then do we do about acceleration”, and you get the case
> from general relativity.
>
> On Oct 1, 2021, at 10:00 PM, Frank Wimberly <wimber...@gmail.com> wrote:
>
> Nick, i hope this helps. Given a fair die that hasn't been thrown the
> probability that it will come up 2 (or any of the other particular values)
> on the next throw is 1/6 by definition of fair. Given that it has been
> thrown and ceterus paribus the a posteriori probability that it shows 2
> given that it does is 1.0. In that case the probabilities of each of the
> other values is 0.0.
>
> The acceleration of an object with constant velocity is 0.0. If the
> velocity is changing the acceleration is the instantaneous change in
> velocity the knowledge of which is limited by the ability to measure that.
> The acceleration of an object whose velocity is described by a closed form
> mathematical function is the derivative of that function as we learned in
> calculus. The derivative is defined by limits. This is theoretical and
> approximates what happens in the physical world.
>
> Questions and comments are welcome.
>
> Frank
>
>
> ---
> Frank C. Wimberly
> 140 Calle Ojo Feliz,
> Santa Fe, NM 87505
>
> 505 670-9918
> Santa Fe, NM
>
> On Fri, Oct 1, 2021, 7:21 PM <thompnicks...@gmail.com> wrote:
>
>> I thought the conversation about probability, category errors, and
>> crossing boundaries between levels of organization was interesting and I
>> was sorry I had to leave it. I want to say that to speak a die as having
>> a probability of 1/6 of coming up 6 on a single throw is a category error
>> because it is not a property that can be displayed on a single throw. It’s
>> the same worry that I have often deployed about the calculus. If we take
>> the idea of a category error seriously, then acceleration is just not the
>> sort of thing an object can have at an instant. But just as clearly as
>> this argument is too strong – lots of very nice longstanding bridges have
>> been built with the calculus – so the argument is also too strong with
>> respect to probability – lots of nice atom bombs have been built with
>> probability theory … or something.
>>
>>
>>
>> I care about this because my standard account of such concepts as
>> “wanting” is that they are properties of the population of responses to an
>> object, not properties of any one of those responses. We encounter the
>> same problem with anecdotes and newspaper photographs designed to
>> illustrate some general fact. If the generally fact is that “very few of
>> the immigrants at the southern border are well treated” a single photograph
>> looking peaked or hungry is irrelevant. Equally irrelevant would be a
>> picture of a bright eyed kid sitting in the lap of a border patrol officer
>> eating a hot-fudge sundae.
>>
>>
>>
>> This makes me wonder about one of the foundations of psychological
>> research, the statistics of inference, which I think Peirce invented. Let
>> a coin be thrown 10 times and each time come up heads. What I think Peirce
>> would have me conclude is that that coin is unlikely to be drawn from a
>> population of fair throws of a fair coin. But, of coure, what we are
>> likely to conclude is that “this coin is not fair.” But that could be as
>> misguided, couldn’t it, as concluding that the kid in the lap of the border
>> patrol officers is being mistreated.
>>
>>
>>
>> I apologize, once more, for sharing my comfusions with you.
>>
>>
>>
>> n
>>
>>
>>
>> Nick Thompson
>>
>> thompnicks...@gmail.com
>>
>> https://wordpress.clarku.edu/nthompson/
>> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson%2f&c=E,1,QU0qVpqNOoJiPM24Dv11INL-P7InBOIA4z4LOnpttneeWXYwPuFzZKWaVU3KPxC8ObCG7JECy2fbQeuL-V9-2OsvQN3I7mXpu9mzsoPaIE0,&typo=1>
>>
>>
>>
>> *From:* Friam <friam-boun...@redfish.com> *On Behalf Of *Frank Wimberly
>> *Sent:* Friday, October 1, 2021 6:46 PM
>> *To:* The Friday Morning Applied Complexity Coffee Group <
>> friam@redfish.com>
>> *Subject:* [FRIAM] Newborn Heart Rate
>>
>>
>>
>>
>> https://pediatrics.aappublications.org/content/61/1/119
>> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fpediatrics.aappublications.org%2fcontent%2f61%2f1%2f119&c=E,1,uD1tIhc7c-0wZqgMnI5_Ki1-cJ9QDa1EyaSQIuM5xQO8giKGtKM8z1rtfEnJ33KUkPyECbG92OSX1Pt-uIL6rgVLiylCxIbiMASMUnV7SEjwSw,,&typo=1>
>>
>>
>>
>> This is for those who attended this morning's vFriam meeting. I was
>> Schachter's colleague, among a couple of others.
>>
>>
>>
>>
>>
>> ---
>> Frank C. Wimberly
>> 140 Calle Ojo Feliz,
>> Santa Fe, NM 87505
>>
>> 505 670-9918
>> Santa Fe, NM
>>
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