Thank you, ERIC!
I KNEW I was going to make that mistake some day. Nick Nicholas Thompson Emeritus Professor of Ethology and Psychology Clark University <mailto:[email protected]> [email protected] <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/ From: [email protected] <[email protected]> Sent: Thursday, May 21, 2020 5:50 PM To: 'The Friday Morning Applied Complexity Coffee Group' <[email protected]> Subject: RE: [FRIAM] anonymity/deniability/ambiguity Thank you, David, I need to think about all of this. A brief early response: There are two things that words do: they stroke and they convey information. AT the core, I think, my authoritarian impatience (to use a word that has recently blossomed in the correspondence on the list) arise when people confuse one use of words for another. When we speak of that of which we cannot speak we are like primates who groom but do not remove any lice. Grooming and being groomed is very nice; but I am really interested in louse removal. Nick Nicholas Thompson Emeritus Professor of Ethology and Psychology Clark University <mailto:[email protected]> [email protected] <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/ From: Friam <[email protected] <mailto:[email protected]> > On Behalf Of David Eric Smith Sent: Thursday, May 21, 2020 5:15 PM To: The Friday Morning Applied Complexity Coffee Group <[email protected] <mailto:[email protected]> > Subject: Re: [FRIAM] anonymity/deniability/ambiguity Signal to Nick: You commented on wanting to understand the conversation about formalists and intuitionists which I have been using in various conversations with Glen and Jon. Now is the chance to do it at low cost. Frank has provided two proofs of irrationality of the square root of 2, one formalist (using proof by contradiction requiring acceptance of the law of the excluded middle) a few days ago, this most recent one being constructive, meaning that it constructs a degree of difference that you can point to concretely, rather than concluding from the syntax that there must be such. One gets at the core of anything I was trying to say by looking at these two proofs, and deciding whether one can see what is different in their sense. For me, these concrete, super-simple minimal pairs are the mental tools to get at the difference between one style of thought and another. I can then try to decide whether, in some much more difficult context, where it is very hard to be concrete, I think I see the same kind of contrast in style. Since I am too slow to almost ever work out the watertight version of anything, and some of these would be too hard for me to do at all, I don’t even seriously intend to check whether my imagistic impression is reliable. I am willing to use the simple cases I do understand as perceptive filters to try to make some kind of approximate sense of the hard cases, as the alternative to just letting it all go by. You commented in one of these emails that you could accept “irreducible” as long as it didn’t mean “can’t be described”, and I have been thinking over the past days whether I can come down on one side of that or the other. You might also have said, “as long as it didn’t mean `can’t be observed’ “. I decided I don’t know. To know what can or can’t be observed, can or can’t be described, is or isn’t behavior, one has to operationalize any of those and decide how reliable the operationalization is. The exchange mostly of Glen, EricC, and Jon about what is or isn’t behavior, often quite tedious, seemed like it took seriously the right caution. One could build comparable tedious harangues around “observe” and “describe”, and perhaps must to resolve this. You might think you can say, as a matter of syntax, that “of course it must be observable” or else one is denying science. Physicists though for almost 200 years that that “of course” was unproblematic, that they had an operationalization that was both flexible enough to extend to more and more subjects, restrictive enough to have content, and expressible in equivalence to mathematical objects. Then they learned that the way they had assumed “of course” it could be done wasn’t the correct formalization to be extended to quantum mechanics. That didn’t mean that there wasn’t a correct formalization, only that a different one was required, to subsume all that had worked before, and also extend where the former one couldn’t go. The proof of inadequacy of the former was only demonstrated by putting one that was more correct in its place and exhibiting the difference (constructive); it seems like it would have been hopeless to anticipate, in the pre-quantum days, that the notion of observability was inadequate in the way it actually was, and even more hopeless to try to use a syntactic argument (formalist) either to assert its sufficiency or identify the specific defect that quantum mechanics would ultimately reveal. So when I ask “what is the value of a formalist-style declaration that inner-ness can’t be a real property, if one is not constructing something to show that to be the case”, this is the style difference I am using as a reference to put that question. I don’t imagine that what we learned about definitions of observability in physics will have any direct relevance to whatever challenges the term may pose in psychology. The physics example is just a nice reminder of ways in which it can be very hard to decide when one is really saying something, and likewise an example that constructing the alternative sometimes seems to give the only perspective from which to see that there had formerly been a problem. Because Pierce et seq. have done so much to try to be precise, practical, and useful in defining what science is, it allows me to be lazy, say “yes I accept and defend all that”, and then ask for an ultra-stripped-down abstraction of what science is then. I may already have written this (senility), but my imagistic definition would be that science is the premise that mistakes aren’t all sui generis, but that they have family resemblances, and that there are methods of practice that give one a better-than-random chance of recognizing that something may be a mistake even short of knowing what ‘the' (or ‘a better’) answer is. I choose that framing in part because it is also the framing that formalizes the notion of error correction in computer science (so I have a mental image to refer to as an exemplar accompanied by some formal tools). One wants to identify the fact that a message contains an error, without having to know, for every message in advance, what it was supposed to have contained (else you didn’t need to be sending messages in the first place). I use the stripped down form in the hope of building a recursive tree of mutual refereeing, for all elements of scientific practice, now appealing to my mental image of Peter Gacs’s error-correcting 1D cellular automaton, which does this by nesting correcting structure within correcting structure. Then I can look for every aspect of our practice that is trying to play this role in some way. A subset include: 1. Intersubjectivity to guard against individual delusion, ignorance, oversight, and similar hazards. 2. Experimentation to guard against individual and group delusion etc, and to provide an additional active corrective against erroneous abduction from instances to classes. 3. Adoption of formal language protocols: 3a. Definitions, with both operational (semantic) and syntactic (formalist) criteria for their scope and usage 3b. Rigid languages for argument, including logic but also less-formal standards of scientific argument, like insistence on null models and significance measures for statistical claims There must be more, but the above are the ones I am mostly aware of in daily work. These are, to some extent, hierarchical, in that those further down the list are often taken to have a control-theoretic-like authority to tag those higher-up in the list as “errors”. However, like any control system, the controller can also be wrong, and then its authority allows it to impose cascades of errors before being caught. Hence, I guess Kant thought that a Newtonian space x time geometry was so self-evident that it was part of the “a priori” to physical reasoning. It was a kind of more-definite-than-a-definition criterion in arguments. And it turned out not to describe the universe we live in, if one requires sufficient scope and precision. Likewise, the amount of a semantics that we can capture in syntactic rules for formal speech is likely to always be less than all the semantics we have, and even the validity of a syntax could be undermined (Godel). But most common in practice is that the syntax could be used as a kind of parlor entertainment, but the interpretation of it becomes either invalid or essentially useless when tokens that appeared in it turn out not to actually stand for anything. This is what happens when things we thought were operational definitions are shown by construction of their replacements to have been invalid, as with the classical physics notion of “observable”, or the Newtonian convention of “absolute time”. I would like to give Pierce’s “truth == reliable in the long run” a modern gloss by regarding the above the way an engineer would in designing an error-correction system. The instances that are grouped in the above list are not just subroutines in a computer code, but embodied artifacts and events of practice by living-cognizing-social behavers and reasoners. And then decide from a post-Shannon vantage point what such a system can and cannot do. What notions of truth are constructible? How long is the long run, for any particular problem? What are the sample fluctuations in our state of understanding, as represented in placeholders for terms, rules, or other forms we adopt in the above list in any era, relative to asymptotes that we may or may not yet think we can identify? How have errors cascaded through that list as we have it now, and can we use those to learn something about the performance of this way of organizing science? (Dave Ackley of UNM did a lovely project on the statistics of library overhauls for Linux utilities some years ago, which is my mental model in framing that last question.) Formal tools to answer more interesting versions of questions like those. I mentioned some stuff about this in a post a month or two ago, and EricC included in a later post by way of reply that Pierce did a lot of statistics, so I understand I can’t take anything here outside the playpen of a listserve until I have first read everything Pierce wrote, and everything others wrote about what Pierce wrote, etc. I suspect that, since Pierce lived before the publication of at least part of what is now understood about reliable error correction, large deviations, renormalization, automata theory, etc., there should be something new to say from a modern standpoint that Pierce didn’t already know, but that assertion is formalist, and thus valueless. I have to do the exhaustive search through everything he actually did know, to point out something new that isn’t already in it (constructivist). Which is why I won’t have time, resources, or ability to do it. So I will never know whether the things said above actually mean something. Eric On May 22, 2020, at 2:44 AM, Frank Wimberly <[email protected] <mailto:[email protected]> > wrote: The badly rendered part: {\displaystyle \left|{\sqrt {2}}-{\frac {a}{b}}\right|={\frac {|2b^{2}-a^{2}|}{b^{2}\left({\sqrt {2}}+{\frac {a}{b}}\right)}}\geq {\frac {1}{b^{2}\left({\sqrt {2}}+{\frac {a}{b}}\right)}}\geq {\frac {1}{3b^{2}}},} <https://wikimedia.org/api/rest_v1/media/math/render/svg/641b9e87f603636755874eee6c5d85875f907483> On Thu, May 21, 2020 at 11:30 AM Frank Wimberly <[email protected] <mailto:[email protected]> > wrote: Clinicians often call that "being oppositional". You say that I've known authorities. I was just talking to John Baez about my advisor Errett Bishop, often called the inventor of constructive mathematics. Here is a constructive proof, with no use of the excluded middle, of the irrationality of sqrt(2) that I found in Wikipedia. Apologies to those who don't care: In a constructive approach, one distinguishes between on the one hand not being rational, and on the other hand being irrational (i.e., being quantifiably apart from every rational), the latter being a stronger property. Given positive integers a and b, because the <https://en.wikipedia.org/wiki/Singly_and_doubly_even#Definitions> valuation (i.e., highest power of 2 dividing a number) of 2b2 is odd, while the valuation of a2 is even, they must be distinct integers; thus |2b2 − a2| ≥ 1. Then <https://en.wikipedia.org/wiki/Square_root_of_2#cite_note-17> [17] {\displaystyle \left|{\sqrt {2}}-{\frac {a}{b}}\right|={\frac {|2b^{2}-a^{2}|}{b^{2}\left({\sqrt {2}}+{\frac {a}{b}}\right)}}\geq {\frac {1}{b^{2}\left({\sqrt {2}}+{\frac {a}{b}}\right)}}\geq {\frac {1}{3b^{2}}},} <https://wikimedia.org/api/rest_v1/media/math/render/svg/641b9e87f603636755874eee6c5d85875f907483> the latter inequality being true because it is assumed that a/b ≤ 3 − √2 (otherwise the quantitative apartness can be trivially established). This gives a lower bound of 1/3b2 for the difference |√2 − a/b|, yielding a direct proof of irrationality not relying on the <https://en.wikipedia.org/wiki/Law_of_excluded_middle> law of excluded middle; see <https://en.wikipedia.org/wiki/Errett_Bishop> Errett Bishop (1985, p. 18). This proof constructively exhibits a discrepancy between √2 and any rational. On Thu, May 21, 2020 at 10:50 AM Steve Smith <[email protected] <mailto:[email protected]> > wrote: On 5/21/20 10:32 AM, uǝlƃ ☣ wrote: > Don't be fooled. "The problem with communication is the illusion that it > exists." Or ie I believe in a stronger form of privacy than you believe in. I KNOW! I know just what you mean! <note to Frank... one of the species of animal in this group is "the Contrarian", but you probably already guessed that> -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam <http://bit.ly/virtualfriam> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ <http://friam.471366.n2.nabble.com/FRIAM-COMIC> FRIAM-COMIC http://friam-comic.blogspot.com/ -- Frank Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 505 670-9918 -- Frank Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 505 670-9918 -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ... FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam <http://bit.ly/virtualfriam> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
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