Rashevsky's mathematics must be seen as exploratory and often is qualified by the admission that assumptions are unrealistic but that more realistic assumptions make the math intractable. The results thus offer insights, not "conclusions." The contrast with alleged microfoundations as practiced by contemporary mainstream economists couldn't be starker. The latter embrace unrealistic assumptions as a feature, not a bug, because it enables them to crank out conclusions based on biases they are seeking to confirm.
Simon Kuznets on growth:
Growth is a concept whose proper domicile is the study of organic units, and the use of the concept in economics is an example of that prevalent employment of analogy the dangers of which have been so eloquently stressed recently by Sidney Hook.Sidney Hook on analogy:
As an argument it is formally worthless and never logically compelling. An argument from analogy can be countered usually with another argument from analogy which leads to a diametrically opposed conclusion. ...
At best an analogy can only suggest a plausible conclusion whose validity must then be established on other grounds. The uncritical use of analogies is the bane of much historical writing, particularly when the resemblances lack clear definition or when they are blurred and presented as identities. ... The belief that society is an organism is an old but fanciful notion. It can only be seriously entertained by closing the eye to all the respects in which a group of separate individuals differs from a system of connected cells, and by violently redefining terms like "birth," "reproduction," and "death."Gregory Bateson on schizophrenia:
...the ‘word salad' of schizophrenia can be described in terms of the patient’s failure to recognize the metaphoric nature of his fantasies. In what should be triadic constellations of messages, the frame-setting message (e.g., the phrase 'as if') is omitted, and the metaphor or fantasy is narrated and acted upon in a manner which would be appropriate if the fantasy were a message of the more direct kind.
Given their unreal assumptions, would not Rashevsky's mathematics also be analogies?
ReplyDeleteDefinitely. But their purpose for Rashevsky is not to "represent" reality but to suggest lines of investigation.
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ReplyDeletei read quite a bit of that book which if i recall is from the 50's.
i also worked for awhile under rashevsky's last grad student at u chicago, where math bio basically got its first real institutional structure via BMB---the Bulletin of Mathematical Biology. He was at ucsf, and his office was next to the emeretus editor of BMB.
I was doing math biology applied to the problem of predicting the secondary structure of RNA from its primary structure ---ie how it folds up. This is part of the 'protein folding problem'---ie taking a look at DNA as a 4 letter alphabet, so the primary strucutre of DNA is a set of 'words' in a code, and one wants to know what they mean---how they get turned into sentence or a 3 (or 4) dimensional protein. I used information theory, and the problem is still open.
thats an analogy.
that book is actually strikingly similar to much later stuff---eg Boyd and Richerson's 'culture and the evolutionary process' and 'genes mind and culture' by e o wilson and cj lumsden (conceptually flawed, but mathematically correct---they just lifted all the equations used by Hermann Haken in 'synergetics' tho they predate him by 50 years, and some are attributed to a soviet mathematician who had stolen them from a jewish mathematician who he had Stalin send to the gulags ---prison camps--so he could get his office). axelrod and hamilton, louis fry richardson, and anatol rapaport are same tradition and style.
the math rashevsky used is slightly different (integral and differential -delay equations and 'old fashioned'---noone today does it that way anymore, any more than they use newton, einstein or darwin's formalisms. but the ideas are there.
the math bio program was kicked out of U Chicago in the 60's and its faculty were exiled to U Bufallo and Dalhousie--i almost went there for grad school (but i was a sort of a southern city person and thought it was a beautiful place but figured i could never fit in. i thought the same of binghampton ny. my ecosystem is the 'inner city ghetto' and 'hicksville, west virginia'---like birds, we migrate. I also had some doughts about the program---person who wrote reference for was from santa fe institute and los alamos labs and i think he thought it was bs---non rigorous speculations.
the analogy between societies and organisms on the mathematical level is actually somewhat rigorous (despite sindey hook, who doesnt know what he is talking about). gregory bateson did according to the state of knowledge at his time. Unfortunately (at least to me) math bio today is basically like alot of economics---they turn everything into a nail so they can use their mathematical hammer to pound it in. This makes it 'tractable', and publishable, to add to human knowledge--or at least the CV. They make a few approximations---basically leave out all conplicating nonlinearities, and turn everything into a gaussian distribution. Not everyone does this but many do. see the 3rd recent post on azimuth https://johncarlosbaez.wordpress.com (relative of joan baez) and great blog---statistical laws of darwinian evolution. brings out the heavy math artillary to solve a trivial problem. i see they didnt delete my comment .
why do these blogs ask you to prove that 'im not a robot'. how would i know? i thought we all live in john searle's chinese room, unless they can claim 'i'm living on a chinese rock' (johnny thunders, refers to a popular kind of powder turned into rocks).
Personally in this realm of mathematical biophysical economics I personally prefer Alfred J. Lotka's 1925 Elements of Physical Biology, reprinted in 1945 as Elements of Mathematical Biology. He was the original discoverer of predator-prey cycles, among other things, applied power law distributions to scientific issues, and posited entropy as playing a role in evolution, as well as enumerating a long set of possible kinds of equilibria.
ReplyDeleteCuriously he was a serious influence on Samuelson, who cited hin Foundations of Economic Analysis, but he went far beyond what Samuelson covered, who mostly adopted his local stability analysis for linear systems. Lotka was brilliant and a true polymath, and his arguments about economics are very current.
I was hoping you would comment, Barkley. And thanks, media, for the interesting narrative. The "Contemporary Art Society" comment is mine. Was using friend's computer and didn't realize she was logged in to gmail.
ReplyDeleteMy interest in Rashevsky is mainly related to the relationship between his approach and Anatol Rapoport's work, which bridges the gap between mathematical models and ethical dialogue.
A simple but very important point that Rapoport makes, again and again, is that science is valuable for what it tell us definitively we CAN'T do. Progress in science builds on awareness of where the dead ends are.
The other argument that Rapoport makes which I think is extremely valuable is that no one ever "wins" a polemic by persuading the other side they are wrong.
i remember j barkely rosser from a whole set of paper sent to my po box in wardensville W VA. someone got me a po box ---they said i shouldnt be totally out of touch. sometimes it was 4 degrees. it was only 4 miles from where i lived. had to bike and walk. then i had family issues and people stole my computer . from chaos to catastrophe.
ReplyDeletewww.pnas.org/content/68/5/980.full.pdf or look up e kerner gibbs ensemble biological ensemble'. that is a linear approximation.
media,
ReplyDeleteSomehow this sounds familiar...