tag:blogger.com,1999:blog-11295132.post115152142545830868..comments2014-11-13T21:22:20.572-08:00Comments on A Neighborhood of Infinity: Laws of Form: An OpinionDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-11295132.post-64488463716943780182013-12-19T20:11:21.869-08:002013-12-19T20:11:21.869-08:00GS-B's book is profound, but I am perfectly wi...GS-B's book is profound, but I am perfectly willing to accept that it is not profound mathematics. Although it is cast as a calculus, for me the primacy of the work lies in showing how the apparent disconnect between the physical and mathematical sciences on the one hand and the biological and social sciences and even the domains of religion, the arts and humanities can be reconciled and united. The latter are intrinsically based in paradox, and self referential logic. On the other hand, we typically maintain the illusion that the former are entirely based on a binary logic: physical statement X is either true or false by physical law. The most elementary pieces of biology are not like this. The two strands of the double helix refer to each other and "cause" each other (replication), while also causing formation of their complement RNAs (transcription). At every level biological systems either oscillate (sleep/wake, hungry/satiated...) or maintain a stable state (temperature, blood glucose etc.) through a homeostatic process that is essentially a negative feedback loop operating in time much like the code you include in the blog "a not with a delay." This is very much like the thermostat in your home heating system, but very much unlike the way we typically think of thermodynamics, mechanics and other fundamental physical principles on which our understanding of the world is based.<br /><br />Of great interest to me is not whether or not G S-B's contract can formalize the logic of biology and other aspects of human experience, but how uniquely it does so. If there is another alternative framework, equally explanatory, I will relinquish claims that this is profound. Sacha Nelsonnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-16601108537858566912012-12-26T11:55:12.511-08:002012-12-26T11:55:12.511-08:00George Spencer Brown is the greatest mathematicia...George Spencer Brown is the greatest mathematician who live today. Laws of Form can be compared to the elements of Euclid. Moshe Kleinnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-77279517385388643242012-11-24T23:35:45.097-08:002012-11-24T23:35:45.097-08:00Suggest you look at N. Hellerstein's Delta Log...Suggest you look at N. Hellerstein's Delta Logic and Diamond Logic that works out the implications of GSB's Laws of Form for Logic.kentpalmerhttp://kdp.menoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-67316425138191148842012-07-23T11:36:08.929-07:002012-07-23T11:36:08.929-07:00There is only a hint of a mention of the "pri...There is only a hint of a mention of the "primary geometry", and the primary arithmetic is known in the trade as a "Dyck Language". The connections can be made via homological algebra-style proofs.<br />--Lee Odegardleeohttp://www.blogger.com/profile/07847246233509945944noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-61483699766968079472010-06-01T01:16:20.116-07:002010-06-01T01:16:20.116-07:00To me, Spencer Brown's contribution is to star...To me, Spencer Brown's contribution is to start mathematics (and, I suppose, also philosophy) from the very beginning, from nothing, and see how to proceed from there, to see how being (inevitably?) emerges from nothingness. He expresses this in a mathematical form; elementary logic emerges as a byproduct of a few simple operations on nothingness and its earliest offspring. <br /><br />If we look at this work from the usual vantage point of established mathematical convention, it seems mostly pointless. <br /><br />If Spencer Brown had had a community of people to help develop this work, as most researchers do, he likely would have avoided most of the pitfalls of working in isolation that became food for gossip and derision.Paulhttp://www.blogger.com/profile/04473326737299320884noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-56156764388815694092010-01-01T10:46:13.989-08:002010-01-01T10:46:13.989-08:00In 1981 or so, I spent a month at the Naropa Insti...In 1981 or so, I spent a month at the Naropa Institute, a Buddhist school in Boulder Colorado, attending a cognitive science course taught by a number of leading New-agey scientists (including the late Francisco Varela). Louis Kauffman presented some material on Laws of Form. He had the assembled students read passages form LoF aloud in unison, as if it was some sort of liturgical text. Amazingly enough, this worked, and after doing this I actually understoond what Spencer-Brown was getting at better than I had before. <br /><br />Whatever the interesting content of that book, it is not really mathematical, but mystical-philosophical. Kauffman went on to present S-B's alleged proof of the four-color theorem, which had obvious things wrong with it, so there's the element of crackpottery.mtravenhttp://www.blogger.com/profile/02356162954308418556noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-83162062948614532062009-05-29T05:05:30.425-07:002009-05-29T05:05:30.425-07:00Hi,
Glad to see your update to this page.
To me,...Hi,<br /><br />Glad to see your update to this page.<br /><br />To me, weird (or better still eccentri) is less pejorative than crackpot, somehow.Ernestromehttp://www.blogger.com/profile/11981270816417905473noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-57241368294444610722009-04-06T18:08:00.000-07:002009-04-06T18:08:00.000-07:00Ernestrome,Only just noticed your comment.Anyway, ...Ernestrome,<BR/><BR/>Only just noticed your comment.<BR/><BR/>Anyway, referencing the Tao Te Ching doesn't make you a crackpot. But writing a book on boolean algebra in the style of the Tao Te Ching is weird in the same way that writing book on arithmetic in the style of E. E. Cummings would be.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-48648250446530625022008-04-06T11:45:00.000-07:002008-04-06T11:45:00.000-07:00It's a shame that reference to the Tao te ching so...It's a shame that reference to the Tao te ching somehow labels one a crackpot.Ernestromehttp://www.blogger.com/profile/11981270816417905473noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-22234984691040166822007-05-15T08:49:00.000-07:002007-05-15T08:49:00.000-07:00I am not sure if the book by August Stern that you...I am not sure if the book by August Stern that you are talking about but there is a synopsis here:<BR/><BR/>http://www.alibris.co.uk/search/search.cfm?chunk=25&mtype=&qwork=9646360&page=1&matches=11&qsort=p&browse=1&full=1Nickhttp://www.blogger.com/profile/00618323461126273299noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-5125948975154973952007-05-06T19:15:00.000-07:002007-05-06T19:15:00.000-07:00Years ago I saw a book called Matrix Logic, by Aug...Years ago I saw a book called Matrix Logic, by August Stern. It promised a revolution in logic, replacing traditional two valued logic by a matrix valued one. I have since occasionaly wondered whether there was anything to it, but have never been able to find a copy of the book at a reasonable price, or a review. I don't suppose you have ever run across it?Ed Pimannoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1151598429723587312006-06-29T09:27:00.000-07:002006-06-29T09:27:00.000-07:00David,I've read and enjoyed many of Kauffman's pap...David,<BR/><BR/>I've read and enjoyed many of Kauffman's papers - the Jones polynomial, braid groups, Chern-Simons 'n' all that were all the rage when I was doing my PhD. But despite my own curiosity about Laws of Form I've found Kauffman's writing on this subject to be less interesting than his other work.<BR/><BR/>Having said that, I can imagine one avenue of research that might be interesting. Reasoning about logic circuits with feedback loops can be fiddly - you have to work through tracking state changes over time. I wonder if such reasoning could be simplified using 'imaginary values' so that you can prove things about these circuits in a 'non-temporal' way, if you get my meaning.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1151587737717337552006-06-29T06:28:00.000-07:002006-06-29T06:28:00.000-07:00I had the same impression of Spencer-Brown. Still,...I had the same impression of Spencer-Brown. Still, <A HREF="http://www.math.uic.edu/~kauffman/" REL="nofollow">Louis Kauffman</A>, a mathematician I admire very much, has found something to like, e.g., <A HREF="http://www.math.uic.edu/~kauffman/Arithmetic.htm" REL="nofollow">here</A>.davidhttp://www.blogger.com/profile/15120207589106619570noreply@blogger.com