Silicon Investor (SI) -- The First Internet Community

STOCKTALK

We've detected that you're using an ad content blocking browser plug-in or feature. Ads provide a critical source of revenue to the continued operation of Silicon Investor. We ask that you disable ad blocking while on Silicon Investor in the best interests of our community. If you are not using an ad blocker but are still receiving this message, make sure your browser's tracking protection is set to the 'standard' level.

Strategies & Market Trends : Booms, Busts, and Recoveries -- Ignore unavailable to you. Want to Upgrade?

To: Terry Maloney who wrote (18223)	4/16/2002 1:16:19 AM
From: smolejv@gmx.net	Respond to of 74559

it's heavy stuff. You see pure mathematics talking about ... it's a she ... herself. Self-referential science. Just an in-time revival for our beautiful minds; dj

To: Terry Maloney who wrote (18223)	4/16/2002 2:06:37 PM
From: jim black	Read Replies (7) \| Respond to of 74559

OT OT OT! re: Godel: Terry et al, though a physician for most of my life I fess up to two degrees in mathematics, the Ph.D work during summers given up as useless anyway when my major professor at the University of Texas, Austin died of colon cancer in 1971, H.S. Wall (continued fractions his specialty). It was during the time of the reign of R.L. Moore at UT, Austin and no one was paying attention to Godel's work of 1965 (there should be an Umlaut over the "o" in his name. At that time in Austin pointset topology was the rage. We studied Godel in a philosophy of science course. It IS quite deep stuff and for mathematics very important work. Simply ( very simply!) put, his conclusions were disturbing and their implications far reaching. He showed in a brilliant indirect proof that in any! axiom system sufficient to deal with something as simple as ordinary numbers and arithmetic it is in and of itself absolutely impossible to prove internal consistency. In other words despite our impressive advancements in science and mathematics we can never know if the axioms systems even of the simplest, non-trivial nature have in them internal inconsistencies that have simply not yet been discovered. It is one of those delicious intricacies of mathematics that delight those of us who are weird enough to think of mathematics as simply the most highly developed and beautiful art form, to use just one description. I often am humbled by returning to an idea first introduced by a popular writer of mathematics for the masses. Consider a typewriter (an old fashion machine many of you have never even seen, I am sure) that has, say, let's be generous, all letter and number keys from 0 to 9, a to z, and let us further be generous and give it a decent maximum line length of say 75 spaces (the numbers get really big, really fast). Now further assume you have lots and lots of time to play and we set the machine a task, namely to start building a system of data so that every space, including a blank one will be filled by one of the letters or numbers or a blank space and let it continue until all possible combinations have been used. It will come to an end because a finite collection of finite sets is finite (simple proof from analysis, basic course). At the end of it, perhaps a googleplex of years from now when your machine is finished and very tired and worn, you will have all possible combinations, and therefore all possible words in all possible combinations in your data bank and hence in English in our thought experiment you have written down somewhere in that very long list, all possible things expressable in English, to wit you have said everything there is to say, conjecture, etc.* The conclusion is inescapable. Human knowledge in so far as it can be written down (and presumsably translated from there to any other human language, is FINITE! There is a theoretical limit to what we are ABLE to know. I find this little excursion on discussion of Godel's Proof absolutely intriguing. Sorry for the rant, but I worked hard on that term paper, one of the few A's I was really proud of, and what the hell, no crazier than Germany selling off its gold Jim Black * Included somewhere in that list will occur the line form Shakespere's Hamlet, "There are more things under Heaven, Horatio, than are dreamt of in all your philosophies." But then most will be nonsensical lines like Jay is the financial messiah, or Maurice is the smartest man in the world because he knows Q cannot fail, or that Arafat is Jesus. Just joking folks, we are tolerant of eccentrics here, right?