Here are three posts copied from Daily Speculations, the first posits a question and the second & third contain combinational answers too it. Keep in mind when you visit the link, the considerations of Anatoly were newer than the larger disccussion preceeding it. For our purposes, the Question asked in Anatolys post was answered before it was asked, thats an interesting but not surprising coincidence.
If anyone wishes to guess where in the lower piece is his question answered, you can PM or email me.http://www.dailyspeculations.com/wordpress/
the forum works by day of month so current posts are always on top, the posts copied here are further down..
Considerations
Anatoly Veltman recounts:
In open outcry Gold futures trading at the Comex in 1989, my volume equaled 10% of the total exchange volume on quiet days — although I was not in the pit, and didn't own a seat at the time. Contrary to popular belief, floor brokers and locals were not raping every customer order going into the pit. Things got progressively worse, as seat prices skyrocketed at the start of this century; it eventually cost $1,000/day for floor rights alone, not to mention all kinds of overhead and error risks! And that's how demand destruction for floor trading took hold. Current electronic execution is much more disadvantageous, from where I stand. Black boxes at a handful of firms scan the exchange order books every millisecond and automatically execute algorithmic trades, ripping any conceivable advantage away from participating public. They are the casino, with structurally embedded multi-billion annual profits — leaving everyone else on the other side of the zero-sum game. Question is: what evolution event will lead to eventual demise of their empire?
Part 2 and 3
1Our Concepts Are Not Merely Arbitrary Constructs, from Adam Robinson
January 1, 2008 | Leave a Comment
As Ouspensky argued well (nearly a century ago) in Tertium Organum (following Kant), our concepts of time and space are human constructs based on our conscious experience as members of the human species, and there is no reason to think they have a basis in reality outside that perspective. Laurence Glazier.
It is naive to believe human concepts are merely arbitrary constructs. Oliver Wendell Holmes drew the distinction between the (simplistic) simplicity on this side of complexity, and the (enlightened) simplicity that emerges on the far side of complexity.
The child believes that things are as they appear. The philosopher doubts that things are as they appear. But perhaps, at a more enlightened level still, the child was correct and things are indeed as they appear. (Perhaps as Samuel Johnson, when he could no longer tolerate the "ingenious sophistry" of philosopher Berkeley's "proof" that matter does not exist, said: "I refute it thus" and kicked his foot on a large stone.)
The belief that space and time are arbitrary constructs is, alas, an insight on the wrong side of complexity. Of course they are arbitrary constructs. So are numbers and mathematics, for that matter.
These are 18th and 19th century insights, and far from the final word. The truly miraculous thing, as Einstein always marveled, is that by manipulating these "arbitrary constructs," we can, astoundingly, make accurate predictions and create real changes in the world.
James Clerk Maxwell envisioned electromagnetism as having hydrodynamic properties, and based on this–as it turns out–false model, derived equations that worked.
So if man-made concepts (as if there were any other kind) are merely arbitrary, how then do we explain the miracle that these constructs enable us to do things in the real world?
I liked Larry's point about Ouspensky's never having traded. There's a great chess quote from Emanuel Lasker he reminded me of:
"On the chessboard, lies and hypocrisy do not survive long. The creative combination lays bare the presumption of a lie; the merciless fact, culminating in checkmate, contradicts the hypocrite."
Nothing like the real world of trading to expose, in the long run at least, the weaknesses in one's thinking.
Jan
1Goedel’s Proof, from Russell Sears
January 1, 2008 | Leave a Comment
It seems to me that Goedel's "Incompleteness Theorem" proves the limits of reason, and science. That in a system complex enough to do arithmetic, that there either exist:
1 True properties that are not provable,
2. or the system is inconsistent.
If you understand his motives and what he thought his incompleteness theory proves: Platonists were right. Not the Sophist: "Man is the measure of all things", not the rigid scientist/empiricist. Nor the Mystic.
It is said that some of Goedel's decent into madness stemmed from him not understand how others could mis-understand the implications of his proof and what was so clear to him.
Few even understand what the proof, proves, let alone the implications, and fewer still the proof.
Goedel was every bit as much the genius as Einstein according to his good friend Einstein.
Jim Sogi responds:
From my read of Luck, Logic & Whies Lies by Jörg Bewersdorff, rather than the limits of reason, Goedel marked the end of a period in the history of math and the beginning of what I might describe as the probabilistic age. Many of the advances in physics and our own market science rests on probabilistic mathematics and this is the new frontier in the same way that the mathematic fiction of a limit allowed Newton to initiate modern science. To me it is a peculiar type of math with variables representing shifting penumbras, but is what gives an advantage over those relying on linear or fixed systems.
Jason Schroeder exclaims:
Don't drag Goedel into this!
Your Bayesian Vagabond cautions over exuberance concerning Mr. G proves limits.
Moving to probabilities does not remove the problem. Probabilities are deductions taken under uncertainty. Otherwise probabilities, including the famous 0 and 1, are mental fixations aiding the proving/deducing process. Incompleteness holds that that abstract process cannot prove everything. Some things require a different tactic or strategy.
More symbols (limits and penumbras and strings of numerals) do not create more possibilities to defeat incompleteness. We all gotta work for our dinner intellectually. Take the risks and change the rules.
Mr. G proves Hilbert championed a dead-end. The scientific air at the time was using phrase "final solution" voiced by Hilbert and his groupies. The German politicians were just being savvy by bringing the notion to the people. Showing the axiomatization, or encoding, or formalistic pretensions that the averagely clever think they automate mapping out a solutions before taking to the field.
"It should anyway be observed that Gödel's theorem is not the anti-scientist panacea… science is primarily seeking questions" not proving correctness before trying (that is called self-righteousness in another tradition).
Remember Popper's love of falsifiability ignores Goedel's work because it is not falsifiable! Goedel refutes Hilbert and Popper.
More from Girard, a mathematical logician:
It is out of question to enter into the technical arcana of Gödel's theorem, this for several reasons :
(1) This result, indeed very easy, can be perceived, like the late paintings of Claude Monet, but from a certain distance. A close look only reveals fastidious details that one perhaps does not want to know.
(2) There is no need either, since this theorem is a scientific cul-de-sac : in fact it exposes a way without exit. Since it is without exit, nothing to seek there, and it is of no use to be expert in Gödel's theorem.
…never forget Turing's contribution to computer science, a ontribution which mainly rests on a second reading of Gödel's theorem ; the fixed point of programs is nothing more than the celebrated algorithmic undecidability of the halting problem: no program is able to decide whether a program will eventually stop, and no way to pass around this prohibition. This is a simplified version of the incompleteness theorem … loses very little …
Russ Sears concludes:
Not having read "Luck, Logic & Whites Lies", but left to judge by your brief decription.
Much has been written about Goedel's proof and its implications from those that don't really understand it. Or if they do they only give the part of the story they want you to hear. This is part of the frustration Goedel had.
To quote an expert on Goedel, Rebecca Goldstein, "…the second incompleteness theorem doesn't say that the consistency of a formal system of arithmetic is unprovable by any means whatsoever. It simply says a formal system that contains arithmetic can't prove the consistency of itself. After all, the natural numbers constitute a model of the formal system of arithmetic and if a system has a model then it is consistent…In other words, when the formal system of arithmetic is endowed with the usual meaning, involving the natural numbers and their properties, the axioms and all that follow from them are true and therefore consistent. This sort of argument for consistency, however, goes outside the formal system, making an appeal to the existence of the natural numbers as a model"
The goal was "to expunge all reference to intuitions-was most particularly directed toward our intuitions of infinity: not surprisingly, finite creatures that we are, it is these intuitions that have prove themselves, from the very beginning , to be the most problematic." … "This can only be done by going outside the formal system and making an appeal to intuitions that can't themselves be formalized."
In other words, my own this time. Goedel ideas no doubt did help herald in what you call "the probabilistic age". He did so by making scientist question even the subtlest assumptions in their methods and models. But I would suggest that Heisenberg principle had much more of an effect in causing a "probabilistic age" than Goedel, if for no other reason than it came first.
The implications to reasons are that a pure Spock is not possible…that intuition must be a part of the process and hence the value of standing like a tree, running 70 miles a week in cold of December. Or, as Einstein and Goedel both did, going for long walks often together can give increase your scientific output, by giving you a chance to put it in perspective.
While this clearly has implication for a speculator, I would suggest that the bigger implication is that finite creatures that we are we should always remain humble and be open to the idea that we even as "counters" are heading down a wrong path. We do not always have an edge, despite what the numbers say. Not that "counting", reason, or science is wrong… rather we are using it wrong, that we missed something in our model. The limit to science and reason is us. |
