Diamond

[ughaibu]

Can anyone give me a crit on this book: http://www.worldscibooks.com/mathematics/3271.html

[Buffy]

Never heard of it but it looks interesting! Seems to be trying to apply quantum indeterminancy to mathematical logic by using recursive methods. I stumbled upon a few sites that talk about the theory in some detail:

http://www.thinkartlab.com/pkl/nlp-w...trategies.html
http://72.14.203.104/search?q=cache:...s&ct=clnk&cd=9

If you read it, post a review here!

Cheers,
Buffy

[ughaibu]

Buffy: Thanks for those links.

[Buffy]

Originally Posted by Turtle

sounds a bit like fuzzy logic with a soul.

Actually, it sounds completely different than Fuzzy Logic: Diamond seems to do tree pruning and optimization via recursion--there are *lots* of complications in optimization of multivariate systems though!

Fuzzy logic is all about applying probabilities to outcomes and computing combinations of them, which is all based on a priori data. Fuzzy actually isn't very fuzzy: it very accurately optimizes your washing machine and keeps your freezer from consuming too much energy! All hail Lofti Zadeh!

Probably,
Buffy

[Turtle]

Originally Posted by Buffy

Actually, it sounds completely different than Fuzzy Logic:
Probably,
Buffy

Nothing is not connected Buff, at least not in my mind. My qualifying 'bit' refers to how both systems go beyond dichotomy. Recursion rules, probability drools.

[Buffy]

Originally Posted by Turtle

Nothing is not connected Buff ... Recursion rules, probability drools.

Then stop contradicting yerself Professor T! I like both recursion and probability. Good goal seeking algorithms (see the link above) *really* have to throw random numbers into the mix in order to avoid "local minimums/maximums" that fool you into thinking you've got the answer. Randomness and probability are the serendipity generators of mathematics!

Oh, lets frob that seed here,
Buffy

[Turtle]

Originally Posted by Buffy

Then stop contradicting yerself Professor T! ..Randomness and probability are the serendipity generators of mathematics!

Oh, lets frob that seed here,
Buffy

Without self-contradiction, there is no zen.
Just because we find probability useful, does not mean it is accurate. Before Copernicus, the method of epi-cycles adequately described/predicted most heavenly body motion. All probability is based on one primary assumption, & I maintain that assumption is false. [Assume equal likely-hood, i.e. fairness]
I like what Trimtab has to say on the subject:

Originally Posted by Trimtab

Probability is not a reliable anticipatory tool; it is stronger than "possibility" but crude in comparison to "navigation" and "astronomy." If probability were reliable, there would not be a stock market or a horse race.

[Buffy]

Dots sure puttin' the cart before the horse! Probability is evil because its not accurate? Yow! You sound like one of my math professors! Its no wonder that statistics has always had to have its own department...

Probability is an essential and *useful* tool to those of us who do math in the real world (oooooh! evil applied mathematics! boo! hiss! ). Nope, ya can't *always* beat the market, but show me a purely analytical tool that can! What it *can* do--which is where the cart-horse issue comes in--is *explain* and *model* whats going on.

Its always been interesting to me that some of the most important breakthroughs in mathematics like Calculus came from a tremendous amount of empirical data being gathered and formulas starting with *approximations*--which is what Diamond seems to be doing.

When doing goal-seeking, you could pick any random direction to go in (ooooh! non-determinism! evil! ), but at least some of your attempts should be influenced by probability in order to find optimums faster (goes into algorithms that learn based on patterns and recognizing similar patterns is based on....probability! yow! ).

Keepin' an open mind,
Buffy

[Turtle]

Originally Posted by Buffy

You sound like one of my math professors! ...

Ouch!

Originally Posted by Buffy

Probability is an essential and *useful* tool to those of us who do math in the real world (oooooh! evil applied mathematics! boo! hiss! ). Nope, ya can't *always* beat the market, but show me a purely analytical tool that can! What it *can* do--which is where the cart-horse issue comes in--is *explain* and *model* whats going on.
Keepin' an open mind,
Buffy

Somewhere here (I can't find it yet) I gave some links to the guys from Stanford who more-or-less got the Chaos Theory ball rolling. They now work on stock market data & as I understand it they do better than the standard issue probability calculations. Recurring theme...?
I hope you don't think I eschew applied mathematics; I certainly didn't mean to imply that.

PS Found it:
http://www.cs.brown.edu/research/ai/...allStreet.html

[Buffy]

Originally Posted by Turtle

Ouch!

Jus' ribbin' you a bit to keep you in line!

Originally Posted by Turtle

Somewhere here (I can't find it yet) I gave some links to the guys from Stanford who more-or-less got the Chaos Theory ball rolling. They now work on stock market data & as I understand it they do better than the standard issue probability calculations.

Yah, BUT Chaos theory *heavily* uses probability! Its *advanced* probability in my book! Has random numbers at its very core, and uses probability to direct its algorithms. "Standard probability" is not incorporating the algorithms, so the synthesis of the two gets more accurate results.

Prune, prune, prune go the leaf nodes,
Buffy