Brazil set off a tornado in Texas?"

Meteorologist Edward Lorenz was running a simulation of weather using a mathematical model of 12 equations via a LPG-30 computer. The next day he wished to continue the run and initiated the program half way through by typing in the numbers from the first run as obtained from a printout. The result was two different weather trajectories.

The computer stored the first results to 6 decimal places; but, it could only be printed out in 3 decimal places. By inputting from the printout, Lorenz had introduced a tiny error quivalent to 1 tenth of one percent. He concluded from the result of divergent trajectories, that perfect weather prediction is impossible with all knowing all of the factors such as humidity, wind velocity, temperature, presuure, and conditions in other parts of the world. Models of weather forecasting could not accurately predict weather outcomes. Hence, something as small a disturbance as a Butterfly's wings fluttering in Bazil could cause a tornado in Texas which replicates the tiny error he introduced.

By showing that certain deterministic methodologies have predictabililty limits (think of Pi), Lorenz's accidental discovery put the final nail into the Cartesian Universe theory (Newton's Laws of gravity and motion promised predictability) and "Deterministic Chaos" emerged from its rubble. Deterministic Chaos was first discovered by Henri Poincare when he discovered that with the introduction of a third celestial body to a system, it was not possible to calculate stability using technology of that day.

Edward Lorenz, the father of Deterministic Chaos, died April 16, 2008 at 90 years old of cancer. He was hiking but 2 weeks prior to his death. He was known for being a gentleman. I hope I made this simple enough to be understood without sacrificing the accuracy of his discovery. His was an important discovery that ranks with the discovery of relativity and quantum physics and came shortly thereafter.

A little science and math for the day.

... The Black Swan, by Nassim Nicholas Taleb.

If you haven't already read it.

His main premise is that humans are very poor at prediction. We like to make up stories about things after they happen, and in this way make believe that we understand much more than we do.

"My major hobby is teasing people who take themselves & the quality of their knowledge too seriously & those who don’t have the courage to sometimes say: I don’t know...."

His principle observations are about our misunderstanding the nature of 'randomness', we tend to think that the world is 'random' in the same way that games of chance are 'random', he points out that the randomness exhibited by games of chance are absolutely known, and the randomness in the 'real' world on the other hand is absolutely unknown/unknowable chaos.

He has less than flatering things to say about economists by the way.

Watt:

A good suggestion and I will take it up as I am voraciously consuming words these days. "Three Soldiers" by Passos right now after finishing "The Rum Diary."

I believe Lorenz accurately portrays the limitation of the decimal. Think Pi . . .

my math teacher introduced pi in his usual way; asking us if we could use all the math we had learned up to that point in time to formulate an equation that would give us the volume of a cylinder. The catch was that we didn't know how to find the area of a circle. I rose my hand and gave the most brilliant answer I have ever offered anyone on this planet; it was a six part formula for the area of a circle (without using pi)... which my teacher then added; okay and then we have to multiply by Length for the volume of a cylinder; yep, let's see if it works... and it did.

I would give my right arm to find that formula; I have no clue what it was. I even used it for a while on my homework and it was solid. My teacher had to introduce pi as a shorter formula, hence, a time saver. And so the lesson continued; but I didn't know how valuable my formula might have been; pi being the sleazy unstable relationship between a diameter and the circumference; God I wish I could see that formula again just to see what it was.

As a high school senior I came up with a method for tri-secting an angle with just a compass and straight-edge. I still remember that one, but that's trivial pursuit compared to a formula for the area of a circle that doesn't rely on pi.

Archimedes cut the circle into successive, same size wedges, and aligned them next to each other in rectangular form. The area of a rectangle is A=LW. The smaller the base of the wedge, the less the error. Take it from there.

... that it's impossible to trisect an angle.

use your compass to create a parallel above the base line of your angle. Keeping the same setting locked on the compass do another parallel line on top of the first one. Now drop a couple arcs from where the two parallel lines intersects the angle line. Using the intersection of the first arc with top parallel line and the intersection of the second arc with the middle parallel line; divide the points. Now do the same for the intersection of the first arc with the base line and the intersection of the second arc with that middle line again.. I've forgotten how they interact but there is a way to divide within the arc enough times to create thirds; the reason being that you can interact with the three parallel lines.

But my formula for the area of a circle only employed elementary school level math; it was spawned from our lessons on fractions; all i remember was that it was six sets of fractions added together; each set was accomplishing something with the circle; something times something that accomplished something added to five other similar operations... you had to have only fifth grade math under your belt; what Run just explained is actually an integral method, this was far more basic; I was in sixth grade!

I showed this to a mother of one of those smart kids at Carnegie Mellon; I can't even remember the name of the University there inbetween Oakland and Shadyside. Anyway, I took a base number and squared it, then after that took it to the third power, then to the fourth power, then the fifth power, and so on. Subtracting the difference between each number, I placed the difference on the level below the number line inbetween the numbers as a second number line. Then did it again below that line and so on. Eventually; you reached a point where the bottom line was in sequence. For example. try this. take one through 20 and square them. your first number line reads:

1,4,9,16,25,36,49,64,81,100,12­1,144,169,196,225,256,289,324,­361,400

okay the next line of difference reads:

3,5,7,9,11,13,15,17,19,21,23,2­5,27,29,31,33,35,37,39

so you could add two and get 41; so 21 squared is 441, and then add two more to get 43, so 22 squared is 441+43=484... and so on. As you use more complicated schemes you may need to drop seven levels of differentiation; but eventually they will fall into a simple addition sequence that can then just be added back up the levels to continue the operation; the result is a computer can perform very powerful calculations using a quick addition scheme; there is also a relationship between the base line; I can't remember the whole gig anymore.

I've always been good at finding relationships betweens items; nowadays I try to dissemble the relationship of the economy with the currency with the world money market to grasp what we could do, to better distribute wealth within a society. Some day, I'd like to feed the poor something more than just the bread of tears.

I got kinda burnt out on HST. I am staring at two or three late books and compilations that I can't bring myself to read.

Might be a good time to re-read F&L on the Campaign Trail though. Denver 2008 has the makings of a good old fashioned party clusterfuck.

No one, and I mean NO ONE could write about insider politics like Hunter.

I got this one in cabbie school.

re your number of lines of differences, you'll have as many as the highest order exponent in the equation, so if you did n to the fifth instead of n squared you'd have 5 lines with the fifth the repeated constant line, etc.

run: thanks for the book refs and commentary, also to whoever mentioned Ariely and Predictably Irrational, fun read.

Sarvis:

It is a story of a young man (Hunter was young when he wrote this - 22) writing for a newspaper in Puerto Rico. Hunter did work for a paper in Puerto Rico for a while. Not a bad read for a 2nd(?) book and it reminded me of Michener's "The Drifters." Both came out in the same decade I think, so they fit the times.

Well detailed, he pulls you into each scene and Al's could be down the block from you serving burgers and rum. Since I was stationed in the Carribean for a year, I could relate. I liked it and it is not overly long.

Picked up a first edition of Song of the Doomed; More Notes on The Death of The American Dream. Used; but I collect first editions. I will read that one next when I finish Three Soldiers.

doesn't matter where you go to school. I've met run and doodahman in person (and Demosothenes2) - it doesn't take much interaction to realize that these are brilliant individuals... SCOTT_TOO is a giant of a person; humble and powerful beyond belief. JackD is a kindly soul with a sharp wit. I think you would appreciate meeting them dave, I really do. I missed meeting Geoff, but if run liked him, I figure he had similar powerful instincts, intellect, and compassion.

turned it on and pointed it toward Brazil. Been running it that way for thirty minutes.

Someone in California do this toward N.Korea.

That'll teach those bastards.

You know, I kicked a rock toward Chicago the day before their earthquake last week. Sorry, my bad. It was such a small rock, I never thought.

YKM

Good for you . . .

This thread is full of ill digested math garbage and puffery, and you just let it go?

If Days trisected a triangle with straight edge and compass, he's ahead of God (at least according to the less devout, God is constrained by logical impossibilities). What are the chances?

The number sequence thingy is accurate, but to any mathematically literate person, a straightforward consequence of the Binomial theorem. The difference of the k-th powers of consecutive integers is a (k-1)th degree polynomial, e.g., (n+1)^2 - n^2 = 2n + 1. It's a typical parlor trick designed to impress the mathematically unsophisticated, and Days is regurgitating it in the most inelegant, awkward way possible (as you hinted): not to entertain, but to prove his childhood genius. Again, what are the chances?

Innumeracy is better than charlatanry anyday.