# Is the earth in absolute mathematical order?

1. Feb 11, 2005

### semidevil

so I mean, after taking 3 years of college math classes, and still going, I've taken many many math classes. and it seems that so many mathematical equations that we use, are used to kind of "control" the world. I mean, statistics, probability, calculus, differentail equations, geometry, it seems that the real world and math, all have some connection.

So I was wondering, is the universe in absolute connection with math? I mean, if given enough time, can we come up w/ an equation for everything that happens? I know that random things can happen, but are they really random, or is there some subtle pattern?

what about predicting the future? With enough information, and basic probability and statistics, one can deduce the next event. Do you think that given enough time and scientists from various fields, one can predict the future for more bigger events w/ reasonable accuracy? i.e, can we predict when the war in iraq will end, or maybe come up with an equation for the lottery numbers for the next 20 years?

just wondering to see what you guys think

2. Feb 11, 2005

### Grogs

Back in the '50's, when 'powerful' computers started coming into being, meteorologists believed that they could program the current weather conditions into a computer and be able to predict the future weather with perfect accuracy. What they found out was that even the smallest thing (the flapping of a butterfly) could have profound effects given enough time. In effect, the weathermen couldn't measure the initial conditions with enough accuracy to generate long term forecasts.

With an 'equation of everything' we would run into a similar problem. In order to predict everything about the Universe, we would have to know the initial position and velocity of every subatomic particle in the Universe. Even if we someday have sufficient technology to measure this, Quantum Mechanics seems to suggest that there is a limit to the accuracy of our measurements. This innaccuracy would propagate throughout the equations and make them useless after a short period of time.

3. Feb 11, 2005

### semidevil

yea...that makes sense. thanks.

but just out of curiosity, what is the butterfly effect? I know the concept is that even the smallest thing can have big consequences, i.e, butterfly flapping it's wing can cause a hurricane.

but what did the name come from? how could the flapping of a butterfly's wing cause such a big event?

4. Feb 12, 2005

### MiGUi

The fact is that a really small change in the weather conditions, can make a totally different evolution of the system.

The equations that modelize the weather have this caothic behavior...

When you study the distribution of temperature in a disc, the temperature don't varies a lot if you put a thermometer in one point, and next in a point 1 mm far that one. This don't happens in weather models. A small variation makes the evolution of the system completely different.

To synthesize this, the butterfly effect says that the small flapping of a butterfly can origine a hurricane, because the weather is very very sensible to small changes.

5. Feb 12, 2005

### Edgardo

Hello semidevil,

maybe you know the Feigenbaumdiagram? It shows how SENSITIVE a certain recursive sequence is to the initial conditions (starting value).

$x_{n+1} = r \cdot x_{n} \cdot (1-x_{n})$

Even the slightest change in the value (e.g. $x_{0}$ = 0.04 and 0.040000001)
results in a totally different sequence.

That's quite the same for the weather.
Your equations for calculating, or better to say predicting the weather
are very SENSITIVE to starting values.
Case a) You don't know about the butterfly and calculate:
=> You get sunshine for 10th day.

Case b) You take into account the butterfly and calculate:
=> You get a rainy day for the 10th day.

In practice:
Metereologists can only predict the weather 3 days in advance.
Then they have to take the new starting values again, because the old ones
would result in a totally different weather prediction. Of course they take new values every day for the weather forecast.

P.S. Does your question also refer Laplace's Demon?
http://www.hypography.com/topics/Laplaces_Demon_112215.cfm
Maybe that link will clear some things.

Regards

Edgardo

6. Feb 12, 2005

### saltydog

Sounds like you're asking "why does Mathematics fit nature so well?". I think it's only because we made it so. Here's my take:

The human brain evolved as a successful survival strategy in a non-linear world. You know, "when in New York, act like a New Yorker". The brain is a non-linear consequence of that strategy. From such a non-linear brain emerged a concept we call Mathematics which is also non-linear in it's actual geometry of construction. You know, if you have a big calculation, one little thing, just a minus sign wrong and it doesen't make the answer a little wrong but rather (usually) really wrong. Other things in math exhibit non-linearity. Math fits nature so well because it is a reflection of nature that we constructed in response to surviving: if nature were linear, then the math we would have created would also have been linear. If nature was a circle . . . well, you get the picture.