Math+and+Beauty

The common paraphrase: "God does not play dice with the universe." Albert Einstein, 1926

The actual quote (translated from German to English): "Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the "old one." I, at any rate, am convinced that He does not throw dice."

=What is Math?= Mathematics is a precise way of describing things and relationships.

We can describe basic things, such as when you have two apples and a friend gives you two more, then you have four. So, you could describe the apples as "the two I had already and the two my friend gave me," or you could describe them as "2+2=4," which is much more efficient. If you were texting, you would probably prefer the latter rather than the former!

It can describe patterns such as the kind of thing that would be used to make a computer generate counting by twos: n=0 n=n+2. In other words, you define a number, n. Then you ask the computer to add two to the number. The new number becomes is n, and the process can start over. The other instructions around this can either send the computer into an infinite loop (if you don't describe the maximum value for n the computer will just keep calculating even numbers until the cows come home or someone disrupts the routine) or give you a nice printed list of even numbers up to whatever number you like. If you start with n=1, then what do you get for n=n+2?

Math can also describe relationships. Einstein's best-known equation, e=mc 2, where e stands for energy, m stands for mass, and c stands for the speed of light. This equation represents the relationship between energy and mass, indicating you can turn mass into energy and vice versa. A simple example is lighting a candle. The wick and wax (mass) get turned into heat and light (energy).

=Where is Math?= If you are reading this wiki online, then you are interacting with mathematics. At the heart of it all is the fact that a circuit can be on or off. Electrons can move or they can stop, which can be described mathematically using base 2. In base 2, there are only 2 numbers (using base 10 to describe base 2 is a little funny!). Here are the numbers in base 2: 0 and 1. Off and on. The way you count in base 2 is this (with the translation into our normal base 10): 0=0 1=1 10=2 11=3 100=4 etc. We use base 10 probably because of the universal manipulatives available: fingers. We have 10 fingers, so it makes since to use base 10 because we can check our math physically by counting on our fingers.

Suppose we used elbows to count instead. Your left elbow would be one and your right elbow would be 10 just the way the first finger you count is 1 and your last finger is 10. The difference is that you didn't suddenly grow an extra bunch of elbows; instead, in any base, the first number is 1 and the last number of the base is 10.

Math is everywhere in human made things, from giant bridges to nanoparticles. In order to make something, a person has to deal with the concept of dimensions as well as the concept of property of materials, even if the process of dealing with it is not always conscious. For example, a potter sits at a wheel to make something out of clay. The potter knows that certain sizes of pots cannot be made on that wheel and also that if you allow the clay to become too thin, then the whole thing will collapse. This kind of knowledge comes about through experience, however, it is based on mathematical concepts, without which, there would be no human-made artifacts.

Do you like music? Music is audible math because just about everything in music involves mathematical relationships: melody (scale degrees--do re mi, etc.), harmony (mathematical relationship of chords to each other as well as between the notes in a single chord), rhythm, tone quality of an instrument, and so forth.

So, if you hate math, you decide to avoid dealing with it by going outside and getting away from human-made math-centered things. But you can't get away from math even outside in a deep forest far away from any other human being. Hear that bird? The bird's twitter has melodic qualities, that can actually be summarized through the frequency (in cycles per second) of each pitch used. Look up into a tree. Tree branching and even the placing of leaves is different for every tree and yet can be summarized and recreated on a computer using a special kind of geometry called fractal geometry.

Finally, your body has math in it besides the math that you know about which is in your brain! Your blood vessels branch in much the same way trees branch. Bodily functions such as heart-rate can be measured and you want your heart rate to stay within a certain range. Your body has size that can be measured; even your feet get measured for shoes!

Math, then, is everywhere. As Einstein said, God does not play dice with the universe. Things are not random and math is the language we use to find and express the patterns in the universe.

=Why Math?=

A very important aspect of math is its ability to express patterns, which means a person can predict what is going to happen next. This could be relatively trivial, such as how you put up tile in your bathroom. But it also could have serious consequences. Imagine people in pre-historical times. Everything must have been scary; even now it's hard to predict weather, but back then it was close to impossible. And people did not have steel-reinforced buildings with central heat to which to retreat when weather got bad.

People began noticing the seasons as well as the movement of the stars in the sky (we tend to watch the stars on tv which are a lot more chaotic than the stars prehistorical people watched). They noticed patterns to the movements of the stars and how the stars changed in relation to large changes in weather--the seasons. Even without sophisticated tools, they noticed that the moon has a 28 day cycle and that a year is more or less 12 28-day cycles. Thus, they could begin to predict what was going to happen and get prepared for it. They could know when planting time came and when harvest time came and created the foundations of agriculture using the math of the moon and stars.

Human beings have certain perceptual limits. For example, there are frequencies of sound (cycles per second) beyond human hearing and frequencies of light (ultraviolet, infrared) beyond what people can see.

An important perceptual limitation is our inability to see the future and therefore predict what will happen. This is why patterns are so important; if you know how something fits into a bigger pattern, then you have a much better chance of predicting the future than if something appears to have no pattern or a pattern you haven't discovered yet. This provides a certain amount of psychological security. When the snow falls, you know that summer will come in a few months and vice versa for when it gets really hot.

Beautiful Math

Here are some examples of beauty that has a mathematical element to it.