Adjectives

I am going to say something that a lot of people will take offense to. If you bear with me then you'll find my explanation makes some smattering of sense.

Numbers do not exist in nature.

I can see you think I'm nuts. You're not the first to say so. This topic is even debated by many mathematicians, some adhering to my claim, others camping on the other side of the topic.

Here is my explanation for my stance. Water has three atoms in its molecular structure: one oxygen and two hydrogen. When its relative temperature is lowered to zero degrees Celsius its structure changes from a liquid to a solid. When its relative temperature is raised to one hundred degrees Celsius then it boils and evaporates as a gas. I say relative because the pressure in which your water boils changes its boiling and freezing point.

Great scientific facts. Now, here's the kicker: does nature care? Does nature care that 1 standard atmosphere must be present for the boiling point of water to be 100 degrees centigrade? Does nature care that the freezing point of water is 0 degrees centigrade? Does nature care that in order for water to be water that there must be 2 hydrogen atoms and 1 oxygen atom?

Nature does not care. If there happens to be hydrogen and oxygen in the same area and the conditions are right, then water will form. If the conditions are not right then water will not form and you'll just have hydrogen and oxygen gas (depending on the local temperature and local pressure). Nature does not count. Nature does not measure. Thus, nature does not need numbers in order to do.

Humans, on the other hand, need numbers. In order to know how much of something we have, whether it be atoms, dollars, or llamas, numbers help us measure and describe the amounts that we are trying to keep track of. Without numbers, we could not understand how the Earth moved through the sky. Without numbers, we could not understand chemistry in order to make the things that build our world. Without numbers, we could not elect our politicians properly. (Actually, that last one wasn't such a good example.)

However, we had to invent numbers. Take the number "0". Before its use, many cultures around the world used the positions on ropes marked off by knots to record the count of items. This was not a very practical way to do math but it was the only way they had at the time. Someone (several websites I've read say the guy is from India) state that he started using a place holder in order to mark where an amount is absent (as in the year of the San Francisco earthquake 19.6). The symbol for "nothing" came shortly after and thus we have the number "0".

Note that there was a way to do math without the number "0" as a placeholder. This is historical evidence that numbers are arbitrary. They were invented so that we could understand our world better. Is the Earth still going to exist if numbers did not? Yes, it would still be here. We could still be using rope to count our sheep and the Earth will still be here.

So, what are numbers if they are not in nature? Numbers are symbols. They are arbitrary in their representation. They will work so long as you are consistent with their use. In other words, if you lay down a set of rules in how to use these symbols, then you have to stick with those rules.

Example: Look at the number line and you can count it off from left to right.

   0, 1, 2, 3, 4, 5, 6, 7, 8, 9

This is the number line as your teachers and your professors have taught you. However, since the numbers are symbols, you can redefine the number line as follows:

   1, 3, 5, 7, 9, 0, 2, 4, 6, 8

Crazy, I know. It can work so long as you stick to your rules. In the second number line if we follow the four basic rules then the following are correct:

   (a) 1 + 1 = 1
   (b) 1 + 3 = 3
   (c) 3 + 5 = 7
   (d) 6 - 2 = 5
   (e) 3 * 3 = 3
   (f) 0 + 0 = 31
   (g) 2 / 7 = 5

And so on. It only looks wrong because we are trained to use the first number line above. The value we ascribe to "1" is universal, but the number itself is not universal. Thus, numbers do not exist outside of our consciousness. They are not natural, but they are our best tools to help shape and understand our universe.