About Consequences of Assumptions

In a previous entry I wrote that numbers do not exist. And though Vi-Hart (or is it Vi-Heart?) has demonstrated that nature seems to use the Fibonacci series to design seeds, pine cones, sea shells, and a plethora of flora plants, I still do not believe that nature creates numbers, but that nature uses amounts, quantities, and (now that I think about it) ratios. The fact that Vi has pointed out the numbers are part of the Fibonacci series could just mean that nature uses convenient ratios that match up to our observations.

Then I remember a joke in one of my High Level Mathematics Classes (or maybe it was my High Level Engineering class) where a professor was talking about the three dimensional math that physicists use.

Here is the story. There was a set of equations that the Physicist could not solve because an inequality was always coming up. The professor was using, at the time, i-hat, j-hat, and k-hat to indicate the directions of normal space. (Engineers and physicists use different terms to separate their work from mathematical work to avoid "confusion".)

The Engineer came along and asked to see the work. The Physicist showed the equations and challenged his friend to solve it. So the Engineer looked at the problem and then, with one stroke of the pen (or chalk if the story was using a chalkboard) placed a negative sign in front of the k-hat.

The physicist looked at the equations and found that the equations were then solvable. He turned to the Engineer and asked, "But why should it be negative?"

To which the Engineer replied, "I don't care. I just know that it works."

For many scientists and intellectuals, the need to know keeps them going forward. The universe does not make sense unless it can be made to make sense. In order to do that, we as a species invented numbers and assigned them values that correlate to the observable universe.

At the time numbers were invented, however, the observable universe could only be seen with the naked eye. Everything before Einstein (I believe) is now called Classical Physics and, within those rules, numbers worked perfectly. They described how the Earth moved and how liquid behaves and how we can breathe.

Everything after Einstein, however, showed that Classical Physics is a special case of Relative Physics. That there are other states of being besides our own has led to new branches of mathematics and theoretical physics that stump even me.

And still I ponder if we are correct. That if our Classical Physics is a special case of Relative Physics, then what if our (to make a correlation) Classical Mathematics is an actual special case of Universal Mathematics. What if the math our high school teachers gave us and that our university professors depend on is just one form of math that we made to fit our view of the universe. Maybe we need a new set of Math rules to help understand our new view of the universe.

Many will say that is what we are doing today. The math today is based on rules like 2+2=4. What if there are other states of being where 2+2=5? Or where 2+2=2. Why are we using math that is based on Classical observations instead of math based on Relativistic observations?

What if our assumptions of math are wrong outside of our existence? What do we do then?