Pythagoras and mathematical realities:

Pythagoras and his followers had an understanding about the mathematical nature of the universe that was 2000 years ahead of its time. Pythagoras believed that all things were numbers. That is, that all things could be represented by (or are representations of) numbers and mathematical concepts.

This idea reminds me of an article published in Discover magazine (06.16.2008) by Cosmologist Max Tegmark, which states that mathematical formulas create reality. This might be a difficult concept to understand, but it might help if you scale down your model. For instance, the computer is a mathematical machine. At its lowest level the processor processes bits and bytes of binary data. Binary is a simple base two numbering system. The higher level programming languages we use to communicate with this machine are also mathematical - using variables, functions, arrays and logarithms. But if you can get this machine to crunch enough numbers you can begin to construct a graphical reality that we can interact with. The movies we watch and webpages we visit are simply graphical representations of mathematical calculations and concepts. So even man (with all of our limitations) has been able to use math to create a visual and interactive "reality". Who really knows what is possible when one learns to master the art of manipulating numerical concepts.

We must also keep in mind that the universe may (and most likely does) contain math we have yet to learn. Now if you scale up this idea you might be able to understand how the universe, and all the visual representations within it, very well could be the product of some serious math. How else could math so accurately describe the events we see and feel every day? Most people don't realize this because they skip over the application part of the study lesson, but math can (and does) represent all real world events.

This leads me to another interesting idea... If math represents all things and we can draft up equations to help us solve problems we face, then what conclusion do we come to when we get a solution with multiple answers? In other words, You are trying to figure out something, you draft up an equation to help you solve this problem. You find that more than one answer will make the equation true. Could this be mathematics giving us a choice to make? Could our free will (freedom of choice) ultimately be a product of universal mathematics? I also am compelled to bring up the Heisenberg "uncertainty principle" and "Schrodinger's cat". According to these principles, you can't know both the location and velocity of a particle, and a particle exists in a state of multiple potentials until it is acted upon. In other words, the particle has the potential to become a 1 or 0 (think alive or dead) until acted on. In fact, before being acted upon, the particle exists in a mixture of states - being both a 1 and 0. If you try to mathematically work out the future state of this particle, the best solution you will get is a range of probability.

So, the future state of participles is not predetermined. By extension then, neither are our futures. So mathematics could actually be the core building block of our free will and freedom of choice. So as you can see, mathematics is more than a way to figure out your business expenses. Mathematics, as Pythagoras believed, is the building block of all reality. This is also how math can tell us about things we can't see and otherwise know about i.e. singularities, higher dimensions etc... Math exists on ALL levels and therefore can tell us about things beyond our normal range of experience. Some new physics theories even suggest that time itself emerges from a more fundamental--and timeless--reality.