The above video shows children learning to master the ancient art of the abacus.

“Children like this show us that with enough practice, super-fast mental calculation is possible.”

Our modern reliance on calculators is, undoubtedly, holding us back in many ways, even as it enables us to quickly perform calculations that would have taken hours to years of calculation by hand (or by abacus) in the past.

I have heard and read from various sources that some physicists and philosophers believe that the root of reality is Mathematics; not the old view that math is a great way to describe the underlying, true reality of the cosmos … but that the underlying, true reality of the cosmos IS mathematics. Don’t mistake this with the idea that mathematics has an objective reality … it is not proposed to be a part of reality, but to be the totality of reality.

One source is Tegmark’s Mathematical Universe Hypothesis;

‘Just’ Math? or ‘Nothing’ But Math?

Immediately, then, you may cry: “how can we JUST be numbers?”; but I wonder where the ‘just’ bit really fits in. It is like the observation that matter and energy are so bound up together that they are essentially the same thing. Thus we hear that we are nothing but energy, or we are just energy, etc. But, in these cases, ’nothing’ and ‘just’ are prejudices, and they miss the critical point! Certainly matter and energy are interchangeable, light can be measured as particles or waves, etc. … but that does not take away the very REAL distictions between matter and energy, waves and particles. It is like water; at a minimum we have ice, liquid water, and steam to consider. They are all ‘just’ water, all ‘nothing’ but H2O … yet you can’t run a steam engine with ice, you can’t skate on liquid water, and you can’t swim in steam. There are very real, practical differences between one state and another — that is why each state is distinguishable and each state is given its own name; each state has its own unique, and perhaps emergent, properties.

But Didn’t Humans Create Mathematics?

Certainly, in a manner of speaking, humans create mathematics; we chose the notation, and we can create thought experiments that are mathematical but (insofar as we can determine) have no manifestation in reality at all. But notation and thought experiments don’t negate the fact that there is usually something real being described. The concept of number is not unique to mankind. Other animals can count. In fact, mathematics has been proposed as the most likely way to communicate successfully with aliens, should any ever show up on our ‘doorstep’, because mathematics seems, well … universal. Human mathematics is like a map; we use it to chart, as best as we are able, the territory of manifest mathematics. Yes, we created the map. No, we are not responsible for the territory that it attempts to chart. Mathematics is not invented so much as it is discovered.

If Everything Real is Mathematical, Does that Make Every Mathematical Idea Something Real?

No. That is like saying all unicorns have horns, therefore all things with horns are unicorns. Go ahead and create a consistent mathematical framework that has its own special notation, forms of rigorous proof, and describes whatever uniqe and twisted pseudo-reality you like … that does not make you a God.

The Question: “Is Ours a Mathematical Universe?” Remains

So we still have the idea, the possibility, of a mathematical reality; that the underpinning of the universe is pure mathematics. This is not ‘just’ long division we are talking about; this isn’t simply some form of obstruse calculus. This is an idea that, if true, will not in any measure lessen the mystery of existence.

Is God the Perfect Expression of the Language of Mathematics?

God is often referred to as ‘The Word’; perhaps, through this phrase, we have known all along that He is, in essence,  the Language that Utters reality; and maybe, just maybe, that language is Mathematics.

What do you think Albert Einstein meant when he said:

“as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality” ?

This was in response to the question:

“how can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”