Does God need to create mathematics?

Question

If someone knows the detail of everything and has endless life, did s/he need to create mathematics to describe the world?

Answer 1

I don't think the Questioner assumes that, or is asking whether, all knowledge is mathematical, only whether a complete description of the world would require (but not necessarily be exhausted by) mathematical description for which the existence of mathematics is plainly necessary.

To the extent that the world is quantitative and relational, it seems to require mathematical description.

Merely as a knower God would not need to create mathematics. Mathematics might already exist. Only if you add that God not only knows everything but created everything (in some fundamental sense) would God need to create mathematics since, ex hypothesi, without God mathematics would not exist and we could not describe the quantitative and relational aspects of the world.

ENDNOTE : MATHEMATICAL CONSTRUCTIVISM

My argument is hypothetical throughout. If there were an all-knowing being, would it need to create mathematics in order to describe at least some aspects of the world ? That was the question, and my answer addressed that hypothesis. It did not assume that there is such a being; and it certainly did not say that if there is mathematics, which there plainly is !, it was or must have been created by an all-knowing being. It is completely neutral on the question whether mathematics is constructed, at least in part, through a process of (human) reflective abstraction. Mathematical constructivism is neither being attacked nor defended.

Answer 2

Who is he/she describing it to?

As short as that is, such a question points at an essential crux in your question, which is what it means to "describe" something. The concept is tricky enough with mere mortals, but using the term for the actions of an omniscient deity really pushes the limits of the term.

Perhaps more to your question, there is indeed an open question in philosophy as to whether mathematics is the language that defines the universe, or if it is a language humans invented to make sense of it. If the former is true, it may not be possible to describe the universe to your particular satisfaction without mathematics. If it is the latter, it is easily possible to do so. But, since that particular question is open, we can't really say one way or another.

Indeed, if you consider other cultures, mathematics may not be able to describe the world completely in the first place. The daoist concept of the Dao is explicitly not completely describable in a written form (often phrased as "The Dao which is written is not the eternal Dao"). However, there would be an interesting question of meaning here: since we have a concept of mathematics, the concept of mathematics is in the Dao. Thus a description of the Dao would have to include a concept of mathematics, even if mathematics was not the language used to describe it.

Myself, I think it would be completely reasonable for a deity, upon deciding they need to describe the world to point right at the world and say "something exactly like that." And, with such omniscience, know exactly what was meant by that.

Answer 3

Surely not. Mathematics is a series of structures and rules that people have defined because at certain times they were useful and/or interesting (or maybe they were under pressure to finish a PhD...). You could argue that a certain differential equation describes the way a ball flies through the air, and use that equation to predict where the ball might land. But you could also just 'know' where the ball will land, without having to create any mathematical structures at all to help you. Personally I think that knowing everything would make mathematics totally redundant.

If a being could hold all knowledge of the past, present and future in their 'mind' simultaneously, creating mathematics to explain or understand it would be like taking a complete picture and drawing the outlines of puzzle pieces onto it. The connections of the pieces are only useful to help build the picture in the first place---if you already have the picture then there are infinitely many, entirely arbitrary ways you could definite its constituent parts and none of them would be necessary, or even helpful, in understanding the picture itself.

Answer 4

Mathematics is the observation of immutable laws and principles. Take a simple observable, immutable reality, such as the conservation of energy. One can express it as an invariant equation such as the following: E(t1) = E(t2)

For any two times t1 and t2. For dynamical laws that involve variability and yet for which there are still immutable constraints (for example, those that conserve total energy in the presence of relative motion), one could create a more detailed equation, for example

KE = (mv^2)/2

And so on.

The observation of all laws in the universe would, if codified, consist of a perfectly consistent and interrelated system of equations. Limited observations could then allow an observer to obtain or constrain unobserved quantities, thereby increasing his knowledge by the application of inviolable laws to eliminate impossibilities.

Any observation of immutable equivalences implies a universal law which could be codified or expressed mathematically.

So yes, the Supreme Governor of the universe would find mathematics mighty handy, not only because He Himself comprehends it, but also it is especially useful for communicating the functioning of the universe to His offspring.