nothing can be created or destroyed, which makes 1a+1a=2a an entirely natural law

 

 

From a review of Converging Realities: Toward a Common Philosophy of Physics and Mathematics (Robert Omnes, 2005).

“Now, advances in the understanding of physics suggest that the foundations of mathematics are encompassed by the laws of nature, an idea that sheds new light on both mathematics and physics…”

This theory of everything, here, explains how human maths derives from physical laws, which are based on the natural – and inescapably inevitable – mathematicality of nature.

Whether it takes the form of a universe or multiverse, there’s a single sum total of ‘everything which exists’, a single ‘Existence’.

Existence = 1

We’ll never know what Existence ‘is’ or what it is ‘made of’, we can only be certain of its quantity. It is the ultimate known *and* unknown.

We don’t know what it’s made of, we only know how many of it there is.

X = 1

But we also know everything which exists is part of Existence: it has been divided, internally, into its constituent parts, over time.

So if X = 1, and everything else is a result of X being divided into smaller and smaller constituent parts over time, which can only occur according to natural laws of combination. The entirety of things which exist, must ‘add up’ to the single Existence they are parts of.

This is where human concepts of number and mathematics intersect with natural laws.

 

 

mathematics and physics both develop from the same fundamental principles

the complexities of each are emergent properties of the application of these fundamental principles to their respective entities/units of existence, real or imagined

mathematics can produce concepts and objects which are impossible in physics, but this  doesn’t disprove the existence of formal connections between the two fields, or the significance of those connections

the fact that it’s possible to creatively develop mathematical concepts which are impossible in physics, shows only that human creativity in mathematics isn’t subject to the same natural constraints as the laws of physical reality

those natural constraints on how a complex physical universe can emerge from first principles may not have been discovered mathematically yet, but they inevitably exist

if you place an object (a) with an identical object (a), together they form a group (a+a)

the ratio of the quantity of a in (a) to the quantity of a in (a+a) is
a:a+a

the ratio of the mass of (a) to the mass of (a+a) is
a:a+a

the physical ratio
a:a+a
is precisely identical to the numerical ratio
1:1+1

the physical ratio
a:a+a
is precisely identical to the numerical ratio
1:2

so
a:a+a = 1:2

human number theory and natural physical laws are based on precisely identical principles

⚫ and ⚫⚫ makes ⚫⚫⚫ (physical quantity)

1 + 2 = 3 (human number)

each of the ‘equations’ describes the same relationship; each is based on the same principles

each expresses inviolable laws which govern the combination of identical entities into groups

natural numbers are physical constants

Part of the reason that the formal, natural connections between mathematics and physics are rejected as significant by most physicists is because the the two fields are so firmly intertwined at the most basic levels that the epistemological becomes confused with the ontological.

In fact, it is not that mathematics underlies physics and it isn’t that they look the same because mathematics is only our tool to examine physics with. It’s that the same fundamental principles – laws which are both natural AND mathematical – underlie them both. But we shouldn’t be surprised at this.

Human concepts of number and maths developed from experience and observation of the real world: geometry can be developed from both theory AND by measuring the physical world; counting systems are based on measuring and comparing the physical properties of different groups of the same or equivalent physical objects.

It’s not so much that either maths or physics underlie the other, it’s more that they develop from the same first principles, and are parts of the same thing. There’s only a single ‘sum total of existence’: you can define the mathematical concept 1, physically. And the first law of thermodynamics can be expressed as 1a+2a=3a.

Issues of efficiency act as constraints on how mathematical complexities develop naturally from first principles into a physical spacetime. These constraints are the difference which leads to a separation of human abstract mathematics from physical mathematicality.

⚫ and ⚫⚫ makes ⚫⚫⚫ (physical quantity)

1 + 2 = 3 (human number)

each of the ‘equations’ describes precisely the same relationship

mathematics is developed from number theory

number theory is developed from a rigorous counting system

a rigorous counting system is based on physical property of quantity

the physical property of quantity is a result of natural laws of physics

 

 

something exists

Existence = 1