a rigorous counting system is, by definition, physics

hence, the natural numbers are a sequence of physical constants

a rigorous counting system is, by definition, physics

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a rigorous counting system is, by definition, physics

hence, the natural numbers are a sequence of physical constants

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the natural numbers are a human invention like the formulation F=ma is a human invention

the physical relationships they describe are real

The mathematical equation 1a + 2a = 3a describes a mathematical law of quantitative relationships. It also describes a physical absolute, according to the law of conservation of energy. Numbers and numerical relationships are not merely abstract concepts, they are developed from the same fundamental principles as physical laws. This is not insignificant, it suggests that the physical universe developed according to natural constraints which are purely mathematical.

If we expect advanced aliens to know the natural number sequence then humans didn’t invent numbers, we discovered them.

If numbers are a human discovery then so are their mathematical relationships.

If mathematical relationships are discoveries not inventions then they’re natural laws.

1+2=3 is a natural law.

This is not insignificant.

1a+2a=3a

this is maths ** and** theoretical physics

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