Archives for category: theory

If we think intelligent aliens would develop a counting system and have knowledge of the natural number sequence, then we acknowledge that the natural number sequence describes natural laws of quantity:

A rigorous counting system is, by definition, physics.

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There is, without any possible doubt, a single entity of Existence which encompasses everything which exists.

Existence = 1

From this, it is inevitable that the natural laws are emergent properties of the increasing mathematical complexity of the sequence 1 = N(1/N).

Max Tegmark, Garrett Lisi and others have proposed theories of everything that rest on the premise that physical reality is governed by natural laws which are naturally mathematical.

Historically there have been many discoveries of connections between patterns found in purely mathematical models and naturally occurring physical phenomena observed in the universe. More subtle connections between number theory and physics are being discovered. They’re directly related.

The law of conservation of energy states:  the total energy of an isolated system is conserved.

That is, that the total energy of a system must be constant over time;

The energy must always add up to the same amount no matter how it is distributed within the system;

1 + 1 = 2

1 + 2 = 3

and so on.

In fact a rigorous counting system is by definition, physics.

The mathematical equation 1/2 + 1/2 = 1 describes a mathematical law of quantitative relationships. It also describes a physical absolute, according to the law of conservation of energy. It describes, mathematically, 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.

a rigorous counting system is, by definition, physics

hence, the natural numbers are a sequence of physical constants

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