Mathematics- Causality

 Mathematics

Mathematics, so I used to say, is the language of physics. I now find the two are inseparable. One could say that the entire universe is one mathematical equation as Max Tegmark demonstrates in his book “Our Mathematical Universe”. Perhaps all the information in the universe, the stuff we see, are simply parameters, values of the variables of a grand causality equation. Consider that in mathematics cause and effect seems to be everywhere. For example, if I was to write an equation that states that…

y=mx+b

…meaning that the value of the variable y will acquire is the value of the sum of b combined with the product of m and x. So y is the effect and by definition must contain m, x and b along with the associated functions. The presence of m, x and b do not pre-suppose the existence of y though.

But even though we have written this simple linear equation with the dependent variable of y it can also be solved for x by a simple rearrangement of the terms therefore turning x from a cause and making x an effect. Most cause and effects are not reversible, they are asymmetric. If I develop a mathematical relationship that says y = mx + b, I can't always apply the formula x = (y - b) / m and say that y caused x. I could state what x would be for a given value of y but I could not necessarily say that a given value of y would cause x to take on the calculated value of x. The two variables are symmetric and intertwined. In the physical world this form of role switching, it doesn’t seem often to take place. This form may not always represent true cause and effect as it can be re-written without changing the meaning. Most effects are a one-way street.

In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the Ultimate Ensemble, is a speculative "theory of everything" (TOE) which was proposed by the cosmologist Max Tegmark in 2014.

Tegmark's hypothesis states that our external physical reality is a mathematical structure. The universe is not just described with mathematics, the physical universe is mathematics in a well-defined sense, and when complexity is enough to contain self-aware substructures like us humans and perhaps elephants and dolphins, we will subjectively perceive ourselves as existing in a physically 'real' world. .

The theory can be considered a form of Pythagoreanism or Platonism in that it posits the existence of mathematical entities; a form of mathematical monism in that it denies that anything exists except mathematical objects; and a formal expression of ontic structural realism. Beauty in itself.

Chemistry

Chemistry has notions of cause and effect as part of its language. A chemical equation consists of the chemical formulas of the reactants (the starting substances which would be components of the cause) and the chemical formula of the products (substances formed in the chemical reaction which of course is the effect). The arrow indicates the direction of the flow of causality.

As an example, the equation for the reaction of hydrochloric acid with sodium can be denoted:

2 HCl + 2 Na → 2 NaCl + H2

The equation indicates that sodium and hydrochloric acid react to form sodium chloride and hydrogen gas. I am not a chemist, but I would assume that no other process or energy is required to make this effect, such as adding heat or pressure. It also indicates that the reaction is not reversible all on its own. This seems to indicate the inclusion of the concept of entropy.

CO2 + 2H2O + Energy photons → [CH2O] + O2 + H2O

The above equation represents the chemical reaction of photosynthesis. It stipulates that energy from photons is required to make it work and shows the carbon dioxide with water as key components. By the way, one cannot produce photons by simply re-arranging the formula though you could combust the CH2O and produce light energy and carbon dioxide with water vapour in the combustion.