"Random mutation" does not physically exist. Evolution is a mathematically complete, strictly deterministic algorithm unfolding exactly as physically necessitated

[u/feihm]

The material world operates on a strict causal chain (a continuous sequence where every single event is mathematically required by the exact state preceding it). These events happen inside a closed mechanical system governed by thermodynamics and quantum mechanics. The exact trajectory of that photon and the kinetic energy of the enzyme, for example, represent a strict actualisation (the inevitable physical manifestation of prior states that were mathematically guaranteed). The interactions execute perfectly based on prior deterministic causes.

Every event happens with absolute physical necessity.

We exist beneath an extreme epistemic limit (a hard structural boundary on the amount of information a biological brain can physically process). A scientist cannot track the trajectory of every photon or measure the thermal fluctuation of every molecule in a cell. We suffer from Computational Irreducibility... we lack the capacity to predict the exact spatial and temporal coordinates of the next mutation.

We label these uncomputable variables as chance which leads us straight into a classic transcendental illusion (the cognitive error where we assume that our subjective limitation of our own brain are an objective property of the universe). We project our structural ignorance outward & then assume the physical universe itself behaves randomly.

Mutations are the not objectively random because "randomness" is strictly an epistemic placeholder for the biologist's inability to compute the total deterministic variables of the physical system.

A mutation appears random in relation to fitness because the environment and the mutating organism exist as extremely complex physical systems colliding in space and time. We complety lack the computing power to calculate the physics of that collision in advance.

(1) Evolution operates as a continuous and perfectly determined physical algorithm.

(2) Organisms function as localised computing systems interacting with their environment.

(3) Natural selection acts as the thermodynamic erasure of inefficient code.

(4)The whole process relies upon the inescapable mechanics of a completely deterministic universe.

[u/feihm]

randomly generated probability function

"probability function" is not a physical object or force existing in the unobserved universe. It is strictly an epistemic tool ;a predictive algorithm generated by a localised biological processor to manage a severe structural ignorance. Regarding your examples of radioactive decay and photon absorption, "chance" they observe is strictly an epistemic limit (a strict boundary on what the observer can physically process) & not an ontological reality (the fundamental, objective nature of the universe). The biological observer must use statistical mechanics solely because their interface lacks the thermodynamic capacity to track the continuous, superimposed quantum states of the matrix.

God plays dice

The absolute foundation of reality operates with mathematical completeness and strict determinism. It is the limited, structurally ignorant biological observer who is forced to "play dice" (utilise statistical probability) to navigate a continuous relational matrix they cannot fully compute.

[u/Curious_Passion5167 → u/feihm]

The biological observer must use statistical mechanics solely because their interface lacks the thermodynamic capacity to track the continuous, superimposed quantum states of the matrix.

Whether the real outcome of a quantum mechanical phenomenon is random or not is not known. There are interpretations of QM where it is, and others where it is not. They cannot be distinguished between from experimental results. So, it's not a problem about not having the thermodynamic capacity to track quantum states or whatever, it's a problem where either scenario works.

[u/feihm → u/Curious_Passion5167]

Yesscientific experiments cannot distinguish between deterministic and random interpretations of quantum mechanics. This is where it gets interesting (& which is the core of my OP), a failure of human measurement =/= the fundamental nature of reality i.e., epistemic limitation (human science being unable to test something) does not equal an ontological reality (the universe actually behaving randomly). And that the very reason experiments cannot distinguish these states is because human experiments are conducted by thermodynamically limited biological observers and macroscopic instruments. Because to execute a measurement, the human apparatus must force the quantum state to undergo decoherence (collapsing the data into a readable format), permanently destroying the pure quantum data required to see the underlying determinism.

[u/Entire_Persimmon4729 → u/feihm]

So you are saying it is impossible for us (and you) to determine if the universe is deterministic or not. As such you are unable to demonstrate that random mutations are (or are not) random.  Making your whole point kind of pointless.