The process of change, associated with evolution, is a reasonable assumption and can be inferred by fossil data.
It isn't an assumption. It is a demonstrable fact that can be observed and quantified in extant populations of living things.
Where I differ is how/why this change occurs. The random and statistical models, common to the Life Science, are pseudo-science.
Statistical models aren't the mechanism of change, they model it. Not a pseudo-science. A method of analysis and description.
Tell me what drives any black box random process?
Genetic variation being acted upon by the non-random selection of the environment.
Is it a drunk goddess called lady luck? Random is an assumption with no tangible or rational source. It is a math assumption and not a statement of fact based on laws of science. Tell me the facts!
The random nature of the variation is the random component. Mutations cannot be predicted other than knowing they will happen. We don't know and can't know what mutations will happen.
Random and statistics are often demonstrated by rolling dice. If I have a set of two, six sided dice, and keep rolling, there are odds for each roll, while all the possible combinations, with enough rolls, will repeat over time. Yet evolution does not repeat over time like dice.
The environment that lead to prior evolutionary paths has changed. The world in which dinosaurs evolved doesn't exist anymore in the sense that the environment over the course of that evolution isn't repeatable under current conditions.
Life from scratch does not happen again,
We don't really know that it hasn't happened, but there is no evidence to show it is happening now. And also, not evolution.
Not yet, but who knows what tomorrow might bring.
The dinosaurs; double sixes, have not reappeared again after millions of rolls of the dice.
Different dice, different table, different casino, different place altogether. The expectation that dinosaurs would arise now, under conditions is non-zero, but not very good.
The current model is not modeling the reality of evolution, which is non repeating novelty and diversity.
The current model does fine and takes the nature of the environment into account. Good enough to accurately predict Tiktaalik, generate hypotheses and valid explanations for obersvations.
The casino model does not work in the reality of evolution. Card games are based on repeatable outcomes and hierarchies of outcomes.
Life repeats. Mutations happen regularly enough to build a clock from them. The environment continues to persist. Gravity seems the same. Atmospheric oxygen has changed over time. Continents have arisen, collapsed and shifted over time. The environment changes over different scales of time. Change may not be as obvious over a single lifespan, but there change happens.
What the data says is, things happen once, and then move to another future state. This is not random but has a sense of direction, forward in time.
There is no linear progression, even as things change over time, which is the most basic definition of the theory.
Faith in a lottery or casino model of evolution is not science.
Using statistics to draw conclusions and make predictions is very scientific. In fact, Fisher, Haldane and Wright dramatically changed how science is carried out and interpreted leading to a much more stable and rapid advance in our acquisition of knowledge.
People have won lotteries more than once; repeat dice model.
Single events going from 0 to 1,000,000,000 in a single step have astronomically infinitesimal odds of success, but a series of small steps over time that accumulate with increasing benefit to fitness do not have the odds so stacked against them.
If we stick to a dice model, evolution behaves more like an infinite sided dice, so it may take infinite rolls to repeat any step.
Infinite dice would still be rolling infinitely with no end or outcome. It's craps before they start rolling.
This would show up as different critters each roll.
A stepwise, gradual branching process selected by the environment is a much better, more parsimonious explanation that is supported by the evidence.
But that infinite sided dice model also implies, it will take an infinite time between each needed step; side, and therefore life should never have occurred, or should still be very basic. Neither are observed.
Agreed, a totally random process is not observed.
The solution is evolution is based on a law of science; 2nd law, entropy. Entropy has to increase. Entropy is not a wave, that repeats like rolls of the dice or energy. It has a linear increase, like we see in evolution.
Unfortunately, for your modeling, a linear increase is not what is observed from the evidence and experimentation. Complexity is a result of evolution, but not a demand of evolution. Simplicity has also evolved where traits are reduced and/or lost.
Since all of current evolutionary science, is based on the pseudo science of dice, what should be done?
It isn't, so nothing should be done. The statistic are employed in experimental design and to help determine if observations are significant and to provide confidence that the results are not merely random chance.
Does separation of church and state come into effect? It is time for moth balls or the fire pit?
No idea what you mean here.
Darwin postulated natural selection, which is also not about dice.
Yes. The non-random component of the phenomenon of evolution.
It is about real logical natural pressures; based on laws of physics, pushing and pulling,
Yes. Agreed.
with increasing entropy the drive for the advances in complexity,
Complexity can advance. It does not have to. Stable environments conserve complexity or even lead to the reduction of it. The Earth is not a closed system and has a continual source of external energy.
over time, that should not repeat no matter how many rolls.
It is the seemingly irreversible change in the environment that results in what is observed. The environment being all the internal, external, biotic and abiotic factors that impinge on the populations. It includes competition, cooperation, symbiosis and all the array of interactions that impact living things and change.
It will quantum step forward and can meet the reasonable time lines. Is it moth balls or fire pit? I am fine either way.
I'm not sure what you mean here either.
You're dismissal of valuable and useful statistical tools is rather puzzling.