Scientifically speaking, randomness can produce order. Order and thermodynamics go hand in hand, and thermodynamics is a random process at its heart. More accurately, thermodynamics is a stochastic process.
If you are referring to a normal distribution or Gaussian curve, then you may be interested in this Wiki page:
That’s the state of the system that resulted from a random process.
How so?
This is news indeed. The rest of the scientific world considers equilibrium constants and equilibrated conditions to be anything but stochastic. I have used large thermodynamic packages for decades without any stochastic treatment - none, zero, zilch… 
It means described in terms of a range of possible outcomes with some probability of different outcomes occurring.
I don’t know anything about the history of the word. Scientists and mathematicians often narrow the meaning of words.
QM typically describes observations in terms of probability distributions, yes.
Random process can have order. The molecules in gas have highly ordered behavior, but we still describe their motion as a random process.
I didn’t learn anything about craps in school, and I don’t know what you learned. If you learned that the probability distribution was a bell-shaped curve, what you learned was wrong.
They showed the curve, and the curve is not a bell-shaped curve. If you think a triangle is bell-shaped, then your problem is that you don’t know what ‘bell-shaped’ means.
Natural selection isn’t some outside force that changes the probability distribution. It’s just a label for the fact that if some trait makes you more likely to have more offspring, than that trait is more likely to spread in the population than if it didn’t have that effect. Do you really not see why a trait that helps you have more offspring is more likely to spread?
Reality determines which mutations are fitter and less fit. And yes, that’s always in the context of a particular environment. I have no idea where your confusion about natural selection lies, or why you think you’ve stumbled on some insight into the importance of ecology that evolutionary biologists have missed.
It becomes more obvious when you start to think about it. Temperature is the average kinetic energy of a system, so you have molecules speeding around and banging into one another. This is a random process. If you bring two materials together with different temperatures the warmer (i.e. faster) molecules will tend to transfer their kinetic energy to the colder (i.e. slower) molecules due to the random movement of the molecules. The same would apply to differences in gas pressure, or movement of dissolved salts in liquids. The random movement causes things to spread out.
Classical thermodynamics describes the results of stochastic processes but its description is not itself stochastic. Statistical thermodynamics is the subfield that deals directly with stochastic processes.
Doesn’t that mean that as long as there is at least a 1% possibility of a different outcome occurring that the process is a random one?.
That makes sense to me, so that is why this does not make sense. This definition makes the meaning of random so broad the it is almost meaningless.
Add QM to this also and what is not “random?”
I have studied the kinetic theory of matter. I would say that the moving molecules of gases give them the order of gases based on heat, pressure, mass, and probably other factors, not the random quality of kinetic motion. The moving molecules of liquids and solids the same. The motion of molecules is not random in relationship to heat.
Hot air rises and cold air sinks. It is not the randomicity that causes this, but gravity which gives weather order. Nature’s laws, including the laws of evolution, work and they are not random.in nature.
In addition I am not saying that probabilistic order is not order. On the contrary I would say that a probabilistic process is not random, because it has definite order.
It looks more like a step pyramid to me.
I guess the question is, Is there a reason why some traits are beneficial and other are not? Or is it all random, that is, is it all luck because no trait is more likely to be beneficial than another because they are all equally as likely to be beneficial?
If some traits are more beneficial than others than there must be a reason or a cause, unless we are talking about magic. If some traits are more beneficial than others we need to specify what traits they are and how they give an advantage, instead of being so broad that the statement cannot be tested. .
To be honest, while it is true that “luck” might play a role in everything we do, we make our own “luck.”
“Reality determines which mutations are fitter and less fit.” YES. Reality in the form of Natural Selection and the ecology. Thank you for finally saying it.
I know that I did not stumble on to something that everybody missed. Indeed every school child knows that it was climate change that did in the dinosaurs and gave the mammals their evolutionary advantage and Karl Popper and others have criticized Survival of the Fittest.
We need to put this issue of Natural Selection to rest before it destroys us It is not a science problem, but how we do science. .
These treatments are specific to particular systems, such as for example solvation of molecules - in such cases, often the system may be described (if possible) by forward and reverse rates, but the specific steps must be known. Equilibrium conditions may not be met, and at a molecular level QM ab initio models may be utilized.
Actually, many distributions in life are log-normal, often with fat tails.
It can be quite easy to model complex random interactions in Excel using the random number generator.
The movement of molecules/atoms is a dynamic process and is often dealt using kinetics. The particular treatment depends on the question asked; energies (enthalpy, Gibbs, entropy and so on) are usually based on properties and behavior of bulk (classical treatment).
Random is a semantic term and I cannot remember this as a scientific term (perhaps you mean entropy?).
Sure. In fact, you can treat deterministic processes as a special case of stochastic ones.
We find it useful.
All real-world processes probably have some random component. How important that component is and whether you happen to be focusing on it will vary.
So? Their individual motion is still random.
Your usage is fine as long as you wish to talk only to yourself. Otherwise, you’d better pay attention to how others use words.
Right – a discrete triangle. Which is not bell-shaped.
Of course there is. White fur on a rabbit is beneficial if it lives in snow, detrimental if it lives in a grassy field.
Sorry, but I’m not following you down this rabbit hole.
Maybe part of the misunderstandings are caused by the fact that natural selection is not the only process playing a role in evolution. Drift plays a role, especially in small populations, and drift is more or less stochastic.
If the number of individuals having an advantage in a particular environment is small, a rare event, such as a hurricane or a mad hunter, may kill most of these individuals. After such an event, the next generation would have less individuals with the adaptation favored by local selection process.
In a large population, the loss of few individuals does not matter much, so the endpoint may seem to be deterministic, although some individuals with the favorable alleles will produce less offspring than some individuals that lack those alleles.
I am trying to find out what is the difference between deterministic and random processes?
“In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables.”
If you define Natural Selection as a "random or stochastic process. then for you is will be a random or stochastic process, even if it objectively is a determinative process. A mathematical model is not the same thing a real life.
Evolution has both random and definitive elements. Variation is random and natural is definitive. Together they make evolution deterministic. Drift can possibly change this, but the factors that you mentions as possibilities are all aspects of the environment, so they are not outside my definition of natural selection as adaption to the environment.
The kinetic motion of molecules is described as random in the literature and I think that that this description as valid, using the definition for randomness as without order. On the other hand @T_aquaticus and @glipsnort ar4e defining all probabilistic mathematical models random, whether they are random or not. They are using a methodological definition of random, not a scientific one.
The kinetic random motion does NOT follow the laws of Newtonian non-random motion, that is, bodies in motion tend to stay in motion, and bodies at rest tend to day at rest. All molecules have heat or temperature and they all have kinetic motion, so they never at rest. Also for Newton every action has an immediate and opposite reaction, while for kinetic energy transfers energy by equilibrium .
Kinetic energy (heat), as opposed to kinetic energy (momentum) can increase and decrease, but never disappear. This would seem to indicates that the kinetic energy that is in our bodies right now originated in the Big Bang with the other kinetic energy in the world today.
Also @T_aquaticusis right that random energy does produce order. Kinetic motion is not directional, but is directed in all directions, which makes it random, but also means that gases are distributed evenly. That means that when we go outside that we do not have to be afraid of moving into a “pocket” where there is not enough oxygen to sustain life. The kinetic motion of molecules is random, without order, but the result is order as only God could create.
We know that the universe is designed by its Creator for the existence of rational life per the anthropic principle. Random kinetic energy is part of this. The fact that part of the process in random, does not make the whole random. The fact that mathematical models can help us to describe how nature is, does not mean that math is nature.
If they are probabilistic then they are random, by definition. If you could predict the outcome then you wouldn’t need probabilities.
" Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force."
Running into another gas molecule and changing momentum follows Newton’s first law.
The probabilities are not random. With the probabilities we can predict, so the outcome is no longer random.
Random does not mean running into another molecule and changing direction and momentum. .
The probability of drawing a specific card from a deck is 1 in 52. Can you predict which card will be drawn next?
The chances of rolling a 6 on a single die is 1 in 6. Can you predict the next roll of a die?
I think that you are making my case here. Drawing a specific card from the deck is a purely random activity, because we there is equal chance to draw any specific card, or one in 52. Knowing the probabilities that that help solve that problem.
On the other hand if I learn that there is a 30% chance of rain tomorrow, that is an valuable piece of information, because it tells me that rain is not random, but may be coming. My point is tghat there isa a huge difference in the character of these two situation, but to characterize them as both random, as if they were the some is misleading.
When I asked Steve @glipsnort about this point he said that they, scientists, find it useful. I do not find it useful and I can see no reason why it would be useful, although I may be stupid or something. I come from a tradition that says if something appears wrong you should question it, because it might be wrong.
“Reality determines which mutations are fitter and less fit…” @glipsnort
My reading of that statement, which is brilliant and true, is that Reality is Natural Selection, because that is exactly what Natural Selection does, “determines which mutations are fitter and less fit.”
Although I seem to disagree with Steve as to how Reality determines the fitness of a variation, the biggest problem is whether Reality is a random process like the drawing of cards from a deck or a non-random process like living one’s life. Dawkins and maybe you say that it is the first, while I say that it is the second.
Why is it misleading?
You aren’t stupid, you just lack the schooling. These types of topics are covered in university level physics and chemistry classes.
One of the strange features of nature is random processes that give rise to seemingly deterministic processes. This is especially true when looking at quantum effects at the atomic level and the results of those processes at the macroscale.
It’s useful because one uses the same machinery to handle random outcomes whether the outcomes have the same probability or not. Why is it useful to use one word to describe the result of rolling one die and another to describe the result of rolling two dice? Same process, but one has outcomes with uniform probability and the other doesn’t. Or suppose you carefully study your single die and conclude that one number is 0.0001% more likely to come up than the others. Why is it useful to change the word you use to describe the result of throwing that die?
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