What's this bizarre obsession with the uniform distribution? There is no uniform distribution on N or R... So, no scientist will assume that it applies for the hole universe.
And I fail to see how your post is related to my post #53.
Again, one cannot say something is random in the system if he does not know what the system "is."
And we cannot say that something is a straight line if we don't see the hole line.
Do you see the problems with your statement? In the physical world, there is nothing we know to be a straight line - and there is nothing we know to be random. Doesn't stop us from doing geometry or probability theory - and geometrical or statistical physics...
I'm pinging a few others who might be interested in some of the following.
Depending on the circumstance, all possibilities may or may not be equally probable.
When a person buys a lotto ticket in a field of a hundred million purchases of lotto tickets, the odds of his winning the prize is announced as a ratio of 1 in a hundred million. That is combinatorics. It is blind like a roll of the dice. Each possibility is equally probable to win the full prize.
But of the hundred million people buying lotto tickets, some are using numbers which represent important things or events in their lives, and very often those numbers are birth months and days. Because there are only 12 months in a year, 28-31 days in a month – and the range of numbers from which to choose ordinarily exceeds those limits --- the odds of such a purchaser winning the total prize amount is significantly diluted. Which is to say, there exists a greater probability of certain number selections and multiple winners having to split the prize. That is Bayesian probability. It is not blind. Each possibility is not equally probable to win the full prize.
If the sports book were based on combinatorics, it would be bankrupted quickly because the possibility of each team winning is not equally probable. Conversely, in sweepstakes each ticket is equally probable to win the prize.
In the crevo debates on this forum, both sides advance either combinatorics or Bayesian probability depending on how they wish to advocate in the debate.
betty boop and I, on the other hand, promote full disclosure.
As an example, Jewish Physicist Gerald Schroeder uses combinatorics to point out that a single typical protein is a chain of 300 amino acids, and that there are 20 common amino acids in life, which means that the number of equally probable combinations that would lead to the actualization of the protein would be 10390.
Conversely, theists often argue that this universe is improbably finely tuned for life - that the laws of physics are precisely tuned so that life will appear in this universe, e.g. the speed of light and the fine structure constant. [The following is paraphrased and/or excerpted from our book, Don't Let Science Get You Down, Timothy.]
Ditto for the strong nuclear force. If it had been just 13 percent stronger, all of the free protons would have combined into helium-2 at the early stage of the big bang, decaying right away into deuterons, which would then fuse to become helium-4. There would be no hydrogen, no water, and no hydrocarbons. A decrease of approximately 31 percent would make the deuteron unstable and remove a step in the chain of nucleosynthesis. Consequently there would be nothing but hydrogen in the universe.
And water, too. The hydrogen bond is the attraction of the electron-rich oxygen atoms of water molecules for the electron-starved hydrogen atoms of other water molecules. This in turn determines the precise H-O-H bond angle of 104.5 degrees. This hydrogen bond is what holds together the two strands of DNA — it also causes the crystalline structure of ice (an open lattice), which is less dense than the liquid form. Thus, ice does not collect at the bottom of lakes and oceans — building up to a frozen earth. Instead, the ice on the surface acts as an insulation, which prevents evaporation and keeps the water beneath warm. No water, no life as we know it.
There’s an even more unlikely process in carbon resonance. Within stars, two helium-4 nuclei merge to make beryllium-8, which only exists for about 10–17 of a second. So a third alpha particle (helium nucleus) must collide and fuse with the beryllium nucleus in a tiny interval of opportunity in order to make carbon. Lucky for us that there is a resonance in the three-helium reaction at the precise thermal energy of a star’s core. If it weren’t so, then most carbon would be quickly processed into oxygen. Again, no life.
But so the debate goes on - combinatorics v Bayesian probability.
But betty boop and I promote full disclosure.
Thus whenever a correspondent advocates that a certain thing in nature is “random” we hold his feet to the fire. He is using combinatorics to make that claim – all possibilities within the scope of the investigation are equally probable - a uniform distribution.
Nor will we stand idly by while he attempts to project the observation in a sample to the whole. (An element of the "observer problem.")
As an example, in the extension of pi - a sampling of numbers from the extension may be random to the observer doing the sample - but because we can and do know what the system "is" - we know it is not random at all, but highly determined by calculating the ratio of the circumference to the diameter of a circle and extending it to the furthest position (n) from which the sample was extracted (3.14159265358979323846...n)
Likewise, a random (uniform distribution) observation in a sample may be belied by correlation observed in a larger sample or in the whole. Causation and no boundary in the extension is why random number generators such as Chaitin's Omega are only "pseudo-random." The same can be said for observations in nature, e.g. physical causation or origins and boundaries of space/time.
Without making the observation, it is impossible to claim uniform distribution. And the extent of physical reality (cosmos, universes, dimensions) is both unknown and unknowable.
Moreover if the correspondent advances “randomness” or “equal probability” in one instance – e.g. quantum mechanics – and then decries it in another, e.g. in Schroeder’s analysis of the probability of proteins – we will call him on the inconsistency and ask him to justify how in one instance each possibility is equally probable while it is not in the other.
Ah! the observer problem again.. In all the great big relativity telescopic view or in the little bitty Quantum Physics microscopic view of stuff, geometry is twisted like a pretzel.. in a three(some say four) dimensional sense.. You know the world of flesh and bone..
If there is a fifth(n#) dimension say a Spiritual Dimension as meta-physicists suppose then geometry could be obsolete.. Maybe SHAPE could be a 3D concept.. if "spirit(s)" could morph into whatever shape.. i.e.. geometry would be silly in that dimension.. There the father son and holy spirit (and others) could merge or separate for some function.. and then re-merge.. Are we merging here? LoL.. Anyway.. my observations go along those lines.. Locked into a geometrical flesh box is just not my cup of tea.. You know sense we're "if'n"...
You see the way I see/observe it.. Humans obsess on shape.. Everything has to have a shape and lines of demarcation.. When that may not be absolute.. Male, female, tall, short, animal, rock, or plasma.. Quantum Mechanics can compute plamoid.. What if spirits are shape shifters.. plasmoidal.. It could then be "relatively" easy for God to become Jesus.. or for Satan to become Hillary Clinton(sic)..