Guv

Originally posted by Guv
In general, I do not understand many of your views. It might be due to our having fundamentally different world views. Many of your posts are clear, and I have no doubt that you are intelligent and knowledgable in many areas.
The reason we get stuck in a lot of cases is on the definitions of several diffuse concepts, in full practice we could agree on most issues but somtimes we disagree just based on fundamental concepts that relies on subjectivity nature.

Randomness is a component you try to eliminate because of it's unpredictability. To define randomness I'll mention two versions:

Boolean randomness
R is a boolean variable which can theoretically be given either false or true but in practice will be assigned false or true as a moment of it's evaluation. R(i) is an array of random boolean values which will be assigned true or false independently.

Probability and statistics is derived from the existance of randomness (unpredictability) and experience of randomness in order to eliminate (or minimize) it in certain issues, that is introducing randomness as a subjective concept into the world of predictability - math, for there to be any practical use of probability and statistics.

ex.
lim x->+infinity (S(n=1 to x)R(n))/n = ½

In practice x will approach a certain value and there will be certain probabilities that the result is 0 or 1, which is definitely not what you call "random" therefore randomness is subjective and depends on in what context you need unpredictability and what is acceptable unpredictability. In the above case if x approaches a big enough value the result has to approach ½.


Analogue Randomness

r is a Real value 1>=r>=0. Can be derived from boolean randomness R:
lim x->infinity (S(n=1 to x)R(n)/(n+1)) = r

r is more close to the rnd() function we use in vb since it returns a floating point variable.

Anyways, my point is that "pseudo random" is a bad term. For a practical case, an equation that needs introduction of a random element, the element has to be unpredictable in the POV of the case, not nessesarily anything else. Say the programmer of an algoritm to calculate a empirical probability could as well have programmed the random number generator as well and be able to predict all numbers generated, but that wouldn't matter since in the result the effect of randomness will be close to eliminated. IN some cases the same random number generator might be flawed, producing unexpected results, simply due to that it is not random towards a certain aspect of the algoritm.

ex.
an algoritm producing 10101010101010101... would still be random to
lim x->+infinity (S(n=1 to x)R(n))/n
but not to
lim x->+infinity (S(n=1 to x)R(2n))/2n

usually you introduce more complexity into the random number generator for it to be appliable for most cases, but it doesn't eliminate the system behind it, and in some cases the algoritm would give flawed results due to interference with the guts of the random number generator.


You seem to have some misgivings about so called random processes and statistical mathematics which I do not understand.
No, you have misunderstood me. I only want to point out the subjectivity of randomness, and that it is based on unpredictability.
The mathematics of statistics and probability theory are as well founded as the mathematics of differential equations. If you quarrel with the mathematics, you are attacking formal logic, which is behind almost every mathematical discipline.
I don't qwestion their practical use.
It is known that certain measurable phenomena are accurately modeled by the mathematics of statistics and probability. If you want to argue that the phenomena are illusions, that is a philosophical issue.
That is correct, but I don't argue for no reason at all, you mentioned pseudo random and chaos, and in practice you enter the philosophical issue in terms of subjectivity.
If you want to argue that the mathematics does a bad job of modeling the phenomena, you are wrong, or perhaps unwilling to accept some well established methods of logic and science.
I use and rely on math and logic all the time, more than most people do, and I value them high as tools, but I don't involve any blind faith in any of them.
If you want to claim that future developments will show that current beliefs are fundamentally flawed, you are being more subjective that the people (like me) who accept current science at face value.
Here you take one step further into a philosophical argument, I didn't intend to go into. You responded agressively last time I argued that a fact is a belief, and flaw refers to a incorrectness of information based on a objective reality for you while it refers to useless information, a very subjective concept, for me.
If I were unwilling to accept current science at face value, I would find it difficult to trust my computer, my auto, the bridges I cross, all of the gadgets of modern technology. My belief in science and disbelief in various forms of nonsense might be a very subjective view of the world, but it seems to work for me.
Anyways as said, I agree with you for the practical use of science.