786:
Also Statistics has not proof for a random event.
That's true. Statistics requires a series or collection of events or observations that can then be analysed for patterns of randomness. Or, to look at it another way, statistics tells us what properties to expect from a number random events taken as a set.
The only thing they can observe is a "random process" which is a series of tries. But the observation that the series of tries leads to a probability curve actually is not proof that a single event is random. That is why in statistics sample size is very important. They can not make any conclusion about a single event.
That's also true, but it requires a little qualification. It is possible to do statistical tests on sets of events, and statistics predicts certain outcomes of those tests. The predictions come from analysing what we'd expect
if the events were truly random. Therefore, if in fact we observe a deviation in the statistical measures from what the assumption of randomness predicts, then we
know that the events were not truly random. On the other hand, if the actual events match what statistics predict, then either (a) the events really were random or (b) the events were very cleverly arranged to give the appearance of randomness.
Every single mutation is a single event- the randomness of each single event is not proved by any theorem.
Are you talking about mutations in biological organisms? That is one of the cases that can be studied. For example, if we look at the frequencies of certain mutations in DNA, we find that they match exactly what we'd expect if the mutations were truly random. Therefore, we conclude either (a) these mutations really are random or (b) something has cleverly arranged for them to mimic true randomness.
If you want to argue that God directs mutation (as I suspect you do), then He is apparently limited (or limits himself) to directing it in a way that is indistinguishable from true randomness.
The application of mathematics is more important. Physics! You could predict the outcome of a coin flip if you would take in account all the properties of the coin and all the forces and Laws that act on it and also the material it will land on. Perhaps not accurately at the moment due to the fact that we can't assume that we have complete knowledge of physics yet. Anything other than what was predicted by physics would be considered "random" but this is because we don't know everything about it yet. So again "random" is only a conceptual word used to define an anomaly for which we currently do not have an explanation (something Atheists usually equate with God)
This is not quite right. There's no problem with our understanding of the physics of a coin toss. We know the physical laws that govern the motion of a coin quite well. The problem is knowing the initial conditions of a flip - the initial orientation of the coin, how much force is exerted on the coin, where it is applied, for exactly how long it is applied, the precise initial angle of the coin and the hand flipping it, the precise effects of air resistance as it flips in the air etc.
If we knew all those things, then in principle the result would be predictable. But this doesn't mean the outcome as far as we can predict it is not truly random. Coin tosses, although they are
deterministic, are
chaotic and therefore unpredictable from the information available to us under ordinary conditions.
If we flip a coin 100 times, on average we'll get 50 heads and 50 tails, but the precise sequence of heads and tails is essentially unpredictable - random. Now, if we were to flip a coin and find that it landed heads 100 times and tails no times, then there's a large probability that something non-random would be going on - perhaps it's a two-headed coin, for instance. The consistent 50-50 proportion confirms that individual flips are random. And not only that proportion, but also the extent to which multiple runs of 100 flips
deviate from a precise 50-50 result, which is one focus of the subject of statistics.
Physics should be able to predict a coin flip if they were told all the variables. Unless you are saying that there is something outside of the laws of physics that act upon the coin? (You can include quantum physics if you want)
No, of course not.
It is worth mentioning, however, that some quantum effects
do have the kind of absolute randomness you're looking for. An electron can be put into what is called a
superposition of two equally-likely spin states, for example. When a measurement of the state is made, the result is truly unpredictable (random), as far as our best current theories of physics can tell. This is not the same as for the coin flip, which is in principle predictable but practically unpredictable. The quantum effect is not predictable even in principle.
Actually no, I'm trying to point out that something which we call a "random number" can not be proven to be random, mathematically.
That's a kind of obvious point. Is 17885 a random number? The question is essentially meaningless. (I've read your article on information theory and randomness linked above; it uses a "different" definition of randomness from the usual.)
Randomness is defined and measured- but only because it is a concept that we use for anything that we currently can't explain- this doesn't attest to its proof or as some sort of actual explanation.
That's not true. There are mathematical rules or "laws" of randomness, as I've explained above. The label "random" can't just be applied to anything we don't understand. Randomness has certain statistical properties that are testable.
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I'm not sure how any of this is relevant to the "God of Science". Are you saying that the concept of randomness replaces God in science?