Doesn't exist in any sense at all?

Of course God exists in various "senses". So does randomness. But not really!

True randomness is surely a miracle!

Randomness isn't an absence of any pattern. Most things which can be considered as random have patterns. The basic example is a fair coin, flipping it gives you 50% chance of heads and 50% chance of tails. So it's a random outcome, but the generating process for the random outcomes has properties that can be analysed and accounted for - in principle anyway.

...until you reach quantum level...

In which case predictions are made routinely.

I'm not sure that God could play dice. Because for me an essential feature of playing dice is not knowing what the outcome will be. Perhaps that's what Einstein meant.

Prediction is not incompatible with determinism.

I'm not sure that God could play dice. — andrewk

So She's "defeatable" by a concept called "randomnesss" ??

I wouldn't like to say. That way leads a discussion about the meaning of Omnipotence, involving questions such as 'Can God make a stone so heavy that He can't lift it?' (I use 'He' because the last time I debated these things was back when I was about eight, with my older brother, and that was before it was discovered that God was female.).

Only God could play dice, and win every throw. That is actually true. Jesus was notorious for winning at the races, and at Dirndle and at Russian Roulette. He had a 1 for one batting average at games of chance.

He eventually gave up gambling, because the random element that makes winning at games of chance addictive, was completely amiss in His history of gambling experience.

By the way, you're not alone in struggling with the notion of randomness. Most statements by philosophers that invoke the concept are pure nonsense, and I have yet to see a definition of randomness proposed by a philosopher that is not hopelessly circular. Purely epistemological definitions can be made, but most ontologists claim that they are inadequate - while being unable to suggest any non-philobabblish alternative.

Every mention of philosophical merit is ultimately circular.

The only variation is the size of the radius.

Randomness isn't an absence of any pattern. Most things which can be considered as random have patterns. The basic example is a fair coin, flipping it gives you 50% chance of heads and 50% chance of tails. So it's a random outcome, but the generating process for the random outcomes has properties that can be analysed and accounted for - in principle anyway. — fdrake

Some can, some can't. Letting 1 stand for heads and 0 for tails, a sequence such as 1010101010... can be generated by the deterministic process "start with 1 and alternate 1's and 0's". So this string isn't very random.

A string such as 11001001000011111101101010100010001000010110100011000010001101001100010011000110011000101000101110000000110111000001110011010001... seems random, but it's not. If you put a decimal point after the first two 1's, this is the binary expansion of pi. So the recipe, "Write pi in binary and drop the decimal point" deterministically generates this string.

On the other hand, many (most in fact) bitstrings (or infinite sequences of coin flips) do NOT have recipes or processes that generate them. The proof is that there are only countably many Turing machines but uncountably many real numbers; and we can turn any bitstring into a real number by putting a decimal point in front of it.

A bitstring can be said to be random if there is no Turing machine, or program, or recipe, or as you put it, "generating process" that cranks out its bits. If you threw a dart at the real number line, the probability is 1 that you would hit a random real; namely, a real number whose digits can not be generated by a finitely-expressible recipe.

There's a lot more to this idea. This is the Kolmogorov/Chaitin idea of randomness. A string is random if it can't be compressed to a simpler string. For example "print pi in binary and drop the decimal point" is a simple string that generates the seemingly random bitstring I showed earlier. Although the bits may well satisfy all the known statistical tests for randomness, the string is not random. In this case it's called pseudo-random. It looks random but it's not.

Note: I hope it's clear that there are short simple algorithms that crank out the digits of pi. That's why the decimal digits of pi aren't random. And since there's a deterministic algorithm to convert decimal to binary, the bitstring isn't random either]

https://en.wikipedia.org/wiki/Kolmogorov_complexity

A string such as 11001001000011111101101010100010001000010110100011000010001101001100010011000110011000101000101110000000110111000001110011010001... seems random, but it's not. If you put a decimal point after the first two 1's, this is the binary expansion of pi. So the recipe, "Write pi in binary and drop the decimal point" deterministically generates this string. — fishfry

Except that the mathematical concept of 'random' doesn't apply to strings of symbols. The concept normal can be used instead, but the expansion of pi is believed to be normal, although IIRC that has not been proved. As to whether the philosophical concept of random applies to them - we'll have to defer that question until somebody comes up with a non-circular, non-epistemological, non-word-saladish concept.

I don't understand your post, but I like it nevertheless. It sounds zen.

Who here can be satisfied with an "explanation" of.. "Oh it's just random" ..?

Who here can be satisfied with an "explanation" of.. "Oh it's just random" ..? — Jake Tarragon

Analogy. When our ancient forebears looked up in the sky, they saw a mighty hunter with his bow. That was their science, that was there belief, that's what their coastal elite believed, as it were. The received wisdom of their time.

From our lofty percth thousands of years in the future. we see it was just a random alignment of certain stars in different galaxies separated vertically from us, ie not in the same plane. It's only as seen from earth that there's even an imaginary hunter there at all.

Now in two thousand years, we may well look just as foolish. Quarks and gluons may look no more scientific to them than Orion the Hunter does to us.

Maybe it's all random. It's certainly possible. And humans -- consciousness -- is the subjective experience that tells stories about it.

I had in mind processes which are modelled using random variables rather than the conception used in algorithmic information theory. Most real numbers aren't computable and most real numbers' complexity is the same as having random bits for their decimal expansion, so in a sense the digits are patternless. This idea doesn't contradict random processes having patterns, just says that they don't necessarily have them.

The examples I had in mind were waiting times in queues and germination times in wild barley. Good to think of as random, but still contain patterns.

I don't know much about probability but I believe you. I'm not really sure what probabalists mean by randomness. Definitely not Kolmogorov et. al. Although Kolmogorov gets credit for the axioms of probability spaces. I'm in an area of my total ignorance so maybe I'll go look at some Wiki pages.

... ( a few mimutes later ) ...

According to https://en.wikipedia.org/wiki/Random_variable,

a random variable ... is a variable whose possible values are numerical outcomes of a random phenomenon.

Well! That is no help at all. What do they mean by a random phenomenon? There is no evidence that there is any such thing in the world. One could argue that a coin flip is 50-50 simply because we lack the calculational power to input all the physical variables like force imparted by your thumb, and the temperature and humidity of the air, and every other factor, and determine exactly how the coin will flip. If you don't believe that's true then you must think the laws of physics can not explain the motion of coin.

So I do not believe this definition is of any help. Certainly not to me. I don't know what a random phenomenon is. I strongly doubt that there are noncomputable real numbers instantiated in the world, since that would be an actual infinity in the world. Or perhaps a couple of centuries from now someone will discover a noncomputable number implemented as a subsystem of our brain ... I'm openminded about the present and the possible future of science.

I feel the same about algorithmic information theory, had to Wiki to make sure the vague recollections I had of incompressibility and complexity weren't bull-crap.

Though I can think of an example tying my point and your point together. Imagine we're drawing a data vector $X$ from a standard uniform distribution. This is one that starts at 0 and ends at 1. It's a standard exercise in probability textbooks to show that this is equivalent to an infinite sequence of independent binary digits:

$.X_1 X_2 X_3 ...$

with $P(X_i = 1) = P(X_i = 0) = 0.5$ for all $i$. So you can get an algorithmically random sequence through a translation of the $X$ (minus its element-wise floor).

Edit: there is a helpful idea of a random variable, I've posted it here before... Will try and find it. Found it!

Let $(O,S,P)$ be a probability space where $O$ is a set of outcomes and $S$ a sigma algebra on the set of outcomes, then a random variable $X$ is defined as a measureable function on $(O,S,P)$ to some set of values $R$. A measurable function is a function $X$ such that the pre-image of every measureable set is measureable (element of the sigma algebra in their respective spaces).

You lost me there a bit. The uniform distribution is the line segment y = 1 between x = 0 and x = 1. Yes? I'm trying to translate my math lingo to your probability theory. I'm fuzzy on this. An infinite sequence of coin flips defines a particular real number. Each individual sequence has probability zero, but the probability that SOME sequence gets hit is 1. That's because probabilities are only countably additive, so there's no contradiction. This is everything I know about it.

When you say "this" is equivalent to an infinite sequence of digits, I'm not sure what "this" is. An arbitrary sequence of digits represents one choice or one element picked "randomly" from the unit interval. That's how I understand this. But I'm not following the point you're making. You get algorithmically random sequences by noting that there are only countably many bitstrings whose bits can be generated by a program. But I didn't get your idea about translating somethign.

I studied a little measure theory but I don't know any probability theory. So I understand most of these concepts, but not the terminology.

It's a line at y=1 between x=0 and x=1, exactly. You can consider the infinite binary sequences (with trailing zeros) as numbers in [0,1]. Also, for the uniform distribution, each number is 'equally likely' (if you like measures the Radon-Nikodym density is 1 at all points in [0,1]). The fact that each number is equally likely in this sense can be shown to imply that if you 'throw a dart' into the interval, sampling a single number within it, its binary expansions' digits are fair coin flips with Heads=0 and Tails=1.

fair coin flips — fdrake

Such a concept is theoretical though and my point is that there is no randomness in physical processes if you delve deep enough.

Who here can be satisfied with an "explanation" of.. "Oh it's just random" ..? — Jake Tarragon

Hi Jake, I can be happy with an explanation that it is 'just random' by understanding the mechanism of the random number generator from which it arises (or realising that there is one).

If we imagine a tree whose branches grow out at random angles grow ever larger, longer and more complex, by understanding the initial conditions that gave rise to the randomness there can be contentment in the observation.

The secret of the randomly sprouting tree is in its code (not necessarily DNA), which allows a variable (or several variables) into its equation. The variable is an ever changing environmental value (heat, light, other plants, wind effects, soil quality, water supply etc).

I think that if there is a sentient God watching, he has set the initial conditions, and now watches in fascination as the randomness spreads through creation. The random bodies that evolve, themselves feed in as variables into other equations.

The key to success though is to have restraint in the code, and never moreso than at the base where it all begins.

If you look at a growing element like a tree, you will notice there are two type of growth happening. The first type stabilises the structure after it has passed through randomness, the second, on the fringes contains the most randomness (grow up, down, sprout a branch, bloom a flower).

If we imagine our tree in a harmonic motion, vibrating to some unseen frequency, then by controlling the base tightly the tree can maintain the resultant random motion without descending into chaos and collapse.

I hope that made sense.

What is the difficulty in randomness? You didn't mention.

To me, randomness is a feature of probability. A specific situation in which ALL events are equally likely.

Probability is a stand-in, a kind of approximation, where deterministic knowledge isn't possible, either due to complexity of the phenomenon or true probability.

My issue, isn't with randomness but with the notion of probability itself. They say the quantum world is probabilistic but, the point is, at a human scale - barring the brain, which may be subject to quantum phenomena - everything is subject to physical and chemical laws. Motion of objects can be predicted, chemical reactions can be predicted. What this implies is that probability at our scale - tossing coins and dice - is nothing more than our attempt to approximate complex, predictable (therefore not probabilistic) phenomena.

Randomness, being only a specific case of probability in which ALL events are equally lik.ely, is therefore moot.

I don't understand your post, but I like it nevertheless. It sounds zen. — andrewk

Ahem. A circular reasoning is one in which the assumption or premise plays a vital role in the system.

All systems depend on premises and logic.

The system can't prove anything that is outside of the system.

Therefore the system can only prove itself, and in doing so, it can only prove its own premises.

"God exists therefore God exists" is a singularly circular reasoning. "Beeelyuns and Beeelyuns of years ago" by Karl Sagan has much more many premises, but they all collapse into the proof of the material world, which is nothing but its own premises.

In the material world, premises are getting discovered and invented all the time, but it does not subtract from the fact that it is a system of circular reasoning.

Therefore I reject the argument "you are using circular reasoning". It is only valid insofar as to say something to the effect, or similar to, "your circular reasoning has fewer features than mine has, and which are essential parts of reality".

A circular reasoning is one in which the assumption or premise plays a vital role in the system. — szardosszemagad

I suspect you are the only person in the world to use that definition. For the rest of us, circular reasoning is where the conclusion is used as a premise.

I can be happy with an explanation that it is 'just random' by understanding the mechanism of the random number generator from which it arises (or realising that there is one). — MikeL

In other words you are not happy to accept "just random ". And if you are like me to do so would feel wrong because effects need causes. Einstein could have said "only God could play dice" rather "God doesn't play dice" because it would require a miracle to have an effect without a cause.

Here is a bit sequence:

A) 101010101010

Taken as a whole, is it meaningful to ask whether A is random or lawful "in itself"?

Here is another bit sequence

B) 101010

Isn't A only "lawful" relative to B?