Randomness

[Jeremiahcp]

I keep running into two different concepts of randomness, so I wanted to see what you all think.

Is random the unpredictable?

Or

Is random a situation with various possible outcomes?

 

[Deathbydefault]

 

[Jeremiahcp]

Because it can't always be both, as if you know all the possible outcomes then none of them are unpredictable.

 

[Quintessence]

Because it can't always be both, as if you know all the possible outcomes then none of them are unpredictable.

If we roll a d20, we know exactly what the possible outcomes are. Precisely what we end up rolling is still unpredictable (psychics notwithstanding). What we can say about the d20 is the probability of rolling something, but what the actual outcome is ultimately unpredictable (that is, when you roll the dice, you can't know you will roll a 13 or something).

At any rate, the term has different meanings in different disciplines and for different conversations. If you want a really good discussion about randomness, talk with your friendly neighborhood statistician. I have some background in that, but not enough to make it interesting.

 

[Jeremiahcp]

If we roll a d20, we know exactly what the possible outcomes are. Precisely what we end up rolling is still unpredictable (psychics notwithstanding). What we can say about the d20 is the probability of rolling something, but what the actual outcome is ultimately unpredictable (that is, when you roll the dice, you can't know you will roll a 13 or something).

At any rate, the term has different meanings in different disciplines and for different conversations. If you want a really good discussion about randomness, talk with your friendly neighborhood statistician. I have some background in that, but not enough to make it interesting.

"Precisely what we end up rolling is still unpredictable"

It is not really unpredictable as we know it has to be one of the 20 numbers. I may not know which one for a single roll, but I know all the possible outcomes. Heck,I could even say, "I will roll a three" and just keep rolling until that happens, because it is a predicable event.

"talk with your friendly neighborhood statistician."

You are talking to him, that is why I find this such an interesting topic.

 

[Jeremiahcp]

After looking into this a bit further this is my current conclusion:

Randomness is about control or lack of control and unpredictability is consequential. Probability is the proportion of the various possible outcomes of the repeated exercise of a random event. So while probability has a relation to randomness, it is itself not randomness.

 

[Quintessence]

"talk with your friendly neighborhood statistician."

You are talking to him, that is why I find this such an interesting topic.

Could you speak a bit more about how randomness is understood in statistical/mathematical contexts? Mostly for curiosity's sake.

 

[Jeremiahcp]

Could you speak a bit more about how randomness is understood in statistical/mathematical contexts? Mostly for curiosity's sake.

We must have posted at the same time. Just look at my above post. =)

 

[Quintessence]

We must have posted at the same time. Just look at my above post. =)

Hah... I was thinking more some citation or other from the literature, but I know that's a bit of a demand. What you wrote there sounds a bit philosophical. Making randomness being about control begs another question, after all - what is control? When we say "controlled" do we just mean "something humans believe they can govern and manipulate?" Do we mean something else? How does determinism (or lack thereof) play into it?

 

[Jeremiahcp]

Hah... I was thinking more some citation or other from the literature, but I know that's a bit of a demand. What you wrote there sounds a bit philosophical. Making randomness being about control begs another question, after all - what is control? When we say "controlled" do we just mean "something humans believe they can govern and manipulate?" Do we mean something else? How does determinism (or lack thereof) play into it?

"Hah... I was thinking more some citation or other from the literature, but I know that's a bit of a demand."

There might be a formal definition somewhere in one of my books, but over all statistics tends to focus on the use of randomness. Random sampling and random assignment (think designed experiments) are used to approximate a normal distribution, and to avoid observational bias. This is partly where I draw the notion of control, as in order to gain both random sampling and random assignment we give up control.

Take your dice example, yes the outcomes are predictable; however, when you toss the dice you give up control on which side it will land. Are there forces that we can't see that will cause a certain number to be rolled? Maybe? Who really knows, and any argument of determinism can only be reduced to unfalsifiable positions.

"What you wrote there sounds a bit philosophical"

That's funny you should say that, because I did run this question by some philosophers.


**Edit: However, I should note that by designing the dice with 20 sides we are actually controlling the possible outcomes to some degree. So maybe the dice is not the best example, but I think it still expresses the point.

 

[Jeremiahcp]

If I look in my books, the closest I can find is the definition of a random sample.

A simple random sample (of size n) is a subset of a population obtained by a procedure giving all sets of n distinct items in the population an equal chance of being chosen.

So I think my understanding holds, but only because each item is given an equal chance, which removes any control we would have on which samples are selected.

So, back to the dice, yes we are controlling the number of possible out comes; however, assuming each side has a fair chance then we are not controlling the outcome, so in that sense the out come can be considered random.

 

[Jeremiahcp]

I suppose someone could make the argument, that there is a formal and informal interpretation of random. Used colloquially random can mean the unpredictable.

 

[Skwim]

Randomness does indeed have different meanings. Commonly, it indicates an outcome we're unable, for whatever reason, to predict, like the roll of dice. Uncommonly, as in the free will Vs. determinism issue, it means "utterly random"; an outcome that has absolutely no cause whatsoever. An event that could just as well be as not be. The common forms of randomness do have causes, but we just don't have the time or wherewithal to figure them out so as to know their combined outcome.
As for different possible outcomes, for common randomness there is no such thing. For "possible" outcome B to emerge rather than "possible" outcome A, something among the causal factors would have to necessarily be different. So the question is, Was there? If so then outcome B has to happen. If not then outcome A has to happen.


.

 

[Jeremiahcp]

The more I think about it, the less sure I am that randomness exist outside our control. You don't find situations in nature where all the various possible outcomes have equal probability. That is something we have to create.

I understand there are informal uses of the word random, but those are very subjective and typically used to express some underlying concept. True randomness may be something we invented.

 

[Parchment]

I keep running into two different concepts of randomness