God's foreknowledge and free will

GrowingSmaller

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Think of the hypersurface of the present in physics, i.e. all the world and skies, heavens etc viewed as a flat sheet.


Next reduce that sheet by another dimension into a hyper-line, so you have a light-sheet rather than a time cone coming from it.

Then reduce that line to a hyper-dot, the hyper-dot of the present, so that the "light cone" emanating from it becomes not a cone, not a sheet, but a light-line.

There we have it, a path it is not possible to veer from, the light-line of the future:


_______________________________________________________________


But, just as photons can have wavelengths, maybe we can have moral influence in a deterministic world?

Our freedonm is not to somehow fall off the line, but to change wavelength!!!


So we habve "sirat al-mustaquim", the "straight path" in Islam, but it is also fitting correct proper etc.

Just as we can imagine spilt tea on in the world around us, also in a light cone, a sheet, a line....

Just as we can imagine a badly lived life, like spilt tea, like the wrong frequency of light etc, all possible in the one line of action.

Note, a light cone diagram from Wikipedia:



481px-World_line.svg.png
 
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elopez

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No. I just don't require the notion to explain my thoughts on free will.
Perhaps it is not required of your view but I still do not think it can be neglected, either. Free will is about choices, and choices are related to desires.

Past experience is one factor, but not all the factors necessary to determine my future actions. So, no, past experience does not explain a full causal determinism.
Right, and I'm not saying past experiences is the only factor. As I stated, environmental, psychological, hereditary. Just to name a few.

Sure. I did it right here in this thread. I had never before seen someone apply formal logic to free will concepts. I had no reason to think someone might have done it. I had no reason to think it could be successfully done. I just started tossing out some arbitrary possibilities off the top of my head in post #145. But once the idea came to me, I did a search and found someone had done it.
You did have reason to think someone had done it. You even said in that post that was the first thing that crossed your mind. You know what formal logic is. You know what free will is. To even have started to spout off those arbitrary possibilities you would have to know what formal logic even is, which is something you learned in the past. Your past learning of formal logic, along with your past learning of free will and your conception of it, along with various other factors all are relevant here. I don't believe this a great example of a choice with no antecedent factors.

I wouldn't say I am, no. How would you establish that you are the sole originator of your choices?
When I said "I am" I meant I am asking that question of your view. That's really what I was asking in the above though, and to which you went on to attempt to explain.

Hmm. I don't see how this squares with your previous statement that you are the sole originator of your desires.
I didn't say that.

You're personifying "experience" in a very Platonistic way that I don't accept.
Well I'm borrowing from Philip Burnard's musings on experiential knowledge. Whether that is Plantonstic or not I am not sure.

I don't care. I'm just trying to guess what it is you want. You seem to think you've said all kinds of things, but IMO you've said very little that is substantive. You want me to show you how my view works, but how exactly do you want me to show it? I'm still looking for that common ground. Do you think we've found any?
Like I said I was trying to further understand your view. And like I also said I've said nothing more than what I have. I have really just been asking you questions of your view.
 
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Resha Caner

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You did have reason to think someone had done it. You even said in that post that was the first thing that crossed your mind. You know what formal logic is. You know what free will is. To even have started to spout off those arbitrary possibilities you would have to know what formal logic even is, which is something you learned in the past. Your past learning of formal logic, along with your past learning of free will and your conception of it, along with various other factors all are relevant here. I don't believe this a great example of a choice with no antecedent factors.

I thought you might answer this way, and so I think it's a very good example. I've never claimed to be completely free of the past, and my example shows that. What I said is that my future actions are an organization of what is available to me according to how I choose. Cases where that creates something new are the easiest to identify, and that is what I did. I took what was available to me from past knowledge, organized it according to the discussion in this thread, and produced a new proposal - a thought I had never had before.

You may not believe that, but you're going to be hard pressed to prove I've ever had such a thought before.
 
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Job8

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The question arises when does God know what the outcome will be? God always knew? God knew just before you decided? What questions does this raise about God being in control?
Why should God's foreknowledge raise any question about "being in control"? "Being in control" is a false concept of God's sovereignty. Had God planned to "be in control" of every circumstance and situation, He would not have created anything that can make choices and decisions. All you would have is the vegetable kingdom.
 
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elopez

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I thought you might answer this way, and so I think it's a very good example. I've never claimed to be completely free of the past, and my example shows that.
Well this is what I was inquring of "I can, for example, guess, predict, or create; I can invent an organization that has no corresponding experience."

I asked of that statement: "Give an instance of say, something you can create which has no past corresponding experience"

You went on to respond to that inquiry, so I thought perhaps you were speaking of past factors. You did say no corresponding experience, which seems to mean no experience at all, which of course would include any and all past experiences.

I realize you said "I wouldn't say I am, no." when I asked if you were the sole originator of your desires or choices, but that was right after you had said what was mentioned above. It was just a little confusing.

What I said is that my future actions are an organization of what is available to me according to how I choose. Cases where that creates something new are the easiest to identify, and that is what I did.
Yet those future actions you cited are only available to you now due to the past. And you didn't really create anything "new"; the concept (free will theorem) had already been around for a decade. "New" to you maybe.

I took what was available to me from past knowledge, organized it according to the discussion in this thread, and produced a new proposal - a thought I had never had before.
Right, yet none of this defies determinism. Especially considering you had to organize your new thought based on past factors.
 
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Resha Caner

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It was just a little confusing.

I understand why that would be. My phrasing wasn't perfect. I'm trying to feel my way through some new ways to explain this to you. :p

"New" to you maybe.

That's irrelevant. Maybe some desert nomad discovered non-Euclidean geometry in 452 B.C. and died on his way back to the village to tell everyone. That doesn't make the work of Lobachevsky frivolous and derivative.

Further, as I said, speaking of the new was just the easiest way I could think of to explain it. I've chosen to eat Mexican food in the past. Yet choosing to eat it today can be due to conditions that have never before arisen. So, to you, observing me externally it appears I've repeated a past choice when that may not be the case.

Right, yet none of this defies determinism. Especially considering you had to organize your new thought based on past factors.

It's the very essence of defying determinism. Not everything involved was a past factor. There was a DOF my friend. Again, this isn't an all or nothing situation. You need to think of the pieces going into it.

I've always found it curious when my "opponents" beat on a point that is rock solid - especially when the weak point seems so obvious to me. I usually know what the weak points in my positions are, but in days past when my aims were more about winning debates, I wasn't about to reveal them. In this case it doesn't matter, so I'll tell you.

The weak point of my view is not that I am in danger of describing something that is indistinguishable from determinism. That is your weak point. My weak point is that I might be describing something that is indistinguishable from randomness.
 
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elopez

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I understand why that would be. My phrasing wasn't perfect. I'm trying to feel my way through some new ways to explain this to you. :p
Lol! :laughing:

That's irrelevant. Maybe some desert nomad discovered non-Euclidean geometry in 452 B.C. and died on his way back to the village to tell everyone. That doesn't make the work of Lobachevsky frivolous and derivative.
Yeah, but that's not exactly what I am saying. It would be more like if someone were to attempt to do the work presently, that was done in the 19th century by Lobachevsky. It wouldn't be anything "new" in any sense of the word, less you were to equivocate.

Further, as I said, speaking of the new was just the easiest way I could think of to explain it. I've chosen to eat Mexican food in the past. Yet choosing to eat it today can be due to conditions that have never before arisen. So, to you, observing me externally it appears I've repeated a past choice when that may not be the case.
What conditions would those be that have never arisen? It's not the first time you would have ate tacos. It wouldn't be the first time you neglected what you want to make your wife happy. You didn't develop some newfound acquired taste for tacos. How is eating tacos not a repeat of a past choice?

It's the very essence of defying determinism. Not everything involved was a past factor. There was a DOF my friend. Again, this isn't an all or nothing situation. You need to think of the pieces going into it.
So what exactly wasn't a past factor? DOF as in degree of freedom? Even then, the only relevant factors involved are antecedent factors. Your introduction to tacos at whatever age. Your past meals of tacos. Etc.

The weak point of my view is not that I am in danger of describing something that is indistinguishable from determinism. That is your weak point. My weak point is that I might be describing something that is indistinguishable from randomness.
Well let's remember your point of view is that not everything is determined. If you can't describe something that is distinguished from a determined event, that point of view is unfounded. Would you say you "theorem example" is an instance of randomness? What is randomness according to your view?
 
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Resha Caner

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Yeah, but that's not exactly what I am saying. It would be more like if someone were to attempt to do the work presently, that was done in the 19th century by Lobachevsky. It wouldn't be anything "new" in any sense of the word, less you were to equivocate.

It could still be new if the person doing it was unaware of past work. Because of that ignorance, the past work would have no impact on what was done in the present.

In terms of our discussion here, just because God knows A1 -> E1 (person A1 caused event E1) doesn't mean A2 -> E1 (it doesn't mean person A2 who is unaware of E1 is determined to also cause E1).

What conditions would those be that have never arisen? It's not the first time you would have ate tacos. It wouldn't be the first time you neglected what you want to make your wife happy. You didn't develop some newfound acquired taste for tacos. How is eating tacos not a repeat of a past choice?

It's not a repeat because of the reasons causing the choice. I'm tempted to turn the question back on you and ask you to think of a situation. The effort might do more to help you understand than me providing them to you. So, let's go deeper into my history. Why did I first have Mexican food? What prompted me to eat something I had never eaten before? I ate my first taco because my dad took me to a Mexican restaurant after a golf game when I was young.

After that, there were several different reasons for choosing to eat Mexican on subsequent occasions. I'll give you one - because it became a "thing" for me and my dad. We ate Mexican after every golf game.

Now your turn. What might be a new reason for me to choose Mexican?

Well let's remember your point of view is that not everything is determined. If you can't describe something that is distinguished from a determined event, that point of view is unfounded. Would you say you "theorem example" is an instance of randomness? What is randomness according to your view?

"Random" can be used in several different contexts.

Type 1: Mathematical randomness
1A: Having a uniform probability distribution
1B: Having some known probability distribution in addition to deterministic factors
1C: Having some known probability distribution

Type 2: Descriptive randomness
2A: An event occurs that can't be described via known deterministic factors
2B: An event occurs independently of the factors under control
2C: An event occurs independently of all factors operating on a closed system

... and there may be others.

Type 2A is usually a matter of being human and not something God would experience. It simply means an event could have determining factors but we don't know what they are. This is the type of randomness that comes up in quantum physics with things like quantum foam where particles and anti-particles are randomly appearing and disappearing. That such events might have a cause can't be ruled out, but it's unlikely we'll ever determine a cause. I believe some physicists would disagree with me on that, and would say it's more a type 2C randomness, i.e. that it is random rather than merely appearing to be random. What bugs me about that, however, is that they use type 1C to codify it, which to me implies unknown deterministic factors. If it were truly random, it seems to me they would use type 1A to codify it ... but that's a long digression from our topic here.

Type 2B is the type discussed in things like evolution and signal processing. When evolution speaks of random mutations, as I understand it they simply mean outside factors cause the mutation that are not dependent upon the DNA itself. The same happens in signal processing - something I'm more familiar with. When someone says a signal has noise, they simply mean outside factors are disrupting the signal (e.g. someone's CB signal cuts into the radio station I'm listening to in the car). It's not as if I don't know what caused it. It's just that I'm not going to install some device that jams every CB signal so I can listen to the radio. So, that situation is codified via 1B.

Noticed I said type 2A is usually a matter of being human and not something God would experience. However, it can also relate to the logical impossibilities of an undetermined future. It's just that distinguishing between the two is extremely difficult. So, even further, there is a type 2Ai and 2Aii, but separating those two is tough.
 
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ecco

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"Random" can be used in several different contexts.

Type 1: Mathematical randomness
1A: Having a uniform probability distribution

If you are saying that a random number has "a uniform probability distribution", I'd ask for the basis of your assertion.
 
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Resha Caner

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If you are saying that a random number has "a uniform probability distribution", I'd ask for the basis of your assertion.

You truncated my list. 1A is one way to describe randomness, but not the only way. And even then I was trying to indicate there is not always agreement on how to relate observations of randomness with mathematical codifications of randomness.

Do you have a problem with randomness described as a uniform distribution?
 
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ecco

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ecco said:
If you are saying that a random number has "a uniform probability distribution", I'd ask for the basis of your assertion.

You truncated my list. 1A is one way to describe randomness, but not the only way. And even then I was trying to indicate there is not always agreement on how to relate observations of randomness with mathematical codifications of randomness.

Do you have a problem with randomness described as a uniform distribution?
Yes, I truncated your list. I was specifically interested in, and asked about, the basis for your assertion that a random number has "a uniform probability distribution".

If you don't want to answer, that's OK.
 
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Resha Caner

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I was specifically interested in, and asked about, the basis for your assertion that a random number has "a uniform probability distribution".

I've no problem telling you. I'm just curious why you singled out that particular item.

I think of a uniform distribution as "absolute" randomness. Think of a dart board with the bullseye (the innermost circle) as your target. 1) Were I to let you walk up to the board and place your darts, I expect they would all end up in the bullseye. That is because you caused them to be placed there - there is a determining factor. 2) If I then made you step back 8 feet and throw the darts at the board, I might expect some kind of beta distribution for the distances of the dart from the bullseye. There is still a deterministic factor involved - your focus on hitting the bullseye - but other random factors that you can't control have entered to create a scatter. So, it seems any shaped distribution is a combination of deterministic and random factors. 3) If you stand before a plain white wall with no target, and all I say is, "Throw darts at the wall" such that you proceed to throw with no focus on a target, I would expect the scatter to increase. As we approach an absolute randomness - no deterministic factors at all are involved - it seems to me we would approach a uniform distribution. Anything else indicates a preference of some kind.
 
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elopez

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It could still be new if the person doing it was unaware of past work. Because of that ignorance, the past work would have no impact on what was done in the present.
Ignorance =/= New.

In terms of our discussion here, just because God knows A1 -> E1 (person A1 caused event E1) doesn't mean A2 -> E1 (it doesn't mean person A2 who is unaware of E1 is determined to also cause E1).
Indeed, this is something I mentioned earlier. What foreknowledge deals with in terms of human agency is the nature of God's knowledge of future contingents, and what that implies.

It's not a repeat because of the reasons causing the choice.
The reason causing the choice doesn't matter; it's a repeat as the experience is being performed again. And still, any reason would have a correlation to an antecedent factor.

Now your turn. What might be a new reason for me to choose Mexican?
Cause' it's taco Tuesday and they're half off at the new Mexican joint down the street.

"Random" can be used in several different contexts.
Yes, but I was asking in what context, and to what meaning you were using random.

So, even further, there is a type 2Ai and 2Aii, but separating those two is tough.
It seems you mean randomness in a QM sense? "Type 2: Descriptive randomness
2A: An event occurs that can't be described via known deterministic factors"

Type 2A is usually a matter of being human and not something God would experience.
Right, cause' God, as you indicated, is the first cause. You can't really give up the concept of cause/effect when it comes to God and the universe.

It simply means an event could have determining factors but we don't know what they are. This is the type of randomness that comes up in quantum physics with things like quantum foam where particles and anti-particles are randomly appearing and disappearing.
It is my understanding that QM is about how on sufficiently small scales, particles stop behaving like particles and start behaving like waves, more than it has to do with human choices and free will. Now, I'm not saying QM strictly explains the microscopic, as of course it can be used to help understand phenomena like superconductivity, which is macroscopic. Still though, that is not relevant to human choice.

And although it's not possible to predict an outcome on QM, all one can do is calculate the probability of one outcome vs. another. These probabilities can be calculated directly from the particle's wavefunction. The probabilities themselves are still things that we can calculate and compare with experiment.
 
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Resha Caner

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Cause' it's taco Tuesday and they're half off at the new Mexican joint down the street.

Yea! You did it! You just created a new choice different from my first my reason for eating a taco. So now everything is clear, we agree, and we're ready to move on ...

The reason causing the choice doesn't matter;

... or maybe not.

This is a very odd statement you will need to explain, because the reasons behind a choice are crucial to this discussion ... as well as the ignorance of the agent to what other agents might have done.

It seems you mean randomness in a QM sense? "Type 2: Descriptive randomness
2A: An event occurs that can't be described via known deterministic factors"

With respect to the difficulties I have with my idea, yes, that would be the type that would apply (And I think it was important to describe some of the varieties to help you hone in on the pertinent one). I know of no way to definitively establish that something is random or is a decided choice. The best I can do is say it feels like a choice, and make the appeal to a fellow theist that it would be strange for God to make it feel like a choice if it weren't. If you reject that, there isn't much I can do about it ... but at least I've got no logical contradictions to wrestle with.

And although it's not possible to predict an outcome on QM, all one can do is calculate the probability of one outcome vs. another. These probabilities can be calculated directly from the particle's wavefunction. The probabilities themselves are still things that we can calculate and compare with experiment.

Your point? If you're trying to make probabilities sound determined, that would be an abuse of the concepts. Have you ever read Asimov's Foundation? He makes a lot of government authorities falling prey to thinking probabilities mean certainties; it's the point on which his plot turns.
 
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ecco

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Resha Caner Previously said:
"Random" can be used in several different contexts.

Type 1: Mathematical randomness
1A: Having a uniform probability distribution
1B: Having some known probability distribution in addition to deterministic factors
1C: Having some known probability distribution
I've no problem telling you. I'm just curious why you singled out that particular item.

I think of a uniform distribution as "absolute" randomness. Think of a dart board with the bullseye (the innermost circle) as your target. 1) Were I to let you walk up to the board and place your darts, I expect they would all end up in the bullseye. That is because you caused them to be placed there - there is a determining factor. 2) If I then made you step back 8 feet and throw the darts at the board, I might expect some kind of beta distribution for the distances of the dart from the bullseye. There is still a deterministic factor involved - your focus on hitting the bullseye - but other random factors that you can't control have entered to create a scatter. So, it seems any shaped distribution is a combination of deterministic and random factors. 3) If you stand before a plain white wall with no target, and all I say is, "Throw darts at the wall" such that you proceed to throw with no focus on a target, I would expect the scatter to increase. As we approach an absolute randomness - no deterministic factors at all are involved - it seems to me we would approach a uniform distribution. Anything else indicates a preference of some kind.

I agree somewhat with 1A. A long string comprising 1000 randomly selected binary digits would show a "uniform probability distribution" insofar as the ratio of ones and zeros would be close to 50/50. However, a short string comprising randomly selected binary digits could be 11111101. There is no uniform distribution apparent.

If something has "deterministic factors" it is not descriptive of randomness.

If something has "some known probability distribution" it is not descriptive of randomness.

I would have to disagree that your three examples are indicative of "Mathematical randomness".[/QUOTE]
 
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Resha Caner

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However, a short string comprising randomly selected binary digits could be 11111101. There is no uniform distribution apparent.

Sure. Probability doesn't deal well with small sample sizes. However, were the string to be 1111110111111111111111111111111111111111111111, the probability of that coming from a system with a uniform distribution is extremely small - to the point that I would doubt it is a uniform distribution. I would consider it very deterministic with one error.

If something has "deterministic factors" it is not descriptive of randomness.

My point was that it's not either/or. I keep getting this feeling people are thinking in very black & white terms. A system can have a mix of deterministic and random variables. As such, that shapes the distribution.

If something has "some known probability distribution" it is not descriptive of randomness.

That you'll have to explain. While your example for small sample sizes and specific instances is true, it has been shown time and again that past data is a good predictor of the future - even for random data. If you're being pedantic about my use of the word "known", I'll concede you're right on a technicality. Maybe I should have said a "representative" probability distribution, or "estimated" - something like that. I think the category is still a proper one.

I would have to disagree that your three examples are indicative of "Mathematical randomness".

Please provide your version then.
 
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elopez

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Yea! You did it! You just created a new choice different from my first my reason for eating a taco. So now everything is clear, we agree, and we're ready to move on ...
Not so fast. I chose this example for a reason. While you may have never are tacos because it is taco tuesday and they're half off, doesn't mean the event isn't influenced by past factors. It is, such as how tacos were always half off on Tuesday starting 10 years ago at said restaurant. Maybe you heard from an ad on TV or radio on Monday about the deal. Just to name a few.

So I mean with that said, which was what I was saying earlier, I am not sure what we agree on.

... or maybe not.

This is a very odd statement you will need to explain, because the reasons behind a choice are crucial to this discussion ... as well as the ignorance of the agent to what other agents might have done.
I guess I'm not saying the reason for choice is not important, more so that just because we have a new reason to do something we have already done still makes it a repeat of the experience. More than anything, I believe the ability to realize and reflect our reasons for acting and choosing may be more crucial than the actual reason itself.

The best I can do is say it feels like a choice, and make the appeal to a fellow theist that it would be strange for God to make it feel like a choice if it weren't. If you reject that, there isn't much I can do about it ... but at least I've got no logical contradictions to wrestle with.
Well we both know feeling something doesn't make it true. I could make the same plea. I think if we were to cohesively define "choice" it'd help the discussion. I think we started to, but got lost along the way.

Your point? If you're trying to make probabilities sound determined, that would be an abuse of the concepts. Have you ever read Asimov's Foundation? He makes a lot of government authorities falling prey to thinking probabilities mean certainties; it's the point on which his plot turns.
QM doesn't seem to be relevant to human choice. I'm not trying to say probabilities are determined. I would like to check out that book though.
 
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ecco

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Resha Caner previously said:
Type 1: Mathematical randomness
1A: Having a uniform probability distribution
1B: Having some known probability distribution in addition to deterministic factors
1C: Having some known probability distribution
Sure. Probability doesn't deal well with small sample sizes. However, were the string to be 1111110111111111111111111111111111111111111111, the probability of that coming from a system with a uniform distribution is extremely small - to the point that I would doubt it is a uniform distribution. I would consider it very deterministic with one error.
It is not a uniform distribution, therefore it is probably not random. I say probably because it is a comparatively short string.



My point was that it's not either/or. I keep getting this feeling people are thinking in very black & white terms. A system can have a mix of deterministic and random variables. As such, that shapes the distribution.
If there is a deterministic characteristic, it is not random. Yes, that is black and white. Something either is or is not random. There is no such thing as "kinda random". At least not in the context of this conversation.


My emphasis...
That you'll have to explain. While your example for small sample sizes and specific instances is true, it has been shown time and again that past data is a good predictor of the future - even for random data. If you're being pedantic about my use of the word "known", I'll concede you're right on a technicality. Maybe I should have said a "representative" probability distribution, or "estimated" - something like that. I think the category is still a proper one.
I agree that past data can be a predictor of the future. Climate and weather are two good examples. We know it probably is going to snow in the NorthEast in January.

However, you were talking about Mathematical Randomness. I can write a computer program to generate random numbers. If I use flawed logic that produces strings like...
101010101010101
101010101010101
101010101010101
...then I can predict that the next time I run the program (the future) I will get a string 101010101010101 based on past data.
If past data is a predictor, then the result is not random.

If my original strings are...
111111101111111
110111111111111
111111111101111
...then I can predict the next string will have a preponderance of 1's
If past data is a predictor, then the result is not random.



Please provide your version then.
This is as good as any:
Random numbers are numbers that occur in a sequence such that two conditions are met: (1) the values are uniformly distributed over a defined interval or set, and (2) it is impossible to predict future values based on past or present ones.
Notice the "and".
Notice the "(2) it is impossible..."

As I stated earlier, I agree somewhat with your 1A. The other two are obviously wrong.
 
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Resha Caner

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If there is a deterministic characteristic, it is not random. Yes, that is black and white. Something either is or is not random. There is no such thing as "kinda random". At least not in the context of this conversation.

I have no interest in arguing semantics with you. If you want to suggest different descriptors for the categories I put forth, feel free. But there are legitimate mathematical constructs associated with what I listed. Consider a simple sine wave: y = A*sin(t). I can give the magnitude of the signal at any time, t. Now add some white noise, w(t) such that y = A*sin(t) + w(t). I can no longer give the magnitude of the signal at any time, t. However, if I study the characteristics of the noise, I can subtract it out and make a very good estimate of the signal within a prescribed confidence band. Engineers do it all the time.

I just mixed something determined with something random. In the real world there is no hard line where I can divide signals into some that are 100% determined and some that are 100% random, or separate signals completely from the noise. It is always a mix with a spectrum of signal to noise ratios.

If past data is a predictor, then the result is not random.

That's not what I was talking about. I'm curious what your background is.

If I study a system and find it fits a specific distribution, then there are things I can predict about that system. So, we'll stick with a uniform distribution of 1s and 0s, and use strings of length 10 (Though 10 is typically too small for a statistically significant sample, I chose it to keep things simple). What I can predict is that I will typically see strings with five 1s and five 0s - I just don't know the order. So, I might get:
1010101010
1100110001
1011001001
and those fit my prediction. Or, I might occasionally get:
1010101011
which is close to my prediction (within a confidence band). But, if I get:
1111111110
I need to revisit my assumption that the system exhibits a uniform distribution.

So, again, I was not speaking of predicting specific instances. Probability doesn't do that. I was speaking of predicting the statistical character of future strings. In that sense, I can predict certain aspects of the future - even for random systems.

This is as good as any:
Random numbers are numbers that occur in a sequence such that two conditions are met: (1) the values are uniformly distributed over a defined interval or set, and (2) it is impossible to predict future values based on past or present ones.
Do you have a source for this definition? It's OK, but I see some problems with it. And what would you call a system that fits a normal distribution?
 
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