Probability, Options, and Determination...

[Scott Mayers]

I wasn't sure where to post this. I prefer the math section but see how this likely will get moved here. It may be interpreted as a puzzle too?

 

This is a question about probabilities as well as how this can relate to the ideas of determinism and indeterminism. In the following illustration, I show a simple diagram that can illustrate how one may have to make decisions. In this one, assume you are in a car to which you come to a T-intersection of which you must choose between going left or right to reach some destination or goal.

 

 

(1) What are the odds of turning left or right?

(2) Given real life, what are the odds of choosing to turn left or right?

 

Can you differentiate between the meanings? If so how?

[sunshaker]

In England most would turn left,

In America most would turn right,

In India your guess is as good as mine.

 

Was my answer for England/America determinism?

 

perhaps my answer for India was indeterminism?

 

I am not great with "isms".

Edited October 8, 2015 by sunshaker

[studiot]

Given the title, I will be interested to see where this opening post is leading and what Scott has not yet told us.

[Scott Mayers]

In England most would turn left,

In America most would turn right,

In India your guess is as good as mine.

 

Was my answer for England/America determinism?

 

perhaps my answer for India was indeterminism?

 

I am not great with "isms".

I could have asked this without using the suffix, "-ism". But you see how I'm opening this inquiry. But reducing this to an individual instead of groups of people, for any one same person, is the probability 1/2 for each of these options, "left" or "right"? Do we say that given a determinate interpretation of reality that if you opt to turn "left", say, is this an inevitable choice such that the odds to turn "left" is 1, while the odds to turn "right" is 0, or vise versa? Or do we interpret the result of the end-goal in mind and assume any option is irrelevant to the goal?

Given the title, I will be interested to see where this opening post is leading and what Scott has not yet told us.

Suspicious a little? My intention is to participate interactively. I can often write long posts that many usually get turned off to because it doesn't fit in their 2" iPhone screens. But yes, I'm leading a bit here but also hope to learn of what kind of thinkers are here who can relate and add some insight on questions regarding the use of math of probabilities and to how physicists use this with regards to Quantum Mechanics, etc.

[dimreepr]

Given the title, I will be interested to see where this opening post is leading and what Scott has not yet told us.

 

 

I’ve no idea what his “pet theory” is but I’m guessing it’s leading there.

I could have asked this without using the suffix, "-ism". But you see how I'm opening this inquiry. But reducing this to an individual instead of groups of people, for any one same person, is the probability 1/2 for each of these options, "left" or "right"? Do we say that given a determinate interpretation of reality that if you opt to turn "left", say, is this an inevitable choice such that the odds to turn "left" is 1, while the odds to turn "right" is 0, or vise versa? Or do we interpret the result of the end-goal in mind and assume any option is irrelevant to the goal?

 

 

Without a cultural influence the distribution would equal the percentage of left handed people. So maybe you’re trying to ask a different question?

Edited October 8, 2015 by dimreepr

[Scott Mayers]

 

 

I’ve no idea what his “pet theory” is but I’m guessing it’s leading there.

Instead of insulting up front, perhaps you might participate?

 

Oh wait. Now that I think about it, here's my hypothesis: I bet that if anyone opts to question something too apparently simple that you'd get suspicious of one attempting to trick others into following one's 'pet' theory, Sorry, I couldn't tell you up front as this would have spoiled the experiment. But you've confirmed my prediction now. Am I now qualified to have a legit theory now?

Edited October 8, 2015 by Scott Mayers

[dimreepr]

Everything is influenced and has influence, even in the quantum world; probability must account for it.

Instead of insulting up front, perhaps you might participate?

 

Oh wait. Now that I think about it, here's my hypothesis: I bet that if anyone opts to question something too apparently simple that you'd get suspicious of one attempting to trick others into following one's 'pet' theory, Sorry, I couldn't tell you up front as this would have spoiled the experiment. But you've confirmed my prediction now. Am I now qualified to have a legit theory now?

 

 

You’re qualified to have a legit theory/hypothesis when you understand the difference.

[Scott Mayers]

 

Without a cultural influence the distribution would equal the percentage of left handed people. So maybe you’re trying to ask a different question?

I'm trying to see if you or others can enumerate the different ways to assign values to a probability or whether you (or others) interpret a strict interpretation here. I also want to later (not necessarily in this thread) introduce the Monty Hall Problem and find this would be a good precursor to discussing that. I'm not so interested in the puzzle as much as I am in interpretation. In other related areas of philosophy, I've also had concerns about what people think regarding whether we have one universe or multiple ones AND how it relates to what one believes regarding various ideas on determination.

 

And on the distinction between hypothesis and theory. Yes, I understand them. But you again default to presuming something about me without charity. I was poking fun at your initial response to just that.

Edited October 8, 2015 by Scott Mayers

[dimreepr]

I'm trying to see if you or others can enumerate the different ways to assign values to a probability or whether you (or others) interpret a strict interpretation here. I also want to later (not necessarily in this thread) introduce the Monty Hall Problem and find this would be a good precursor to discussing that. I'm not so interested in the puzzle as much as I am in interpretation. In other related areas of philosophy, I've also had concerns about what people think regarding whether we have one universe or multiple ones AND how it relates to what one believes regarding various ideas on determination.

 

And on the distinction between hypothesis and theory. Yes, I understand them. But you again default to presuming something about me without charity. I was poking fun at your initial response to just that.

 

 

Bolded mine.

 

So which is it; probability or game theory?

[Scott Mayers]

 

 

Bolded mine.

 

So which is it; probability or game theory?

Not going to digress here on this. I only want to determine how most interpret the initial question set up and why?

[dimreepr]

Not going to digress here on this. I only want to determine how most interpret the initial question set up and why?

 

 

Then you've been answered.

[studiot]

I'm trying to see if you or others can enumerate the different ways to assign values to a probability or whether you (or others) interpret a strict interpretation here. I also want to later (not necessarily in this thread) introduce the Monty Hall Problem and find this would be a good precursor to discussing that. I'm not so interested in the puzzle as much as I am in interpretation. In other related areas of philosophy, I've also had concerns about what people think regarding whether we have one universe or multiple ones AND how it relates to what one believes regarding various ideas on determination.

 

And on the distinction between hypothesis and theory. Yes, I understand them. But you again default to presuming something about me without charity. I was poking fun at your initial response to just that.

 

I thought as much.

 

So why didn't you say so in the first place?

 

I think your hastily thrown together example is a poor one to use for this purpose.

I also have this trouble when constructing examples because making a good one is very difficult and usually involves lots of work.

Edited October 8, 2015 by studiot

[Scott Mayers]

 

I thought as much.

 

So why didn't you say so in the first place?

 

I think your hastily thrown together example is a poor one to use for this purpose.

I also have this trouble when constructing examples because making a good one is very difficult and usually involves lots of work.

You'll see how this fits in to the other issues later if I raise them. I need to ask this without concerning my motives at this point and only mention what I did as it appears I'm being defaulted with being hideous or deceptive by some of these posts. The diagram I made is sufficient for my purpose in this thread and the topic at hand thus far.

[dimreepr]

And on the distinction between hypothesis and theory. Yes, I understand them.

 

 

If you actually understood the difference, then...

 

 

But you again default to presuming something about me without charity. I was poking fun at your initial response to just that.

 

 

 

You’d know my presumption wasn’t my default.

[studiot]

Before discussing probabilities in general you need to set out what exactly you mean.

 

Mathematics recognises more than one form of probability and the meaning of a statement such as 'the probability of event X is 1' will depend upon which definition you are using.

Further to establish a probability you have to be able to identify the beginning and the end of an event.

,

With regards to your example,

 

In the quantum world there is a probability that the traveller will turn neither right nor left but

 

1) Be reflected back along her path

 

2) Go straight on regardless and reappear at the other side of the square (this is called quantum tunnelling).

 

Funnily enough using Sunshaker's response in relation to traffic flow can also lead to these responses.

 

1) Years ago I was cycling around the Fens and came to a T junction that had a signpost point left that said Cambridge as well as a sighpost pointing right that said Cambridge. Since my destination was not Cambridge I turned round and went back.

 

2) When working in the desert I found many fomer nomads who had converted from camel transport to truck would go stright on across such a junction. They said "This is what we would have done with our camels so why not our trucks"

Edited October 8, 2015 by studiot

[Scott Mayers]

Before discussing probabilities in general you need to set out what exactly you mean.

 

Mathematics recognises more than one form of probability and the meaning of a statement such as 'the probability of event X is 1' will depend upon which definition you are using.

Further to establish a probability you have to be able to identify the beginning and the end of an event.

,

With regards to your example,

 

In the quantum world there is a probability that the traveller will turn neither right nor left but

 

1) Be reflected back along her path

 

2) Go straight on regardless and reappear at the other side of the square (this is called quantum tunnelling).

 

Funnily enough using Sunshaker's response in relation to traffic flow can also lead to these responses.

 

1) Years ago I was cycling around the Fens and came to a T junction that had a signpost point left that said Cambridge as well as a sighpost pointing right that said Cambridge. Since my destination was not Cambridge I turned round and went back.

 

2) When working in the desert I found many fomer nomads who had converted from camel transport to truck would go stright on across such a junction. They said "This is what we would have done with our camels so why not our trucks"

Interesting post. As to defining probabilities in question, I'm looking for the various interpretations regardless. But I'm being literal to the paths given as presented. That is, I am not asking for additional elements beyond the choices presented. If I was, then a "god" answer would just as well be as equally possible. So to reflecting back upon ones path OR to quantum tunneling, I'm not concerned as these involve adding more detail that I haven't presented.

 

The beginning of the event is the person approaching the intersection, the end is the "goal" defined and intended [the turn around option is not relevant], and the options entering the loop are strictly determined by the "left" or "right" options. Just in case you might add any concern further, upon either choice (or selection option), since the goal is defined essential, there is no option but to turn to the goal and so continuing to loop around are irrelevant too.

 

I do gather thus far that you interpret the possibility of different interpretations at least.

 

Do you think that the perception of the observer counts too? That is, can you agree/disagree whether you define whether we are discussing different probabilities with respect to the driver approaching the intersection or our ideal "god's-eye" perspective looking in on the puzzle?

 

In respect of the examples you give above, even though I'm not dealing with this at present, does the probability also change if we consider 'trust'? Thus, in your mention of opting to turn around can be about being informed that your decision to drive that way is not your goal (trusting the signs, that is).

Edited October 8, 2015 by Scott Mayers

[studiot]

 

If I was, then a "god" answer would just as well be as equally possible.

 

Do you think that the perception of the observer counts too? That is, can you agree/disagree whether you define whether we are discussing different probabilities with respect to the driver approaching the intersection or our ideal "god's-eye" perspective looking in on the puzzle?

 

In respect of the examples you give above, even though I'm not dealing with this at present, does the probability also change if we consider 'trust'? Thus, in your mention of opting to turn around can be about being informed that your decision to drive that way is not your goal (trusting the signs, that is).

 

 

I'd rather leave God out of the discussion.

 

As regards the left v right turn only, this means that something is forcing the left or right turn, that is there are additional undefined constraints involved.

If you can quantify the relative strengths of the left and right forcing functions you can use these to create an estimated frequency value for each turn.

This frequency can be interpreted as an 'a priori' probability.

 

There I have gone and mentioned one of the recognised forms of probability so let me observe that I don't think you have fully appreciated the types of probability available in your response to the other main point in my last post.

[Scott Mayers]

 

I'd rather leave God out of the discussion.

 

As regards the left v right turn only, this means that something is forcing the left or right turn, that is there are additional undefined constraints involved.

If you can quantify the relative strengths of the left and right forcing functions you can use these to create an estimated frequency value for each turn.

This frequency can be interpreted as an 'a priori' probability.

 

There I have gone and mentioned one of the recognised forms of probability so let me observe that I don't think you have fully appreciated the types of probability available in your response to the other main point in my last post.

I wasn't placing a God in this at all (nor would). But your reference to quantum tunneling or reversing directions both are just this type of thing considering what it is beyond what I was discussing. That was my point on that.

 

I have a good background in logic, much of maths, philosophy, and the sciences, among many others. You are adding inferences in the problem that I'm not interested in. The components involved are a person (not important whether actually driving a car, bus, or walking), the abstract drawing to represent a split path with two distinct options (left and right) and a goal. I don't think 'force' is necessary here either. The only technical 'force' is that the person intends the generic unspoken 'goal' to go to and the intersection where he/she's 'forced' to make a decision.

 

If you want to introduce concepts you learned that you believe I'm unaware of, your welcome to. Just define them and explain.

 

For instance, although the first respondent was partially just being humorous, he pointed out some of the intentional factors involved.

 

That with respect to the person facing these options they can be intrinsically determined to favor one option. He used background reference to cultures but appears to understand the point regardless. In this case, if we are to interpret the nature of ones' determination via physics, this person would be 'determined' to select one unique option. That is, if he/she turned "left", while there may be many complex factors going into it, he/she would always turn left if we were to have recorded it and checked back on the recording. This would mean that this person would be determined to turn left 100% and right 0 %. It's unimportant to define times to reference frequencies as this is not necessary. It could be considered one event only at this point. So,

 

100% = (1 unique option)/(1 unique event at this intersection) = 1

0% = (0 unique option)/(1 unique event) = 0

 

If we consider 'fairness' in that the person is equally indeterminate to take either left or right (like in a multiple world's interpretation OR using repeated stats or frequency), then the event would be

 

50% = 1/2 for left

50% = 1/2 for right

 

If we consider 'predicting' as an outsider looking in to this problem, because it may the be case that nature is 'unfair' as we cannot determine it in practice, the odds might be completely indeterminate until we witness the actual decision like predicting the weather 30 days in advance.

 

These are ones that I can think of. Are these valid interpretations of possible measures here? Are there others?

[studiot]

 

There I have gone and mentioned one of the recognised forms of probability so let me observe that I don't think you have fully appreciated the types of probability available in your response to the other main point in my last post.

 

 

Just to repeat this from my previous post.

 

You really do need to gain a more complete grasp of the nature of probability before making assumptions about assigning probabilities.

 

Every possibility has an associated probability.

 

What ever the type of probability employed the total of all associated probabilities must sum to 1;

 

Since there are more possibilities than left and right, the probabilities for left and right alone cannot sum to 1.

 

With regard to assigning probabilities to a left or right turn, there are constraints in action that you are not accounts for so your model is flawed.

[Scott Mayers]

 

Just to repeat this from my previous post.

 

You really do need to gain a more complete grasp of the nature of probability before making assumptions about assigning probabilities.

 

Every possibility has an associated probability.

 

What ever the type of probability employed the total of all associated probabilities must sum to 1;

 

Since there are more possibilities than left and right, the probabilities for left and right alone cannot sum to 1.

 

With regard to assigning probabilities to a left or right turn, there are constraints in action that you are not accounts for so your model is flawed.

What the hell are you talking about? You seem to be commanding you know my intent better than I do myself! I was using as layman terms as I could to appeal to anyone who might read this with different backgrounds. I am GIVING the scenario. Don't impose stuff I haven't a need for here. If you are sincere to some background in probability, don't be so strict to your preferred language or depths beyond what I'm asking. If you studied these, did you learn from one set of unique books? Did you learn the theorems by proof or did you just skip to the conclusions and memorized them in trust they work?

 

I have mentioned nothing of flaw here. AND the odds DO happen to add up to 1 in what I have demonstrated above. There are NO possibilities except for the two I'm giving by definition. It simplifies the options to a binary set of choices to focus on how to weigh each possibility to a probability. I showed the variants above I see so far. What is your specific disagreement about as I cannot read your mind and you are just making blanketed statements without reference?

[studiot]

Rudeness does not improve the validity of your claim.

 

Probabilities cannot be imposed.

They are what they are.

 

And yes your analysis is flawed.

No, of course you did not say that, I did.

 

Your analysis is flawed because there exist possibilities you cannot exclude.

For instance your traveller may drop dead at the junction and simply not proceed.

 

There is always a finite possibility of this, and therefore a finite 'a priori' probability (do you know what this means?)

Edited October 8, 2015 by studiot

[Cuba]

Looks like he just wants you to make a choice between A or B and define the probabilty of either choice. I agree the model is flawed as it implies further choice. However I will play along, I'd most likely take a right probably because I am right handed and American. I am still taking into account outside forces though (my own experience) which I think futher flaws your statement that the odds add up to 1.

 

Bit out of my depth on this one though as far as the maths go.

[Scott Mayers]

Rudeness does not improve the validity of your claim.

 

Probabilities cannot be imposed.

They are what they are.

 

And yes your analysis is flawed.

No, of course you did not say that, I did.

 

Your analysis is flawed because there exist possibilities you cannot exclude.

For instance your traveller may drop dead at the junction and simply not proceed.

 

There is always a finite possibility of this, and therefore a finite 'a priori' probability (do you know what this means?)

Don't mind me if I ignore further goading.

 

While I don't mind including other factors like death or other points that might be related, this is the first point you actually made that at least doesn't break the limitations of the givens since it involve the 'person' I defined in it. But it appears that you're purposely more interested in diluting my point like an attorney might burden their opposition by dumping an unusual excess of trivial paper work to hide the evidence like a needle in a haystack.

 

As to Cuba's response, what 'further choices' are you thinking of?

 

If you assume an indeterminate reality to humanity ("free choice" as it is often referred to) by the perspective of the person at the intersection, and their choice is sincerely 'random', we would assign both "left" and "right" as valid possible options and grant them as equivalent values = 1/2. 1/2 "left" + 1/2 "right" = 1.

 

If you assume a personally determinate means based on things like 'right-handedness' or other complex factors, one may actually have no real 'choice' other than one's delusion of it and opt to always turn "right". In this scenario, you may be assured to (always go right without exception). So in this scenario, only the right selection counts and is = 1, while the "left" option = 0. 1 "right" + 0 "left" = 1.

 

What's so difficult to understand what this means? I'm only asking if you or others agree to this much? I don't think that other options are discounted either. But I'm focusing on moving forward by getting a 'nod'. If it is about some preferred preference for using different symbols, that's alright.

 

studiot mentions 'death' as a possibility. How might we represent this? I'd first have to distinguish between at least two kinds of death: one where the person dies indeterminately (like some unpredictable heart attack), one where the person dies determinately (like someone adding an additional premise of some third person in the picture or themselves as motivators) These last ones cannot count as I have not defined an extra person and have predefined the person as intending to reach the 'goal', so suicide would not be an allowed possible motive affecting the person. What's left is indeterminate and incommensurate without having specific information about this arbitrary person. Thus this removes "death" as a factor of assigning values.

[Cuba]

As to Cuba's response, what 'further choices' are you thinking of?

 

If you assume an indeterminate reality to humanity ("free choice" as it is often referred to) by the perspective of the person at the intersection, and their choice is sincerely 'random', we would assign both "left" and "right" as valid possible options and grant them as equivalent values = 1/2. 1/2 "left" + 1/2 "right" = 1.

 

If you assume a personally determinate means based on things like 'right-handedness' or other complex factors, one may actually have no real 'choice' other than one's delusion of it and opt to always turn "right". In this scenario, you may be assured to (always go right without exception). So in this scenario, only the right selection counts and is = 1, while the "left" option = 0. 1 "right" + 0 "left" = 1.

 

I'm not thinking of further choices I simply see more choices when I look at your model. In fact the instant I see it I automatically am dubious of either choice you present. Seems like a trick question.

 

As for the odds adding to 1, you factor in the left and right choices but not outside influence, which regardless of the motion in your model there will always be. You imply that we are observing, is not that in itself an outside influence?

[Scott Mayers]

I don't follow you. Although I agree to other possible factors my intent is to the discuss the abstraction of this diagram's meaning to reality limited to what I've given. Yes, you can include us as an observer (like a god looking down on this world). So if we do this like an accountant might initialize an accounting system, we could lay out all the elements involved. I already mentioned the given path, the T-intersection going in, you might include the T-intersection going out. Call the source route going in as the origin, the end as the 'goal' as labeled. An arbitrary person, beginning at the start and aiming to get to the goal. and the particular options of direction. Then we can include us as the 'god' perspective as we observe and the person's perspective.

 

Elements involved (brainstorm)

Origin location (left side in the diagram)

End location labeled "goal" (right side of diagram)

the mapped rout of the road from origin to goal as illustrated

a Person

a direction towards the goal

a T-intersection going into loop

a T-intersection going out loop

A "left" direction

a "right" direction

the perspective from the position of beginning of Person

the perspective form the position of beginning of our perspective

the perspective from the position of the first T-intersection of Person

the perspective from the position of the first T-intersection of our perspective

the perspective from the position of the second T-intersection of Person

the perspective from the position of the second T-intersection of our perspective

the perspective form the position of end of Person

the perspective form the position of end of our perspective

velocity or rate of Person

 

Do you have any extras you think are relevant? You wanted more complexity. Here you go.

I don't follow you. Although I agree to other possible factors my intent is to the discuss the abstraction of this diagram's meaning to reality limited to what I've given. Yes, you can include us as an observer (like a god looking down on this world). So if we do this like an accountant, we might initialize a set of accounts to brainstorm all the elements involved. I already mentioned the given path, the T-intersection going in, you might include the T-intersection going out. Call the source route going in as the origin, the end as the 'goal' as labeled. An arbitrary person, beginning at the start and aiming to get to the goal. and the particular options of direction. Then we can include us as the 'god' perspective as we observe and the person's perspective.

 

Elements involved (brainstorm)

Origin location (left side in the diagram)

End location labeled "goal" (right side of diagram)

the mapped rout of the road from origin to goal as illustrated

a Person

a direction towards the goal

a T-intersection going into loop

a T-intersection going out loop

A "left" direction

a "right" direction

the perspective from the position of beginning of Person

the perspective form the position of beginning of our perspective

the perspective from the position of the first T-intersection of Person

the perspective from the position of the first T-intersection of our perspective

the perspective from the position of the second T-intersection of Person

the perspective from the position of the second T-intersection of our perspective

the perspective form the position of end of Person

the perspective form the position of end of our perspective

velocity or rate of Person ? (yeah/no?)

 

Do you have any extras you think are relevant? You wanted more complexity. Here you go.

Edited October 9, 2015 by Scott Mayers