A math Problem

[leroy]

Again, your citation was irrelevant to what we are discussing. Beyond that, whether you realize it or not, that is your burden and you keep running from it. What were the odds when you picked 7312004874512? If you would answer this simple question, instead of running from it, you would already see the flaw in your thinking.

I am not running away, I openly and unambiguously have admitted multiple times that I don’t know the odds, because I don’t how to quantify all the variables that affected my choice.
There are methods that would provide an “almost exact” answer, but I don’t have the budget, nor the time, or the interest to do it, all we know (and has been proven) is that the probability of selecting 7 is grater than the possibility of selecting 7312004874512

Again our only point of disagreement is whether if we humans can make a completely random selection of a real number, I already provided a source that proves that we can´t. what else you I do? Should I provide additional sources?


Given that human selection is not completly random, not all numbers have the exact same probability of being chosen, then the probability of picking 7 are not necessarily zero and not necesairly the same as picking 7312004874512.

In fact according to this source https://www.rd.com/culture/number-7/ the probability of picking “7” is around 10%

 

[Master_Ghost_Knight]

I'm going to have to side with leroy on this one.
A human is on average far more likely to pick low numbers than to pick high one.
Although this statement is absolutely true for a variety of reasons, it also happens to be irrelevant. As far as I have been following the conversation, leroy had made some sort of claim in the lines of "picking any real true random number with equal probability" has the odds of 1/infinity and so the probability of picking any number is 0 (or whatever). Well it isn't. So your argument is invalid.
And there seams to be a tremendous failure to comprehend compound probability here. And the entire thread as spun out of control around a completely stupid argument.

 

[Master_Ghost_Knight]

Oh and FYI. The answer to your question can be found Here

This is the probability of winning the lottery by day X given your progression.
I have kept the numbers more sedate because even computers have trouble computing large numbers.
In the formula replace 1000 by the day you wish to check (i.e. probability of winning the lottery by day 1000)
And where you see 10, replace it by the probability of winning the lottery on day 1.
As you can see this is a monotonically function that approaches 1 as the number of days approaches infinity.
Your argument is wrong.

</thread>

 

[leroy]

I'm going to have to side with leroy on this one.
A human is on average far more likely to pick low numbers than to pick high one.
Although this statement is absolutely true for a variety of reasons, it also happens to be irrelevant. As far as I have been following the conversation, leroy had made some sort of claim in the lines of "picking any real true random number with equal probability" has the odds of 1/infinity and so the probability of picking any number is 0 (or whatever). Well it isn't. So your argument is invalid.
And there seams to be a tremendous failure to comprehend compound probability here. And the entire thread as spun out of control around a completely stupid argument.

Don worry you don’t have to read all the conversation, it all started because hack asserted (and HWN agreed) that events with zero probabilities happen all the time.

hackenslash wrote:I should add,just in case you don't read the post, thatr even events with a zero probability happen all the time, and this is trivial to demonstrate.

Pick any number on the real number line. Let's say, for example, that you choose the number 7. The probability of choosing that number at random is zero. How? Because the reals are infinite, and any number divided by infinity is zero, hance the probability of choosing 7, or indeed any other number, is exactly zero, yet the probability of choosing some number is exactly one.

I am granting the fact that under this hypothetical scenario the probability of picking “7” would be zero, but in the real world this scenario is impossible (and therefore does not happen all the time) because humans can’t make a completely random selection of a number. (some numbers are more likely to be selected than others)


HWN is still affirming that events with zero probability can happen in the real world,

 

[leroy]

Oh and FYI. The answer to your question can be found Here

This is the probability of winning the lottery by day X given your progression.
I have kept the numbers more sedate because even computers have trouble computing large numbers.
In the formula replace 1000 by the day you wish to check (i.e. probability of winning the lottery by day 1000)
And where you see 10, replace it by the probability of winning the lottery on day 1.
As you can see this is a monotonically function that approaches 1 as the number of days approaches infinity.
Your argument is wrong.

</thread>

Are you saying that

1/1,000,000,000,000 + 1/2,000,000,000,000 + 1/3,000,000,000,000....... tends towars infinity?

 

[Master_Ghost_Knight]

Are you saying that
1/1,000,000,000,000 + 1/2,000,000,000,000 + 1/3,000,000,000,000....... tends towars infinity?

No, I mean.
That does tend towards infinity, but that is not what I'm saying.
That is not how you calculate the probability. You need to compensate the probability of the second day with the probability of not winning on the day before.
Because as soon as you win, you win, and you don't progress further.
What I'm saying is that the probability of winning tends towards 1, i.e. certainty.

 

[Master_Ghost_Knight]

HWN is still affirming that events with zero probability can happen in the real world,

There is no such thing has events with probability exactly equal to zero which occur.
But this is due to reasons, that quite frankly are beyond each of your comprehension.

PS. I have also realized that the probability expression could be simplified like this, and it might be easier to understand.

 

[leroy]

Perhaps this example would help HWN
Imagine a spaceship that traveled from earth to a distant star that is 100 light years away. He arrived at his destiny in 1 year
¿at what speed was the spaceship traveling?
Well according to the math distance / time… he was traveling at 100c (100 times the speed of light) the mathematical approach is correct and the resolution of the equation is also be correct.

But in the real world we know that this scenario is not realistic because it is impossible to travel faster than the speed of light.

hackenslash wrote:I should add,just in case you don't read the post, thatr even events with a zero probability happen all the time, and this is trivial to demonstrate.

Pick any number on the real number line. Let's say, for example, that you choose the number 7. The probability of choosing that number at random is zero. How? Because the reals are infinite, and any number divided by infinity is zero, hance the probability of choosing 7, or indeed any other number, is exactly zero, yet the probability of choosing some number is exactly one.

The same is true with this example, sure the mathematical approach is correct and the resolution is correct, the answer would be ZERO, but in the real world it is impossible for a human to make a completely random selection of a number (as my source shows) therefore events with zero probability don’t happen all the time, the event described by Hack is simply an impossible event that cant happen.

 

[Master_Ghost_Knight]

Perhaps this example would help HWN
Imagine a spaceship that traveled from earth to a distant star that is 100 light years away. He arrived at his destiny in 1 year
¿at what speed was the spaceship traveling?
Well according to the math distance / time…

Your math is wrong. You haven't accounted for length contraction or time dilation.

he was traveling at 100c (100 times the speed of light) the mathematical approach is correct and the resolution of the equation is also be correct.

In what reference frame? I can assure, that no matter what reference frame you do the calculation, you will never get 100c.
You either calculate on a reference frame stationary to the destination, in which case the space ship couldn't travel the distance in less than 100 years.
Or you calculate on the reference frame of the ship, in which case the distance is no longer than 1 light year.
But you can not do both, you can't mix and match.

The same is true with this example, sure the mathematical approach is correct

No its not correct. Mathematics is not the real world, it was never made to model the real world.
Mathematics has things like perfect circles, or infinitesimally thin lines that stretch away to infinity.
It doesn't have hamburgers, or chairs, or humans who get bored really quick and are not willing to sit and waste an infinite amount of time and energy (a resource that they have no access too anyway) describing a number because someone decide to ask them a number between 0 and infinity and they wanted to give a fair pick up to infinity.

Also maths, doesn't have "occurrences", nothing "happens" in math. If you roll a die, and you find out it is a 7, it is an instance of a particular event either real or hypothetical, but not mathematical.

 

[leroy]

[No its not correct. Mathematics is not the real world, it was never made to model the real world.
Mathematics has things like perfect circles, or infinitesimally thin lines that stretch away to infinity.
.

that is the point that I was trying to make, hopefully you understood it.

 

[Master_Ghost_Knight]

that is the point that I was trying to make, hopefully you understood it.

I fail to see that was the point you were making. On the very first post you describe the problem exactly:

everyday the probabilities of winning the lottery are less.
John will buy 1 ticket every single day and he will play the lottery every single day for an infinite amount of time, will he ever win the lottery?
I´ll say that the answer is NO, but before justifying my answer I would like to read some opinions,

Which is demonstrably wrong.
Just because someone else who was arguing against you made points that were incorrect, it doesn't mean that you are then right by default.

 

[leroy]

that is the point that I was trying to make, hopefully you understood it.

I fail to see that was the point you were making. On the very first post you describe the problem exactly:

everyday the probabilities of winning the lottery are less.
John will buy 1 ticket every single day and he will play the lottery every single day for an infinite amount of time, will he ever win the lottery?
I´ll say that the answer is NO, but before justifying my answer I would like to read some opinions,

Which is demonstrably wrong.
Just because someone else who was arguing against you made points that were incorrect, it doesn't mean that you are then right by default.

the point that I was making (with the spaceship) was related to the conversation that I am having with HWN, regarding events with zero probability. Not with my original post.

 

[Rumraket]

The probability becomes lower and lower =/= it will therefore never happen.

No logical argument or mathematical calculation can derive the conclusion "therefore it will never happen" from the premise "the probability becomes lower and lower every day by some X amount".

It doesn't follow. Your conclusion doesn't follow. Stop making an argument that is patently logically invalid. The only conclusion that follows from the premise "the probability becomes lower and lower every day by some X amount" is the statement contained in the premise itself. You cannot derive an absolute prohibition from a statement of non-zero probability. It can't be done.

 

[Master_Ghost_Knight]

The reason why there is no such thing has events with zero probability that can occur in the real world is partly related to:
1. The distinguishibility principle. I.e. If A and B can not be told apart, they are the same state.
2. The only way we have ever found to distinguish state (which includes virtual states in computers), involves re-arranging physical particles that can be measured and distinguished.
3. As far as we know, there is a finite number of particles in the universe. And if space is not finite, surely the range at which you can set particles in order to measure them certainly is.
Then you can just view this like a classical computer. That although very large, the number of distinguishable states you can set the universe it is definitely finite.
And this presents a limit on what can be represented. There is such a thing as numbers that can not be represented in the universe. Actually the set of representable numbers is quite small compared to infinity, given that this set is finite.
You would think that the distribution of representable numbers would be necessarily small or continuous, although there is a bias for small numbers (due to the nature of infinity), it is certainly not evenly distributed. For example numbers like infinite or pi, take only a few words to represent, and in fact there are multiple ways of representing them, for example if you saw the same description of pi on some other post or a different line, you wouldn't think this to represent a different number.

This also means that some numbers must necessarily be harder to represent, requiring more matter (and energy) to do so, which also reduces the number of permutations that you would allow it to represent the same number.
Since energy is quite a limited resource to humans, there would be a bias for humans to be able to represent a very limited amount of small numbers, most of which represented only on the account of particular "representation shortcuts" that are able to provide numbers with a very peculiar meaning of interest (for example pi, irrational number, but ratio of diameter to perimeter of a circle, easy to represent because of shortcut).

So given that the universe is a state machine with a finite set of possible states, which also progresses in time. This means that one can describe a state transition function, that changes the Universe from state A to B. Since the number of states is finite, this also means that given an unbounded progression (infinite time) some states must necessarily repeat.

But this doesn't mean that all states must necessarily occur. There might be some states "C" of the universe that given the current state "A" can not be mapped by the transition function. I.e. that there is no path the transition function can take that could lead from "A" (actual) to "C". In this case we can say as a shortcut that state "C" has 0 probability.
All other states must have a bigger than 0 probability if there is a path in the transition function that can map to it, because the number of states is finite.
The transition function doesn't need to be deterministic, it can be non-deterministic, the only difference is that in a non-deterministic function the transition from one state to another has a branching pattern with a probability function associated to each transition path instead of a having single transition path.
By this logic, if an event occurs, i.e. the Universe is in state "D", then by definition its probability couldn't have been zero, because the state "D" could obviously be mapped by the transition function given that it did occur.

And I bet that what I have just said is the same as Chinese to you, and you didn't understand a word of it. Unfortunately this is the only right answer, and I'm pretty sure none of you were thinking of it.
And I'm pretty sure no one was arguing at this level.

You may think you were right, but I assure you that you were no more right then trying to divinate the weather trough tea leaves.
The points attempted to be made in the later stages of this thread have nothing to do with the original point. They are kind of irrelevant, they are pointless. They have no bearing on the validity of the original question no matter which one is right.
That is why I said the points being made were stupid. Because they flew of on a tangent that had nothing to do with the original topic, and then never came back.

 

[leroy]

The reason why there is no such thing has events with zero probability that can occur in the real world is partly related to:......................


.

Good luck convincing HWN and Hack, they still believe firmly that events with zero probability can happen.

 

[leroy]

The probability becomes lower and lower =/= it will therefore never happen.

No logical argument or mathematical calculation can derive the conclusion "therefore it will never happen" from the premise "the probability becomes lower and lower every day by some X amount".

It doesn't follow. Your conclusion doesn't follow. Stop making an argument that is patently logically invalid. The only conclusion that follows from the premise "the probability becomes lower and lower every day by some X amount" is the statement contained in the premise itself. You cannot derive an absolute prohibition from a statement of non-zero probability. It can't be done.

aboout my original post (that has nothing to do with the zero probability BS that hack and HWN are promoting)

leroy
John is planning to play the lottery, the probability of winning the lottery is 1 in 1,000,000,000,000

tomorrow there will be an other lottery where the probability of winning is 1 in 2,000,000,000,000

the next day 1 in 3,000,000,000,000

the next day 4,000,000,000,000

after 100 days 100,000,000,000,000

the probability of winning the lottery is 1 in 1,000,000,000,000N

N = The number of days that has passed since day 1

etc

everyday the probabilities of winning the lottery are less.


John will buy 1 ticket every single day and he will play the lottery every single day for an infinite amount of time, will he ever win the lottery?




I´ll say that the answer is NO, but before justifying my answer I would like to read some opinions,

It is not a logical argument; it is simply a mathematical conclusion.
If you add 1/ 1,000,000,000,000 + 1/ 2,000,000,000,000 + 1/ 3,000,000,000,000…….1/infinity, you will never get to a point where the result is greater than 0.5 (or 50%) therefore chances say that you won’t win the lottery.

agree?

 

[Master_Ghost_Knight]

It is not a logical argument; it is simply a mathematical conclusion.
If you add 1/ 1,000,000,000,000 + 1/ 2,000,000,000,000 + 1/ 3,000,000,000,000…….1/infinity, you will never get to a point where the result is greater than 0.5 (or 50%) therefore chances say that you won’t win the lottery.
agree?

No. This is demonstrably wrong. I have explained this to you.
First that is not how you calculate probabilities.
Secondly 1/ 1,000,000,000,000 + 1/ 2,000,000,000,000 +... is just a pedantic form of SUM[n,1,Inf](1/n)*1/K where K is equal to 1,000,000,000,000.

SUM[n,1,Inf](1/n) approaches infinity. So SUM[n,1,Inf](1/n)*1/1,000,000,000,000 approaches infinity as well. I.e. It not only can be larger than 0.5, it is even larger than 1, it is actually larger than any real number you like. Which should tell you that there is something wrong with your probability function since you can not have probabilities grater than 1.
You have no idea what you are talking about.

 

[leroy]

It is not a logical argument; it is simply a mathematical conclusion.
If you add 1/ 1,000,000,000,000 + 1/ 2,000,000,000,000 + 1/ 3,000,000,000,000…….1/infinity, you will never get to a point where the result is greater than 0.5 (or 50%) therefore chances say that you won’t win the lottery.
agree?

No. This is demonstrably wrong. I have explained this to you.
First that is not how you calculate probabilities.
Secondly 1/ 1,000,000,000,000 + 1/ 2,000,000,000,000 +... is just a pedantic form of SUM[n,1,Inf](1/n)*1/K where K is equal to 1,000,000,000,000.

SUM[n,1,Inf](1/n) approaches infinity. So SUM[n,1,Inf](1/n)*1/1,000,000,000,000 approaches infinity as well. I.e. It not only can be larger than 0.5, it is even larger than 1, it is actually larger than any real number you like. Which should tell you that there is something wrong with your probability function since you can not have probabilities grater than 1.
You have no idea what you are talking about.

Agreed, I did my homework and noted my mistake.

 

[he_who_is_nobody]

And the entire thread as spun out of control around a completely stupid argument.

It was a thread started by dandan/leroy, thus that is to be expected.

HWN is still affirming that events with zero probability can happen in the real world,

There is no such thing has events with probability exactly equal to zero which occur.
But this is due to reasons, that quite frankly are beyond each of your comprehension.

I honestly would not mind reading an explanation for why I am wrong. In addition, it does not look like I will ever get that from dandan/leroy. He would rather run. The way hackenslash stated it earlier seems so rational.

But in the real world we know that this scenario is not realistic because it is impossible to travel faster than the speed of light.

[...]

The same is true with this example, sure the mathematical approach is correct and the resolution is correct, the answer would be ZERO, but in the real world it is impossible for a human to make a completely random selection of a number (as my source shows) therefore events with zero probability don’t happen all the time, the event described by Hack is simply an impossible event that cant happen.

Are you now saying that the real numbers are not infinite? Please stick to one and stop changing your mind.

And I bet that what I have just said is the same as Chinese to you, and you didn't understand a word of it. Unfortunately this is the only right answer, and I'm pretty sure none of you were thinking of it.
And I'm pretty sure no one was arguing at this level.

Not Chinese, and thank you. Something like this is what I was expecting from dandan/leroy. I was never wed to either idea, I just thought the way hackenslash summed it up was kind of brilliant. I also just wanted dandan/leroy to explain himself with more than "It does not seem right to me" that I kept getting from him. Thus, you were correct, in that we were not even close to that level.

That is why I said the points being made were stupid. Because they flew of on a tangent that had nothing to do with the original topic, and then never came back.

That is because Rumraket and hackenslash exposed the flaws in dandan's/leroy's OP within the first few posts, whether dandan/leroy realized it or not).

 

[leroy]

so he_who_is_nobody he_who_is_nobody

Do you finally agree that events with zero probability don’t happen?