Is infinite chain of effects in the universe possible?

[leroy]

There are infinitely many points on a line.

I dont see why is this relevant, but no, in my view points and lines do not excist. Do you afirm the existence of those objects?

And even if they do , they would be independent objects (unless you prove otherwise)

 

[leroy]

Another aspect of the 6000 year old earth and the 4.5 billion year old earth,

Suppose we are determining this from the decay of U-238, we can determine the probability, based on our observations, that the actual age is 6000 years versus 4.5 billion years. of course, we need to build in error bars into each, so maybe go 5500-6500 years vs 4.3-4.7 billion years.

So, let A be our observations so far, B be the event that the Earth is 5500-6500 years old and C the probability that it is 4.3-4.7 billion years old.

We want to compare P(B|A) and P(C|A). The parameter in this is the decay rate.

And, of course, when such probabilities are computed (do you want me to do this?), the first probability is incredibly small (but not 0) and the second is well above 95%.

The basic mistake you are making is the assumption that all possibilities are equally likely: in other words, that the probability is uniform. But this is definitely NOT the case.

The decay rate is a continuous variable (so, infinitely many possibilities) and we can compute the probabilities of various observations based on this variable. And the different possibilities are NOT uniformly distributed: it is like a weighted coin of loaded dice.

The basic mistake you are making is the assumption that all possibilities are equally likely

Granted on the real (fineite ) world possibilities are not equally likely

But once we introduce your infinite mess, suddenly and magically, all probabilidades become the same, so ether reject infinite or accept the implications

If you have an infinite number of U-238 you will have the same number of atoms that decay ay 5500-6000 years, than at 4.5-4.7B years

it is like a weighted coin

Exactly, in the real world you will have more tails than heads if the coin is weighted in favor of tails.

But if you throw a coin infinite times you will have the same amout of tails than heads , which is absurd.

 

[sayak83]

Yes and I learned about negative numbers in 3rth grade, I learned to solve things like 2-5=-3 but that doesn't mean that you can have -3 ballas in a room in the real world.

Infinities and negatives are just usefull tools, but not realistic in the real world


To say that event with zero probability can happen is absurd, but if you insist in that absurdity you have to accept the implications of this possition, which includes that all random events are equally likely , therefore it is equally likely that this planet is roughly 6000yo that 4.5B yo

No it can be mathematically proved that even if we have an infinite possible events, there exists many many probability distributions where the probability density value around a random event has a finite value and they are NOT equally likely. So your statement is provably false (eg. Normal distribution. Look it up).

I just established to you using examples of gravitational potential energy and quantum wavefunction that ALL numbers, positives, negatives,real and imaginary are equally "real. Do you have a counter argument? Otherwise please do not repeat an argument that has been shown to be wrong.

 

[sayak83]

Granted on the real (fineite ) world possibilities are not equally likely

But once we introduce your infinite mess, suddenly and magically, all probabilidades become the same, so ether reject infinite or accept the implications

If you have an infinite number of U-238 you will have the same number of atoms that decay ay 5500-6000 years, than at 4.5-4.7B years



Exactly, in the real world you will have more tails than heads if the coin is weighted in favor of tails.

But if you throw a coin infinite times you will have the same amout of tails than heads , which is absurd.

You do understand that the universe can be finite in extent but infinite in time correct? The non-terminating causal chain does not require a universe that is infinite in extent but rather infinite through time.
In any case even if a universe is infinite in space, then also we can coherently define the number density (no of atoms per unit of space) of uranium particles at any given time and express the decay probabilities in terms of number density...ie. how many uranium atoms will likely decay in a certain unit volume of space with time.
What this shows is merely that a set of different property metrics is required to characterize the state of a system that is unbounded in some way and a coherent physics can be had using such set of metric. This is no cause for concern at all. Finite systems are different from infinite systems and will require different ways to characterize their states. This is par for the course.

 

[Polymath257]

Granted on the real (fineite ) world possibilities are not equally likely

But once we introduce your infinite mess, suddenly and magically, all probabilidades become the same, so ether reject infinite or accept the implications

This is simply wrong.

For example, consider the infinite set of natural numbers: 1, 2, 3, 4, ...

Let the probability of the number n be 1/2^n. This defines a probability measure on the set of natural numbers for which NO non-empty set has measure 0.

Or, look at any continuous probability distribution. The probability of a single point is 0, but the probability of many collections is non-zero. And no, the probabilities are NOT all the same.

If you have an infinite number of U-238 you will have the same number of atoms that decay ay 5500-6000 years, than at 4.5-4.7B years

Irrelevant to the probability. It is possible for two sets to have the same cardinality and yet have different probabilities. In fact, this is common.

Exactly, in the real world you will have more tails than heads if the coin is weighted in favor of tails.

But if you throw a coin infinite times you will have the same amout of tails than heads , which is absurd.

No, it just shows that cardinality is not a very refined notion of size.

 

[Polymath257]

Why would I use an equal statement, when I'm saying it's the negation?

But it isn't the negation either. The negation of 'p-->q' is 'p and not(q)', not 'not(p)-->not(q)'.

 

[Link]

But it isn't the negation either. The negation of 'p-->q' is 'p and not(q)', not 'not(p)-->not(q)'.

You are correct. My mistake, it's the opposite.

The opposite happening is expected since finite is technically the opposite of infinite and vice versa.

 

[Polymath257]

You are correct. My mistake, it's the opposite.

The opposite happening is expected since finite is technically the opposite of infinite and vice versa.

Nope. Finite and infinite are negations of each other. To be infinite is literally to not be finite.

 

[Link]

Nope. Finite and infinite are negations of each other. To be infinite is literally to not be finite.

They are also opposites. No chain can be negation of either.

 

[Polymath257]

They are also opposites. No chain can be negation of either.

You have to be careful. There is no implication in the definitions of finite and infinite. But, you claimed that a certain implication is true. To prove that by contradiction requires dealing with the negation and not the opposite.

 

[leroy]

No it can be mathematically proved that even if we have an infinite possible events, there exists many many probability distributions where the probability density value around a random event has a finite value and they are NOT equally likely. So your statement is provably false (eg. Normal distribution. Look it up).

Well that is one of many absurdities with inifinites, once you have an actual infinite number of things, it doesn’t matter how you do the distribution, the probability will always be the same for any random selection.

I just established to you using examples of gravitational potential energy and quantum wavefunction that ALL numbers, positives, negatives,real and imaginary are equally "real. Do you have a counter argument? Otherwise please do not repeat an argument that has been shown to be wrong.

Yes that is my point negative numbers (and imaginary numbers) are useful fictions.

Negative and positive charges are not “things” they are just useful things that humans invented to represent things in the real world, (like the fact that 2 opposite charges neutralize each other) the negative and positive labels are arbitrary, one could have change them for “black charges” and “white charges”

 

[leroy]

You do understand that the universe can be finite in extent but infinite in time correct? The non-terminating causal chain does not require a universe that is infinite in extent but rather infinite through time.
In any case even if a universe is infinite in space, then also we can coherently define the number density (no of atoms per unit of space) of uranium particles at any given time and express the decay probabilities in terms of number density...ie. how many uranium atoms will likely decay in a certain unit volume of space with time.
What this shows is merely that a set of different property metrics is required to characterize the state of a system that is unbounded in some way and a coherent physics can be had using such set of metric. This is no cause for concern at all. Finite systems are different from infinite systems and will require different ways to characterize their states. This is par for the course.

and express the decay probabilities in terms of number density...ie. how many uranium atoms will likely decay i

Once again that is part of the absurdities of infinity , those coherent and obvious probability statements collapse once you insert infinite stuff.

If you have an infinite number of radioactive atoms, then

1 an infinite number of atoms will decay today



2 and infinite number of atoms will decay tomorrow

3 and infinite number of atoms will decay in the next 4B years

So the exact number of atoms will decay 1 day than in 4B years (which is absurd) which is why infinites are absurd.

also we can coherently define the number density (no of atoms per unit of space) of uranium particles at any given time and express the decay probabilities in terms of number density.

If you have infinite units of space, then any combination will happen an infinite amount of times, so you will have “volumes of space” where all the atoms decayed in 1 day and the exact same amount of volumes of space where none of the atoms decayed.

 

[sayak83]

If you have infinite units of space, then any combination will happen an infinite amount of times, so you will have “volumes of space” where all the atoms decayed in 1 day and the exact same amount of volumes of space where none of the atoms decayed.

Yes. That is what probability entails and that is what is expected. There will certainly be volumes of space where all the atoms would have decayed and other volumes where none have. But the probability of encountering such volumes in a random sample taken from the infinite set of such volumes would be close to (but not exactly) zero.

 

[leroy]

This is simply wrong.

For example, consider the infinite set of natural numbers: 1, 2, 3, 4, ...

I cant, numbers are not real objects, they are just man made stuff, there are no "infinite numbers” there are only as many numbers as one can imagine.

Let the probability of the number n be 1/2^n. This defines a probability measure on the set of natural numbers for which NO non-empty set has measure 0.

Sure, but you are not dealing with actual infinites in this example, this are “potential infinites”

You never get to a point where N becomes infinite, but under your view, the big bang occurred after an infinite amount of events/time………. In this case N becomes infinite,


[

 

[leroy]

Yes. That is what probability entails and that is what is expected. There will certainly be volumes of space where all the atoms would have decayed and other volumes where none have. But the probability of encountering such volumes in a random sample taken from the infinite set of such volumes would be close to (but not exactly) zero.

No, I f you have infinite samples then the probability of picking one sample is zero (not close to zero) but literally zero. Picking a volume where 99% of the atoms decayed is equally likely than picking a volme where only 1% of the atoms decayed . (in the same amout of time)

Which is why infinites are absurd.

 

[Link]

You have to be careful. There is no implication in the definitions of finite and infinite. But, you claimed that a certain implication is true. To prove that by contradiction requires dealing with the negation and not the opposite.

The opposite conclusion is obvious in this case. And finite and infinite are opposite to each other.

We see that in finite sets, the highest will cause all of the chain, to command eventually or at least that it's possible. But with infinite chain of commanders, there is no highest, and so it is impossible to pick one and so commanders will never command.

Its simple conclusion. Now this doesn't prove infinite regress is impossible with time itself, except, its used as analogous to time and states preceding one another. If the analogy holds, then the argument by analogy proves infinite regress in time is impossible as well.

 

[Polymath257]

Well that is one of many absurdities with inifinites, once you have an actual infinite number of things, it doesn’t matter how you do the distribution, the probability will always be the same for any random selection.

Once again, that is simply false. Just ask anyone in a basic probability and statistics course dealing with continuous distributions.

Yes that is my point negative numbers (and imaginary numbers) are useful fictions.

No more so than 2 is. They are just useful for different things.

Negative and positive charges are not “things” they are just useful things that humans invented to represent things in the real world, (like the fact that 2 opposite charges neutralize each other) the negative and positive labels are arbitrary, one could have change them for “black charges” and “white charges”

Absolutely, and the black and white charges would cancel, giving a scenario that is isomorphic to the integers.

 

[Polymath257]

The opposite conclusion is obvious in this case. And finite and infinite are opposite to each other.

We see that in finite sets, the highest will cause all of the chain, to command eventually or at least that it's possible. But with infinite chain of commanders, there is no highest, and so it is impossible to pick one and so commanders will never command.

For a finite number of commanders, it is possible that there is more than one 'highest commander'. And why would a commanderneed to be picked? That is the whole point: the commands are always being given while each waits for his own command, just like a sequence of events in an infinite regress.

Its simple conclusion. Now this doesn't prove infinite regress is impossible with time itself, except, its used as analogous to time and states preceding one another. If the analogy holds, then the argument by analogy proves infinite regress in time is impossible as well.

OK, we are just going around in circles. You clearly do not understand what I am saying.

 

[Link]

For a finite number of commanders, it is possible that there is more than one 'highest commander'. And why would a commanderneed to be picked? That is the whole point: the commands are always being given while each waits for his own command, just like a sequence of events in an infinite regress.



OK, we are just going around in circles. You clearly do not understand what I am saying.

Its to set up an analogy.

 

[Polymath257]

Its to set up an analogy.

Yes, I get that. And the analogy doesn't show what you think it does.