Is infinite chain of effects in the universe possible?

[Link]

Not infinitely,. No matter how many numbers you have you can always add one to the pile.

There is infinitely more real numbers then integers proven by set theory. I'm going biking will be back later.

 

[ChristineM]

There is infinitely more real numbers then integers proven by set theory. I'm going biking will be back later.

Uncountably more numbers. I am not sure uncountabe is the same as infinity.

Even though a set is uncountable you can always add a number in which case its becomes uncountably bigger

 

[Link]

Uncountably more numbers. I am not sure uncountabe is the same as infinity.

Even though a set is uncountable you can always add a number in which case its becomes uncountably bigger

There are infinitely more real numbers between any given two integers then all integers themselves which may seem counter intuitive but it's true. This is all proven in set theory.

 

[Polymath257]

This is just one of the components usually debated with the cosmological argument hence I have it in the religious debate section. Although it's part of cosmological argument, the topic is just this component of it.

I put this analogy before:

Infinite commanders all different rank to one another. All won't give an order unless one higher up gives it. There is infinite, so who is highest? There is no highest, and so you would wait forever, and never get an order.

Infinite effects all different stages of time to one another in the universe. All won't come to be unless one previous effects it to be . There is infinite, so who is first? There is no first, so you would wait forever, and never get an effect.

Does the analogy hold?

The problem is that your conclusion that the absence of a highest implies that there will never be an order is incorrect.

ONE solution of your scenario is that no orders are ever given.

ANOTHER solution is that there is *always* an order being given.

So, label the commanders by positive and negative integers (which is possible assuming there are only a countably infinite number of commanders). At time n, commander n gives the command to commander n+1.

Your mistake is thinking that the absence of a first means that no commands are ever given. It is also possible they are always being given. There is *always* an infinite number of commands that have already been given and an infinite number of commands yet to be given. Also, there is no 'first command given'.

This gives a *wave* of commands coming up the line of negative integers. At each step the commander that was just given an order then gives an order to the next commander and the process is *always happening*. Each one waits until his superior commands and each eventually gets a command.

 

[TagliatelliMonster]

Infinite commanders all different rank to one another. All won't give an order unless one higher up gives it. There is infinite, so who is highest?

First part doesn't follow. Second part is loaded with assumptions not in evidence.

There is no highest, and so you would wait forever, and never get an order.

Infinite effects all different stages of time to one another in the universe. All won't come to be unless one previous effects it to be . There is infinite, so who is first? There is no first, so you would wait forever, and never get an effect.

Does the analogy hold?

First, why do say "who"? Why not "what"?

Having said that, if the universe expands indefinetly, then it would be infinite into the future, with a finite past.

 

[TagliatelliMonster]

Whether "effects" all need a cause does not change this component. The reason is because time and state of the universe comes from a previous state. This would be true even if quantum level things happen without a cause as some people might claim.

There is no logical "before" the universe.
And when you label something as an "effect", then you imply a cause preceded it.

 

[Polymath257]

Not infinitely,. No matter how many numbers you have you can always add one to the pile.

Yes, there are infinitely many more real numbers than there are natural numbers.

Uncountably more numbers. I am not sure uncountabe is the same as infinity.

Even though a set is uncountable you can always add a number in which case its becomes uncountably bigger

Uncountable is a *description* of a certain size of infinite set.

And no, if you add a single element to an uncountable set (actually of any infinite set, countable or not), it does not change its cardinality.

 

[TagliatelliMonster]

Salam

I'm not sure I understand the paradox, as there is infinitely more real numbers then integers for example. There is different "levels" of infinity, and without this calculation of different sizes of infinity, programs and their algorithms will fail. So set theory is necessary to know to be a computer scientist for this reason.

Just because we can conceive of an infinite amount of numbers simply by the concept that we can always add another digit to it, doesn't mean at all that that also exists in the real world.

There is a difference between conceptual things and actual things.

As for the start of the universe if no infinite chain of events, I will open a thread about that. This is another component to the cosmological argument debated, but this thread is not about that.

There is nothing to be debated about that, because the cosmological argument is a cesspool of logical fallacies.

No matter how many times you try to reword it. If the underlying logical fallacies aren't addressed, it remains the same nonsense.

As the ancient flemish saying goes:

Even if pigs wear beautiful rings, they are and remain ugly smelly things.

 

[Polymath257]

Salam

I'm not sure I understand the paradox, as there is infinitely more real numbers then integers for example. There is different "levels" of infinity, and without this calculation of different sizes of infinity, programs and their algorithms will fail. So set theory is necessary to know to be a computer scientist for this reason.

As for the start of the universe if no infinite chain of events, I will open a thread about that. This is another component to the cosmological argument debated, but this thread is not about that.

I think you overstate the case. For *theoretical* computer science, the distinction between countably infinite and uncountably infinite is useful, but no program fails or succeeds simply because of that difference. Also, computer science never deals with more than the simple distinction between countable and uncountable. the whole infinite hierarchy of sizes of infinite sets is irrelevant.

 

[Polymath257]

Salam

Every state of the universe comes from a previous state. As @paradox said, infinite set of past events is proven impossible by this analogy.

So you think an order is possible in the commander scenario? Only one commander has to give an order that his higher level, but it will never happen, since they would wait forever for the one more higher up with no end in chain.

Do you think the analogy holds or not?

Yes, the analogy holds.

No, that does not prove that no order is ever given, nor that an infinite sequence of events is impossible.

 

[TagliatelliMonster]

I'm talking about virtual particles, they pop into and pop out of existence, cause is unknown.
But just because cause is unknown is not proof that things can be uncaused.

I don't know of any other events for which cause is unknown?

This is where quantum physics gets spooky.
But it is incorrect to say that "the cause isn't known". It's not even correct to refer to these phenomenon as "events". Quantum fluctuations do not have a cause. They aren't even events. At least not in the sense that they are things that "happen" with a time component involved.

They are rather things that just "are". No cause, no reason, no intention.


Our human minds have a tendency to see them as things that happen "in time" with a time component involved. But that's just us and our limited perception of reality.

To quote Lawrence Krauss: we evolved to avoid being eaten by lions, not to understand quantum mechanics.
We have minds that are used to deal with medium gravity and medium speeds and a rather consistent flow of time.

General relativity doesn't come "intuitively" to us.
Quantum physics doesn't either.
Particle physics,...

All those things are extremely counter intuitive.
Our minds can't conceive of an object that is measured "here" while showing up "there". To our minds, that seems to violate basic laws. An item can't be in 2 places at once. But particles seem to be able to do exactly that.

It's spooky (to us).
Our minds didn't evolve to comprehend such things.

These things, instead, are revealed to us through the mathematical equations that describe these phenomena that we observe. Our minds can't comprehend these things. But our minds don't dictate how the universe works.

So no, it's not correct to say that scientists say that they are uncaused out of "ignorance" or whatever and that that means that we simply don't "know" about the cause.

That's just not true.

These things, like quantum fluctuations ARE uncaused. That's what the math says. And the math is ridiculously accurate when tested.

 

[leroy]

It holds,

Likewise if there is infinite amount of past events in the universe then today may never be reached.

@Link

My favorite argument in support of the impossibility of an infinite is the following. If the age of the universe is infinite then events with zero probability happen (which is absurd)

Background (context)

The probability of a given random event “X” to have happen at some moment in time (T) is 1/the number of moments (say seconds)

So assuming that the universe is 100 seconds old, the probability of an event happening at second 5 is 1/100 (or 1%)…. (each particular second has a probability of 1%)

If the universe is infinite then the probability of an event (say the big bang) to have occurred 14B years ago would be

1/infinite (one divided by infinite)

But one divided by infinite is Zero.

So the probability of the big bang to have occurred 14B years ago is Zero and the same applies for any other event.

But we know that the big bang (and/or other events happened)

So accepting an infinite past implies that events with probability zero can happen (which is absurd)

 

[Polymath257]

@Link

My favorite argument in support of the impossibility of an infinite is the following. If the age of the universe is infinite then events with zero probability happen (which is absurd)

Background (context)

The probability of a given random event “X” to have happen at some moment in time (T) is 1/the number of moments (say seconds)

So assuming that the universe is 100 seconds old, the probability of an event happening at second 5 is 1/100 (or 1%)…. (each particular second has a probability of 1%)

If the universe is infinite then the probability of an event (say the big bang) to have occurred 14B years ago would be

1/infinite (one divided by infinite)

But one divided by infinite is Zero.

So the probability of the big bang to have occurred 14B years ago is Zero and the same applies for any other event.

But we know that the big bang (and/or other events happened)

So accepting an infinite past implies that events with probability zero can happen (which is absurd)

That probability 0 <---> impossible only applies to measure spaces on finite sets.

For example, the probability of picking a rational number out of the interval [0,1] is 0, but it is still possible.

 

[leroy]

That probability 0 <---> impossible only applies to measure spaces on finite sets.

For example, the probability of picking a rational number randomly of the interval [0,1] is 0, but it is still possible.

(I added letters in red.)

No that cant be done. You would need a computer with infinite power in order to do that.

In the real world you don’t consider all the numbers ( you only consider as many as you can imagine) (or as many as your computer can handle) and not all numbers have the same probability of being selected.

 

[Polymath257]

(I added letters in red.)

No that cant be done. You would need a computer with infinite power in order to do that.

In the real world you don’t consider all the numbers ( you only consider as many as you can imagine) (or as many as your computer can handle) and not all numbers have the same probability of being selected.

Who said anything about a computer? The probability of picking a rational number from the collection of real numbers in [0,1] is 0.

Your mistake is thinking that probability 0 implies impossibility and using that as an argument against infinity. But the implication does not hold for infinite sets.

 

[Evangelicalhumanist]

This is just one of the components usually debated with the cosmological argument hence I have it in the religious debate section. Although it's part of cosmological argument, the topic is just this component of it.

I put this analogy before:

Infinite commanders all different rank to one another. All won't give an order unless one higher up gives it. There is infinite, so who is highest? There is no highest, and so you would wait forever, and never get an order.

Infinite effects all different stages of time to one another in the universe. All won't come to be unless one previous effects it to be . There is infinite, so who is first? There is no first, so you would wait forever, and never get an effect.

Does the analogy hold?

It does not seem possible that there can be an "actual infinite."

Think what infinite means: "a number bigger than every possible number" might be one way to express it. Now, add 1 to it -- what does that become? Better yet, multiply it by itself! OMG, now what have we got? And is there any reason you can't raise infinity to the power of infinity?

OH! Having done that, what's to say I can't add an infinite number of powers: infinity raised to (infinity raised to infinity) raised to ..... there won't be room in a trillion universes just to store all those numbers!!!

Quick....stop me before I go mad! (And no, such thoughts did not make Cantor insane.)
-------------------------------------------------

Having said that, I want you to try to understand something very, very subtle -- that if the quantum world is such that it is entirely probabilistic, then quantum particles can both appear without cause -- and disappear without cause.

 

[Link]

The problem is that your conclusion that the absence of a highest implies that there will never be an order is incorrect.

ONE solution of your scenario is that no orders are ever given.

ANOTHER solution is that there is *always* an order being given.

So, label the commanders by positive and negative integers (which is possible assuming there are only a countably infinite number of commanders). At time n, commander n gives the command to commander n+1.

Your mistake is thinking that the absence of a first means that no commands are ever given. It is also possible they are always being given. There is *always* an infinite number of commands that have already been given and an infinite number of commands yet to be given. Also, there is no 'first command given'.

This gives a *wave* of commands coming up the line of negative integers. At each step the commander that was just given an order then gives an order to the next commander and the process is *always happening*. Each one waits until his superior commands and each eventually gets a command.

Salam

It's not a mistake in my scenario. Infinite chain of commanders, none of which are the highest, and each waiting for a command from higher up, would leave no commands in place. Of course, if any given of them were commanding, then the chain that follows it would be in place and all lower commanders would be able to command.

The point of the commanders was to apply an analogy. If you can see where the analogy fails then show it. Obviously if the whole chain was ever in motion it would be able to continue. The argument by analogy is to show it's not possible with the condition. When analogy applies to time, and the condition in time effect and cause, it shows infinite chain of events preceded by effects and causes of one another are impossible.

 

[Link]

Yes, the analogy holds.

No, that does not prove that no order is ever given, nor that an infinite sequence of events is impossible.

You are missing the point of the analogy. If things are in motion, they are in motion. The point of the analogy was to show with the waiting condition, commanders won't command. The analogy applied this with cause and effect states in the universe in time.

The first analogy in itself doesn't show infinite chain impossible perhaps. But with analogy to time and events caused by preceding events, it's shown it is impossible for the universe to be an infinite chain of cause and effects.

 

[Polymath257]

Salam

It's not a mistake in my scenario. Infinite chain of commanders, none of which are the highest, and each waiting for a command from higher up, would leave no commands in place.

And this is wrong. If there are an infinite number of such commanders, it is possible to have no 'highest', each waiting for a command from another, and to always have commands be given.

You are assuming there needs to be a first to get the process going. Instead, consider what happens if the process is always going.

Of course, if any given of them were commanding, then the chain that follows it would be in place and all lower commanders would be able to command.

The point of the commanders was to apply an analogy. If you can see where the analogy fails then show it. Obviously if the whole chain was ever in motion it would be able to continue. The argument by analogy is to show it's not possible with the condition. When analogy applies to time, and the condition in time effect and cause, it shows infinite chain of events preceded by effects and causes of one another are impossible.

The analogy holds, but your conclusion about the infinite string of commanders doesn't follow. And, similarly, there is no logical issue with an infinite sequence of previous events for every event.

Once again, don't assume there needs to be a start if the process is always happening.

 

[Polymath257]

You are missing the point of the analogy. If things are in motion, they are in motion. The point of the analogy was to show with the waiting condition, commanders won't command. The analogy applied this with cause and effect states in the universe in time.

Each particular commander is waiting in my scenario. But the whole process is always happening: there is no first commander to get the process going. Nor does there need to be.

The first analogy in itself doesn't show infinite chain impossible perhaps. But with analogy to time and events caused by preceding events, it's shown it is impossible for the universe to be an infinite chain of cause and effects.

No, it actually does not. In fact, the solution is the same in both cases: simply have the process always ongoing with no start. Each step is preceded by infinity many, but does eventually happen.