Well it’s true of any infinite series of random digits, so I suppose it’s true of pi (which is not random, but still).

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

i asked because i seem to remember a discussion on the original forum about an infinite universe. something along the lines of “just because it is infinite doesn’t mean everything is possible or going to happen”.

ChrispenEvan said:

i asked because i seem to remember a discussion on the original forum about an infinite universe. something along the lines of “just because it is infinite doesn’t mean everything is possible or going to happen”.

That’s where nearly infinite fits in.

ChrispenEvan said:

i asked because i seem to remember a discussion on the original forum about an infinite universe. something along the lines of “just because it is infinite doesn’t mean everything is possible or going to happen”.

But that would require time to be infinite.

kii said:

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

Pi e .

poikilotherm said:

kii said:

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

Pi e .

e pi is more you line poik.

ChrispenEvan said:

i asked because i seem to remember a discussion on the original forum about an infinite universe. something along the lines of “just because it is infinite doesn’t mean everything is possible or going to happen”.

In the case of irrational but non-random sequences (like pi) it is possible that some sub-sequences might be excluded (although afaik there is no reason to think that should be the case).

In the case of an infinite universe, if it is non-uniform (i.e. it is not like the visible universe), then it is possible that not every possible thing happens.

In the case of an infinite uniform universe, or an infinite universe with a finite variation, then every possible event will be repeated an infinite number of times, provided that events are defined to be of finite size and resolution.

Not everyone agrees with that, but those who disagree are wrong.

Peak Warming Man said:

ChrispenEvan said:

i asked because i seem to remember a discussion on the original forum about an infinite universe. something along the lines of “just because it is infinite doesn’t mean everything is possible or going to happen”.

But that would require time to be infinite.

No.

The Rev Dodgson said:

Peak Warming Man said:

ChrispenEvan said:

i asked because i seem to remember a discussion on the original forum about an infinite universe. something along the lines of “just because it is infinite doesn’t mean everything is possible or going to happen”.

But that would require time to be infinite.

No.

Just stop right there Pilgrim.
You’re not saying that there would be multiple or even infinite universes are you.

The Rev Dodgson said:

In the case of an infinite uniform universe, or an infinite universe with a finite variation, then every possible event will be repeated an infinite number of times, provided that events are defined to be of finite size and resolution.

Read this many times still don’t understand it. Would that mean in another universe which is the exact same configuration as ours there might be another Second World War repeating with every soldier by the same name falling to the same bit of enemy shrapnel as occurred in our universe?

kii said:

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

I asked a friend.

I have NFI.

Peak Warming Man said:

The Rev Dodgson said:

Peak Warming Man said:

But that would require time to be infinite.

No.

Just stop right there Pilgrim.
You’re not saying that there would be multiple or even infinite universes are you.

No, the opposite.

I’m saying if there is an infinite continuous space with properties similar to the space we can see, and if we define “events” to have finite extent in space and time and finite resolution, then there are a finite number of possible events, so any possible event will be repeated an infinite number of times.

AwesomeO said:

The Rev Dodgson said:

In the case of an infinite uniform universe, or an infinite universe with a finite variation, then every possible event will be repeated an infinite number of times, provided that events are defined to be of finite size and resolution.

Read this many times still don’t understand it. Would that mean in another universe which is the exact same configuration as ours there might be another Second World War repeating with every soldier by the same name falling to the same bit of enemy shrapnel as occurred in our universe?

Yes, but the same applies in this universe, if it is infinite.

The Rev Dodgson said:

Peak Warming Man said:

The Rev Dodgson said:

No.

Just stop right there Pilgrim.
You’re not saying that there would be multiple or even infinite universes are you.

No, the opposite.

I’m saying if there is an infinite continuous space with properties similar to the space we can see, and if we define “events” to have finite extent in space and time and finite resolution, then there are a finite number of possible events, so any possible event will be repeated an infinite number of times.

Vibrations occur in space time across all the whole frequency spectrum.

Atomic particles vibrate.

Are these events are vibrations?

The Rev Dodgson said:

Peak Warming Man said:

The Rev Dodgson said:

No.

Just stop right there Pilgrim.
You’re not saying that there would be multiple or even infinite universes are you.

No, the opposite.

I’m saying if there is an infinite continuous space with properties similar to the space we can see, and if we define “events” to have finite extent in space and time and finite resolution, then there are a finite number of possible events, so any possible event will be repeated an infinite number of times.

So somewhere out there points roughly there will be a right wing nutter TRD and a left wing nutter PWM.
Great and terrible thing.

Tau.Neutrino said:

The Rev Dodgson said:

Peak Warming Man said:

Just stop right there Pilgrim.
You’re not saying that there would be multiple or even infinite universes are you.

No, the opposite.

I’m saying if there is an infinite continuous space with properties similar to the space we can see, and if we define “events” to have finite extent in space and time and finite resolution, then there are a finite number of possible events, so any possible event will be repeated an infinite number of times.

Vibrations occur in space time across all the whole frequency spectrum.

Atomic particles vibrate.

Are these events are vibrations?

If you want to go down to that level, yes.

Peak Warming Man said:

The Rev Dodgson said:

Peak Warming Man said:

Just stop right there Pilgrim.
You’re not saying that there would be multiple or even infinite universes are you.

No, the opposite.

I’m saying if there is an infinite continuous space with properties similar to the space we can see, and if we define “events” to have finite extent in space and time and finite resolution, then there are a finite number of possible events, so any possible event will be repeated an infinite number of times.

So somewhere out there points roughly there will be a right wing nutter TRD and a left wing nutter PWM.
Great and terrible thing.

If such things are possible, yes.

The Rev Dodgson said:

Tau.Neutrino said:

The Rev Dodgson said:

No, the opposite.

I’m saying if there is an infinite continuous space with properties similar to the space we can see, and if we define “events” to have finite extent in space and time and finite resolution, then there are a finite number of possible events, so any possible event will be repeated an infinite number of times.

Vibrations occur in space time across all the whole frequency spectrum.

Atomic particles vibrate.

Are these events are vibrations?

If you want to go down to that level, yes.

But in the context of the discussion, I’m thinking more of the scale of events that can be observed un-aided by a human-like entity. At that scale I’m saying that if two “events”, such as someone drinking a cup of tea whilst typing into an Internet forum known as The Holiday Forum, are indistinguishable to all those involved, then those events will be repeated an infinite number of times.

The same applies for much larger, but still finite events, such as large groups of people fighting a war known as The Second World War.

Also, for every exact repeat, there will obviously be a huge number of repeats with small variations, and a hugely more huge number with larger variations.

Do space and time both have to be infinite?

Tau.Neutrino said:

Do space and time both have to be infinite?

No, either/or.

Yes

No

I wonder how far you’d have to travel out into the infinite universe to find another solar system just like ours

Pi is one number with an infinite number of decimals.

But there is an infinite number of numbers that have an infinite number of decimals, and only one (pi itself) appears in pi.

Cymek said:

I wonder how far you’d have to travel out into the infinite universe to find another solar system just like ours

Long way.

Bubblecar said:

Pi is one number with an infinite number of decimals.

But there is an infinite number of numbers that have an infinite number of decimals, and only one (pi itself) appears in pi.

That’s why with the events in the universe repeating analogy, the events have to be finite in size and duration, and have finite resolution.

The point is that all you have to do is change the position of any digit in pi and you have a new number that doesn’t appear anywhere in pi. And there’s an infinite number of such changes you could make.

So-called “real numbers” (with infinite decimals) are of higher cardinality than the natural numbers, so can’t be counted by them (placed in a one-to-one correspondence). The natural numbers are countably infinite, the real numbers are uncountably infinite.

In those infinite universe threads I asked whether an infinite universe could be considered countably or uncountably infinite, and how this would relate to “the set of things that are possible”.

Apparently it depends on whether or not space-time is quantized.

I remember asking on SSSF about pi and the real practical use of it only applies to a few tens of even less digits

Bubblecar said:

The point is that all you have to do is change the position of any digit in pi and you have a new number that doesn’t appear anywhere in pi. And there’s an infinite number of such changes you could make.

So-called “real numbers” (with infinite decimals) are of higher cardinality than the natural numbers, so can’t be counted by them (placed in a one-to-one correspondence). The natural numbers are countably infinite, the real numbers are uncountably infinite.

In those infinite universe threads I asked whether an infinite universe could be considered countably or uncountably infinite, and how this would relate to “the set of things that are possible”.

Apparently it depends on whether or not space-time is quantized.

No, it just depends on whether events are finite or not. The cardinality of different sorts of infinite numbers has nothing to do with it.

The Rev Dodgson said:

Bubblecar said:

The point is that all you have to do is change the position of any digit in pi and you have a new number that doesn’t appear anywhere in pi. And there’s an infinite number of such changes you could make.

So-called “real numbers” (with infinite decimals) are of higher cardinality than the natural numbers, so can’t be counted by them (placed in a one-to-one correspondence). The natural numbers are countably infinite, the real numbers are uncountably infinite.

In those infinite universe threads I asked whether an infinite universe could be considered countably or uncountably infinite, and how this would relate to “the set of things that are possible”.

Apparently it depends on whether or not space-time is quantized.

No, it just depends on whether events are finite or not. The cardinality of different sorts of infinite numbers has nothing to do with it.

In order to have a universe in which every event that could happen does happen, the set of what could happen and the set of what does happen need a one-to-one correspondence.

So Westpac will open an account for your newborn with $100 in it for free.
New parents would be crazy not to take that up.

Peak Warming Man said:

So Westpac will open an account for your newborn with $100 in it for free.
New parents would be crazy not to take that up.

How much interest could you get after twenty years?

Bubblecar said:

The Rev Dodgson said:

Bubblecar said:

The point is that all you have to do is change the position of any digit in pi and you have a new number that doesn’t appear anywhere in pi. And there’s an infinite number of such changes you could make.

So-called “real numbers” (with infinite decimals) are of higher cardinality than the natural numbers, so can’t be counted by them (placed in a one-to-one correspondence). The natural numbers are countably infinite, the real numbers are uncountably infinite.

In those infinite universe threads I asked whether an infinite universe could be considered countably or uncountably infinite, and how this would relate to “the set of things that are possible”.

Apparently it depends on whether or not space-time is quantized.

No, it just depends on whether events are finite or not. The cardinality of different sorts of infinite numbers has nothing to do with it.

In order to have a universe in which every event that could happen does happen, the set of what could happen and the set of what does happen need a one-to-one correspondence.

That’s true if you define indistinguishable events that occur at different times and places as different events, but what conclusion do you draw from that?

I miss Donde.

sibeen said:

I miss Donde.

I bet you don’t, really.

Tau.Neutrino said:

Peak Warming Man said:

So Westpac will open an account for your newborn with $100 in it for free.
New parents would be crazy not to take that up.

How much interest could you get after twenty years?

SFA, and that doesn’t equate to “significant fiscal amount”

Well it’s true of any infinite series of random digits, so I suppose it’s true of pi (which is not random, but still).

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

To do all of those, even if you use all the atoms or even subatomic particles in the visible universe – there aren’t nearly enough.

The theoretical value of pi can’t be measured, or even calculated, to an accuracy high enough to do many of those things.

Which opens the question of what can be done with the calculable digits of pi? Pi has been calculated to 2.7 * 10^12 digits.

“The name of every person you will ever love” would require about 10^12 digits, give or take a factor of a hundred, so it’s a close-run thing.

“The date, time and manner of your death” would require about 10^9 digits for the date and time, and a further 10^4 or so digits for manner of death (if the manner is spelled out in English), again it’s a close-run thing.

“A pixel-perfect representation of the first thing you saw on this earth”. Well, a newborn baby’s eyesight is exceptionally poor. Buffy could help out here. Say 16 colours and 1000 pixels. Still, we’re talking of the order of 10^48 digits of pi here. Can’t be done. All the rest, not a chance in hell.

mollwollfumble said:

Well it’s true of any infinite series of random digits, so I suppose it’s true of pi (which is not random, but still).

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

To do all of those, even if you use all the atoms or even subatomic particles in the visible universe – there aren’t nearly enough.

The theoretical value of pi can’t be measured, or even calculated, to an accuracy high enough to do many of those things.

Which opens the question of what can be done with the calculable digits of pi? Pi has been calculated to 2.7 * 10^12 digits.

“The name of every person you will ever love” would require about 10^12 digits, give or take a factor of a hundred, so it’s a close-run thing.

“The date, time and manner of your death” would require about 10^9 digits for the date and time, and a further 10^4 or so digits for manner of death (if the manner is spelled out in English), again it’s a close-run thing.

“A pixel-perfect representation of the first thing you saw on this earth”. Well, a newborn baby’s eyesight is exceptionally poor. Buffy could help out here. Say 16 colours and 1000 pixels. Still, we’re talking of the order of 10^48 digits of pi here. Can’t be done. All the rest, not a chance in hell.

So he lied ?

mollwollfumble said:

Well it’s true of any infinite series of random digits, so I suppose it’s true of pi (which is not random, but still).

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

To do all of those, even if you use all the atoms or even subatomic particles in the visible universe – there aren’t nearly enough.

The theoretical value of pi can’t be measured, or even calculated, to an accuracy high enough to do many of those things.

Which opens the question of what can be done with the calculable digits of pi? Pi has been calculated to 2.7 * 10^12 digits.

“The name of every person you will ever love” would require about 10^12 digits, give or take a factor of a hundred, so it’s a close-run thing.

“The date, time and manner of your death” would require about 10^9 digits for the date and time, and a further 10^4 or so digits for manner of death (if the manner is spelled out in English), again it’s a close-run thing.

“A pixel-perfect representation of the first thing you saw on this earth”. Well, a newborn baby’s eyesight is exceptionally poor. Buffy could help out here. Say 16 colours and 1000 pixels. Still, we’re talking of the order of 10^48 digits of pi here. Can’t be done. All the rest, not a chance in hell.

Yes, that’s why we are talking about an infinite series of numbers or infinite space, rather than the miniscule numbers given in your example.

Cymek said:

So he lied ?

Who lied?

dv said:

Cymek said:

So he lied ?

Who lied?

It wasn’t me, and anyway you cant prove it.

“Pi is at least a million, maybe a million and a half, people tell me it is the greatest pi ever.”

The Rev Dodgson said:

mollwollfumble said:

Well it’s true of any infinite series of random digits, so I suppose it’s true of pi (which is not random, but still).

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

To do all of those, even if you use all the atoms or even subatomic particles in the visible universe – there aren’t nearly enough.

The theoretical value of pi can’t be measured, or even calculated, to an accuracy high enough to do many of those things.

Which opens the question of what can be done with the calculable digits of pi? Pi has been calculated to 2.7 * 10^12 digits.

“The name of every person you will ever love” would require about 10^12 digits, give or take a factor of a hundred, so it’s a close-run thing.

“The date, time and manner of your death” would require about 10^9 digits for the date and time, and a further 10^4 or so digits for manner of death (if the manner is spelled out in English), again it’s a close-run thing.

“A pixel-perfect representation of the first thing you saw on this earth”. Well, a newborn baby’s eyesight is exceptionally poor. Buffy could help out here. Say 16 colours and 1000 pixels. Still, we’re talking of the order of 10^48 digits of pi here. Can’t be done. All the rest, not a chance in hell.

Yes, that’s why we are talking about an infinite series of numbers or infinite space, rather than the miniscule numbers given in your example.

Have you considered aleph null vs aleph one?

It’s OK, I’m just kidding, aleph null suffices.

But try figuring out for yourself how the probability of the last case on the list compares with the number of atoms in the visible universe.

Btw, I did make one calculation error in the above.

Can I just mess things up a bit by saying that the universe may not be like pi. The universe might be such that it is infinite in scope yet not contain all conceivable worlds.

Is this true?

“The cards, the cards, the cards will tell
The past, the present and the future as well”

If the cards contain the digits of pi?

mollwollfumble said:

Which opens the question of what can be done with the calculable digits of pi? Pi has been calculated to 2.7 * 10^12 digits.

“The name of every person you will ever love” would require about 10^12 digits, give or take a factor of a hundred, so it’s a close-run thing.

“The date, time and manner of your death” would require about 10^9 digits for the date and time, and a further 10^4 or so digits for manner of death (if the manner is spelled out in English), again it’s a close-run thing.

“A pixel-perfect representation of the first thing you saw on this earth”. Well, a newborn baby’s eyesight is exceptionally poor. Buffy could help out here. Say 16 colours and 1000 pixels. Still, we’re talking of the order of 10^48 digits of pi here. Can’t be done. All the rest, not a chance in hell.

Can someone please explain in greater detail why the above examples of reasonably mundane events need such large numbers to explain?

I haven’t read his book, but I saw an interview with the guy who wrote The Bible Code. Apparently all sorts of things were predicted in the original text of the Torah.

https://en.wikipedia.org/wiki/Bible_code

Perhaps the original texts of the bible/Torah are based on pi *cue spooky music *

Witty Rejoinder said:

mollwollfumble said:

Which opens the question of what can be done with the calculable digits of pi? Pi has been calculated to 2.7 * 10^12 digits.

“The name of every person you will ever love” would require about 10^12 digits, give or take a factor of a hundred, so it’s a close-run thing.

“The date, time and manner of your death” would require about 10^9 digits for the date and time, and a further 10^4 or so digits for manner of death (if the manner is spelled out in English), again it’s a close-run thing.

“A pixel-perfect representation of the first thing you saw on this earth”. Well, a newborn baby’s eyesight is exceptionally poor. Buffy could help out here. Say 16 colours and 1000 pixels. Still, we’re talking of the order of 10^48 digits of pi here. Can’t be done. All the rest, not a chance in hell.

Can someone please explain in greater detail why the above examples of reasonably mundane events need such large numbers to explain?

Because ,mundane events are extremely complex when closely examined.

Divine Angel said:

I haven’t read his book, but I saw an interview with the guy who wrote The Bible Code. Apparently all sorts of things were predicted in the original text of the Torah.

https://en.wikipedia.org/wiki/Bible_code

Perhaps the original texts of the bible/Torah are based on pi *cue spooky music *

Do I even need to tell you it’s garbage?

dv said:

Because ,mundane events are extremely complex when closely examined.

I get that but still can’t get my head around what is being calculated. Are we talking quantum mechanics?

Witty Rejoinder said:

dv said:

Because ,mundane events are extremely complex when closely examined.

I get that but still can’t get my head around what is being calculated. Are we talking quantum mechanics?

I’ll let moll account for himself but I guess so

dv said:

Divine Angel said:

I haven’t read his book, but I saw an interview with the guy who wrote The Bible Code. Apparently all sorts of things were predicted in the original text of the Torah.

https://en.wikipedia.org/wiki/Bible_code

Perhaps the original texts of the bible/Torah are based on pi *cue spooky music *

Do I even need to tell you it’s garbage?

I’ll put on a tinfoil hat just in case.

mollwollfumble said:

The Rev Dodgson said:

mollwollfumble said:

Well it’s true of any infinite series of random digits, so I suppose it’s true of pi (which is not random, but still).

Yes. That doesn’t mean pi is magic.
e is the same way

Any irrational number will be the same.

To do all of those, even if you use all the atoms or even subatomic particles in the visible universe – there aren’t nearly enough.

The theoretical value of pi can’t be measured, or even calculated, to an accuracy high enough to do many of those things.

Which opens the question of what can be done with the calculable digits of pi? Pi has been calculated to 2.7 * 10^12 digits.

“The name of every person you will ever love” would require about 10^12 digits, give or take a factor of a hundred, so it’s a close-run thing.

“The date, time and manner of your death” would require about 10^9 digits for the date and time, and a further 10^4 or so digits for manner of death (if the manner is spelled out in English), again it’s a close-run thing.

“A pixel-perfect representation of the first thing you saw on this earth”. Well, a newborn baby’s eyesight is exceptionally poor. Buffy could help out here. Say 16 colours and 1000 pixels. Still, we’re talking of the order of 10^48 digits of pi here. Can’t be done. All the rest, not a chance in hell.

Yes, that’s why we are talking about an infinite series of numbers or infinite space, rather than the miniscule numbers given in your example.

Have you considered aleph null vs aleph one?

It’s OK, I’m just kidding, aleph null suffices.

But try figuring out for yourself how the probability of the last case on the list compares with the number of atoms in the visible universe.

I already know that (to a very rough order of magnitude), but what does that have to do with anything?

We are talking infinite universes here, not the tiny bit of one that we can see.

mollwollfumble said:

Btw, I did make one calculation error in the above.

I didn’t suggest that you did.

dv said:

Can I just mess things up a bit by saying that the universe may not be like pi. The universe might be such that it is infinite in scope yet not contain all conceivable worlds.

It doesn’t have to.

We are discussing if an event that did occur in an infinite universe would occur an infinite number of times.

If an event never occurred in an infinite universe, then that event would be impossible in that universe.

The Rev Dodgson said:

mollwollfumble said:

The Rev Dodgson said:

Have you considered aleph null vs aleph one?

It’s OK, I’m just kidding, aleph null suffices.

But try figuring out for yourself how the probability of the last case on the list compares with the number of atoms in the visible universe.

I already know that (to a very rough order of magnitude), but what does that have to do with anything?

We are talking infinite universes here, not the tiny bit of one that we can see.

mollwollfumble said:

Btw, I did make one calculation error in the above.

I didn’t suggest that you did.

But he did nonetheless

dv said:

The Rev Dodgson said:

mollwollfumble said:

I already know that (to a very rough order of magnitude), but what does that have to do with anything?

We are talking infinite universes here, not the tiny bit of one that we can see.

mollwollfumble said:

Btw, I did make one calculation error in the above.

I didn’t suggest that you did.

But he did nonetheless

Quite possibly, I didn’t check because I don’t see the numbers as being relevant, no matter how big they are (if finite).

The Rev Dodgson said:

dv said:

Can I just mess things up a bit by saying that the universe may not be like pi. The universe might be such that it is infinite in scope yet not contain all conceivable worlds.

It doesn’t have to.

We are discussing if an event that did occur in an infinite universe would occur an infinite number of times.

If an event never occurred in an infinite universe, then that event would be impossible in that universe.

We can conceive of a universe where the answer to that question is “not necessarily”.

The Rev Dodgson said:

dv said:

The Rev Dodgson said:

I didn’t suggest that you did.

But he did nonetheless

Quite possibly, I didn’t check because I don’t see the numbers as being relevant, no matter how big they are (if finite).

I didn’t check either.

dv said:

The Rev Dodgson said:

dv said:

Can I just mess things up a bit by saying that the universe may not be like pi. The universe might be such that it is infinite in scope yet not contain all conceivable worlds.

It doesn’t have to.

We are discussing if an event that did occur in an infinite universe would occur an infinite number of times.

If an event never occurred in an infinite universe, then that event would be impossible in that universe.

We can conceive of a universe where the answer to that question is “not necessarily”.

Sure, but I restricted the discussion up there somewhere to ones with uniform properties (or an infinite sub-space of uniform properties), like the unverse we can see a bit of.

dv said:

Witty Rejoinder said:

dv said:

Because ,mundane events are extremely complex when closely examined.

I get that but still can’t get my head around what is being calculated. Are we talking quantum mechanics?

I’ll let moll account for himself but I guess so

All the examples he gave were macro scale. No QM involved.

The Rev Dodgson said:

All the examples he gave were macro scale. No QM involved.

Sorry i’m not making myself clear. I think i will need to see the calculations to understand Moll’s claims.

Divine Angel said:

I haven’t read his book, but I saw an interview with the guy who wrote The Bible Code. Apparently all sorts of things were predicted in the original text of the Torah.

https://en.wikipedia.org/wiki/Bible_code

Perhaps the original texts of the bible/Torah are based on pi *cue spooky music *

The letters of the Hebrew alphabet are also numbers, so any word written in Hebrew is also a number. This led some to believe that words that represent the same number must, in some sense, represent the same thing, or that text that means one thing also means something else; since the Torah is believed by devout Jews to be the written word of God himself, it follows that it must contain information about the future, which can be extracted using the gematria or notarikon (the names of the methods described above.) There are references to π in the Torah, but it’s defined as 3.

The Rev Dodgson said:

dv said:

Can I just mess things up a bit by saying that the universe may not be like pi. The universe might be such that it is infinite in scope yet not contain all conceivable worlds.

It doesn’t have to.

We are discussing if an event that did occur in an infinite universe would occur an infinite number of times.

If an event never occurred in an infinite universe, then that event would be impossible in that universe.

PermeateFree said:

The Rev Dodgson said:

dv said:

Can I just mess things up a bit by saying that the universe may not be like pi. The universe might be such that it is infinite in scope yet not contain all conceivable worlds.

It doesn’t have to.

We are discussing if an event that did occur in an infinite universe would occur an infinite number of times.

If an event never occurred in an infinite universe, then that event would be impossible in that universe.

dv said:

The Rev Dodgson said:

dv said:

But he did nonetheless

Quite possibly, I didn’t check because I don’t see the numbers as being relevant, no matter how big they are (if finite).

I didn’t check either.

I didn’t check either.

Weird ha? What are the odds of that?

the ratio, or correspondence between circumference and diameter, in the world of things (outside the math and geometry done by minds) has nothing to do with the numbers we employ to describe it.

I mean the physics doesn’t do what it does in decimal, for example.

neither does it start at 3.

transition said:

the ratio, or correspondence between circumference and diameter, in the world of things (outside the math and geometry done by minds) has nothing to do with the numbers we employ to describe it.

I mean the physics doesn’t do what it does in decimal, for example.

It does it in whatever form we choose to use to describe it.

transition said:

neither does it start at 3.

I say it does.

Obviously you could use a different symbol to describe it, but whatever symbol you use, the number would still be the number we call 3.

>the ratio, or correspondence between circumference and diameter, in the world of things (outside the math and geometry done by minds) has nothing to do with the numbers we employ to describe it.

Then how do we know our description is accurate?

The Rev Dodgson said:

Tau.Neutrino said:

Do space and time both have to be infinite?

No, either/or.

Normally in cosmology, finite time and finite space are linked.

The Rev Dodgson said:

AwesomeO said:

The Rev Dodgson said:

In the case of an infinite uniform universe, or an infinite universe with a finite variation, then every possible event will be repeated an infinite number of times, provided that events are defined to be of finite size and resolution.

Read this many times still don’t understand it. Would that mean in another universe which is the exact same configuration as ours there might be another Second World War repeating with every soldier by the same name falling to the same bit of enemy shrapnel as occurred in our universe?

Yes, but the same applies in this universe, if it is infinite.

I find it hard to believe that enough butterfly’s would flap their wings in synch enough to bring about a perfect recreation of the Second World War. And not just once, an infinite amount of times presumably. I ain’t no mathematician but if that is a prediction of the maths then I think there must be something screwy with the maths.

AwesomeO said:

The Rev Dodgson said:

AwesomeO said:

Read this many times still don’t understand it. Would that mean in another universe which is the exact same configuration as ours there might be another Second World War repeating with every soldier by the same name falling to the same bit of enemy shrapnel as occurred in our universe?

Yes, but the same applies in this universe, if it is infinite.

I find it hard to believe that enough butterfly’s would flap their wings in synch enough to bring about a perfect recreation of the Second World War. And not just once, an infinite amount of times presumably. I ain’t no mathematician but if that is a prediction of the maths then I think there must be something screwy with the maths.

https://www.youtube.com/watch?v=Uj3_KqkI9Zo

6min video on Hilbert’s Hotel. infinity is screwy.

>I say it does.
>Obviously you could use a different symbol to describe it, but whatever symbol you use, the number would still be the number we call 3.

dunno.

i’m saying the ratio correspondence is not a number.

you can give it a number.

AwesomeO said:

The Rev Dodgson said:

AwesomeO said:

Read this many times still don’t understand it. Would that mean in another universe which is the exact same configuration as ours there might be another Second World War repeating with every soldier by the same name falling to the same bit of enemy shrapnel as occurred in our universe?

Yes, but the same applies in this universe, if it is infinite.

I find it hard to believe that enough butterfly’s would flap their wings in synch enough to bring about a perfect recreation of the Second World War. And not just once, an infinite amount of times presumably. I ain’t no mathematician but if that is a prediction of the maths then I think there must be something screwy with the maths.

Doesn’t require any maths. It’s just a requirement of the concept of infinity.

Perhaps a different perspective would help.

Start by collecting all the planets orbiting a star of the same size as our Sun, and the same size and orbit as Earth (an infinite number)
From those select all those where the land-forms are identical to those on Earth (to some arbitrary level of precision). A miniscule proportion, but still an infinite number.
From those select those where animals identical to humans have evolved. Still an infinite number.

and so on.

At each stage the proportion of selected planets is way less than one per observable universe, but if you start with an infinite number of planets, each sub-set is also infinite.

AwesomeO said:

The Rev Dodgson said:

AwesomeO said:

Read this many times still don’t understand it. Would that mean in another universe which is the exact same configuration as ours there might be another Second World War repeating with every soldier by the same name falling to the same bit of enemy shrapnel as occurred in our universe?

Yes, but the same applies in this universe, if it is infinite.

I find it hard to believe that enough butterfly’s would flap their wings in synch enough to bring about a perfect recreation of the Second World War. And not just once, an infinite amount of times presumably. I ain’t no mathematician but if that is a prediction of the maths then I think there must be something screwy with the maths.

Doesn’t require any maths. It’s just a requirement of the concept of infinity.

Perhaps a different perspective would help.

Start by collecting all the planets orbiting a star of the same size as our Sun, and the same size and orbit as Earth (an infinite number)
From those select all those where the land-forms are identical to those on Earth (to some arbitrary level of precision). A miniscule proportion, but still an infinite number.
From those select those where animals identical to humans have evolved. Still an infinite number.

and so on.

At each stage the proportion of selected planets is way less than one per observable universe, but if you start with an infinite number of planets, each sub-set is also infinite.

AwesomeO said:

The Rev Dodgson said:

AwesomeO said:

Read this many times still don’t understand it. Would that mean in another universe which is the exact same configuration as ours there might be another Second World War repeating with every soldier by the same name falling to the same bit of enemy shrapnel as occurred in our universe?

Yes, but the same applies in this universe, if it is infinite.

I find it hard to believe that enough butterfly’s would flap their wings in synch enough to bring about a perfect recreation of the Second World War. And not just once, an infinite amount of times presumably. I ain’t no mathematician but if that is a prediction of the maths then I think there must be something screwy with the maths.

Doesn’t require any maths. It’s just a requirement of the concept of infinity.

Perhaps a different perspective would help.

Start by collecting all the planets orbiting a star of the same size as our Sun, and the same size and orbit as Earth (an infinite number)
From those select all those where the land-forms are identical to those on Earth (to some arbitrary level of precision). A miniscule proportion, but still an infinite number.
From those select those where animals identical to humans have evolved. Still an infinite number.

and so on.

At each stage the proportion of selected planets is way less than one per observable universe, but if you start with an infinite number of planets, each sub-set is also infinite.

mollwollfumble said:

The Rev Dodgson said:

Tau.Neutrino said:

Do space and time both have to be infinite?

No, either/or.

Normally in cosmology, finite time and finite space are linked.

Ref?

The Rev Dodgson said:

AwesomeO said:

The Rev Dodgson said:

Yes, but the same applies in this universe, if it is infinite.

I find it hard to believe that enough butterfly’s would flap their wings in synch enough to bring about a perfect recreation of the Second World War. And not just once, an infinite amount of times presumably. I ain’t no mathematician but if that is a prediction of the maths then I think there must be something screwy with the maths.

Doesn’t require any maths. It’s just a requirement of the concept of infinity.

Perhaps a different perspective would help.

Start by collecting all the planets orbiting a star of the same size as our Sun, and the same size and orbit as Earth (an infinite number)
From those select all those where the land-forms are identical to those on Earth (to some arbitrary level of precision). A miniscule proportion, but still an infinite number.
From those select those where animals identical to humans have evolved. Still an infinite number.

and so on.

At each stage the proportion of selected planets is way less than one per observable universe, but if you start with an infinite number of planets, each sub-set is also infinite.

you going for an infinite number of posts identical?

transition said:

>I say it does.
>Obviously you could use a different symbol to describe it, but whatever symbol you use, the number would still be the number we call 3.

dunno.

i’m saying the ratio correspondence is not a number.

you can give it a number.

Well I’m saying it is a number. Ratios are numbers.

The Rev Dodgson said:

AwesomeO said:

The Rev Dodgson said:

Yes, but the same applies in this universe, if it is infinite.

I find it hard to believe that enough butterfly’s would flap their wings in synch enough to bring about a perfect recreation of the Second World War. And not just once, an infinite amount of times presumably. I ain’t no mathematician but if that is a prediction of the maths then I think there must be something screwy with the maths.

Doesn’t require any maths. It’s just a requirement of the concept of infinity.

Perhaps a different perspective would help.

Start by collecting all the planets orbiting a star of the same size as our Sun, and the same size and orbit as Earth (an infinite number)
From those select all those where the land-forms are identical to those on Earth (to some arbitrary level of precision). A miniscule proportion, but still an infinite number.
From those select those where animals identical to humans have evolved. Still an infinite number.

and so on.

At each stage the proportion of selected planets is way less than one per observable universe, but if you start with an infinite number of planets, each sub-set is also infinite.

In my cosmology the chances of a perfect reproduction of the Second World War would be beyond infinite, infinity + 1.

infinity is not just a big number.

old jungle saying.

ChrispenEvan said:

you going for an infinite number of posts identical?

Yes

I may be some time.

AwesomeO said:

In my cosmology the chances of a perfect reproduction of the Second World War would be beyond infinite, infinity + 1.

Doesn’t need to be perfect. Just close enough so no-one would notice the difference.

There are a finite number of particles, that can go in a finite number of locations, so the number of different arrangements is finite.

The Rev Dodgson said:

AwesomeO said:

In my cosmology the chances of a perfect reproduction of the Second World War would be beyond infinite, infinity + 1.

Doesn’t need to be perfect. Just close enough so no-one would notice the difference.

There are a finite number of particles, that can go in a finite number of locations, so the number of different arrangements is finite.

When I stipulated that a named soldier was killed with a particular bit of shrapnel that indicates to me a perfect reproduction.

AwesomeO said:

The Rev Dodgson said:

AwesomeO said:

In my cosmology the chances of a perfect reproduction of the Second World War would be beyond infinite, infinity + 1.

Doesn’t need to be perfect. Just close enough so no-one would notice the difference.

There are a finite number of particles, that can go in a finite number of locations, so the number of different arrangements is finite.

When I stipulated that a named soldier was killed with a particular bit of shrapnel that indicates to me a perfect reproduction.

That’s why I keep on about finite resolution.

But you can have two or more copies that are indistinguishable, including exact names and bits of shrapnel that look identical, but still have finite resolution, and hence a finite number of possible arrangements of the available finite sized particles.

The Rev Dodgson said:

AwesomeO said:

In my cosmology the chances of a perfect reproduction of the Second World War would be beyond infinite, infinity + 1.

Doesn’t need to be perfect. Just close enough so no-one would notice the difference.

There are a finite number of particles, that can go in a finite number of locations, so the number of different arrangements is finite.

In any time including WWII, their are also an infinite number of variables to make accurate reproduction impossible for a moment, let alone any period of time.

PermeateFree said:

The Rev Dodgson said:

AwesomeO said:

In my cosmology the chances of a perfect reproduction of the Second World War would be beyond infinite, infinity + 1.

Doesn’t need to be perfect. Just close enough so no-one would notice the difference.

There are a finite number of particles, that can go in a finite number of locations, so the number of different arrangements is finite.

In any time including WWII, their are also an infinite number of variables to make accurate reproduction impossible for a moment, let alone any period of time.

No, there are a large but finite number of variables.

The Rev Dodgson said:

PermeateFree said:

The Rev Dodgson said:

Doesn’t need to be perfect. Just close enough so no-one would notice the difference.

There are a finite number of particles, that can go in a finite number of locations, so the number of different arrangements is finite.

In any time including WWII, their are also an infinite number of variables to make accurate reproduction impossible for a moment, let alone any period of time.

No, there are a large but finite number of variables.

physics precludes some varables?

ChrispenEvan said:

The Rev Dodgson said:

PermeateFree said:

In any time including WWII, their are also an infinite number of variables to make accurate reproduction impossible for a moment, let alone any period of time.

No, there are a large but finite number of variables.

physics precludes some varables?

We are talking about an infinite universe (or part of a universe) with the same physics as the bit we can see, so yes, physics does preclude some variables.

The Rev Dodgson said:

PermeateFree said:

The Rev Dodgson said:

Doesn’t need to be perfect. Just close enough so no-one would notice the difference.

There are a finite number of particles, that can go in a finite number of locations, so the number of different arrangements is finite.

In any time including WWII, their are also an infinite number of variables to make accurate reproduction impossible for a moment, let alone any period of time.

No, there are a large but finite number of variables.

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

PermeateFree said:

The Rev Dodgson said:

PermeateFree said:

In any time including WWII, their are also an infinite number of variables to make accurate reproduction impossible for a moment, let alone any period of time.

No, there are a large but finite number of variables.

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

PermeateFree said:

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

The probability is always finite, so long as the object or event has finite size, duration, and resolution.

The numbers are huge, but finite.

PermeateFree said:

PermeateFree said:

The Rev Dodgson said:

No, there are a large but finite number of variables.

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

infinite monkeys, infinite time.

PermeateFree said:

PermeateFree said:

The Rev Dodgson said:

No, there are a large but finite number of variables.

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

It was the blurst of times.

PermeateFree said:

PermeateFree said:

The Rev Dodgson said:

No, there are a large but finite number of variables.

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

It isn’t impossible at all if you have an infinite number of monkeys.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In fact the monkey would almost surely type every possible finite text an infinite number of times. However, the probability of a universe full of monkeys typing a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).

PermeateFree said:

PermeateFree said:

The Rev Dodgson said:

No, there are a large but finite number of variables.

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

today’s monkeys with ‘incorrect spelling’ would get it right.. probably

ChrispenEvan said:

PermeateFree said:

PermeateFree said:

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

infinite monkeys, infinite time.

infinite monkeys or infinite time would be enough.

Although if you had infinite time you’d need infinite monkeys in total, unless they had an infinite life-span

The Rev Dodgson said:

PermeateFree said:

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

The probability is always finite, so long as the object or event has finite size, duration, and resolution.

The numbers are huge, but finite.

No, it would just go on forever. You also need intelligence and feed back to have even the remotest chance.

http://www.bbc.co.uk/programmes/b00snr0w/episodes/downloads

infinite monkey cage. brian cox and robin ince, worth a listen.

PermeateFree said:

The Rev Dodgson said:

PermeateFree said:

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

The probability is always finite, so long as the object or event has finite size, duration, and resolution.

The numbers are huge, but finite.

No, it would just go on forever. You also need intelligence and feed back to have even the remotest chance.

forever=infinite.

ChrispenEvan said:

PermeateFree said:

PermeateFree said:

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

infinite monkeys, infinite time.

Still an impossible task.

PermeateFree said:

The Rev Dodgson said:

PermeateFree said:

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

The probability is always finite, so long as the object or event has finite size, duration, and resolution.

The numbers are huge, but finite.

Just saying it doesn’t make it true. It’s quite easy to work out what the probability is for any text with a defined finite size and complexity, and the result is always greater than zero.

No, it would just go on forever. You also need intelligence and feed back to have even the remotest chance.

The Rev Dodgson said:

PermeateFree said:

PermeateFree said:

If you take the monkey scenario of give an infinite period of time they could reproduce the entire works of Shakespeare. Not only do the words need to have the letters in the same order, but the words, then the sentence, pages, chapters, etc. The further you go the higher the improbability, and that is a simple example.

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

It isn’t impossible at all if you have an infinite number of monkeys.

It is, you need more than time, you also need intelligence and feedback.

The Rev Dodgson said:

PermeateFree said:

The Rev Dodgson said:

The probability is always finite, so long as the object or event has finite size, duration, and resolution.

The numbers are huge, but finite.

Just saying it doesn’t make it true. It’s quite easy to work out what the probability is for any text with a defined finite size and complexity, and the result is always greater than zero.

No, it would just go on forever. You also need intelligence and feed back to have even the remotest chance.

yep, it isn’t a real experiment after all, just a philosophical argument.

ChrispenEvan said:

PermeateFree said:

The Rev Dodgson said:

The probability is always finite, so long as the object or event has finite size, duration, and resolution.

The numbers are huge, but finite.

No, it would just go on forever. You also need intelligence and feed back to have even the remotest chance.

forever=infinite.

almost forever

PermeateFree said:

The Rev Dodgson said:

PermeateFree said:

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

It isn’t impossible at all if you have an infinite number of monkeys.

It is, you need more than time, you also need intelligence and feedback.

no. just the monkeys and time.

Arts said:

ChrispenEvan said:

PermeateFree said:

No, it would just go on forever. You also need intelligence and feed back to have even the remotest chance.

forever=infinite.

almost forever

don’t start!!!!

ChrispenEvan said:

PermeateFree said:

The Rev Dodgson said:

The probability is always finite, so long as the object or event has finite size, duration, and resolution.

The numbers are huge, but finite.

No, it would just go on forever. You also need intelligence and feed back to have even the remotest chance.

forever=infinite.

Yes.

PermeateFree said:

The Rev Dodgson said:

PermeateFree said:

I might add that as soon as a single letter was incorrect, the monkey would need to start again, and again get everything correct in the right place before it could proceed further. It is an impossible task.

It isn’t impossible at all if you have an infinite number of monkeys.

It is, you need more than time, you also need intelligence and feedback.

Let’s do the numbers:
Suppose at each step the monkeys have 100 choices, and the text is 1 million characters long (including spaces, line breaks, page breaks etc).
Also suppose that at each step half the monkeys shit on the text, or do something else to muck it up.

The probability of a single monkey getting all 1 million characters correct is then 1/((2×100)^1,000,000).
A very small number, but finite.

ChrispenEvan said:

PermeateFree said:

The Rev Dodgson said:

It isn’t impossible at all if you have an infinite number of monkeys.

It is, you need more than time, you also need intelligence and feedback.

no. just the monkeys and time.

In the words of D Trump. It will never happen!

PermeateFree said:

ChrispenEvan said:

PermeateFree said:

It is, you need more than time, you also need intelligence and feedback.

no. just the monkeys and time.

In the words of D Trump. It will never happen!

Trump would never say anything so succinctly

The Rev Dodgson said:

PermeateFree said:

The Rev Dodgson said:

It isn’t impossible at all if you have an infinite number of monkeys.

It is, you need more than time, you also need intelligence and feedback.

Let’s do the numbers:
Suppose at each step the monkeys have 100 choices, and the text is 1 million characters long (including spaces, line breaks, page breaks etc).
Also suppose that at each step half the monkeys shit on the text, or do something else to muck it up.

The probability of a single monkey getting all 1 million characters correct is then 1/((2×100)^1,000,000).
A very small number, but finite.

However, if only once an error is made, they would need to start again and retype the exact same content as before, only then would the monkey have an additional 100 choices. And so on for every small error, it would go on forever, because the task is impossible.

Arts said:

PermeateFree said:

ChrispenEvan said:

no. just the monkeys and time.

In the words of D Trump. It will never happen!

Trump would never say anything so succinctly

Probably produced on the day the monkey was sick.

PermeateFree said:

The Rev Dodgson said:

PermeateFree said:

It is, you need more than time, you also need intelligence and feedback.

Let’s do the numbers:
Suppose at each step the monkeys have 100 choices, and the text is 1 million characters long (including spaces, line breaks, page breaks etc).
Also suppose that at each step half the monkeys shit on the text, or do something else to muck it up.

The probability of a single monkey getting all 1 million characters correct is then 1/((2×100)^1,000,000).
A very small number, but finite.

However, if only once an error is made, they would need to start again and retype the exact same content as before, only then would the monkey have an additional 100 choices. And so on for every small error, it would go on forever, because the task is impossible.

we have “forever”.

ChrispenEvan said:

PermeateFree said:

The Rev Dodgson said:

Let’s do the numbers:
Suppose at each step the monkeys have 100 choices, and the text is 1 million characters long (including spaces, line breaks, page breaks etc).
Also suppose that at each step half the monkeys shit on the text, or do something else to muck it up.

The probability of a single monkey getting all 1 million characters correct is then 1/((2×100)^1,000,000).
A very small number, but finite.

However, if only once an error is made, they would need to start again and retype the exact same content as before, only then would the monkey have an additional 100 choices. And so on for every small error, it would go on forever, because the task is impossible.

we have “forever”.

And hence it would not happen.

PermeateFree said:

ChrispenEvan said:

PermeateFree said:

However, if only once an error is made, they would need to start again and retype the exact same content as before, only then would the monkey have an additional 100 choices. And so on for every small error, it would go on forever, because the task is impossible.

we have “forever”.

And hence it would not happen.

the probability of it happening is finite which is a lot smaller than infinite.

PermeateFree said:

However, if only once an error is made, they would need to start again and retype the exact same content as before, only then would the monkey have an additional 100 choices. And so on for every small error, it would go on forever, because the task is impossible.

What you have just said is that the probability of a single monkey getting all 1 million characters correct is then 1/((2×100)^1,000,000).

Thanks for the agreement and good night.

ChrispenEvan said:

PermeateFree said:

ChrispenEvan said:

we have “forever”.

And hence it would not happen.

the probability of it happening is finite which is a lot smaller than infinite.

And a bit smaller than nearly infinite.

Peak Warming Man said:

ChrispenEvan said:

PermeateFree said:

And hence it would not happen.

the probability of it happening is finite which is a lot smaller than infinite.

And a bit smaller than nearly infinite.

heaps.

ChrispenEvan said:

PermeateFree said:

ChrispenEvan said:

we have “forever”.

And hence it would not happen.

the probability of it happening is finite which is a lot smaller than infinite.

You seem to be under the impression that just because you have infinite time, that whatever happened before will happen again. That is simply preposterous, as events are not determined by time, but by circumstance. And even then you will need various events to occur in order for that to happen. Some events are just not repeatable in any times scale.

PermeateFree said:

ChrispenEvan said:

PermeateFree said:

And hence it would not happen.

the probability of it happening is finite which is a lot smaller than infinite.

You seem to be under the impression that just because you have infinite time, that whatever happened before will happen again. That is simply preposterous, as events are not determined by time, but by circumstance. And even then you will need various events to occur in order for that to happen. Some events are just not repeatable in any times scale.

ChrispenEvan said:

No, it is not true that pi being an infinite nonrepeating decimal means that every possible number combination exists somewhere within it. For example, the number 0.101001000100001000001000000100000001000000001… is also an infinite nonrepeating decimal but clearly does not contain all possible number combinations.

Whenever someone asks whether an infinite space of some sort contains all possibilities, I usually mention Burnside’s problem.

KJW said:

ChrispenEvan said:

No, it is not true that pi being an infinite nonrepeating decimal means that every possible number combination exists somewhere within it. For example, the number 0.101001000100001000001000000100000001000000001… is also an infinite nonrepeating decimal but clearly does not contain all possible number combinations.

Whenever someone asks whether an infinite space of some sort contains all possibilities, I usually mention Burnside’s problem.

KJW is correct. I wish I’d spotted that.

mollwollfumble said:

KJW said:

No, it is not true that pi being an infinite nonrepeating decimal means that every possible number combination exists somewhere within it. For example, the number 0.101001000100001000001000000100000001000000001… is also an infinite nonrepeating decimal but clearly does not contain all possible number combinations.

Whenever someone asks whether an infinite space of some sort contains all possibilities, I usually mention Burnside’s problem.

KJW is correct. I wish I’d spotted that.

I agree that the statement as stated is correct, but this does not mean that pi does not contain every possible finite number combination, it just means that the fact that pi is infinite and nonrepeating does not prove this fact.

However, a truly random infinite collection of integers does include every possible finite arrangement of those integers. I expect this is probably true of pi as well, but I don’t know how you would prove it, or if it is provable.

As for the Wiki statement of the Burnside problem, I’m afraid it contains too much maths jargon to mean much to me.

PermeateFree said:

PermeateFree said:

ChrispenEvan said:

the probability of it happening is finite which is a lot smaller than infinite.

You seem to be under the impression that just because you have infinite time, that whatever happened before will happen again. That is simply preposterous, as events are not determined by time, but by circumstance. And even then you will need various events to occur in order for that to happen. Some events are just not repeatable in any times scale.

Good to see you posting a cartoon critical of your own position on this question.

Well done!

The Rev Dodgson said:

PermeateFree said:

PermeateFree said:

You seem to be under the impression that just because you have infinite time, that whatever happened before will happen again. That is simply preposterous, as events are not determined by time, but by circumstance. And even then you will need various events to occur in order for that to happen. Some events are just not repeatable in any times scale.

Good to see you posting a cartoon critical of your own position on this question.

Well done!

You are a poor loser Rev.

PermeateFree said:

The Rev Dodgson said:

PermeateFree said:

Good to see you posting a cartoon critical of your own position on this question.

Well done!

You are a poor loser Rev.

nah, you just don’t understand the infinite monkey theorem.

PermeateFree said:

The Rev Dodgson said:

Good to see you posting a cartoon critical of your own position on this question.

Well done!

You are a poor loser Rev.

I don’t think you have provided any evidence that the Rev is wrong. The real world implications of numerical infinities is very complex and quite counter intuitive.

Witty Rejoinder said:

I don’t think you have provided any evidence that the Rev is wrong. The real world implications of numerical infinities is very complex and quite counter intuitive.

In fact I don’t think he has provided any evidence of an sort at all.

The Rev Dodgson said:

Witty Rejoinder said:

I don’t think you have provided any evidence that the Rev is wrong. The real world implications of numerical infinities is very complex and quite counter intuitive.

In fact I don’t think he has provided any evidence of an sort at all.

yes. just the logical fallacy of personal incredulity.

The Rev Dodgson said:

Witty Rejoinder said:

I don’t think you have provided any evidence that the Rev is wrong. The real world implications of numerical infinities is very complex and quite counter intuitive.

In fact I don’t think he has provided any evidence of an sort at all.

The Rev: Telling it like it is!

I think Permeate was distracted by the monkeys. It’s just a random letter generator, you don’t have to worry about the monkeys.

Bubblecar said:

I think Permeate was distracted by the monkeys. It’s just a random letter generator, you don’t have to worry about the monkeys.

phew, that takes caring of the feeding problem. and waste.

Bubblecar said:

I think Permeate was distracted by the monkeys. It’s just a random letter generator, you don’t have to worry about the monkeys.

Yes, in fact monkeys are not truly random at all, so it is a misleading analogy.

ol’s thick as two planks

but wouldn’t the measurement of anything analogue taken to infinite resolution (and converted to numbers) give you something like that

be gentle

I have been trying to get you guys to open your minds and think rationally, but so far without any success. You seem to be stuck in your pigeon hole assessment, where you have decided where the above belongs and refuse to examine the problem from another point of view. After all philosophy is all about teaching you how to think.

Despite it being of little purpose trying to get you to think otherwise, I shall put my argument again.

If you state that the monkeys can reproduce the entire works of Shakespeare given enough time, you expect it to be possible. However, the monkeys cannot read and have no sense of grammar or even structure, yet you claim they could do so without fault for tens of thousands of words and arrange them in perfect order without error.

It is not just arranging letters to make a word, this can be done reasonably easily, but then you must place a space to then start another word, which also must be spelt correctly; then another space and another word and so on until a sentence is not only made, but will make sense. This will of course be pure luck as the monkey has no idea what they it is doing, only pressing keys. The monkey must then continue, word after word, using grammar, meaning, plus being word perfect for tens of thousands of times. And any mistake will mean the monkey must start again from the first letter.

You don’t need to be a mathematician to work out the odds, because it would be an impossible task to do in any time frame. There is nothing you can say that it could ever be done, other than blind faith. Therefore, it is as likely to be as impossible to do, as it is possible. It is one of those silly exercises in philosophy where anything is possible, because it is nothing but a thought process with no foundation in reality.

I’ll post this again for those that didn’t read it.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

ChrispenEvan said:

I’ll post this again for those that didn’t read it.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

I’ll post this for those that didn’t read it; it is an extract from the above link, which verifies what I have been saying.

“The probability of Hamlet is therefore zero in any operational sense of an event…”, and the statement that the monkeys must eventually succeed “gives a misleading conclusion about very, very large numbers.”

In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.

ChrispenEvan said:

I’ll post this again for those that didn’t read it.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

PF will have to amend wikipedia.

PermeateFree said:

ChrispenEvan said:

I’ll post this again for those that didn’t read it.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

I’ll post this for those that didn’t read it; it is an extract from the above link, which verifies what I have been saying.

“The probability of Hamlet is therefore zero in any operational sense of an event…”, and the statement that the monkeys must eventually succeed “gives a misleading conclusion about very, very large numbers.”

In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.

sigh. put it in the context in how that part is written.

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In fact the monkey would almost surely type every possible finite text an infinite number of times. However, the probability of a universe full of monkeys typing a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).

First para.

your quote is given as a probability in real universes which are not infinite.

ChrispenEvan said:

PermeateFree said:

ChrispenEvan said:

I’ll post this again for those that didn’t read it.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

I’ll post this for those that didn’t read it; it is an extract from the above link, which verifies what I have been saying.

“The probability of Hamlet is therefore zero in any operational sense of an event…”, and the statement that the monkeys must eventually succeed “gives a misleading conclusion about very, very large numbers.”

In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.

sigh. put it in the context in how that part is written.

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In fact the monkey would almost surely type every possible finite text an infinite number of times. However, the probability of a universe full of monkeys typing a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).

First para.

your quote is given as a probability in real universes which are not infinite in time.

ChrispenEvan said:

ChrispenEvan said:

PermeateFree said:

I’ll post this for those that didn’t read it; it is an extract from the above link, which verifies what I have been saying.

“The probability of Hamlet is therefore zero in any operational sense of an event…”, and the statement that the monkeys must eventually succeed “gives a misleading conclusion about very, very large numbers.”

In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.

sigh. put it in the context in how that part is written.

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In fact the monkey would almost surely type every possible finite text an infinite number of times. However, the probability of a universe full of monkeys typing a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).

First para.

your quote is given as a probability in real universes which are not infinite in time.

fixed, by adding in time.

the first sentence in your quote

“However, for physically meaningful numbers of monkeys typing for physically meaningful lengths of time the results are reversed.”

Witty Rejoinder said:

ChrispenEvan said:

I’ll post this again for those that didn’t read it.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

PF will have to amend wikipedia.

But it is there in the link! For goodness sake what do you want me to do, feed you with a spoon?

ChrispenEvan said:

PermeateFree said:

ChrispenEvan said:

I’ll post this again for those that didn’t read it.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

I’ll post this for those that didn’t read it; it is an extract from the above link, which verifies what I have been saying.

“The probability of Hamlet is therefore zero in any operational sense of an event…”, and the statement that the monkeys must eventually succeed “gives a misleading conclusion about very, very large numbers.”

In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.

sigh. put it in the context in how that part is written.

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In fact the monkey would almost surely type every possible finite text an infinite number of times. However, the probability of a universe full of monkeys typing a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).

First para.

your quote is given as a probability in real universes which are not infinite.

The full quote! You really should read the links you post.

Probabilities

However, for physically meaningful numbers of monkeys typing for physically meaningful lengths of time the results are reversed. If there were as many monkeys as there are atoms in the observable universe typing extremely fast for trillions of times the life of the universe, the probability of the monkeys replicating even a single page of Shakespeare is unfathomably small.

Ignoring punctuation, spacing, and capitalization, a monkey typing letters uniformly at random has a chance of one in 26 of correctly typing the first letter of Hamlet. It has a chance of one in 676 (26 × 26) of typing the first two letters. Because the probability shrinks exponentially, at 20 letters it already has only a chance of one in 2620 = 19,928,148,895,209,409,152,340,197,376 (almost 2 × 1028). In the case of the entire text of Hamlet, the probabilities are so vanishingly small as to be inconceivable. The text of Hamlet contains approximately 130,000 letters. Thus there is a probability of one in 3.4 × 10183,946 to get the text right at the first trial. The average number of letters that needs to be typed until the text appears is also 3.4 × 10183,946, or including punctuation, 4.4 × 10360,783.

Even if every proton in the observable universe were a monkey with a typewriter, typing from the Big Bang until the end of the universe (when protons might no longer exist), they would still need a still far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10500 chance of success. To put it another way, for a one in a trillion chance of success, there would need to be 10360,641 universes made of atomic monkeys. As Kittel and Kroemer put it in their textbook on thermodynamics, the field whose statistical foundations motivated the first known expositions of typing monkeys, “The probability of Hamlet is therefore zero in any operational sense of an event…”, and the statement that the monkeys must eventually succeed “gives a misleading conclusion about very, very large numbers.”

In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.

“…they would still need a still far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10⁵⁰⁰ chance of success….”

way smaller than infinite.

ChrispenEvan said:

“…they would still need a still far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10⁵⁰⁰ chance of success….”

way smaller than infinite.

It’s nearly infinite.

</BC>

sibeen said:

ChrispenEvan said:

“…they would still need a still far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10⁵⁰⁰ chance of success….”

way smaller than infinite.

It’s nearly infinite.

</BC>

don’t you start!

ChrispenEvan said:

“…they would still need a still far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10⁵⁰⁰ chance of success….”

way smaller than infinite.

>>In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.<<

And that is a long way short of the works of Shakespeare = impossible in any time frame.

ChrispenEvan said:

“…they would still need a still far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10⁵⁰⁰ chance of success….”

way smaller than infinite.

It’s now obvious (well actually it was pretty obvious all along, if I’d been paying attention), that PF has no interest in discussing the subject of the thread, so I’ll let it drop.

ChrispenEvan said:

PermeateFree said:

ChrispenEvan said:

I’ll post this again for those that didn’t read it.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

I’ll post this for those that didn’t read it; it is an extract from the above link, which verifies what I have been saying.

“The probability of Hamlet is therefore zero in any operational sense of an event…”, and the statement that the monkeys must eventually succeed “gives a misleading conclusion about very, very large numbers.”

In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.

sigh. put it in the context in how that part is written.

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In fact the monkey would almost surely type every possible finite text an infinite number of times. However, the probability of a universe full of monkeys typing a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).

First para.

your quote is given as a probability in real universes which are not infinite.

It should however be added that it is widely accepted that our Universe may be actually infinite.

That is infinite as in having no boundaries, and not being a closed system, not not infinite as in being pretty big, but finite.

I think that is quite unlikely myself, but that’s probably just due to my unconscious engineering bias.

But even if the universe in which we live is finite, it seems likely that there are an infinite number of other universes, an infinite number of which have physical systems indistinguishable from ours, so it comes to the same thing anyway.

Quite likely, an infinite supply of monkeys at typewriters is a real possibility (although not one we could ever even start to investigate).

The Rev Dodgson said:

ChrispenEvan said:

“…they would still need a still far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10⁵⁰⁰ chance of success….”

way smaller than infinite.

It’s now obvious (well actually it was pretty obvious all along, if I’d been paying attention), that PF has no interest in discussing the subject of the thread, so I’ll let it drop.

I know you don’t like being wrong Rev, but you shouldn’t rubbish your lack of logic too.

The Rev Dodgson said:

It should however be added that it is widely accepted that our Universe may be actually infinite.

That is infinite as in having no boundaries, and not being a closed system, not not infinite as in being pretty big, but finite.

Not not infinite?

I think that is quite unlikely myself, but that’s probably just due to my unconscious engineering bias.

Could be either, as far as I’m concerned.

The Rev Dodgson said:

ChrispenEvan said:

PermeateFree said:

I’ll post this for those that didn’t read it; it is an extract from the above link, which verifies what I have been saying.

“The probability of Hamlet is therefore zero in any operational sense of an event…”, and the statement that the monkeys must eventually succeed “gives a misleading conclusion about very, very large numbers.”

In fact there is less than a one in a trillion chance of success that such a universe made of monkeys could type any particular document a mere 79 characters long.

sigh. put it in the context in how that part is written.

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In fact the monkey would almost surely type every possible finite text an infinite number of times. However, the probability of a universe full of monkeys typing a complete work such as Shakespeare’s Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).

First para.

your quote is given as a probability in real universes which are not infinite.

It should however be added that it is widely accepted that our Universe may be actually infinite.

That is infinite as in having no boundaries, and not being a closed system, not not infinite as in being pretty big, but finite.

I think that is quite unlikely myself, but that’s probably just due to my unconscious engineering bias.

But even if the universe in which we live is finite, it seems likely that there are an infinite number of other universes, an infinite number of which have physical systems indistinguishable from ours, so it comes to the same thing anyway.

Quite likely, an infinite supply of monkeys at typewriters is a real possibility (although not one we could ever even start to investigate).

Hope you read the other posts Rev. You might learn something. :)

dv said:

The Rev Dodgson said:

It should however be added that it is widely accepted that our Universe may be actually infinite.

That is infinite as in having no boundaries, and not being a closed system, not not infinite as in being pretty big, but finite.

Not not infinite?

I think that is quite unlikely myself, but that’s probably just due to my unconscious engineering bias.

Could be either, as far as I’m concerned.

Yeah, I don’t think anyone claims that it is definitely infinite or definitely finite.

No true scientists anyway.

The Rev Dodgson said:

dv said:

The Rev Dodgson said:

It should however be added that it is widely accepted that our Universe may be actually infinite.

That is infinite as in having no boundaries, and not being a closed system, not not infinite as in being pretty big, but finite.

Not not infinite?

I think that is quite unlikely myself, but that’s probably just due to my unconscious engineering bias.

Could be either, as far as I’m concerned.

Yeah, I don’t think anyone claims that it is definitely infinite or definitely finite.

No true scientists anyway.

Don’t think you are scientist Rev, although you apply science. Big difference as to how you view information.

There might be an infinite number of universes.

There might be an infinite number of possible vibrations over the whole frequency spectrum across all of space time in this universe.

The Rev Dodgson said:

dv said:

The Rev Dodgson said:

It should however be added that it is widely accepted that our Universe may be actually infinite.

That is infinite as in having no boundaries, and not being a closed system, not not infinite as in being pretty big, but finite.

Not not infinite?

I think that is quite unlikely myself, but that’s probably just due to my unconscious engineering bias.

Could be either, as far as I’m concerned.

Yeah, I don’t think anyone claims that it is definitely infinite or definitely finite.

No true scientists anyway.

As KJW correctly pointed out, Douglas Adams hypothesis is false. The hypothesis is:

… darn, can’t find it … something like …

“In an infinite universe, everything that you can imagine and many things you would rather not, exist somewhere”.

.. found it …

“in an infinitely large Universe such as, for instance, the one in which we live, most things one could possibly imagine, and a lot of things one would rather not, grow somewhere.”

mollwollfumble said:

The Rev Dodgson said:

dv said:

Could be either, as far as I’m concerned.

Yeah, I don’t think anyone claims that it is definitely infinite or definitely finite.

No true scientists anyway.

As KJW correctly pointed out, Douglas Adams hypothesis is false. The hypothesis is:

Well no, he didn’t point that out, and if he had he would have been wrong.

What he did point out was true, but related to pi (and other irrational non-random numbers).

The Rev Dodgson said:

Yeah, I don’t think anyone claims that it is definitely infinite or definitely finite.

No true scientists anyway.

;-)

dv said:

The Rev Dodgson said:

Yeah, I don’t think anyone claims that it is definitely infinite or definitely finite.

No true scientists anyway.

I keep telling the forum that the size of the universe is near-infinite, with a greater than 50% probability of it being exactly infinite.

mollwollfumble said:

dv said:

The Rev Dodgson said:

Yeah, I don’t think anyone claims that it is definitely infinite or definitely finite.

No true scientists anyway.

I keep telling the forum that the size of the universe is near-infinite, with a greater than 50% probability of it being exactly infinite.

Yes, but you’ve got your sums wrong.

You should use the radius, rather than the curvature.

Something can be nearly infinitesimally small too.

Peak Warming Man said:

Something can be nearly infinitesimally small too.

The difference in definition between infinitesimal and infinite is QI.

If Wikipedia got it right that is.

The Rev Dodgson said:

Peak Warming Man said:

Something can be nearly infinitesimally small too.

The difference in definition between infinitesimal and infinite is QI.

If Wikipedia got it right that is.

:)

PermeateFree said:

The Rev Dodgson said:

Peak Warming Man said:

Something can be nearly infinitesimally small too.

The difference in definition between infinitesimal and infinite is QI.

If Wikipedia got it right that is.

:)

I got it right. But you’d have to read my monograph about it.

The Rev Dodgson said:

I agree that the statement as stated is correct, but this does not mean that pi does not contain every possible finite number combination, it just means that the fact that pi is infinite and nonrepeating does not prove this fact.

Yes. I was quite careful with my wording so as not to deny the possibility that pi contains every possible finite number combination, but rather to deny that pi necessarily contains every possible finite number combination.

The Rev Dodgson said:

However, a truly random infinite collection of integers does include every possible finite arrangement of those integers.

I’m not so sure about that. The problem is that every possible finite arrangement includes arrangements that, though finite, are unlimited in size, and that the probability of inclusion may decrease with increasing size too rapidly to guarantee inclusion under truly random conditions.

The Rev Dodgson said:

As for the Wiki statement of the Burnside problem, I’m afraid it contains too much maths jargon to mean much to me.

In the past, I discussed a simplified form of the problem on SSSF. There, the problem was to consider a sequence of 0s and 1s such that no subsequence of any length repeated five or more times in a row. The question was whether the sequence is necessarily finite. If the sequence can be infinite, this would indicate that infinite sequences can be quite restricted in what they contain.

Bubblecar said:

So-called “real numbers” (with infinite decimals) are of higher cardinality than the natural numbers, so can’t be counted by them (placed in a one-to-one correspondence). The natural numbers are countably infinite, the real numbers are uncountably infinite.

In general, the set of all subsets of a given set can’t be placed in a one-to-one correspondence with the given set. However, the set of all finite subsets of the natural numbers can be placed in a one-to-one correspondence with the natural numbers (so that it’s the infinite subsets of the natural numbers that make the set of all subsets of the natural numbers uncountable). Thus, an infinite sequence of digits can contain every possible finite subsequence of digits.

KJW said:

The Rev Dodgson said:

However, a truly random infinite collection of integers does include every possible finite arrangement of those integers.

I’m not so sure about that. The problem is that every possible finite arrangement includes arrangements that, though finite, are unlimited in size, and that the probability of inclusion may decrease with increasing size too rapidly to guarantee inclusion under truly random conditions.

In the context of the discussion, we can put a limit on the size. For instance, we might limit the size to a sheet of paper with the letters “to be o”.

If we do that, and satisfy ourselves that up to that limit the same observations will repeat in an infinite universe (or infinite number of finite universes of sufficient size and type), then we can add 1 additional detail, perhaps “to be or”, and satisfy ourselves that this sequence will still repeat infinitely.

We can then repeat that process until we have the complete works Fred Shakespeare (which happen to be identical to the complete works of William Shakespeare on this planet), or a complete reproduction of WW II, or any other finite possible thing.

Can’t we?