The idea of an infinite past

[Kharakov]

This reminds me of 2+1=1

Two holes close by. Dig one between them, but oops, now there's just one large hole. The gap between the two holes was just an inch apart, and the post hole digger is more than an inch wide, so, while 1 added to another makes 2, the addition of the 3rd yields not 3 but 1.

There are no holes.

- - - Updated - - -

Add two drops of water together. 1 + 1 = 1.

How is a drop of water "one"?

Faith, the drop of water is one with Jesus.

Don't break our bot.

 

[Speakpigeon]

This reminds me of 2+1=1

Two holes close by. Dig one between them, but oops, now there's just one large hole. The gap between the two holes was just an inch apart, and the post hole digger is more than an inch wide, so, while 1 added to another makes 2, the addition of the 3rd yields not 3 but 1.

This seems to explain the mystery of the Trinity.

And this makes true that 1000 + 1 = 1, or even N + 1 = 1, where N is any number, even any large number. Provided you can steal enough of the taxpayer's money to pay for a big enough hole.

However, this seems to prove the infinite doesn't exist, since ∞ + 1 = ∞, not 1. So, there seems to be a contradiction there. Maybe there isn't enough of taxpayer's money to dig a hole infinite enough to absorb an infinite number of holes.

At least we know now how entropy works.
EB

 

[Speakpigeon]

How is a drop of water "one"?

Faith, the drop of water is one with Jesus.

Don't break our bot.

Unbeerable.

That would be the straw that breaks the U-bot's back.
EB

 

[untermensche]

The bot is the one that has had the same consistent position for a while now.

The un-bots are starting, some of them, to figure out that they can in no way defend the idea of a real completed infinity.

Some still claim infinities exist yet can offer no proof of such claims.

A real completed infinity is not a mathematical concept.

The only way it could appear is all at once like a miracle. There is no other way to have one.

The believers in real completed infinities want us to believe that a completed infinity of time just popped into existence. And then time until now passed after that.

The stupidest idea I have heard in a while.

 

[beero1000]

Well, who knows, maybe we could get to agree on a pragmatic solution to this difficult question of whether infinity is real or not.

So, obviously lots of people will use irrational numbers without much thinking about the metaphysical implications, but maybe we could help them.

So, first, what is an irrational number?

Here's a dictionary definition:


That should be clear enough to all of us around here I guess.

Now, the example given here, π is also a transcendental number. What's that?

Here it is:


That's a bit more technical but you all know more about this stuff than I do so it should be good enough.

We all understand how π is used in life but the question is, do we really need to see it as a transcendental number, or would it be enough to cut it down to size to a more ordinary perspective.

So, first, here's the definition of π:

π
2. (Mathematics) A transcendental number, approximately 3.14159, represented by the symbol π, that expresses the ratio of the circumference to the diameter of a circle and appears as a constant in many mathematical expressions.

So, it's made clear here that π is a very useful number. To cut it down to size, it's also very easy. We would just have to replace in the definition of π "approximately 3.14159" with "equal 3.14159", and just use this in our calculations.

Now, this should be considered as a pragmatic decision. No more metaphysical debate now. A "yes", or a "no"!

And, oops, sorry, also why, but only in terms of practical consequences of doing it or not doing it.
EB

No takers?

Yes? No?
EB

No.

There is already a number equal to 3.14159, namely 3.14159. Renaming that pi just means we need to come up with a new name for the circle constant, which is not equal to 3.14159. You can use rational approximations for it, but those are just approximations, and yield errors that propagate and grow. Depending on the specific calculations that need to be done, the errors created by your fixed-precision approximation can be arbitrarily large.

I believe NIST standard currently uses a 32-digit approximation (quadruple-precision) for computations with pi, with the understanding that more digits may be necessary for extremely precise (or long-running) calculations. If we didn't have the exact value, we wouldn't be able to do that.

 

[Kharakov]

I typically stay around 128 (2*quad floats), but sometimes I go as high as 2048-4096 bit precision to check something when error (drift) gets too high.

 

[Speakpigeon]

No takers?

Yes? No?
EB

No.

There is already a number equal to 3.14159, namely 3.14159. Renaming that pi just means we need to come up with a new name for the circle constant, which is not equal to 3.14159. You can use rational approximations for it, but those are just approximations, and yield errors that propagate and grow. Depending on the specific calculations that need to be done, the errors created by your fixed-precision approximation can be arbitrarily large.

I believe NIST standard currently uses a 32-digit approximation (quadruple-precision) for computations with pi, with the understanding that more digits may be necessary for extremely precise (or long-running) calculations. If we didn't have the exact value, we wouldn't be able to do that.

I knew I could trust you on that. Excellent!

No objections. So, that's settled. Thanks!
EB

 

[Speakpigeon]

I typically stay around 128 (2*quad floats), but sometimes I go as high as 2048-4096 bit precision to check something when error (drift) gets too high.

GMP?

arbitrary-precision arithmetic
https://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision.

___________________

Still, I wonder if it's possible that we would one day decide we won't be needing to use more decimal places than we do at the time? We've known about the quantum of energy for more than a century now, so presumably this tells us we won't need to go beyond that. Could that happen for decimal places?

Another interesting angle to this question, sort of, is whether we could reach our own limit. Suppose we need to use a much larger number of decimal places to improve somehow our knowledge of the world but that this number now exceeds in some way our capabilities or resources, not only on the moment, but for ever. Could that happen?

I would say 'yes' to both.
EB

 

[Speakpigeon]

I don't think anyone could possibly know for a fact that the past hasn't been going on for an infinitely long time.

I also don't think there is any contradiction in the idea of an infinite past.

So, on that basis, I would say that it seems possible to me that the past has been an infinite past, i.e. a past without a beginning.

If anyone disagrees here, please explain why.
EB

Nobody pointed out the implicit but mistaken assumption in the OP, that no contradiction implied possibility. That's not true in the ordinary sense of these words. Unless otherwise specified, no contradiction is the same thing as logically possible, but logically possible is, obviously, a restriction of the notion of possibility and therefore does not imply it. Possible indicates that something may happen, exist, be true, or be realisable. So, the absence of contradiction in the concept of an infinite past, including that of an actually infinite past, does not imply that infinity is actually possible, i.e. that it may exist in reality.

I'm not sure anyone here paid any attention to this distinction. I'm confident nobody has shown there's a contradiction in the concept of an infinite past. And that's good. However, we cannot conclude from this that an infinite past is possible. Sure, we can all believe so. We can also all say that we don't know that it is impossible. That still doesn't make it possible.

More precisely, however, I think that the notion of possibility is that of no contradiction with what we know of reality. I can't see how a more restrictive notion of possibility could be cogent. On this understanding, I believe an infinite past would be possible. Certainly, nobody here brought up any contradiction with known facts. Still, that wasn't made clear in the OP.

So, those who don't believe in the possibility of an infinite past are invited here to explain how this concept would be in any way in contradiction with what we know of the physical world.

And please, straight to the point. Don't just repeat yourself.

Thanks, and sorry for the cockup.
EB

 

[untermensche]

The idea that conflicts with reality is the idea of a real completed infinity. The claim that a real completed infinity is somehow possible is a positive claim.

That is the claim that needs defending if we want to look at this rationally.

If the idea of a real completed infinity cannot be defended then rationally it is rejected and we are done with it.

 

[Speakpigeon]

Please, don't just repeat yourself.

Where is the contradiction with known facts?

That's all you have to do.

Thanks.
EB

 

[Beer With Straw]

Only God has an infinite past because only God is infinite!

 

[untermensche]

Please, don't just repeat yourself.

Where is the contradiction with known facts?

That's all you have to do.

Thanks.
EB

How is the claim that a real completed infinity is possible not a positive claim?

Why do you think positive claims do not need to be supported?

What kind of clown show are you running here? Since when do we just accept wild claims without proof?

 

[Speakpigeon]

Please, don't just repeat yourself.

Where is the contradiction with known facts?

That's all you have to do.

Thanks.
EB

How is the claim that a real completed infinity is possible not a positive claim?

Why do you think positive claims do not need to be supported?

Read again, more carefully:

More precisely, however, I think that the notion of possibility is that of no contradiction with what we know of reality. I can't see how a more restrictive notion of possibility could be cogent. On this understanding, I believe an infinite past would be possible.

The claim is that it is possible, not that it exists.

Where would be the contradiction with known facts?
EB

 

[untermensche]

A claim that a real completed infinity is possible is the claim that needs to be defended here. You have not defended it in any way.

Nobody has defended it.

Therefore we rationally reject the unsupported magical claim.

But this is only if we want to behave rationally.

 

[Speakpigeon]

I rest my case.
EB

 

[untermensche]

I rest my case.
EB

You have no case.

You have no ability to think rationally.

You think we must prove unsupported claims are not true before we totally reject them.

That is not rational thinking.

To think rationally means that positive claims, like a real completed infinity is possible, must be proven to be possible before they are accepted as possible.

What is your proof that a real completed infinity is possible?

 

[untermensche]

If I claimed Hillary Clinton is a shape shifter do we need to prove she isn't before we reject the claim?

What is the difference between that and a claim that a real completed infinity is possible?

 

[DBT]

If infinity/eternity is not possible, how did time/space/universe begin? A first cause? A causeless first cause?

 

[untermensche]

If infinity/eternity is not possible, how did time/space/universe begin? A first cause? A causeless first cause?

Since real completed infinities are assumed to be impossible until they can be proven to be possible we can reasonably assume the past was finite.

Do you disagree?

If not you have to prove a real completed infinity is possible.

Go for it.