What does it mean for something to be "logically possible"?

[Kharakov]

Just for a break, The Nature of Nothing
[YOUTUBE]X5rAGfjPSWE[/YOUTUBE]

 

[untermensche]

Completing a real infinity is like reciting all the integers.

Impossible.

Completing a real infinity is really, really easy.
Again, here is a traditional one.
When I shoot an arrow at a target it has to get half way there. It has to get halfway there again. And again. Always going half way.

So you are saying you never get there?

Because if you get there you clearly did not have to make infinite movements to get there.

The only way to get there is if it takes finite moves to get there.

 

[untermensche]

....Each moment of time had an at least imagined prior moment....

That doesn't make it possible for infinite moments to pass.

Infinite moments are not something that can ever be completed. Like reciting the integers.

It is impossible there were infinite moments before any given moment.

 

[untermensche]

Completing a real infinity is like reciting all the integers.

Impossible.

Spin around once. You just faced an infinite amount of directions in smooth spacetime. Congratulations. You've completed multiple infinities- because any finite pivot covers an infinite amount of directions in smooth spacetime.

I mean, that's simple. You aren't even aware of the infinite amount of infinities you cross over and encounter daily (none of us are), but... infinity happens.

There are infinite directions if each direction is zero degrees from the next.

That is not something real.

 

[Kharakov]

Spin around once. You just faced an infinite amount of directions in smooth spacetime. Congratulations. You've completed multiple infinities- because any finite pivot covers an infinite amount of directions in smooth spacetime.

I mean, that's simple. You aren't even aware of the infinite amount of infinities you cross over and encounter daily (none of us are), but... infinity happens.

There are infinite directions if each direction is zero degrees from the next.

Spacetime is smooth, so you can go 1 degree, then 1/2 degree, then 1/4 degree...... If you keep on dividing the distance turned by 2, you only trace out 2 degrees, but you've faced an infinite amount of directions.

Same thing applies to any pivot you make- any time you turn, you face an infinite amount of directions in smooth spacetime.

 

[untermensche]

Spacetime is smooth, so you can go 1 degree, then 1/2 degree, then 1/4 degree...... If you keep on dividing the distance turned by 2, you only trace out 2 degrees, but you've faced an infinite amount of directions.

Only if we end up saying a change in direction is zero degrees.

It breaks down to absurdity immediately.

Like all alleged real infinities.

 

[Kharakov]

There are an infinite amount of finite changes in direction you make when pivoting any finite amount. You can pivot 1 degree, 1/2, 1/4..... You pivot through each and every possible arc length below the amount you pivoted when you pivot- an infinite amount of directions.

Anyone know of a good video on this?

 

[ryan]

Completing a real infinity is like reciting all the integers.

Impossible.

Think of a simple universe, by "universe", I mean absolutely everything. All that exists is one spinning broom and an object as a reference to its spin.

There, now asking when this object began to spin is not relevant. Asking when it will stop is just as irrelevant. It's spin is infinite; it spins an infinite number of times.

Is there anything illogical about this universe?

 

[George S]

Completing a real infinity is really, really easy.
Again, here is a traditional one.
When I shoot an arrow at a target it has to get half way there. It has to get halfway there again. And again. Always going half way.

So you are saying you never get there?

This is why Xeno's paradox is a paradox.

Because if you get there you clearly did not have to make infinite movements to get there.

Your arrow has passed over an infinity of integers.

The only way to get there is if it takes finite moves to get there.

That is what the ancient Greeks thought, too.
The Tortoise and the Hare race:
The tortoise gets a head start.
The while the hare gets to the place the tortoise started, it is no longer there.
So the hare gets to the place the tortoise is now, only to find it is no longer there.
If you repeat the steps an infinite number of times the hare catches up.

It really happens. Since the ancient Greek mathematicians didn't believe in infinity either it was to them an impossible description. Paradox.

 

[fromderinside]

Paradox? Not really. To do as suggested the rabbit needs to keep slowing down.

 

[George S]

Paradox? Not really. To do as suggested the rabbit needs to keep slowing down.

Of course not. The hare completes an infinity of catch-ups without slowing down.

 

[untermensche]

There are an infinite amount of finite changes in direction you make when pivoting any finite amount.

No there are not.

There are a finite amount.

A line of direction cannot be a line of zero dimension.

You are pretending it is possible, not proving it.

- - - Updated - - -

So you are saying you never get there?

This is why Xeno's paradox is a paradox.

That's why it has no connection to reality.

The arrow gets there.

Your arrow has passed over an infinity of integers.

Prove it.

Very quickly divisions of space are meaningless and you cannot make a meaningful division after that.

That is how the arrow get's there.

It travels over a finite amount of space with a finite amount of minimal movements.

 

[untermensche]

Any and all claims of a real infinity when actually checked devolve almost immediately into absurdity.

An infinite amount of anything that occupies space would not fit in infinite universes.

Infinite divisions are physically impossible.

Things in the real world can only be divided so far.

We have a Large Hadron Collider that makes the smallest possible divisions of matter that we know of.

 

[Kharakov]

There are an infinite amount of finite changes in direction you make when pivoting any finite amount.

No there are not. There are a finite amount. A line of direction cannot be a line of zero dimension.

By your words you indicate you don't understand that an arc length can be bisected, then that arc length, then that arc length.... never being "0".

Spacetime appears smooth- all experiments indicate that it is, the foundations of modern physical science assume that it is and make correct predictions using that assumption. This means that spacetime can be subdivided infinitely. This means that any time you spin around, you've faced an infinite amount of directions.

If you turn your head 1 micron, you're scanning a huge volume of space. If you turn your head .5 microns, you're scanning a huge volume of space.... so on and so forth. You're not going to get meaningful information without a telescope array, but...

 

[ryan]

Any and all claims of a real infinity when actually checked devolve almost immediately into absurdity.

What was absurd about the universe that I suggested where the only thing that exists is a spinning object. Is the number of times that it spins finite?

 

[abaddon]

Your arrow has passed over an infinity of integers.

George, I'm curious what you think of my argument below, in light of what you say about the arrow.

The arrow flying over an infinity of integers doesn't even have to entail passing over "ALL the integers". Infinity != the absolute entirety of an endless set.

{... , -3, -2, -1] is infinitely long, for example. Even if it "ends" at one end of the "line", it doesn't end at the other.

I don't think you could count all integers within even {..., -2, -1, 0, 1, 2, ...}. It'd just be an ongoing count. And yet an infinity of them will have been counted by an integer-reciting time-walker if he's been counting forever, regardless if at any moment he has not finished them "all".

 

[George S]

Your arrow has passed over an infinity of integers.

George, I'm curious what you think of my argument below, in light of what you say about the arrow.

The arrow flying over an infinity of integers doesn't even have to entail passing over "ALL the integers". Infinity != the absolute entirety of an endless set.

{... , -3, -2, -1] is infinitely long, for example. Even if it "ends" at one end of the "line", it doesn't end at the other.

I don't think you could count all integers within even {..., -2, -1, 0, 1, 2, ...}. It'd just be an ongoing count. And yet an infinity of them will have been counted by an integer-reciting time-walker if he's been counting forever, regardless if at any moment he has not finished them "all".

My comment was about passing over an infinite number of integers in finite time, not counting or reciting.

A recitation of increasing integers, no matter when begun, will never complete. It takes time to recite. If counting each second as it occurs, there will be numbers that cannot be recited in a single second. More seconds must pass than can be named aloud.

The set {..., -2, -1, 0, 1, 2, ...} is not a good model for time. A better model is the set of real numbers.

 

[untermensche]

No there are not. There are a finite amount. A line of direction cannot be a line of zero dimension.

By your words you indicate you don't understand that an arc length can be bisected, then that arc length, then that arc length.... never being "0".

Spacetime appears smooth- all experiments indicate that it is, the foundations of modern physical science assume that it is and make correct predictions using that assumption. This means that spacetime can be subdivided infinitely. This means that any time you spin around, you've faced an infinite amount of directions.

If you turn your head 1 micron, you're scanning a huge volume of space. If you turn your head .5 microns, you're scanning a huge volume of space.... so on and so forth. You're not going to get meaningful information without a telescope array, but...

What is 360 degrees divided by infinity?

How many degrees are these alleged infinite divisions?

 

[abaddon]

My comment was about passing over an infinite number of integers in finite time, not counting or reciting.

A recitation of increasing integers, no matter when begun, will never complete. It takes time to recite. If counting each second as it occurs, there will be numbers that cannot be recited in a single second. More seconds must pass than can be named aloud.

The set {..., -2, -1, 0, 1, 2, ...} is not a good model for time. A better model is the set of real numbers.

I agree. I only talk in terms of integers because the writer of the Opening Post does. To be clear, I'm not questioning your point so your point needs no clarification at all. I'm asking for a comment on my point.

To fit the arrow example more directly to untermensche's "reciting" integers analogy (in spite of it being a crappy model), let's say it's an arrow that has been flying forever (the OP talks about "infinite yesterdays") but lands in its target. Apparently to untermensche that kills infinity. To my mind, the flight that ended was still infinite regardless of ending. (Though it's debatable that it "ended").

untermensche's infinity-killer idea (or one of them) was that ending anywhere (like at the present moment) stops infinite yesterdays from being possible.

A recitation of increasing integers, no matter when begun, will never complete.

Right. That's what untermensche was on about, but saying it undoes infinity. My point is it does not, the completion or lack of it doesn't matter. You and Kharakov seem more adroit at discussing things at this level of abstraction so I'm asking for other views (and manners of expressing them) than mine on this.

Thanks!

 

[George S]

I agree. I only talk in terms of integers because the writer of the Opening Post does. To be clear, I'm not questioning your point so your point needs no clarification at all. I'm asking for a comment on my point.

To fit the arrow example more directly to untermensche's "reciting" integers analogy (in spite of it being a crappy model), let's say it's an arrow that has been flying forever (the OP talks about "infinite yesterdays") but lands in its target. Apparently to untermensche that kills infinity. To my mind, the flight that ended was still infinite regardless of ending. (Though it's debatable that it "ended").

untermensche's infinity-killer idea (or one of them) was that ending anywhere (like at the present moment) stops infinite yesterdays from being possible.

A recitation of increasing integers, no matter when begun, will never complete.

Right. That's what untermensche was on about, but saying it undoes infinity. My point is it does not, the completion or lack of it doesn't matter. You and Kharakov seem more adroit at discussing things at this level of abstraction so I'm asking for other views (and manners of expressing them) than mine on this.

Thanks!

In the context of modern physics it sure makes sense to have a beginning of time. If the universe is expanding it was smaller in the past. The limit of smaller is 0, and our math breaks down there.
I wonder what happened before time zero.
I mean, let's face it, Big Bang conditions are in a peculiar state. Very low entropy. I remember from Penrose's Road to Reality that he discussed this very matter.

I favor a theory (Sean Carroll mentioned it as one of dozens of origin theories.) that postulates a mirror universe before time zero.

If you care to follow along, it starts with the startling fact that if you run time backwards physics works [maven alert: yes you must change particles to anti-particles and change parity]. Running time backwards we get to Big Bang conditions at time=1, when the universe was smaller than a proton and yet has all the energy all crunched up. Let's assume that as time goes from 1 to -1 through zero it does not change. Going further negative from Big Bang conditions (lowest entropy). As the absolute value of time increases so does entropy. The Big Bang going in both time directions.
Now let's start at -14 billion years and run time our way (physics works -- this is valid) and we find a universe condensing into Big Bang conditions. They see the same, a universe collapsing into their Big Bang. An advantage here is that everything is caused, and the universe loves causation.
This universe is {...-2,...,-1,] U [1,...,2,...} where this is a real-valued continuum.



The video I posted earlier on "Nothing" postulates an empty universe with quantum fields and time. Then we get a universe. Flatline for infinity or zero time (they are the same when nothing is there) and then the universe turned on. A quantum fluctuation. And there it was, Big Bang conditions. Expanding in the time direction(s).