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Originally Posted By: redewenur
One might ask the same regarding two infinite sets of integers, one containing all positive integers, the other containing all negative integers. There is, of course, the equivalent of the road without the bridge, i.e. the set of all integers, both positive and negative.


The difference is numbers are imaginary things, bridges are usually assumed to be actual and real unless one starts talking about imaginary bridges.

So my answer is you can't have an infinite real bridge but you can have an infinite imaginary bridge ... choose your bridge gives you an answer but I am not sure it takes us anywhere.

To make numbers actual and physical you have to have a computable function which is the issue Bill S is trying to dodge by somehow thinking an imaginary bridge and a real bridge can be equated without a computable function and they can't.

To show how stupid the example is ... in what does one build an infinite imaginary bridge a bigger than infinite universe perhaps ... but the bridge can't be infinite then because the universe is bigger? So what's next you define the universe as the bridge? So the answer from an imaginary bridge is imaginary and bears no relevance to anything real or actual.

The question your thought experiment sets up is logically flawed it of the typical variety that goes like this

Can GOD microwave a burrito or pizza pocket so hot that even he couldn't eat it? Any answer is not good for GOD smile

You know the typical format of the question is given below and they have a name.

Make (impossible condition 1) logically lead to (impossible condition 2)

Now lets see if you can work out why these sort of stupid logic questions work ... and I will give you a hint it has to do with zero.

Last edited by Orac; 02/04/14 06:31 AM.

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Orac. To quote Bill, in response to you: "I credit you with the intelligence to recognise a thought experiment/scenario when you see one, so I can only assume you are being deliberately obtuse". Bill is a generous fellow.

As is frequently is the case, Orac, you are trying to be too clever by half. You plainly do not have the local monopoly on intellect, conceptual ability, nor scientific insight, and it's long past time that you got down of your illusory high horse and desisted from your offensive remarks that so often cross the line from disparaging to insulting. Perhaps Bill S. has infinite time and patience for you. I have a seemingly infinite length of garden to mow.


"Time is what prevents everything from happening at once" - John Wheeler
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So can GOD microwave a burrito or pizza pocket so hot that even he couldn't eat it?

It's a perfectly valid thought experiment according to you laugh

It is every bit as valid and follows the same form as Bill S thought experiment

"If I have an infinite bridge and cut in two do I have two infinite bridges now?"

I thought this was a science forum not some Theatre of the absurd ... my mistake.

"The Parrots dead, that's what's wrong with it."
"It's not dead it's just resting"
"The parrot is dead"
"The Norwegian Blue prefers kippin' on it's back!"

I thought if Bill S was serious he might care to work out why the question isn't valid and what defines validity in a science sense, which is actually interesting and relevant to a science forum.

I will leave you and Bill S with your Norwegian Blue shall I.

Last edited by Orac; 02/04/14 08:31 AM.

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Quote:
So my answer is you can't have an infinite real bridge but you can have an infinite imaginary bridge


I don't know where you found the infinite bridge; perhaps you are just reading what you think is there. That would certainly explain some of your answers.

I am serious, and I am trying to communicate but I have much the same feeling now that I had when trying to communicate with Pre.

If you find the discussion frustrating and want to drop out, that's certainly your choice. That would be unfortunate, though, because there have been signs that our thinking might overlap in more places than you seem to believe.

Quote:
So can GOD microwave a burrito or pizza pocket so hot that even he couldn't eat it?


I'm not going to grace that with an answer, but it brings a thought to mind.

Q. What's the difference between God and Orac?

A. God doesn't think he's Orac. laugh


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Originally Posted By: Bill S.
I don't know where you found the infinite bridge; perhaps you are just reading what you think is there. That would certainly explain some of your answers.


Sorry road and bridge got confused when I translated they are close in my native language, uur ancestors really didn't have bridges smile

So my new correct answer is you can't have an infinite real road but you can have an infinite imaginary road.


Originally Posted By: Bill S.
I am serious, and I am trying to communicate but I have much the same feeling now that I had when trying to communicate with Pre.

If you find the discussion frustrating and want to drop out, that's certainly your choice. That would be unfortunate, though, because there have been signs that our thinking might overlap in more places than you seem to believe.


I agree but you don't want to look at the really interesting thing your thought experiment actually brings up which is what makes things valid and how do we decide logic.

Your thought experiment is classical in that it creates a problem only for certain sorts of logic operations.

Let me show you thought experiment under Intuitionistic logic which is one of the many forms of logic.

http://en.wikipedia.org/wiki/Intuitionistic_logic

=> In intuitionistic logic are not assigned any definite truth value at all and instead only considered "true" when we have direct evidence, hence proof.
=> Operations in intuitionistic logic therefore preserve justification, with respect to evidence and provability, rather than truth-valuation.
=> Intuitionistic logic is a restriction of classical logic in which the law of excluded middle and double negation elimination are not admitted as axioms.


So lets look at your example using Intuitionistic logic

"if you have an infinite road and you cut it in half do you then have two infinite roads"

Problem 1: infinite road ... no proof can exist assigned to vacancy state

Problem 2: infinite cut in half ... no proof can be done as we haven't seen an infinite road as per above and is infinity odd or even to divide ... so assign to vacancy state

Double negation elimination are not allowed so the question and thought experiment is not valid

Note that proof in Intuitionistic logic doesn't mean it can't exist it just means you haven't seen a clear example to determine any justification for an answer.

Russian science which I studied under uses Intuitionistic logic and so your thought experiment is completely invalid.

Interestingly however your thought experiment holds together under Western science which uses classical logic and I will leave them to defend it which Rede is doing I assume smile

Can you see that GOD and his pizza pocket resolves the same way for me as a nonsensical thing and yet causes angst with people using classical logic.

So perhaps the more interesting part I felt was to look at putting your example through different sorts of logic.

The one I was most interested myself in doing was putting it through a new sort of logic developed in 2003 called computability logic after all we are supposed to be a simulation according to some smile

http://en.wikipedia.org/wiki/Computability_logic


Logic determines validity and so the really interesting thing to do with your rather crazy example is look at it under different logic schemes and see what we get.


Originally Posted By: Bill S.

Q. What's the difference between God and Orac?
A. God doesn't think he's Orac. laugh


Wrong there is no difference we both don't exist please use Intuitionistic logic laugh

Last edited by Orac; 02/05/14 02:39 AM.

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Originally Posted By: Bill S.


Q. What's the difference between God and Orac?

A. God doesn't think he's Orac. laugh


Assuming the religious definition, he might if he spent a short while entertaining himself with the thought, or after eating the worm at the end of a bottle of tequila while on vacation playing skee ball on the boardwalk.


I was addicted to the Hokey Pokey, but then I turned myself around!!




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Originally Posted By: Orac
I think the first time I ever realized there are major issues with infinity was very early when studying Schrödinger's equation. The solution has to be linear and finite to get a proper time evolution to work.


Did that surprise you? Are solutions that produce infinities not usually problematic?

Quote:
"Wigner's friend"


Originally Posted By: Roger Penrose
The state of the observer's perception is considered to be entangled with the state of the cat. The perception state 'I perceive a live cat' accompanies the 'live-cat' state and the perception state 'I perceive a dead cat' accompanies the 'dead-cat' state. [..] It is then assumed that a perceiving being always finds his/her perception state to be in one of these two; accordingly, the cat is, in the perceived world, either alive or dead.[..] I wish to make clear that, as it stands, this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat.


Is this the sort of thing that Jim Baggott means by “fairytale physics”?

Quote:
So first under Schrödinger and that follows into QM that if there is a real infinity nothing measurable/observable or real exists there. In other words you can treat infinity in the normal mathematical way that it simply means a non existent number that represents a very large and finite number which you don't know.


Perfect! For mathematical infinities.


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Originally Posted By: Orac
(A) Absolute nothing can not and does not exist as evidence by the fact you are here.

(B) There is some GOD, Deity or whatever who can make something from absolute nothing.


They are the only two possible start points choose (A) or (B).


(A) is, in fact the only choice here, because God would have to be “something”.

Does your convoluted logic permit you to take the next step and agree that if “Absolute nothing can not and does not exist”, then something must always have existed?


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Originally Posted By: Bill S.
Did that surprise you? Are solutions that produce infinities not usually problematic?


Strange statement there are many solutions that produce infinities which aren't in any way problematic. The most obvious even layman are familiar with is the formula for a straight line produces an infinity which is never remotely an issue in normal use.


Originally Posted By: Bill S.
Is this the sort of thing that Jim Baggott means by “fairytale physics”?


Bit like your answer above I am not sure remotely what you have an issue with.


Originally Posted By: Bill S.
Perfect! For mathematical infinities.


And many real world infinities as well I am not sure why you feel you can just exclude them and this has been my issue all along you keep trying to avoid the issue of validity by just declaring it so, I am at least trying to put a formal definition under validity which is the interesting part of this rubbish.


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Originally Posted By: Bill S.
Does your convoluted logic permit you to take the next step and agree that if “Absolute nothing can not and does not exist”, then something must always have existed?


Nope I have no experience of a god so all I can do is fill it in as vacant in the logic table. Thus it is an invalid question.

There is nothing going wrong here and it doesn't concern me at all because Intuitionistic logic is about justification not about any idea of being able to answer absolutely every question.

In other words Intuitionistic logic is about making sure one does not make a mistake rather than worrying you might get stuck and might not be able to make a decision.

Intuitionistic logic leads to intrinsically safe results but many people who use classic logic complain that it is like doing science with one hand behind your back but any conclusion reached is also valid under classical logic the reverse as we have seen is not true.

So now we have the next thing about logic ... it implies a goal. If there wasn't a goal there would be only one sort of logic and there are hundreds.

So state your goal of your logic you intend to use please Bill S ... I gave you mine which can be technically stated as to make sure that my logic I use preserves justification. I am excluding anything that does not have verifiable and testable justification.

It will be very interesting to get the goal of the logic you wish to use.

Maybe someone in Western science would care to volunteer the goal of classic logic?

TT I am guessing your logic is going to be one of the philosophical ones care to share it?

Last edited by Orac; 02/05/14 06:48 AM.

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I should actually add I don't think anyone's choice of logic is better than another they simply are due to different goals. That is why I have no issue with Paul's answer I think it is perfectly fine.

I certainly don't think my logic is in anyway superior it just serves the purpose for which I want and is better for what I wish to achieve as my goal for science.

I still stand by that any answer given is probably correct to the person giving it but you seem to want to install a global truth Bill S and that is what I am struggling with do you really think there is just one and correct logic because your comment about my logic sort of intimate that?

As an aside and patch up there is also a new article on adding the natural numbers, 1 plus 2 plus 3 and so on all the way to infinity and it equals -1/12 smile

http://www.nytimes.com/2014/02/04/science/in-the-end-it-all-adds-up-to.html

Last edited by Orac; 02/05/14 01:57 PM.

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If I didn’t know what logic was, and had to try to work it out from your sesquipedalian responses I would assume it was the art of avoiding answering questions by employing exuberant and obfuscating verbosity.

Let’s take this one step at a time. Do you accept that you said: “Absolute nothing can not and does not exist”?


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Originally Posted By: Orac

TT I am guessing your logic is going to be one of the philosophical ones care to share it?

If I put that question together with the following statement:
Originally Posted By: Orac
See your basic behaviour in the post you know you piss us off we find you a pain in the arse and we have told you that or are you to thick and stupid to register that. Why you piss us off isn't important maybe it's our problem maybe it's yours who gives a [censored], only in your feeble dropkick mind is that even important.

Logic would tell me that I would only open the door for more verbal abuse.

Philosophically speaking, wink a scientist can't leave relative values behind to step into something more abstract. Without firm footing in something concrete, he can't argue for his limits and definitions.


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VERY VAST IS THE EXPANDING rubber sheet of the space-time continuum. Should we not call it infinite?
No, as a matter of fact, we should not, not unless we want to get into an interminable argument with both physicists and philosophers – the kind of argument where people steeple their fingers and say, very slowly, ‘We-ell, it all depends on what you mean by “infinite”.’ And go on saying it, with variations, till the beer runs out. If you are very unlucky, they will explain how infinities come in different sizes.

- 'The Folklore of Discworld' ,by Terry Pratchett & Jacqueline Simpson

Originally Posted By: Bill S.
...sesquipedalian...

Wonderful word, I must write that down. Thanks Bill smile


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Good quote Rede. Certainly worth remembering.

I also like TP's description of a thought experiment as “One that you can’t do, and which won’t work”.

(Pratchett Terry & Jolliffe Gray. The Unadulterated Cat)

That book also contains the best explanation of Schrodinger Cat I have ever seen.


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Originally Posted By: Bill S.
If I didn’t know what logic was, and had to try to work it out from your sesquipedalian responses I would assume it was the art of avoiding answering questions by employing exuberant and obfuscating verbosity.


I have answered the question in detail that is true you haven't remotely told me what logic you are using and what it's goal is ... you still haven't and you accuse me of avoiding the question smile

Originally Posted By: Bill S.
Let’s take this one step at a time. Do you accept that you said: “Absolute nothing can not and does not exist”?


That is true by definition under Intuitionistic Logic because if I can't measure it then it doesn't exist remember my goal is not to solve every question in the universe it is to answer questions with justification.

So "absolute nothing" doesn't exist but nor does "God", "Invisible forces", "Green aliens", "Flying Pigs" or a vast array of other things.

So that is not a unique or unusual thing to me and yes that is a true statement to me under science but take care it may not be the absolute truth the "flying pig" may exist I just haven't found a way to measure it's existence.


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While waiting to take one step at a time with Orac, I thought I might complete my thought scenario.

There is a road of infinite length, in the middle of which there is a bridge.

How do I know the bridge is in the middle? I know that because the road must extend to infinity on either side.

Of course, we all know that, physically, there cannot be a road of infinite length because, as far as we know, the only places where a road could be placed are finite, but this is a "thought scenario".

One night the Finite Defence League blow up the bridge, so no one can cross from one side to the other. We know that the road extends to infinity in both directions, but can each section really be considered infinite?

What do we have? Is it two halves of infinity, two infinite roads or two finite roads?

Intuitively, one might say that, as each half goes to infinity, we must have two infinite roads. That seems more reasonable than "two halves of infinity".

However, consider that if you are at a point (eg 1km from the bridge site) along the road, and you travel towards the break; in 1km you come to the end of "infinity". Does this make sense?

Because we reach an end, whichever side we approach from, it is tempting to argue that the road segments are finite. However, if members of the People’s Infinite Front decide to repair the bridge, but they are infinitely far away along the road; can they ever reach the bridge? The answer must surely be “no”.

We were able to reach the end, so in our frame of reference, the road is finite; but the PIF, who were infinitely far away could never reach the bridge, so in their frame of reference it must be infinitely far away. For them, the road segments are go on infinitely in both directions.

Does this mean that infinity is relative? It would seem to suggest that.

If infinity is relative, so must eternity be. This must raise the question: Could there be a frame of reference in which there might have been absolutely nothing, yet there might still be something now?

Perhaps it would save crossed wires if I say that I think there would not be, but I could have missed something.

It might be argued that we cannot, with justification, extrapolate from what we observe in the Universe to what might be the conditions outside, and that we cannot say with certainty that, outside the Universe causality could not be such that something could be "spawned" by absolutely nothing.

Personally, I think that's "a bridge too far", but that is just a non-expert opinion.


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Quote:
Absolute nothing can not and does not exist.


Saying that you believe something doesn’t exist is not quite the same as saying it “can not and does not exist”.

Are you seriously saying that “Green aliens” cannot exist, because you have never measured one?

Would you not have to be personally acquainted with everything in the cosmos to justify such a claim?


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Originally Posted By: Bill S.
Saying that you believe something doesn’t exist is not quite the same as saying it “can not and does not exist”.


Ahh finally you get it.

Science and science logic does not setup and can not setup to test that form because it is based on current knowledge => “can not and does not exist” defies that premise.

So nothing in science "can not and does not exist" not even an absolute nothing because to know that you would need all knowledge smile


Originally Posted By: Bill S.
Are you seriously saying that “Green aliens” cannot exist, because you have never measured one?


No does not exist ... you keep changing "does not" to "cannot"

It's subtle but you keep doing it.


Originally Posted By: Bill S.
Would you not have to be personally acquainted with everything in the cosmos to justify such a claim?


Correct so “Green aliens” do not exist but as to whether they cannot exist I have no idea nor care.

And so from science absolute nothing does not exist but I have no idea if it can not exist nor do I care it's not relevant to the field of science because I can't measure it.

So lets complete the loop now to infinity which is where this all began a long long time ago.

Science (I should subset that to Russian science I guess) says an actual physical infinity does not exist but it does not say an actual physical infinity can not exist it is silent on that matter.

Last edited by Orac; 02/06/14 01:30 AM.

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Orac, you said, and accepted that you had said: “Absolute nothing can not and does not exist”.

Now you say: So nothing in science "can not and does not exist".

You also say that I keep changing "does not" to "cannot".

I am simply quoting what you said. If you need to change what you said, that is your prerogative, but it doesn’t help reasonable discussion if you wrongly accuse me of misquoting you.


There never was nothing.
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