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piffle
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PostPosted: Wed Sep 01, 2004 5:06 pm    Post subject: Reply with quote

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I was just trying to say that if someone were to present a simple proof (irregardless of axioms used) that someone could check it and say "yes if we accept those axioms then your conclusion follows".

Only if everyone agrees on the same rules of inference. As I mentioned, not everyone (the constructivists in particular) accepts material implication as a valid means of logical deduction.

This thread has rambled on for 20 odd pages. I, at least, have no compunction against getting off-topic.
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PostPosted: Wed Sep 01, 2004 5:10 pm    Post subject: Reply with quote

piffle wrote:
Well, I'm gay, you know -- what would I do with 500 concubines anyway!

Give them to me?
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piffle
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PostPosted: Wed Sep 01, 2004 5:11 pm    Post subject: Reply with quote

Think of the electric bill!
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PostPosted: Wed Sep 01, 2004 5:12 pm    Post subject: Reply with quote

piffle wrote:
But you don't have such -- the answer to "what is mathematics" depends on who you ask! There are set-theorists nee Hlibert-style formalists. There are contructivists, and intuitionists. Do you accept material implication? Do you accept the uncountable Axiom of Choice? What about the Continuum Hypothesis? People don't agree on these most fundamental things.

The way it's done is that there is a number of basic set theory of axioms that everyone generally accepts as the starting point. If you read a math book, when a theorem requires an additional axiom (like the axiom of choice), it will clearly state so, and if you don't like to use the axiom of choice in your work, you are free to avoid that theorem (or to find a proof that doesn't require that axiom). Mathematics is the process of deriving conclusions from axioms. If you add axioms, you get additional conclusions, and the fact that some researchers don't like to use a certain axiom doesn't mean that mathematics is badly defined. Continuum hypothesis is another a statement that cannot be derived from axioms of set theory, except that unlike the axiom of choice, no-one actually uses it.
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piffle
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PostPosted: Wed Sep 01, 2004 5:17 pm    Post subject: Reply with quote

I never said mathematics was "badly defined." I said that mathematics was not a unique object that "exists" somplace outside the physical world. You said as much yourself: mathematics is a process, at tool, and one that can be customized to suit the task at hand.
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PostPosted: Wed Sep 01, 2004 5:31 pm    Post subject: Reply with quote

piffle wrote:
Quote:
But there still exists the wave function associated with the object

Really, exists where? Quantum mechanics is our convenient way of organizing our observations about the world. But the universe just does what it does, our models are dictated by it, not the other way around. So, where is the particle, since that's what we ultimately care about?

It exists same place where "mass", "energy", "momentum", "electrons", and "piffle" exist. You don't go out and see mass - it's a convenient model for explaining why it takes effort to push stuff, so I accept it as a high-probability model for reality. Similarly, I don't actually know that the gentoo forum member "piffle" exists; perhaps my box has been 0wned and some philosophically-inclined hacker is toying with me. However, the gentoo forum member "piffle" is a good model for reality (based on my experimental observations), so I stick with it. Wave function is similar - you can't see it, but it lets us predict stuff as accurately as we can measure, so might as well say that it's out there.

piffle wrote:
I promise you , the modern "conventional theory of science" does not suppose an objective reality. You can go read about as much even in your Griffith's Introduction to Quantum Mechanics.

I read it. Griffiths seems to support the Copenhagen interpretation (wavefunction exists, measurement creates observables from it). In what chapter does he deny reality?

piffle wrote:
As an aside, the "collapse of the wavefunction" is easy enough to describe mathematically -- you just zero off all the off-diagonal elements in some matrix -- but it is completely unmotivated. You can't derive it from anything, and it certainly does not follow from the normal unitary time evolution which holds immediately before, and after an observation.

If one accepts the existence of a wavefunction that can't actually be measured, why not accept the magical nature of measurement?

piffle wrote:
I said that mathematics was not a unique object that "exists" somplace outside the physical world.

And why not? Given a few starting axioms, any entity following the rules of logic will be forced to arrive at the same conclusions, so we can say that the graph linking the class of all possible axioms and all possible conclusions objectively exists independent of an entity capable of browsing it.

EDIT : bbcode error
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piffle
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PostPosted: Wed Sep 01, 2004 5:33 pm    Post subject: Reply with quote

Quote:
I read it. Griffiths seems to support the Copenhagen interpretation (wavefunction exists, measurement creates observables from it). In what chapter does he deny reality?

Page 4, among other places. ;)

But if you want the full story, I listed (a few posts up) several papers from the literature which will elucidate the present situation far better than I could here.
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PostPosted: Wed Sep 01, 2004 5:41 pm    Post subject: Reply with quote

Holy wow, this thing got way ahead of me while I slept. I'm sorry that I don't have time to go back to everything (though I have a hunch that you all aren't :)). Sadly, I have to go make a mockery of the game of golf and then I'm going to be incommunicado in the mountains of Colorado for the rest of the week. I'd like to hit one or two of the points, though.

piffle wrote:
Quantum mechanics is our convenient way of organizing our observations about the world. But the universe just does what it does, our models are dictated by it, not the other way around.


But there is a universe there to dictate our models. If there weren't some reality there to describe, we couldn't even make models. The whole process would be in vain. The question isn't really whether the particle is there, but whether the universe behaves in a manner that is consistent with the model. As the particle model is found to have weaknesses, it will be revised or scrapped, but I don't think it's reasonable to say that there is no underlying behavior or characteristic there that we are describing with increasing accuracy.

This is vulnerable to hellbeinger's point about the possibility of a reality that is not actually objective, but simply acts objectively. I don't think that it would be possible to distinguish between two such realities, so the question is moot. If reality behaves in an objective (even if it isn't deterministic) fashion, then I have no problem at all saying that that is because there is an objective reality.

As far as your question about rights existing without people, piffle, this is precisely why I appeal to truth in these discussions. I think that truth does indeed exist independent of people. It may be an assumption, but I think it a reasonable one.

Anyhow, what this boils down to for me is that, even if it is impossible to know whether there is an objective good, or whether our lives have meaning, we don't have to give up on the idea of living our lives as though they do have meaning. You don't have to go hard-core relativist and scrap the search entirely.

Hm - I seem to be stepping on Shurik's toes just a bit. Sorry. :)
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PostPosted: Wed Sep 01, 2004 5:42 pm    Post subject: Reply with quote

piffle wrote:
Quote:
I read it. Griffiths seems to support the Copenhagen interpretation (wavefunction exists, measurement creates observables from it). In what chapter does he deny reality?

Page 4, among other places. ;)

But if you want the full story, I listed (a few posts up) several papers from the literature which will elucidate the present situation far better than I could here.

page 4 wrote:
Bell's discovery effectively eliminated agnosticism as a viable option ... experiments have confirmed decisively the orthodox interpretation.

Seems to me that Griffith is saying Copenhagen interpretation is right, wavefunction exists, before measurement particle has no properties, and measurement causes a particle's property to take on a value with a probability based on the wavefunction.
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PostPosted: Wed Sep 01, 2004 5:50 pm    Post subject: Reply with quote

BaronVonOwn wrote:
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Perhaps. She has become quite the bugaboo. All I know of Rand is from The Fountainhead, which I loathe. I don't agree that her conclusions inevitably flow from this line of reasoning, for a lot of the reasons that piffle stated about quantifying harm.

Yeah, my smear campaign against her was quite effective, wasn't it? The Swift Boat Veterans for Truth would be proud. It is interesting that people much more easily accepted my 3-4 posts of personal attacks than they did my usual posts of reasoned argument, don't you think?


Heh. Personal attacks wouldn't be so popular if they didn't work. :)
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PostPosted: Wed Sep 01, 2004 5:50 pm    Post subject: Reply with quote

jetblack wrote:
This is vulnerable to hellbeinger's point about the possibility of a reality that is not actually objective, but simply acts objectively. I don't think that it would be possible to distinguish between two such realities, so the question is moot. If reality behaves in an objective (even if it isn't deterministic) fashion, then I have no problem at all saying that that is because there is an objective reality.

Good point - the universe might not be objective, there might not be anything at all like the wavefunction, but that doesn't mean I should stop pretending it objectively exists. :)
I minor point - determinism and objectivity have nothing to do with each other. A universe can be (and is, AFAIK) objectively probabilistic.
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piffle
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PostPosted: Wed Sep 01, 2004 6:01 pm    Post subject: Reply with quote

Quote:
Seems to me that Griffith is saying Copenhagen interpretation is right, wavefunction exists, before measurement particle has no properties, and measurement causes a particle's property to take on a value with a probability based on the wavefunction.

The eixstence or nonexistence of the wavefunction is immaterial (although, again, where exactly in the physical universe does it "exist?"). We are talking about particles and their properties, which according to quantum mechanics, have no definite existence before a measurement is made. Note also that Griffith's succinctly describes the orthodox position as "The particle wasn't really anywhere." Although, again I refer you to the literature, I can provide more detailed citations if you like.

Perhaps we are at odds over the definition of "objective reality." If a thing does not have defined properties at every single instant, in what sense can it be said to possess objective reality?


Last edited by piffle on Wed Sep 01, 2004 6:10 pm; edited 1 time in total
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piffle
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PostPosted: Wed Sep 01, 2004 6:08 pm    Post subject: Reply with quote

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I think that truth does indeed exist independent of people. It may be an assumption, but I think it a reasonable one.

I don't think it is reasonable. Where does this truth reside, and how may I observe it?
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PostPosted: Wed Sep 01, 2004 6:10 pm    Post subject: Reply with quote

piffle wrote:
The eixstence or nonexistence of the wavefunction is immaterial (although, again, where exactly in the physical universe does it "exist?"). We are talking about particles and their properties, which according to quantum mechanics, have no definite existence ("objective reality") before a meausrement is made. Note also that Griffith's succinctly describes the orthodox position as "The particle wasn't really anywhere."

OK, I finally see what you mean. Yes, of course, the particle isn't anywhere except at the moment of measurement. By the term "objective reality" you meant the position of particles (by the way, why such infatuation with position eigenstates? I prefer energy eigenstates, personally). Meanwhile, by the term "objective reality" I meant the wave function, and considered the position of particles to be merely the ephemeral manifestation of aspects of objective reality on my mind.

Now that this is settled, where would you place the wavefunction? Do you consider it objective?
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PostPosted: Wed Sep 01, 2004 6:14 pm    Post subject: Reply with quote

piffle wrote:
Quote:
I think that truth does indeed exist independent of people. It may be an assumption, but I think it a reasonable one.

I don't think it is reasonable. Where does this truth reside, and how may I observe it?

Can you give me a convincing reason to argue with someone who does not accept the existence of truth?
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PostPosted: Wed Sep 01, 2004 6:16 pm    Post subject: Reply with quote

piffle wrote:
Quote:
I think that truth does indeed exist independent of people. It may be an assumption, but I think it a reasonable one.

I don't think it is reasonable. Where does this truth reside, and how may I observe it?

Depends on the definition of truth, I guess. If you equate truth with "logical validity", then yes, it objectively exists since any intelligent being can derive it if he so chose. But if truth means "correspondence with the real universe", then I am doubtful, because IMHO the real universe cannot be known for certain (see above for arguments about quantum mechanics).
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PostPosted: Wed Sep 01, 2004 6:20 pm    Post subject: Reply with quote

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(by the way, why such infatuation with position eigenstates? I prefer energy eigenstates, personally)

It is a great irony (to me, at least) that the most "physically intuitive" way to frame quantum mechanics to a wide audience (position eigenstates) is in fact the most mathematically thorny, involving unbounded observables with continuous spectra, and requiring Rigged Hilbert Space theory for its full "rigorization." I harped on position states because they seemed convenient and easiest to present.

Quote:
Now that this is settled, where would you place the wavefunction? Do you consider it objective?

I think that state kets (in whatever basis) are merely elements of mental models. They "exist" only in my head, and if I manage to communicate them to you, in your head. They aren't "things" so I am not sure how you would even describe them in terms of objectivity or lack thereof.
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PostPosted: Wed Sep 01, 2004 6:23 pm    Post subject: Reply with quote

Jetblack wrote:
Can you give me a convincing reason to argue with someone who does not accept the existence of truth?

Do we agree on a common set of rules of inference for drawing deductive conclusions from a given set of premises? Then we have a framework for examining our different viewpoints, and where, specifically, our views diverge. Logical "truth" has nothing to do with any "absolute" truth.
shurik wrote:
Depends on the definition of truth, I guess. If you equate truth with "logical validity", then yes, it objectively exists since any intelligent being can derive it if he so chose.

Assuming we agree on what constitutes the set of allowable rules of inference, we will reach the same conclusions. People do not, and the use of "non-standard logics" has certainly been investigated. Furthermore, the use of logical inference has it's limits, since any deductive system strong enough to represent the whole numbers will contain propsitions that can neither be proved nor disproved (see a few posts back).


Last edited by piffle on Wed Sep 01, 2004 6:29 pm; edited 1 time in total
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PostPosted: Wed Sep 01, 2004 6:29 pm    Post subject: Reply with quote

So.. I guess the consensus of this thread is that concepts like the wave function are the same as other physical laws and rights? They exist in our minds (and on paper or whatever) and are thus subjective, but rooted in the same, objective, but indeterminate reality. I'd like to hear back from Mnemnia to see if his opinion has changed or if any opinions have changed :lol:
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PostPosted: Wed Sep 01, 2004 6:34 pm    Post subject: Reply with quote

GOBY wrote:
So.. I guess the consensus of this thread is that concepts like the wave function are the same as other physical laws and rights? They exist in our minds (and on paper or whatever) and are thus subjective, but rooted in the same, objective, but indeterminate reality.

Personally, I would put it the other way around: mathematics, wave functions, logic actually exist in some objective fashion. Meanhile, that which people usually call "reality" is actually deeply uncertain, subjective, and unknowable.
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PostPosted: Wed Sep 01, 2004 6:41 pm    Post subject: Reply with quote

eek. The mother of all bootstrap problems. How can the only absolute objective things sit on a subjective platform? Why flip it that way around?
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PostPosted: Wed Sep 01, 2004 6:42 pm    Post subject: Reply with quote

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Personally, I would put it the other way around: mathematics, wave functions, logic actually exist in some objective fashion

So you really believe that mathematics exists in some non-physical noumenal realm, and that through some unobserved and unquantifiable mathematical sixth sense, we apprehend truths from this Platonic hinterland? Sounds like voodoo to me.
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PostPosted: Wed Sep 01, 2004 6:48 pm    Post subject: Reply with quote

piffle wrote:
So you really believe that mathematics exists in some non-physical noumenal realm

Yes.
piffle wrote:
and that through some unobserved and unquantifiable mathematical sixth sense, we apprehend truths from this Platonic hinterland?

No. We apprehend the truths through logic (don't ask me how we can do logic, I don't know the first thing about how brains work). But even if we lacked the capacity to do math, it would still be there, and Alpha Centaurians or the Orion Machine People would still be able to derive the same theorems.
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PostPosted: Wed Sep 01, 2004 6:53 pm    Post subject: Reply with quote

GOBY wrote:
eek. The mother of all bootstrap problems. How can the only absolute objective things sit on a subjective platform? Why flip it that way around?

The problem is the I/O layer connecting brain to the physical universe. It's broken in so many ways it's not funny. If quantum mechanics is correct, the I/O can't even be fixed. On the other hand, the brain can internally recreate the universe of logic any time it feels like, which is why we can be much more certain about it.
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PostPosted: Wed Sep 01, 2004 7:08 pm    Post subject: Reply with quote

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We apprehend the truths through logic (don't ask me how we can do logic, I don't know the first thing about how brains work). But even if we lacked the capacity to do math, it would still be there, and Alpha Centaurians or the Orion Machine People would still be able to derive the same theorems.

This relies on the assumption that the rules of logic are unambiguous and unassailable. But what constitutes acceptable logic is a matter of contention. Furthermore, attempts to found mathematics on logic alone all failed. Even Russell and Whitehead eventually conceded this point.
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