Once again, you have brought into the light one of the most profound questions at the intersection of mathematics and physics:
"Can the fact of inquiry--interaction; the forming of information--effect not only physical systems, as in waveform collapse, but mathematical truths as well?"
Did you really mean 'effect' as in "to bring into being," or 'affect,' as in "to alter a prior condition?"
The conventional interpretation of quantum mechanics largely prefers the former meaning; a discrete observation -- a measurement -- creates a reality that was not there before. If the meaning "affect" is applied, one presumes a continuous reality that is continuous not only in terms of spacetime; it is continuous with the discrete mathematics that describes both the nature of spacetime and the changing relative states of the mass-energy points that are part of the continuum.
The latter is closer to both Einstein's relativity and Wheeler's participatory universe. That is, discrete sets are the results of an evolving continuous reality, not the cause of it.
Tom
Tom,
I don't think the issue is quite so deep and/or complicated.
In the statement "The set of all sets which Douglas Hofstadter is considering at the moment.",...
How does the use of the word "considering" differ from mentally "observing", as the latter word is used in the statement: "Indeed, there's an oddly waveform-like quality to such sets, such that they cannot ever be "observed" to contain no elements; and yet, by inference, we can know that, in their "unobserved" state, they must." ?
The set being considered is the observed set. The number of elements in this set is not defined to be a constant, nor is it required to be equal to the number of elements in an unobserved/unconsidered set.
It is ultimately no different than asking why the number of elements (molecules) of water, in an empty glass, differs from the number that may exist in a glass that was not defined to be empty. One glass/set is in the state "empty" *by definition*, the state of the other is *undefined*, and can only be determined by an act of "considering" or "observing". Attempting to compare such dissimilar types of entities, is a "category" mistake. The state of one is "contingent" upon some action. The state of the other is not contingent upon anything; unlike the former, it is what it is, by definition.
Rob McEachern
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Tom, Rob,
We do need to extract our perception of reality from the continuum. Consider the function of photography. The continuum of light must be filtered, focused, timed, the aperture set, lighting considered, position selected, etc. Otherwise you just have white light. It is in many ways the same process used to measure quantum behavior and how the results reflect our measuring devices.
Leave the shutter open a little longer and you have "momentum." Shorter and you have "position." You can't do both in the same picture.
It is balancing many dichotomies; Content and context. Dynamic and static. Distinction and connection. Energy and information. Continuum and discretion. Focused and distributed. Etc.
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Robert H McEachern replied on Jul. 15, 2013 @ 21:36 GMT
Tom,
I don't view it as ignoring a fundamental question, rather, in my view , that question is not fundamental. Observation only create observations. They do not create "reality", nor do they describe discrete changes in a continuous phenomenon. However, by band-limiting continuous phenomenon, they may enable that phenomenon to be described via discrete bits of information. This is what...
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Tom,
I don't view it as ignoring a fundamental question, rather, in my view , that question is not fundamental. Observation only create observations. They do not create "reality", nor do they describe discrete changes in a continuous phenomenon. However, by band-limiting continuous phenomenon, they may enable that phenomenon to be described via discrete bits of information. This is what Shannon's Information Capacity is all about.
If I *define* a realizable procedure to observe the door attached to my head, you may be able to implement that procedure. Nevertheless, you will not have succeeded in observing the door attached to my head, since there is no door attached to my head. This is analogous to the uncertainty principle; that principle asks you to perform an observational procedure, and declares that you will not be able to make certain observations of a pair of variables. That is true, but only because the pair has been selected such that it is impossible *by definition* of what a Fourier Transform Pair is. It is a consequence of a purely logical definition, and is devoid of any relevance to actual physics. Communications Engineers abandoned it decades ago, in favor of observation of variables like "instantaneous frequency", rather than "Fourier frequency", since the former is defined in such a manner, that its measurement is not impossible by definition.
Let me give an example of the nature of the problem that I see in Orem's open letter:
1) I create a circle "A" and a circle "B"
2) I create a figure "A" and a figure "B"
Can you determine if "A" and "B" have the same shape? Can you do so without observing them?
In other words, is your ability to answer the question "contingent" upon making an observation?
If you describe the procedure by which you make these determinations, did your ability to answer the question indicate that a "State Collapse" occurred? But since (1) can be answered without every even attempting an observation, much less succeeding in make an observation, what caused the state to collapse?
My point is that "circle" is a "defined" term". "figure" is not. And definitions enable many questions to be answered, without observations. The question "Does an empty set have any elements?" can be answered without ever making an observation.
Rob McEachern
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Robert H McEachern replied on Jul. 15, 2013 @ 22:07 GMT
John,
You stated that "You can't do both in the same picture." and I agree.
But the point that you have missed is that you have, in effect, by invoking a "picture making process", specified not only what is to be measured, by also the (inappropriate) procedure by which it is be measured. The same light can be processed by a different, more appropriate, "non-picture" process, that can provide simultaneous, accurate estimates of both momentum and position. RADAR systems do this all the time. If I asked if you can understand this text, and then asked if you could still understand it if you removed all the consonant letters, I think you would agree that the reason why you cannot understand the latter text, has nothing to do with the text per se. It has to do with the inappropriate process you performed on the text, prior to attempting to understand it. In effect, this is what the uncertainty principle does; bet you won't be able to accurately measure this combination of variables, after I select an inappropriate combination of variables, that has absolutely nothing to do with what the "text" is doing.
Rob McEachern
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Thomas Howard Ray replied on Jul. 15, 2013 @ 23:50 GMT
"Can you determine if "A" and "B" have the same shape? Can you do so without observing them?"
Of course I can, Rob. Mathematicians do it every day. What Wheeler added was a general solution to the problem using physical criteria -- the quantum bit. The state doesn't collapse -- it changes over the continuous manifold of solutions in a specific direction dependent on the initial condition ("The asking of one question precludes the asking of another").
Tom
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John Brodix Merryman replied on Jul. 16, 2013 @ 01:59 GMT
Rob,
Yes, with radar and lasers, but you are focused an a particular set of parameters. The point is knowledge is isolating the parameters that you want to know about. Wouldn't you consider the concept of "absolute knowledge" to be an oxymoron?
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Robert H McEachern replied on Jul. 16, 2013 @ 04:11 GMT
Tom
Of course you can? Really?
OK. So does the figure "A" that I just drew, have the same shape as the figure 'B" that I just drew?
Rob McEachern
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Robert H McEachern replied on Jul. 16, 2013 @ 04:59 GMT
John,
One does not require "absolute knowledge" in order to possess a priori knowledge. As you stated in an earlier post, "We do need to extract our perception of reality" Possession of a priori knowledge regarding how to extract that perception may enable one to actually do so, in cases where doing so would otherwise be impossible. One cannot decipher a one-time-pad cipher, unless one knows, a priori, the one-time-pad.
Ordinarily, one does not know either "what ought to be observed" or "how to perform the observation", in order to best estimate the nature of an observable entity. But in the fortunate cases in which one does know, then that knowledge can be exploited.
For example, suppose there was a graph of a dozen data points, that vaguely looked like a straight-line. Is it a noise-corrputed line? Should you fit a straight-line to the data? Or is it a noise-less curve that just happens to resemble a line? Maybe it is a 5th order polynomial, that has a large linear component. How can you tell, from such limited data? The point is, if you know, a priori, that the data is from a noise-corrupted line, then you do not have to even attempt to determine, from the data, the otherwise undeterminable answer to the question "Should you model/fit the data, with a straight-line?"
If one knows, a priori, that there is a better method, than "taking a picture", for determining whatever it is you wish to determine about the nature of some observable light, then why even bother to take the picture?
As you said, "Consider the function of photography." That function is *NOT* to maximum the amount of information that can be recovered from the light. In fact, a photograph eliminates more than 99.99999999 percent of the information available in sunlight. That is why "You can't do both in the same picture."
Rob McEachern
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Thomas Howard Ray replied on Jul. 16, 2013 @ 09:52 GMT
Hi Rob,
You write, "So does the figure "A" that I just drew, have the same shape as the figure 'B" that I just drew?"
That's like asking, "What number am I thinking of between zero and infinity?"
To point out again that you are ignoring the fundamental question -- the issue isn't of whether one can mind-read or can see things that are unobservable. It is a question of whether one can use the principle of self-similarity to deduce the global shape of things unseen from knowledge of a shape locally observed -- and whether that deduction actually creates the unseen shape (the POV of probabilistic quantum mechanics that you subscribe to), or merely describes the prior condition self similar to the local description.
Tom
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John Brodix Merryman replied on Jul. 16, 2013 @ 11:01 GMT
Rob,
My point is that the answer to Tom's question, "Does the act of observation (measure) actually create a discrete physical phenomenon, or describe discrete change in a continuous physical phenomenon?"
Is both. Our reality is a nature vs. nurture type feedback loop between observer and observed, rather than either a fourth dimensional blocktime or platonic determinism, or some multiworlds scenario.
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Robert H McEachern replied on Jul. 16, 2013 @ 13:12 GMT
Tom,
You ask "can one use the principle of self-similarity to deduce the global shape of things unseen from knowledge of a shape locally observed"
The general answer is no. Because, in general, one does not know that self-similarity exists. Knowing that requires a priori knowledge. That is precisely the distinction between the two cases I discussed previously. In the first, I used a term, "circle", for which you had a priori knowledge, that was directly relevant to answering my question, specifically, that all circles have self-similar shapes. In the second, I did not use such a term, hence you lacked a priori knowledge of the relevant self-similarity, hence you cannot answer the question, even though you claimed that you could.
Deductions create conclusions. They do not create the entities those conclusions are about.
It does indeed "merely describe the prior condition self similar to the local description". But that is not the issue. The issue is whether or not that description is accurate. If you assume self-similarity where there is none, then it will not be. Physics has made many such bad assumptions; such as assuming that wave-functions exist outside the mind, which are self-similar to the Fourier transform based wave-functions that exist within the mind, which are being used to describe the entities outside of the mind.
Rob McEachern
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Thomas Howard Ray replied on Jul. 16, 2013 @ 15:09 GMT
Rob,
"Physics has made many such bad assumptions; such as assuming that wave-functions exist outside the mind, which are self-similar to the Fourier transform based wave-functions that exist within the mind, which are being used to describe the entities outside of the mind."
By your nonstandard view, even the principle of cosmic uniformity doesn't apply. In fact, one could not demonstrate that any physical phenomenon is objective and replicable. I'll pass on the solipsism.
I will address, "In the first, I used a term, 'circle', for which you had a priori knowledge, that was directly relevant to answering my question, specifically, that all circles have self-similar shapes. In the second, I did not use such a term, hence you lacked a priori knowledge of the relevant self-similarity, hence you cannot answer the question, even though you claimed that you could."
The claim is true. I didn't claim that I could magically replicate the shape, i.e., without expending energy. The replication would require the paring to essentials, such as suggested by Wheeler's "it from bit" hypothesis: Is the object continuous? Is it orientable? Can it be described in less than five dimensions? Four? Three?
Prior knowledge is not required. Only a theory and a model that can be tested against objective criteria.
Tom
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Robert H McEachern replied on Jul. 16, 2013 @ 17:16 GMT
Tom,
"one could not demonstrate that any physical phenomenon is objective and replicable"
What does the word "replicable" mean in science? It means that repeated observations will generate self-evident, self-similar results. That is how it is demonstrated. One does not need to assume self-similarity, when one can simply observe it. That is why replicability is the gold-standard of science. It remains the *only* known self-evident, self-similar "starting-point", upon which deductive logic can be applied, in order to generate valid conclusions, without having to make any other assumptions.
"Prior knowledge is not required." In many cases that is true. But if you want to, for example, "beat" the uncertainty principle, it is. As you know, that principle states that one cannot simultaneously, accurately measure a pair of Fourier transform variables. That much is absolutely true. But assuming that that implies that one can never *know* both variables is absolutely false. One can be known, a priori, without measurement, such as when an experimenter deliberately puts one of the variables into a precisely known state, and then the other can be known through measurement. The same is true of the EPR paradox. If one knows a priori, that a self-similarity exists (anti-parallel spins) then a single observation is sufficient to know both spins; there is no spooky action at a distance or mysterious quantum correlation. There is merely an a priori known self-similarity, that has been incorrectly accounted for by the theory.
Rob McEachern
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Thomas Howard Ray replied on Jul. 16, 2013 @ 18:23 GMT
Rob,
"What does the word "replicable" mean in science? It means that repeated observations will generate self-evident, self-similar results."
Yes; however, those results have be deduced from theory and translated to a model. Theory is primary.
" ... assuming that . . . one can never *know* both variables (of a pair of Fourier transform variables) is absolutely false."
I agree. I address the matter in my
essay. "One can be known, a priori, without measurement, such as when an experimenter deliberately puts one of the variables into a precisely known state, and then the other can be known through measurement. The same is true of the EPR paradox."
You bet. Reverse the order of experimentation to measure first, and classical time reversibility appears as conservation of angular momentum, as I explain.
"If one knows a priori, that a self-similarity exists (anti-parallel spins) then a single observation is sufficient to know both spins; there is no spooky action at a distance or mysterious quantum correlation. There is merely an a priori known self-similarity, that has been incorrectly accounted for by the theory."
No argument from me. We certainly agree on the unrealized potential of classical physics to explain quantum phenomena.
Tom
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Robert H McEachern replied on Jul. 16, 2013 @ 19:05 GMT
Tom,
I'm glad that you now see that we agree on many things. I do indeed often view things from what you have frequently termed a "nonstandard view". But I was trying to point-out that I am actually looking at the same things you are looking at. I just turn them over and over and view them from different perspectives, in an attempt to find a view-point that is self-evidently less weird than the standard view-point, and then invite others to view them in a similar manner. As I have stressed repeatedly throughout these discussions, unlike many others, I am not proposing any new theories. I am merely attempting to point-out that the "standard view" or "interpretation" of these theories has adopted a most unfortunate view-point, that makes the theory appear much weirder than it actually is. One does not need to alter the theory, in order to remove the weirdness. One only needs to view it from a different perspective.
Rob McEachern
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John Brodix Merryman replied on Jul. 16, 2013 @ 19:52 GMT
Rob,
You start ironing out the wrinkles and there is a lot that would disappear.
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Thomas Howard Ray replied on Jul. 17, 2013 @ 09:56 GMT
Thanks, Rob. I get it now.
Tom
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