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QM - Fact or Fantasy

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andie holland

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It is inside the operation called counting to which I am referring. Establishing and agreeing upon what apples are is a different application of the law of identity. In the science of mathematics, specifically within the scope of arithmetic, the question is how does the operation identified as counting violate the law of identity?

A Godel-esque reply would be that to talk of the operation of counting without reference to counting things is to do nothing but to reiterate back to Kant: humans are born with the innate ability to quantify (Crit #1, or Pure Reason).

 

In this sense, yes, you're correct. Our innate ability to quantify establishes the identity of what we just counted. So if you want to call said identity a 'law', that's fine. Kant, oth, simply left the observation on the level of one of our many human capacities.

 

But as Godel went on to say, Kant wasn't happy with this, his own description because real thought involves a whole picture of the thinking human that accounts for content. So in the Kantian sense, there's far more to human thought than an a priori imposition of space, time, and quantity upon its object (qv). Therefore, he wrote Crits Two and Three.

 

As a mathematician, one of Godel's ostensible solutions was to investigate whether or not pure math can explain how we think. In this regard, his work was a reply to Whitehead, Russell, and Wittgenstein. Well, it simply cannot; rather, it's 'incomplete'. Adding any content--in order to give us a complete picture of a real-thought operation would involve adding another axiom. 

 

So if Principia were right, Lof I would hold as true in a meaningful sense because it would stand as the first axiom from which real, working logic can be deduced. 

 

And If. per Wittgenstein, Tractatus' 'picture' was complete, all facts that 'fell' within the frame of reference would maintain their primacy (A-ness). 

 

But again, not, per Godel.

 

A more severe Post-Kantian understanding of our innate abilities would find talk of the re-statement of a priori capacities as "laws' to be utter nonsense. Why not a bladder law, too, that describes the biological necessity to pee?

 

Now of course, there's far more to the discussion that the Kantian conceptual box. For example, Rand herself stated that arithmetic, being the basis for math, comes from the act of counting..something.

 

And the something that's counted leads directly into science, and its method for doing so--which is basically to put A-ness into question as a hypotheses. This, again, is our subject. If QM is a fantasy, then so is the rest of science, as well.

 

AH

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A Godel-esque reply would be that to talk of the operation of counting without reference to counting things is to do nothing but to reiterate back to Kant: humans are born with the innate ability to quantify (Crit #1, or Pure Reason).

 

In this sense, yes, you're correct. Our innate ability to quantify establishes the identity of what we just counted. So if you want to call said identity a 'law', that's fine.

With the exception of the inane notion of "innate ability", that's what we do here, andie. It is about isolating and identifying the crucial differences. In what sense are things correct? That's what we ask. That's what we investigate. That's why I would have no problem purchasing and utilizing a quantum computer, if, and, ultimately when, they exist.

 

If you truly get this point, then in this sense, it was worth it, to me. If not, then I've wasted my time. If you do get this point, then it's up to you to make sense of the rest of your knowledge.

I'm more or less done here. Thanks for the battle of wits. The rest is up to you.

Edited by dream_weaver
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With the exception of the inane notion of "innate ability", that's what we do here, andie. It is about isolating and identifying the crucial differences. In what sense are things correct? That's what we ask. That's what we investigate. That's why I would have no problem purchasing and utilizing a quantum computer, if, and, ultimately when, they exist.

 

If you truly get this point, then in this sense, it was worth it, to me. If not, then I've wasted my time. If you do get this point, then it's up to you to make sense of the rest of your knowledge.

I'm more or less done here. Thanks for the battle of wits. The rest is up to you.

No, it's not a battle of wits. My position is that Identity, being  useful only with respect to logic is a useful rule of formal ordering. As such, however, it says nothing of content.

 

Science, of course, follows formal logic as an aide to ordering data.and devising experiments.

 

However, at the point of saying, "If the observed (content) appears to contradict said formal rules, then the far-greater advantage by far by far is to work out the logicality post facto. This is what we do when we establish 'cause'. 

 

What, therefore, is up to you qua Objectivist is to offer up a plausible account as to how real science works. Yet so far, you've failed to do this: again, hardly an issue of wits.

 

AH

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I would recommend Harriman's book "The Logical Leap", if your interested in a plausible account as to how real science works from an Objectivist perspective..

Thanks. The issue, however, is how others might discuss him. 

 

In this sense, yes, I agree with him per title: science does make 'logical leaps'. That's because, for science (as i contend, at least), logic serves as a heuristic: if results and observations don't seem logical, then try again. 

 

AH

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To my mind Andie has yet to show that they have an inkling of what the LOI even is. She/he also does not show a single bit of evidence of having listened to Harriman. Are you here trying to pull a Sokal hoax off Andie?

Andie, do you want to be understood? You are failing in that regard. I have asked you direct questions to facilitate this, which you have yet to answer.

Do you accept the notion that an existent can have and not have the same property at the same time? Do metaphysical contradictions exist? Can one ever "observe content" that is not what it is?

If you don't give a straight, non obfuscating answer I will be done with you as well.

The equivocation between essence and Identity has still not been unpackaged in this discussion.

Why is your only interest in "how others might discuss him"? Are trying to apply a constructivist analysis here?

Edited by Plasmatic
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The most absurd example of this is gravity. Experimental data clearly indicates that the Newtonian principle is wrong because matter does not have an attractive property.

 

You're right, Ilya Startev; it's the work of the Phlogiston.

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To my mind Andie has yet to show that they have an inkling of what the LOI even is. She/he also does not show a single bit of evidence of having listened to Harriman. Are you here trying to pull a Sokal hoax off Andie?

Andie, do you want to be understood? You are failing in that regard. I have asked you direct questions to facilitate this, which you have yet to answer.

Do you accept the notion that an existent can have and not have the same property at the same time? Do metaphysical contradictions exist? Can one ever "observe content" that is not what it is?

If you don't give a straight, non obfuscating answer I will be done with you as well.

The equivocation between essence and Identity has still not been unpackaged in this discussion.

Why is your only interest in "how others might discuss him"? Are trying to apply a constructivist analysis here?

The attitude of my Physics instructors in college mirrored that which you can easily find in any decent YouTube explanation of QM. Basically, it's 'So what?'

 

Again (to belabor the point), no one disagrees that QM is weird, illogical, whatever. The point in question is the extent to which formal properties of logic should or should not direct research. My response is that it's always served as a heuristic in all sciences. Harriman's search for a logical golden age of science is a total failure.

 

For example, yes, photons as 'existants' have contradictory properties at the same time because the equations put them in many possible places...at the same time (duh!). This is the basis for quantum computers as well as transistors and GMR for hand-held computers, as well.

 

so the question I'm posing back, directly, is how you reconcile the lived reality of Quantumworld with the admitted illogicality of its theory.

 

Lastly. feel free to unpackage essense and identity. I'll begin by stating that the ongoing hypothetical method of science denies essense as meaningful. 'Identity' itself is contingent upon proofs of any particular hypotheses via investigative method.

 

AH

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Harriman was seeking a logical golden age of science? Still sounds like someone not interested in doing his homework.

 

Andrew Bernstein in "The Myth of the Robber Barons" moved to rename the era with Carnegie, Edison, Rockefeller from the Guilded Age to the Inventive or Innovative Age. If that takes, it should free up the term Guilded Age, (which suggests a superficial layer of something precious overlaying a more baser material.) to be applied to something more appropriate.

 

Considering an example given in Harriman's book:

a thirsty toddler drinks a glass of water and his thirst disappears. What does he perceive? "I  stopped (got rid of, slaked, quenched) my thirst by drinking water. . . My drinking water made my thirst go away. . . . I caused my thirst to go away by drinking water. . ." Again, the content of "cause" is present in the experience itself. The quenching of one's thirst is an object of direct (introspective) experience. It is an experience of one thing causing another, since to quench is to cause a certain effect. Thus the experience of the quenching is the perception of the causing.

 

Plasmatic, I know you don't like applying the term first-level concept to the action side of identity. Harriman borrows the notion of first-level and applies it to generalizations here, essentially setting the precedence for laying the base or groundwork of generalizations directly perceived, distinguishing them as the base of what can be used to build on, hierarchically.

 

If concepts move in two interacting directions, both more intensive or extensive in nature or a combination of the two, would you suppose the same might be true about induced generalizations?

Edited by dream_weaver
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Harriman was seeking a logical golden age of science? Still sounds like someone not interested in doing his homework.

 

Andrew Bernstein in "The Myth of the Robber Barons" moved to rename the era with Carnegie, Edison, Rockefeller from the Guilded Age to the Inventive or Innovative Age. If that takes, it should free up the term Guilded Age, (which suggests a superficial layer of something precious overlaying a more baser material.) to be applied to something more appropriate.

 

Considering an example given in Harriman's book:

a thirsty toddler drinks a glass of water and his thirst disappears. What does he perceive? "I  stopped (got rid of, slaked, quenched) my thirst by drinking water. . . My drinking water made my thirst go away. . . . I caused my thirst to go away by drinking water. . ." Again, the content of "cause" is present in the experience itself. The quenching of one's thirst is an object of direct (introspective) experience. It is an experience of one thing causing another, since to quench is to cause a certain effect. Thus the experience of the quenching is the perception of the causing.

 

Plasmatic, I know you don't like applying the term first-level concept to the action side of identity. Harriman borrows the notion of first-level and applies it to generalizations here, essentially setting the precedence for laying the base or groundwork of generalizations directly perceived, distinguishing them as the base of what can be used to build on, hierarchically.

 

If concepts move in two interacting directions, both more intensive or extensive in nature or a combination of the two, would you suppose the same might be true about induced generalizations?

FYI, as a metaphor, 'golden age' refers to many periods. Athenian golden age of Pericles, Persian golden age of poetry, Spanish and Russian golden ages of literature, etc...

 

OTH, 'guilded' takes on the suggestion of cheapness and pasted over with a shiny golden substance. Such would ostensibly apply to late 19th century legal thuggery. with, or without the assistance of Bernstein's 'history'.

 

To the point: Harriman states that Newtonian science is a model of identity-logic. I've demonstrated that gravity lacks identity-logic even by today's standards of research.Doing science the old way really wasn't. 

 

Moreover, Harriman should be informed that, by far, most biological processes work beneath our sensory threshold. For example, the child that guzzles down the water will not be aware as to whether or not his thirst will be slaked at the cost of ingesting deadly microorganisms. Or to use harrimanese, said content of fatal cause is hardly present in the experience itself. 

 

AH

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Harriman was seeking a logical golden age of science?

 

I think it was implied by the brief chapter about modern physics, at the very end.

 

 

I've demonstrated that gravity lacks identity-logic even by today's standards of research.

 

Demonstrated- without reference to identity?

 

For example, yes, photons as 'existants' have contradictory properties at the same time because the equations put them in many possible places...at the same time (duh!).

 

When the concept of locality appears to lead to metaphysical contradictions, one does not accept them; one throws out locality.  Holding the law of identity as an absolute is how one reaches a 'logical golden age of Science' (in which things may seem strange, indeed- but not contradictory).

 

duh!

Edited by Harrison Danneskjold
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I think it was implied by the brief chapter about modern physics, at the very end.

Would that make ancient Greece giving rise to Aristotle, and the The Renaissance, say giving rise to Ayn Rand,  golden ages in contrast against the Dark Ages in philosophy?

I suppose I could be just more caught up in the inductive aspects of the book.

 

In that sense, i can see that Harriman is exposing the base material of a superficial cross section towards the end of his book after examining the earlier slice for the more homogenous material discovered therein.

 

 -

 

OTOH, you can see andie's suggestion that  'guilded' takes on the suggestion of cheapness and pasted over with a shiny golden substance. is a direct parallel to Bernstein's point.

 

"Such would ostensibly apply to late 19th century "legal thuggery". with, or without the assistance of Bernstein's 'history'."

This would rate an "A" in many college courses.

 

The fact that Bernstein directly contrasts conventional history with one that combines economic historians against the facts of more traditional empirical historians undercuts andie's arguments with anyone that cares to actually familiarize themselves with facts - as opposed to what their "robed professors" might have to offer.

 

-

 

Until andie discovers what intellectual honesty actually entails, (s)he is another sad empirical example of what can happen when one surrenders one's mind to the forces that suggest that philosophy is a mere bauble of the intellect.

Edited by dream_weaver
Mostly formatting, some grammar.
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I think it was implied by the brief chapter about modern physics, at the very end.

 

 

 

Demonstrated- without reference to identity?

 

 

When the concept of locality appears to lead to metaphysical contradictions, one does not accept them; one throws out locality.  Holding the law of identity as an absolute is how one reaches a 'logical golden age of Science' (in which things may seem strange, indeed- but not contradictory).

 

duh!

[Gravity is ]Demonstrated- without reference to identity?

 

Newtonian gravity is a property of mass itself, which is false. Therefore, this identity is false, as well. In other words, A is not A if the right hand descriptor of A-ness is not true.

 

Our present understanding of gravity is given by General Relativity, in which gravity is a force field that exists within space itself. In this sense, the equations works to describe cosmological reality. Therefore, gravity's right sidedness (what it equals) is true, yet incomplete. As we do not know the properties of a gravation beyond the equation for relativity, the left side A (of what is equaled) remains only a descriptive outcome.

 

...Locality.... 

 

>> I take your duh-ness to indicate that you're willing to toss the reasons why transistors and GMR work, and why Quantum computing will work, for the sake of saying that the L of I is an 'absolute'. 

 

But then again, you're only statement as to why it's an 'absolute' is to label it an 'axiom': a really nice thought which becomes reality when we click our heels together three times, not forgetting to wear the magic ruby slippers. of course.

 

Otherwise, it's simply a case of rape followed by seduction. What scientists painstakingly discover by the means of their method becomes, for the really deep-thinking non-scientific, an 'identity'. 

 

This 'identity' holds just long enough for the next scientific breakthrough to negate said identity. Oops, said Einstein: the Newtonian F=MA is revised by a third coefficient, the Lorentz, therefore F=MAG, etc...

 

AH

i

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The part I meant is under "Abandoning the Inductive Method".  It seems, on reexamination, like it doesn't actually mention much about modern physics, explicitly; just things like "A physicist who accepts the rationalist epistemology will seek an abstract, fundamental theory that is allegedly validated by characteristics such as 'simplicity,' 'clarity,' 'beauty' or 'internal coherence' (not by its relation to observable evidence)."  When I was first reading that, I automatically took it as a reference to String Theory.

So I suppose. . .

 

I think it was implied by the brief chapter about modern physics, at the very end.

 

Would be more correct as "I think it was implied by certain things which are applicable to modern physics, in the brief chapter at the end."

 

OTOH, you can see andie's suggestion that  'guilded' takes on the suggestion of cheapness and pasted over with a shiny golden substance. is a direct parallel to Bernstein's point.

 

Oh, yes.  Andie's made his/her opinions quite clear; as well as the fact that (s)he has, as much as possible, Abandoned the Inductive Method.

 

Until andie discovers what intellectual honesty actually entails, (s)he is another sad empirical example of what can happen when one surrenders one's mind to the forces that suggest that philosophy is a mere bauble of the intellect.

With a special twist of irony.  You see, when Andie squawks that:

 

A is not A if the right hand descriptor of A-ness is not true.

 

Or any other attack on Identity, what (s)he wants is to invalidate the mind.  The special irony is that- eventually- (s)he'll get exactly that.

 

The same is true of Ilya (whom I suspect may also be Andie).

Edited by Harrison Danneskjold
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Newtonian gravity is a property of mass itself, which is false.

Relativistic gravity doesn't contradict Newtonian gravity, any more than 'mass' is anything other than a measure of 'matter'.  And Newton's gravity is still an exact description of Einstein's gravity, for every single observer on the planet Earth (including you).  All Einstein did was to elaborate on Newton's gravity, to show how it works for masses that are mind-bogglingly dense or moving at mind-boggling speeds.

 

I mean, if that's incorrect then can you really claim to speak English, by your own standard?

 

Therefore, this identity is false, as well.

What identity?  Gravity?  Newtonian gravity?  If Newton were wrong then his concept of gravity would still be his concept of gravity (I don't see you fumbling to name nor describe it); it just wouldn't correspond to reality.

 

In other words, A is not A if the right hand descriptor of A-ness is not true.

Then what is Newtonian gravity?

 

Unless I can take this sentence to mean that "'Newton's gravity' is no longer 'Newton's gravity', because it's false" (in which case I'd really like to know what you now believe Newton's gravity to be)- unless that's what this sentence means, it's just gibberish.

 

Nice job refuting Identity without appealing to things like 'true,' 'false,' 'this' or 'it,' by the way; good to see you hold yourself to the same standards that you apply to Newton (if he is still Newton).

 

Our present understanding of gravity is given by General Relativity, in which gravity is a force field that exists within space itself.

 

 

Yep; just like an electromagnetic, nuclear-strong or nuclear-weak field.  You have something correct.  :thumbsup:  :thumbsup: :thumbsup:

 

In this sense, the equations works to describe cosmological reality.

And that was pulled directly out of your rectum.

 

I take your duh-ness to indicate that you're willing to toss the reasons why transistors and GMR work, and why Quantum computing will work, for the sake of saying that the L of I is an 'absolute'. 

 

1-  Maxwell's equations do not contradict the law of Identity (in fact, I believe they probably require it), so toss transistors straight out.

2-  I don't know what GMR is.

3-  Totally.   :thumbsup:  :thumbsup:  :thumbsup:

 

But then again, you're only statement as to why it's an 'absolute' is to label it an 'axiom'

Have I?  Silly me; always throwing my list of magickal axioms around.  :worry:   Its membership on my magickal list isn't why it's an absolute, though.  It's an absolute because there is no way for you to disprove it without assuming it (like when you used 'this,' 'is' and 'false' in your gravitational ramble).

 

And, in earnest sincerity, day you can do that will be the day it comes off of my list.  Seriously.

 

Otherwise, it's simply a case of rape followed by seduction.

 

I'm sorry; did you intend to make that into some sort of analogy, or are you just venting some expletives?

 

This 'identity' holds just long enough for the next scientific breakthrough to negate said identity. Oops, said Einstein: the Newtonian F=MA is revised by a third coefficient, the Lorentz, therefore F=MAG, etc...

 

"Oops," said Einstein, "this sentence wasn't properly formed"!  There goes whatever else you said.  B)

 

Consistency's a bitch.

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Relativistic gravity doesn't contradict Newtonian gravity, any more than 'mass' is anything other than a measure of 'matter'.  And Newton's gravity is still an exact description of Einstein's gravity, for every single observer on the planet Earth (including you).  All Einstein did was to elaborate on Newton's gravity, to show how it works for masses that are mind-bogglingly dense or moving at mind-boggling speeds.

 

I mean, if that's incorrect then can you really claim to speak English, by your own standard?

 

What identity?  Gravity?  Newtonian gravity?  If Newton were wrong then his concept of gravity would still be his concept of gravity (I don't see you fumbling to name nor describe it); it just wouldn't correspond to reality.

 

Then what is Newtonian gravity?

 

Unless I can take this sentence to mean that "'Newton's gravity' is no longer 'Newton's gravity', because it's false" (in which case I'd really like to know what you now believe Newton's gravity to be)- unless that's what this sentence means, it's just gibberish.

 

Nice job refuting Identity without appealing to things like 'true,' 'false,' 'this' or 'it,' by the way; good to see you hold yourself to the same standards that you apply to Newton (if he is still Newton).

 

Yep; just like an electromagnetic, nuclear-strong or nuclear-weak field.  You have something correct.  :thumbsup:  :thumbsup: :thumbsup:

 

And that was pulled directly out of your rectum.

 

 

1-  Maxwell's equations do not contradict the law of Identity (in fact, I believe they probably require it), so toss transistors straight out.

2-  I don't know what GMR is.

3-  Totally.   :thumbsup:  :thumbsup:  :thumbsup:

 

Have I?  Silly me; always throwing my list of magickal axioms around.  :worry:   Its membership on my magickal list isn't why it's an absolute, though.  It's an absolute because there is no way for you to disprove it without assuming it (like when you used 'this,' 'is' and 'false' in your gravitational ramble).

 

And, in earnest sincerity, day you can do that will be the day it comes off of my list.  Seriously.

 

 

I'm sorry; did you intend to make that into some sort of analogy, or are you just venting some expletives?

 

 

"Oops," said Einstein, "this sentence wasn't properly formed"!  There goes whatever else you said.  B)

 

Consistency's a bitch.

Since your first sentence is absurdly wrong, there's no need to do anything but split the difference: My Quantum course at Harvard taught one thing, yours at Ayn Rand U quite the contrary. By mutually exclusive standards, each is talking bs to the other.

 

Yet as a visitor to this site, you might want me to describe standard Relativistic Physics as taught outside of your ARU, but perhaps not.

 

Otherwise, Maxwell's equations will not suffice to describe a transistor's workings, and you really ought to look up GMR for yourself. If you can't understand the real language of non-ARU Physics, i'll be happy to assist--assuming politeness on your part.

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2-  I don't know what GMR is.

It's probably referring to Giant Magnetoresistance.

 

Quite frankly, if I was interested in understanding the subject better, I would be better off researching the topic myself, than dealing with the combative and condescending overtones embedded in andie holland's efforts to describe it here thus far.

Edited by dream_weaver
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It's probably referring to Giant Magnetoresistance.

 

Quite frankly, if I was interested in understanding the subject better, I would be better off researching the topic myself, than dealing with the combative and condescending overtones embedded in andie holland's efforts to describe it here thus far.

With respect to this thread, the only interesting aspect of GMR is that, like transistors (and soon,  quantum computers), it works off of QM principles.

 

In this regard, my question is simple and direct: How can you call any theory/concept/principle a 'fantasy' which we depend upon to produce objects that run our daily lives?

 

My own view of philosophy is that it's supposed to be a way of deriving meaning: In other words, what's the significance in the fact that we employ an admittedly 'illogical' theory to such great positive effect?

 

As for HD, I found his tone to be dripping of sarcasm as well. At the very least, those who use childish emoticons are hardly qualified to ridicule the trivial grammatical errors of others.

 

Yet more to the point, HD's errors with respect to basic Physics are legion. Here's one more: while the right-side of Special Relativity adds the Lorentz coefficient to the Newtonian--therefore, an 'addition' of sorts-- the equation for General Relativity is totally different than that of the Newtonian for gravity.

 

That's because while Einstein is describing a capacity of space itself, Newton describes that of matter. 

 

AH

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If Harriman is so wrong, - why are you bothering with trying to get others to help you understand his position? Why not just let reality be the final arbiter and allow others to discover the facts for themselves?

The wrong-ness of Harriman's argument goes to the heart of this debate in three ways:

* He gives a misunderstanding of how science has always worked.

** He misunderstands the heuristic benefits of logic within science.

*** He fails to answer my question,which I believe to be central: again, how can you reject QM while at the same time using it as applied principle on an indispensable, daily basis?

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The point is, you think he's wrong. So what? Who cares? Why do you care? What difference could it possibly make?

The point is that the name of this thread is 'QM, fact or fantasy?'; Harriman is the point of reference for the 'fantasy' claim which I dispute. how a situation could be any more simple is beyond me.

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You've not shown me where Harriman erred in his reasoning in a manner which I can grasp it. I've read the book and listened to several of his lectures. He comes across as pretty compelling to me.

 

Again, What if he is wrong? So what? Who cares? What difference could it possibly make?

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I work with computer aided drafting software. I started my career before such software was developed. One of the courses I took to acquire my set of skills is descriptive geometry.

 

For those that might not be aware, descriptive geometry has it's roots in Euclidean geometry. Lines and circles drawn with the aide of straightedges and compasses. This stuff has been around for thousands of years, and is well understood. Things like how to draw two lines perpendicular to one another and how to divide a line into multiple segments provide the evidence that it works and that it is valid.

 

Descriptive geometry goes further than that. I do not know who discovered the means to use views to relate different perspectives of the same geometry for consideration. Following the methods taught, the relationship between two lines established in two views can be projected by a method which would demonstrate if they intersect or not. Again, the evidence of the senses, in conjunction with an understanding of the method provide validation.

 

These methods can be combined to render all the primitives. From simple cubes, cylinders, cones, etc, to complex manifold shapes that proliferate our world today in all the various forms of any of the objects manufactured today.

 

After drawing a simple cube, I can place dimensions in the appropriate views in such way that I can verify that the dimensions are equal to the geometry used to describe them. The cube is 100mm by 100mm by 100mm. Taking the appropriate scale (ruler), setting it next to the lines, look at the indexes, and it looks close enough. Is it 100mm's? It is, within say 0.25mm. It can be seen to fall on the mark easily within that precision. Can it be manufactured to exactly 100mm? Can it be manufactured within 0.25mm of 100mm? 100mm ±0.25mm. Measure the drawing, measure the part - it either is (valid) or it is not (invalid).

 

Model the cube on a computer. Dimension it the same way. Get the same results.

 

Modeling can get complex. Look at your monitor and keyboard. Chances are, somewhere in the world is a 3 dimensional model that corresponds feature for feature for each component.

 

Most keyboards today are comprised of multiple components. they need to be assembled. Other examples might be the wheel assembly on an automobile. In changing a tire, the lug nuts are removed from the studs, the tire is removed from the axle the spare tire is aligned over the studs and the lug nuts are tightened.

 

If I take three blocks, each drawn and manufactured to 100mm ±0.25mm, setting them side by side, I can measure them to see if the dimension is 300mm ±0.75mm. As long as the measurement falls between the indication marks it is good (valid). This adds up. The sum of the parts equals the whole here.

 

With a tire, the relationship between features can be analyzed by learning how to add and subtract the dimensions on the two interrelated components to determine if the holes will always fit over the studs. Early on, combinations of methods as the one used to assess the three blocks where developed Each of these methods rely upon and relate back to Euclidean principles developed thousands of years ago.

 

As designs grew more complex, it made a difference on how the dimensions where put on the print, and how the parts where measured. Communicating what features related other features became important. Placing a cube on a granite surface and checking it with a height gauge yielded three different dimensions, depending on which face was adjacent to the surface. Measuring just became much more complicated.

 

By differentiating the faces from one another, it could be communicated "which way is up". Labeling a feature as a datum became a means of ensuring that the intended setup could be repeated more reliably, thus ensuring that validity is maintained all the way back to the Euclidean principles it was developed from. Geometric Dimensioning and Tolerancing was introduced as a standard reference guide. Terms like flatness, roundness, parallel, perpendicular, and position were assigned symbols that could be applied to a drawing, with boxes containing letters that related back to the datums enabling more precision in communicating how to measure and evaluate the features in the models, the relationship between differing features from differing models, and correspond them to the parts in order to assess if they are valid or not.

 

To understand how this guide could be used, it helps to grasp how each symbol, the associated tolerance(s), and the relationship back to their respective datums relate back to Euclid. Is the circle a circle? One of the symbols, circularity, used with a clearly stated allowable tolerance identifies the scope by which a circle can vary from a circular shape and still be, within (valid) or out of (invalid) tolerance, considered a circle..

 

Robert E. Knapp picked a title for his book. Mathematics is About the World, So far, it's measuring up to reality as I see it. The evidence of my senses simply confirm it.

Euclid dealt in statements said to be axiomatic ('worthy') because they were always true. Regardless of the measurement, which will always produce a level of variance against a given tolerance, geometric axioms are not supported by empirical proof. Rather, the means are sad to be 'formal'. 

 

This, in a nutshell, is what distinguishes Greek math from the far-older traditions of Babylonia and Egypt. The pyramids were built to 'perfection' without any mental-object as to what that perfect shape was.

 

As a student of Gauss, Riemann devised a means of measuring standard geometric objects on a curved surface. For example, One commonly says today that triangles have 180 degrees only on a flat surface. 

Degrees of variance from 180 are plotted against a unit of curvature. 

 

This, of course, gave rise to the present-day calculus of geometry, or its 'differential'. For one, both the 'Riemann' and its offspring, the 'Ricci' are present in the field equation of General Relativity. 

 

In passing, no, these figures, being in four dimensions, are nearly impossible to visualize. Despite lot's of imaginative padoodling, they fundamentally remain mathematical objects.

 

AH

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You've not shown me where Harriman erred in his reasoning in a manner which I can grasp it. I've read the book and listened to several of his lectures. He comes across as pretty compelling to me.

 

Again, What if he is wrong? So what? Who cares? What difference could it possibly make?

i've only listened to the tapes, and have not read the book. Perhaps, then, you might inform me as to what's in the book that I've missed.

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