Talk:Where Mathematics Comes From/Archive

This archive is mostly a discussion between AxelBoldt and the infamous "24".

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This article is about a specific theory, and should be titled with the name of the theory. So long as it is properly identified in the opening paragraph whose theory it is, it's a fine subject for an encyclopedia, even if it's not taken seriously by many people (of course, opponents to the theory are free to include their views here too). --LDC

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This is false. Physicists do *NOT* believe that human cognition changes reality. People who don't understand quantum mechanics something think that physicists think this, but they don't. There are a number of pages on QM in wikipedia which go into detail about this issue.

This was contrary to a growing body of evidence in quantum physics that observers did in fact alter what they observed, and that the process of human cognition itself changed "reality".

the Uncertainty Principle argues that you can't get position and velocity at the same time *BECAUSE TESTING FOR ONE DISTURBS THE OTHER* - also the who notion of resolution of events backwards in time in QM models seems very clearly to say that the choice to observer or not, as per Schrodinger, must be said to have some impact on "reality". A narrower claim would be fine, but I don't know how to write that, so I invite you QM types to try to do so.

This is an incorrect interpretation of the Uncertainty Principle. Testing for one may disturb the other or not, but it has nothing to do with the uncertainty principle. -- Olof

I'm getting a little tired of the way physicists use the phrase "nothing to do with". As I was taught the Uncertainty Principle in high school, along with billions of others I am sure, you can't know both the position and momentum of any particle below a certain size, because testing for one disturbs the other. "The more precisely the POSITION is determined, the less precisely the MOMENTUM is known" in Heisenberg's terms. Now, you may *claim* that there are underlying factors that "cause" that relationship to be true, and I won't argue that there aren't, and the "because" of high school physics teachers is always suspect... -- 24.150.61.xxx

Perhaps reading the entry on the Uncertainty Principle will wake you up. The fact that you were taught in high school that "testing for one disturbs the other" is a good interpretation of Uncertainty Principle tells us more on the quality of your teachers than it tells us about the meaning of the Uncertainty Principle. Here's an example to illustrate the true meaning of the Uncertainty Principle :

My car gets about 30 miles to a gallon of gasoline ( 12 km / liter ). I know that because I put in about 10 gallons of gasoline every 300 miles. I can keep meticulous records so that I know, over the past year, exactly how much gasoline went in and how many miles I drive. A also know where my car is tonight, because I park it in my garage. I know exactly where my car is tonight. However, measuring the position of my car and its gas mileage at the same time turns out to be a more difficult problem. How accurately can I measure the gas mileage of my car when I'm at exactly mile 182 on Interstate 5? Note that measuring how much gas I put in the car does not affect the car's position: I look at the gas pump when my car is parked at the gas station. Furthermore, measuring the distance driven doesn't affect the car's position: I look at the odometer when it is parked in my garage. I repeat: "measuring gas mileage does not affect the position of the car". Nevertheless, the rate in gallons per mile at which my car burns gasoline and its position can be thought of as conjugate variables, related by an uncertainty principle. I really don't know what the car's gas mileage is at any one given point ( except when it is running and not moving, at which point I get 0 miles per gallon no matter what). And conversely, although I do know that it got 30 miles per gallon last year, I can't tell you exactly where the car was when it was getting those 30 miles per gallon. -- Olof

I think you just made my high school teacher's point. the conditions of measurement of gas mileage (requiring one to know the exact state of the gas tank) are incompatible with the car's motion (sloshing, hanging off a moving car to stick a dipstick in the tank)... while the conditions of measurement of the car's position (stable enough in space for the report to be meaningful, i.e. the car isn't moving) are incompatible with measurements of mileage (i.e. there is no mileage unless it's moving). the conditions of testing for one are incompatible with the conditions of testing for the other. I repeat, I am getting tired of the way physicists use the phrase "nothing to do with" when what they mean is "not reductionistic enough for us physicists who reduce everything beyond the point of being meaningful". -- 24.150.61.xxx

If by 'beyond the point of being meaningful' you mean 'enough to show the flaw in a high school teacher's false conception', then I agree with you. The sloshing of the gasoline is irrelevant: whether or not the gas sloshes, the gas mileage is unchanged, and the position of the car is unchanged.

how do you know that? those are both assumptions based on things you haven't measured, but pretend to know about cars and their engines... you are inserting knowledge about cars that you can't possibly have about atoms...-- 24.150.61.xxx

Measuring the car position doesn't disturb the gas mileage, and measuring the gas mileage doesn't disturb the position. And it is easy enough to measure the position of a car when it is moving. This is how, for example, they decide who wins automobile races. The important part is that

not from *inside the car* it isn't. And you don't determine the winner of an automobile race by bouncing an armor piercing shell off the winning car as it crosses the line first... the best analogy to the degree of interference that position or momentum testing on electrons could have... the shell is likely to tear the car's hood off and send it flying - changing its momentum substantially.-- 24.150.61.xxx

Never heard of GPS, eh? In any case, it is obvious you haven't understood ( perhaps haven't even looked at ) the section of the Uncertainty Principle page with the explanation on why this doesn't apply to the Uncertainty Principle. -- Olof

doing the measurement doesn't change the gas mileage. That's why this is a good example for pointing out why your initial statement "*BECAUSE TESTING FOR ONE DISTURBS THE OTHER*" is wrong. On the other hand, I completely agree with your statement that 'the conditions of testing for one are incompatible with the conditions of testing for the other.' This is exactly how any pair of conjugate variables are linked. If it is not clear to you what the difference is in the two statements, then, by your definition, this discussion has not yet reduced things beyond the point of being meaningful.-- Olof

you have shown the "because" to be a typical false assumption of causality by correlation. "Because" the testing conditions interfere, the tests interfere. But this is most truly splitting hairs. I can see what *you* mean by "conditions of testing" versus "testing" - but I can also see that you are assuming a model (of a car, of an atom) in making that hair split. I agree with Lakoff that this hair simply doesn't need to be split, that if the conditions of testing interfere, arguing whether they interfere at the stage of setting up apparatus or conditions, or at the actual moment the tank fires its armor piercing shell into the car, changing its momentum, is the furthest thing from relevant.-- 24.150.61.xxx

No, I have shown the 'because' to be flat out wrong. The testing conditions need not interfere with each other. 'incompatible with' does not mean 'interferes with' , and furthermore, you seem to be confusing "testing property A is incompatible with testing for property B" with "testing property A disturbs property B" Repeat: The tests can be made so that the tests do not interfere with each other. The armor piercing shell analogy is compelling, but it is wrong. I say that sloshing does not affect the gas mileage not because I have any knowledge about fuel injection, but because , as in quantum mechanics, an experiment ( or a gasoline tank) can be constructed such that measuring property A doesn't affect property B, and measuring property B doesn't affect property A. -- i.e. where the measurement is made even if the armor piercing shell misses. The uncertainty referred to in the Uncertainty Principle comes from somewhere else, not in any interference between testing methods. Please go back and try to understand this issue before trying to spread your false conceptions about physics. Especially pay attention to the part on the Uncertainty Principle page that says "The uncertainty principle is sometimes erroneously explained by..." -- Olof

this states the relationships more precisely. Perhaps, however, Schrodinger or entanglement resolution is a better example of this issue? I want to know whether any aspect of QM claims that "observers did in fact alter what they observed, and that the process of human cognition itself changed "reality". Does it, or not?

To say that the observer affects the "reality" of the observed thing is already to assume that the observed thing has its properties, the observer exists apart from it and has his own properties, and that one affects the other in a particular direction. That's not the best way to look at it. It

I think you confuse "best" with "most convenient" here... what's wrong with an ontology of three actors: observer, observed, and invisible (and not directy testable) foundation/reality? Properties are things "observed" have - there are no "properties" in the foundation/reality, merely the bonds/orders.

more like the experience of observation itself is a very complex phenomemon that emerges from the interaction between the observed thing and the observer. This doesn't make either of them less "real", or the result of the observation any more subjective or informative; it's just the nature of our

thus I stick to the very neutral terms like "foundation" or "zoo" - but ideologically, Axel objects despite the extremely common use of the term "zoo". I am willing to keep "zoo" out of titles but not out of articles.

being physical things, which we have to account for. That which we observe as "position" and that which we observe as "momentum" are not independently-existing things. They are mathematically related, and appear as interactions with our instruments, but they aren't determined in any way by our choice of measurement, because they aren't "contained" in the observed thing at all-- they are properties of the measurement itself. It so happens that these

fine, so the observer-to-observed measurement process has properties too, probably mirroring some constraints in the foundation (like "dark matter" in observations of the universe perhaps).

interactions follow some pretty simple rules that let us predict things like what furute measurements will be, what the probability distributions will be, etc. That's very handy, otherwise science wouldn't be able to produce handy working gadgets out of these things. But to say that our "choices" (whatever

it's the production of "handy working gadgets" versus the production of actual insight into human action and choice that's at issue. Exactly that.

that is) affect reality is a mistaken interpretation; we choose what measurement devices to set up, and they behave the way the behave when they interact with things, which happens to be very strangely in some situations. --LDC

perhaps it would be less strange if you would accept the hidden third player - the foundation - and the necessity of the foundation ontology if only to end disputes on what constitutes reliable measuring devices. I repeat: two Popper scholars had no answer to "infrastructure" as the buck-stopper.

Also the new cognitive bias article could use more update of that kind.

There have been occasionally interpretations of QM which said that the concious observer changes reality, but they are minority positions. There are no experiments to support the view; all experiments can be explained by saying that the measurement process itself affects reality, independent of whether a concious being later looks at the measurement outcome or not.

so, the culture or notation bias dominates, not the cognitive bias? OK.

I also wonder what this has to do with a cognitive science of mathematics; QM is just one example of a (probably false) physical theory. AxelBoldt

only relevant to the degree one considers the Four Bell States, the Uncertainty Principle, and physical constants to be part of a foundation ontology, e.g. the particle physics foundation ontology.

So if somebody were to consider these things as part of a "foundation ontology", what would that say about mathematics? Precisely nothing. If QM is disproven tomorrow, mathematics will still be exactly the same. You confuse physics with mathematics. AxelBoldt

assuming these things in a foundation ontology would validate the mathematics that predicts them. The question is the opposite way around - if one questions the objectivity of certain styles of mathematics, e.g. complex analysis, as Erdos did (else why bother with all those re-proofs?), then some highly mathematical fields like QM or PP will be called into direct question on falsifiability. Also, physics and mathematics drive each other to new theories and proofs, regularly - read Greene's "The Elegant Universe". Has this math been really widely inspected? No, almost no one understands it. Can the physical geometry proposed be tested? No, not yet. It's protoscience and "protomath". It is *you* who confuse both physics and mathematics with the underlying "reality" whereby the universe-to-observer and observer-to-universe pointers get bound to each other, below measurable limits or outside cognition itself. Bohm's "implicate order" or Plato's "ideal forms" or "sacred geometry" or whatever.

Best taken up in those entries, with new ones on culture bias (generalizing paradigm shift and such), and notation bias (generalizing this "cognitive science of mathematics" which is only one example of a claim of strong notation bias).

if we keep cognitive bias, culture bias, and notation bias separate in our own minds, I don't doubt we can find consistent non-controversial ways to express doubt regarding this Lakoff/Nunez thesis, and all the other epistemology problems it raises.

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Removed this statement. It's not a consensus among physicists.

Among technically literate people, there is a general consensus that mathematics is a neutral point of view, indeed that if logic itself is a valid mode of investigation, mathematics must equally be one.

it came from someone else, but I liked it, and thought it valid of at least technologists and all 19th century scientists. So qualified, would you find it acceptable? The link between logic and math probably has to be made here. Also now that there is a good cognitive bias article it should make reference to it, and to culture bias and notation bias issues.

I also recall a *terrific* quote from Whitehead on this issue that impressed me so much I forgot it (like a joke that is just too good). It was in "Dialogues with Alfred North Whitehead and his wife", by Lucien Price, 1936, still the most illuminating book ever written on this topic I think... Remember, Whitehead had been educated in the 19th century in the classic way and then had participated with Russell in the biggest hack at the foundations that had yet occurred, before World War I, then after that war worked like Russell to prevent World War II (unsuccessfully). An extremely interesting figure who will probably be ultimately credited with founding this thing that Lakoff thinks he founded.

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Who wrote this nonsense?

This nonsense was mostly written by a notorious contributor called "24" (after his IP number) who has since been forced to leave Wikipedia. The Lakoff book is very interesting, but this article is utter crap. AxelBoldt

according to the wikipedia-l, "24" was banned for two days and did not return, he she or it was not 'forced' to permanently leave. this is a lie.

We should probably remove it entirely, or reduce it to what one of us can say is verifiably true (and then probably give it a different title...). --Larry Sanger

I tried to do that; I read the book. It's not bad actually. AxelBoldt 00:24 Oct 12, 2002 (UTC)

if crap points you to non-crap, how crappy can it be? would you have read the book if not for "24"? seems you are exposing your own bias here