Posted on 04/06/2010 7:07:19 AM PDT by truthfinder9
I probably should have added that the variables in the equation, the Xs, can represent “real world” things.
Not real "things" but real numbers i.e. 1,2,3,4, etc. and not theoretical integers, i.e. x,,y,z, etc. That doesn;t make them "real."
Such mathematical arguments are equivalent to theoretical discussions how many angels we can fit ona pin of a needle. I am quite familiar with such polynomials with respect to aspheric surfaces.
They have no bearing on the real world beyond the 5th order simply because production and shop testing techniques can be carried out only to finite precision; the rest is simply theoretical.
Give me a real life example of something that is true but not provable.
Pi? At least not yet.
BTW, I really find your posts interesting. It's particularly fascinating to read you shred the "inerrancy" of Scripture while knowing that you are a faithful Orthodox. It's an excellent reminder that the Church and Christianity are not book bound, so to speak, content to experience the Divine in print and paper only but to undergo, endure, contemplate divinization or theosis. Tahnks.
Why is Pi not provable?
It's particularly fascinating to read you shred the "inerrancy" of Scripture while knowing that you are a faithful Orthodox
Well, I have had a change of heart.
So 2+2=4 isn't "real" and C2= A2+ B2 is not a "real world" proof?
You don't get a tighter real world proof than mathematics.
Huh? Diophantine equations are definitely possible. Hilbert's tenth problem is about whether such forms are solvable in a finite number of steps.
C2= A2+ B2 is not a "real world proof" ? should be
Proof of C2= A2+ B2 is not a "real world proof"?
Depends. By the way, just because 2 + 2 = 4 does not follow that a2 + b2 = c2, as your example next to it suggests (which is true of a hypotenuse of a right angle triangle). If you square an equation such as a + b = c then (a + b = c)2 is not a2+ b2 = c2 but a2 + 2ab + b2 = c2. In other words 22 + 22 ? 42 just because 2 + 2 = 4. Rather 22 + 22 = (2.8284271...)2 or just plain 8.
Ptolemy's navigational system "works" even though his model is flawed (there are no epicycles), because it accounts for all the motions and positions consistently, but does not necessarily represent reality and therefore is not true. The fact that it "works" cannot be used as "proof" that it represents the way the world is, that it is a true picture of the world. Neither can quantum mechanics.
We know that Ptolemy's method is not reality because we can prove it through reality. Quantum mechanics by definition cannot be proven by reality, because the reality "breaks down" in that model. Who knows, maybe another Leibniz and/or Newton will emerge one day serpenditiously and proclaim a new math that will provide answers to our indeterminate equations.
But math itself must be verified by the perceived world. Math itself does not determine what the real world is. Math is still a human method that attempts to describe the perceived world, and is real only to the extent that it can be verified by the real world. Math is no different than words; it is a descriptive language restrained by rules.
So, then, math can be sued to describe real events but it can also be used as fiction, to describe imaginary world, just as we can write a "realistic" story of people who don;t exist, or even a fairytale, where physical laws "break" down and all sorts of "magic" takes place.
No it is not. The real world is the proof of the mathematical description, not the other way around. The real world is the proof; not the math. Math must correspond to the real, detectable, perceptible, measurable, etc. world or else is a theoretical fiction.
In theory it is but the number has yet to be definitively defined.
Well, I have had a change of heart.
Regarding Scripture or Orthodoxy?
The myth?
" Evidence suggests 6th century BC."
That's when the Babylonians pillaged Jerusalem and hauled the Jews off into captivity. That's when their books would have been destroyed along with the temple. I don't believe that story about Sargon. It's likely the Babylonians ocpied the story, not the other way around.
That is just a shortcoming of our mathematical working model. Just as simple geometry can describe area and volume of fixed geometrical shapes (circles, squared, rectangles, triangles), etc., it can only approximate that of more complex shapes.
It takes calculus to describe areas and volumes of irregular shapes through integration using limits. We just haven't discovered the type of mathematical model that will give us a finite solution for π.
Calculus was essential in the development of mathematical expressions for optical design, because you could dispense with actual geometrical "ray tracing" and simply apply 3rd order or higher equations using derivatives to obtain solutions without tedious logarithmic traces.
Our mathematical tools are incapable of solving for π; the exact solution of π does not prove or disprove π. It is a fact and it is provable without a single real number.
Regarding Scripture or Orthodoxy?
Yes the myth that God dictated the books to moses word-for-word. However, scholars seems to agree that the Five Books of Moses were not written by one author or in the same period,iirc.
That's when the Babylonians pillaged Jerusalem and hauled the Jews off into captivity. That's when their books would have been destroyed along with the temple.
I believe there is evidence that the oral tradition was reduced to writing c. 6th century BC, while in Babylonian captivity. Idon't think the OT speaks of any destruction of the scriptures, but only of the Temple.
Well, duh. It was two different examples. You mentioned real numbers and "theoretical integers, i.e. x,,y,z, etc." (whatever that is.) So I gave examples of numbers and variables .
Quantum mechanics by definition cannot be proven by reality, because the reality "breaks down" in that model.
No, gross mistaken over-simplification. Theory is tested and proved by "reality." In experiments. Bell's theorem for example, the wave/particle duality of light, photons, sub-atomic particle cloud chambers, the Large Hadron Collider, etc. (For the record, these are different examples.)
So, then, math can be used to describe real events but it can also be used as fiction, to describe imaginary world…
Certainly, there is abstract math - though it follows the real world rules of all math - but the examples I gave are not abstract, they are set theory, polynomials, and basic math. I hope you're not next going to exclude calculus as not "real world."
Your initial reply requested specificity in "facts, truth, proof." Math is the most specific, most precise language. Unfortunately for the argument that "provable" and "true" are identical sets, math proves it wrong.
Some time ago, humans discovered that the quantifiable part of the real world is understandable and successfully modeled by mathematics. That if you take 2+2+2+2 apples you'll have 8 apples and if you cut them in half, you'll have 16 pieces. Every time.
Math works every time in the quantifiable real world. You can prove something by math and you have proved it "in the real world." If you won't take math as proof, you can't take logic as proof, and you have to cut every apple in half to "prove" 1+1=2. Until you find another apple.
Math proof has been considered "real" proof for a long long time.
Bell's theorem is just that, a theorem, not a fact. A theorem simplpy means something that is proposed on the basis of previously agreed upon rules or axiomatic assumptions, not necessarily on facts.
The problem with experiments is that some of them are not real. For example, an optical flat can be certified only to the degree limited by the interferometric device used and the ability to control all other parameters. Our measurements are as good as the precision (and errors) of our instruments. If we can't measure something then it is an approximation, not a fact.
the wave/particle duality of light, photons
The wave particle issue has to do with our inadequate mathematical models. Just as a quadratic equation can have two distinct solutions but never one. The problem is in our math, which is inadequate to provide answers as to the nature of a "particle' of radiant energy.
Ancient math was unable to do what calculus was bale to achieve, but ti took Leibniz and Newton to discover that mathematical model.
Quantum theory is still theory, not a fact. Even is something is mathematically provable does not mean that it reflects or describes the real world. Ptolemaic navigational systems comes to mind.
Let's set your sophism aside for a moment. Facts must be provable or else they are not facts. They are baseless claims.
Without reality to corroborate it, math is just numerical fictional prose. Math does not make reality "real" but rather the observed reality makes math real.
Experiments in the real world are used to test it. THAT was the point.
Our measurements are as good as the precision (and errors) of our instruments
Another "duh." Doesn't change the point of the accuracy of math - given the precision of the measurement of quantity.
The wave particle issue has to do with our inadequate mathematical models.
What? Are you now re-writing the science of light? Your "theory" here is novel.Quantum theory is still theory, not a fact
A theory that works in a multitude of devices you use every day.
that it reflects or describes the real world.
It works precisely because it reflects the real world. Remember, I'm the one who posted the initial point about models.
Facts must be provable or else they are not facts.
I AM talking about proof. Are you off trying to deny mathematical proof now? Math does not make reality "real" but rather the observed reality makes math real.
Uh, without the real world, there's no math. Ok. You do believe 2+2=4, right?
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.