Segregation has to be defeated every generation or so.

[Baruch]

But physics is a faith not based on proof too ... proof only applies to math, and even in math is limited in value (pesky assumptions ... oops ... I mean axioms). Physics can be demonstrated though, in public, laboratory, repeatable terms. I can in a public and repeatable way demonstrate the existence of the Catholic church ... though I don't think they would appreciate being moved from their sanctuary to a laboratory to be poked and prodded by me Whether or not part of their dogma is true or not ... that can't be demonstrated one way or another ... but the existence of it can be.

Well I do have to be clear about what words I use and how I use them, and that is what you were doing to. Appealing to dictionaries by either of us, is just an appeal to authority. Alas there is more than one dictionary, and English is a messy and imprecise tongue. The Latin roots of some of our English words are not going to go away, no matter how much New Speak the lexicographers mix in. But I am still uncertain that you realize that using that phrase the way you do, is like trying to get a fish more wet, in my case. I am not so confused like so many other believers, because I do take the time to understand what I mean, and mean what I say. We are all individuals, that doesn't validate or invalidate anything.

Shalom

[Kurt]

Truly. You and I talking about what we mean specifically by the words we choose is, for me, well worth the effort, as it has huge potential to help us understand each other more clearly. I see dictionaries more as reference point than authority. Where either of us can demonstrate a better communicative usage of a word than those found in a dictionary, the dictionary would conceivably lose any possible authority. That hasn't happened yet, but who knows...?

Kurt

[evangelicalhumanist]

But physics is a faith not based on proof too ... proof only applies to math, and even in math is limited in value (pesky assumptions ... oops ... I mean axioms). Physics can be demonstrated though, in public, laboratory, repeatable terms. I can in a public and repeatable way demonstrate the existence of the Catholic church ...

I think there are various usages of even such words as "proof," as is evidentwhen you look at the meanings of that word in civil or criminal trials. And certainly, the very fact that you can demonstrate some feature of the physical world, over and over again repeatedly, while circumstantial, can be highly convincing after some arbitrarily large number of demonstrations. I admit, though, that there can never be enough demonstrations to constitute an absolutely certain truth, in the way that a mathematical proof can be shown (always assuming the acceptance of those pesky axioms).

But I think we need to ask ourselves a very simple question, and that is, how would mathematics proceed if, say, approximately 1/3 of the world accepted the usual axioms as given, another 1/5 of the world adopted slightly different axioms, and all of the foregoing, of course, based on a few axioms original accepted by a group of which there is ony a tiny remnant left in the world. We would not, I think, have a very robust mathematics as we now appear to do.

By the way, coincidently, about 1/3 of the world claims to be Christian, about 1/5 Muslim, and they all claim descent from the Jews, of whom there really is only a tiny remnant by comparison.

And of course, by that analogy, we have some other "mathematics" out there, understood by large contingents of their own, that bear very little resemblance.

[Baruch]

Well apparently you are unaware that Non-Euclidean geometry is just as rigorous as the Euclidean kind. Also that different sets of axioms can be used to derive the same theorems ... that the starting point is a little arbitrary. The development of mathematics hasn't proceeded along the lines that Pythagoras imagined it would, any more then Jewish folk imagined that Christianity or Islam would develop. I would expect the Buddha would find the development of Mahayana and Vajrayana Buddhism to be bewildering also. So that remnant metaphor does indeed apply. There are probably a few genuine Pythagoreans still around, some few aboriginal Buddhists as well.

In the case of courts, given the frequent conviction of the innocent and freeing of the guilty ... the use of the word "proof" is a travesty only a lawyer would be guilty of

Shalom

[evangelicalhumanist]

No, I am perfectly aware (though with some unsophisticated mathematical understanding) of non-Eucludian geometry. I don't truly grok, for example, how the very "geometry" of the universe might imply that parallel liines converge, diverge or never meet. But that's the essential assumption, isn't it?

Still, I've long thought something quite similar when dealing with asymptotes. It has always seemed to me that in a "closed, unbounded" universe (whatever that might mean!) there may well be a return-upon-itself place where the x-axes and y-axes may well meet, and where, consequently, the graph of (for example) 1/x may well resolve itself in a sort of "lissajous" graph. (The trick to understanding what I'm saying is to place the graph on a greater-than-3-dimensional curved surface, rather than our usual 2 dimensional Cartesian plane. If you do that, you may well see that there's a way in which division by zero makes some as-yet unknown, but important, existential statement about the nature of our universe. ...... Or maybe not. )

[Baruch]

Very wise Grasshopper, you might be allowed out of the Shao Lin monastery on school holiday! But if you rub your legs together too fast, you will start a fire!

Lissajous ... is that some cocktail from New Orleans? Yes, you do have the qualitative idea ... at least in the large scale sense. On the small scale, you probably already know, that Special Relativity basically says that the length of things (in the direction of motion) and the timing of things ... varies depending on the inertial motion of the observer vs what is being observed. So basically rulers and watches can't be fully trusted to be consistent. What is happening locally in General Relativity is that even when the observer stationary, thanks to the gravitational field, the length of things in any direction varies from the non-gravitational situation, and further varies depending on where you are, which direction you are pointing in, and on the time. And time varies, even when the observer is stationary, depending on where you are, and on the time. So space-time becomes relative to inertial motion in the first theory, but also relative to position, time and direction in the second theory. In short, the Paris Metric Standard ... is an unachievable ideal ... though until we had extremely good measuring devices, we couldn't prove that. Paris time and Paris distance, is only accurate at Paris, at a certain time, and only with the platinum meter bar pointing in a particular direction. Tweedle-Dee and Tweedle-Dumb exclaimed ... "That's logic!" ... but I exclaim "That's metrology!". But then Greenwich Mean Time, is only true because the British Navy was so mean

I was just working in Complex Variable theory the other night, and what you are referring to is the Riemann Sphere, where ordinary infinity is just another number. It gets hairy when you then expand that idea to Riemann surfaces in general, where some surfaces are cork-screws and some surfaces are one-sided. IMHO ... the point at infinity of the Riemann Sphere, is the Big Bang cusp.

Shalom