Re: Skolem's Paradox and why is math the way it is?
From: J.E. (troubled6man_at_yahoo.com)
Date: 11/15/04
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Date: 14 Nov 2004 17:39:43 -0800
raf@tiki-lounge.com (Ross A. Finlayson) wrote in message news:<3c6b9c1e.0411131833.6930411c@posting.google.com>...
> troubled6man@yahoo.com (J.E.) wrote in message news:<39d6e584.0411130812.6fd67d86@posting.google.com>...
> > raf@tiki-lounge.com (Ross A. Finlayson) wrote in message news:<3c6b9c1e.0411111847.18c54c37@posting.google.com>...
> EF is the natural/unit equivalency function. I named it thus to
> illustrate a bijection between the naturals and the unit interval.
Isn't EF outside the model, so don't you need to say bijection* or
something?
> One of its least values, EF(1), is also called iota, another i, and
> that's part of a consideration of the real numbers where the successor
> of sorts of zero within the real numbers is i. S is for Summation.
Pardon my rudeness but this sounds insane, did you accidentally delete
parts of your post?
> Obviously enough the positive infinitesimal has relative
> infinitesimals, each non-zero infinitesimal is basically the same
> thing. If you query the existence of infinitesimals, a 360 degree
> revolution is 2Pi radians.
Query? "Basically the same" for WHAT purpose? This isn't clear at
all, and you've said that you aren't trying to be vague, but I have
more and more trouble acxcepting that.
> I just thought a proton was millions of times the mass of an electron.
> I researched after reading that and some numbers have it being 4000
> times, not 2000 times. I don't particularly care. Is it twice or
> half? The mass/charge ratio is not the mass ratio of the proton and
> electron.
Now I *know* that we are not communicating, you clearly did not read
my post I said "I have NO idea why you think a proton has a
mass/charge ratio that is vastly more than 2000 times that of an
electron, why would you believe that?" where I discussed the q/m ratio
of a proton compared to the q/m ratio of an electron, and remarked
that I didn't know why you thought one was vastly more than 2000 times
that of the other. To construe anything other than that from what I
said is to simply read in whatever you please into my text, which
could be fun for you personally, but hardly bears merit for a debate.
> If space-time is curved, then when there is any relative motion of
> massy objects, then the curve changes to reflect that: it is curved
> in the pop-Einsteinian interpretation because of the "gravity well".
> There is some kind of massless tendency for space-time to be flat.
>
> I got to the consideration of the distance between two rocky points on
> a bay. The straight line is the shortest distance, the straight line
> right along the coast between them.
This is either incoherent babbling, or just too subtle or deep for me
to grasp, you honestly think we are communicating well?
> You can switch models, and that is quite vague of you to do so. There
> are, I guess, models where space-time is "flat."
If I couldn't switch models, how could I compare one to another? Yes
there are models where space-time is flat.
> Ah, here was my idea, about the determinant of the vectors, and how
> the determinant is a scalar. That's inadequately the large extent of
> that idea. That quote of Cartan had some meaning towards the
> self-sameness of vectors and scalars, and i, i, and i and the
> pseudoscalar and the square root of negative one. Page 37: "We shall
> conclude this chapter with a study of multivectors from the point of
> view of their irreducibility with respect to the group of rotations."
>
> My question about the astronomy is if the average visible light shift
> of visible objects in the skies was zero. That might imply: a: no
> big bang, and b: infinite universe. Where that is not so, I'm not
> certain that it disproves those things. A cursory average of a chart
> shows a tendency towards red-shift, separation. It's generally
> accepted that the universe is infinite in the three spatial
> dimensions, but the status quo has that it is toroidal in four
> dimensions, but travelling in three dimensions will never lead to a
> return to the origin. Now _that's_ some mumbo-jumbo: the origin is
> everywhere.
More confusion, and your idea of "generally accepted" is very much at
odds with mine. Are most physicsists hiding from me, from you, both,
or is one of us just wrong?
> In casual learning of Planck's and the fine structure constant and
> other dimensionless radixes of sorts, it doesn't seem clear to me why
> 60 orders of decimal magnitude would be enough of a difference for
> (in)finitistic effects to take over. Those things are measured.
I don't know what effects you are talking about. Why you think
Plank's constant is dimensionless is unfathomable to me, as as a
dimensioned constant, it's order of magnitude clearly relates to the
standard definition of the sizes of the units meter, second, coulomb,
etc.
> In that opacity, there do seem to be some issues that will be resolved
> by these contemporarily non-standard considerations of the infinite.
So you honestly expect or hope that opacity will shed light on
anything?
> If there can be determined some means of scaling multiple dimensions,
> or rather transforming, then that would be a thing. Consider the
> infinitesimals, say you have a two coordinate system. You take the
> infinitesimal, perhaps twice, of one coordinate, and then something
> along the lines of e2 is e1 i^2. Then, you could represent those two
> co-ordinates uniquely with an unordered pair of scalars, a set. In
> that sense, one set of real numbers = infinite dimensional coordinate
> system, plus every single thing gets its own ordinal(s).
R is already the same size as R^2, even without going outside the
model to bring an EF, so what is your point?
> Heh, the origin is everywhere.
>
> In a post-Cantorian set theory, in light of Skolem, etcetera, the
> well-ordering principle, where every set is countable, the theories of
> Cantor's transfinite cardinals are taken into account.
>
> Here's the idea of EF: it maps the natural numbers in natural order
> to the unit interval of the reals in ascending order. I'm the main
> proponent of it, you can read discussions about it on sci.math.
If this is an example of what you think "a discussion" is then I doubt
it. You seem to think that a bijection* can preserve orderings, why?
There is no proof that the arena outside the model is strong enough to
provide it, so is this another assumption in your system without
axioms?
> One thing I like about the foundations of mathematics, logic, to some
> extent even philosophy, is that it is used to describe all science.
Not every foundation is used in all of science.
> How many dimensions is the universe again?
The universe is, and the dimension of a model of the universe depends
on the definition of dimension, and the specific model. Any theory
about fishfry's opinion that your question reflects on me in some way?
- Next message: Doug Goncz : "Re: A fairly simple proposition"
- Previous message: Tom Roberts: "Re: The *REAL* story of co-variant vs. contra-variant?"
- In reply to: Ross A. Finlayson: "Re: Skolem's Paradox and why is math the way it is?"
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