Re: Skolem's Paradox and why is math the way it is?
From: Ross A. Finlayson (raf_at_tiki-lounge.com)
Date: 10/26/04
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Date: Tue, 26 Oct 2004 12:57:26 -0700
"J.E." wrote:
> raf@tiki-lounge.com (Ross A Finlayson) wrote in message news:<200410190133.i9J1X0o08046@proapp.mathforum.org>...
>
> > >> Oh no, they're gluons.
> > >>... please tell me what they are, J.E.
>
> I don't know what you mean by "kind" of energy. There is rest (or
> invarient) energy (or mass), which is the length of a four vector (the
> energy momentum four vector), there is a frame dependant kinetic
> energy, E=-mc^2+sqrt((pc)^2+((mc^2)^2)), and there is potential
> energy, which is the source of new kinetic energy. But why are you
> asking me to explain this? Either you already know, or you aren't
> going to believe *me* just because *I* say so. So read a good book on
> SR, or read a good book on GR. Then you will know what I'm talking
> about, it's not like this is something only I know about.
> ...
> > J.E., you're a troll. I think you should study space groups. Hey, now
> > I'm studying space groups, too.
>
> I'm NOT a troll, but I have to admit that I'm starting to wonder if
> YOU are. You are misquoting me. I didn't say that g (more rightly G)
> varied. G is a constant. It represents that falling objects fall at
> the same rate. I also will grant you that some authors use different
> terminology, discuss rest mass m_0 and rest energy c^2*m_0 and compare
> that to mass m=gamme*m_0 and energy E=gamma*c^2*m_0. Whereas other
> authors (the ones I prefer) talk about mass m and total energy
> E=gamma*m*c^2 or better yet avoid gamma altogether so that massles
> objects can be talked about more ealiy with the same eqations, just
> have E^2=(pc)^2+(mc^2)^2, then if m=0, we have E=pc and m can just be
> defined as the frame invariant length of the four vector
> (1/c)*(E/c,p_x,p_y,p_x).
>
> Let's get some "wrong laws of physics" out of the way OK, F=m_0*a,
> E=m_0*c^2.
>
> There are better laws, like F=pdot and E^2=m^2c^4+p^2c^2 to use
> instead. If you do general relativitiy, you notice that the source of
> curvature is the stress-energy tensor, not a mass tensor. If you look
> at the nucleus you notice that most of the "rest mass" of the nucleus
> is potential energy and the kinetic energy of the constituents, not
> the rest (invariant) mass of the constituents. So all forms of energy
> are treated equally by GR, this is very very boring standard model
> kind stuff.
>
> If you are so mean (or clueless) as to conclude that I'm saying (or
> that you think) that that implies that G varies, then please please
> please just stop trying to read my posts because I'm not *trying* to
> confuse you and I'm just going to be offended if you continue to
> misquote me and call me names. As for space groups, I've never heard
> of them, and I don't find "someone who calls me a troll said to study
> it" to be a good reason to start taking up the study of any particular
> topic, and hence I have no inclination to study this topic suggested
> by someone who calls me names, and who I'm not sure has any clue what
> he and/or she is talking about.
Hi J.E.,
Please disregard the troll comments, troll.
I have to tell you that I have very little understanding of physics, and I believe you when you say that those are the kinds
of energies.
In a recent post Koskensilta implies that the IF-logic was able to express models of itself all within first-order logic, so
it is first order logic, and metamodels and metalogics are representable in first-order logic.
I have neither tens nor dozens of years of study of the formalisms of logic and metalogic.
One reason that I saw your demand for suitable mathematical foundations for use by physics as something that I was qualified
to dicuss was that you frame it in the notion that physics needs something that can be consistent in terms in mathematical
foundations, de facto regardless of mathematical or physical unobservables. You mention the work of Skolem, and invoke
"countable metamodels of any theory" and similar notions as were being discussed on other concurrent discussion threads on
sci.math, perhaps the most widely read and distributed unmoderated mathematical discussion forum in the world.
There has been a lot of discussion for more than the past ten years about the contentions of cardinal math in terms of the
foundations of mathematics, and as well the suitability of given formalizations of the foundations of mathematics in light
of demands for consistency, completeness, and concreteness.
One thing I've seen over the years here on sci.math is a general move towards acceptance that there can be uniform random
probability distributions over the naturals, reals, or other generic sets of numbers. While there are still pedagogical
concerns, calling the "functionals" and so on, something along the lines of "select a random real from the unit interval,
what is the probability that it is less than one half" are readily answered instead of short-circuited by saying "no such
distribution exists." That's an example of a notion that was basically taboo in mathematics, and is now accepted because
people can understand that regardless of its construction or even lack thereof, that a uniform probability distribution over
the reals would be exactly that.
That may well be the most prominent example of something in sci.math where previous declaimants have become adherents,
without saying in so many words.
A similar notion over a larger timespan is that of the infinitesimal. Considered by the ancients and used quite ably be
enlightenement thinkers, and then basically banned on further consideration of the ancients, infinitesimals have a fixed
place these days and people can refer to mathematicians from the '60's to justify in the tried-and-often-true sense of
academic reference their use for any purpose.
J.E., you came to sci.math and requested a foundational theory that can handle your notion of physics, which is probably
quite accurate. What do your physics need from mathematics?
J.E., I'm relatively well-known on this forum as promoting that infinite sets are equivalent, that there is one mathematical
theory and that it has no axioms, that all sets are ordinals and ordinals are ubiquitous, that there are bijective functions
between the naturals and the unit interval of reals provided, and that that is all in total concordence with all mathematics
that not directly nullified, because it is consistent, complete, and concrete.
I want a better understanding of why the gluon as spring is the force of gravity, or the primary component. Why is that
so? You addressed some reasons why gravity is attraction and not repulsion, it is yet in a way both, and leads to
consideration of immovable objects, and thus unstoppable forces, and the teleportation from point A to point B.
Teleportation, there's another one of those things that used to be considered quite impossible, now the problem is that
while IBM can zap a few molecules from point to point in their lab, it is destructive or rather not creative because of "no
new information."
What do you think about "quantum encryption"? If it's based upon perception, how firmly do you have to think you observe to
disrupt all quantum communications? Is not quantum encryption a shared secret, the entangled photon, that is. Has Gravity
Probe B yet failed to physically verify the large part of GR?
Do you see mathematical foundational roadblocks to physics? List them.
Warm regards,
Ross F.
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