Interesting recent article, Praxeology and Certainty of Knowledge, by Objectivist Gennady Stolyarov II, editor of The Rational Argumentator (Le Quebecoise Libre). Relies heavily on Hoppe’s and Mises’s praxeology and epistemology.
Source link: http://blog.mises.org/4655/praxeology-and-certainty-of-knowledge/
Praxeology and Certainty of Knowledge
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Gennady is one of my students. I think we’ll see a lot more from him in the years to come.
And in the days to come since we have an essay he ha s written for mises.org.
If the spatial qualities of humans and all the objects they observe and interact with can be described and measured only through Euclid’s system, there is no point in asserting that any non-Euclidean geometry can also be true: it cannot be true if it describes nothing that exists!
Does Stolyarov mean to assert that the theory of General Relativity as developed by Einstein and Hilbert cannot not possibly be true? I am not a physicist but I do have a layman’s
interest in the subject.
Hoppe mentions non-Euclidean geometry in a footnote in his Economic Science and the Austrian Method (p76, n62). In Hoppe’s work he seems to imply that Euclidean geometry is necessarily prior to any understanding of non-Euclidean geometry, and not that non-Euclidean geometry is impossible.
I am not familiar with the epistemlogical foundations of relativity and would appreciate any comments.
P.S. For what it is worth there is some recent and IMHO very interesting work being done by Dr. Myron Evans at http://www.aias.us. Using differential geometry as developed by Elie Cartan, Evans has extended GR to encompass all four fields known to physics and has shown how all known equations of quantum mechanics and general relativity can be derived from a single set of field equations. All of this is done within the four standard dimensions of Einsteinian spacetime and shows quantum phenomena to indeed be governed by causal physical laws.
Anyways, it maybe interesting for anyone interested in physics and causal quantum mechanics in particular.
It’s “le Québécois Libre”, in case you can’t copy-paste properly.
– Yer french spaling pardna
Re. Evans:
The Dutch theoretical physicist Gerard t’Hooft,
who might be regarded as a rather knowledgeable
authority, does not seem to think too highly
of Evans’ work:
http://www.phys.uu.nl/~thooft/theoristbad.html
Evans is most definitely very full of himself but if you look past all of his ramblings about feedback stats, civil list pensions, etc, etc. and actually take a look at his work it is still very interesting. t’Hooft fails to make any criticism of Evans’ actual work and Evans has provided refutation after refutation of Bruhn’s critques.
Note there are plenty of “rather knowledgeable
authorities” in Establishment Economics who would say Mises, Rothbard, etc. were full of crap, and that doesn’t necessarily mean they are right.
From the introduction to Evans’ book:
“It is therefore possible in theory to build counter gravitational devices based on the engineering of gravitation with electromagnetic devices.”
Flying cars! Woot! I hope the maths work out…
I’ve never had a grasp on non-Euclidean geometry, but it sounds like Stolyarov is applying some kind of basic Aristotelian logic to it.
If A is TRUE then NOT A is FALSE.
Is that a law of logic? It seems it must be.
Anyways, if it is true, then the argument perhaps goes like this:
Therefore,
if Euclidean geometry is TRUE, then NOT Euclidean geometry is false.
or in other words,
if Euclidean geometry is TRUE, then non-Euclidean geometry is false.
On the surface, and intuitively, and logically, it seems kind of undeniable. But like i say, i have no grip on non-Euclidean geometry.
Maybe non-Euclidean geometry is simply accounting for the fact that we are all moving wrt a truly fixed location in space; maybe non-Euclidean geometry is handy because it accounts for this, in an otherwise, truly Euclidean universe.
Both Euclidean and non-Euclidean geometry are true. Points in space, equations, and laws can be mapped from Euclidean to/from non-Euclidean via a global diffeomorphism (non-linear mapping). The difference between Euclidean and non-Euclidean geometry is the assumptions made about the nature of the coordinate frame that motion is referenced to. Euclidean geometry assumes that the coordinate frame is made of planes at right angles to one another and is also called cartesian (generally 3 planes, such as up/down, left/right, and forward/backward). Non-Euclidean geometry does not make this assumption and allows for cyclindrical and spherical coordinate frames.
The primary benifit of non-Euclidean geometry vs. Euclidean geometry is that by mapping non-linear terms into a non-linear space the equations can be simplified to into linear terms.
Examples of non-Euclidean geometry in use are:
- global navigation (lat & log are part of a spherical coordiate frame)
- aircraft dynamics
- robotics
- dynamics on ANY rotating structure
As a side note, anyone claiming non-Euclidean geometry is null set and not useful should probably take a few minutes to review a highschool or college intro. physics book (Newtonian physics).
CC
CC,
That sounds pretty straight forward. I am quite familiar with Cartesian coordinates, and if that mapping sums up the essence of non-Euclidean geometry, then that leaves little room for controversy. So much then, for the shortest path between two points is a curved line!
Paul-
Check out the Wikipedia discussions on Euclidean and Caresian. Most of my knowledge comes from applications of Eulidean and non-Eulidean geometry in engineering, specifically model of system dynamics for servo control.
I always found the “shortest path is a curve” funny – after all you could just dig a tunnel through 1/2 the earth for a shorter route if you wanted to go through the effort.
CC
Not mentioned is the concept of “frame of reference”, i.e., cartesian coordinates approximate reality within a certain frame of reference. Equations that can be shown as periodic functions on a cartesian coordinate graph are an example. In the vast majority of human observable frames of reference, a cartesian graph has a lot of descriptive power. But where in nature do we find a cartesian plane – virtually no where. But for adequately controlled frames of reference, cartesian planes approximate reality just fine.
But another key concept is “approximate”. In the real world, answers that are claimed to solve a given problem are in reality in fact usually close approximations to the answer, valid only within the frame of reference within which validity can be demonstrated.
An example of where this breaks down is the disconnect between Newtonian and Einsteinian physics. Newtonian physics concerning objects in motion carries a certain approximate validity at most human observable points (i.e. less than light speed and more than sub-electron level), but breaks down near the speed of light, for example, a marginal case that humans cannot observe directly.
Einstein and subsequent workers developed different systems of theory that are valid and predictive at these speeds and levels of atomic structure (quantum theory)where Newtonian physics is of little use. Einstein himself has been superseded in additional cases.
This still does not completely invalidate Newton as a good approximation in the human-observable realm (or Einstein in his quantum realm) – it’s a good enough approximation for most macro uses, and does not require studying many years of advanced mathematics to understand most phenomena adequately well. You can build a perfectly servicable bridge using Newtonian physics, no quantum mechanics required.
But if you want to, for example (as Feynman desired) build a quantum computer, Newton is clearly not up to the task. And we have not arrived yet at a unified field theorem adequate to explain the macro and the micro adequately with simple, easy equations.
A diffeomorphism might have something to do with
the differentiability of the mapping, and not
its “nonlinearity” (“global” or otherwise).
The shallowness of some of these comments is
quite striking.
See
http://en.wikipedia.org/wiki/Diffeomorphism
BTW, Evans (an obvious crank) shows no indication
that he has any knowledge of the modern
rendition of differential geometry. He obviously
intends to snow neophytes.
Actually I doubt if Evans understands *any*
differential geometry, much less its
modern formulation:
http://opensys.blogsome.com/2005/07/01/
good post, i will be sure to comeback to this site again for some more informative articles. by the way does anyone know if this site that says i can
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