"Vortex Based Mathematics by Marko Rodin"

Originally posted by -PLB-
Yes.

That's the extent of your response?

Is this your way of saying that you see nothing in Maxwell's original equations that is lost to electrical engineers today?

Originally posted by Mary Rose

Originally posted by -PLB-
Yes.

That's the extent of your response?

Is this your way of saying that you see nothing in Maxwell's original equations that is lost to electrical engineers today?

And are you saying that you see something in Maxwell's equations that has been lost?

Originally posted by buddhasystem
Mary, of course, would rather rely on intuition rather than on info and/or experience.

No, Mary considers more than one source for interpretation and information.

reply to post by Mary Rose


I can't think of anything that isn't covered by the current 4 equations, everything can be derived from them. If you or Bearden thinks there is, then show what it is.

Originally posted by -PLB-
. . . I could also not find the original paper by Heaviside. . . . Too bad I can not verify what Heaviside actually published. If anyone knows where I can find this publication I would be happy to hear it.

Originally posted by Mary Rose
Bearden references the Proceedings of the Royal Society of London for Heaviside's discovery and publication, but I haven't figured out yet how to locate a 19th century document.

Originally posted by -PLB-
I would try a library

Do you intend to try a library?

Originally posted by Mary Rose

Originally posted by buddhasystem
Mary, of course, would rather rely on intuition rather than on info and/or experience.

No, Mary considers more than one source for interpretation and information.

Oh please, you emphatically rejected information offered for you perusal because you said you had intuition telling you that whatever you learn from it would be false, even before looking. So you don't "consider" jack.

reply to post by -PLB-


I believe this may have been posted on the thread and I will have to dig it up. Or find it fresh. There is a wealth of information, with references, on Bearden's site.

If you were really curious, you could also search his site.

Originally posted by Mary Rose
Do you intend to try a library?

No, although I find the subject interesting, I have absolutely no doubt that the current maxwell equations are correct. So I am not as excited as you are.

reply to post by Mary Rose


It is only the most important thing supporting Beardens arguments. I expect it to be the most important section in the notes your wrote down during your research.

Originally posted by Mary Rose

Heaviside simply chopped off the scalar component of the quaternion and discarded it, then formulated this new "truncated to a vector" version as a much simpler mathematics, albeit of decreased topology.

A scalar is a magnitude.

If you take vector, and chop off the direction, you're left with a scalar.

An example of this is if you are driving northeast in your car at 60mph, that's a velocity vector because it has both magnitude (speed) and direction (northeast). If you chop off the direction and just look at the speedometer, you have only a scalar that says you're going 60mph, but you don't know what direction. That's the difference.

So the vector has more information than the scalar. For this reason NASA states dealing with vector quantities is a little more complicated than scalars. This is especially true in some of NASA's applications as is described later in this post.

Scalars and Vectors

Vector quantities have two characteristics, a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type, you have to compare both the magnitude and the direction. For scalars, you only have to compare the magnitude. When doing any mathematical operation on a vector quantity (like adding, subtracting, multiplying ..) you have to consider both the magnitude and the direction. This makes dealing with vector quantities a little more complicated than scalars.

If you add directional components to a scalar, you have something very much like a vector, you have a magnitude and direction, but instead of saying the direction is northeast as the vector in the previous example, you have an easterly component and a northerly component (and a vertical component which really doesn't apply in your car on a flat road). That's a bit of a simplification of quaternions but that's the idea.

It turns out that using quaternions is actually easier for rotations and orbital mechanics, etc, so NASA actually does use quaternions, but only because they are easier to use in those applications:

From the mid-1880s, quaternions began to be displaced by vector analysis, which had been developed by Josiah Willard Gibbs, Oliver Heaviside, and Hermann von Helmholtz. Vector analysis described the same phenomena as quaternions, so it borrowed some ideas and terminology liberally from the literature of quaternions. However, vector analysis was conceptually simpler and notationally cleaner, and eventually quaternions were relegated to a minor role in mathematics and physics. A side-effect of this transition is that Hamilton's work is difficult to comprehend for many modern readers. Hamilton's original definitions are unfamiliar and his writing style was prolix and opaque.

However, quaternions have had a revival since the late 20th Century, primarily due to their utility in describing spatial rotations. The representations of rotations by quaternions are more compact and quicker to compute than the representations by matrices. In addition, unlike Euler angles they are not susceptible to gimbal lock. For this reason, quaternions are used in computer graphics,[8] computer vision, robotics, control theory, signal processing, attitude control, physics, bioinformatics, molecular dynamics, computer simulations, and orbital mechanics. For example, it is common for the attitude-control systems of spacecraft to be commanded in terms of quaternions.

Game developers apparently have the same math issues in rotating things as NASA. I found some interesting discussions between game developers regarding which math is easier for which applications, but I didn't find a single argument that they thought they were dealing with anything other than relative complexity between using the two mathematical approaches.

In other words, you're not missing anything by using quaternions versus vector math or vice versa. You will choose whichever is easier depending on what you are trying to accomplish, or in the case of game developers, the choice may not be what is easiest for them personally, but what uses the least resources and memory of the customer's PC.

Originally posted by -PLB-
No, although I find the subject interesting, I have absolutely no doubt that the current maxwell equations are correct. So I am not as excited as you are.

What happened to your curiosity about:

Originally posted by -PLB-
Where is the experimental data that shows this "giant curled EM energy flow component" really exists? How did Bearden came to the conclusion it exists other than "Heaviside said so"? Too bad I can not verify what Heaviside actually published. If anyone knows where I can find this publication I would be happy to hear it.

reply to post by Mary Rose


Still there and still waiting. But not on top of my to do list.

From Bearden's “'Maxwell’s' vector equations taught in university are actually Heaviside’s truncated equations, and are only a simplified version of what Maxwell originally wrote.":

reply to post by -PLB-


Okay! I'll buy that.

Originally posted by Mary Rose

Mary, this pic illustrates nicely that only garbage can come out of a garbage-filled mind.

Quaternions are not numbers and can't be a part of "number system". Even then, if we just consider them mathematical instruments beyond simple arithmetic, they were not the first, because complex numbers were conceived in the 16th century.

And that part is just completely idiotic:

Quaternions: higher topology than vector or tensor algebra

What???

Originally posted by Mary Rose
What happened to your curiosity about:

Originally posted by -PLB-
Where is the experimental data that shows this "giant curled EM energy flow component" really exists? How did Bearden came to the conclusion it exists other than "Heaviside said so"? Too bad I can not verify what Heaviside actually published. If anyone knows where I can find this publication I would be happy to hear it.

PLB, you were looking for what Heaviside published? He never published it according to this unreliable source which I don't condone, but only provide to answer your curiosity about why you won't find it published by Heaviside (see third paragraph):

www.emref.net...
There were three sacks of unpublished notes and scribblings found under some loose boards in the floor of his residence after he died, which apparently have been deemed by imaginative people to have the secrets of everything from free energy to antigravity. (Hmm I've heard similar claims about Tesla papers).

You can see some of Heaviside's unpublished notes in this pdf along with a description of their contents that lacks the antigravity and free energy claims: www.vrije-energie.nl/books/Scientific_Papers/Heaviside%20Papers%20under%20floorboards.pdf

reply to post by Mary Rose


He writes that as if the first equations Maxwell wrote down were some sort of biblical revelation, the undisputed word of god. Thank god that is not how science works.

He nowhere shows what aspect of the original equations exactly got "truncated". The reason he does not do that is because it didn't happen. All we have is the bare assertion from Bearden (yawn). That is why my interest is so limited. My interest has a historical motive, not a "current maxwell equations are wrong" motive.

I have already clearly laid out why the Lorentz gauge was correct; it is correct because it is in agreement with all known observations. Did you remember I wrote that a law describes reality, and not dictates reality?

That basically concludes the case Bearden for me. His work interests me no further until he substantiates his claims.

reply to post by Arbitrageur


It isn't clear what publication Bearden is talking about as he doesn't seem to add references to his claims. I did find this paper: On the Forces, Stresses, and Fluxes of Energy in the Electromagnetic Field

I will give it a look later.

reply to post by -PLB-

I didn't peruse it but I skimmed it.
It's written in 1891, published in 1892, which is after the Michelson experiments in 1881 and 1887 showing there was no ether.

Yet in section 3 of that paper it appears he's discussing the effects of assuming the ether is stationary versus the ether in motion. I knew it wasn't until Einstein's relativity theory was accepted that everyone pretty much dropped the luminiferous ether concept, but it's interesting to read a paper discussing it a decade after the 1881 experiment showed it didn't exist.

Originally posted by -PLB-
It isn't clear what publication Bearden is talking about as he doesn't seem to add references to his claims.

What claims are you talking about? Bearden has tons of references for his papers.

Be specific!

Originally posted by -PLB-
He nowhere shows what aspect of the original equations exactly got "truncated".

You're serious??

In that graphic??

Bearden has tons of information on his website and you demand detail like that in that graphic?

How quickly you have drawn a conclusion! Unbelieveable!

And decidedly unscientific.

Originally posted by -PLB-
The reason he does not do that is because it didn't happen.

Oh, really?

Just like that. Case closed. No further research necessary on your part?

Okay. Whatever.

Originally posted by -PLB-
I have already clearly laid out why the Lorentz gauge was correct; it is correct because it is in agreement with all known observations.

You're not curious enough to research whether or not observations are limited by what is being looked for in the first place because of what is believed to be possible?

In other words, you're not curious about what has been omitted or ignored?