usenet weirdness

The complex numbers and quaternions and hypercomplex numbers, about the geometric algebras or the Clifford algebras, after deMoivre-Euler-Gauss with Argand and Wessel the usual complex analysis with Hilbert space and modeling of rotation planes and screw arithmetic, and rather distinctly about Elie Cartan and models of reflections and rotations, have seen a great development since it's piling on to the usual notions already given of the Cartesian, which is called the analytical setting since it makes an origin as for a Cartesian space and the usual Cartesian attachment of an origin to a Euclidean space, then as for parametric forms and linear algebra and vector spaces and linear vector spaces, is a great account and after trigonometry having the ready forms of the wave equation and the periodic motion.

Then, there are at least two settings that are not that way. For example, the convolutive setting is always rather symmetrical and reflective, basically about the difference between "addition formulae" of vector addition, and "subtraction formulae" of vector cancellation. So, the convolutive setting is basically going to zero instead of off to infinity, the vector addtion.

Then another setting is here called "original analysis" instead of "complex analysis", about 0 being the trivial solution of many systems of differential equations and as well about 0 being the envelope or singular about many system of integral equations, then for that the identity function f(x) = x or x = y = z or e_1 = e_2 = e_3 ..., that the identity function is the envelope for many integral equations like the linear fractional equation, Clairaut's equation, d'Alembert's equation, and so on, so it's singular to those settings, much like dividing by zero, about singular integrals. All functions in the first quadrant with their inverses are symmetrical about it.

So, the derivations of physics are usually given as getting into roots of unity then discarding a bunch of that then Argand and Wessel making a diagram "connecting" R^2 to C and ignoring that complex numbers would have _two_ definitions of division not one, i.e. that the usual definition of division in complex arithmetic is contrived, then attaching linear algebra of R^2 to that to model screw-arithmetic for periodic motion (Wick rotation after Eulerian-identity Gaussian-screw), then as about triangle/Cauchy-Schwarz inequality, later also Holder inequality as about Hilbert spaces, that's the usual stack.

Then the convolutive setting gets attached to that in a bunch of places as well, Haar and so on, since differential and integral analysis often is very organized about Sturm-Liouville and making things linear for linear algebra of vector spaces, and that's all it knows.

Then, an _original_ setting makes for a complement to the _complex_ setting, basically being the opposite.

Einstein devoted a lot of his life to that and didn't get anywhere. You are probably rather less talented than he was.

It might be wise to put off the effort until we have rather more experimental evidence available to constrain our thinking.

So you have invented an unnecessary simple explanation for the Pioneer anomaly. You seem to have a false target.

I'm not holding my breath.

That's beautiful. I'll add it to my word salad collection.

John Larkin Highland Tech Glen Canyon Design Center Lunatic Fringe Electronics

The matters of "complex analyticity" and "real analyticity", where analyticity is about the "analytical character" or content that makes it so that numbers add up, has that often there is definition in Hilbert spaces or complex spaces, i.e. in C, and in Banach spaces about Polish spaces and for R^2, then the abstract algebra's usual account of "the uniquness up to isomorphism of complete-ordered-fields" saying their same, has that they're not, where for example I've written field equations before to equip [-1, 1] with field operations and make another one, so that Stone-Cech compactification about the real analytic makes for that the complex analytic falls apart, especially since numerical methods (approximations) thusly fail to hold up the triangle-inequality / triangle rule, thusly that the trapezoid rule fails and about the real analytical character of these derivations.

So, the measure problem, for example, is sort of inevitable since the setting is often after deMoivre-Euler-Gauss, about the rather ridiculousness of the Euler identity, them thusly not knowing any different or why that the perceived "complex analyticity" in C isn't the "real analyticity" in R^2.

For examples, analysts like Zariski, Lescop, and especially Kodaira, then work up ways to attempt to repair complex analyticity, helping show that differential analysis and the usual account of differential analysis ignorant the singular integral analysis, is doomed to fail.

I.e., before even getting into matters of convergence and emergence, there's that, for example, division (as it's usually defined) in complex numbers is not the only inverse to complex multiplication, the Euler identity and its usual ubiquity is a wider development with its implicits than the form itself, and Hilbert and Banach spaces are not the same thing, even if R^2 and C share a diagram on the Argand or Wessel plane.

Then, the "original analysis" here for an "identity dimension" gets into singular integral analysis and "roots of zero". Also, for examples, if for the original analaysis living only in the first quadrant instead of the line or plane or infinite-dimensional hyper-space about the "hypercube distance" and the "Zeno's swath", then complex-complex left-right division diagram charts out that division in usual accounts of the complex numbers is an axiom.

It's usually good to know where the food comes from, and, to thoroughly chew the food.

Here though it's considered "word soup" (after alphabet soup, back when food was interesting), nutritious, since "word salad" has negative connotations.

The triangle inequality or what makes for metric and separately norm, length and distance, that's about the most common placeholder for what gives the trapezoid rule so numbers add up, or, cancel.

Thanks for writing.

I had friend who was a serious pure mathematician - he worked in the geometry of algebraic fields (or possibly the algebra of geometric fields). This was back around 1967, but I was never sure which, even back then.

Sometimes he would talk about his work, and I learned that it was futile for me to try to follow what he was saying, but one aspect of the conversations was pretty reliable. At some point he would say "and it generalises!" and we could get back to talking about stuff that I could follow.

I was doing quasi-mathemtical stuff at the time, but it was more data analysis than mathematics. I ended up writing my own Fortran program to do least squares curve fitting to fit my data to a three parameter non-linear model, and pulled out confidence limits on each of the parameters at the end of the fitting process.

The confidence limits were a bit optimistic. I'd assumed random noise, but there was clearly a 1/f component in the noise. There were ways to take that into account, but I'd have needed to accumulate a lot more experimental data to do that and my grant was running out.

Hm. "ECF: Error correction factor"?

The linear regression and least squares is a great thing and naturally regresses to the mean, when the relation is linearly correlated, then for example about the usual ideas of the log-linear, and then usual ideas of the feedback or hysteresis, about things like diminishing returns.

Then, two great concepts from mathematics about the finding numbers or intercepts, are as after the "generalized linear model" and gradient descent, and, "principal component analysis", when figuring out what are independent and dependent variables in functional relations and their accuracy.

The least squares naturally adds up for the most usual accounts of regression to the mean, vis-a-vis autoregression and autocorrelation, so it fits very well with the Central Limit Theorem and what's usually enough called college statistics, in fact, _too well_, since it can't tell the difference between correlated and anti-correlated.

So, ..., most of probability theory its standard linear curriculum's standard development: funnels right into the Central Limit Theorem then for the great accounts of Fisher (Sir Ronald Aylmer) and Student about Chi-squared and t and so on, analysis of variance and then for analysis of covariance, and about that being univariate then about the multivariate.

The "standardization" and "normalization" in probability theory making everything look like a bell curve has that there are other limit theorems besides the Central limit theorem, about Uniform and Polar limit theorems.

Analysis:

One of the most usual things showing up in any setting of Fourier-style analysis and signal reconstruction is "Gibbs phenonmenon", "the hysteresis".

The "interpolation" and "extrapolation" has many ways to write curves parametrically.

AI-generated banter is killing this newsgroup. I have a hard time understanding why Sloman keeps arguing with it.

Jeroen Belleman

Is the Ross guy an AI bot? That makes sense.

Verbose mode.

John Larkin Highland Tech Glen Canyon Design Center Lunatic Fringe Electronics

"If I knew then what I know now, I wouldn't know now what I knew then."

Knowledge is a learning experience.

Wel, yes, if you average over the orbit.

This is a mistake. There is no tidal dissipation in the sun. As with the tides of the moon, the dissipation is in the Earth's oceans. (mostly at the edges)

Jan

True.

Nonsense. Your naive positivism is playing up again. Best counterexample: general relativity. It wasn't based on any observation. Au contraire, once formulated it predicted what to observe.

You can hardly blame him for not inventing quarks and weak interactions from first principles.

And it is easy asy to say 'premature', with nine decades of hindsight, and nobody having done better in the meantime,

Jan

Our thinking does not need constraining. Au contraire, there is more than enough unexplained evidence. (like all the 'free parameters' of the standard model for example)

What's needed is not more evidence, it is a good idea for making sense of the evidence there is,

Jan

Sure, it was based on some madness of an insane crazie instead.

And since you believe deeply that you have no choice but to observe what The S*it told you - you do.

Now that we're dragging Einstein into Relativity Theory, I'd suggest his book "Out of My Later Years" since it's about the most recent publication.

If you're bored or interested, I found a copy of it and read through the relevant sections in my video essays "Reading from Einstein's "Out of My Later Years"".

One thing to note is that he doesn't so much declare that it's about "total field theory", instead it's his ideas as they were framed in the language of Relativity Theory, which as he puts it is the idea of "just imagine that in this Universe of Absolutes that there's not absolute Motion", basically saying that that's a fixed place to consider the things. So, quite very much it's about "absolutism" and for _continuity_ a "total" field, theory.

About matter, Einstein has thoroughly that matter is _inert_, about being an _inertial system_ the theory with regards to matter. I.e., it's not entertained the weak nuclear and electroweak forces, and also light's on the side. In "Out of My Later Years" he doesn't much talk about E & M at all.

Then, about "Relativity Theory" its formalism, he describes it as a _differential system_, that essentially representing its continuity, and furthermore that _why_ it's so is he attaches a clock hypothesis to that. So, what's "the needful" for the theory is that it's as much an integral-system as a differential-system, as long as it's a continuum mechanics. This also makes for that it's Euclidean, the geometry.

Then, Einstein makes some apologetics about SR, and about that "SR is local", again putting light rather on the side, where instead there's "GR first", an inertial-system and differential-system.

So, then Einstein makes a nice little defense of Newton, which is after Galileo and the Mertonian school and since concepts of power and resistance and power and potential. Then, what he does is setup an attack on Newton, since after the motion/motion and rest/rest bits the equal/opposite is contrived. This sets up his account of a second mass/energy equivalency derivation about the centrally symmetric and radially symmetric since kinematics are essentially un-linear, "Einstein's Bridge".

Then, that about being it, that sort of account got attached to Bose-Einstein condensates after Einstein-Podolsky-Rosen the condensed matter physics, yet really it's to be connected, "Einstein's Bridge", directly to mechanics, to make an account of real space-contraction-linear and space-contraction-rotational.

Here then that's a usual concept of "heft", after "mass" and "weight". I made that up, though.

If you aren't rude about it, people have no reason to stop posting it.

He seems to be a mathematician. I've known a couple. They can talk very intelligibly when not talking about mathematics. With at least one at least my eyes would glaze over until he said "and it generalises" and we got back to stuff I could follow. Nice guy and he married a nice girl.

My father was physical chemist who worked in the paper industry, and needed to analyse his data. He talked to the professor of statistics at his old university (one of his nephews had the job for a few years some thirty years later) and ended up buying R.A.Fisher's "The Design of Experiments". I grabbed it after he died. It's the third edition, published in 1942 (the year I was born) and still has the original dust cover, but he did use it.

Poisson comes to mind.

Don't remind me. I once put together a random noise generator for female friend before I knew about Gibbs oscillation, and I had to apply a Hamming window to the 32 resistor values in the tapped shift register filter to get it to work as intended. Every last one of them had to be changed, which took me about an hour with the soldering iron. Her sending it back to me in England from Germany took about a week, and it took as long for me to send it back. Embarrassing but educational. Eventually it confused her bats echo-location as intended.

There are a host of good ideas, or at least ideas that strike the people who think them up as good. If they don't fit the experimental evidence it's easy enough to throw them out, but if there isn't enough experimental evidence it gets harder to kill off the bad ideas.

The March 7 2026 New Scientist - which got to me today - talks about something like this happening with the