usenet weirdness

The, "constancy, consistency, completeness, concreteness" are generally included among "requirements and desiderata" of theory.

Perhaps think of it where necessarily truth is the quantity, the continuous truth, conserved itself.

Then, getting a "the time" and a "the space" figured out is for a usual idea of matters of perspective and projection as for geometry as motion.

Usual notions these days after logicist positivism which is after Occam's nominalism after Plotinus'/Philo's, about theories of truth like pragmatic, correspondent, coherent theories of truth, may simply have that since Chrysippus and Duns Scotus and 20'th century idealists and realists that it's pragmatic/correspondent/coherent to have theories of real absolute Truth instead of fallibilism. Similarly "Tarski-true" just lives in a little box next to "material implication"'s, the "quasi-modal".

One "true" theory should suffice.

Then for that being for matters of perfection, to which agreeably that human beings as above machine and animal have minds yet are finite, imperfect creatures, is for idealistic perfection.

There's something to be said for computational advantage, about informational advantage (and intellectual advantage) as for notions of mechanical advantage, about that "large, competent, conscientious, co-operative reasoners", often result thinking alike.

Here, at SPR, some of the great lights may tell you that it is all a conspiracy of Einstein-worshippers.

In the olden days, pre-WWII, students tended to travel a lot, moving between universities, to take courses from reputed professors. Letters of recommendation played an important part.

Americans and Australians with the good luck of having a scholarship likewise made European tours, of a few months in several places.

Nowadays there are the Erasmus scholarships and for that, but that is EU only, (those dumb Brits locked themselves out of it)

Jan

"Letters" is its own world.

"One of the great challenges in this world is knowing enough about a subject to think you're right, but not enough about the subject to know you're wrong."

--Neil deGrasse Tyson, astrophysicist and science communicator (in his MasterClass promotion video:

More precisely, their _cardinality_ is ℵ₀ (strictly: _alef_-0).

Otherwise correct (as purportedly proven by Georg Cantor at the end of the

The misconception that this would not be so can arise from the assumption that ℚ = ℤ × ℤ. But actually, ℚ ⊊ ℤ × ℤ since e.g. 2/2 = 1/1 and ℤ/0 ∉ ℚ as ℚ := {p/q : p, q ∈ ℤ, q > 0}.

But then |ℚ| < |ℤ × ℤ|; and while |ℤ| < |ℤ × ℤ|, |ℤ| < |ℚ| does NOT follow, and is fact false: |ℤ| = |ℚ| < |ℤ × ℤ|.

ISTM that Bill Sloman's statement would be true when comparing the cardinalities of ℤ (or ℚ) and ℝ, the set of _real_ numbers, instead. ℤ (and ℚ) is/are countable (countably infinite), while ℝ is uncountable (uncountably infinite, as also purportedly proven by Cantor). |ℤ| = |ℚ| = ℵ₀; |ℝ| = 2^ℵ₀, and (ISTM uncontroversial that) ℵ₀ < 2^ℵ₀, so then |ℤ| = |ℚ| < |ℝ|.

"One of the great challenges in this world is knowing enough about a subject to think you're right, but not enough about the subject to know you're wrong."

--Neil deGrasse Tyson, astrophysicist and science communicator (in his MasterClass promotion video:

More precisely, their _cardinality_ is ℵ₀ (strictly: _alef_-0).

Otherwise correct (as purportedly proven by Georg Cantor at the end of the

The misconception that this would not be so can arise from the assumption that ℚ = ℤ × ℤ. But actually, ℚ ⊊ ℤ × ℤ since e.g. 2/2 = 1/1 and ℤ/0 ∉ ℚ as ℚ := {p/q : p, q ∈ ℤ, q > 0}.

But then |ℚ| < |ℤ × ℤ|; and while |ℤ| < |ℤ × ℤ|, |ℤ| < |ℚ| does NOT follow, and is fact false: |ℤ| = |ℚ| < |ℤ × ℤ|.

ISTM that Bill Sloman's statement would be true when comparing the cardinalities of ℤ (or ℚ) and ℝ, the set of _real_ numbers, instead. ℤ (and ℚ) is/are countable (countably infinite), while ℝ is uncountable (uncountably infinite, as also purportedly proven by Cantor). |ℤ| = |ℚ| = ℵ₀; |ℝ| = 2^ℵ₀, and (ISTM uncontroversial that) ℵ₀ < 2^ℵ₀, so then |ℤ| = |ℚ| < |ℝ|.

Cardinality is rather _less precise_ than other matters of size relation like, for example, asymptotic density.

Or, "half of the integers are even".

Cardinality establishes a transitive inequality among sets, where "cardinals" themselves as equivalence classes of sets having any transitive bijective relation, are, besides zero, rather too large to be sets in ordinary set theories like ZF(C).

Cardinality is rather specific to sets, and, set theory rather _describes_ numbers than _is_ numbers, that though "descriptive set theory" is a great account of formalization in mathematics.

Emil duBois-Reymond discovered various arguments for the uncountability of reals, later Cantor wrote them in set theory.

About the Continuum Hypothesis of G. Cantor, there's that Goedel showed it consistent one way and von Neumann another, then P. Cohen added an axiom to make it independent instead of inconsistent, set theory.

As one might imagine, that's a bit messy, since then thusly one may derive contradictions in set theory itself, and not even talking about how to derive contradictions in set theory about description of other theories of one relation, like ordinals for order theory or about class/set distinction, or about theories of other objects like those of geometry or number theory, as modeled in ordinary set theory.

Or, I suppose that was Paul if not Emil duBois-Reymond, mea culpa.

It's also for duBois-Reymond the idea of all the expressions of real-valued variables, in the language of those then and by their differences in the asymptotic, then that these each cross the line at zero the abscissa, the "long line" of duBois-Reymond, is only everywhere crossing the line itself, so is a continuous domain, while though its cardinally larger than the usual definition of the Archimedean complete ordered field, usually written "R" in blackboard-bold font.

Then, that the "line-reals" or "drawing the line", "line-drawing", is the usual account of that drawing a line makes a line segment each as of points, in a line: these "iota-values" are also a continuous domain, with extent density completeness measure, though, that's countable, not uncountable.

How then that's not inconsistent according to set theory's models of these as different sets that have the same topological properties, is simply enough for line-reals the function establishing them, a "natural/unit equivalency function" for their cardinal equivalency or equipollency, is simply enough not a Cartesian function, then that besides itself falling out of the results otherwise for un-countability as not disqualified and rejected, then as non-Cartesian isn't connected transitively, to be disqualified and rejected as a bijection between ordinary naturals and a bounded continuous domain.

This isn't usually brought up in class, yet, it's an exercise you can verify yourself. For example, I regularly have put it to large, competent, conscientious, co-operative reasoners.

What a load of ignorant hyperbole. The whole point of the mRA vaccine against Covid-19 was that it didn't replicate the whole virus but rather just the segment that latched onto the ACE-receptor.

That segment couldn't mutate much without crippling the capacity of the virus to infect us, so it was stable target, and it couldn't do anything else so it wasn't going to get into the human viriome.

In other words you haven't got a clue about what was actually gong on.

Both look identical to pig ignorance. Doctor Johnson talked about arguing precedence between a flea and a louse. I'm not going to bother.

A theory is always an explanation of why an observed process follows the paths we see.

Successful ones explain more observations than less successful ones.

That is they encode more observations. They do tend to be over-simplifications and encode less precisely than we'd like.

Trying to create theories about theories is chasing you own tail.

Theories about theories are a waste of time.

Humans are animals, and animals are mechanisms. Perfection is a target, but most people who try to attain any kind of perfection lose sight of the fact that their perceptions are imperfect, and indulge in unfortunate self-deception.

They might. Insanity doesn't seem to stop people being good at math.

That's what we are using here. No language - no discussion.

Sometimes the cooperative reasoning produces useful results. Religion has produced a lot of counter-examples.The MAGA movement is a more recent case in point. Science is about managing cooperative reasoning to produce useful results, but then we have IQ tests.

He invented the Dirac function, and bra-ket notation. He was notably more deft with math than most of his contemporaries.

Conspiracy theory nutters don't go in for realistic abuse.

Those with the resources to pay for it did. There weren't many of them.

Laurence Bragg was one of them, but he did travel with his family.

There's a memorial travel grant for my wife that offers that to one graduate student every year at the University of Western Sydney where she was a professor when she died.

Somehow I didn't die. Yet, ....

I'm curious, how many times you got the jab, and whether you were ever, "positive", for COVID.

Here about half the population didn't get the jab.

Stories of reactions are widespread.

Whether it reduced transmissibility is arguable, since it's clear that 100% of the population got COVID.

These days pretty much everybody still has a nominally non-zero COVID virus load.

First time I ever saw a dead body laying out on the street, ....

That cat was already out of the bag.

Over on sci.math there was a great long thread "What's the best vaccine for COVID-19?", then it was appreciated that medical journals opened up, and it was rather thoroughly studied here.

Matters of macropinocytosis and the like and issues with platelets and fibrosis has that the COVID-associated is a head-to-toe disease, or as rather, toe-to-head.

Don't get me wrong, I'm up on MMR and tetanus and polio and about hep b, yet, not shingles, which is also endemic, I contracted the chicken pox as a youth, and not to forget pertussis or for that matter D68 or tuberculosis, and within a few weeks of going to college there went mononucleosis.

No miRNA, though.

I recall one person, over the bookstore counter, I asked how are today and Bree said "I've been out a couple days. I got the COVID shot and overnight a painful baseball-sized welt grew on my arm, accompanied with other deleterious reactions." I was like, "Then what happened?". And she said, "I called my doctor and asked her if this was normal. And she said 'Yeah right. "Normal"'"

Anyways the TMV and Omicron saved a lot of people.

If you're interested in theory and Foundations, recently over on sci.physics.relativity and sci.math and sci.logic I made a panel of all the AI reasoners readily available and got them to thinking, or, you know, as they demonstrated it via means of inference in language in communication, about why there's a particular good theory.

Making a panel of them, and sending each their outputs among all the participants, it was rather remarkable that the "convergence" as was put it of the reasoning, makes for what was declared a singular sort of account of "21'st Century Foundations".

So, I'd wonder, do you think there is at all a "Theory of Everything", ..., even if such perfection we may only merely "attain" to, vis-a-vis "obtain"?

If there is, a "Theory of Everything", true, then, isn't it true there's only one of them?

I've had about five or six anti-Covid innoculations. I did eventually catch it after I'd had a couple, and it put me in hospital for four days. My digestive system was where it struck, which was messy and disabling.

That's poor health care.

Of course they are. Alarmist rumours spread like wildfire.

It does reduce transmission - people who catch it after having been innoculated don't get as sick, and don't stay sick for as long, so they spread less of the virus. Back when the population was still getting vaccinated it was noticed that those who had been vaccinated were much less likely to die of the disease if they did get infected.

What makes you think that? Long Covid does exist, but it's not all that common.

It hadn't been invented back then.

Not my experience or that of my wife.

The mRNA vaccines saved many more.