Re: Very basic mistakes

<victor_meldrew_666@xxxxxxxxxxx> wrote:
So maybe he calls himself a mathematician (or maybe not), but his
website indicates an interest in physics rather than mathematics,

He is a moderator of sci.physics.foundations, and mathematics is a most
important foundation of physics. If there are basic mistakes in
mathematics
then they may affect physics.

Then that is a matter for physics, and a physics newsgroup
is more appropriate for such discussion.

Today he (OhNo) wrote in spf, thread Physics vs. mathematics:
"The course of the last 60 years at least has been one in which
mathematicians are kept out of physics and in which the
standards of mathematics applied to physics are inadequate
to deal with the fundamental problems facing physics."
If I understood him correctly, he merely considers mathematics not
correctly interpreted rather than blaming it imperfect or even wrong.

He is not ready to accept that I found out that uncertainty is not
restricted to Heisenberg's complex criterium but seems to be a more
general property, since it also exists in IR+.
I consider the relationship between IR and IR+ and the relationship
between Fourier transform and cosine tranform worth to be clarified
by mathematicians who are aware of consequences and open for
corrections within mathematics if necessary.

Are you familiar with the jungle of ZF, ZFC, NF, NBG, ... ?

Hardly ...

The more theories mutually exclude each other,
the less is the probability that a particular one is correct.
Maybe, they are partially wrong altogether.


Do you know why mathematics suddenly demanded the pointless
quarrel about for instance AC?

"pointless quarrel": loading your terms again, Herr Blumsheit.

My name here is Salviati. Is there any tangible benefit from AC?

the use can't have "spread" from mathematics.

Hilbert intended to also create an axiomatic physics and metaphysics.

Then discuss Hilbert's ideas on physics in sci.physics (or worse).

There is little reason for that. Years ago, there was a belonging
paper in Physics in Perspectives illustrating how Hilbert tried to
transfer his axiomatic method from mathematics to physics.

While aleph_0 and aleph_1 can be interpreted as the infiniteness
of the natural numbers, and the fiction of perfect infinity,
respectively,

... Bumschien))

... Herr Blumschien.

Set theory lacks any tangible basis.
I conjecture that what you mean by tangible is physical,
No. I mean logical.
Then you are wrong. ZF set theory is formalizable in first-order
logic.

After the decisive tacit assumptions were omitted.

Fraenkel in 1923 admitted that there is a
so called 4th logical possibility besides =, >, and <:
uncomparable.

Inequality signs are not logical symbols, they are
predicate symbols.

Is = an inequality sign?

Examples of totally ordered sets
include N, Z, Q and R with the standard ordering.

In what differs R from Q if both are totally ordered?

I add: Even the rational number 4 is incomparabel with the
real number 4.

The image of 4 under the natural embedding of Q into R is
*equal* to (not incomparable in any sense) to the real number 4.

"Natural embedding" sounds begging for agreement.
It reminds me of Dedekind's suggestive style of argumentation.
The real number 4 is something that cannot be exactly addressed
because infinite acuity is a fiction.
In Q there are distances between single elements.
If one did consequently distinguish R from Q,
then every piece of it would consist of an uncountable
amount of fictitious elements.
So far mathematics is still far from admitting this.

A rational number and a (genuine) real number are
within quite different categories.

There is a natural embedding of the field Q of rationals
into the complete ordered field R of reals. In many
(but not all contexts) it causes no harm to identify
Q with its image in R.

Well, that's why 1,000,000.00 Mark were paid in 1925 for
somone who dealt with Vaihinger's theory of "as if".
Let me add, that the image in R is nonetheless literally an imagined one.
What harm did you mean?

Application and comprehensive selfconsistency are valuable
touchstones for mathematics.

I presume this means that you want to subjugate mathematics
to physics.

Not at all. I see the relationship rather a mutual one reminding me
of that between legislative (theory) and executive (application).

Dedekind admitted that he did not have any evidence for his guess
that the entity of all rational numbers can be split into larger and
smaller ones wrt his cut.

Reference?

Stetigkeit und irrationale Zahlen, Vieweg, Braunschweig (1872).

Alas I don't read fascist languages :-(

I share my mother tongue with virtually all who are to blame for
your possibly questionable mathematical education.
Having experienced bad things, I feel very unhappy with the
word ueberabzaehlbar (= more than countable). It reminds me
of Nietzsche's word Uebermensch.
Cantor's thinking and Hilbert's wording often correspond to the
hollow pathos of the German empire.
Nonetheless, you need to be able to understand the roots of
what might be at least questionable. In order to fully reveal all
nonsense you should even be familiar with the bible.

For instance, Buridan's donkey has primarily to do with poorly
understood
logical fundamentals rather than with physics.

Buridan's ass has nothing to do with mathematics.

Perhaps you are too ignorant.

Not as ignorant in mathematics as you Herr Blumshcein.

Isn't this once again an insult?

But this is typical: instead of demonstrating the relevance of the fable
of Buridan's ass to mathematics you resort to insult.

A fable? No, a serious problem, perhaps an ancient one,
maybe it came from Byzanz. Similar to Zenon's paradoxes it
makes us aware of an overlooked failure in our notion of numbers.

When I asked mathematicians how to deal with the neutral zero
in case of splitting IR into IR+ and IR-, I got as many different
answers as there are possibilities. they all were arbitrarily chosen.
None was convincing to me. I found the perhaps compelling one
myself.

Again, as with all your anti-mathematical
arguments, you do not isolate any contradiction in the mathematics

Pointing to a putative very basic mistake is not anti-mathematical.

There's the rub: you called your posting "very basic mistakes"
yet now you admit that that "very basic mistake" is singular and only
putative.

When you argued that there is no contradiction then you tacitly
restricted to ZFC, didn't you?
My main topic is IR+. However you ignored what I am claiming.
The mistakes are more or less related to each other.
However, denial of the categorical difference between Q and R
seems to be a standard ritual in "modern" mathematics.

Schroedinger's kitty seems to indicate that it harms.

And even so you have failed to point to anything that
might fit that description.

Let me start listing in brief what I consider related to very basic
mistakes:

- A number is a number is a number. (I argue that discrete numbers and
uncountables mutually exclude and complement each other.)
- Dedekind: One can split the entity of ALL rational numbers: >, =, or <.
(I argue: The entity of ALL rational numbers is identical with the reals.)
- Dedekind: There are more reals as compared to the rationals.
(See Salviati)
- Weyl: Rationals are embedded in the reals like bones in a sauce.
(I argue: This would be the case if quite different objects were forced
together.)
- Cantor: Deliberate ignorance of the 4th possibility: incomparability.
- Cantor: Untenable definition, abandoned by Fraenkel without substitute.
- Hilbert: The axiomatic method remedies the belief of naive set theory.
- Ebbinghaus: Naive set theory is based on an obvious error but valuable.

Commonly accepted mistakes:
- IR+ is not worth to be taken seriously.
(I claim that it is tailor made for any just positive quantity and
prevents
a lot of problems.)
- Cosine transform is just a particular case of Fourier transform,
and one has to integrate from -oo to +oo, in general.
(I maintain that in practice it is often better to restrict to (0, oo).
- Complex representation provides in general an additional degree of
freedom.
(This is an illusion if the original is or can be made one-sided.
Belonging Hermitian symmetry in complex domain is redundant and often it
gives rise to misinterpretation.)

Enough for today.

Regards,
Salviati:
... in ultima conclusione, gli attributi di eguale
maggiore e minore non aver luogo ne gl'infiniti,
ma solo nelle quantità terminate.
IR>|>IR+>|>IR


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