EG, I wish you and AG the best for your book.

I think it is known – at least I have seen it several times – that if a function has a jump discontinuity at some point, it can be written in terms of the Heaviside step function and then using that the derivative of the Heaviside step function is the delta function, one can write an expression for the derivative of the function that includes the point of discontinuity, too. But both the step and delta functions are distributions.

To explain what I mean, if f has a discontinuity at x0, then f can be written as

f(x) = (1-H(x-x0))f(xx0), where f(xx0, and H(x) is the Heaviside step function, which is zero at x0.

Then using that H'(x)=δ(x) and the product rule, the derivative of f can be expressed in terms of the delta function. But as I mentioned, it is a distribution.

Sure,if you use the Lagrange definition and nilpotent elements.

Then there are situations where differentials behave as finite normal variables. You are not always culpable as Robinson in Non Standard Analysis.

However I dont get using only Q or modular arithmetic etc. I dont see any way the incompletness of the real axis can possibly help with this.

Ann

Did you learn how to do vector analysis using things like

dx dx=0 and dx dy +dy dx =0, the way it is explained in some advanced books.? Perhaps that is the way you escaped from vectors, but not entirely from differentials.

PS vectors may be old fashioned, but work in any dimension, same as the new stuff.

Ed, Ann

Pardon, but

That vectors are restricted to 2D, and not used, is a bit rediculous.

Higher dimension vector spaces, perhaps Hilbert spaces are almost inescapable in QM

Vector fields in 3D are quite trusted in electromagnetism.

Of course numbers are scalars.

In the cases of higher dimension of interest you dont use the

vector product anyway, but you do a lot of other usefull things. The wedge or outer product is amply used in many of the references to algebras you give.

Then what else are you possibly expressing badly or confused about?

Its not good to get carried away by the trendy latest fashion math, which I think is pretended here.

Ed

Apart from a theoretical math posture of distingushing a psedo vector from a vector, of no real relevance in applications; it shows wide disrespect for recognized books of revered authors

like Jackson(EM) or famous mechanics texts on your part.

You should at least read one of the books

of Jackson, Panovsky Philips, Frances Kipp, Reitz Milford etc.to cite just one of the fields that makes extensive usage of vector analysis and fields in 3D

Plus most of the formulas used have nothing to do with vector product.

Im not crazy enough for scientific suicide to claim usage of only Q versus R,

or to abandon the use of vectors. Well, go ahead if you like playing such game. Its not productive, Im 100% certain.

Real numbers with physical units is enough to factually provide metrics.

I think people should take into account that math evolves slowly, and no epoch is entirely abandoned.

Indeed new styles of math have evolved, many are tentatively, some badly described by mathematician Roger Penrose in Road to Reality. In some cases using new versions shows one is perhaps up to date, but looses clarity and readership.

One of the best sections is the translation of EM into fancy new equations,

but hides the primitive Maxwell equations, ie. hides the actual physics almost beyond recognition. High faluting theorists like it, but practical electricians would toss it to the flames.

The trend of too much speculation is rather damaging...

Wow, even amplifying specious atack on sdandard SR, everyone knows relativistic mass is just gamma m(0) where m(0) is rest mass.

So you think this alledged abrupt silence is due to you?

Happy holidays

As Louis Kauffman writes in his chapter on "Virtual logic -- infinitesimals and zero numbers": "...The whole structure of the calculus can be based on this simple system of infinitesimals. Eventually this will be the way calculus is taught in the schools." (p.87)

But, the question is essentially, Can infinitesimals Not be used? Clearly, the answer is "No" if we are talking of the traditional calculus of continuous and differentiable functions. Otherwise, we are talking about a calculus of difference equations, etc., perhaps as discussed by Norman Wildberger, et al. If physical Universe is not continuous, as some contend, then indeed the infinitesimal may be unneeded.

But the task of our mathematics is to provide the broadest tool-kit, not to judge or prescribe Universe. Therefore, the question that might better be asked is: "What math tools are best in a non-continuous,or infinitely rarefied, universe, and what is the likelihood of such a universe?"

In my opinion, maybe the new mathematics has the ability to remove them, Infinitesimals but it can still be effective in some problems.

Infinitesimally close manifolds are the arena for representation of their similar cousin in calculus .. .. functions tangent to two neighboring ones prove orthogonality ( and therefore impossibility of removing) infinitesimal topological brinks . . .

Infinitesimals are mere abstract ideations of our mathematical mind . One does not know whether we are duty-bound to make them emanate physicalistic sense . Applicative topology makes it a tiny bit easier for us to see borderlines between their staying merely in the World of Mathesis or starting to follow a Peano-like logicization programme .

Perhaps it is safe to say that infinitesimals in the sense of Robinson is probably a fairy story, but not enough attention is paid to a possible role of non real elements similar to i, namely the nilpotent e.

After all the smalest of the posible positive real numbers can be shown not to exist. Non standard analysis is between error (due to finite) and non existance.

The notion of zero is no less biased by our expectations than the idea of infinitesimal . Beware similar mistakes in calculus: we deal with tiny numbers that look like zero to us, but we can’t do math assuming they are . We need to “do the math” in other dimensions and convert the results back. For instance : ”0 + i”, a purely imaginary number, is it the same as zero?

AG :

I could NOT make it out where and how you deemed my statement(s) to be philosophy AND your own statements to be pure math...........

regards

REZA

Ann

You are trying to muzzle us. Free speach please.

Cannot talk about this or that? My goodness.

Ed

Well, I suppose you know the correct term. Close aliado to Ann? With similar tendency?

Ed

I did give above a rather technical math answer;

You meant it distracts.

RS is not too technical, but certain stuff I will defend him on.

Ed Gerck

" RS: What field did you study? "

Bachelors Degree : Applied Mathematics

Master's Degree : Bio-Physics

1st PhD : Philosophy of Science

2nd PhD : Atomistic Bio-physics

Juan Weisz

Ed Gerck

Ann Gerck

Juan is correct . Ed and Ann do not hold the right to muzzle others from expressing their views on this thread or any other thread . Ed has the serendipity notion that since a couple of day ago , the year has changed and , therefore , everybody has to change their manners and ideas . This is not to the normal human sense . Ann has gotten a Bachelor's degree in Arts . Still , she does have the right to post up here in these boxes the total falsifications that she has the habit of publishing .RG is for everybody .

Ed Gerck

It is exactly because this thread is not Wild West that I am recommending you not to dare to call peers "Dogs" . I am not lawyer to Juan Weisz : But again I can hardly believe he is a "Dog" in your words . Nor am I . Your answers are badly off-topic themselves : Exactly those Absurdities which you yourself happen to exotically deem as re-affirmations of the wonder-kid of co-authors like your beloved Ann .

• BTW : That so-called Planalto ripple-ideation production firm , is itself no more than a plagiarizer of non-fake writings into disfigured ones .

And one last point :

The EU has more-than-a law on fake publications .I strongly recommend disengagement .

Regards

REZA

Ed Gerck

" Math needs an overhaul. "

Some improvements hither and thither MAY be needed in Math . But it is an egregious claim to come out with Math needs an overhaul.

I agree that there are reasons to suspect historic infinitesimals,so that part may be understandable . But not vectors, by any strech.

Maybe if you start attacking infinitesimals too much, the ,limit concept of a derivative may sucum also? Because in the end you deal with something like 0/0 without it really being 0.

But everyone knows this works well in practice, so whats the fuss?

Be ready with altrnatives when students ask about epsilon delta language.

I do know an alternative , a nilpotent element instead. An ideal in a ring algebra, actually.

This it is implicit in some of the language already, the unfathomable language of

dx dx=0 ; dx dy+dydx=0, etc. used in vector calculus and in which curiously a vector product is extensible to any dimension.

Because an n vector (or covector perhaps) is written

a1 dx +a2 dy+ a3 dz +a4 dw + ....+ an dv is simply multipied by another of the same form, according to above rules. The result comes out in terms of dxdy, dx dz, basis.(indicates different kind of object)

These dx are not really the same as historical ones. A popular interpretation, a wedge or outer product of 2 very short identical vectors.

Ann Gerck

" It's not only infinitesimals that became outdated. Today, vectors are also no longer used " . . .. . . .

" Vectors do not work past 2D. "

Be kind enough to put up some proofs here in this thread for these various outrageous claims . . . . .

Those who wish to mimic geniuses , should naturally act like geniuses , too AND talk and write with proofs .

Regards

Reza

Zachary Knutson

could you please go to the trouble of telling us all what the above post of yours mean ?? !!

Do you like other "Gerckians" to write like that ?

Zachary Knutson

Can you yourself grasp the meaning of the quasi-query ??

Zachary Knutson

May I ask you what your degree is ??

Are you a native speaker of English ??

One of the most obvious signs of charlatanism is announcing as solved a deep problem which has not been solved at all . I shall have a series of lectures on the philosophy of mathematics in the United States this coming summer . There , I will bring up the so-called "Solved" Problematic(s) of total elimination of infinitesimals in calculus the way Mr Ed Gerck claims he has been successful to do.........

shall be glad to visit Ann Gerck there ,too ;;;;;;;;;;;;

REZA SANAYE

Zachary Knutson

Are you against spiritualism ?

Is this thread devoted to spiritualism or anti-spiritualism ?

Zachary Knutson

You talk the way Ann Gerck and Ed Greck have the habit of talking :

" thread is into Socratic rhetorical irony... This pone was brought to you by #Monster Energy "

Zachary Knutson

Abstrusely

Figuratively

Overly bombastic

Metaphorically . .. . . .

Ed Gerck and Ann Gerck , have , of course ,by now , managed to flee away by dropping their names out of the list of the mentioned participants in this thread ( seeing that they are both facing rigorously-educated Mathematicians ) . . ... ...

My brotherly advice to you is that you do not even so flimsily support their Pseudoscience as I am to blacklist them in March ;;;;;;;;;;;;;;

Respectfully

Reza

Usually only reality at atomic scales, at least when things like superconductors do not take us by surprise.

No mostly physics. Math is often just a cultural diversion.

I think we need more basic description of things, before QM or fancy math.

Dear friends of gravity, relativity, fundamental physics, quantum physics and elementary particle physics,

Most basically, energy and matter form vacuum, that vacuum causes curvature of space time (including Newton’s law of gravity as an approximation or in an appropriate frame) as well as the expansion of space since the Big Bang (Carmesin 2021a) as well as the wave function of quantum physics, whereby the postulates of quantum physics can be derived from the vacuum dynamics (Carmesin 2022a). Phase transitions of that vacuum describe the formation of matter (Carmesin 2021b), the structure of which describes the fundamental interactions (Carmesin 2021c, Carmesin 2022b).

ALTOGETHER, the different fields of present-day physics are unified on the basis of the dynamics of cosmological vacuum (Carmesin 2022c).

Hereby, all results are in precise according with observation, whereby no fit is executed and G, c and h are invariant universal constants.

I am looking forward to your reply.

Literature:

Carmesin 2021a: https://www.researchgate.net/publication/350373240_Quanta_of_Spacetime_Explain_Observations_Dark_Energy_Graviton_and_Nonlocality

Carmesin 2021b:

https://www.researchgate.net/publication/353851329_Cosmological_and_Elementary_Particles_Explained_by_Quantum_Gravity

Carmesin 2021c:

https://www.researchgate.net/publication/355889856_The_Elementary_Charge_Explained_by_Quantum_Gravity

Carmesin 2022a:

https://www.researchgate.net/publication/358581911_Quantum_Physics_Explained_by_Gravity_and_Relativity

Carmesin 2022b:

https://www.researchgate.net/publication/359426539_The_Electroweak_Interaction_Explained_by_and_Derived_from_Gravity_and_Relativity

Carmesin 2022c:

Carmesin, H.-O. (December 2022): Unification of Spacetime, Gravity and Quanta. Berlin: Verlag Dr. Köster.

Kind regards,

Hans-Otto Carmesin

QM can have values unknown, but not uncertain. Likewise, RG questions. Please stay on topic, per question. Do not be uncertain yourself. This space is to discuss only this question, otherwise it is off-topic.

Opinions do not matter, every opinion is right and should be, therefore, not discussed.

But, facts? Mass is defined (not a choice or opinion) as the ratio of two absolutes: E/c^2. Then, mass is rest mass. There is no other mass.

This is consistent, which is the most that anyone can aspire. Not agreement, which depends on opinion. Science is not done by voting.

Everyone can, in our planet, reach consistency -- and the common basis is experiment, a fact. We know of other planets, and there consistency may be uncertain -- or ambivalent, and even obscure. A particle, there, may be defined, both, as the minimum amount of matter of a type, or the most amount of quantum particles of a type.

We can entertain such worlds in our minds, more or less formed by bodies of matter, and have fun with the consequences using physics. But, and there is my opinion (not lacking but not imposing objectivity) we all -- one day -- will be lead to abandon matter. What will we find? That life goes on. The quantum jump exists. Nature is quantum.

A college already warned me. There are certain skills that my generation developed, for example how to analytically do integrations or analytically solve ordinary differential equationns. These were the prized skills.

Nowadays students just pull out the necesary application to give the answer,

or if not just prefer to give a numerical calculation.

However, the later has drawbacks, a row of numbers is just that, it does not tell you what it is in function terms., no analytic understanding. In physics you must understand your answer.

It seems at least one or a few great promoters of just numerical calculations , and forget about functions , are among us. Reduction to just one of the simplest kind of number, rational. Perhaps symbolic computation is at least as important.

Let us discuss if we are getting too far into the purely computable world..

Could creativity be suddenly stopped?...Just leave it to machines?

Do we care about computation time when computers are that fast?

"Every path in a complex space must begin and end with a rational number"

needs serious clarification. I would say begin and end with a complex number.

Barrabasadas, E/cc is not rest mass. Not good enough to define mass.

Juan Weisz \

Quote :

" It seems at least one or a few great promoters of just numerical calculations , and forget about functions , are among us. Reduction to just one of the simplest kind of number, rational. Perhaps symbolic computation is at least as important...

"....."Every path in a complex space must begin and end with a rational number"

needs serious clarification."

It so appears here that a person here leading the ignorant into even more ignorance , has absolutely NO intentionality to clarify things , , , ,On the contrary : He seems to be making even clear things vague . . . . .

I agree Reza, so far cannot talk sense.

Something already has phase, the C they want to eliminate,

arctan(y/x). Heard of polar coordinates?

If you really want to supplant i try

this algebra.

i=e-e(T)

ee=0

e(T)e(T)=0

e e(T)+e(T)e =1

Modeled after superalgebra and Elie Cartan stuff.

Then square i to get -1 from the cross terms.

But let us accept what people mostly use...

Abstract? Not more than i itself.

The identity which does properly deal with rest mass m(0)

reads

E=gamma m(0) cc

basically in first approx, nonrelativistic this is a sum of m(0)cc the bare

mass energy and KE 1/2 m(0) vv in norelativistic expression.

Juan Weisz

• This is a thread of debates and discussions whose original questioner [ ed Greck/Is Reality quantum? ] from a charlatan clique by the name of Planalto Research HIMSELF FILLS OUT UP TO 89% OF THE TOTAL POSTS AND CONTENTS OF THIS BIZARRE THREAD !!

OK, I quit,

Zachary also not understandable

overall failure this thread

This represents the one-sided, effective, end of trolls in RG answers: deny them a public, free, citable audience. Deny abuse masquerading as virtue.

No more, and more, ..., "relativistic mass", "discussion" of SR, fake "non- acceptance" of a macroscopic quantum reality, acceptance of "continuity", defense of "mathematical real-numbers", and other loss of time in RG,under the name of free speech. To yell "FIRE" in a theater is a crime under US law. Evolution is upon us!

The comments above show (some now deleted) how following the RG ToS is necessary for a scientific conversation.

But the legal responsibility of enforcing the RG ToS falls only on RG, per EU law.

Meawhile, it is suggested to read the question text and references. Also, private messaging is available.

See also the questions:

https://www.researchgate.net/post/Can_one_end_trolling_in_RG_answers and

https://www.researchgate.net/post/Can_questions_become_a_research_tool_in_RG

Mr Ed Gerck is very obviously violating ALMOST ALL ordinary common-sense rules and regulations of a natural non-distorted debate in a public forum over a branch of exact sciences . Innovation is , of course , welcome {{ in case he had any }} . . . . . . But the extremely high levels of "his" autocracy and interior monologue turned a puppet show of prowess here , are transgressing absolutely vital principles for conducting a logical discussion to very end of it .

New and old questions are following a new standard in RG, where every opinion is respected, and yet research can be developed.

This is explained in:

https://www.researchgate.net/post/Can_questions_become_a_research_tool_in_RG

Quantum theory is the theoretical basis of modern physics. It explains the natural behavior of matter and energy at the atomic and subatomic level. This behavior of matter and energy at the lowest level is sometimes referred to as quantum physics or quantum mechanics. The human brain can influence not only the perception of reality, but also reality itself. Information, i.e. spirit, changes biology, i.e. matter. Our observation also changes what we see. In the experiments of quantum physics, reality only arises through measurement each time .

This question is now CLOSED. Focusing on the discrete Weyl-Heisenberg group, as motivated by SN, this question was expanded in a new question, where it was answered with YES in +12 areas:

https://www.researchgate.net/post/Is_it_possible_that_RQ

Thanks for the cooperation!