Hello Victor and Prof. Florentin,

I fully agree that "calculus" is a deeply troubled theory of mathematics,

which lead to the more troubled theory of mathematics called topology

which ended up with a largest play ground for "problem solvers" to

enumerate problems and publish papers endlessly.

Going back to the calculus, historically it is false that this was

developed by Newton and Leibniz. About three hundred years before it was

developed in India. They did not use it for building Physics. They just

wanted to build a mathematical model of celestial system to be used for

agriculture. I do not know if these two developments are independent.

The issue in Calculus a la Europe is that it was impossible to define the

concept of "limit" articulately. It took about two centuries for European

(mostly German) mathematicians to gain this concept properly using the

theory of complete ordered field and epsilon-delta argument. This approach

developed into general topology from which the so called algebraic

topology came out.

It was unfortunate that this method though worked fine had little to do

with the original calculus used in early physics in which naive concept of

infinitesimals were used. In fact, the topological calculus was developed

as an anti-thesis to the infinitesimal based calculus. This is what most

student learns in the university. Rarely infinitesimal caluclus is taught

thought we have modern and complete infinitesimal calculus as developed by

Abraham Robinson in 1960. The reason for all of this is because the naive

concept of infinitesimals is apparently paradoxical as even George Cantor

complained. Certainly it is trouble some to figure out what kind of

numbers are "positive numbers each of which is smaller than all positive

real numbers".

Robinson was a most important mathematical logician (model theorist) in

the history of mathematics though due to the advanced and difficult nature

of his work, it went over the head of popular scientists and did not get

appreciation which so badly deserved. It is my view that this had a lot to

do with the anti-logic culture of theoretical physics. As you know well,

logic was developed to very high level by the Scholastic Philosophers in

Vatican who wanted to prove that God exists. Unlike Physicists, they were

quite open and honest. They realized that in all of their proofs for the

existence of God, they assumed the existence of God in one way or the

other. So, they said predicate logic will not do. This lead them to the

development of modal logic in which they tried to prove the necessity of

God instead of existence. As the bloody history of theoretical physics

proves, basically admitting the error and defeat is the last thing for the

King of science would do. This ended up with the situation where even

secondary school students become highly critical of this entire activity.

The final outcome is that the King of Science left this ugly expensive

CERN and highly questionable authority to dominate at any cost.

Notwithstanding, as a professional logician, I can tell you that we

logicians are still learning from the Vatican cosmology, though we learned

very little from the so called theoretical physics. The problem is that

all we see in theoretical physics as we know of now looks nothing but a

mountain of errors and deceptions created by earthly expectations. After

all, to be fair, we logicians learned from QM as the development of

quantum logic. This strangest logic became a fashion for a decade or so,

long time ago and nobody even remembers.

Anyhow, regarding QM, it is a very good example of how logically

inconsistent theory whose inconsistency is well concealed by the politics

of intimidation, black mailing and name calling can create total illusion

and thrive as "science fiction" as exactly happening now.

So, going back to infinitesimal calculus of Robinson. To be honest only

very strong experts in mathematical logic can follow what he did. It

starts with a strange theory of the first order real numbers. This is

needed as we define infinitesimal calculus as the nonstandard model of the

first order calculus, taking advantage of the weakness of the first order

theory. Using fully developed model theory (to its development Robinson

was a major contributor), using the ultra power construction and

collapsing it to quotient structure using the provable equality of the

first order real number theory, he obtained full infinitesimal calculus.

In easier language, as we define real numbers as infinite sequences of

rational numbers separating rationals and irrationals represented as

infinite sequences of rationals, Robinson considered infinite sequences

of real numbers as nonstandard real numbers and separated those which

converges and which do not as real numbers and infinity. As the reciprocal

of infinity he defined infinitesimals.

After all of this basically without using limit, we can develop full

calculus. Limitless calculus meant topology-less calculus. Indeed the

topology of infinitesimal calculus is trivial T0 topology.

I think one of the reason why Robinson was never appreciated in mainstream

mathematics community has a lot to do with the pressure from the community

of mathematical physicists who felt threatened by his work which will

make their work unnecessary complication. After fleeing from Nazi

persecution, he fled to Israel and then came to Canada. He became a member

of mathematics department at U of Toronto. Despite his great work, he was

not appreciated and so he moved to UC Irvin to chair the math department

and shortly after that he died young by cancer. The sad fact is that he

never worked for places like Stanford or Harvard.

However, we do have some problem with Robinson's infinitesimal calculus.

His infinitesimals have little to do with what Leibniz and Newton meant.

Physical interpretation of Robinson's infinitesimals is not as obvious as

it should be. I learned that there are some other infinitesimal calculus

developed after Robinson. But, I do not think any of them are as powerful

as Robinson's and have any better fit with infinitesimals physics needs.

For example I do not see how we can associate a fixed charge for a

mathematical infinitesimal. This is a common way to use infinitesimals in

Physics.

What is tragic is that due to the specialization and stupid ego trips, the

communication between physics and pure mathematicians ceased to exist.

Despite this concern, I am already a senior citizen and have not much time

left. So, I hope young researchers will take up this kind of very

fundamental problems for the advancement of science.

AKDear Prof. Akira and Prof. FlorentinGreetings,Just thought you will like this paper:http://vixra.org/pdf/1305.0033v1.pdfHumbly yours,Victor Christianto*Founder and Technical Director, www.ketindo.comE-learning and consulting services in renewable energy**Founder of Second Coming Institute, www.sci4God.comHttp://www.facebook.com/vchristiantoTwitter: @Christianto2013Phone: (62) 812-30663059***Papers and books can be found at:http://nulisbuku.com/books/view_book/9035/sangkakala-sudah-ditiuphttp://www.unesco.chair.network.uevora.pt/media/kunena/attachments/731/ChristologyReloaded_Aug2016.pdfhttp://fs.gallup.unm.edu/APS-Abstracts/APS-Abstracts-list.htmhttp://independent.academia.edu/VChristiantoHttp://researchgate.net/profile/Victor_Christianto/Http://id.linkedin.com/pub/victor-christianto/b/115/167http://www.amazon.com/Victor-Christianto/e/B00AZEDP4Ehttp://www.amazon.com/Jesus-Christ-Evangelism-Difficult-ebook/dp/B00AZDJCLAHttp://gospel.16mb.comhttp://www.kenosis4mission.tkhttp://www.twelvegates.tk

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