What is new and what is advantageous in calculus without limits?

This question is often asked. Here is the short answer (in the terse Indian sutra style)

It makes math easy, by eliminating the religious bias in it, and gives a better math, physics and history.


A longer answer (an abstract)

Calculus without limits has the following advantages.

1. It makes math easy. (Advantage: that enables non-math students to get over their math phobia and do calculus, hence understand science. For math students, it enables them to solve tougher problems.)

2. It eliminates the religious bias in math.(Limits relate to formalism which turns math into metaphysics. This metaphysics has nil practical value for any applications. It is NOT universal. It agrees with the Christian theology of infinity, and is contrary to all other relgious beliefs, including Islam, Buddhism and Hinduism. Advantage: calculus without limits enables the student to focus on practical value of math and throw out the subtle religious indoctrination which has been made part and parcel of math teaching today.)

3. It improves mathematics.(Elementary calculus courses teach that a differentiable functions must be continuous. Advanced courses teach to the contrary that a discontinuous function may be differentiated, as in the Schwartz theory, but not multiplied. As typical of metaphysics we can have our cake and eat it too: a discontinuous function is both differentiable and non-differentiable according to present-day math. Curiously, both ways tell us that it is not meaningful to talk of discontinuous solutions of nonlinear differential equations of physics. But we actually observe shock waves which involve discontinuities (unavoidable in general relativity where we cannot shift to statistical mechanics). The way out today suggested within formal math by theories like those of Colombeau are absolutely hopeless. Calculus without limits helps to resolve this problem, and get substantively new conditions for shock waves and a new way to renormalize quantum field theory.)
 

4. It improves physics. (Because Newton did not understand the calculus, he thought the notion of d/dt could be made rigorous by making (equal intervals of) time (t) metaphysical. This mistake about time in his physics, was corrected by the theory of relativity. But important corrections were left out. The “laws of motion” have to be changed from ordinary to functional differential equations. Advantage: The correction makes physics non-mechanical and better suited to biological organisms. There is no need to deny the experience of mundane creativity as an illusion. A further correction is needed to Newton’s law of gravitation as well. That resolves the problem of galactic rotation curves and the NASA flyby anomaly. Further, the approach to differentiating discontinuous functions in point 3 leads to a reformulation of Maxwell’s equations which helps to resolve the problem of runaway solutions and preacceleration in electrodynamics.)

5. It improves history. (We are taught calculus and indirectly to worship Newton and Leibniz as creators of the calculus. The true history shows in what social and physical context the calculus originated in India, and was later transmitted by Jesuits, and Westerners wrote its false history well knowing what the truth was, as is their customary practice. This false history was used to change the education system, by Macaulay, and to produce an indoctrinated class of “natives” who helped to colonise and control vast populations in countries like India. Advantage: the improved history leads to freedom from Western mind-control and hegemony.)

Still more?

Will give more details in future posts with references to my published work.

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