Alternative mathematics 2-Calculus without limits

Some preliminary clarifications

Abstract has been chopped. Full abstracts of both parts put up at http://ckraju.net/IIT-BHU.

If this is part 2 where is part 1?

• The program committee rejected part 1. Why? They said only one paper per person.
  
• Part 1 is a pre-requisite for part 2. So, my suggestion: accept only part 1 then.
  
• They refused. Gave no reason.
  

Critique of NCERT

• Actually, part 1 criticises the existing NCERT teaching of math
  
• (And suggests an alternative way.)
  
• To avoid the critique, they want me to skip the pre-requisite.
  

Censorhip and math

• Can't reject both papers: already a huge scandal about censorship of my work: google "math and censorship".
  
• or google "to decolonise math stand up to its false history".
  

The critique

• I'll just take one or two points of the critique. (Full critique is posted at http://ckraju.net/geometry/ and http://ckraju.net/geometry/NCERT critique-and-outline-of-alternative.pdf.)
  

Point 1

• Chp. 5 of class IX math text is titled "Euclid's geometry"
  
• Euclid did not exist: my Euclid challenge prize of Rs 2 lakhs for evidence about Euclid standing for ten years
  

Some references

• Paper Goodbye Euclid,
  
• video, Goodbye Euclid (just google "Goodbye Euclid")
  
• book Euclid and Jesus (just google "Euclid and Jesus")
  
• discussion David Fowler, in 2002.
  

Why is it important? Whether or not Euclid exists?

• 1 If NCERT can't answer question (what is the evidence for Euclid?) no school teacher can.
  
• The NCERT authors blindly trust the West, and teach that students should too.
  

Why?

• To teach that Westerners and whites are superior. They are the masters, and our children are their future slaves. Slaves cannot question the master.
  
• This was the aim of colonial/church education: to teach the colonised to be good slaves
  

Post colonial colonial agenda

• NCERT is faithfully carrying forward that agenda 70 years after independence.
  
• Their unstated aim is to teach blind imitation of the West.
  
• But do we want our children to be slaves? Or to be leaders?
  

Why "Euclid" is important?

• Reason 2: it has a direct bearing on the questions ** "why is math difficult?" and
  
• "how to make it easy?"
  

Why is math difficult?

• Not because of bad teachers or bad students
  
• But because we teach the wrong math.
  

Wrong math? Isn't math universal? No.

• We teach formal math
  
• not normal math
  
• on the ground that formal math supposedly done by Greeks like "Euclid" is superior. (False: No one did formal math before the 20th c.)
  
• And on the ground that traditional Indian math was inferior since practical. (NCERT class IX, chp. 5)
  

What is the difference?

• Normal math accepts facts like science.
  
• Formal math prohibits facts. Begins from postulates/axioms.
  

Difference (contd.)

• normal math uses normal reason = reason plus facts
  
• formal math uses formal reason = reason minus facts
  
• Double speak about reason: people wrongly take it to mean normal reason.
  

Who used reason?

• False that only "Greeks" used reason.
  
• ALL Indian systems of philosophy accept reason or anumana as a means of proof.
  
• Aryabhata deduced that the earth is round from the fact that far off trees cannot be seen.
  

Who used reason? (Contd.)

• False that Greeks used formal reason. Not a single pure deductive proof in "Euclid's" Elements.
  
• Prior to 20th. c. only church used metaphysical reason = reason minus facts.
  
• E.g. how many angels can fit on a pin
  
• starting from the postulate that an angle occupies no space.
  

Church propaganda

• False claim that Greeks did "superior" math hides church connection.
  
• Teaches millions to imitate the metaphysical methods of church rational theology.
  

Why is math difficult? How to make it easy?

• Math is difficult becase of useless metaphysics in formal math.
  
• The way to make math easy and practical is to revert to traditional normal math
  
• in both geometry and calculus.
  

Example 1. 1+1=2

• Because of junk metaphysics Russell took 378 pages to prove 1+1=2
  
• too difficult for most people.
  

Two cartoons.

• This proof adds NOTHING to the practical value of arithmetic in a grocer's shop.
  

Example 2. Invisible points.

• Class VI text says geometric points are invisible.
  
• How do you even measure the distance between invisible points? (Cartoon).
  
• What is the practical value of invisible points?
  
• Has anyone here done any geometry with invisible points?
  

Example 3. Calculus

• NCERT texts provide zero knowledge of calculus:
  
• Here is my pre-test for undergrad calculus.
  
• Clearly students learn nothing except blind imitation of a metaphysics of infinity: limits, reals, sets, etc. (allied to church dogmas of eternity)
  
• because that is the NCERT/colonial/church purpose to teach blind imitation of the West.
  

So what's the solution?

Re-examine the false history and bad philosophy of math ab initio.

• E.g. calculus developed in India since Aryabhata 5th c.
  
• was transmitted to Europe, by Cochin-based Jesuits in the 16th c.
  
• in connection with the European navigational problem
  
• which required precise trigonometric values.
  

Madhava's sine values

• precise to third sexagesimal minute (about 9 decimal places)
  
• Indian method of summing infinite series
  
• was not correctly understood in the West
  
• (Hence Newtonian gravitation failed.)
  

More details in

• Book: Cultural Foundations of Mathematics
  
• Videos: talk at MIT, talk at Durban
  
• Articles: teaching math with a different philosophy: (google)
  

Different philosophy

• Indian calculus involved a different philosophy of normal math.
  
• Does NOT require formal/fanatasy "real" numbers
  
• Calculus as numerical solution of differential equations.
  
• Can be done on computers using floating point numbers.
  

Focus on practical value:

• Limits, real numbers irrelevant to practical value of calculus
  
• All practical value comes from numerical solution.
  
• To send a rocket to the moon, ISRO or NASA uses computer simulation of the trajectory.
  
• computers stick to the real world; use floating point numbers, NOT fantasy "real" numbers.
  
• This makes calculus easy (e.g. tutorial sheet).
  

Different philosophy/techniques

• Apart from numerical solution of differential equations,
  
• Indian calculus uses non-Archimedean arithmetic (= अव्यक्त गणित) of Brahmagupta
  
• together with a philosophy of zeroism (शून्यवाद)
  
• to sum infinite series.
  

Better calculus

• Advantage: this allows discontinuous functions to be differentiated
  
• as required for discontinuities in solutions of partial differential equations.
  

Improves science

• e.g. theory of gravitation: my retarded gravitation theory.
  
• See extended abstract of talks in (a) University of Cape Town, (b) Palestine,
  
• Search "uct", "palestine" in http://ckraju.net/papers
  

Cannot explain everything here

• and NCERT conference team insisted: don't explain easy pre-requisites
  

Conclusion

• A high level PUBLIC review is needed of NCERT math books to eliminate false myths, superstitious metaphysics, and impractical math in them.
  
• Reject blind imitation of the West where practical value cannot be demonstrated.
  
• If practical value is the reason to teach math, focus on normal math.