The alleged 'universality' of mathematics is therefore double-speak for an assertion of the superiority of colonial mathematics over traditional mathematics. The unique feature of 'reasoning' in both church theology and formal mathematics is exclusion of the empirical. Everyone accepts that empirical evidence is fallible due to possible senses (the classic example in Indian philosophy is that one can mistake a snake for a rope or vice versa).
Fallibility is especially true of an indoctrinated mind (such as that of Westerners during the 'Dark Ages', the Crusades and the Inquisition) or the captured mind of the colonized. Therefore, such "errors of the indoctrinated mind," as happened in the case of the Elements, are far more persistent than the errors of the senses. The frequent and persistent errors of the mind in mistaking invalid deductive evidence for valid evidence show that deductive evidence is more fallible than empirical evidence.
Excluding the empirical from a proof means that it must also be excluded from the postulate. This fallacy of 'reasoning', due to the lack of empiricism, lends itself well to church politics, for by choosing the right premises (over force. Arrow's impossibility theorem goes against the common belief that the good of the many must prevail over the good of the few.
This superstitious belief in the accuracy of mathematics could not be reconciled with the highly practical value of the infinite series of the Indian calculus in deriving the exact (but not exact) trigonometric values required for navigation (upon which European dreams of wealth rested).
Decolonised Math 1: Geometry
Teaching that reality is 'wrong' prevents students from applying common sense to the objects they can see, as they may not accept the authority of the text. The only source of knowledge about the geometry of invisible points is the colonial authority of the text. I compared the stupidity of the invisible dots to the stupidity of the emperor's new invisible clothes and burst out laughing.
Remember that Hilbert sided with Russell and tried to 'correct' the author of the elements that 'went wrong'. Subsequently, the School Mathematics Study Group (School Mathematics Study Group 1961) recommended the teaching of Birkhoff's axiomatic metric geometry (Birkhoff 1932), a geometry that adhered to axiomatics but did not attempt to present an elaborate excuse for the apparent prolixity of the element, as Hilbert attempted . A protractor comes ready-made, and students are also unable to explain how the circumference of the protractor is divided into 180 equal parts, or even what equal parts of a curved line mean.
It also explains the radial measure of angles, since the length relative to the radius of the circle, about which students were accustomed to the protractor and the degree measure of angles, is typically unclear. While the number called π today is defined in the usual way as the ratio of the length of the circumference to the diameter, the length of the curved circumference is now significant, and there are easy ways to calculate that number. Holding one end of the rope makes it possible to draw a circle; so the rope replaces the compass.
Many other practical applications in real life, such as finding the time and cardinal directions from the shadow of a gnomon, finding the radius of the earth and the local latitude and longitude, are explained in the draft text of Rajju Ganit, which has been prepared as part of the experiments with teaching decolonized geometry in school. This renders irrelevant the exact order of the propositions in the Elements, an order required to be ritually followed (Taylor 1893) even by the revised Cambridge syllabus of the late 19th century. Now, if a and b are the two sides of rectangle and c is the diagonal, then instead of the Manava sulba sutra states.
5 The full text of the Manava sulba sutra is archived at http://ckraju.net/geometry/manava_shulba_sutra.pdf, while the English translation of 10.10 is posted at http://ckraju.net/geometry/translation- Manava-10.10 .pdf. The alleged accuracy of the Pythagorean theorem is misleading and students should be informed of this. However, the Government of Karnataka, which supported one of the workshops, agreed that school texts should be corrected if they were incorrect.
Decolonised Math 2: Calculus without Limits
But they have never been taught what a tangent is and cannot define a tangent except by using the false definition8 that a tangent 'just touches' a curve at one point. Decolonization finds that the source of calculus's problems is the unnecessary metaphysics within it: the way that unnecessary metaphysics used Whitehead and Russell to prove 1+1=2. By eliminating this unnecessary metaphysics, calculus is so easy that it can be learned in five days, regardless of the student's disciplinary background.
Decolonization begins with the realization that the main concern of the colonized should be the practical value of mathematics, not the imitation of colonial practices. For example, in decolonized calculus is defined in a very simple and rigorous way as the solution of the differential equation with . But since teachers do not teach elliptic functions themselves, they treat the textbook formula as exact and wrongly teach students that time period is independent of amplitude (Raju 2006b).
Finite geometric sequences are ancient and are found in the "Eye of Horus." fraction, and the Yajurveda 17.2.). However, let's look at some simpler aspects of the mischief caused by colonial calculus. Using the colonial calculus and formal 'real' numbers results in something strange: it forces time, in physics, to be like the 'real' line, simply to write down the equations.
Recall also that the first creationist conflict occurred in mathematics, not biology, when in the sixth century John Philoponus wrote On the Eternity of the World: against Proclus (who had said that time was 'cyclic'). Philoponus' argument was that this would be contrary to the doctrine of creation described in the scriptures. This conclusion is the core of their book: "The actual point of creation, the singularity, is outside the currently known laws of physics" (Hawking & Ellis 1973: 364).
Very few learned people will realize that this postulate corresponds exactly to the metaphysics of the church's politically motivated curse on 'cyclical' time against early Christianity. Tipler points out that we should accept this as 'mainstream' physics, derived from singularity theory, on the authority of the reputable journal Nature, in which he has published several articles. This is what enables Hawking and Ellis to give a cosmic significance to the supposed breaking of the 'laws' of nature.
At best, this means that smooth solutions of the differential equations of general relativity cannot extend beyond a singularity. Even within formal mathematics one can make sense of the differential equations of physics using Schwartz's theory and something called non-standard analysis (Raju 1989).
Advancing Decolonisation: Exposing Colonial Shenanigans
How can it be reconciled with students' demonstrated ability to solve elliptic integrals with the decolonized calculus.
The Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of Calculus from India to Europe in the 16th Century.
