It was with a sense of shock that I heard of the passing away of Uncle Idris, which was untimely even at 93. When I last met him in March he was unwell, and in hospital, but looked well enough to carry on for another five years, or at least Read more…
Since the NCERT tried to evade all issues in the first grievance, a second grievance has been filed, asking NCERT to produce primary evidence for “Euclid” or delete all 63 mentions and image of Euclid from its 9th standard text. Further falsehoods will be taken up subsequently. The new grievance Read more…
The NCERT class IX textbook on mathematics has its chapter 5 entitled “Euclid’s geometry”. A public grievance was lodged with the government pointing out numerous other falsehoods in the book. The grievance in the 4000 character text format specified for grievances is posted at http://ckraju.net/geometry/NCERT-grievance-note.txt. There is also a detailed Read more…
After my book Cultural Foundations of Mathematics: the nature of mathematical proof and the transmission of calculus from India to Europe in the 16th c. CE (Pearson Longman, 2007) it is well known today that calculus developed in India a thousand years before Newton and Leibniz. Cochin based Jesuits stole Read more…
At my IIT (BHU) lecture (see also previous post), I emphasized Bertrand Russell’s remark that there is neither meaning nor truth in (formal) mathematics. Hence, any nonsense proposition one desires (such as “All rabbits have two horns”) can be proved as a formal mathematical theorem from appropriate postulates: Russell’s sole criterion being that the postulates should be “amusing”.
To drive the point home, I pointed out how, long ago, when I still believed in formal math, I used to teach a course (A) on Real Analysis while also teaching a more advanced course (B) on Advanced Functional Analysis, in the math department of Pune University. In the elementary course (A) I taught
Theorem: A differentiable function must be continuous. (Therefore, a discontinuous function cannot be differentiated.).
In the more advanced course (B) I taught
Theorem: Any (Lebesgue) integrable function can be differentiated infinitely often. (Therefore, a function with simple discontinuities can be differentiated infinitely often.)
I have made exactly this point earlier in this blog.
“Now, for several years I taught real analysis to students and mathematically proved in class that a discontinuous function cannot be differentiated. I also taught advanced functional analysis (and topological vector spaces and the Schwartz theory according to which every Lebesgue integrable function can be differentiated). In the advanced class, I mathematically proved the exact opposite that a function with a simple discontinuity can be differentiated infinitely often (and the first derivative is the Dirac δ).”
The question is which definition of the derivative should one use for the differential equations of physics? As pointed out in Cultural Foundations of Mathematics (or see this paper) the issue can only be decided empirically, unless the aim, like that of Stephen Hawking and G. F. R. Ellis, is to spread Christian superstitions about creation using bad mathematics.
Superstitions go naturally with ignorance. One such ignorant professor from the IIT mathematics department was present during my lecture. His knowledge was limited to the first of the theorems above, and he ignorantly believed that it was some kind of absolute truth, which everyone was obliged to believe. He objected to my claim that a discontinuous function can, of course, be differentiated, and walked out to show his contempt of my claim.
Even the students had heard of the Dirac δ, and agreed with me. The next day during the workshop, I explained that I had engaged with this question since my PhD thesis. But the professor remained absent, though his ignorance was exposed before the students. He is welcome to respond by email; I will post it publicly since it is sure to further expose his ignorance.
Oliver Heaviside applied first applied this to problems of electrical engineering over a century ago, and Dirac, formerly an electrical engineer, then applied the Dirac δ to physics. It remains very useful because it is the Fourier transform of white noise (flat spectrum or the unit function), and used even in the formal mathematical theory of Brownian motion.
Earlier in the lecture, the same professor, contested my claim that probability was invented in ancient India, and taken from India in the 16th c., where credit for it was later falsely given to people like Pascal and Poisson. (more…)
Will be giving the institute lecture at IIT (BHU), the century old first engineering college in India, on the 18th of Jan, followed by a workshop on “Alternative math” on 19th of Jan. (The Workshop is from 10 am to 5 pm with tea breaks and a lunch break.) Core Read more…
Was honored before a mass audience at Bijapur. The award was conferred by Karnataka MP Shri Basavraj Patil, and the Vice Chancellor of the Central University Karnataka. Kalaburagi, Prof. H. M. Maheshwaraiah. Below is a picture of the audience. For more honors earlier this year see http://ckraju.net/blog/?p=150.
A conference on decolonisation of humanities was organized at Al Maaref University, Beirut.
The big concern was how colonial education has altered human values. But Western education did not come for humanities, therefore my point was that merely changing humanities education won’t result in the desired change. The facts are (1) Western education came to the colonised as church education. (2) It was and is justified on the grounds that the colonised need science. The net effect of (2) is that the colonised foolishly trust the authority of church institutions like Cambridge, Oxford, and Paris. This way the church is able to mix all sorts of subtle poison in university education, even through math and science.
Though Western education ostensibly came for science it ensures that the mass of educated are ignorant of math and science, so they are forced to trust authority (of the West, obviously). It further anti-educates them by planting myths, and teaching them to think in terms of stories. For example, due to such indoctrination, the colonised are trapped in the myth that science and church are at war. They failed to notice the obvious fact, contrary to this myth, that colonial education came as 100% church education, and that, for example, the best science colleges, even in India, are still church institutions.
Mind control of the colonised was the work of the church, in collusion with the colonial state. This persists, like Western education, even after direct political control of the colonised ended. Once the colonised are rendered ignorant, and taught to trust Western authority and myths, as Western education teaches, there is no solution for them.
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A reporter from Africa met me recently in India to find out about the events concerning the panel discussion on decolonisation in Cape Town, a year ago. Someone here asked: could he be a church agent, who may again present a biased picture? I don’t know. But he does not seem to know any math, and may not have understood my critique of formal math. So, to make sure that others (especially the ill-informed) do not “control the narrative”, and totally misrepresent it, it is time I put up my side of things.
An important background, to the debate last year in the University of Cape Town, which has not been adequately mentioned, is my book The Eleven Pictures of Time (Sage 2003). In it I extensively criticised the book Large Scale Structure of Space-Time by Stephen Hawking, and G. F. R. Ellis, of the University of Cape Town. (Note, in passing, that Hawking unethically collaborated with Ellis at a time when there was an academic boycott of apartheid.) My key issue with the Hawking and Ellis book was that their conclusions about a “singularity” involved bad mathematics, and a bad understanding of calculus (even from within formal mathematics).
But let us go one step at a time. First, their conclusion that the cosmos began with a “singularity” was not science (since not refutable on Popper’s criterion). Second, their conclusion was of great political significance to the church, through the claim that science supports the church’s religious dogmas of creation. The mathematical conclusion of a singularity is explicitly connected by Hawking and Ellis to religious beliefs about creation and other dogmas. The key takeaway of their book (p. 364) is that “the actual point of creation, the singularity, is outside the presently known laws of physics.”
The belief that God rules the world with eternal “laws” of nature is itself a religious church dogma first articulated by Aquinas, not a scientific (refutable) belief. Simply put, the church supports it, but Hinduism, Buddhism and Islam deny it. (See this minuted discussion for example, which explains that Hinduism accepts rta, but not immutable laws, for Buddhism, see the video “Buddhism and science”, for Islam see the keynote and article on Islam and science.) Further, other religions accept continuous creation, or the creativity of living organisms (not continuous creation in the mechanistic sense of the theory of Bondi, Gold, Hoyle and Narlikar). The big bang theory alone is NOT the opposite of continuous creation. The “singularity”, interpreted as a beginning of time, relates to creation more clearly than the big bang, which need not be a true beginning of time, but could be just the other side of a big crunch in an oscillating cosmos.
There is no doubt about the religiosity of the book by Hawking and Ellis. Ellis got the million dollar Templeton award, for putting together science and religion, and Hawking never got the Nobel prize! The church greatly glorified Stephen Hawking, and that church propagandist support helped sell millions of copies of his book Brief History of Time which restated the conclusions of singularity theory for a lay audience. But singularities and creationism are simply not physics. Therefore, much as Hawking desired the Nobel prize, and much as the Nobel prize committee may have wanted to give it to him, they simply could not do so.
The physicist F. J. Tipler (Physics of Immortality) pushed this connection of science and religion via singularity theory. He explicitly claimed that singularity theory proves the truth of Judeo-Christian theology. In the opening paragraphs, Tipler said his book aimed
“to show that the central claims of Judeo-Christian theology are in fact true, that these claims are straightforward deductions of the laws of physics as we now understand them. I have been forced into these conclusions by the inexorable logic of my own special branch of physics…the area of global general relativity…created…by the great British physicists Roger Penrose and Stephen Hawking.”
The colonised mind may talk against creationism, in support of Darwinism, but it never dared contest this kind of religious claim of creationism backed by Western authority. Despite the millions who read Stephen Hawking’s book, Brief History of Time, I have not heard a SINGLE other dissenting voice in the last thirty years. (more…)
Yesterday (26 November, Constitution Day) at Constitution club, I received the Nilakantha honor from the Dalit organization “Kabir ke log” from a former Union deputy education minister (and scholar) Dr Sanjay Paswan). Click for a related article on dalit scientific achievements, in Jansatta. Earlier I had received the Bharatiya Dharohar Read more…