Millions of people across the world have heard of Stephen Hawking, whose recent death hence made headlines. Everyone speaks of his ALS. But is it proof of his indomitable will? Or did he hence make a Faustian pact with the devil incarnate: the church? Daring to raise this question will doubtless arouse the rage of his admirers. But if we weigh it against the possibility that millions have been deluded using their trust in science, it is our public and ethical duty to raise the question. To answer the question Hawking’s disease is irrelevant, and we need to examine the merits of Hawking’s scientific work dispassionately.
But it is near impossible to do so. While millions revere him, very few understand the mathematical intricacies about calculus related to his work, especially on Penrose-Hawking singularity theory. That theory was the basis of his best-selling book A Brief History of Time. The widespread ignorance about it became starkly obvious during my debate with Roger Penrose, in Delhi, in 1997, attended by various professors of physics from Delhi University and JNU whose blank faces told the story.
What the vast majority believe is a story about science, a story they blindly trust. So deep is their trust that, from a position of ignorance, they are quite certain a contrary opinion is not to be trusted! “Millions of people believe this, they can’t all be wrong can they?”. Such a “proof by numbers” is convincing because it has survival value, as explained in my book The Eleven Pictures of Time: there is often safety in being part of the herd. But this psychology also provides an easy route to propaganda to fool a mass of people. For centuries, millions of Westerners fervently believed in the idea of a powerful God who appointed the church as his broker. The belief persisted just because the church reviled any dissenters as heretics and atheists, and, for centuries, killed them most brutally.
The Christian theology in Hawking’s work
Therefore, common sense may be a better guide to the truth than guesswork based on trust. What even the most gullible person cannot fail to notice is the way singularity theory connects to the notions of a Judeo-Christian God and a specifically Judeo-Christian notion of creation.
I have pointed this out repeatedly over the last twenty years, but the faithful, and our secular liberals, just ignore it. So, it is necessary to point it out yet again. Hawking’s popular book was preceded by an academic book, The Large Scale Structure of Space-Time, which he co-authored with G. F. R. Ellis who won the Templeton award for connecting science and religion. That book concludes that the cosmos has a singularity. What does that mean? The authors interpret it to mean a moment of creation. The bottom line of the book [p. 364] asserts: “the universe began a finite time ago. However, the actual point of creation, the singularity, is outside the presently known laws of physics.” God created the cosmos and then set the clockwork of eternal laws in motion.
For those who don’t understand this, the meaning is made explicit in a book co-authored by Hawking, “A briefer history of time”. It explained [p. 141] that: “At the big bang and other singularities, all the laws [of physics] would have broken down, so God would still have had complete freedom to choose what happened and how the universe began.”
An SF writer wanted to explain a singularity to the layperson. So, he asked Hawking, what exactly happens at a singularity. Well, the “laws of physics” fail, so anything at all can happen! So, what is there to do if one comes face to face with a singularity? Obvious: kneel down and pray!
Any doubts anyone may have about the relation of singularity theory to Judeo-Christian theology are entirely removed by F. J. Tipler who has published on singularity theory in the authoritative journal Nature, the publishers of which also published his book Physics of Immortality. The book [p. ix] “purports 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.” Tipler adds, “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.”
Note the claim that it is ONLY Judeo-Christian theology which is proved by present-day physics, not Islamic theology for instance. Let me elaborate for those who don’t understand the finer points here. A big bang beginning for the cosmos is not necessarily a beginning of time: it is compatible with an oscillatory cosmos, as in Hinduism, a cosmos which was created trillions of years ago, but goes through a series of big bangs and big crunches (days and nights of Brahma, each of which lasts for billions of years). Singularity theory seeks to exclude this possibility, and identify the current big bang as a true moment of creation. Cosmology, not biology is the natural playground of creationism. The first creationist conflict actually took place between Proclus and John Philoponus in the 6th c. over the issue of one-time creation of the cosmos.
Likewise, as explained in my article on Islam and Science, or in this minuted discussion, or in this recent video, the belief in one-time creation followed by the “laws of physics” is an anti-Islamic aspect of the crusading Christian theology of Aquinas. Islam believes in continuous creation of the world at each instant, a creation conditioned by habit, but not determined by the past on any rigid laws. Since we actually observe changes in the world every instant, Buddhism too has a similar belief in a new world at each instant, conditioned by the past but not determined by it. (Of course, physics can be remodeled to accommodate this observed mundane spontaneity in the world, and my equations with a tilt in the arrow of time, in my book Time: Towards a Consistent Theory, provide such a model.)
This fact about singularity theory, that it aligns with church theology, is quite contrary to the other naive belief that many people have, that “all science is opposed to all religion”. The fact is Stephen Hawking’s “science” is anti-Hindu, anti-Islam, anti-Buddhist but supports church dogmas about Christianity (as distinct from original Christianity). It is important to make the last distinction, because the church is about acquiring and maintaining power through lies, and not about real Christianity.
There is no doubt at all that Stephen Hawking himself is responsible for this pro-church bias of singularity theory. Thus, the formal mathematical theorems of singularity theory depend on its postulates. Hawking and Ellis introduce a postulate called the chronology condition which says, roughly speaking, that there is no cyclicity in time. We are supposed to accept this on their authority.
Now, the belief in quasi-cyclic time, and the accompanying belief in reincarnation, is at the core of Hindu, Egyptian, and Sufi beliefs about the soul, and these belief persisted into early Christianity, and are reiterated by Origen, as I have explained in The Eleven Pictures of Time, and in Euclid and Jesus. After Constantine, the church acquired state power, and found this equitable belief in the soul an impediment to its power. To hold on to power, it sought instead to strike terror in the hearts of people, by changing beliefs about life after death. The church’s new formula was simple: people got only one life, time would end soon, and people would thereafter be resurrected and those who disobeyed the priest would be punished eternally in hell. In support of this formula, the church cursed “cyclic time”, a curse pronounced in Hagia Sofia, Istanbul in 552, by the fifth ecumenical council and (separately) by the king Justinian.
This change of doctrine was championed by Augustine, who argued in favour of resurrection (against reincarnation) by misrepresenting Origen. For that glorious falsehood, which enhanced its power, the church declared Augustine a saint. Further, as I have explained in The Eleven Pictures of Time, there is a very tight similarity between the bad arguments of Augustine, and the bad arguments advanced by Hawking and Ellis in favour of the chronology condition.
In short, the pro-church bias of Hawking’s singularity theory is a consequence of a postulate, the chronology condition, which deliberately casts church dogma in mathematical form, and passes that off as science.
That pro-church bias makes it easy to understand why Hawking’s book sold so many copies—a huge and invisible sales force of committed church believers was pushing it. So, did Hawking unscrupulously misuse science to support the church? If so, he was surely a crook.
Blind faith in science
The blind belief that people have in Stephen Hawking, namely that everything he did was great science, is just the sort of blind faith which helped sell his popular book: A brief history of time. The people who believe it is science cannot even explain why Hawking never got the Nobel prize though all the political cards were stacked in his favour. Blind faith does not bother to answer questions: it explodes in rage when the object of its reverence is challenged. But rage is irrelevant to scientific truth.
Blind faith in science is surely not the same as scientific temper. Science is about why one believes something, not what, as I am tired of repeating. Blind faith in science is still an act of blind faith, not superior to blind faith in anything else. The superstitions of the gullible believers can be exploited by unscrupulous elements in exactly the same way.
Real science requires understanding, first of all of what is real science. A rough and ready way to separate science from non–science is to use Popper’s criterion of refutability: a scientific theory must be testable. If the singularity theory Hawking did is science, how exactly does one test the existence of a singularity? Did Hawking suggest any way to do so? No, he did not, for there is no way to test or refute the existence of a singularity. So it is not science in the Popperian sense. (That is why he never got the Nobel prize.) Hawking’s so-called science is not science at all, it is just an articulation of pro-church beliefs in the trappings of science with a view to fool the gullible.
What is a singularity?
So, what exactly is this untestable thing called a singularity? During my debate with Penrose, he avoided giving a physical interpretation of a singularity, rightly so, for it is purely a formal mathematical construct. As Russell explained, formal mathematics has nothing to do with meaning and truth. But those who do interpret the notion of a singularity do so as follows. They regard a singularity as the beginning or end of a time-like geodesic. Since a timelike geodesics is, roughly speaking, the world-line (past and future history) of a hypothetical point-particle of matter, a singularity could be interpreted as the creation or destruction of an unspecified hypothetical test particle.
Note that today’s scientist is no crusader for truth. The test of “good science” today is publication in a journal, and the related amount of money one can raise for research. So, today’s “scientific method” is just about publication through the church process of secretive “peer approval”. Accordingly, today’s scientists are slaves to community opinion, on which their funding and careers depend.
So, we have two types of science today: community science which may be reputable without the slightest experimental consequences, or relation to reality, and real science which has experimental consequences, and is refutable. The above “interpretation” of a singularity is community science, just something “accepted” by the scientific community, there may be no trace of truth in it. Specifically, the term “particle” in the above interpretation ought not to be confounded with more-real particles such as an electron. The hypothetical particles which are supposedly created or destroyed are not even some “idealized” point masses, for any finite point mass will result in a black hole on general relativity.
Singularities and calculus
So, is there an alternative way to understand a singularity? Yes. What supposedly breaks down at a singularity are not the “laws of physics”, but the mathematical understanding of certain differential equations used to model physics such as the equations of general relativity. But even this “breakdown” may be just a case of bad mathematics, due to a bad understanding of calculus. On the calculus as today taught in schools and undergraduate level, a differentiable function must be continuous; to write down the equations of general relativity, the metric must be twice continuously differentiable, so its derivative must be continuous. Strictly speaking most university students of calculus are only told about continuity; they are actually taught a bit more about it in more advanced courses on mathematical analysis (which I used to teach in Pune University, in the 80’s).
But casting aside this formal mathematical wisdom, physicists have been merrily differentiating discontinuous functions from the time of Oliver Heaviside in the 19th c. Better known today is the Dirac delta function which is the derivative of the discontinuous Heaviside function. Indeed, at a still more advanced level, calculus is taught in the university as advanced functional analysis (another course I used to teach). Here, one teaches the opposite: that discontinuous functions can be differentiated, as often as one wants. This is done on several mathematical theories, the most prominent (socially acceptable) one being the theory of the French mathematician Laurent Schwartz.
Of course, the Schwartz theory has its limitations: as a linear theory it does not readily work for those differential equations of physics which are non-linear. However, four decades ago I suggested a solution to this problem as part of my PhD thesis, using a new development in formal mathematics called non-standard analysis. I also explained in a paper on “Junction conditions in general relativity“, included in my PhD thesis, how one could make sense of the equations of general relativity in the presence of discontinuities. Several years later, in 1988, in a paper presented at the fifth Marcel Grossman meeting on general relativity at Perth, I explained how to handle higher order discontinuities. Such discontinuities arise most commonly in shock waves, generated for example by an exploding star, but include singularities. I didn’t pursue this since I left formal mathematics shortly after that.
About a decade later I began researching on the Indian origin of calculus and its transmission to Europe via Jesuits based in Kochi. In my book Cultural Foundations of Mathematics, As one of the proofs of transmission I proposed my epistemic test: that Europeans copied Indian calculus without understanding how Indians summed infinite series. Europeans later proposed a metaphysical doctrine of limits to understand infinite sums. As usual, Europeans pretended that anyone who did not imitate them was inferior. Actually it is the European method of limits which is inferior to the method used by Indians to sum infinite series. The Indian way, using what is today called non-Archimedean arithmetic, was the only aspect of non-standard analysis required for my earlier solution to the problems with the Schwartz theory. So, it gives a better calculus.
On recognising the inferiority of the European doctrine of limits, in calculus, I devised a new course on Calculus without Limits, and started its experimental teaching at the Universiti Sains Malaysia. Later, calculus without limits became the core of my program of decolonising mathematics, and teaching an alternative mathematics.
South Africa and decolonisation of math
As is well-known, students in South African universities have been agitating for the last few years for decolonisation. It was in this context that I repeatedly visited South Africa. On my last visit, the University of Cape Town organised a panel discussion, the several related videos are in the following hyperlinks: video 1, video 2, video 3, video 4. For this panel discussion, I submitted a summary in advance, which can be found here. Now, the co-author of Stephen Hawking’s academic book, Ellis, is from the same university. Therefore, I offered to speak and debate at length the mathematical technicalities involved. This is clear from the advance summary.
A key aspect of the agenda of decolonising science was to eliminate the church dogmas in science which are present in various ways such as claims about “laws of nature”, but mainly creep in through formal mathematics. This is also explained in a keynote address at the 11th Higher Education Conference, Durban, and a related TV discussion on decolonisation. The upshot? Singularity theory is not a work of genius but a perfect example of such trash, dogmatically-loaded science which needs to be junked in the process of decolonisation.
Naturally, those who have spent their entire lives smuggling in politically-loaded church dogmas into science were alarmed that Hawking’s “science” would be exposed as mere church propaganda. Those who have repeatedly claimed that science cannot be decolonised were alarmed that Western superstitions in mathematics and science would tumble out of the closet putting a complete end to false claims of the universality of science. My decolonisation thesis asserts that such religious biases creep into science through formal math, which involves church superstitions, which we should reject in favour of normal math. (In the present instance, we should reject both, the postulated chronology condition, and the way of doing calculus with limits.) This exposure of Hawking would have exposed the false claims of superiority of his racist supporters in the University of Cape Town.
Specifically, my offer to debate in the math department seems to have frightened Hawking’s co-author Ellis out of his wits. He naturally guessed that this debate, unlike my earlier debate with Penrose, would be video recorded, if in no other way than with a mobile device. But Ellis also knows he is ignorant, and such a recording would expose his ignorance and inability to respond. He has never done non-standard analysis or applied it to advanced functional analysis. He was aware that such exposure of ignorance would have made a strong case for decolonisation of math. Blacks would understand that his and Hawking’s attempts to inject the worst kinds of creationist church superstitions into science, and would forever make fun of it.
Indeed, though I did not visit it, the whole math department in the UCT seems very weak. The person who debated with me, Henri Laurie, tried to later engage with me over email, but was unable to prove 1+1=2 in formal real numbers. He complained that I had suddenly switched from natural numbers to real numbers :). Obviously, they were in no position to face my critique of formal math except by the usual false claims of superiority common to church, racists and Westerners.
So, Ellis ran away from the debate. He along with his student Jeff Murugan put the usual “we are superior you are inferior” claims, in their most abusive form, through the press which would not allow me to respond appropriately. This is the classic way in which the church has defended its superstitions by running down critics as heretics. Like the church, Ellis and his student Murugan just poured on the falsehoods but did not provide any evidence. If they had any evidence, there would have been no need to run away: they could have paraded the evidence and celebrated a victory. The use of this strategy make is very clear that Ellis is an intellectual charlatan of the worst sort who has tried to pass off Western superstitions as science for decades, getting pots of money for it, and thinks that such charlatanry can be defended by abuses.
But what of Stephen Hawking who wrote his academic book with such a co-author? Wasn’t he aware of his co-author’s character? Wasn’t he aware that the man came from a starkly racist land? Didn’t the great genius realize, that to cooperate with white South Africans then was an unethical and unnatural act? I am sure his supporters will find lots of excuses for this vilest of ways in which science has been defiled. But it seems that Western society is so rotten that it is the scum which very often rises to the top.
Hawking may have made his Faustian pact with the devil, but we need to rise above the evils of Western society and decolonise math and science to save our children. A simple formula for decolonisation is this: whenever you hear a dialogue from a Westerner which sounds like “we are superior x is inferior” distrust it. Demand evidence. If no evidence is forthcoming, as there is none for the centuries old Western belief in Euclid as the father of math, throw that belief in the trash can where it belongs.