Can physics be done without infinity as taught in math (real analysis) today? Someone demanded an explanation in an email sent to my son. (I guess the Raju family has the same problem as the Bernoulli family in Europe! .)
Ordinarily, I would not have responded, for people ought not to demand an explanation by email without bothering to read or understand what I have already written. But, similar doubts were expressed by a young woman (with a PhD in functional analysis) who attended my talk in Ramallah. They may again arise in future. So, I decided to respond.
Infinity is metaphysics. Infinity relates to eternity, so that the Western concept of infinity in present-day math is saturated with the church metaphysics of eternity.
Ironically, the figure for infinity, ∞, is still shaped like a serpent coiled back on itself and eating its own tail, and is an old symbol of quasi-cyclic time.
The linkage of infinity to eternity led to the first creationist controversy: over the nature of eternity, not evolution. In the 6th c. John Philoponus objected to Proclus’ notion of eternity based on quasi-cyclic time. Philoponus’ problem was that if the cosmos is eternal (as Proclus conceived it) it would not be created. That creationist controversy is still going on.
For example, Stephen Hawking claimed the cosmos was created with a “singularity”. (A “singularity” is nothing but an infinity of some sort.) He concluded his only serious scientific book by identifying the “singularity” with “the actual point of creation” where there is a breakdown of the “laws of physics”. This conclusion is pure metaphysics, for there is no way to check it empirically.
In his popular book, Hawking explained the point of this metaphysical conclusion: because the “laws of physics” break down at the “singularity”, that leaves God free to create the world of his choice. Note that this is in accordance with the Christian notion of one-time creation (and contrary to the Islamic notion of continuous creation, or the Buddhist notion of non-creation, or the “Hindu” notion of periodic creation and destruction). The church heavily promoted this “scientific proof” of the correctness of its (post-Nicene) Christian theology.
People may be suspicious of the church but they implicitly trust scientists today. And, though few (perhaps 2 or 3 among the 1.25 billion in India) have read or understood Hawking’s scientific work, hundreds of millions of people strongly believe he is a great scientist. Such gullibility and implicit trust is bound to be exploited by the church, which is ever on the lookout for new ways of doing its propaganda. Few people are even aware that Hawking reached his conclusion by postulating his “chronology condition” which denies quasi-cyclic time, and does so using exactly the same bad argument that Augustine used against Origen, and which argument is at the foundation of post-Nicene Christianity. So, what Hawking did was to use the metaphysics of infinity to promote the politics of the church, like Augustine.