At first glance, this post has nothing to do with data science. I hope that by the time you finish, you will understand why it has everything to do with data science. The connection is the distinction between objective reality (being an object) vs. being a trace of an object.

Data science (and machine learning) is an iterative application of statistical math. Only the loss function changes, and the number and treatment of parameters. That's it.

Statistics, once the black sheep of mathematics, has come back with a vengeance, aided by its combination with matrix math. Statistical truths are compelling, but they are not truths, strictly speaking.

No essence of a thing is defined via statistical aggregation. You can chop the fourth leg off of every cat on the planet, and still, a cat has four legs, by definition. Thus, truth does not drift the way density functions drift.

This essential difference is captured in most pure form, in the consideration of the difference between "eternity" and "infinity." A difference, which I believe cannot be grasped without appeal to concepts that are fundamentally religious.

The following excerpt is from Kierkegaard The Concept of Anxiety, in which he argues that anxiety just is what it feels like to be a creature endowed by her creator with free will.

If time is correctly defined as an infinite succession, it most likely is also defined as the present, the past, and the future. This distinction, however, is incorrect if it is considered to be implicit in time itself, because the distinction appears only through the relation of time to eternity and through the reflection of eternity in time. If in the infinite succession of time a foothold could be found, i.e., a present, which was the dividing point, the division would be quite correct. However, precisely because every moment, as well as the sum of the moments, is a process (a passing by), no moment is a present, and accordingly there is in time neither present, nor past, nor future.

OK. Let's stop here for a second, because this is already getting dense. It's written in 1844 by an aristocrat with nothing but leisure time on his hands. The elevator pitch version (god help me for using this corporate metaphor) is this: The concept of time as succession is insufficient to explain the present. In other words, if time is always falling away, passing by, decaying, etc., then when is Now?

If it is claimed that this division can be maintained, it is because the moment is spatialized, but thereby the infinite succession comes to a halt, it is because representation is introduced that allows time to be represented instead of being thought. Even so, this is not correct procedure, for even as representation, the infinite succession of time is an infinitely contentless present (this is the parody of the eternal).

Again, let's stop to digest this bit. It says that you can try to conceptualize Now with a spatial metaphor, but that just yields a parody of now. I totally get this idea of drawing out the succession of time, before my mind's eye, in a literal timeline, and putting a blank circle in the middle of that timeline, in order to represent Now. But using a mental picture to make time stand still doesn't represent the present.

[…]

The present, however, is not a concept of time, except precisely as something infinitely contentless, which again is the infinite vanishing. If this is not kept in mind, no matter how quickly it may disappear, the present is posited, and being posited it again appears in the categories: the past and the future.

The eternal, on the contrary, is the present. For thought, the eternal is the present in terms of an annulled succession (time is the succession that passes by). For representation, it is a going forth that nevertheless does not get off the spot, because the eternal is for representation the infinitely contentful present. So also in the eternal there is no division into the past and the future, because the present is posited as the annulled succession.

Time is, then, infinite succession; the life that is in time and is only of time has no present. In order to define the sensuous life, it is usually said that it is in the moment and only in the moment. By the moment, then, is understood that abstraction from the eternal that, if it is to be the present, is a parody of it. The present is the eternal, or rather, the eternal is the present, and the present is full.