Why do we tend towards discretizing things around and within us? Do our senses (for space and time) fool us into this notion all the way into the need for discretizing abstractions themselves, e.g. An abstraction Truth is discretized into a word (a packet) and then we become inclined to encapsulate its meaning within that word. Other examples: I see a table and sense through sight and touch that it is bounded by a physical discontinuity (edges). I hear a musical note and it too is bounded in time. This effect conditions my thinking into seeking edges in abstract thought.
Don't you think you also tend to build continue representation of obviously discrete objects? Think how films are working: 27 pictures per seconds and there you think it's a continuous movement. Your mind even don't bother to inform your conciseness it's an illusion.
Both discrete and continue approach are used in our everyday representations of the world, as well as in abstract theories.
I propose the reason is a contemporary distrust of holistic thinking, combined with a contemporary obsession with analytic thinking. Consider the persistent myth of right vs. left brain. According to the myth:
right brain: emotion, intuition, creativity
left brain: logic, critical thinking, numbers, language
Regardless of it being a myth, I have found that those in philosophy and the sciences have a strong preference for 'left brain activity'. There is a different way to break this down, provided by William James in his Pragmatism: A New Name for Some Old Ways of Thinking. He breaks philosophers down into two categories:
THE TENDER-MINDED Rationalistic (going by 'principles'), Intellectualistic, Idealistic, Optimistic, Religious, Free-willist, Monistic, Dogmatical.
THE TOUGH-MINDED Empiricist (going by 'facts'), Sensationalistic, Materialistic, Pessimistic, Irreligious, Fatalistic, Pluralistic, Sceptical.
Regardless of right vs. left mythology, human psychology does seem to break down into the above two natural kinds—at least, the above two categories form helpful extremes. Now, many modern scientists tend to accept philosophy that is, or is derivative of, Logical Positivism. Today people tend to call themselves 'naturalists' or 'empiricists' or 'physicalists' ('materialist' has gone out of fashion, given the preeminence of thinking in terms of energy in physics today), and while only LP strictly entails being 'tough-minded', many seem to be nonetheless. An example can be found in the article Heretic: Who is Thomas Nagel and why are so many of his fellow academics condemning him?
Roughly, rationalistic philosophy values coherence and beauty over specific matching of reality in all respects, while empiricist philosophy values correspondence with reality over coherence and unity. This needs verifying, but I suspect that rationalistic philosophy has not been credited with much advancing of science in the last several hundred years, while empiricist philosophy has. Massimo Pigliucci suggests this might be a problem:
Lee Smolin, in his “The Trouble with Physics” laments the loss of a generation for theoretical physics, the first one since the late 19th century to pass without a major theoretical breakthrough that has been empirically verified. Smolin blames this sorry state of affairs on a variety of factors, including the sociology of a discipline where funding and hiring priorities are set by a small number of intellectually inbred practitioners. Ironically, one of Smolin’s culprit is the dearth of interest in and appreciation of philosophy among contemporary physicists. This quote is from Smolin’s book:
“I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today — and even professional scientists — seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historical and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is — in my opinion — the mark of distinction between a mere artisan or specialist and a real seeker after truth.” (Albert Einstein)
Note the "thousands of trees but has never seen a forest". This would be a preference to focus on particulars—an empiricist attitude—over and above a focus on universals—a rationalist attitude. I propose that Albert Einstein, Lee Smolin, and Massimo Pigliucci are correct: we need to find new, productive, holistic ways to think about science, ways which don't just discretize and reduce to basic elements.
The current scientific view of nature is that it is discrete. Discrete particles arising from quantum fields make up the standard model of physics. Continuous systems arising in classical physics are just approximations for when the particle numbers get very large. We are physical systems (including our brain), so maybe the two are related.