# Continuous versus Discontinuous

1. Sep 7, 2014

### afcsimoes

Considering:
a) The logical foundation of Mathematics and Mathematics as the foundation of Physics.
b) The principle of excluded middle (nothing can be simultaneously something and its opposite).
c) The ultimate physical reality: It must be discontinuous or continuous; it can neither be simultaneously both nor one or the other in random mode.
d) The concepts of Field and Wave are in the domain of the continuous and the concept of Particle is in the domain of discontinuity.
e) The Uncertainty Principle (Heisenberg) as a barrier to our knowledge.
f) Randomness versus uncertainty.
g) Godel's Theorems: the discontinuous “kingdom” cannot demonstrate its own consistency.
h) The Hypothesis of the Continuous versus Discontinuous and the Zermelo–Fraenkel set theory with all the possible axiom schemata.
i) The Field Equations and Wave Equations (continuous) versus infinite series (discontinuous).
j) In essence, the mathematical "operation" of "passing to limit” is an amazing jump to the void, a thinking inference that builds a bridge between the discontinuous and the continuous (and that works fine…).
k) The mathematical concept of integral (continuous entity) as the boundary for a series of a succession of terms, or the series of “infinite” infinitely small parcels, i.e. as small as you wish.
l) The same for the mathematical concept of derivative or derived function, based on the concept of "infinitesimal" and in the limit resulting from a sequence of tangents.
m) The perimeter of the circle as the polygon limit.
n) And so on…
All this seems to me that points to the following conclusion(s):
ULTIMATE REALITY is of continuous nature and multidimensional, which does not exclude the existence of entities apparently in the domain of the discontinuous, or so we interpret them as.
We are discontinuous entities of 3 or 4 dimensions and cannot perceive, in their full “glory”, entities of more dimensions.
Those entities appear to us like discontinuous ones because their multiple dimensions are “winded within themselves”, thus creating a region in the continuous space so different from the remaining that we observe them as a separated one from all the background.
We can describe the behavior of these seemingly discrete and discontinuous entities with equations of the domain of discontinuity, but that does not invalidate the nature of ultimate REALITY as Continuous.

2. Sep 7, 2014

### Drakkith

Staff Emeritus
PF rules do not allow for personal speculation or philosophical discussions. Thread locked.

Also, remember that math is a tool. Just because the math suggests something does not make it true. Ultimately, our theories have to match reality. That is the ultimate test of science. As such, it is impossible to find an "ultimate reality" since we can never know whether our theories are true or if they just appear to be true.