Editing The Road to Reality Study Notes (section)

===3.5 Discrete numbers in the physical world===
What might it mean to say that there are minus three cows in a field?  An interesting question to start us thinking about the nature of discrete numbers and negatives in our world as defined as scalar quantities. Penrose states that only in the last hundred years that the integers in the negative seem to have direct physical relevance.

Electric charge is quantified in terms of integral multiples, positive, negative, or zero.  Further, the three quarks within protons have charges 2/3, 2/3, -1/3.  Is this the fundamental entity, and as such, the basic unit of charge is 1/3?  This is just one example of an [https://en.wikipedia.org/wiki/Multiplicative_quantum_number#:~:text=A%20given%20quantum%20number%20q,electric%20charge%20is%20one%20example. additive quantum number] and Penrose notes that our present knowledge is that “all known additive quantum numbers are indeed quantified in terms of the system of integers…” Further, Dirac’s [https://en.wikipedia.org/wiki/Antiparticle antiparticle theory] shows us a physical and meaningful use for the negative numbers in which the additive quantum number of the antiparticle has precisely the negative of the value that it has for the original particle.

Penrose ends the chapter by stating that there are other kinds of number that appear to play a fundamental role in the universe, the most important and striking of which are the [https://en.wikipedia.org/wiki/Complex_number complex numbers].  While they are fundamental to mathematics, “it is an even more striking instance of the convergence between mathematical ideas and the deeper workings of the physical universe”.