Een brief die nooit zal aankomen

Een brief die nooit zal aankomen

En vermoedelijk, zo goed als zeker, ook nooit zou zijn verzonden. Gericht aan Stephen Hawking.

An analogy between mathematics and the universe

Consider the graph resulting from a logical inference process for a given axiom system. Each node in the graph represents a logical sentence and therefore a tautology within the axiom system.
Now let some set of physical laws correspond to some nodes resulting from the graph accompanying a supposed axiom system describing the universe.
Furthermore, let the universe itself be a spatial representation of the graph resulting from the axiom system describing it, including all of its patterns and complexity.
This analogy may perhaps provide some inspiration in developing an additional view on the possibly self explanatory nature of the universe and its seemingly intrinsic connection with mathematics. To continue the analogy, a choice of boundary conditions for the universe may correspond to a choice of axiom system which in turn may correspond in its spatial form to the basic patterns and building blocks from which all spatial complexity results. An obvious flaw of this analogy would be the static nature of the infinite graph in contrast to the perceived dynamic nature of the universe. In an effort to overcome this flaw, the arrow of time may point in the direction of the expanding process of logical inference.
As an educated mathematician consiously limited in my capabilities, I dare to cherish the dream of a bijection in some form or the other, accompanying this mere analogy. Furthermore, may I dare to dream to have planted a fertile seed of thought into a fellow sufferer of fate far outreaching my own capabilities of investigating the value of this idea.

As this thought crossed my mind, I felt the need to share it with someone who might appreciate its, at least to me, inspiring character, for I am only human.


P.S.: I have greatly enjoyed the parts of your popular work I have yet had the chance to read, in particular The Emperor’s Mind and A Brief History of Time.

Mijn kijk op de relatie tussen wiskunde en de fysische werkelijkheid is ondertussen wat veranderd. Ik heb wiskunde meer aanvaard als een menselijke poging om zijn omgeving te kunnen bevatten in geïdealiseerde concepten.
Hoewel ik ook nu niet kan weerstaan aan de gedachte dat wiskunde waarde op zichzelf heeft en niet ondergeschikt is aan de werkelijkheid waarin de mens deze heeft bedacht of ontdekt, dus toch weer richting een meer Platonische interpretatie. Enfin, we kunnen hierover blijven doorbomen.
Misschien toch nog rechtzetten dat “The Emperor’s New Mind” van de hand van Roger Penrose is :-).

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