The Ockham Number
In this article, we will discuss the most important numbers in mathematics. When asking this question, , e, and i quickly come to mind. Slightly lesser known, but almost as important is the Ockham number. It reads:
864693479168447112251843599746282721640117719691245341864095905779036837961987439577508253143454375639656154381577119866841396926624582286205694192259244728774538892928151397460403074025894630594094594243042413689989468450326622129668087203805282692487000901835505868902065855514618000635846030314201373733206499158342554007121512289665910818015283095296784409270070279052349823894111903323351456497247523544978345560916587451773271003521023709225512167011420664230320744071454346477592018671521234944
This number is massive. In fact, it exceeds the expected number of atoms in the observable universe. Besides that, what makes this number so special? Based on the size of the number, you might already have a guess, but it will become clear with the introduction of the formula on the left (known as Tuppers formula):
We can plot all the points in the x,y-plane that satisfy this inequality (they are coloured black). The idea is to plot a section of the x,y-plane. More specifically, a 106 by 17 grid where x ranges from 0 to 106 and y ranges from k to k+17. Choosing a different value for k will give you a different graph. Plotting can be done by coding Tupper’s formula by yourself or by using the calculator at https://tuppers-formula.ovh/. Check what you get if you plot Tupper’s formula with the Ockham number as its k value.
You should get a recognizable result. Strange right? This number and this formula have always existed since the dawn of time and the obtained result has existed since the dawn of time as well. Only one conclusion can be taken, the Ockham Logo is immortal.
The magic (or maths) of this result lies in the formula itself. Tupper’s self-referential formula (or the “everything formula”) is a famous mathematical formula that plots everything. Well, it iteratively plots all possible 17 by 106 grids on top of each other. Essentially, every grid can get a unique 1802-bit ID, where the squares that are black and the squares that are white of a certain grid correspond to a binary number. Converting this number to base-10 and multiplying the number by 17 gives you k. Everything that can fit in this window is located somewhere in the graph of Tupper’s formula. This means the formula plots itself, your name, your kid’s name, and the UT logo.
Inspiration and reference: https://www.youtube.com/watch?v=_s5RFgd59ao&t=361s
Article by S.T.C. Fokkema (Math Track).
