In 2007, I had the chance to work with Stephen Wolfram to design a medal to celebrate Gregory
Chaitin's contributions to mathematics for his 60th birthday.
Chaitin was still a teenager in the mid 1960s when he came up with the idea to characterise
randomness by looking at the shortest computer programs able to encode or algorithmically
compress a sequence.
Greg Chaitin is the only one living founder of algorithmic complexity among the three
main founders of the theory together with Kolmogorov and Solomonoff.
The motivation of the medal came from a coin or medal designed by Gottfried Leibniz.
A sketch drawn by Leibniz himself used to appear at the bottom of Greg Chaitin's homepage.
Scholars and curators from museums in Germany believe and agree that the coin or medal was
never struck or coined.
Chaitin has spent his career working on foundational questions in mathematics and computation,
and more recently in biology in which me and my team have recently made some contributions
that Chaitin himself follows closely and encourage us to continue doing so.
In some ways Chaitin has been a modernizer of Leibniz ideas regarding connecting computation
with areas of philosophy and epistemology.
Leibniz may have been the first computer scientist.
Early in his life, Leibniz developed binary arithmetic and the medal he sketched was somehow
in celebration of it.
I once visited Chaitin at his office and also at his house in New York by his invitation
and I had the chance to see first-hand his large collection of many items and books related
to Leibniz.
We spent the day talking about many ideas of Leibniz, the way he saw things were developing
for algorithmic complexity, and how he got to meet Kurt Gödel but he missed a meeting
he had with him in New York due to snow.
Here is a picture I took of him at the entrance of his office at the IBM Thomas Watson building
in New York.
According to the story, Kurt Gödel was very impressed by Chaitin's ideas and the reformulation
that Chaitin did of his incompleteness theorems in terms of information in combination of
Turing's work on computation.
Chaitin uses to think that algorithmic complexity is the result of blending classical information
theory and computability.
Stephen Wolfram is another great follower of Leibniz and he has written some great blog
posts about him where he covers some of his interests on early computation anticipating
approaches that we haven't even fully realised today, such as making the application of law
fully algorithmic or computational and he also shows some of his handwriting calculations
in binary as coming from a modern course in discrete mathematics or computation [http://blog.stephenwolfram.com/2013/05/dropping-in-on-gottfried-leibniz/].
[Chaitin cutting an \[CapitalOmega] cake at his 60th birthday party in 2007 with Leibniz
cookies and napkins printed with an \[CapitalOmega], also in the pictures are Stephen Wolfram and
Paul Davies.
Pictures by H. Zenil]
It was obvious that if we wanted a medal for Chaitin's birthday party, the medal had to
include the letter \[CapitalOmega] representing his \[CapitalOmega] number and so we used
Calude's calculation of the first digits of an \[CapitalOmega] number.
The halting and non-halting results for Calude's \[CapitalOmega] were represented by arrows
and lines below the letter \[CapitalOmega].
The upper background of the medal is a binary circular array.
Like Leibniz did, we wanted an inscription in timeless Latin, so we began looking for
a text to inscribe on Greg's medal, one that was related to his seminal work, soon we decided
that one of the Leibniz quotations appearing on Chaitin's webpage would be more appropriate.
And we also realised that this was the chance to finally cast Leibniz' medal after almost
300 years!
So I went about reconstructing it, noting every single detail.
I wrote some Mathematica code to incorporate every detail which could be used for an electronic
design to be finally struck.
Stephen Wolfram presented the medal to Chaitin during the NKS Science Conference on the 15th.
of July, 2007 at the University of Vermont, Burlington, U.S.
After discussions with Wolfram, we agreed on two of Chaitin's own most often quoted
statements encapsulating his most seminal contributions: "Everything can be summarized
in one thing, but that thing cannot be reached" (In other words: All computable facts can
be summarized in Chaitin's \[CapitalOmega] number, but that number is not itself computable);
and "Mathematical facts are true for no reason" something that Chaitin believes his \[CapitalOmega]
number implies.
The Latin inscription on Leibniz's medal can be read "To make all things from nothing unity
suffices", that is "You can represent every number using just the digit 1" while in the
inscription on Chaitin's medal says: "Everything can be summarized in one [\[CapitalOmega]],
which cannot itself be attained".
The original solid silver medal was given to Chaitin and nine more copies were made
of Merlin gold, one of which belongs to me.
The others were given to some of Chaitin's relatives, and to Armand D'Angour who contributed
with the Latin texts.
Cristian Calude and Stephen Wolfram have a copy.
Here are pictures of my own copy: