Well... Now that we've had a nice little romp through history and answered pending mysteries via mathematics, philosophy, and the occult; it's time to make some decisions. Is there truly a third undiscovered Philosopher's Stone, and would revealing it it be more or less dangerous than the other two?

The Valenzetti Equation

The inciting article for our journey was "The Numbers" where I intended to expound on prime numbers, but introduced the television series LOST as a literary diversion. In the conclusion I asserted the LOST numbers, in the end, were numerical symbols and didn't function as actual numbers at all. Here's an update:

After the TV series started, some pople couldn't get enough of the mythology, including the writers and producer. They introduced additional material in the Lost Experience online. Part of the backstory was the origin of the numbers that Hurley believes are cursed. The LOST numbers are six variable values which plug into the Valenzetti Equation. Enzo Valenzetti was a reclusive Princeton mathematician who was tasked by the UN to predict the exact date and time of human extinction. It was a "Doomsday Formula" and the point of the DHARMA Initiative was to do anything to alter those values, which they never accomplished.

Diamond (Dog) Legacy

In "Comprisation" we moved on from prime numbers to discussing a unique combinatorial technique. My point was that the great thinkers have missed important discoveries because some types of problems present a maze, where a valid solution also precludes discovering the entire answer. It only requires a tiny diversion...

Issac Newton became a topic after I introduced planetary symbols in a puzzle. Essentially, I stumbled into Renaissance Alchemy, practiced by the greatest mathematicians of all time. A cascade of coincidences overflowed from there.

The banner art representing Newton features a section of burnt manuscript.

There really was a fire, but its cause and the extent of lost research is controversial. Newton claims he lost 20 years of experimental data when his dog knocked over a candle and ignited his papers.

That quote stuck me as odd even as I was first reading it. Aside from the "dog ate my homework" trope, "O Diamond, Diamond" seems somehow incongruous. Hennig Brand had recently revealed his discovery of white phosphorous. Given Newton's enthusiasm for alchemy I can imagine he obtained a sample and was surprised when it spontaneously ignited amongst his notes. The timeline fits perfectly.

Then, reading about the history of Tarot cards I discovered the popular card suit of Diamonds was renamed the suit of Pentacles, a symbol of Alchemy. Seemed like a fit, except the Rider-Waite (RW) Tarot deck only introduced "Pentacles" in 1910. Apophany? Maybe not. It turns out the RW deck was inspired by Sola-Busca Tarot deck from the 15th Century, back when the suit of Pentacles was still designated as the suit of Coins. A current scholar in describing the Sola-Busca deck writes,

"This is particularly evident in the suit of coins, which apparently illustrates the process of coin minting, but in reality alludes to the complex and secret practices of the Opus Alchemicum, that is, the method used to create the lapis philosophorum, the philosopher’s stone, alchemic instrument of immortality and perfection."
— Francesca Bezzone, PhD

So my theory is Newton started a lab fire while engaging in alchemy and encoded what happened by blaming his "Diamond." This is an entertaining aside, speculative, but not critical to our journey.

More interesting is the incidental selection of singed paper for the banner image. Newton was trying to determine the exact measurements of the Great Pyramid of Giza in this document. From these he hoped to update the measurement of the Earth given by the Greek Eratosthenes (yep, the Sieve of Eratosthenes and Armillary Spheres inventor again). Newton believed superior methods of measurement had been lost to time and with the precise calculation he could discover the sacred cubit of the Hebrews. From this he could reveal the architecture of the Temple of Solomon and thereby determine an accurate timing of the coming Apocalypse!

Careening Toward Catastrophe

In my "Traveling Salesman" article I mention an excellent book titled In Pursuit of the Traveling Salesman by William J. Cook. Cook dangles promise of a milion dollar prize to anyone who can definitively solve the Traveling Salesman Problem. The prize is offered by the Clay Institue of Mathematics because it would also be a solution to the P=NP problem. Overly simplified, an NP (Non-Polynomial) problem describes a problem space which grows in a Linear fashion while the work required to reach the solution grows exponentially. The Traveling Salesman Problem exemplifies this as each individual Location added requires an exponential number of new paths to be explored. Even with the best hardware, the amount of potential solutions explode into non-computability. The Prime Number problem is the quintessence of this type.

Aside from the promise of riches, Cook mentions a cautionary tale: The sci-fi story "Antibodies" by Charles Stross. The story starts when a software engineer is copied on an email with an algorithm, solving any Traveling Salesman Problem in finite time. He brings it to a coworker who's doctorate is in Discrete Number Theory:

"If this is true then every encryption algorithm except the one-time pad has just fallen over. Take a while to be sure, but . . . that crunch you heard in the distance was the sound of every secure commerce server on the internet succumbing to a brute-force attack."

"I wandered over to the coffee station, thinking very hard. People hung around and generally behaved as if it was just another day; maybe it was. But then again, if that paper was true, quite a lot of stones had just been turned over and if you were one of the pale guys who lived underneath, it was time to scurry for cover. And it had looked good to me: by the prickling in my palms and the gibbering cackle in the back of my skull, something very deep had recognized it. "

The story procedes with the message of the algorithm disappearing off the internet, the mathematician who announced it is killed by police in an unexplained "standoff", and a superintelligent AI begins hunting down and eliminating anyone who may have seen the proof.

The Enigma Machine

A sci-fi story seems like a good place to over exaggerate the dangers of an algorithm. Seriously, it's just math. Except "just math" can be deadly serious.

In 1939, mathematician Alan Turing extended the clock method of Polish code-breakers to defeat the German Naval Enigma machine. Many German soldiers were intercepted and killed as a consequence. Had Germany known Alan Turing held the solution to break their encryption methods, would they have sought him out for assassination? In a heartbeat!

Fortunately, Turing had the protection of his English Government, and by extension, all of the Allied Countries. But what if you broke the encryption of your own government, and in fact, the banking system of the entire world? Who would protect you then? And assuming you promised to keep it secret and perhaps even go into a modified "witness protection program," every military enemy of your country would seek you out, as would every international criminal organization. In "the interest of National Security" (or even Global Security), you may become marked for death. And like victims of the superintelligent AI in Antibodies, your friends and family would also be at extreme risk.

Millennium Prize or Sting Operation?

If the CIA is not already funding the million dollar "Clay Mathematics Institute's Millenium Prize" they should. Having "first dibs" on someone who can provide a solution seems wise given the inevitable consequences. A conspiratorial take would liken the Millenium prize to a "lottery sting" operation where fake prize announcements irresistibly pull in wanted fugitives. Mathematicians are not criminals, but intent doesn't preclude dire consequences (think "Sorcerer's Apprentice").

There are several individual categories of the Millenium Prize, and only the "Poincare conjecture" has been considered solved. Russian Mathematician and former UC Berkley fellow, Grigori Yakovlevich was offered the Clay Millenium Prize and a "Fields Medal" but declined both on "ideological" grounds. Instead he quit professional mathematics, refuses all interviews, and lives in seclusion in Saint Petersburg, Russia. Clearly a smart guy. Perhaps he read "Antibodies."

Is it Safe?

An astute reader should have concluded by now that I led them into an area of dangerous knowledge, or they are safe because this is fictional entertainment, or I am a kook.

When I first had success with the Prime Clock I did experience the described "prickling in my palms and the gibbering cackle in the back of my skull." I removed network backups of the project, and disconnected the computer from the internet. I was also very cagey about putting anyone else at risk until I had done more research into what exactly I had discovered. It didn't start with "Hey, I think I know how find the Philosopher's Stone," but rather, "What is this math thing that actually works, but supposedly shouldn't. Does this break encryption? Why so many coincidences surrounding this topic? Is this somehow forbidden knowledge?"

What started as a programming challenge has developed into a story on its own. I didn't hunt down things that seem coincidental, and honestly I don't like coincidence. Coincidence frequently tricks you into chasing false meaning. My article "Pareidolia" goes deeper into this. I try to call out some "Apophanies" I've had along the way so you will possibly be more receptive to the true Epiphanies. Frankly there are so many coincidences and repeating characters that come up organically that it would not feel very objective to sweep them all under the rug.

Here are some assurances:

• I am not a kook. I don't hold any undeclared metaphysical bias. My bias is to seek objectivity.
• This is not fiction. It's all true. I include a lot of links and references you can check. My goal is to communicate something fundamental. Entertaining presentation is so you stay engaged.
• It's unlikely I broke encryption and put you in danger. The Prime Clock might be something else I wasn't expecting to create. But I will use some occult techniques just in case.

Let's see what went into building the Prime Clock.

PART TWO »