☞ Timestamping Science and Magical Text

How do you demonstrate that you know something—or discovered something first—without giving away your secret? This was an issue that loomed large in the early years of modern science, as scholars wished to maintain priority without telling everyone what they had figured out, especially if it involved work that was still in progress.

So, when I was reading James Gleick’s biography of Isaac Newton recently (it’s fantastic, so please go check it out), I was intrigued by the following quotation:

5accdæ10effh11i4l3m9n6oqqr8s11t9y3x: 11ab3cdd10eæg10ill4m7n6o3p3q6r5s11t8vx, 3acæ4egh5i4l4m5n8oq4r3s6t4v, aaddæcecceiijmmnnooprrrsssssttuu

This odd string of letters and numbers was written by Newton in a letter, as a way of demonstrating via a sort of encryption that Newton had figured out various aspects of calculus.

How did this work? As explained here, “he used a simple procedure: he wrote a sentence (in Latin) and then just counted letters in it. And the anagram consisted of the list of letters and how many times each letter occurs in the message.”

And this is not the only example. In another of Newton’s letters, there’s also this string, “6accdae13eff7i3l9n4o4qrr4s8t12ux,” used to establish priority for another facet of calculus.

These long strings of letters and numbers remind me of the output of hash functions, like MD5 or SHA-2, which are often used as checksums, to ensure such things as a file having been transferred correctly. The problem with this anagram method though, is that it is much easier to reverse. While modern hash functions that are intended for cryptographic use are designed to be one-way—that is, you can’t figure out the original data from the function’s output—this needn’t be true for these anagram-based trusted timestamp approaches.

In fact, an attempt to reverse one of these actually led to an inadvertent discovery. Galileo had used an anagram to disguise his discovery of the bumpy shape of Saturn—which were its rings, though he wasn’t quite sure what it was and described it has having three parts—through the use of this string: SMAISMRMILMEPOETALEUMIBUNENUGTTAUIRAS

Fellow scientist Kepler, however, attempted to actually determine what the converted phrase said by reversing the anagram. And in a strange twist, he came up with an entirely different Latin phrase, but one that was actually correct: that Mars has two moons! These moons weren’t discovered though until more than two hundred years later (the entire story can be read about here).

I would like to think that we have come far since these anagram-mad days, though I still think that scientific publication could use more than a few updates. That being said, seeing these scientific hash functions reminds me a bit of the writer Robin Sloan’s recent experiments with NFTs to create text-based amulets: short bursts of text that have a particularly rare cryptographic hash, giving them a special sort of value.

Are these mad alphanumeric strings from hundreds of years ago perhaps a bridge then between alchemy and magic and our modern understanding of our world?

Abracadabra, please meet 6accdae13eff7i3l9n4o4qrr4s8t12ux.

And as a bonus, I made the connection between magic and mathematics yet more explicit with this short snippet of code that hashes text into a string of alchemical symbols from Unicode:

Welcome to my laboratory

is transmogrified into


Please feel free to play with the code for Base🜀.


I recently had the pleasure of participating in a wide-ranging conversation that touched on the complexity of technology, the nature of knowledge, and much more. Watch it here.

A few links worth checking out:

Until next month.