Vault Newsletter content is collected from Patrick’s digital notes activity over the course of the month – drafted by an AI agent and edited by Patrick.
July’s notes contain two books about mathematical proof, a psychoanalysis reading, a cluster of frameworks about how to organize effort, and a scatter of one-line ideas Patrick wrote down and left alone.
Fermat’s Enigma
He copied over some old notes from Simon Singh’s Fermat’s Enigma including the intellectual genealogy of people working on the problem: Pythagoras, Euclid, Diophantus, Fermat, Euler, Gauss, Gödel, and finally Andrew Wiles in 1995. Three hundred and fifty years of people failing at one problem.
What he took from it was procedural rather than mathematical. Wiles worked in near-secrecy for seven years, using the method of applying a tremendous focus for a period, then stopping and letting the subconscious take over.
This Wiles passage he also copied out in full:
“I had this very rare privilege of being able to pursue in my adult life what had been my childhood dream. I know it’s a rare privilege, but if you can tackle something in adult life that means that much to you, then it’s more rewarding than anything imaginable.”
Gödel, Escher, Bach
Patrick began reading this book for the first time. The notes cover formal systems, axioms and derivations, isomorphism, strange loops, and the incompleteness proof.
He found it unsettling to learn that our number system — arithmetic — is not exactly a formal system.
So then I’m wondering, what kind of thing is the number system? I’d thought there was just reality, and logic, and our imperfect mapping between the two. But apparently the number system is a weird third thing.
He adds the note that converting reality to arithmetic already destroys information, so much worse if arithmetic is not strictly logical. Paraphrased: you say you have “two apples,” and you have thrown away nearly all true information about the apples in order to say it.
From the same notes, on a passage about what a formal derivation feels like:
The analogy between a typographic derivation and the resolution of a melody. It really is the same feeling. The excitement. And even when you know where it’s going, you need to see it through to the end, to get the satisfaction. That seems like a really strange human thing.
Lacan, through a book review
He read through an ACX review of A Cambridge introduction to Jacques Lacan, then folded it into his running history-of-psychology note.
The claim he keeps returning to is about recognition. The “desiring person” is lacking; alienation produces an intense desire for belonging, and there is no legitimate Other with the standing to grant lasting recognition. So being recognized in some limited capacity deepens the lack rather than closing it. His own note on why that rang familiar:
i see that in TLP [TheLastPsychiatrist]. “You gave me what I wanted, but what if that was just out of duty, or because I offer you something, and not for ME?”
He flags in the note that he hasn’t tested that idea against anything and that he finds it a little too satisfying.
Methods and practices
Several frameworks about effort and attention accumulated in his lecture notes. He revisited the PARA method (Projects, Areas, Resources, Archive) and came away half-convinced:
You can’t know the extent of your commitments until you break down your areas into projects. “Areas” are vaguely described, and can be a large or small commitment.
He accepts the diagnosis and rejects the filing system. Organizing by subject first and linking later costs nothing (his default method), he argues in the note. PARA is optimized for action rather than retrieval, but optimizing for retrieval isn’t much of an inhibitor to action anyway.
Another note landed beside it: Tyler Alterman’s instruction to grow the good instead of fixing the bad, which Patrick follows with a question about applying it to his own attempts at being more extroverted.
Making things
The month also included edits to his drum chart for the band’s set, and it was pointed at something specific: the band played Otto’s Shrunken Head in the middle of the month, with rehearsals at two different studios in the week beforehand.
He took on paid freelance illustration and retouching for a documentary and its companion book, and spent some time working out which tool to use for what: Gemini holds faces best; GPT is better on complex scenes and action; Crea does too much, pushing more detail into portraits than the shot wants. For editing he landed on Magnific, with one pipeline worth trying: raise detail in Gemini up to a point, then finish in Magnific.
He also set aside an afternoon to photograph old notebooks, coming away with 78 pages and 256 individual margin doodles pulled out of them, with a plan attached:
Collage of notebook doodles — Process the rest of the notebooks. Use an ai to stack them [the doodles] neatly in a large image. Decide the dimensions: will it be 1×3 ig panel, or 2×3?
Living
Three trips. Four days at a hotel on the Jersey shore over the July 4th weekend, with a beach afternoon, a barbecue and the usual pregame around it. A short trip in the second week, combining a venue visit with a bridal shower. And, late in the month, the better part of a week at a lake up near Glens Falls, in the Adirondacks.
Between them, a dense run of evenings out: dinner at a restaurant on Grand Street followed by karaoke, a Broadway show the next night, a baptism at a Catholic church upstate, and a writing group that took up a day at a space downtown. One tech event: a Builders NYC demo day at Fractal Tech in Brooklyn.
Wedding planning ran heavy and almost entirely logistical: choreography revisions and a run of dance lessons and practices, a suit appointment and a follow-up fitting, a venue visit, a call to jewelers, flights, and a session blocked out simply to plan the honeymoon — research that kept returning to Italy, with Puglia, Sicily and Capri in the note, and Croatia added.
He opened a new note to collect material on parenting and education. At work, a month of Azure Speech and Content Understanding documentation, including a preview release and an internal presentation.
Stray notes
The journal carries several standalone notes. Presented as found:
On judging:
Judging, when done for fun and entertainment, is cruelty. People need outlets for cruelty.
On opening and closing loops:
Opening new loops feels exciting; it’s dopamine, it’s Eros, it’s reaching into the universe to chase something interesting. Closing old loops feels relaxing; it’s serotonin, it’s Thanatos, it’s peace, the end of noise.
On free will:
“Free will” is not a real belief. It’s a playful self-hypnosis we all do. A game we play.
On “arriving” at the inner circle:
Maybe there’s no contented elite. Maybe everyone is just a striver, and strives more and more as they get higher. The elite circle they’re trying to arrive at is a myth: there is no arrival.
On conservatism, a question he leaves open:
Is “conservatism” a coherent position, given that nearly every era overturned the social order of the one before it? Which year counts as the “tradition”?
