• George Samuels

Set Theory, Life Illusions & Bitcoin Databases

Note: This post was taken from a newsletter to my premium subscribers


I had a massive revelation last night...

It all started with a TikTok video:

This was related to the news about the Multiverse Theory being proven after the latest imagery of deep space was shared by NASA.

As I got thinking about how small we are, relative to the expansiveness of the cosmos, I then learned about Georg Cantor's Set Theory, which then led me to Cantor's Paradox, which led me to think about how we perceive "God" and basic human reality. Finally, it all collapsed into me realizing how Bitcoin's original design reflects the same principles 🤯

Let me attempt to explain.

1 - The Universe does not exist, but what's contained within it does

According to Set Theory, the size of a set is determined by its contained elements. This works if you can define the set maximum (e.g. a group of 4 dogs vs. a group of 4 cats are said to be of the same "size"). But what happens if you're dealing with an "infinite set" (like our expanding universe)?

The issue is that humans, nor our machines, can technically 'count' infinite numbers - we essentially run out of steam or energy somewhere. So we perceive there to be a limit or boundary. But these limits or boundaries are necessary illusions in order to make other (human) things more calculable, measurable, or simply comprehensible.

And if a universe essentially expands until it collapses or reverses, it doesn't technically "end", it simply starts over or its energy transforms. What seems like an end is the beginning of another cycle. The famous infinity ∞ and Ouroboros symbols visualize this well. Even the Aztecs used Quetzalcoatl (the feathered serpent) to illustrate the same concept:

2 - The illusion of separation

Ancient cultures have often spoken about the "illusion of separation" in our physical reality. The "we are all one" mantra.

The West looks at time linearly yet, as I have talked about in previous issues, some ancient cultures saw time as cyclical. Time "ends" if you coil out the serpent and lay it flat. But time loops if the snake "eats its own tail." The illusion of separation comes from laying the snake out and seeing the world similarly. It becomes one again if you re-connect the endpoints.

There's another aspect to the human condition here that is important to note. Most of us cannot fathom infinity, so we set agreed-upon conditions or boundaries to make sense of it. You see this play out in our day-to-day lives, even at a professional level.

For example, if you're a creative professional, you'll know the chaos that ensues when a client says you have "free reign," but in reality has hidden expectations of the outcome. Without setting some boundaries on the creative brief, you cannot align expectations. Boundaries provide focus. Kind of like a furnace for the fire.

Another example is say a CRM or database of contacts. The main database has a comprehensive list of all known contacts. But for you to make sense of any of them, you need to filter what's relevant for you or your task at hand. So you create filtered views.

By creating filtered views, you hide the rest of the database, in order to give you a sense of organization and control. A way to "bring order to chaos" or simply focus on what matters right now. Most humans cannot deal with everything, everywhere, all at once (head nod to the recent film of the same name below).

3 - A future Bitcoin world through the lens of {Notion} databases

The main revelation came when all these thoughts collapsed in on what a future Bitcoin world could look like.

I was speaking to a friend, showing her how I have all my Notion databases set up, and then it hit me 💡 this behavior I'm exhibiting, and what Notion is enabling, is what a future Bitcoin world could look like!

Because Notion makes the creation and management of databases so simple and intuitive, I've started using it to hold almost all my personal information, workflows, bookmarks, etc. And because it allows me to integrate with so many other popular platforms I use on a day-to-day basis, my dad in Notion is my source of truth, not my data spread across multiple other platforms (our current, Account-based model of the world - you'll hear this often talked about in the blockchain world).

In a UTXO (Unspent Transaction Output) model, data is served via the user, which is hosted on a public blockchain, and other accounts/platforms ask permission from the user in order to access their data on a blockchain.

It flips the entire model of how we currently host and engage with data in general.

In today's account-based world, users trust platforms to host their data. Those platforms trust a hosting provider (e.g. Amazon Web Servers). The only thing that would (technically) need to change, in a Bitcoin (UTXO-based) future, would be where these providers host their data. They wouldn't. Because the user would have it hosted "on the blockchain" themselves. Users would store and own their own data.

Applications like Notion - a popular productivity platform - could act as a wallet/interface where they see all their data. This means the future tech giants would be those who figure out how to create the best visualizers or aggregators of data, versus having to worry about being hosts, custodians, or data processors themselves.

And then when a user integrates with other platforms via their 'central' wallet, providing the appropriate permissions, other platforms will have to pay for access in the form of micropayments.

That's the future I see. But it has taken all this time to synthesize using current-day examples. I'll leave you with a quote from Charles Petzold, author of The Annotated Turing:

"For millennia, our ideas about numbers have been completely skewed and distorted. As humans we value neatness, order, and patterns, and we live in a world of compromise and approximation. We're interested only in numbers that have meaning to us. From counting farm animals, we have invented the natural numbers. From measurement, we have invented the rational numbers, and from higher mathematics, we have invented the algebraic numbers. We have plucked all these numbers from the continuum while ignoring the vast depths in which they swim like microscopic bacteria in the ocean. We live under the comforting illusion that rational numbers are more common than irrational numbers, and algebraic numbers are more numerous than transcendental numbers, and certainly they are in our manufactured lives. In the realm of the continuum, however, virtually every number is transcendental."

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