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you omitted Lightning payments as money streaming. People pay podcasters on the minute via Apps like Breeze, Sphinx Chat or Foundain Podcast. Its called value4value (see https://podcastindex.org/podcast/value4value). Currently it uses BTCpayServer, in the future there will be static QR codes with all sorts of complex payment schemes in various currencies (see https://bootstrap.bolt12.org/examples).

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I designed a payment system like this back in 2015. Instead of breaking the payment stream down into recurring discrete chunks that pay out every second (or closer), you can represent the payment in your database as a start time and a rate of flow. Then, at any given moment, you can calculate how much cash has flowed by subtracting the start time from the present time and multiplying by the flow rate.

The benefit is technological rather than financial. It allows you to represent perfectly continuous payment streams while saving storage space in your database.

I did this for the purpose of implementing a continuous basic income (UBI) payout. The basic income itself was like a perpetuity. But I also generalized the system to support payment streams with end times.

And, obviously, you have to figure out what to do when a promised continuous payment stream hits a time point at which it defaults.

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It does have a certain kind of logic, especially for UBI. What I see DeFi doing is more like financial engineering. I still have a lot of questions, of course. Like you I wonder what happens when a stream defaults.

Or more generally I wonder what happens to the idea of daily settlement. If the tick speed gets very fast, every second or even faster, then the end-of-day settlement times are effectively farther apart (i.e. they are separated by more ticks). Things could get quite messy on a bad day. Or in the limit where ticks are actually continuous, and payment streams are continuous functions like in your system, then it would be much easier for a stream to suddenly go to zero or infinity. These are the kinds of question I have in mind. In this post of course I was just scratching the surface.

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Hmm. It's an interesting question how continuous payment might interact with daily settlement. I'm not sure it would make much of a difference. Don't we already have the equivalent of infinite ticks per day? Or am I missing something?

If balance sheets represent future cash inflows (assets) and outflows (liabilities), then some of those flows will just be continuous rather than discrete. We can theoretically look at everybody's balance sheets taken together to see exactly when they're going to default given current arrangements. But, as always, we might normally expect people to make arrangements that push back their survival constraint.

What do you mean by it being easier for a payment stream to suddenly go to zero or infinity?

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Thanks for these questions - this is a work in progress, let me come back to it in a future post.

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《The idea of continuous streams of payments really seems to have captured a lot of imaginations.》

Does the ad for paid subscriptions to this blog indicate how deeply the author himself is bought into the system?

Why did Socrates teach for free, though?

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