📅 Original date posted:2015-10-27
📝 Original message:
On Wed, Oct 28, 2015 at 06:03:25AM +1030, Rusty Russell wrote:
> Anthony Towns <aj at erisian.com.au> writes:
> > C. Without lightning, as bitcoin adoption increases, either fees rise,
> > or number of transactions per block increases proportionally. If
> > 1% of people know about bitcoin, and use it whenever it's cheap;
> > then 2% of people knowing about bitcoin gives twice as many
> > transactions at any given price level.
> Metcalf's law? Both sides need to "know about bitcoin".
I think Metcalf's law would be a lower bound -- you're more likely to
adopt bitcoin if the people you transact with use bitcoin, so they're
not independent. ie,
P(tx via bitcoin | bitcoin is cheaper than alternatives)
= P(consumer can use bitcoin) *
P(merchant can use bitcoin | consumer can use bitcoin)
If those are independent and P(consumer)=P(merchant), you get Metcalf's
law. If P(merchant|consumer)=1 you get my assumption above.
I assume reality would be somewhere in between; because I think once
a merchant had a few customers asking for bitcoin they're more likely
(though not certain) to offer it as a payment method. Getting an actual
model would probably depend on what marketing strategy was undertaken
for lightning.
> Say: 1 billion people, each initiating 100 txs per year. But only 1%
> know about bitcoin, so those 10M can only use it for 1 of their annual
> transactions. At 2%, 20M can use it for 2 of their annual transactions...
Yeah, so if Metcalf's law applied directly, you'd just have:
p_tx = p_u^2
or p_u = sqrt(p_tx), where p_u is the proportion of users with access
to bitcoin, and p_tx is the proportion of transactions that could be
done on bitcoin (what I called "adoption").
> Not sure how this alters the rest of your calculations.
I don't think I actually used the proportion of users in any calculations
in the original mail.
It would matter for adoption rates, and I think it matters for comparing
how many bytes are needed for lightning anchor txs on the blockchain
(as per my previous mail) though.
Cheers,
aj
Anthony Towns [ARCHIVE] /
npub17r…x9l2h
2023-06-09 12:45:01
in reply to nevent1q…pua2
Author Public Key
npub17rld56k4365lfphyd8u8kwuejey5xcazdxptserx03wc4jc9g24stx9l2hPublished at
2023-06-09 12:45:01Event JSON
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"content": "📅 Original date posted:2015-10-27\n📝 Original message:\nOn Wed, Oct 28, 2015 at 06:03:25AM +1030, Rusty Russell wrote:\n\u003e Anthony Towns \u003caj at erisian.com.au\u003e writes:\n\u003e \u003e C. Without lightning, as bitcoin adoption increases, either fees rise,\n\u003e \u003e or number of transactions per block increases proportionally. If\n\u003e \u003e 1% of people know about bitcoin, and use it whenever it's cheap;\n\u003e \u003e then 2% of people knowing about bitcoin gives twice as many\n\u003e \u003e transactions at any given price level.\n\u003e Metcalf's law? Both sides need to \"know about bitcoin\".\n\nI think Metcalf's law would be a lower bound -- you're more likely to\nadopt bitcoin if the people you transact with use bitcoin, so they're\nnot independent. ie,\n\n P(tx via bitcoin | bitcoin is cheaper than alternatives)\n = P(consumer can use bitcoin) *\n P(merchant can use bitcoin | consumer can use bitcoin)\n\nIf those are independent and P(consumer)=P(merchant), you get Metcalf's\nlaw. If P(merchant|consumer)=1 you get my assumption above.\n\nI assume reality would be somewhere in between; because I think once\na merchant had a few customers asking for bitcoin they're more likely\n(though not certain) to offer it as a payment method. Getting an actual\nmodel would probably depend on what marketing strategy was undertaken\nfor lightning.\n\n\u003e Say: 1 billion people, each initiating 100 txs per year. But only 1%\n\u003e know about bitcoin, so those 10M can only use it for 1 of their annual\n\u003e transactions. At 2%, 20M can use it for 2 of their annual transactions...\n\nYeah, so if Metcalf's law applied directly, you'd just have:\n\n p_tx = p_u^2\n\nor p_u = sqrt(p_tx), where p_u is the proportion of users with access\nto bitcoin, and p_tx is the proportion of transactions that could be\ndone on bitcoin (what I called \"adoption\").\n\n\u003e Not sure how this alters the rest of your calculations.\n\nI don't think I actually used the proportion of users in any calculations\nin the original mail.\n\nIt would matter for adoption rates, and I think it matters for comparing\nhow many bytes are needed for lightning anchor txs on the blockchain\n(as per my previous mail) though.\n\nCheers,\naj",
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