Good morning Orfeas,

The thread is now off-topic, thus I changed the subject.

> > This can be made "the same" by any of the following methods:
> >
> > -   Burning the up-front fees.
>
> This would impose a hard maximum of 21 * 10^6 * 10^8 global lifetime hops, 
> and a much lower practical one. PoW OTOH doesn't impose such limits. Hence 
> different dynamics.

Granted, but do note that we can trivially "move the decimal".
Perhaps not "trivially" but it is possible to do so, thus still the same 
overall dynamics.

>
> > -   Locking the up-front fees for a time, then reverting them to the 
> > original sender.
>
> This means that I can burst-spam today, wait until unlock, repeat. If the PoW 
> scheme somehow enforces fresh PoWs (e.g. by needing (nonce || recent block 
> hash) as proof), I can't do this attack.

But in order for PoW to actively limit spam, the PoW target must be high enough 
that you can burst-spam today, wait until you get your *next* 
passes-the-threshold PoW, repeat.
The difference is that PoW has more variance, but that variance itself can 
limit non-spam usage (in much the same way that too high an up-front locktime 
would also limit non-spam usage).

I do not think you can get better than this, given the physics of this universe.
Money represents the allocation of available energy (by the simple mechanism of 
purchasing energy using money; the invisible hand is really the mechanism which 
directs energy towards the production of goods that are demanded), and PoW is a 
proof that somebody allocated available energy for the production of the PoW.
I do not know what argument you would consider "formal enough" but that is the 
only argument I have, and I find it sufficient.

Would this be enough?

We postulate that there is an amount of energy E, whose consumption produces a 
proof-of-work we can present on network, and that this required amount of 
consumed energy E is sufficient to deter spam.
The proof-of-work attesting to this energy E can be bought in a sufficiently 
mature market, using money, and thus this amount of energy E has some 
equivalent market price of money M, the spending of which is sufficient to 
deter spam.
If spending amount M was not sufficient to deter spam, or equivalently if M is 
too cheap to deter spam, then spammers will spend M to get E to drive 
proof-of-work instead of deriving their proof-of-work directly, increasing 
demand for energy until the market price of E becomes M' such that M' is 
sufficiently high enough to deter spam.

Or in simpler terms: with a stable enough monetary system and market, you can 
buy PoW, thus PoW and fees are equivalent.

Regards,
ZmnSCPxj
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