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I think you're arguing the wrong way around.

Useful PoW is totally fine for a cryptocurrency the same way useless PoW is - you have to solve a particular instance of some kind of problem, not just "computation that you were going to do already". I think Primecoin is a good example: the general problem that's being solved for mining happens to have a useful byproduct, but you still have to provide PoW on the particular instance that is on the chain.

Even Bitcoin has provided useful work for a very weak definition: it has created incentives for MASSIVE research and development in cracking or otherwise breaking SHA-256. I don't know where I could find data, but I would bet that there's an inflection point in "crack speed" around 2009, and that further progress probably correlates pretty well with the USD-BTC exchange rate.

Consider a situation in which the US government realises that primecoin's output is crucial to further quantum computer research. They pump 100s of billions into mining primecoin. Now, 99.9999% of hashpower and full nodes belong to the US government - an entity whose only interest in primecoin is as a minor return on some work to reduce costs.

In this case, every assumption of trustlessness and censorship resistance has gone out the window.

A consensus algorithm using proof of useful work will become a market of miners for whom the mining rewards and thus the integrity of the network are merely a secondary concern.

Mining inherently means whoever is most efficient ends up with 51% of the market. If companies X spends less than anyone else per hash they will end up at 51% unless they intentionally hold back.

However, proof of useful work could be a public good. Though that makes coming up with an algorithm much harder.

> Even Bitcoin has provided useful work for a very weak definition: it has created incentives for MASSIVE research and development in cracking or otherwise breaking SHA-256

And chip performance in general. It wouldn't surprise me if Bitcoin ASICs nudge the state of the art in chip design and fabrication forward.

Another (very marginally) useful bit of work mining does: converting electricity to heat.

I doubt many miners are currently using the heat, but it seems inevitable that eventually most miners would be located in areas where 1) electricity is very cheap, and 2) the heat produced by mining can be used productively

> Another (very marginally) useful bit of work mining does: converting electricity to heat.

In a stupidly wasteful way, though. Large-scale heat generation with electricity is better done with heat pumps, which have 400-500% efficiency.

Right, I agree that a useful PoW is possible in theory[1], but the requirements imposed (by needing to work as PoW for a blockchain cryptocurrency) are burdensome:

1) The difficulty must be adjustable so that you can make it harder or easier as computational power joins or leaves the network -- so it can't be some generically hard problem with no free parameter that affects the hardness.

2) The difficulty must be precisely predictable, so you know how much to adjust it for 1). That probably rules out NP-complete problems, where it's hard to generate random instances while ensuring you'll get one of the hard ones.

3) The problem must be capable of being arbitrarily generated from a random string, so that your work is associated with a specific ledger update (block), and so the work must have started after that node became aware of the block. This would require you to optimally "compress" the problem space so that a random string decompresses to a valid instance. But if you could compress the problem space that way, it wouldn't be hard!

Partial hash inversion (used in Bitcoin) satisfies those because:

1) You can adjust how many digits of a match are required.

2) There is no shortcut to guessing all the nonces, and each output is effectively a random number with predictable properties.

3) You can require the nonce to be prefixed by the Merkle root of the new block + previous Merkle root.

Edit: Primecoin was a good start, but it quickly exhausted all of the academically useful primes, and is unable to meet 1) while still being useful.

[1] At least, I don't know of a rigorous impossibility proof.

Your list is missing verifiable. What makes hashing < vale is useful is you get a high probability that someone handing a solution actually did a lot of work. Someone getting lucky could find a solution within a second using a CPU miner today, they are not going to keep getting lucky for 100 blocks.

Nobody is going to get lucky and find a solution within one second on a CPU miner, it's a 1 in 750000000000 chance.

Did you calculate that?

750000000000 chance every 10 minutes * say 1,000,000 CPU miners = 1 / 750000 per 10 minutes, and 1 in 14.27 per year. I don't think their are 1,000,000 CPU miners, but I suspect their are at least a few thousand of them for the lul's.

The ideal would be useful work that is a public good - no one can profit from it individually (other than by using it as a PoW), but the world benefits from it in some way.

Like carbon sequestration?

That's an interesting idea, but is there a way to prove carbon sequestration, except by providing me with some physical carbon?

It was more of an off-handed comment, but I suppose you could rig some sort of carbon sensor that measures X amount of carbon pulled from the atmosphere. Of course any sort of sensor to the physical world can be rigged to produce a false signal.

That's a really interesting thought. Would you consider public information (e.g. the result of a mining computation) to already be a public good?

E.g. see discussion of information goods here https://en.wikipedia.org/wiki/Public_good#Challenges_in_iden...

I wonder about some tasks that people already do for charity with their computers...like protein folding, finding super huge prime numbers. I don't know enough about the algorithms involved though to assert they satisfy the POW requirements. But some infrastructure already exists to distribute these problems.

Satoshi style PoW algorithms are intended to waste as much energy as possible.

PoW mining just raises the capital cost to control the network without ever improving the speed or functionality. It's a system that increases the waste as time progresses.

There is a market for public good: charities

You and I were thinking on similar lines. Since it's tech, my idea was the money went to FOSS nonprofits that focus on infrastructure like OS's, servers, crypto libraries, and so on. Even the GetRichCoin types building on that kind of foundation might do some incidental good for tech scene even if their plans don't work out.

Like Protein folding, Search for ExtraTerestrials, Asteroids, etc... there are a lot of them, some of which structured properly could provide public benefit.

https://en.wikipedia.org/wiki/List_of_distributed_computing_...

I'd like to suggest "AlienCoin": Proof of work consists of processing SETI@Home blocks, and mining rewards are paid out to whoever finds an alien civilization.

Gridcoin [1] has been a thing for a while and you mine coins by participating in BOINC [2] projects like SETI@home.

[1] http://www.gridcoin.us/

[2] https://boinc.berkeley.edu/

This isn’t mining is it?

If true (and I fear they are), then your arguments form a good reason to oppose cryptocurrencies as they exist today. They're wasting huge amounts of energy (and at this point significantly contributing to our energy and climate problems) for arguably little benefit coming from (IMO misguided) attempt at building a trustless system. Also, most participants seem to really be interested in them as get-rich-quick, fuck-authorities scheme, which makes cryptocurrencies an epitome of the concept of externality.

"if suddenly we've got useful works, such that you can apply that $X million in electricity to solve problems that are actually not wasteful, and worth perhaps $X million dollars in solutions"

first if we ignore the part "not everyone is going to have equal access to people who are willing to pay for solutions of useful work"

I think this can never happen.

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People should think PoW as lottery.

Every X minutes there is a prize draw giving you Y coins.

But ticket price converges to market value of:

ticket price = (Y coins)/(total tickets sold)

So if you add a value to 'not winning ticket' by introducing 'useful work', you are changing ticket price to:

ticket price = (Y coins)/(total tickets sold)-'work value'

so you are just giving coins more value, means making 'new ticket' more expensive.

new ticket = old ticket + work value

In the end you will still 'waste' the same amount at equilibrium.

Excellent reminder of why 'useful PoW' is a very bad idea. Furthermore, the value of 'useful' may vary over time to the point where it exceeds the value of mining. That is when a 'useful' corporation takes over mining and decides to kill the chain because 'useful inc.' is promoting its own corporate token (another bad idea: bad ideas generally lead to other bad ideas).

They could still be used for quid pro quo and rate limiting situations. I feed you a problem that is useful to my company and I provide you a free service in return. Because you have to have a PoW it’s more difficult for you to spam my service (you have to break other laws to do so), and even if you do I get reimbursed after a fashion anyway.

The thing being "spent" is no longer electricity but rather is the value of the work being completed.

That means the value would change if new ways to solve the problems arise. But currently the value changes based on your electricity bill (new tech could disrupt that too).

On a side note: it's proven PoW is centralized and does not in fact secure the coin. Only guarantees work, not security. Just not being used to double spend yet.

Can you elaborate? By whom and when was that proven?

Like every hashrate chart? https://medium.com/@homakov/stop-calling-bitcoin-decentraliz...