Ergo, Bitcoin is Nash's Ideal Money

The math here might need fixing, but the idea presented is the correction direction to think.

Satoshi Nakamoto stated, “Bitcoin is an implementation… Nick Szabo’s Bitgold proposal” Here we want to explore the relationship between the two projects from a generalized view of Bitgold and in relation to Nash’s Ideal Money.

Bitgold is an extension of Hal Finney’s proof of work from a writing by Nick Szabo. Hal Finney’s Reusable Proof of Work allowed for the validation and transfer of proof of work tokens (as an extension of Adam Back’s Hash Cash idea/proposal). In a revision of Bitgold Szabo explains the crux of Finney’s implementation as well as the limitations of it:

Hal Finney has implemented a variant of bit gold called RPOW (Reusable Proofs of Work). This relies on publishing the computer code for the "mint," which runs on a remote tamper-evident computer. The purchaser of bit gold can then use remote attestation, which Finney calls the transparent server technique, to verify that a particular number of cycles were actually performed.

The main problem with all these schemes is that proof of work schemes depend on computer architecture, not just an abstract mathematics based on an abstract "compute cycle.

The incentive to create proof of work token’s creates a specialty hardware demand which then must be factored into the equation; from an economic standpoint:

...it might be possible to be a very low cost producer (by several orders of magnitude) and swamp the market with bit gold.

Szabo makes a critical distinction about Bitgold in this regard and this draws heavily on his thesis (and our thesis draws on this distinction extending it to Bitcoin):

Unlike fungible atoms of gold, but as with collector's items, a large supply during a given time period will drive down the value of those particular items. In this respect "bit gold" acts more like collector's items than like gold.

This is a tricky point to traverse. We can repeat his point in a different way and the reader can test the translation back with the quote. Gold, Szabo notes, doesn’t work how we are going to observe bitgold and collector’s item’s work. With gold if you flood the markets, it's fungible, you don’t necessarily decrease its market valuation. With bitgold, like collectors items, you do.

This point wouldn’t sit right with a lot of people. But what Szabo is referring to is the cost to produce a unit. When the gold market increases the supply of gold, it's typically not because of a dramatic reduction in the cost to produce but rather because of an increase in the demand for it.

Gold in this sense has a demand driven supply. Supply that exceeds that demand would devalue the units but gold is well understood to have a strong market equilibrium in this regard. Bitgold however, as an extension of Finney’s RPOW, did not have a supply cap nor such a thing as a difficulty adjustment algorithm.

The Synthesis of Ideal Money and Bitgold

Szabo made an innocent but in hindsight I think an extremely clever observation about Bitgold which was based on the fact that any Bitgold created or mined had a timestamp. Way back with Hash Cash there needed to be a central server that held a database of challenge strings otherwise the proof of work granted was always IRREVOCABLE. With reusable POW a user can exchange the POW for a new token, thus representing an exchange (to a 2nd user), which validates the initial work was done but invalidates the initial token so the receive benefits from from the valid work but the token can’t be double spent by the initial users that passed the token on. This was done with a central authority, a server, in which the code could be reliably audited (trustworthy but not fail proof etc)

The observation Szabo made is what we want to generalize into a formula:

…since bit gold is timestamped, the time created as well as the mathematical difficulty of the work can be automatically proven. From this, it can usually be inferred what the cost of producing during that time period was.

Here we can begin to see how Bitcoin is, in part at least, an implementation of Bitgold. But instead of having a finite supply of Bitgold and a difficulty adjustment algorithm Szabo notes that Bitgold from each period will have a relationship to the amount of units created in that period. If this ‘ratio’ is used as a value comparator between different periods then their values could be grouped such that they would be fungible from a cost of production basis:

Thus, bit gold will not be fungible based on a simple function of, for example, the length of the string. Instead, to create fungible units dealers will have to combine different-valued pieces of bit gold into larger units of approximately equal value.

This optimized comparative ratio is what we synthesize as being, by definition, Nash’s concept of Ideal Money which is a money that has a stable cost to produce per unit. However there are caveats to explore in this regard.

Nash’s is often misunderstood to be attempting to stabilize prices. Rather it is the effect of constituting a globally held inflation target that Nash was after. It was a certain type of depoliticization of the supplies of major global currencies. The basis for that target itself becomes susceptible to the political and economic pressures implied. A commodity that didn’t have a form of resistance to this economic significance would succumb to the pressures of such a role.

One such negative repercussion would be supply shocks created by technological advance. Nash’s is explicit about this and how weakness in this area would be a detriment to the usefulness of a commodity used as a global basis for our money supplies:

We can see that times could change, especially if a “miracle energy source” were found, and thus if a good ICPI is constructed, it should not be expected to be valid as initially defined for all eternity. It would instead be appropriate for it to be regularly readjusted depending on how the patterns of international trade would actually evolve.

Here, evidently, politicians in control of the authority behind standards could corrupt the continuity of a good standard, but depending on how things were fundamentally arranged, the probabilities of serious damage through political corruption might becomes as small as the probabilities that the values of the standard meter and kilogram will be corrupted through the actions of politicians.

This relationship between the cost to produce units and the quality of the money is something Szabo was discovering and referring to as “unforgeable costliness”. That is the crux for bitgold was the idea that you could forge the concept of the ‘work’ but not without spending the cost. The relationship between the cost to produce units was key.

It is not at all easy to understand these concepts, their significance, and their relationship to each other and it is quite interesting that both these men found ways to approach the same end from different angles.

Szabo goes so far as to explain Bitcoin as if understanding Bitgold is critical:

Here are some more specific reasons why the ideas behind Bitcoin were very far from obvious:

(1) only a few people had read of the bit gold ideas

This is reasonable because most economic philosophers, and notably but not limited to, the Austrian school, cannot explain their way past conventional paradigms to explain how otherwise wasteful efforts could create units of a money that have value in the market before they are denoted universally as money (not having a non-money use case.).

Asymptotically Ideal Money as a Process Control Solution to Bitgold

Szabo’s general observation about Bitgold seems to allude to a centralized market service that would provide a complex solution to a complex problem of evaluating all of the different Bitgold created in every period for all time.

But consider a generalized formula or rather the rearranged verbal implication of his observation when we ask “Why not adjust the difficulty of the problems to the totality of the computational efforts per period?”

This leads to the realization of the limitation that we can never predict the current/next period’s total computational efforts in order to prepare the proper difficulty adjustment.

Then then we have, I am told, a simple process control problem. We can simply set the new or next difficulty to the last period’s total mining efforts in order to re-adjust the new period to the target.

This process control solution then, if we are allowed to call Szabo’s intent to “re-group” different period’s supplies of bitgold in an optimized fashion an effort to ‘idealize’ the units, would be referable as ‘asymptotically’ Ideal Money. In such a scenario the cost to produce the units would constantly be behind the optimized goal but always re-averaging to ‘try’ to catch up to it the next period. For Szabo’s end it would be evermore so Ideal; for Nash’s end it would have the special stress resistance characteristic needed for use an Ideal basis.

Bitgold As a Formalized Implementation of John Nash's Ideal Money

From Nick Szabo’s BitGold:

…however, since bit gold is timestamped, the time created as well as the mathematical difficulty of the work can be automatically proven. From this, it can usually be inferred what the cost of producing during that time period was.

The total supply of bitgold:

Supply = sum of the periods of (problem difficulty / total architecture output)

Thus for each period:

Diffp = Sp (Wp)

With bitgold, anyone could mine as much as they want, but timestamps allowed for the distinctions of periods in which bitgold was mined. Szabo noticed we can equate pieces of bitgold by considering their value as ratios of their supply in a given period which values them at a ratio of their total POW.

Wp = Diffp/Sp

If 100 production units are mined in a time period and 200 production units in the next time period, the first bundle of 100 production units might be called 1 bitgold unit but the 200 production units mined in the next time period would also be 1 additional bitcoin gold unit.

Bitgold is a Eureka moment. In proto-cryptoexchangelandea all of a sudden there is digital gold everywhere.

Interestingly Nash calls for a money that has a supply governed in relation to the underlying production cost. Pieces of bitgold assayed with respect to the cost/production ratio are units of Nashian Ideal Money (whereas the production units are comparatively not Ideal).

The differences in production units per period and the effect on cost can be thought of as ore sent to be refined. We can consider 100 production units in a period versus 200 production units in a period each equalling 1 unit of Bitgold as if the former went through a doubly efficient refinement process.

Supply = sum of the periods of (problem difficulty / total architecture output)

Consider our formula where produced units are constant such that refinement is effectively at its optimum or negated as a factor. This is not unlike a scenario where miners are extracting ore and refining it at their optimums.

In real life this is a reasonable consideration also because it removes the need for an assaying mechanism/market.

The difference between the latter scenario as the optimal schedule and the former as the measured is the adjustment needed to recalibrate the ‘production unit supply’ aka stabilize refinement.

Consider Nick Szabo’s essay on dead reckoning which requires tuples involving direction, speed, time:

A dead reckoning itinerary can be specified as a sequence of tuples { direction, speed, time }. It can be drawn as a diagram of vectors laid down head-to-tail. However, as mentioned above, this diagram by itself, for nontrivial sea and ocean voyages, contains insufficient information to map the arrows accurately onto a Ptolemaic map (i.e. maps as we commonly understand them, based on celestial latitudes and longitudes), yet sufficient at least in theory to guide a pilot following such directions to their destination.

Here the direction gets us to our goal which is supply/period and thus to be over or under the rate in a given period is to be missing our direction (perhaps by left or right or west versus east etc). Every period the captain wakes up, reprimands his crews for veering off course, straightens the course and goes back to sleep.

With bitgold for any next period we can ‘assay’ the sum of the previous periods and adjust the difficulty based on the assumption of the previous period's architecture (the assumption being in an efficient market the previous period is the best guess of the POW of the next period).

This is comparable to governing by moving averages.

When, for each new period, we measure and re-target for a constant supply of production units the adjustment is the deviation of the average cost to produce/unit from Nash’s Ideal Money, For this the process is such that it asymptotically fluctuates around what is Ideal by Nash’s accord.

Notice we haven’t limited the supply but only governed quality of units from the Nashian and Szabian sense (of unforgeable costliness for Szabo).

A Means for Introducing a Money with a Standard Value

We had originally thought, at the time of writing the paper in the Southern Economic Journal, that the way to introduce a money which would have a value corresponding to the current market value of a "basket" of commodities having well-defined international market values would be to have, essentially, a variety of "currency board" which would issue the primary currency as well as functioning to stabilize the value of the currency.

But I also knew that, for commodities with typically fluctuating values, that it would be more desirable to use "moving averages" to stabilize the values used for those commodities.

But really, fundamentally, a link to a commodity like silver or gold has been, historically, a means for keeping governments, and the politicians in governments, honest about their service to society in providing a medium for exchange, for reserves, for savings, etc.

IF the concept can be accepted that "honesty is the best policy" then, achieved by honestly striving "central bankers" and governments, a procedure analogous to "inflation targeting" would be sufficient (and perhaps ideal). The inflation rate target would be ZERO (!!), but this would be measured in relation to commodities and/or services that are not in intrinsically limited supply. (There is a subtle point here.)~Ideal Money

What’s So Bitgold and Ideal about Bitcoin?

Thus, for example, were the “basket” of goods forming the index composed ONLY of the single item of gold, Element 79, then the rule would be for the gold price to be, in an average sense, constant. (So this is the same as a sort of "gold standard".) On the other hand typical standard "cost of living" commodities could be used.

My opinion now is that it is desirable that a standard for a comparatively "ideal" currency should be structured so that the form of money established would have some attractiveness for "hoarding" (so that sometimes people might hide some of it in their mattresses!). Thus, connecting with this desideratum, the use of commodities with more stable and more permanent values seems to have merits.~Ideal Money

Bitgold with a process control solution does render Bitgold to have a similar characteristic that Bitcoin has with the difficulty adjustment algorithm. Bitcoin has much more complex stages of evolution, however, here we mean to call attention to the concept of mean block time that is the effect of the difficulty adjustment algorithm that Satoshi implemented with Bitcoin.

We have already noted that Bitcoin as a low cost settlement medium would imply convergence of competitive valuation of major currencies should Bitcoin become a significant player on the global scale. Furthermore and finally, we make the observation, ergo, units of Bitcoin as an extension of, or produced in relation to, the asymptotically Ideal and constant supply rate of blocks, are then and thus themselves by Nash’s definition, Ideal Money.