Tuesday, January 29, 2013

Physics, Economics, and the Value of a Bitcoin

Grand Unified Theory of Physics and Economics

Here I set forth a conceptual unification of fundamental physics and economics, the basis of which is the unification of the concepts of energy and money.  Just as energy is only useful for doing meaningful work to the extent that it is organized into relatively rare & unlikely low-entropy configurations (in other words, has high negentropy, i.e. has a greater purity of free energy content), likewise money - any item to be exchanged for services - can only cause meaningful work to be done if that money is embodied by a relatively rare, well-organized configuration of mass-energy, for example a bar of gold - and even "abstract" forms of money such as bank balances and Bitcoin accounts fit this definition, since for a large amount of notional money such as this to be concentrated into a single account is a relatively rare occurrence, or must be if that currency is to be valuable.  

I will argue that this similarity of properties is not just a coincidence, but rather that, at a deep level, money and energy are fundamentally the same thing; it's simply that money is a form of energy that is organized on typically very high level, in a form that's well suited for causing or impelling useful work to be carried out by complex economic actors (e.g., humans and organizations), not just simple machines.  Sophisticated modern forms of money such as financial derivatives, Bitcoin balances, etc., are simply very complex arrangements of energy.  Their usefulness hinges on their rarity, just as the energy flowing from the sun is useful only because a spherically-symmetric radially-directed flow of energy is relatively rare and well-organized, compared to a configuration wherein energy is flowing uniformly in all directions, i.e. a thermal heat-bath with a blackbody spectrum, which is the maximum-entropy configuration, from which, in isolation, no useful work can be derived.

One form of organized monergy.
Now, some would argue that money cannot possibly be equal to energy, because the price of, say, oil in dollars fluctuates over time.  But this merely has to do with the relative sizes of our estimates of how much work can be done with a given quantity of money/energy (henceforce called "monergy") in these two forms.  If the entire universe was nothing a giant blob of light sweet crude petroleum, it would have no capacity to do any useful work, and therefore no value, because (without suitable machinery, or even oxygen to burn it) there would be no way to transform it into interesting new configurations.  Similarly, if the U.S. government declared that any slip of paper with a number of dollars written on it was henceforth to be considered legal tender, all dollars would immediately become worthless because (since anyone can easily create them in unlimited number) they would provide no one any motivation to do any useful work.  The end result in both the all-oil world and the free-dollars world would be the same - no useful work can be done with monergy in those forms (oil-universe, handwritten bills), only the details of the failure mechanisms are different.

Exchange rates therefore reflect economic actors' assessment of the relative utility of monergy (a.k.a., assets) in different configurations, which depends on factors such as their rarity, and the available instruments for causing useful work to be done by them.  Exchange rates do not reflect the total underlying amount of monergy contained in, or represented by those assets.

A device for extracting 50% of total mass
as useful monergy.
In fact, when talking about total monergy, it is equal (by E=mc2) to mass, and so in raw monergy terms, a kg of lead is equal to a kg of gold, even though their utility in the present economic environment is different.  However, if we had a small black hole nearby, and a mechanism for extracting work from objects by lowering them into it, the two kilograms would have exactly the same value, namely the energy equivalent of 1/2 kg (the extra value of the gold as gold would be negligible in comparison).  So, exchange rates always vary depending on the availability in the environment of mechanisms for harnessing a given form of monergy for a given purpose. 

Locking up valuable paper documents is much
more intuitive than mastering computer security.
In the case of Bitcoins, they will automatically gain value as tools for securing them from loss/theft and exchanging them become more readily available.  Arguably, gold is only more valuable (in toto) than Bitcoin today because anyone can easily lock their gold in a safe, and gold stores are available on (it seems) almost every street corner, and gold has a long and reliable tenure as a medium of exchange.  If Bitcoin were similarly accessible to (and trusted by) the layperson, it might have comparable value.  Every application for generating Bitcoin accounts ought to have an option to print out the private keys (or key-generation passphrase) as a sequence of human-readable words (like Electrum does), so that the user can write it down and lock it in a safe, or a safety deposit box, if he wishes.  People understand safes, and safety-deposit boxes.  And they understand securing valuable paper asses, like savings bonds, in that way.  Keeping keys for long-term wallets in electronic form is not advisable for the average user, due to the potential for theft via malware/hacking.  Paper records, on the other hand, are simple, intuitive, and unhackable without direct physical access.

How much monergy is a Bitcoin potentially worth?

The purest form, perhaps, of monergy is the traditional concept of the Joule of stored work energy, a.k.a. "free energy."  A 101.97-gram deadweight mass which has (under Earth standard gravity) a 1-Newton weight, raised up on a pulley to a height of 1 meter, is one canonical example.  An efficient generator can easily convert its gravitational potential energy to other useful forms such as electricity.  In general, the set of mechanisms that can convert monergy into other forms with close to 100% efficiency define a set of forms that monergy can be in that are effectively equivalent to each other.  No form of monergy can be more valuable than those in this set, because these are the forms that are most generally useful.

What is the long-term exchange rate between Bitcoin monergy and these "pure Joules," as it were?  This is perhaps the most meaningful measure of the value of Bitcoin, since the more traditional measures of value (e.g., sovereign currencies) are tainted by their potential for debasement and hyperinflation.  Even gold suffers from a long-term potential for debasement by over-mining and nuclear synthesis.

A typical supertanker today carries about 2 million bbl
of crude oil, worth about 10 aspirational bitcoins.
Well, we can, at least, set an upper bound on Joules-per-Bitcoin, and that is simply this:  If Bitcoin is to successfully take over the world economy, Bitcoin (as a movement) must (eventually) secure its position by being able to purchase at least half of the total world energy reserves in Joules that are known to exist at any given time, since otherwise a sufficiently determined attacker could potentially accumulate the majority of those reserves, and use them to buy enough computing resources to out-compute the rest of the network, and thereby take over the block chain, with potentially malicious intent.  This means the total value of Bitcoin needs to eventually become equal to at least half the world's energy reserves, to secure majority control.  Since the limiting number of Bitcoins is 21 million, this means that 1 BTC will eventually (in this scenario) attain a value of 1/(42M) of the world's energy reserves.  (Was Satoshi a Douglas Adams fan?).  Total energy reserves are a moving target, due to development of renewable energy sources, but as of today, reserves from non-renewable (fossil-fuel) resources are estimated at 57 ZJ (zettajoules) (en.wikipedia.org/wiki/World_energy_resources).  That puts the aspirational monergy value of 1 BTC today (just counting non-renewables) at 1.36 PJ (petajoules).  In standard barrels-of-oil-equivalent (boe) terms, that is 231,500 barrels (roughly 1/10th of a supertanker), which, at today's crude oil prices of around US$100/barrel, means about $23 million, in today's dollars.  This puts 1 Satoshi (the smallest Bitcoin unit, 0.01 microbitcoin) as worth about 0.365 liters of crude oil, or $0.23. 

A typical thermal solar power plant.
What about renewables?  Arguably, a sane global power would use its reserves of non-renewable energy strategically to build up its industrial capacity for producing renewable energy, since that is the only way to ensure its continued dominance after the non-renewables run out.  Arguably, this is what many of the world's major powers have been busy doing, to some extent, for the last century or so, namely, racing to build up their industrial capacity with an eye towards that end-game.  So, a portion of the value of even non-renewable energy today derives from their perceived future utility in terms of deployed industrial capacity to produce energy from renewable sources.  Thus, to some extent, the value of the non-renewable reserves reflects the net present value of all future renewable energy produced from all sources, so basing the above calculation on non-renewables only is still meaningful.  Currently, renewables (even including food crops) supply only a relatively small portion of total energy used annually by the industrial economy.

The Local Group of galaxies, as the largest gravitationally-bound
object of which we are a part, is the aspirational Bitcoin empire.
1 BTC can get you a duchy with a hundred thousand stars.
In the more distant future, if we imagine that our civilization moves to renewable energy, masters space travel, and eventually colonizes our galaxy and the other galaxies to which it is gravitationally bound (i.e. the local cluster), we can foresee that eventually we may command all of the free energy in that part of the universe.  With the local cluster weighing in at about 5 trillion solar masses, if we carefully compacted it into a black hole, we could theoretically extract about half of that mass as pure energy, or about 5×1059 joules.  A 42-millionth portion of this, the pure-energy equivalent of about 100,000 solar systems, would be about 1052 joules, or 1.8×1042 boe, or equivalent to about 1036 supertankers of oil.  Therefore, in this scenario, 1 Satoshi or micro-bitcent is the very-long-term, aspirational, monergy-equivalent of about $2 trillion trillion trillion in today's dollars. 
The globular cluster M15 has about 100,000 stars, or about one 42-millionth the
mass of the Local Group, so it might sell for about 1 Bitcoin someday.
Of course, before then, the Bitcoin protocol might need to evolve somewhat, since a civilization spread out around a 2.5-trillion-solar-mass black hole would require more than the canonical block-generation interval of 10 minutes to distribute new blocks to the whole network even at the speed of light, so there would be a lot of block-chain forking if this were not fixed, and also double-SHA256 would probably be easily hackable by then, so the proof-of-work hash function would need to be upgraded.  However, these are not fatal flaws, and might be easily fixable by community consensus.  I previously described how secure electronic voting can be carried out through the blockchain, so that the community can reach consensus regarding what protocol changes to adopt.


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