Time, Energy, And The Triangle Game

allen farrington
6 min readFeb 20, 2021


Part III of the Bitgenstein Serialization

photo by Ryan Geller, via Unsplash

Have you ever played The Triangle Game? Here’s what you do: get in a big group and instruct everybody to mill around aimlessly. While this is happening, instruct everybody to pick two other people, but keep their choice to themselves. Then, on a signal, tell everybody to move to form an equilateral triangle with the two people they chose. Then, watch chaos ensue. Even if the activity of the network as a whole ever seems to calm down, it can just as easily spiral out of control again with one step because one person moving may be reacted to by others, which may be reacted to by others still, and so on. Every individual decision has effects that permeate unpredictably through the entire network, unevenly over time, while every individual decision-maker is only immediately aware of the dynamics in their small locality, just like in a network of economic exchange.

Asking an individual to evaluate an invariant of the economic aggregate in terms of only their own supplies and demands is rather like asking a participant in The Triangle Game to explain the average speed of every player solely in terms of their own next step. You can’t even begin to explain it. And that’s holding just about everything we can constant in a small environment: if millions of participants started periodically changing their choice of vertices and entering and exiting the game, all while the geography on which the game was being played was shifting under their feet, that might start to better resemble real economic activity.

We need to ask what participants in an economic network are giving and getting in a deeper sense than the highly circumstantial and reflexive prices at which they are faced with buying and selling. What opportunity cost do they all have in common? Consider that rather than accepting a price that is dependent on literally every other demand and supply in the network, you could always make the widget yourself. If there are literally no widgets for sale anymore, you needn’t assume your purchasing power has “infinitely decreased” if the inputs can still be purchased and the knowledge of how to combine them still exists and can be accessed. You can still “purchase” a widget, and you can still sensibly conceive of its cost: that of the initial purchase of the inputs, plus the opportunity cost of your own time and energy, since any time and energy you devote to making a widget you can’t devote to making or doing anything else that might later be traded for money.

If, on the other hand, widgets are still mass-produced, you will very likely find that the difference between the cost of the inputs versus the available market price of the finished widget is one you cannot reconcile as a viable opportunity cost of your time and energy turning one into the other. Since so much effort has been put into minimising this exact opportunity cost of time and energy on the part of the widget manufacturer as a requirement to stay competitive, you will probably rather pay the difference than commit this time and energy yourself.

Upon reflection, this process and mentality is exactly the same for anybody who transforms one good or service into another in order to later sell at a profit: that the price is deemed by buyers to be an acceptable equivalent of their time and energy, that the costs were treated in the same way by the (current) seller, and that the hoped-for profit is deemed the best use of their time and energy in transforming one into the other. In setting out to make our own widgets, whoever we buy the squidgets from will have gone through the same thought process and calculations. The gwidget-makers (you need a gwidget to make a squidget) will have done the same.

And so on, all the way down to the absolute origin of the supply chain of every good or service. If a good, extracting raw materials, which, if you own the land, takes only time and energy; if a service, only time and energy; if, in either case you nonetheless require tools, back into the loop you go. The entirety of the chain of prices across all exchanges is shown to be a series of independent and real-time decisions about how to value one’s own time and energy and best guesses as to how others value theirs.

We can readily imagine, if you go back to trying to create your own widget, just how long it would take if you were committed not to use money to pay any upfront costs for inputs but to spend only your own time and energy fashioning everything required from beginning to end. The difference between however you value this presumably enormous amount of time and energy and the cost you actually pay for the inputs, is exactly the value created by money intermediating a much more specialised series of exchanges.

Back to our original circumstances, if the prices of widgets have gone up because resources have been pulled from squidgets, etc., what this really means is that a great many economic actors no longer believe their time and energy to be best allocated to widget making. Although we can articulate their reasons for believing this, we cannot say it is objectively right or wrong. It is as “right” as they end up profiting by how they allocate their time and energy instead. The invariant measure we require is therefore not of widgets, specifically, but of the aggregate contribution of time and energy to productive enterprises as collectively valued by their output. Widgets might matter to you, but we can tell by the fact of their being produced far less (or not at all) that they no longer matter as much to the network. Time and energy matter to the network, but circumstances and behaviors have changed what time and energy can be transformed into.

Readers may have noticed I sneakily begged the question when I introduced natural disasters in Part II: I said this would cause “real costs” to soar. But what is a “real” cost? If we aren’t measuring costs in money, then what are we measuring them by? Now we have our answer: in human time and human energy. In the case of a natural disaster, we are assuming a great deal of intermediate resources of production is destroyed and we have to devote time and energy to rebuilding it all if we hope to maintain the same output. Whatever output we achieve will cost more money because it will take more time and more energy.

And so, “maintain purchasing power” as a property of money can only sensibly mean: if, at t0, it can purchase a given proportion of the whole output of the economic network, then, at t1, it can purchase that same proportion. Regardless of what has inevitably changed in the meantime, money is useful to the extent it lets us contribute time and energy to the network at one point in time knowing that our claim will not be diluted, and that at any future point in time we can receive the same proportion back.

The semantic theory leaves us hanging with ungrounded promises of “storing value”. Value as decided by whom? And stored relative to what? It is far more fruitful to understand money as preserving a contribution of time and energy relative to the economic network that uses it. A new money could not be helpfully described as providing utility as a “store of value” from its beginnings — although, in the long run, being sound certainly wouldn’t hurt its chances in this regard …

Even if it is clear its contribution will be preserved, it will not be at all clear what will happen to the network itself and hence how valuable this preservation really is in the wider scheme of things. But the better a money can preserve such contributions and protect them from dilution, the greater the chances its network will attract time and energy, and hence value. The semantic theory assumes the incumbent money’s network is mature and total, and hence can’t make any worthwhile sense of a challenger “gaining share” of “time and energy stored”. If it is messy and confusing in real life, then of course it is messy and confusing from the perspective of such static and limited definitions.

What it would seem like if it did seem like a new money were emerging would be superficially extreme uncertainty masking such a substantial improvement in the promise of protection from dilution that the nuisance of the uncertainty of the period of emergence could credibly claim to be outweighed.

continue to Part IV:

or go back to Part II:

n.b. This is a serialization of my previous trilogy on Bitcoin, economics, and capital markets: Wittgenstein’s Money, The Capital Strip Mine, and, Bitcoin is Venice.

follow me on Twitter @allenf32



allen farrington

I’m an investor. I think about things. I write some of it down.