Friday, November 18, 2011

Spreng's triangle

There, I've done it again. I came across some figure in the passing and ended up digging out the original reference in an attempt to make sense of it. In this case the figure is the energy-time-information triangle, proposed by Daniel Spreng in 1978, also known as Spreng's triangle. It supposedly conveys the message that new information technology (whatever that was in 1978) allows to save either time or energy, or a combination thereof. Clearly, I thought, the paper was written before the dawn of Wikipedia...

Spreng has a background that is noteworthy. Trained as a physicist, he later worked as engineer and developed an interest in economics. His triangle is an attempt to connect these areas, and as such very interesting. The example he starts with is purely thermodynamical. A reversible process, without loss of energy, would take an infinite amount of time. Any faster, and the process becomes irreversible. The faster it is, the more energy is needed (at least in the examples Spreng discusses). So there is a trade-off between time and energy that carries over to manufacturing. Information then comes in as an improved technology that makes the process more efficient, and so, more information saves time or energy. That is the basic idea.

Spreng's original paper is here, but I couldn't get access to it, so I settled for the 1993 remake and the following is my summary. You can find the original version of Spreng's triangle on page 13 of this file. I've redrawn it for your convenience, click to enlarge.

Spreng's Triangle

Spreng's triangle is a plane with 3 axes at 120° to each other. The 3 axes are energy (E), time (T) and information (I) respectively. I have drawn lines with constant time in blue, constant information in red, and constant information in green. In the lower right E=0 corner, that Spreng refers to as the "starving philosopher," one needs no energy, but has an infinite amount of time and all the information in the world. In the lower left, I=0, corner, that Spreng refers to as the "primitive man," one has no information and needs an infinite time to get anything done with maximal energy. In the upper corner, the "industrial man," one has plenty of information and energy to get things done in zero time. The corners are however unrealistic limits that shouldn't be taken too seriously, they're just to show the trends if you move around in the diagram.

Now to define a point in a plane you only need two axes, so the relevant statement here would be that all possible points of combinations E,T,I lie in a plane. I say "would be" because I will argue in the following that though superficially plausible and appealing, I don't think it is actually the case.

In his paper, Spreng discusses in which way energy, time, and information partly substitute for each other from several different aspects.

At some point, he claims for example that in industrial countries on a national level working hours substitute for energy use, citing himself in mentioned earlier paper that I had no access to. So I plotted the working time per year per worker from this table, against the annual energy consumption per capita from this table (in kilogrammes of oil equivalent per year).

I don't know about you, but I can't see any correlation or anti-correlation in that. Well, the data I used is from 2003, so, possibly 40 years ago that looked different, but I can't say I am very convinced. However, this turns out not to be of much importance later, he just uses this because he wants to send a message that civilization should slow down the hamster wheel (invest time) to instead save energy:
"Whether the time saved is simply used to produce and consume more, or whether some saved time is set aside as time for cultural development is of prime importance."

One easily sees from Spreng's discussion, that the "information" he is referring to is ill-defined. To be fair however, it does become clear that he is talking about manufacturing processes and their improvement. So Wikipedia isn't really a counterexample. At some point he specifies information to mean 'relevant' information, yet one doesn't know relevant for what. Maybe it's the information needed to decrease energy or time, but then the argument becomes circular. I think the name "information" is very misleading. What he seems to mean is something like the complexity of a technological process. Not that this is better defined.

However, just when I was about to throw the paper in the garbage, Spreng goes and admits that the "relevant information" is totally ill-defined and pulls the following trick that helped me to make more sense out of his triangle. He says, let's just consider information as an unknown parameter and assume it is measured by the market: "[T]he market measures the information content of goods and services." So, let Y be the market value of a good or service, then he defines information (I) by the following equation
    Y = pL L+ pE E + I

where L is input to production of the good in working hours, pL the price per hour, E is the energy input in some units, and pE the price for that energy unit.

That would indeed define a surface if this equation would be fulfilled, so the question is, does it work? First, we note that this equation almost certainly isn't fulfilled for goods with cultural value like, say, Marilyn Monroe's dress. I don't see what difference it should make for the right side of the equation whether Marilyn or I wear a dress before auction, yet I have some doubts anybody would pay me some million bucks for that, so it does make a difference for the left side of the equation which is no good.

So then let's look at goods without cultural value, if such exist, maybe a banana will do. Still, something seems to be really funny with this equation. The alleged market value of the good doesn't at all depend on supply and demand for that good. I mean, I don't know a lot about economics, but if you're growing bananas in your backyard with input E,I,L and suddenly all bananas in Brazil fall victim to epidemic monkey obesity, your backyard bananas would be in high demand and up goes Y without any change to the right side of the equation.

This is not to say that it is not possible to make sense out of Spreng's triangle, but at least from what's in his 1993 paper it seems to me it would take more work to integrate this idea with economics. Spreng concludes his paper with the words
The importance of new information technology, NIT, in respect of future energy use can hardly be overstated. However, NIT can do two things. It can be used to substitute time by information or to substitute energy by information. NIT can, in other words, both be used to speed up the pace of life (work and leisure), thus promoting a society of harried mass consumers, or it can be used to conserve precious natural resources (energy and non-energy) by doing things more intelligently and improving the quality of life without adding stress to the environment. It is up to the society as a whole, politics of course included, to decide which of the
two roads are taken.”

You could then summarize my criticism as these are not the only two roads. Your NIT can also cost you more energy and more time. Like this damned Windows that never seems to finish updating and keeps popping up a message that I have to restart.

Bottomline: Plausible ideas are the most dangerous ones.


  1. This parallels the price-performance-quality trade-offs.

  2. Isn't "whether Marilyn wore the dress" information? Then "that dress!" is enough more information to justify the auction price, more-or-less.

  3. It's not just a problem with Wikipedia. I remember the same problem occuring while using the physical Encyclopedia Brittanica.

  4. Hi Peter,

    Well, as I said, what Spreng means with information is actually what technology went into the production. Either way, I would argue that "Sabine Hossenfelder wore the dress" is also information, it's just not particularly interesting information. Best,


  5. Hi Philip,

    Yes, that's right. However, I think what Spreng was trying to do is to connect economic activity with physically measurable quantities to get rid of vague properties like "quality" and "value". Actually, he's trying more than that, he's trying to substitute them. Best,


  6. There would need to be some “fittingness”, a degree of mutual information between the nature of the energy supply and the companion system’s energy requirements. If we consider water as an analog for energy, an earthy example would be the practice of flood irrigating a field versus a drip irrigation system.
    This would seem to be a truism for biological systems. The energy required to incubate a clutch of eggs, both thermal and mechanical, is highly particular over time.
    Our bodies learn to distribute energy most efficiently. In lifting hundred pound bags of potatoes, the first bag will seem heavier than the fifth because our bodies learn which muscles are actually needed and how to coordinate them.

  7. Economics is rigor, elegance, and application - not empirical validation. Creeping failures drive immense cashflows from productive cohorts to managerial cohorts. The EU's incipient collapse is unavoidable for the nicest of reasons.

    Waste abundant resources to conserve dear ones versus legislated misappropriation (always with positive feedback). "No Child Left Behind" trades thin streams of valuable inputs and outputs for distended cloacas at both ends. The larger the scale the worse the implementation, for reality's tolerences add not average. Sum local optimizations rather than impose global fits.

  8. Hi Don,

    Yes, good point. I suppose Spreng implicitly assumed that the energy is used as efficiently as possible within the given time with the given information. Best,


  9. Interesting table. Could you please send it to your chancellor to see herself how many hours the Greeks work with respect to rest of the Europeans?
    This should stop the German propaganda about the lazy Greeks:-)

  10. Yes! I was stunned, the Greeks seem to work like crazy. Best,


  11. Well, golly Bee, I fear I am having another attack of errant enthusiasm.

    I don’t think we will progress very much further without a couple of more words to discriminate what sort of “information” we are talking about. I was assuming Spreng was talking about one sort of information, but apparently he was talking about the more prosaic kind.

    So, light of heart and for present purpose, let’s call Spreng’s information “Librarian’s Information” or LI. This information is the artifact of human measurement or description, the Wikipedia/Shannon sort of information, a more or less passive commodity that we excel in abstractly conveying from one place to another (a capacity which was enabled by Shannon’s metric).

    On the other side of the looking glass is what we will call, for lack of better physics, the “Pauli Information” or PI. This is the business end of physical information. Rather than passive it is actively declarative. It arises from deep natures capacity to make a real choice between one state/path and another.

    So LI arises from and is descriptive of PI, but it is not the same thing. PI is intrinsic to a particular local , germinal to the discrimination of one place from another and hence one path from another.

    So, going back to drip irrigation, LI may be descriptive of a system, but it is PI that physically enables the real articulation of pathways.
    I suppose this is actually an old philosophical saw.
    I hope something here translates into a more proper framework.

  12. Pretty much agree with Al on this. (sorry, I've been away) All complex physical systems, which economics most certainly is, require feedback to maintain balance over time. Often things aren't required to maintain balance over time but I would tend to categorize them as then not defining a complex system.

    Economics as a complex system could be defined similarly to the human body. In order to keep individual cells, or cell types, from unregulated growth at the expense of other cells you need governing methods to stop them. The human body is filled with systems that govern and regulate these processes so we don't develop cancer.

    The similarity between national economies and biological entities is that both change over time. They do it by growing or shrinking, but there is a constant need for the different cell types, to remain (more or less) at a constant proportion to each other.

    On one end of the axis everyone is supposed to be treated exactly the same no matter their individual merit. On the other end there would be no regulation at all and it would be the law of the jungle with the winner take all. It would be like the game of monopoly where no matter how much your individual merit you will eventually not survive unless you happen to be the lucky 1 out of the 7 billion currently on the planet.

    The commonality is that in the sweet spot in the middle of the axis is where we always want to be. And in that sweet spot everything changes but the proportionality of the different functions comprising the economy do not. It's pretty tricky to execute that sweet spot. I think that's why people and economies often succumb to uncontrolled growth in certain segments which kills off the entity as a

  13. You could also carry the analogy of death due to agedness and cancer to the opposite extreme. I suppose in a perfect communist system where everyone would be treated exactly alike it would be like an early undifferentiated fetus. There would be huge potential that would be as yet unexperienced. The stem cells had not yet differentiated.

  14. Hi Don,

    Spreng starts out talking about information in the physical sense, rspt entropy actually, but then realizes that this type of information isn't relevant for his purposes. After a lot of blabla, he finally says he doesn't know what the information is he talks about, so let the market measure it. Spreng's information is clearly not passive - it's the information needed to construct or produce something. Best,



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