Saturday, January 29, 2011

More Thoughts on the Thermodynamic Imperative, What's the Maximum Population on our Planet, & Thought Experiment/Game on Maximizing Entropy Production

So, in my previous blog (Thoughts on the Thermodynamic Imperative), I didn't talk much about the problems with believing in the Thermodynamic Imperative. This post is intended to show the problems associated with the Thermodynamic Imperative, and the blog will end with a Thought Experiment/Game involving three Colonies building solar power plants (one of which believes in the Thermodynamic Imperative.) Read on, and you'll see which Colony wins the game.


As a summary before proceeding, the Thermodynamic Imperative states that we should try use the available exergy to the best of our ability. (Note: Exergy is related to the potential to do work if there were no irreversible processes.) Normally, the people who believe in the Thermodynamic Imperative think that we should maximize the efficiency of any process that consumes exergy.

It turns out that this is a decent philosophy to hold if there are a finite number of resources available, but this is a very dangerous philosophy if the sources of exergy grows as we convert the potential to do work (i.e. exergy) into actual work (i.e. electricity or motion of your car.)

It turns out that we are no where near the limit of exergy resources here on Earth. For example, there are roughly 125,000 TW of sunlight that strike the Earth at any given moment. Let's imagine that we could convert 1/125 (0.8%) of this sunlight into electricity, then we would be generating 1,000 TW of electricity. On average, the power consumption per person is 300 W. (Though, in the US it's closer to 1500 W. So, let's use a round number of 1 kW per person.) But let's also assume that for each 1 kW of electricity, each human needs the equivalent of 9 kW from plant and animal sources supporting him or her. So, even with an equivalent electricity consumption of 10 kW per person, the Earth could support a human population of 100 billion people. If we can increase the efficiency of sunlight to electricity, we might be able to support an even larger population, but let's just say 100 billion to be conservative. (We're a tenth of the way to the rough limit.)

But so far, we've only started counting the number of people who can live on Earth. There are many other places to live. Both the Moon and Mars will be livable once we send self-replicating solar machines to start collecting sunlight and generating/storing electricity for us to use to construct buildings to protect us from their harsh environments.

So, one of the problems we face today is that we are living in a world in which many people do not realize the philosophy they are practicing is not helpful for the world in which we live in. The philosophy of the Thermodynamic Imperative is hidden inside of a lot of well-meaning philosophies today, such as environmentalism and conservationism.

I don't necessarily have a problem with environmentalism or conservationism. I value life and I value preserving life. I value life so much that I want to see it spread to other planets, and eventually other solar systems. My problem is with the Thermodynamic Imperative, and the idea that we must use exergy with the greatest efficiency possible. Instead, we need to be using exergy to maximize the rate of return on investment. Then, we can increase the size of the population and make us all wealthier at the same time. Eventually, as mentioned above, we'll send robotic missions to the Moon and Mars with self-replicating solar machines.

It turns out that there's a reason why we want to maximize the rate of return on investment. (There will probably be people out there that agree with the statement "we want to maximize the rate of return on investment," but will disagree with the following statement.) Maximizing the rate of return on investment is actually the best way to increase the entropy production rate of the universe, and the fastest way to bring the universe to equilibrium. It turns out that the goal of life processes is to bring the universe to equilibrium as fast as possible.

So, here's a thought experiment I came up with:

There's a near-infinite source of exergy (let's say from sunlight). There are three different groups living on Earth: Colony A, Colony B, and Colony C.

Each Colony lives by a different philosophy.
In Colony A, the philosophy is to maximize the rate of return on investment.
In Colony B, the philosophy is to maximize the efficiency of electricity generation.
In Colony C, the philosophy is to maximize the initial rate of entropy production.

Here are the ground rules for the game:
1) It takes 1 round to build a new solar power plant
2) On the 10th round after a solar plant started being built, it is decommissioned. (The cost to decomission is zero. i.e. you can sell the equipment for exactly how much it takes to decommission it.)
3) Each Colony builds power plants of varying capital costs, exergy efficiency, and rate of return on investment.
4) If the Colony has the money to build a new power plant, it must build a new power plant.
5) Each Colony starts with $40 and no power plants at Round Zero

Colony A builds power plants with a capital cost of 10 monetary units ($), a exergy efficiency of 25%, and a Rate of Return on Investment (RROI) of 20% per round. We'll ignore fuel, labor and maintenance costs. So, this means that each solar power plant generates $3 per round. RROI is calculated as:  [($/round) / (Capital Cost $)]  -- [ 1 / (Lifetime in rounds) ]  with overall units of % per round.  (similar to %/yr for RROI in real life)   The exergy destruction rate of each plant is equal to $12 per round.  (Remember that the entropy generation rate is equal to the exergy destruction rate times the temperature of the planet.)

Colony B builds power plants with a capital cost of 40 monetary units ($), a exergy efficiency of 50%, and a Rate of Return on Investment (RROI) of 10%/round. So, this means that each solar power plant generates $8/round. The exergy destruction rate of each plant is equal to $16/round.

Colony C builds power plants with a capital cost of 10 monetary units ($), a exergy efficiency of 10%, and a Rate of Return on Investment (RROI) of 10%/round. So, this means that each solar power plant generates $2/round. The exergy destruction rate of each plant is equal to $20/round.
 
Each Colony is trying to maximize something that their philosophy tells them is good to maximize. Colony A wants to grow and become larger. Colony B wants to maximize efficiency (because everybody believes in the Thermodynamic Imperative.) Colony C thinks that the best way to maximize the entropy generation rate of the universe is to operate inefficient machines that generate a lot of irreversibility.

Only one of the Colonies will win the game of life: to maximize the entropy generation rate of the universe, and bring the universe to equilibrium sooner. Only one of these Colonies will win in the end, and you can guess which one.
Clearly, Colony B will come in last place. Colony B is trying to minimize entropy generation and does a pretty good job at this. Colony C starts off really well. In fact, in the first 13 rounds, Colony C is in first place as far as total exergy destruction (and hence entropy production.) But in Round 14, the industrious Colony A pulls out into the lead. By round 100, Colony C is puny compared to the size of Colony A. (And let's not even talk about Colony B!)
In the end, an exponential grows always wins out over the initial higher rate of entropy generation.
This thought experiment/game is just here to show you that the largest exponential growth rate wins out, and we should always try to maximize the rate of return on investment, and in the end, we'll end up winning the game of entropy generation, even though that was not our intention.


_____________________________
For those of you who are interested, here's what the game looks like in the first 11 rounds:
AP = Colony A's # of Solar Power Plants at the start of the round
A$ = Colony A's $ in the bank at the start of that round
ATED$ = Colony A's Total Exergy Destruction in units of $
BP = Colony B's # of Solar Power Plants at the start of the round
etc...

Round     AP     A$    ATED$            BP      B$    BTED$          CP     C$    CTED$
0             0       40           0                0        40         0             0       40          0
1             4         0           0                1          0         0             4         0         0
2             4       12         48                1          8       16             4         8        80
3             5       14         96                1        16       32              4      16       160
4             6       19       156                1        24       48              5      14       240
5             7       27       228                1        32       64              6      14       340
6             9       28       312                1        40       80              7      14       480
7            11      35       420                2          8       96              8      20       620
8            14      38       552                2        24     128             10      16      780
9            17      50       720                2        40     160             11      26      980
10          18      51       924                2        16     192               9      28     1200
11          23      55     1140                2        32     224              11     26     1380
12          28      74     1416                2        48     224              13     28     1600
13          34      88     1752                3        24     224              14     34     1860
14          41     110     2160                3        48     336              16     32     2140
15          51     123     2652                3        32     384              18     34     2460

Note that you can guess that Colony A will win out after ~ 11 years from the following formula.


10*(1.1)^(x)  =  4*(1.2)^(x)     x ~ 10.7 rounds

(This formula neglects a lot of the dynamics of the game above, but gives you a feel for how many rounds in which Colony C will lead over Colony A as far as cumulative destruction of exergy.  Also, note that I used units of $ for exergy, and the reason for this goes back to my equating $ with kW-hr in a society with electricity backed currency. See the link below for further details.)

Electricity Backed Currency

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