Chapter 8 Understanding Magnitudes

A horse-power is 745.7 watts. Now you know.
A color television set consumes about 500 watts.
A racing bicyclist puts out about half that much. But not for long.
A laborer, in field or factory, can operate for prolonged periods at about the 100 watt level. Think of a bright lightbulb. But just one.

A human brain puts out about 25 watts. Bright enough.



'To dig," according to an informant in the argot of youth, means "to understand and to appreciate." 

Perception and perspective. These may be the most important attributes of the rational woman and man. 

To look and to see, to listen and hear, to inquire and comprehend -- that's perception. But what about perspective? 

Perspective has to do with gauging the size of things, generally the relative size -- the proportions of an issue. 

Three "discernment ranges" come readily to mind: increments, factors, and orders of magnitude. 

Inflation is invariably expressed as a percentage. Economists are fond of increments. When the speed limit gets reduced from 60 MPH to 55 MPH, that, too, is an incremental change, although you might prefer to call it a decremental one. Fractional differences in value, space, speed -- these are the "increments" we enjoy or suffer from or adjust to. Smaller increments, we might not even perceive. 

When some variable increases by 100%, we often say it has gone up by a factor of two. Thus, in the city, an automobile may be a factor of two times faster than a bicycle; on the highway, a factor of three. A moped at 100 miles per gallon gives only a factor of three improvement over a compact car. Conversion of 100% of personal transportation from automobiles to mopeds would extend the petroleum age by no more than a factor of three. 

It is generally agreed that an order of magnitude is a factor of ten. When considering the order of magnitude of something, perspective takes a beating. Factors don't count for much, and increments vanish into insignificance. It doesn't matter at all whether a jet is flying at 500 MPH or 550 MPH (an increment of 10%) when compared to an automobile. Nor does it matter very much whether the car is going 25 MPH or 50 MPH (a factor of two). The jet is said to be one order of magnitude faster than the automobile -- and the bicycle.

Action at a Distance

A bicyclist can easily interact with people 5 miles from home on a daily basis. And still get home in time for dinner. 

An incremental increase in the bicyclist's time away from home can extend that range by as much as a factor of three -- to 15 miles. 

To commute 50 miles on a bicycle -- an order of magnitude increase over the original 5 mile value -- is a practical impossibility. Thus do differences in degree produce differences in kind. 

During the petroleum age in a few countries, the automobile was made to operate faster than the bicycle by factors of two or three and thus facilitated an order of magnitude increase in commuting range. The consequent differences in kind ramified throughout all of life's activities. Not always for the better, sad to say. 

The jet aircraft technologies increase the one-day range of a few persons another order of magnitude -- at a profligate consumption of fossil fuels. Thus, the round-trip journey from Los Angeles to San Francisco is routine for some and from New York to Boston a ho-hum trek for others. And most get home in time for dinner. 

Another alternative for daily personal interaction has arrived. None too soon, either. 

The "information age" is here. Combining the best features of telecommunications, including satellites, with those of computers, the new-age technologies are obviating trips to far-away places for information gathering and to achieve influence. 

Moreover, "teleconferencing centers" are coming to your neighborhood, so when it's absolutely necessary you can hold meetings by video. 

Soon the person who must go jetting and automobiling all over the place in order to accomplish action at a distance will be considered as obsolete as a person today who doesn't know how to dial a phone. 

Better keep your bicycle in good repair, though. In the post-petroleum age, you might need it to get to the neighborhood teleconferencing center. 

Or to go a-courtin'.


An automobile at 55 MPH and a bicycle at 17 MPH are said to be of the same order of magnitude in speed.

A light plane at 170 MPH is about on order of magnitude faster than a bicycle.

A space shuttle at 17,000 MPH is about three orders of magnitude faster than a bicycle.

Three orders of magnitude is a thousand. Long ago, a thousand-thousand got to be called a million. Then a thousand-million, a billion. 

In Europe, billion is finally starting to be used by journalists and public figures. The term has been a little slow to catch on. You can understand their reluctance. By making it too easy to express ever larger quantities, you can actually destroy perspective. 

Look what has happened in the U.S. We now hear straight-faced statements using the term trillion -- a thousand-billion -- for things like national debt and military budgets. Every once in a while, someone comes along and, in a vain attempt to restore perspective, describes a gee-whiz scenario -- dollar bills stacked to the moon or something. 

So, conventional discernment ranges -- including order of magnitude -- are apparently not always enough. We have come to use "illions." Perspective suffers a lot. 

Consider the emerging field of information processing. 

Just look at what's happened to component densities, calculation speeds, and memory capacities. Some have gone up by factors of millions in the past three decades. 

Technology has driven the costs down accordingly. A thousand-dollar personal computer today has more capability than a ten-million-dollar monster did back when. That's one ten-thousandth, or four orders of magnitude. Probably unprecedented in all of history. 

If the price of a bicycle went down by the same four orders of magnitude, a $100 ten-speed would sell for about a penny. How's that for perspective?

Natural Legislation

Energy cannot be created or destroyed. Sound familiar? That's the first law of thermodynamics. 

You may recall the first law as the "conservation of energy" principle -- not to be confused with a "conservation of energy" policy, which gets bandied about in governmental circles from time to time.

The first law is widely understood. It says you can convert one form of energy to another: electricity to light, chemical to heat, height to speed. But if you add up all the energy you start out with and all the energy you end up with, you'll find the sums always come out the same.

Energy can be stored: a wound-up spring, a charged-up battery, water behind a dam, a gallon of gasoline.

Energy can be transported: in wires, pipes, and tankers -- even in a vacuum from the sun to earth.

Energy can be concentrated: a parabolic reflector, a chemical still, a watershed, a green plant.

Energy can be wasted or saved, sold or hoarded, understood or forgotten.

But it cannot be created nor destroyed.
Since it's already an inviolate law of nature, why all the fuss about energy conservation? The issue is not the first law of thermodynamics. It's the second law.
That one is harder to explain.

Supremacy of Work

The second law of thermodynamics has special importance for all mankind. It underlies the most significant issues of our time. Here's a try at explaining the second law. 

Energy comes in different forms. Some forms are, well, "superior" to others. 

The most superior form of energy is work. Work is what comes out of an engine through its drive shaft. Work is the lifting, the pulling, the pushing of things. It is the product of some force and some motion. 

The least superior -- all right, the most "inferior" -- form of energy is heat. Heat comes out of gasoline when it bums and goes into water when it boils or into ice when it melts. Heat doesn't actually exist, strictly speaking, unless it is going somewhere. 

An automobile engine converts heat from the gasoline into work. But not all of it. The heat left over also comes out of the engine (got to obey the first law, remember). 

That waste heat, by the way, represents the thermodynamic inefficiency in the engine. 

The second law of thermodynamics says that you cannot convert all of a given amount of heat into work. There'll always be some left over. 

It says much more, but that's enough for now.


According to the second law of thermodynamics, it's not possible to convert all of heat into mechanical energy, or work. Well, the opposite is actually possible; you can convert 100% of a given amount of work into heat. 

That's exactly what happens in the brakes of your car. 

You're driving along, pressing on your accelerator pedal. Refined petroleum pours into your engine where it is burned to make heat, only part of which gets converted into work, that supreme form of energy which endows your car with kinetic energy. 

A signal turns red far ahead. 

Your foot continues to command precious fossil fluid into combustion. Approaching the intersection, you tardily but firmly apply your brakes. Kinetic energy now bleeds off abruptly into heat, imperceptibly warming the environment. 

You're stopped. 

When the light turns green again, your foot returns to the accelerator to invest more noble juice in the effort of re-instating kinetic energy to the vehicle. 

Notice how it doesn't matter which pedal your foot presses on, accelerator or brake. The result is petroleum consumption. Often more than necessary. In fact this accounts for most of the difference between the mileage estimates listed for the "Federal Urban Cycle" and the "Federal Highway Cycle." 

You're actually quite a lot better off if you would let your car coast as much as possible. Press your foot on neither pedal unless you simply have to. It takes a little more planning usually -- a metaphor, perhaps, for the waning days of the petroleum age. 

Of course, if you're really fond of pressing pedals, ride a bike. Forget the second law of thermodynamics.

Thought Bottle

Energy is one thing. Available energy is another. 

Unavailable energy is an unavoidable waste product of all processes. Unavailable energy, therefore, is always increasing. Not being created, mind you. The first law of thermodynamics forbids that. Unavailable energy is always getting derived from other forms -- mandated by the second law. 

Fortunately, there's a handy tool for dealing with such abstractions: the gedanken (thought) experiment. 

Fix in your mind a thermos bottle -- a perfect one, into or out of which energy cannot get. This one is special in another way; it has two chambers inside. One has air in it at a high pressure, the other at low pressure. Never mind how they got that way. 

If the two chambers were connected together with a turbine wheel in between, mechanical motion could be induced in that wheel as the air flowed through it from the high-pressure chamber to the low-pressure one. Mechanical energy could thus be brought outside the bottle by a shaft through the side. There's available energy in that bottle, you might say. 

A big enough bottle and you could propel a bicycle down the road. But we digress. 

Next, change the thought experiment slightly. Permit the air to leak from one chamber to the other without doing any "work." A bypass tube would do it. 

Both chambers would soon reach the same pressure. However, the total energy inside the thermos bottle has not changed! (The insulation, remember, prevents any thermal energy from entering or leaving the bottle.) Now the turbine wheel can do no work at all. Our "gedanken" bike won't go anywhere. 

Some portion of the energy inside the bottle -- which was formerly available to do work -- got converted into....unavailable energy. 

By the way, you may have heard of unavailable energy by its special name, "entropy."


Electricity has some handy features. It can be converted with high efficiency into work. That's what electric motors do. It can also be used to produce heat, as in home heating. Here again, you can get all electricity converted into heat but not vice versa. Heat, you'll recall, is the most inferior form of energy. 

Consider what is meant by the all-electric home. 

Take petroleum, the noble substance, out of which can be made plastic heart valves and long-playing records, and bum it. You have heat to run an engine to make work to drive a generator to make electricity to make heat again to warm your house. There are losses at every step: thermodynamic, conversion, distribution, leakage. 

Heating of homes is probably the worst use of electricity. Undoubtedly it's the best use for solar energy. No conversions required. And solar energy is pre-distributed. 

In the daytime.

Unbroken Law

The bicycle is the most efficient form of transportation in the world. 

Transportation efficiency is measured in calories of energy consumed per gram of payload per meter traveled. The bicycle compares favorably with all other things that move, animal or machine, on land, in water, or through the air. The difference is not just incremental either. The bicycle is better by big multiplying factors. 

The efficiency of the bicycle, of course, depends on the efficiency of the human body, which also happens to be its payload. Here we encounter something of a surprise, an apparent violation of the second law of thermodynamics! 

The human body, according to ergonometric measurements, can convert up to 25% of ingested food energy into mechanical work energy while pedaling a bicycle. That may not sound like much, but the second law of thermodynamics mandates that an ideal heat engine would be required to operate at a temperature of over 260 degrees Fahrenheit in order to achieve a 25% efficiency. 

That's more than 150 degrees hotter than the human body ever gets. It's nearly 50 degrees hotter than boiling water. 

The explanation is simple. The human body isn't a heat engine. It uses neither internal nor external combustion. We're more like fuel cells. As such, our muscles are capable of converting chemical energy directly into mechanical energy, both being what we've come to call thermodynamically superior forms of energy. 

Some bicyclists might find pleasure in supposing that they can exceed the limits imposed by the second law of thermodynamics while puffing along the road. It isn't so. 

A marvel is how amenably the bicycle matches and extends the human energy output, doing violence neither to nature nor to nature's laws.

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