Saturday, August 4, 2007

Flop on Pop

My new baby daughter loves to sleep on papa.

Unfortunately, this tends to pin papa down. Here's a quick review of some of the things that go through your mind when even a slight shift of position could throw your entire household into screaming chaos.

1. The best way to stay sane when you can't move a muscle is to invent word games on the spot and then try to play them. I have created dozens of these (see Word Puzzles for the Seriously Smart), and I'm constantly thinking of more. One game I'm playing lately is to think of what I call "unambiguous words." These are words that have only one meaning. By that I mean that the word has only one definition in your dictionary of choice. So far I have thought of the following examples, which have only one meaning in the American Heritage Dictionary, 4th Edition:


I think it would be fun to assemble hundreds of these words and then use them to write poetry or short fiction. Would the paucity of meaning and the poverty of connotation lead to flat writing? Or would every word appear to be, in virtue of its specificity, "le mot juste"?

2. SLEW strikes me as an interesting word, because it can be interpreted as a noun - as in, "a slew of examples" - or as a past-tense verb (Cain slew Abel). So another game I'm playing is trying to find more words like this. The solutions tend to be rather choice. Here's what I have so far:


I love these examples because (1) as verbs, they can only be past-tense; and (2) the noun sense and the verb sense have absolutely no conceptual connection to each other. A word like CUT is a past-tense verb and a noun, but CUT is also a present-tense verb, so it violates (1). A word like THOUGHT is a past-tense verb and a noun, but the verb sense and the noun sense are obviously related conceptually. Would love to see more examples satisfying (1) and (2), feel free to add more in the comments section.

3. As we all know, there is no such thing as "up" or "down." Better to think of it as "away from the center of the earth" and "towards the center of the earth." A propos of nothing, I wonder if you could raise a child in such a way that she understood this from the beginning. For example, you would never allow yourself to say things in front of the child like "What goes up, must come down." Instead you'd say, "What goes out, must come back in." Or when a song came on the radio like "Love Lift Us Up Where We Belong," you'd say, "What they really mean, honey, is Love Push Us Out Where We Belong."

Eh. Probably wouldn't work.

4. Although you can't move when you're sitting in that rocking chair, the upside is that you have lots of time to think about moving. Here is something I devised while thinking about locomotion and how it works on planet Earth.


The cosmic speed limit of 300,000,000 meters per second imposed by Einstein's theory of relativity is well-known. But it was only recently that I realized there's a way in which ordinary Newtonian physics also places some practical limits on your ability to move quickly from point A to point B on this planet.

To see how this comes about, let's suppose you plan to travel a distance D, beginning in a state of rest and arriving at your destination in a state of rest. Suppose also that your mode of travel relies on friction with the ground to make it work.

I should say, restricting yourself to a friction-based form of locomotion is not as limiting as it may seem. If you plan to run, walk, cartwheel, ride a bike, drive a car, or piggyback on the shoulders of a friendly robot, you'll be using friction to get where you're going. Among animals also, friction underlies the hopping of a toad, the inching of an inchworm, and the slithering of a sidewinder. For eons of evolutionary time, friction has been the basic engine used by man and beast for traveling on land.

An acceleration generated by friction will always scale as b*g, where g = 9.8 is the strength of the earth's gravitational field in standard units, and the dimensionless coefficient b characterizes the roughness of the two surfaces involved - say, the pavement and the soles of your shoes. The presence here of a material property such as the coefficient of friction needs no explanation. The reason for the presence of g is that, as it turns out, the maximum friction force attainable between two surfaces scales directly with the strength of the contact force pressing the two surfaces together. This is why you use "elbow grease" to get out a stain: by pressing harder as you scrub, you are making available a larger friction force to pull the dirt loose. In the case of locomotion, it's the earth's gravity that applies the elbow grease, pressing you to the ground. Hence, the maximum friction force you can use to push yourself forwards ultimately scales with the gravitational field strength g.

The implication of the acceleration-scale b*g is that, for a journey powered solely by friction, the time required to complete a journey of distance D will scale as (D/b g)^(1/2). Turning the reasoning around, we find that the greatest distance D you can cover under "friction power" within a fixed time T is given by D ~ b g T^2.

Plugging in some numbers, we find that in a lifetime of threescore and ten, the greatest possible distance you can cover - and still come to rest when the good Lord says you must - will be on the order of 10^(19) meters. This is a hundred times further than the earth-sun distance, meaning that the friction limit is not one that we'd actually bump up against in practice!

Here I've taken the coefficient of friction b to be of order unity, which is typically the case. Of course, the coefficient of friction does vary in value, depending on what sort of surface you're walking on (rough or slippery); and likewise it depends on what sort of material your bootsoles are made of.

So, one moral of the story: If you want to go far in life, wear track spikes.


The Newtonian limit of 10^(19) meters is actually not as strict as the Einsteinian limit, which is c*T ~ 7*10^(17) meters. But the two limits coincide when b g T^2 ~ c T, or when b ~ c/gT ~ 0.01. On a highly polished planet, the Newtonian limit would actually be the sharper of the two.


The friction limit is not fundamental physics. For example, it doesn't apply to travel by jet (or, what is much the same, travel by rocket). Rockets move by harnessing a controlled explosion near the rear of the craft. Essentially, the debris from the explosion bangs against the backside of the ship, knocking it forwards. Using a jet engine, you can lift gently off the ground, accelerate forwards at a great rate, coast at high speed, and then reverse the thrusters to bring you back to a state of rest, touching down gently at your destination. The material properties of the intervening land will have nothing to do with your trip time.

An ordinary propeller plane is a closer analogy to the friction limit. This is because a propeller plane depends for its propulsion on the viscosity of the air - and viscosity is more or less the fluid equivalent of friction between solids. A similar mechanism would be an oceangoing ship's propeller screw: it depends for its effectiveness on the viscosity of water. As Rayleigh observed in the 19th Century, if water had no viscosity - today we can produce such "superfluids" in the laboratory - then a ship's propeller would be useless; the ship would merely agitate in place, going nowhere, as the propeller blades slipped through the water without generating any thrust. Of course, as Rayleigh probably also observed, if water had no viscosity, ships would hardly need propeller screws; you could just give the ship a good shove, and it would glide through the water for miles.


In a watery environment such as the sea, organisms have a choice between using friction on the seafloor to drive them forwards, or using the viscosity of the water to generate thrust. Creatures who swim leave creeping things in their wake; but on land, where the parameter values are vastly different, the best horizontal runners and the best horizontal flyers enjoy similar speeds, topping out in the 70 mph range.


Earlier, I argued qualitatively that a friction-powered trip cannot be completed in a time less than about T ~ (D/bg)^(1/2). A detailed analysis shows that the precise lower limit is T_min = 2(D/bg)^(1/2). The analysis leading to this bound assumes that during the trip, your center of mass remains within a plane parallel to the ground. However, if you can launch yourself through the air Incredible-Hulk-style, then you can actually get to your destination faster. This is because, during the liftoff phase, you'll be pressing into the ground with a force greater than your own weight, and this extra "elbow grease" will allow you to generate a larger horizontal friction force than you otherwise could. Of course, you'll waste some time rising into the air and coming back down; but if you launch yourself at the shallowest attainable angle (ArcTan(1/b)), then the gambit proves worthwhile. In fact, it turns out that a distance D can be leapt in only a time T_min = (2D/bg)^(1/2). The factor of 2 in the ground-based strategy has become a factor of 2^(1/2), which is a time savings of about 30%.

If D is a distance of many meters, then leaping all the way to the destination will be out of the question for a mere human. But thinking of D as being only a meter or two, we see that the strategy of loping is superior to that of a gliding walk. While this observation hardly explains exactly how or exactly why humans spontaneously break into a run to save time - that depends on metabolism and the shapes of our bodies - it may go some ways towards explaining why running as a strategy exists among animals at all.


If you find this kind of thing at all interesting, let me recommend a wonderful book, Life's Devices, by Stephen Vogel. This book is the On Growth and Form of our times.


My scientific hero, John Bell, once said that impossibility proofs in physics are proof of a lack of imagination. My proof that you can't travel a distance D in a time less than (2D/bg)^(1/2) is no different. For, rather than leaping the distance D, you could simply invent the starting block and get to your destination as fast as you like. (Don't forget the anabolic steroids.)

I sometimes wonder if the cosmic speed limit imposed by Einstein's relativity theory has a similarly simple countermeasure.


If you've made it this far, I end with a scrap of creative writing inspired by the foregoing.


The Ribenians secrete a thin fluid from their pores, which renders their bodies nearly frictionless. Life in their society is very difficult for this reason.

Efforts to clothe the Ribenians proved fruitless. After many attempts, a shoe was placed on the foot of a child. It slid off as soon as he rested his foot on the ground. Adults, bound in linen cloth, soon faced into their wrappings, or writhed out of them entirely.

The Ribenians organize themselves into clans. Each clan lives in a hollow, where the clan members wriggle over one another in a great tangle of bodies. Life in the clan is a continual struggle to reach the higher levels, where there is more light and air, and where one may drink fresh rainwater instead of ground-seepage. The traditional technique for ascent is to migrate to the bottom of the hollow, then push directly downwards with the feet, with enough force to propel oneself upwards through the layered bodies to reach the surface. The overzealous individual emerges with too much residual momentum, expelling himself from the clan. He glides smoothly along the gently rising grade of the hollow. Slowing continuously, he may eventually fall back towards the clan, or he may slide over a crest and into a neighboring clan's hollow. Such events allow the Ribenians to maintain genetic diversity in their tribes.


Jilly said...

How to they procreate without friction? :)

Greg said...

I like your Unambiguous Words. I have a word I really like that has multiple, very different meanings: sap. "I got out my sap and sapped the sap and he fell into the barrel of sap, which sapped his strength." Exactly opposite of unambiguous. Isn't language grand? Very interesting blog. Thanks.

Anonymous said...

jilly, perhaps Ribenians procreate a la fish: female excretes eggs and male excretes sperm on top of them (i.e., not much fun)?

perhaps the eggs and sperm do NOT excrete the fluid that makes mature Ribenians nearly frictionless?

perhaps sexual maturity coincides with ability to produce the friction-damping fluid?

this would help prevent the young from accidentally launching themselves out of the clan?

Anonymous said...

Unambiguous Words: a complete list would probably include many rarely-used, scientific, taxonomic, and trade-specific terms, such as names for types of plants, the parts of a ship. I infer a built-in resistance to such words for consideration, though.

Noun/PTV: broke? rose?

joe holt said...

You so did not know what dug n. was before looking it up.

joe holt said...

What fun. More...

bore strike that, darn
clove and cleft

This makes me wish clung was a noun. What seussian thing would it be?

It's a bonus-points challenge to find non-irregular verbs that do this. Moped is a great one. I can't think of any other -ed verbs.

Jilly said...

out, out and away in my beautiful
my beautiful

JasonZimba said...

Thanks for the comments! - yes, in my word games I usually frown on jargon; so examples of unambiguous words such as "Feynman parameters" are to be avoided. I even considered taking "mattock" out, because it's not a very common word, outside of the hard-boiled noir fiction that I so enjoy. (Mattocks make great murder weapons.) Also common in that genre are brutal slang terms for parts of the body, so you often see the word "dugs" used in such writing. At this time however I can offer no specific evidence that I knew the meaning of the word before playing the game, though!

I considered adding a condition (3) to the Noun/PTV puzzle, which is that the word also *not* be an adjective or other part of speech. For this reason I shied away from rent, bent, bound, ground, etc. But it seemed like adding too many conditions.

In the same way that Joe said he wished "clung" was a noun, I kept wishing WATERSHED was a verb, prounounced "WA-tersht". Likewise UNDERFED (UN-derfed) and so on.

JasonZimba said...

(sorry, RENT works even with (3) I suppose)

Jilly said...

check it out

I just realized that at the South Pole up is actually down. I never thought about that before.