naming the humanly scaled set

reminder of intent

The present writing is concerned with how Planck quantities are perceived--especially with their perception as natural units, which is what both George Stoney and Max Planck originally called them when introducing them as a set. To experience quantities as units means above all to become acquainted with using appropriate decimal multiples of them descriptively. As was noted in the introductory chapter, the concrete reality of Planck quantities can be emphasized by the way we handle them: by identifying and using humanly scaled decimal multiples such as a penny's thickness and a mile. Other aspects which I said I would emphasize are their involvement in everyday experience and the opportunities they provide for a fresh look at physical law, but the particular business of this chapter is the identification of certain exact or approximate power-of-ten multiples.

Planck quantities scaled for direct perception

Identifiying humanly scaled versions is intended to provide a concrete handle on the Planck quantities themselves. In what follows I will briefly indicate why I think the suggested names are justified.

quantity	conventional value	rough equivalent	possible name
10	0.539056(34) second	0.54 second	semi(second)
10	1.61605(10) kilometers	statute mile	mile
10	4220.50(81) cm	avg. US&Brit. gallons	gallon
10	16.1605(10) centimeters	thumb to forefinger	span
10	12.1056(15) newtons	2.72 pounds	stone
10	1.95633(13) joules	2.0 joules	spanstone
10e	1.60217733(49) coulomb	1.6 coulomb	dram
10e/	2.97219(19) ampere	3.0 amps	amber
10 /e	1.221044(78) metric volt	1.2 metric volt	volt
10	1.221044(78) metric eV	1.2 metric eV	eevee
10	1.41695(10) kelvin	1.4 kelvin	degree

For the time being, in some cases, only a rough indication of the size is provided. The corresponding quantities will be defined more precisely later on. Values for members of the Planck set, adapted from the 1996 Handbook of Chemistry and Physics, have here been adjusted up or down by the appropriate powers of ten so as to make them recognizable and suitable for direct perception at human scale. Values which the Handbook does not explicitly give have been derived from those it does. For instance the Planck volume is not given in the Handbook but is readily derived by cubing the Planck length . The published uncertainty for and is 64 parts per million and I estimate the uncertainty for at 125 parts per million--standard deviations in the last two digits are given in parenthesis.

The eevee would not ordinarily be considered as human-scale. One reason it is included in the list is that 2.0 eevee light is directly recognizable as green. The retina is sensitive to a range of photon energies and interprets energy as color--the approximate boundaries of the visible spectrum are 1.5 and 2.5 eevee, with green in the middle. So although 2 eevee is far too small to feel as mechanical work, it is associated with a recognizable sensation.

semisecond

In choosing names for the humanly scaled Planck quantities, it seemed advisable to borrow those of traditional units if any the right size were available. But in the case of time there were no properly sized traditional units from which to choose. I decided on semisecond, a name that was reasonably self-explanatory for this half-second-like interval. And if one was in a hurry one could always just call it a "semi" for short.

The Handbook value for the Planck interval of time, brought up to human scale by the appropriate power of ten was the elaborately precise 0.539056 second with uncertainty in the last two digits. I wanted to get as close as was practical to this, and to more recent Handbook data as it became available, but for convenience to have a definite number of semiseconds in an hour. As it turned out, the number of semiseconds that fit into an ordinary hour is 6678. This means 111.3 to an ordinary minute.

As was mentioned earlier, the semisecond interval corresponds to a tempo which can be heard and recognized. The rhythm of a metronome set at or near 111.3 per minute (beating at semisecond intervals) is intermediate between andante and allegro. It is labeled tempo moderato on some metronomes, and is easy to snap fingers in time with. One way to visualize the speed of light is to picture a flash traveling four times around the earth (a hundred thousand miles) every time you snap your fingers.

mile

Having introduced the semi as a recognizable humanly scaled decimal relative of Planck time, I should remark the coincidence that light travels 100,000 miles in one semisecond. Taking this figure of 100,000 to be exact actually defines a reasonably sized mile with a precise equivalent in meters. Accordingly we shall define the mile as the distance light travels in 1/100,000 of a semi (at its usual speed). This has the effect of making a mile be a certain exact but messy number of meters. To sufficient approximation it is 1616.13. I won't write it out every last digit. For all practical purposes it is equal the scaled-up Planck quantity 10 to the extent of accuracy with which the latter can be measured.Our mile is also close in size to the US statute mile--officially 1609.344 meters.

There is some latitude as to what can legitimately be called a mile. Our mile is within half a percent of the ordinary US version, and thus easily qualifies. This unit, defined by the Romans as a thousand paces, has been used for millennia and has varied by a percent or so, from place to place and time to time. The Planckish mile just defined is obviously a recognizable, traditionally named, decimal cousin of the Planck length.

One millionth of a mile is roughly the thickness of a penny. One tenthousandth of a mile, likewise a decimal relative of Planck length, happens to approximate the spread between the tips of thumb and forefinger and also the width of a hand with thumb extended. A cube with that distance as side is gallon-sized, as well as being a power-of-ten scale-up of Planck volume.

gallon

Webster's traces the gallon back through the Old French galon to the Medieval Latin word galeta, which stood for both a liquid measure and a bucket. Quite a range of volumes have traditionally been called gallon. For instance the US gallon is 3785 cm and the British gallon is 4546 cm to the nearest cubic centimeter. The average of these two is roughly 4200 cm, not far from the humanly scaled Planck volume. We have, in effect, a Planckish gallon falling virtually at the midpoint of a traditional gallon range--a kind of unintentional Anglo-American compromise. This gallon clearly constitutes a recognizable, traditionally named, humanly scaled, decimal relative of the Planck volume.

In this connection it may be interesting to note that Roman soldiers used two alternative sorts of protective headgear, one of which, a leather helmet, was called a galea. The word which Julius Caesar would have used for "a helmeted man" is galeatus, which sounds a little like the Medieval Latin word galeta. There is a remote and undocumented possibility that our word for this cousin of Planck volume contains an echo of the earlier Latin, testifying to the military practice of fetching water in one's helmet. One's head does tend to be gallon-sized--as I've noticed at the supermarket when see the other customers passing by rows of those gallon plastic containers.

span

The following length is intended to be slightly over 16 centimeters on your screen--and also somewhat in excess of 6 inches--the exact value being determined by the fact that light travels a billion times this length in one semisecond. By a remarkable coincidence, there have been several traditional units which were approximately this size--which is both humanly scaled and power-of-ten related to Planck length.

(thumb to forefinger span--width of all eight fingers--width of one hand with thumb extended)

This approximate length served as a measure both for the English (the Anglo-Saxon name for it was sceaftmund) and for the ancient Greeks (the Greek term was dichas). According to Webster's, one shaftment is "the distance from the tip of the extended thumb across the breadth of the palm, about 6 inches". Among other things, the six-inch sceaftmund length was typical of the feathered tail section of an arrow--which was also called the arrow's "shaftment". The name thus referred both to a unit of measure and to a definite part of a real arrow. Apparently fletchers would decide how long to make the shaftment of an arrow by comparison with the width of a hand, thumb extended.

Webster's gives the length of the ancient Greek dichas as 6.07 inches. The Greek measure was equal to 8 daktyloi or fingerwidths, and could have been pictured as the width of both hands, or of all eight fingers placed side-by-side. The was half of a , Greek for foot, and the name connotes division into two equal parts.

Rather than refer to the Planckish length as "sceaftmund" or "dichas", which are awkward and obscure terms, I believe it is justifiable to refer to it as a span. There was a traditional measure by that name, one which has fallen into disuse. The traditional span was hand-related: representing the spread between the tips of thumb and little finger, and was approximately nine inches rather than six. Depending of course on the size of one's hands the decimally scaled-up Planck length, 10 , is apt to match the spread between the tips of thumb and forefinger, a kind of reduced version of the traditional span. As a hand-referent measure our Planckish span has at least a general similarity with the traditional measure, justifying our recycling the name.

Light travels exactly a billion span in a semisecond. Ten thousand span is of course one mile. A cubic span happens to fall in the range of volumes called gallon--as was mentioned earlier, it is a kind of unintended compromise between the US and the British gallons. A pennywidth is one hundredth of a span.

stone

The power-of-ten relative of Planck force which is most readily recognized by hefting in one hand is 2.7 pounds. A traditional name for that approximate weight is oke or oka. A recent edition of Webster's (1987) defines this as "any of three units of weight varying around 2.8 pounds (1.3 kilograms) and used respectively in Greece, Turkey, and Egypt." From a visit to the Aegean some years back, I can personally recall food in island markets being sold by the oka. There appears to have been a similarly sized measure in the East Indies at one time as well. Here are some excerpts from a table of weights found in the second edition of Webster's New International. Webster's Ionian Island entry comes the closest to what we want.

The last entry suggests that the Turkish government, in an effort to Europeanize, may have tried modifying the original measure so as to make it agree in weight with the kilogram. Webster's traces the Turkish word back through Arabic to a Greek word onkos meaning weight. Despite its exotic sound, oka could serve provisionally to name a Planckish measure of force. We might think of an oka as 12.1 newtons or 2.7 pounds of force, and consider the Planck force to be 10 oka.

On our mantlepiece there is a collection of fist-sized riverbed stones each weighing about 2.7 pounds. Now and then I heft one of the stones to keep my hand accustomed to this human-scale cousin of Planck force. Each oka stone is a smooth rounded handful. A while ago, I immersed one of these oka stones in a bowl of water and afterwards immersed my hand for comparison, up to the wrist. The stone and my hand (whether clenched or open) displaced the same amount of water, showing that an oka stone is in fact hand-sized. In case you want to familiarize yourself with Planck force in like manner, such stones are not difficult to find. In my case and possibly also in yours, the weight of a relaxed forearm supported level at the wrist is also about right.

The fact that hand-sized riverbed stones have this weight suggests using the word stone to name a correspondingly sized force. I will save the precise definition of this quantity for later. The word has traditionally been used to name units of weight, but at least in the US it has become obsolete and available for recycling. According to Webster's, the stone is "a varying unit of weight..." Besides the English stone of 14 pounds, "other values are or have been in use varying from 4 to 26 pounds." Stone is permissible, I think, as a familiar word which has traditionally been used for measures of weight and which can evoke an appropriate image.

spanstone

Spanstone, like the traditional name footpound, needs no comment. Applied to energy in any form, it designates an amount equivalent to that delivered by pushing for the extent of a span while exerting a stone of force. To be specific, you could picture it as the effort of lifting a fist-sized stone by the width of a palm with thumb extended. The Planck energy, to the accuracy with which it can be experimentally measured, is one billion spanstone.

dram

The practice of quantifying electricity is so recent that little in the way of traditional vocabulary has accumulated. Lack of alternatives to the metric measure of electric charge necessitates a minor exercise of philological taste. I judge it permissible to borrow the name of a traditional measure of some other type of charge--in this case an explosive charge of gunpowder. A dram of gunpowder was the typical charge of explosive used to load small firearms such as flintlock pistols.

The word charge derives from the Latin carrus meaning wagon and is connected with the idea of loading a container or carrier. Essentially, to charge means to load. The word dram comes from the Greek word drachma, fortuitously associated with a variety of charges. There is yet another connection in which the word dram is evocative. The once-familiar dram-shop sold spirits by the shot. Electricity has traditionally been seen as a subtle fluid metaphorically akin to fire, which can suggest the image of a volatile essence. Patrons at a dram-shop consumed drams of distillates which in other contexts have been called "fire-water" and "white lightning". A dram-shop customer was subject to becoming loaded, in the modern colloquial sense, and to being charged as well.

Judging from the specs printed on the side, each of the rechargeable nickel cadmium D cells I see around the house can, in the course of a discharging cycle, supply close to 10,000 drams of charge at a potential of 1.25 conventional volt. When it comes to precise definition, we will make a dram correspond to the charge on 10 electrons.

vôlt

From a traditional perspective the Planckish volt is slightly too large to be called volt. Historically there has been some variation in volts but never, as far as I know, as much as 20%. But there is no other common name for a measure of this type, and hence no acceptable alternative. Applying any other word seemed to be a jarring impropriety. I decided to use a circumflex accent to distinguish between our Planckish volt and the conventional one. And to drop the accent mark later if it seemed unneeded.

Voltage indicates a provision of energy per unit charge, so it would be possible to express the unit of energy as a dram vôlt which is the energy of one dram of charge delivered at one vôlt potential. The other way we have of referring to the unit of energy is spanstone--the work performed by pushing with a stone of force for the distance of one span--and the two are equivalent. The household D cells mentioned earlier are rated by the manufacturer at 1.25 conventional volts, which is close to one of our volts. Each is, in effect, a one vôlt cell able to deliver ten thousand drams on a single charging. Accordingly, each fully charged cell represents a store of energy which is on the order of ten thousand dramvôlts.

amber

The Greek word elektron, which meant shining, was applied to the substance amber. Appied to the practical Planck unit of current, the name amber is double play on words, because it also sounds like ampere. One amber of electric current consists of 10 electrons passing by in a semisecond--in other words one dram per semisecond. By way of illustration, when the rechargeable D cell mentioned earlier is supplying one amber of current at one vôlt it is delivering energy at the rate of a voltamber (3.6 conventional watts). It can supply one amber of current for approximately ten thousand semiseconds, in other words ninety minutes.

eevee

An eevee (short for electron vôlt) is the quantity of energy which a one vôlt cell supplies with each electron circulating from it. During some interval of time, if the cell circulates 10 electrons then it delivers 10 eevee of energy. This is a microscopic measure of energy. Light consisting of 2 eevee photons is seen as green. Although a small quantity, the eevee can be regarded as a practical unit for a variety of reasons besides its connection with eyesight. A mnemonic rhyme may be appropriate here.

In burning diesel fuel or wheat,
An Oh-Two count will tell the heat.
For every molecule you see
The yield is three-point-four eevee.

In burning ordinary hydrocarbon fuels or in metabolizing carbohydrates, despite the different fuel values there is not much difference in the energy released if it is calculated per molecule of oxygen consumed. Whether the fuel is wood, oil, ethanol, or spaghetti, the energy yield is typically close to 3.4 eevee per O₂ molecule involved.

In an earlier section on heat capacity we were somewhat hampered by not having already introduced this unit. There is an exact identity, in humanly scaled terms, according to which the Boltzmann constant k=/=10^-4 eevee per degree. More discussion of the degree of temperature is coming up shortly.

The name eevee is commonplace and requires no discussion. Because the unit is so convenient (light, chemical reactions, heat at the molecular level), it seems advantageous to have it in clear power-of-ten relation to the others. And indeed one of our practical Planck energy units, a spanstone, is equal to a dramvôlt, which is equal to exactly ten-to-nineteen eevee.

degree

If you are studying nature there is no use to any but an absolute temperature scale, that is one that begins at the REAL zero of temperature rather than at some arbitrary false zero. This is because temperature works in nature by its proportionality to a host of little energies in the environment--at the level of molecular and crystal lattice motion, at the level of bits of heatshine, and so on.

In the metric system the step on the absolute scale is called the kelvin. IT IS INCORRECT, according to a ruling handed down in 1967 by the thirteenth General Conference on Weights and Measures, to say DEGREES kelvin. You are supposed, if you are a proper metric-speaker, to just say "273 kelvin" for the melting point of ice. As metric-speaker, you are not supposed to say degrees.

Evidently, the official body in charge of the metric system objects to "degree" as the step on temperature scales, and has consigned the word to retirement. So lucky us, we can have it for free. In practical Planck units, a degree is equivalent to 1.417 kelvin. And it is as close to 10 of Planck temperature as the latter can be experimentally determined. Here are some sample temperatures on the practical Planck scale:

The microwave background is 1.93 degrees.
Ice melts at 193 degrees.
The average temperature on the earth's surface is 200 degrees.
A chilly outdoor temperature is 200 degrees (Fahrenheit 50).
Room temperature is commonly 207 degrees.
The conventional norm for body temperature is 219 degrees.
A good oven setting to bake bread is 320 degrees.
The tungsten filament of a hundredwatt bulb operates around 2000 degrees.
The sun's surface is around 4080 degrees, shown by its color.

The Boltzmann temperature coefficient k, should you be familiar with it, has an exact value in practical Planck units of 10 spanstone per degree. Any temperature scale is fundamentally an alternative scale of energy. In the present case, the characteristic energy k associated with the Planck temperature is the Planck energy .