Anthropic units: Wikis

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The ability to characterize, quantify, and measure objects in the physical world is an essential milestone towards the development of complex human civilizations. A vast number of measurement standards have evolved over time, and these standards have arisen from many disparate sources. However, in a broad sense, one can categorize these standards as being either a part of nature or a construct of humanity.

The term “natural units” designates measurement standards which arise from aspects of nature which are independent of human physiology, behavior, and culture. In the physics community the term natural units is used in an even more restricted sense, to only include units which are defined in terms of universal physical constants, such that some chosen set of physical constants each have a numerical value of exactly 1 when expressed in those natural units.

In contrast to natural units, the term “anthropic units” (a neologism meaning human units) describes measurement units which explicitly arise from human physiology or behavior, or which are primarily a construct of human culture. Some were derived directly from the dimensions of the human body, and as such, are commonly referred to as anthropomorphic (meaning human shaped). Other anthropic units evolved indirectly from human activities such as walking or farming, or were invented by humans to support human endeavors.

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Anthropomorphic units

Anthropomorphic units are a special subclass of anthropic units. Anthropomorphic units are derived directly from the dimensions of the human body (form), and many have names which reference the specific part of the body from which the unit originated. Some common examples are as follows:

Hand-derived units of measurement:
1: Shaftment
2: Hand or handbreadth, commonly used to represent the width of the palm, sometimes including the thumb when closed against the palm
3: Palm, sometimes also represented by four fingers held together, which is slightly less than the true width of the palm at the knuckle
4: Span
5: Finger or fingerbreadth
6: Digit slightly smaller than a finger)
Digit 
Digit is a Latin word meaning finger. As a unit of length, the digit is currently standardized to be a sixteenth of a foot. In English the word “finger” or “fingerbreadth” is also a unit of length, although the finger length is slightly larger than the digit. From a practical standpoint, fingerbreadths can easily be used to measure by simply placing ones hand on an object and counting the number of fingerbreadths that cover a specific distance.
Inch 
The English word “inch” was derived from the Latin “uncial” meaning one twelfth, and the inch is defined to be a twelfth of a foot. The historical origin of the inch as a length is disputed, but there is evidence relating it to the average width of a man’s thumb. Other European languages have similarly sized anthropomorphic units with names directly derived from the word for thumb in that language, so it is reasonable to assume that the English inch is an anthropomorphic derivation of the thumb width.
Palm and Hand 
Palm and hand, or handbreadth, have both historically been used in English to refer to specific lengths. The hand or handbreadth is currently standardized to be four inches, whereas the palm is standardized to be three.
Shaftment 
A shaftment is the width of the fist and outstretched thumb. The lengths of poles, staves, etc. can be easily measured by grasping the bottom of the staff with thumb extended and repeating such hand over hand grips along the length of the staff. The shaftment is currently standardized to be six inches, or half of a foot.
Span 
A span is the width of a human hand, from the tip of the thumb to the tip of the pinky finger. The span, from ancient times, has been considered to be 1/2 cubit (as described below). The span is currently standardized to be nine inches.
Foot 
The human foot can easily be used to measure floor distances by placing one’s right heel against a wall, and placing the left foot in front of the right foot with the heel of the left foot touching the toes of the right foot. Then step forward placing the right foot in front with the heel touching the left toes. Repeat this foot over foot placement across the floor distance, counting footsteps. The standardized English foot is defined to be twelve inches, although this is larger than what is typically found in human populations.
This derivation of the Vitruvian Man by Leonardo da Vinci, depicts nine historical units of measurement: the yard, the span, the cubit, the Flemish ell, the English ell, the French ell, the fathom, the hand, and the foot. The Vitruvian Man was drawn to scale, so the units depicted are displayed with their proper historical ratios.
Cubit 
The cubit is the length of the forearm (from the elbow to the fingertips). The cubit is a very old unit of measurement used in many ancient cultures with different length values. The modern cubit is standardized to be 1.5 feet, or 18 inches.
Fathom 
A number of anthropomorphic techniques have evolved for measuring cords and textiles, and these techniques have resulted in various anthropomorphic measurement units. The fathom is a unit of length derived from an old English word meaning outstretched arms. It is currently standardized to be six feet or 72 inches. A technique for measuring ropes is to hold a length of rope taut between one’s hands while holding the left hand out as far as possible to the left side of the body and the right hand out as far as possible to the right side of the body. When the hands are brought together this length of rope will form a loop. This loop may be placed in the left hand while the hands are again outstretched to grasp another length and then brought together to form another loop. By repeating this process, the rope can be completely gathered into loops. The length of each loop will be equal to one fathom (the length of ones outstretched arms). Therefore, the total length of the rope in fathoms can be determined by counting the number of loops.
Ell and Yard 
The ell (meaning arm) and yard are both anthropomorphic units with origins similar to the fathom described above. The English ell is the length from a hand to the opposing shoulder, currently standardized to be 45 inches. The yard is the distance from a hand to the center of the chest, currently standardized to be 36 inches. These lengths can be used to measure ropes and textiles using a technique similar to that described above for the fathom, but with slight variation. A fathom of rope is obtained by holding the rope taut between the hands with the hands outstretched as far as possible. An ell is obtained when the rope is held taut with the left hand outstretched to the left of the body, while the right hand is held close to the right shoulder. A yard is obtained when the left hand is outstretched to the left while the right hand is held near the center of the chest.

Other Anthropic units

Some anthropic units were not directly derived from any part of the human anatomy, but rather, evolved indirectly from human behaviors such as walking or farming. A few examples are as follows:

Farm-derived units of measurement:
  1. The rod is a historical unit of length equal to 5½ yards. It may have originated from the typical length of a mediaeval ox-goad.
  2. The furlong (meaning furrow length) was the distance a team of oxen could plough without resting. This was standardised to be exactly 40 rods.
  3. An acre was the amount of land tillable by one man behind one ox in one day. Traditional acres were long and narrow due to the difficulty in turning the plough.
  4. An oxgang was the amount of land tillable by one ox in a ploughing season. This could vary from village to village, but was typically around 15 acres.
  5. A virgate was the amount of land tillable by two oxen in a ploughing season.
  6. A carucate was the amount of land tillable by a team of eight oxen in a plowing season. This was equal to 8 oxgangs or 4 virgates.
rod
The rod has essentially the same meaning now that it originally had, being a straight branch or pole. The length of the rod may have originated from the typical length of a mediaeval ox-goad. The rod is currently standardized as 5.5 yards.
furlong 
The furlong is a unit of length derived from the Old English words furh (furrow) and lang (long). It was originally defined as the length a plough team was to be driven without resting. It was later standardized to be 40 rods or 220 yards.
acre
The word acre is derived from an old English word meaning an open field. It was approximately the amount of land tillable by one man, behind one ox, in one day. A rectangle of length 1 furlong and width 4 rods (1 chain) has an area of 1 acre. There are 640 acres in a modern square mile.
pace
A pace is a measure of distance used in Ancient Rome. It is the measure of a full stride from the position of the heel when it is raised from the ground to the point the same heel is set down again at the end of the step. Thus, a distance can be "paced off" by counting each time the same heel touches ground, or in other words, every other step. In Rome this unit was standardized as five Roman feet (about 1.48 metres or 58.1 English inches).
mile 
The mile is a modern derivation of the Ancient Roman “mille passus” which literally means "a thousand paces" in Latin. The Roman pace was standardized as five Roman feet, so the Roman “mille passus” was 5,000 Roman feet (about 1,480 meters, or 1,618 modern yards). The current definition of a mile as 5,280 feet (as opposed to 5,000) dates to the 13th century.
league 
The league is an ancient unit of length defined as the distance a typical person could walk in an hour. In ancient Rome the league was standardized to be 1.5 Roman miles. In modern times the league is generally standardized to be 3 miles.

Anthropically Scaled Natural Units

Anthropic units and natural units each have unique advantages and disadvantages. Anthropic units, which arise from human physiology and behavior, often have the advantage of being accessible to humans and useful for human purposes. The disadvantage of anthropic units is that they are often difficult to standardize.

Some of the scale factors used in metric unit definitions are illustrated in the images below. The length of the line below each scale factor is a logarithmic representation of the value. A black line indicates that the scale factor is currently used in the definition of the unit. A red line indicates that the scale factor is no longer in use. And a green line indicates that the scale factor is being considered for future use.

  • The conventional weber is equal to four hundred and eighty three billion, five hundred and ninety seven million, nine hundred thousand quanta of magnetic flux.
  • The modern second is equal to nine billion, one hundred and ninety two million, six hundred and thirty one thousand, seven hundred and seventy periods of the caesium 133 hyperfine transition frequency.
  • The modern Kelvin is obtained by using absolute zero and the triple point of water to define a temperature range, and then dividing that range by a scale factor of two hundred and seventy three and sixteen hundredths.
  • The conventional ohm is obtained by dividing the von Klitzing constant by a scale factor of twenty five thousand, eight hundred and twelve, and eight hundred and seven thousandths.
  • The modern metre per second is obtained by dividing the speed of light by a scale factor of two hundred and ninety nine million, seven hundred and ninety two thousand, four hundred and fifty eight.

The cubit (forearm length), for example, is an ancient unit used in many cultures. A person’s forearm is almost always available, and using one’s forearm to measure distances removes the necessity of carrying additional measuring devices. Also, the forearm is a good standard length for measuring human scaled objects such as buildings and ships. However, one person's forearm length might vary from another person's forearm by as much as a few inches. A boat might be 30 cubits long to a large person but as much as 40 cubits to a small person. This could cause difficulties where collaboration is required. Also, human bodies continually grow and change shape over time, so anthropomorphic measurement systems are inherently unstable.

Natural units have the advantage of being independent of human culture and behavior. Some examples are the circumference of the earth, the duration of a day, the mass of an electron, and the triple-point of water. Since these values are independent of human populations and outside of human control, they can be used as international standards without discriminating against any particular person, group, or nation. Also, unlike the dimensions of the human body, natural values can be determined to a high degree of accuracy and are unlikely to change over time. Therefore, they are ideal for collaboration and standardization.

Natural units, however, have their own unique set of disadvantages. The primary disadvantages being that natural units are often inaccessible to common people and not useful for human purposes. For example, it would be difficult for an untrained person to measure the circumference of the earth to any degree of accuracy. And even if they could, it would be difficult to use this length for human purposes. For example, how tall are you in terms of the earth’s circumference?

There has been a trend in the last few hundred years towards the use of anthropically scaled natural units. In an anthropically scaled system, one chooses a natural unit and then multiplies that unit by a scale factor to obtain a base unit that is useful for human purposes. Anthropically scaled natural units harness the advantage of being both natural and anthropic. Some examples are as follows:

Universal Time (UT
Our current system of dividing the day into 24 hours, with 60 minutes in each hour and 60 seconds in each minute, is perhaps the oldest example of an anthropically scaled natural system. The day is a natural unit of time, since its duration is beyond human control, but the duration of the day is too long to be suitable for many human time measurements. Therefore, to obtain a set of time units suitable for human activities, the day was divided into hours, minutes, and seconds.
nautical units 
The nautical system of length units is another example of an anthropically scaled natural system. The nautical system divides the circumference of the earth into 360 degrees, with each degree being divided into 60 nautical miles, and each nautical mile being divided into one thousand nautical fathoms. Also, in analogy to the statutory league, a nautical league is defined to be 3 nautical miles.
grain mass 
In many cultures, a grain was a natural unit of measurement of mass that was based upon the mass of a single seed of a typical cereal. These grain mass units were often too small for common human purposes; therefore, a scale factor was used to obtain a larger more useful anthropic mass unit. The avoirdupois pound, for example, was defined to be 7,000 barley grains. The troy pound was defined to be 5,760 barley grains. And the tower pound was defined to be 7,200 wheat grains (or 5,400 barley grains).
Fahrenheit Temperature 
In the early 1700s, when Daniel Fahrenheit manufactured mercury- and alcohol- filled thermometers, he used three temperatures to determine a temperature range: the first temperature was obtained by mixing water and ice with ammonium chloride, the second by mixing water and ice without ammonium chloride, and the third by placing the thermometer in the mouth or armpit of a healthy person. However, these three temperatures alone were insufficient for human purposes, so Daniel used a scale factor to obtain additional values. The mixture of water, ice, and ammonium chloride was used to define a temperature of zero degrees Fahrenheit. The human body was used to define a temperature of ninety six degrees Fahrenheit. This placed the freezing point of water at thirty two degrees Fahrenheit.
metric units 
When the French invented the original metric system in the late 1700s, they used survey data to estimate the length of one quadrant of the earth (the distance from the equator to the north pole). To achieve a manageable length unit, the French divided the earth’s quadrant into 10 million equal parts. The length obtained through this method was named the metre. The French then used the metre to define other measurement standards. The standard volume, the litre, was defined to be a thousandth of a cubic metre. And the standard mass, the gram, was defined to be a thousandth of the mass of a litre of pure water. These original metric units were all anthropically scaled natural units, based on the circumference of the earth.
International System of Units 
In the subsequent two hundred years since its inception, the metric system has evolved into the International System of Units (SI). There are currently seven base SI units: the metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd). The definitions for the base units of the metric system have changed over time, but most are still anthropically scaled natural units, the notable exception being the modern kilogram which is defined in terms of an artifact. There is, however, currently a movement in the international community to increase the accuracy of the kilogram by redefining it in terms of an anthropically scaled natural value.

Anthropically Biased Natural Units

The above image illustrates a human bias in the original definitions of the metric system. Two units, the metre and second, were respectively derived from the shape and rotational period of the earth. The metre was defined to be one ten millionth of a quadrant of the earth and the second was one eighty six thousand four hundredths of a day. Three other metric units, the Kelvin, the kilogram, and the mole, were derived from major components of the human body. About 70% of the human body is water. Another 25% is carbon based organic substances. The definition of the Kelvin is such that the freezing and boiling points of water differ by 100 K. The kilogram is a thousandth of the mass of a cubic metre of pure water. And the mole is the number of carbon 12 atoms in 0.012 kilograms.

Natural units are intended to be directly derived from nature and to be free of human influence. However, our selection of a particular unit is often driven by a human preference. Therefore, we might use the term “anthropically biased natural units” to designate natural units which were selected because of a particular human prejudice, preconception, bias, or preference. The following are examples of an anthropic bias in the selection of natural units:

Motions of the Earth and Moon
Most of the units used in human time measurement were derived from the motions of the earth and moon. Some examples include the year, the month, the day, the week (7 days), the hour (day / 24), the minute, and the second. The motions of the earth and moon figure prominently in human lives. These motions cause changes in the weather from one season to the next, and they cause changes in ambient brightness from night to day and from new moon to full moon. Given the profound impact of these motions on human life, it is not surprising that humans have an anthropic preference for using these motions to measure time.
Dimensions of the Earth,
A number of measurement units were derived from the dimensions of the earth. These earth-derived units include the nautical league, the nautical mile, the nautical fathom, the metre, the litre, and the kilogram. Humans live on the earth, and the shape of the earth is an important factor in human endeavors such as navigation. So using the shape of the earth to obtain measurement units is a clear example of an anthropically biased choice.
Triple Point of Water
The Kelvin temperature scale is obtained by using absolute zero as the Kelvin zero point, and then setting the triple point of water as the Kelvin scale value of 273.16. This definition may not immediately appear to be anthropically biased. Water is a natural substance, and the triple point is a fundamental property of any natural substance. Therefore, the triple point of water is a fundamental value of nature and not an anthropic value. However, there may be an anthropic bias in the selection of water for this purpose. The earth is the only known planet to have large quantities of water in all three states, solid, liquid, and gas. This abundance of water on earth may have given humans a preconceived notion of the importance of water. Hence, humans have an anthropic bias towards using water to define measurement units.
Carbon-12 Atoms
The mole is currently defined as the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. The selection of Carbon 12, as the element used in this definition of the mole, is similar to the use of water in the definition of the kelvin described above. Carbon is one of the most important elements for human life. In fact, Carbon is a component in all organic substances. Therefore, humans have a prejudice in favor of the element carbon, and this prejudice may have guided the decision to use carbon in defining the mole.

The Anthropic Principle

The term “universal physical constants” is used in the scientific community to designate those constants of nature which represent the least amount of anthropic bias. To understand the meaning of this term, it is helpful to imagine highly intelligent non-human beings existing in some remote part of the universe. With such beings in mind, one can classify various natural constants in terms of the relative importance that these imaginary beings might place on them.

For example, human astronomers often use the “astronomical unit” (AU) as a reference for measuring distances in the solar system. The astronomical unit is defined as the mean distance of the earth’s orbit from the sun. This distance is an important reference for humans because it represents the orbit of our planet. But this distance probably wouldn’t be important to intelligent beings in some remote part of the universe. So the astronomical unit is not a “universal” constant of nature.

As a less obvious example, humans use properties of both water and the element carbon to derive measurement units. Water and carbon are both universal substances (believed to exist everywhere in the universe), so intelligent beings in some remote part of the universe might have access to these substances. However, they might not place the same importance on these substances. To understand this, consider that computers display some of the attributes of human intelligence. But unlike humans, computer chips are primarily composed of silicon. So if intelligent beings elsewhere were composed of silicon then they might not value carbon as an element.

Although still a topic of debate, Scientists have achieved a level of consensus with respect to the universal status of certain physical constants. The constants which appear most likely to be universal are the following:

The masses and various other properties of elementary particles and the coupling values associated with the strong, weak, and electromagnetic interactions are also considered to be universal.

As a final twist, some scientists now believe in the existence of other universes. The exact nature of these other universes and their topological connection to our universe is a topic of speculation and debate. But if they do exist, then some scientists further speculate that the values of universal constants may not be the same in each of the universes as in the others. For example, the speed of light might be faster or slower in one universe than it is in another. Scientists further speculate that if the universal constants are different in differing universes, then some universes may have values which support the evolution of intelligent life and others may have values which repress the evolution of life. Scientists and philosophers further speculate that it may be impossible for a universe which does not support intelligent life to exist, because existence is verified through observation by an intelligent being; therefore, a universe can not exist without an observer.

This belief in many universes, together with the belief that some universes have natural properties which prohibit the evolution and existence of intelligent life, is known as the anthropic principle. If the anthropic principle is correct, then one might rightly conclude that all units of measurement are anthropic units. This conclusion is drawn from the fact that we live in a universe which supports human life; therefore, our universe is an anthropically biased universe. Furthermore, any constants of nature that exist in our universe will be anthropically biased. Hence, our units of measurement will be anthropically biased.

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