Measure for measure

In yesterday's post we looked at one bizarre human obsession, which is drawing lines all over the place and pretending they represent something real.  Today we're going to look at another, which is our penchant for quantifying everything.

Certainly, accurate measurement is critical in science; data, for the most part, is numerical, and most models these days are mathematical representations of reality.  But still, there's a strange aspect to it, which British science historian James Burke got at in his brilliant series The Day the Universe Changed:

[T]he structural view of things at the time controls what science does at every level.  From the cosmic questions about the whole universe, to what bits of that universe are worth investigating, to how far you let the questions take you, what experiments to do, what evidence you can and can't accept.  And down at that detailed level, the control still operates, because it even tells you what instruments you should use.  And of course, at this stage, you're looking for data to prove your theory, so you design the kind of instruments to find the kind of data you reckon you're going to find.  The whole argument comes full circle when you get the raw data itself.  Because it isn't raw data.  It's what you planned to find from the start.

He goes on to make the important point that true leaps in understanding occur when the unexpected occurs, and some piece of the data doesn't fit with the existing model; then (assuming the data are verified and found to be correct), there's no choice but to revise the model -- or trash it entirely and start over.

[Image is in the Public Domain]

But what this has done is created a morass of different units of measurement, and I'm not referring solely to my own country's pig-headed insistence on avoiding the use of the metric system.  Imperial units -- feet, miles, pounds, quarts, and so on -- are certainly cumbersome (check out this hilarious video if you want to find out just how awkward they are), but they're not the weirdest ways that humans have chosen to subdivide the natural world.  So for your edification, here are a few of the stranger units of measurement I've run into:

• the micromort -- defined as a one-in-a-million chance of death.  For example, smoking a cigarette and a half increases your chance of dying by about one micromort.
• a jiffy is 1/60 of a second, from the vertical refresh period on NTSC analog video hardware running on American (60 Hertz) alternating current.  So next time someone tells you, "I'll be back in a jiffy," you can confidently respond, "I seriously doubt that."
• so many people in Britain publicly compared the areas of geographical regions to the size of Wales that it led to a unit of area, the nanowales -- one billionth the area of Wales, or about 20.78 square meters.
• the Sverdrup, named after Norwegian oceanographer Harald Sverdrup, at least has its basis in metric units.  It's a unit of flow rate, equal to one million cubic meters per second.  Being as huge as it is, you might imagine it has limited utility -- in fact, it's pretty much only used in oceanography and meteorology.  (For reference, the flow rate of the Gulf Stream varies between 30 and 150 Sverdrup, depending on where you measure it and what you consider its boundaries to be.)
• the dolor is a unit of pain.  One dolor is equal to the difference between two levels of pain that is just noticeable.  The subjective nature of pain has resulted in it not being widely accepted in the medical community.
• a millihelen is a unit of beauty, named after Helen of Troy -- the amount of beauty required to launch one ship.
• when I taught dimensional analysis in physics, I had students practice converting from one set of units to another -- a useful skill when doing science.  I always made a point of having them convert velocities from meters per second to furlongs per fortnight, which firmly cemented in their brains that I have a screw loose.  (For what it's worth, a furlong is 660 feet, or about 201.17 meters; a fortnight is fourteen days, so 1,209,600 seconds.  Thus, the speed of light is about 1.8 terafurlongs per fortnight, a factoid you can bring out at the next cocktail party you attend, especially if you want people to find ways to avoid you for the rest of the evening.)
• one mickey is the smallest resolvable movement possible with a computer mouse.  Most of them have a sensitivity of about five hundred mickeys per inch.
• a Smoot is a unit of length, named after Harvard student Oliver R. Smoot.  The story is that one day in 1958, Smoot got falling-down drunk, and his buddies (who were also snookered but not as badly as Smoot was) were basically dragging him home, and decided to measure the length of the Harvard Bridge in Smoot-lengths (about 170 centimeters).  The bridge, they found, was 364.4 Smoots in length plus a little bit, so there's now a plaque saying "364.4 Smoots and an ear" on the bridge.  (Smoot went on, I shit you not, to be the chairperson of the American National Standards Institute and president of the International Organization for Standardization.  Talk about being destined for a particular career.)
• the weirdest unit of volume I've ever heard of is the Hubble-barn.  This combines the Hubble length -- the radius of the known universe -- with a unit of area called the barn, which is used to measure the scattering cross-section of atomic nuclei and is equal to 10^-28 square meters.  One Hubble-barn is the volume of a rectangular solid that has a square face with an area of one barn stretching across the entire known universe.  If you do the calculation, it's way less volume than you'd think -- on the order of 13.1 liters.
• last, we have the ohnosecond, which is the time elapsed between making a mistake and recognizing it, such as pressing "send" on an email describing details of some illicit but highly pleasurable activities you want to experience with a coworker with whom you're having a clandestine dalliance, and realizing too late that you forgot to change the "to" line from "Reply All."

So there you have it -- some ways to measure the world, some serious, some not so much.  In any case, I'd better wrap this up.  So far I've had only about 0.02 Hubble-barns of coffee, so I'm moving at a velocity of around a furlong per fortnight.  I should post this, and hope that there are at least a few ohnoseconds between hitting "Publish" and seeing what I've wrought.

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Egyptian light speed

There's a claim I've now seen three times on social media stating that the ancient Egyptians knew the speed of light.

This is pretty outlandish right from the get-go, as there is no evidence the Egyptians had invented, or even had access to, any kind of advanced technology.  Plus, even with (relatively) modern technology, the first reasonably decent estimate of the speed of light wasn't made until 1676, when Danish astronomer Olaus Roemer used the difference in the timing of the eclipses of the moons of Jupiter when the Earth was moving toward them as compared to when the Earth was moving away from them, and came up with an estimate of 225,300,000 meters per second -- not too shabby given the limited technology of the time (the actual answer is just shy of 300,000,000 meters per second).

But there's something about those ancient Egyptians, isn't there?  There have been "secrets of the Pyramids" claims around for years, mostly of the form that if you take the area of the base of the Pyramid of Khufu in square furlongs and divide it by the height in smoots, and multiply times four, and add King Solomon's shoe size in inches, you get the mass of the Earth in troy ounces.

Okay, I made all that up, because when I read stuff about the "secrets of the Pyramids" it makes me want to take Ockham's razor and slit my wrists with it.  But I was forced to look at the topic at least a little bit when the aforementioned post about the speed of light started popping up on social media, especially when a loyal reader of Skeptophilia said, "You have got to deal with this."

The gist is that the speed of light in meters per second (299,792,458) is the same sequence of numbers as the latitude of the Pyramid of Khufu (29.9792458 degrees north).  Which, if true, is actually a little weird.  But let's look at it a tad closer, shall we?

[Image licensed under the Creative Commons Jerome Bon from Paris, France, Great Pyramid of Giza (2427530661), CC BY 2.0]

29.9792458 degrees of latitude is really specific.  One degree is approximately 111 kilometers, so getting a measurement of location down to seven decimal places is pretty impressive.  That last decimal place -- the ten-millionths place -- corresponds to a distance of 0.0111 meters, or a little over a centimeter.

So are they sure that last digit is an 8?  Measuring the position of the Great Pyramid to the nearest centimeter is a little dicey, given that the Great Pyramid is big (thus the name).  Even if the claim is that they're measuring the position of the top -- which is unclear -- the location of the top has some wiggle room, as it doesn't come to a perfect point.

But if you're just saying "somewhere on the Great Pyramid," there's a lot of wiggle room.  The base of the Pyramid of Khufu is about 230 meters on an edge, so that means that one-centimeter accuracy turns into "somewhere within 23,000 centimeters."

Not so impressive, really.

There's a second problem, however, which is the units used in all the measurements in the claim.  The second wasn't adopted as a unit of time until the invention of the pendulum clock in 1656.  The meter as a unit of length wasn't proposed until 1668, and was not adopted until 1790.  (And some countries still don't use the metric system.  *glares at fellow Americans*)  So why would the ancient Egyptians have expressed the speed of light -- even assuming they could figure it out -- in meters per second, and not cubits per sidereal year, or whatever the fuck crazy units of measurement they used?

Oh, and while we're at it, the first person to slice a circle up into 360 degrees -- the basis, of course, of our system of latitude -- was Hipparchus, who lived in the second century B.C.E.  Which, not to put too fine a point on it, was two-thousand-odd years after the Great Pyramids were built.  So to sum it up: what we're being asked to believe is that the ancient Egyptians sited the Great Pyramid based upon a quantity they didn't know how to measure, expressed in terms of three units that hadn't been invented yet.

Makes perfect sense.

So as expected, this claim is pretty ridiculous, and not even vaguely plausible if you take it apart logically.  Not that there was any doubt of that.  In fact, this is only one of dozens of examples of pseudoscientific metrology, which is the general name for claims that the measurements of ancient structures have some relevance to scientific findings.  The bottom line is that the ancient Egyptians were cool people, and the pyramids they built are really impressive, but they weren't magical or advanced or (heaven help us) being assisted by aliens.

No matter what you may have learned from the historical documentary Stargate.

Oh, and for the record, I didn't invent the unit of "smoot" for length.  A smoot is 1.70 meters, which was the height of Harvard student Oliver R. Smoot, who in 1958 got drunk with his fraternity buddies, and as they were dragging the semi-conscious Smoot home, they decided to measure the length of Harvard Bridge in Smoot-heights.  It turned out to be 364.4 smoots long, plus or minus the length of Oliver R. Smoot's ear.

And considering they were drunk at the time, it's pretty impressive that they thought of including error bars in their measurement.  Better than the damn Egyptian-speed-of-light people, who couldn't even get their measurement to within plus or minus 230 meters.

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Orders of magnitude

Our minds tend to boggle when numbers get too large or too small.

It's why we get in trouble talking about things like the national debt.  To a lot of people, a million dollars, a billion dollars, and a trillion dollars all sound pretty much alike; "more money than we're ever likely to see in our lives."  Explaining that a trillion dollars is "the amount of money owned by a million millionaires" helps some, but the fact remains that we can't really wrap our brains around numbers that big.

The same thing happens on the small end.  I remember trying to get my students to grok the difference between the sizes of small things -- say, an amoeba, a virus, a DNA molecule, and an atom.  My analogy for the size of the atom is that if you had as many grains of sand as there are atoms in a typical raindrop, you'd have enough sand to fill a trench a foot deep, a mile wide, stretching from New York City to San Francisco.

It was a good "oh wow" moment, but once again, I'm not sure how much good it did to fight the general trend of our not being able to conceptualize things that are very far outside of the scales we're used to.

The more we find out through science, though, the wider the actual scales of our understanding need to grow.  This is why if you want to have a prayer of getting anywhere in science, you need to understand scientific notation -- a way of notating very large or very small numbers, such as the speed of light, which is 300,000,000 meters per second -- or, as it's put in scientific notation, 3x10^8 meters/sec.  The bigger (or smaller) the numbers get, the more useful scientific notation is; take, for example, the distance to the Andromeda Galaxy, which is 2.4x10^19 kilometers (24 followed by eighteen zeroes).  With something that large, just counting the zeroes to get an idea of what magnitude you're talking about becomes unwieldy.

On the other hand, for unwieldy, you can't beat the English units of measurement. This is a chart of the relationships between the ones for length. The rest of them are just as bad. [Image licensed under the Creative Commons Christoph Päper, English length units graph, CC BY 3.0]

The same thing happens on the other end of the scale.  The width of one of your DNA molecules is about two billionths of a meter; in scientific notation, 2x10^-9 meters.  (The negative sign means the decimal point is moved to the left; this is 0.000000002 meters.)

To obviate the need for such large exponents, there are prefixes used to get rid of some of the zeroes.  Some are familiar -- "kilo-" for a thousand, "milli-" for one-thousandth, "micro-" for one millionth, and so on.  This, in fact, is the reason this comes up; we've plunged so deep into the realms of the very large and the very small that the previous ones have proven insufficient, so they've invented four new ones and tacked them onto the outside of the scale.

It's not like we didn't already have some pretty extreme prefixes.  On the large end, we go up to "yotta-," meaning 10^24.  On the other end, "yocto-" means 10^-24.  But now we have "ronna-" and "quetta-" (10^27 and 10^30, respectively) and "ronto-" and "quecto-" (10^-27 and 10^-30, respectively).  (Abbreviations are, in order, R, Q, r, and q.)  For reference, the Sun has a mass of about two thousand quettagrams; an electron, one rontogram.

The funny thing is, even these won't cover all contingencies.  When you get to galactic masses, you're talking about something that would require scientific notation even if you measured it in quettagrams.  And in the realm of the very small, when you get down to where physicists believe even such quantities as length and time are quantized (made up of chunks that can't be subdivided any further), you're still in the negative exponent range.  These Planck units of length and time are, respectively, 1.6x10^-35 meters (1.6x10^-5 quectometers) and 5.4x10^-44 seconds (5.4x10^-14 quectoseconds).

So we're still not out of the woods.  But I don't mind, because "quectosecond" is fun to say.

I'm not sure if this does anything to help the original problem -- that our brains can't really handle very big and very small numbers.  Anything more than a couple of orders of magnitude outside of what we deal with every day, and we boggle.  Which is why I think, science geek that I am, that I'm going to stick with my friend's favorite large unit of mass, which is the "metric shit tonne."

At least I have a pretty good idea of what that means.

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