Prefixes and Standard Non-Scientific Measurements - What fun!

coco
seca
kilo
milli
mega
micro
giga
forever ever more
nano
tera
pico
femto
exa
peta

When I was a young Physics student, I was convinced that the SI system of measurement was a critically important component in the collective understanding of the universe. Combined with the standard prefixes used by the Presets in the lyrics above, just about anything could be described in SI, and scientists and laypeople everywhere could comprehend size, mass, energy, and just about every possible dimension in the universe.

Hah. 

Apparently there are different units of measurement which are more practical for ordinary people, according to science, journalism and communications, and popular culture. Sometimes they are silly. Sometimes they are intuitive. Sometimes they are critical to ongoing scientific progress.
I figured this contradiction was worth a post.

Silly: The large African herbivore as a measure of mass or dimension

This is strange to me for two reasons. 

Firstly, animals do not have standard weights. A tram weighs as much as 30 rhinos? How about that! Hangon, which gender? Which species?

Rhinos range in mass from the smallest, the Sumatran, averaging 800kg, to the largest, the Greater One-Horned Rhino averaging 1900kg. The males of both species are typically 130% the weight of the females. 

The second problem is lack of familiarity with large mammals.

Rhinos are endangered. I do not live in a rhino habitat. I have seen no more than a dozen rhinos in my life, in various zoos. In a 500km radius of my house, there are only about 6 rhinos, all at the Werribee Open Range Zoo. 

On the other hand, there are 6 trains an hour on my local tram route, outside peak times. 12 trams during peak times.

(Trams do not have standard weights either. The chock-full peak hour tram is clearly going to be heavier than the 11AM tram with only the two feral kids wagging school and the smelly hobo lady with the trolley who is talking to herself.)

So how is it that a poster which compares a completely unfamilar, and highly variable, large mammal with a very familar form of transport can in fact help people better understand how a tram stops?

Also in common use are:

"... as tall as [n] giraffes"

"... [n times] as fast as a cheetah"

And not so commonly used, but I do find it quite upsetting when I hear this standard non-scientific measurement of money:
"... [a/b proportion] of the [black market size/per kilo cost] of [rhino horn/elephant tusk/tiger spleen/other endangered African or Asian mammal body part]

The animal thing just doesn't work for me.

Intuitive: The local football stadium as a measure of population

Our iconic local football stadium is the MCG, with a capacity of 100,000. So when a million people are rendered homeless by a natural disaster, or infected with a nasty disease, the 6PM news presenter invariably says "... the equivalent to ten full MCGs...". 

 

When we lived in Toulouse, France, the local stadium only had a capacity of 35,000. So all the news disaster estimates were out by a factor of 3.

Then living in Newcastle, New South Wales, the Hunter stadium can only hold 27,000 people. We had to recalibrate again. 

Neurologically, this makes more sense than the rhino thing.

Human brains are not built to deal with large population numbers.

According to a British anthropologist called Robin Dunbar, human cognitive capacity can only conceptualise and cooperate with about 150 other human beings. To think about more people than this is hard. And to feel sympathetic emotions about anything over 150 people is harder than empathising with one individual's story. In fact, a detailed personal account is always much more compelling to other people than any numerical population statistic. So in order for the news to be watched, it must evoke concern and sympathy for lots of strangers, and this requires use of specific emotive analogies. For most urban or suburban humans, a full stadium is about the largest mass of other humans they are likely to see, and the nice thing about a home crowd is that everyone is screaming in support of the home team at full volume, they are all bonded by a powerful common emotion: CARN THE KNIGHTS! (or whoever).

Thus the way to convey human feeling and meaning following a natural disaster is to remind TV viewers of the largest group of people they have ever had a powerful sympathetic feeling in common with, and then multiply that population by a small integer, less than 20. And then get a presenter to follow it up with an on-the-ground personal account of some kind.

Silly: The "If we laid all the [objects of a type] in the world [end to end/side by side/one on top of the other] it would reach [around the world/to the moon/to the sun] n times" ie distance as an analogy for quantity

In my view this is mental sloppiness. I have what I begin to understand as uncommon familarity with large numbers of objects. In Grade 5, I folded six hundred paper cranes - it took me another 2 years to get to the 1000. I have counted 15,050 white stripes on the road during an overnight bus trip from Chicago to Houston. I have helped in stocktakes by emptying and counting packets of 500 capacitors for numerous consecutive days. Ten thousand components fill a medium bin. I can think and convert between massive scales with reasonable fluency.

I begin to understand that this is not a universal talent. Terry Pratchett has a joke about dwarf counting, which applies to all of us at some breakpoint. It goes like this:
One

Two 

Three

Many

Many-one

Many-two

Many-three

Lots.

My 2 yr old bugs out at 20 objects - which is pretty good for a 2 yr old. That's when she hits "lots".

A friend of mine gets bored after a million. She's a good woman, not numbers-minded, and she reads the glossy magazines and says'wow' about very rich people. But after a million she loses track. A million is "lots".

As for me, I automatically convert money into what they could do: 1 million is of the same order of magnitude as your basic civil works project: building a big roundabout normally costs about 3 million. Ten million is the annual turnover of a company of about 15 people. A hundred million will almost buy you half a desalination plant. A billion is a modest defense budget. Ten billion dollars is a year's space program.

I bug out not very far past that.

Where a large number of dollars (or occasionally objects) is involved, and the science journalist is concerned that the raw number loses impact, how exactly does it help to calculate the linear length of all the crayons/blood vessels/bottles/dollar bills in your question, and then convert them to earth circumferences? Is it as simple as taking a more-or-less-incomprehensible large number and converting it to a smallish integer multiple of a marginally-comprehensible large distance? OK every person has something in common, we all live on the same planet with an equatorial circumference of about 40,000km (24,000 miles), but my brain has no real concept of how far that really is. If I piloted an aircraft or sailed a boat across, say, the Pacific Ocean, it might have a little more tangible meaning.

In India, where the gap between rich and poor has been mind-bendingly large for a very long time, there are handy words for dealing with large amounts of money.
A lakh is 100,000 rupees.
A lac is a million rupees (although a proportion of people explaining it on the web get this wrong - indicating that this is the "lots" point for many people)
A crore is 10 million rupees.

And these can be multiplied. A lakh lakh is 10^10. A lakh crore is 10^12, which I call a trillion, but this is not a consistent global definition.

And a crore crore is "lots".

So I ask all those science journalists again:

How, exactly, does it help your readers understand large numbers to mentally stack up US$1 bills and measure the height of an unfeasible tower? Can't we just get the community accustomed to the perfectly adequate larger-number definitions of lakh, lac and crore?

Critical for scientific progress: The selective use of a prefixed SI unit as a framing mechanism

Scientists struggle like anyone else when trying to conceptualise numbers in context. Throughout the history of science, as a new unit was invented it was often disconnected from other units - and after some experimentation and often a heated academic argument, some retrospective conversion factor brought it into line with the other units. Often these are named after the grand old gentleman who "discovered" them (the link goes back to a previous rant of mine). In time, a proportion of these personalised measurement units were found to be redundant, while others have been accepted for ongoing use with SI.

In science, the unit selected always has a framing function. The progress of scientific research is highly dependent on funding from public grants and private patronage, to whom scientists must pitch. Raw numbers with a (x 10^ something) don't immediately give general scientists a meaningful reference point on the field-specific small-to-big scale - and when nuclear physics grants are being evaluated by marine biologists and industrial chemists on the grants committee, lack of an appropriate unit can be the death of a whole field of research. Massively successful science programs always always always use snappy and exciting units of measurement.

For example, back in the 18th century, a new unit was invented to pitch the steam engine: "So that an engine which will raise as much water as two horses, working together at one time in such a work, can do, and for which there must be constantly kept ten or twelve horses for doing the same. Then I say, such an engine may be made large enough to do the work required in employing eight, ten, fifteen, or twenty horses to be constantly maintained and kept for doing such a work…"

The framing function of the choice of unit was a large component of the marketing success of steam power.
Unsurprisingly, there was much quibbling over the breed and gender of the horses in question. Retrospectively, the SI value of one horsepower finally stabilised at 746 watts.
But for electrical motors and internal combustion engines, power is still always measured in horses.
I am, for reasons I won't go into yet (hi Geoff!), watching the Ninja Mega Kitchen System telemarketing ad. They are advertising the power of the blender as two horses. Not 1400 watts. Who counts up to 1400? Only geeky engineers who actually make electric motors. Anyone who has to sell one measures it in horses.

 

Here's another example. The Large Hadron Collider team chooses to measure particle energies in 7 tera electron volts rather than 1.12 microjoules. Same energy value, but 'tera' sounds big and 'micro' sounds small. And for a particle, one electron volt is a normal number. 7 tera is indeed a lot.

I unequivocally support the selective use of standard non-scientific units to market scientific research. I would like undergraduate science and engineering students to be taught this in a marketing subject. I also look forward to the retrospectively standardised rhino-stop replacing the kilogram meter per second to measure the linear momentum of a tram.

But Geoff, I am still not buying the Ninja Kitchen System.