What Counts?

by James Morris

Happy New Year! We just completed another cycle around the sun and counted down to another new year. This got me thinking about the surprisingly difficult task of counting.

Counting seems simple. What can be easier than counting a number of items? Children as young as two years old can count up to 10, and most kindergartners have “number sense” – they can not only recite the numbers but also count objects around them.

NumbersCounting requires just three basic skills. First, it requires knowing the language of numbers. In other words, it means knowing the words “one, two, three, etc.” and the symbols “1, 2, 3, etc.” as well as their order. Second, it requires what’s called one-to-one correspondence, where each item in a group counts just once and each item corresponds to a unique number. Third, it requires the ability to categorize. That is, if you are counting blocks, you have to know what’s a block, so that you only count blocks and not other items.

What can be simpler? And yet, in science and even politics, counting can prove to be surprisingly difficult.

Take the number of species on this planet. How many different species are there on Earth? You would think that this would be easy to answer, but figuring out how many species are alive today is not as simple as it sounds.

We know how many species have been given a name and described – it’s about 2 million. However, this number only scratches the surface of the total biodiversity on this planet. Based on the number we know, we can extrapolate to the number we don’t know. This number may be as few as 10 million to as many as 100 million. In other words, we actually don’t know something as fundamental as the number of species on Earth.

One indication of how little we know is that new species are being discovered all the time. Here are just a few of numerous examples: Several new species of deep-sea bioluminescent worms were discovered in 2009; one of the smallest known frogs was found in Borneo in 2010; a new species of dolphin was discovered off of the coast of Australia in 2011; a new species of monkey was found in 2012; a new species of beetle was discovered by biology students in the bustling city of Manila in 2013; a new deep-sea animal that defies classification was discovered in 2014; new dwarf dragons were found in the Andes in 2014; an Appalachian lichen named for Dolly Parton was found in 2015; and an entirely new species of whale was found in 2016.

Scientists have the freedom to name new species whatever they want, so nine new species have actually been named after President Obama.

New species can be found almost everywhere, in rain forests and coral reefs to be sure, but also in such unlikely places as Central Park in New York City. A new species of lacewing (a kind of insect) was even discovered, of all places, on the internet. A Malaysian photographer took a picture of the lacewing and posted it online. The photograph was seen by an entomologist, who suspected and later confirmed that it was a new species.

The difficulty of counting species stems from the fact that the numbers are so large, and so much of the Earth has not been explored with an eye toward finding species. As a result, we will probably never know the number with any kind of certainty.

A different kind of difficulty is illustrated by the problem of counting chromosomes. Humans have 23 pairs of chromosomes, one set from each parent, or 46 chromosomes in total.

Source: National Cancer Institute

Source: National Cancer Institute

Surprisingly, scientists had the number wrong for over 30 years, from the 1920s to the 1950s. In the 1920s, T. S. Painter, an American scientist, declared that humans have 24 pairs of chromosomes, or 48 chromosomes in total. This number was confirmed by several scientists and then stuck, unexamined and unquestioned, for decades.

It would be easy to explain away this famous error and its eventual correction by pointing to improvements in microscopy. But scholars who have explored the persistence of this error argue that it likely says more about our assumptions and the social context of science, rather than on visualization technology.

Another counting problem can be found by looking at the number of genes that humans have. Early estimates placed the number of human genes at around 100,000. One of the surprises of sequencing the human genome (all of our genetic material) was that the number is actually much lower, around 20,000.

Even today, however, we have not settled on an exact number. The difficulty here is deciding what a gene is. Many scientists define a gene as a segment of DNA that provides the instructions for the building of a protein. However, we are also discovering segments of DNA that don’t code for proteins, but instead for RNAs that carry out their own functions. These are small and numerous. Should these be counted as genes or not?

Problems of determining what counts can be seen outside of biology too. Take the number of planets. Most of us learned that there are nine planets and may have even recited counting songs or learned mnemonics to help us remember their names and order from the Sun – Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.

Recently, however, astronomers decided that Pluto doesn’t really count as a planet. Instead, it’s one of thousands of small, icy objects that orbit beyond Neptune as part of the Kuiper belt. As a result, the number of planets went from nine to eight. But, in an interesting twist, a “new” ninth planet (dubbed for now “Planet Nine”) was discovered well beyond the orbit of Neptune. This massive planet has not actually been seen yet, but instead has been detected based on its gravitational effects on nearby Kuiper belt objects.

What’s clear is that have to agree on what belongs in a particular category – planets, genes – before we can accurately count items in that category. This problem is not unique to science, but also comes up in politics. Recall the 2000 Bush-Gore US Presidential election, which came down to a handful of votes in Florida. One of several issues that came up had to do with punch card ballots (which are no longer used). Some of these ballots had incompletely punched holes that left a “hanging chad” with one corner still attached or a “fat chad” with all corners still attached. Should these count or not? Again, we need to agree on what belongs in a category in order to be able to count it.

Recounting these stories serves as a nice reminder that even simple tasks can be unexpectedly complicated, which should provide some reassurance as we count our resolutions for the new year.

museedorsee© James Morris and Science Whys, 2017

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