Cousins or Siblings?

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Imagine two sets of identical twins: Alice & Amelia, and Bob & Benjamin. Now imagine that Alice marries Bob, and Amelia marries Benjamin, and that both couples have a child: Alice & Bob give birth to Charlie, and Amelia and Benjamin give birth to Catherine.

By law, Charlie and Catherine are first cousins (i.e. the children of your parents’ brothers and sisters are your first cousins). Genetically, however, the situation is very different: Alice and Amelia have the same genes, as do Bob and Benjamin. Charlie and Catherine will get fifty percent* of their genes from each parent, but as their parents are genetically identical they will share fifty percent of their genes with each other (rather than the normal 12.5%), making them genetically brother-and-sister. Also, because their uncle and auntie are genetic clones of their parents, Charlie and Catherine will share 50% of their genes with each of their uncle/auntie, so genetically speaking they would be indistinguishable from parents or siblings.

In the UK, marriages between cousins have been permitted since the time of King Henry VIII. If Charlie and Catherine are legally cousins, but genetically siblings, should they be permitted to marry?

* I should point out that it won’t be exactly 50% in any of these cases, but considering the huge number of genes and the population as a whole the average will be 50%.

Endangerment Categories

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The International Union for the Conservation of Nature (IUCN) is an international organisation with the aim of finding “pragmatic solutions to our most pressing environment and development challenges”. One of their most important jobs is assessing the conservation status of various species, which they categorise into one of seven categories in their Red List of Threatened Species.

endangerment-categories

Extinct (EX)

e.g. Dodo, Santa Cruz Pupfish, Cape Verde Giant Skink (799 species total)

Extinct species are those which have no living members (or only one non-pregnant member). Some species that have been considered extinct have been rediscovered.

Extinct in the Wild (EW)

e.g. Hawaiian Crow, Socorro Dove (61 species total)

Species which are Extinct in the Wild are those which live only in captivity or which exist as naturalised populations outside of their normal habitat.

Critically Endangered (CR)

e.g. Blue-throated Macaw, Clifton’s Anguola (4286 species total)

Critically Endangered species are those that face a very high risk of extinction (in the wild). CR species can be considered “possibly extinct”, a category used by BirdLife International, but not by the IUCN.

Endangered (EN)

e.g. Uluguru Dusky Grasshopper, Narcondam Horbill (6451 species total)

Species categorised as Endangered are those that will likely become extinct. Species considered Endangered are often protected by conservation laws that prevent hunting, destruction of habitats, etc.

Vulnerable (VU)

e.g. Ethiopian Banana Frog, Steelhead (10?549 species total)

Vulnerable species are those at risk of becoming Endangered if their habitats are not protected or if other risks to their survival (hunting, disease, etc.) are not mitigated.

Near Threatened (NT)

e.g. American Bison, Northern White Rhinoceros (4822 species total)

Species which are Near Threatened are those which are considered to be at risk of extinction in the near future, but which are not currently considered to be worthy of elevation to a more endangered category.

Least Concern (LC)

e.g. Humans, Cats, Dogs (32?486 species total)

Species in the Least Concern category have been evaluated by the IUCN, and do not qualify for any other categories. Put simply, they are considered to have no risk of extinction.

Data Deficient (DD) and Not Evaluated (NE)

These categories are fairly self-explanatory: either sufficient data on their populations does not exist, or data has not been collected. For obvious reasons, the number of species in these categories is very uncertain. Undiscovered or newly discovered species would fall into these categories until their discovery and/or evaluation.

Why You Shouldn’t Worry About Melting Icebergs

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iceberg

When the topic of climate change comes up, a common refrain is that the melting of icebergs is going to drown us all. This is not true. Even if every iceberg in the world melted, we wouldn’t notice the difference.

Archimedes’ Principle states that an object which displaces a fluid (i.e. a liquid or a gas) will experience an upward force that is equal to the weight of the fluid displaced. If an object displaces one cubic metre of water it will experience an upward force of around 9810 newtons, regardless of what it is made from. If its own weight is greater than 9810?N it will sink; if it is less than this it will float.

The density of ice is approximately 920 kilograms per cubic metre, and the density of seawater is approximately 1025?kg/m3. If a cube of ice with sides of one metre is placed into water it will push down on the water with a force of 9030?N (920?kg × 9.81?N/kg), and the water will push upwards on the ice with a force of 10?100?N (1025?kg × 9.81?N/kg). There will therefore be a net upward force on the ice cube of 1030?N and it will float to the surface. However, the ice cube will not float completely above the surface of the water – some of the ice cube will stay submerged.

The volume of the ice cube that is submerged will be equal to the volume of water that has the same weight as the cube itself, or mathematically:

We can find the volume of the ice that is submerged by calculating:

V_{\mathrm{submerged}} \times \rho_{\mathrm{water}} \times g = W_{\mathrm{ice}}

That is, the volume of the ice that is submerged (V_{\mathrm{submerged}}) multiplied by the density of the water (\rho_{\mathrm{water}}) multiplied by the strength of the gravitational field (g) is equal to the weight of the ice cube (W_{\mathrm{ice}}).

An iceberg, with the submerged portion clearly visible underwater.

Using the data we know, we find that the volume of ice submerged is 0.898?m3. This result applies regardless of the shape or size of our ice cube, so we know that 89.9% of any iceberg is below the surface of the water, and 10.2% is above. People seem to be worried that when the ice melts, this above-surface water will be added to the volume of the world’s oceans. However, this fails to take into account the different densities of ice and liquid water. As the ice melts into liquid water its density increases and thus the level of the water remains the same. You can prove this to yourself very easily: place an ice cube into a glass of water, draw a line at the level of the water, and wait for the ice to melt. The level of the water will not climb above your original line.*

What people should be worried about is not icebergs but ice caps. Ice caps are ice that it sitting on land and therefore is not already displacing water. If this ice melts and runs into the oceans it certainly will increase sea levels.

What people should also be worried about is that the density of water changes with temperature. As climate change increases the temperature of the oceans it will expand, and again sea levels will rise.

Note: This is all based on a mathematical-physical model. When other factors are taken into consideration, melting icebergs may contribute very slightly (about 50 micrometres per year) to an increase in sea level.

Text Figures and Lining Figures

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Are you using the correct sort of numbers? Numbers come in two forms: old style and lining.

oldstyle-proportional-equalOld style figures

lining-proportional-equalLining figures

The difference between old style and lining figures is how they sit relevant to the text’s baseline and x-height.

handgloves-oldstyle-baseline handgloves-lining-baseline

Generally speaking, old style numbers look better within normal text, because they keep the same “pattern” of ascenders and descender; and lining numbers look better when used with text set in all caps as they match the height of the line.

supernova-capitals-oldstyle

With the text in all caps the old style numbers stand out as odd, but the all caps text looks much better when the old style figures are replaced with lining figures.

supernova-capitals-lining

With normal text, the old style figures help the text to look more normal, but the name of the supernova still stands out as looking a bit odd.

supernova-oldstyle

But the best option is a combination of both old style and lining figures as shown below.

supernova-mixed

Both old style and lining figures can come in proportional and monospaced (fixed-width) varieties. Monospaced figures are sometimes called tabular figures, because they are used in tables so that columns of tens, hundreds, thousands, etc. line up properly.

comparison-oldstyle
L-R: Proportional old style figures and tabular old style figures.

comparison-lining
L-R: Proportional lining figures and tabular lining figures.

Stop Putting Commas In Your Numbers

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or Why you need to read Le Système international d’unités (8e édition)

How do you write very large or very small numbers? How, for example, would you write the speed of light out in full?

If you would write c = 299,792,458 m/s then please stop, because you’re doing it wrong. You can argue all you want about tradition, and “the way things have always been done” but you are still totally, absolutely, unequivocally wrong. There is a right way, an official, standardised way, to write very large and very small numbers, and it’s not with commas in them.

“Following the 9th CGPM (1948, Resolution 7) and the 22nd CGPM (2003, Resolution 10), for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading. Neither dots nor commas are inserted in the spaces between groups of three.”

The correct way to write the speed of light is c = 299 792 458 m/s. Ideally you’d use a special Unicode character, known as “NARROW NO-BREAK SPACE (U+202F)”, which stops text from wrapping around half-way through a number, but this isn’t very well supported, so the better-supported “THIN SPACE (U+2009)” or even just a normal space will do.

The reason for this is that the decimal point isn’t always a decimal point. Only 60% of countries use a full stop, whereas other countries use other marks. For example, a number that would traditionally be written in the UK as 123,456,789.01 would be written in France, Germany, Spain and many other countries as 123.456.789,01 and in Canada as either, depending on whether you’re working in English or French. This confusion (see this for example) was deemed undesirable and as such the scientific community declared in 2003 that:

The 22nd General Conference [of the BIPM],
considering that a principal purpose of the International System of Units is to enable values of quantities to be expressed in a manner that can be readily understood throughout the world …
reaffirms that “Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups”, as stated in Resolution 7 of the 9th CGPM, 1948.

Remember that thousand separators are also used when dealing with very small numbers. I’ve provided some examples below if you’re struggling to get your head around them.

Incorrect Correct Incorrect Correct
123 123 0.123 0.123
1234 1234 0.1234 0.1234
12,345 12 345 0.12345 0.123 45
123,456 123 456 0.123456 0.123 456
1,234,567 1 234 567 0.1234567 0.123 456 7
12,345,678 12 345 678 0.12345678 0.123 456 78