A Tale of Two Skulls: Part 2

Sorry this post was so long in coming, I’ve been really busy with my PhD!

The Great Dying may sound like an exaggeration of a name, but if anything it is an understatement. The extinction that occurred at the end of the Permian, ushering in the Triassic, was the most catastrophic since animals appeared on the planet—96% of all marine species, and 70% of all terrestrial vertebrate species, were wiped out1. It was the only mass extinction of insects, 83% of all genera were destroyed: to appreciate this number, a genus is a group of species, and a genus is only considered extinct if every single species within it is wiped out.

This period of mass volcanism, runaway-greenhouse effect, increasing aridity and anoxia ended the synapsid and amphibian dominance over land: with all the large land-dwelling amphibians driven to extinction, their predators—such as Dimetrodon—also died out. The only large land amphibians that remained were aquatic, filling the niches occupied by modern-day crocodiles2,3.

Life on Earth would recover, but it would take 30 million years4, and synapsids would not reclaim their former dominance. Instead, diapsids would claim the land, diversifying into two major groups: lepidosaursthe ancestors of modern lizards and snakes; and the formerly-mentioned archosauriformes. Meanwhile, ocean-dwelling diapsids saw the rise of Ichthyosaurs5, fish-like lizards that ruled the seas.

Shonisaurus popularis, an Icthyosaur from the late Triassic, by Nobu Tamura.

The ‘crocodile-lizard’ archosauriformes would diversify throughout the Triassic, with many forms, from small lizard-like animals to metres-long crocodile-like monsters. By the mid-Triassic, one group of archosauriformes would start to stand out: the archosaurs6.

Archosaurs are best recognised by their descendants, as they would proceed to dominate the world for the next two hundred million years. Earliest to break off were the ancestors of modern crocodylomorphs7—crocodiles and their nearest relatives.

Ornithosuchus woodwardi, a late Triassic archosaur related to crocodiles, by Nobu Tamura.

The remaining archosaurs had, by the late Triassic, diverged into two further groups: the pterosaurs8, flying reptiles that ruled the skies; and the dinosaurs9, the most famous animals of the era.

At the end of the Triassic, two hundred million years ago, these groups had become well-established, and it was just in time: the Triassic closed with another mass extinction, the imaginatively-named Triassic-Jurassic Extinction Event10. This was the final nail in the coffin for any remaining giant amphibians, while marine life was devestated, with the extinction of over a third of all genera—including an entire class11. The cause of this extinction is unknown, but climate change marked with mass volcanism are two of the leading candidates. Whatever the cause, the Jurassic had begun.

A Conodont, the marine class extirpated in the end-Triassic extinction event, by Nobu Tamura.
A Tale of Two Skulls: Part 2

A Tale of Two Skulls: Part 1

The early colonisation of land by animals more complex than insects was lead by a group known as reptilomorphs, early fish-like animals that had developed four simple limbs to enable them to explore this new world. This began 370 million years ago1, and while these animals were initially aquatic, over the following tens of millions of years they evolved to spend increasing amounts of time outside the water, becoming increasingly amphibian-like.

It’s important to understand what kind of world they emerged into—the late Devonian mass extinction was ongoing, devastating sea life and culminating in the Hangenberg event which ended the Devonian2. On land, it was wet, warm, and completely alien—giant fungus trees up to eight metres tall dominated the landscape, with mats of liverwort covering the ground3. Ferns and the earliest trees dotted the land, creating the world’s first forests4.

By the start of the Carboniferous period 360 million years go, the amphibian-like reptilomorphs successfully colonised the land, but over the next fifty million they faced a new challenge. They were still semi-aquatic, and as such needed to lay their eggs in water, which was fine in the wet warmth of the early Carboniferous, but the world began to cool and dry. The trees of this world had evolved lignin in their wood, but no organism had evolved yet that was able to eat it, meaning that when a tree died it was buried, removing carbon from the atmosphere and laying down vast beds of coal5.

However, one group of reptilomorphs evolved to become increasingly lizard-like, and 310 million years ago they evolved the ability to lay eggs on land, without the need to return to the water6. The reptilomorphs were now two distinct groups: the amniotes, with their new-found ability to lay eggs on land, and the amphibians, who are still recognisable today.

The amniotes spread across the world, but there are two groups of particular interest to this story—the synapsids and diapsids. These two groups were named after a curious feature of their skulls, with the synapsids possessing one hole behind the eye7, and the diapsids two8, and these are the skulls that will form the basis of our story.

As the world continued to cool, the rainforests that allowed the ancestors of amniotes to colonise the world began to collapse, creating new niches that amniotes could inhabit but amphibians couldn’t, allowing them to spread and diversify. This marked the dying days of the Carboniferous, and as the ice age rolled in 300 million years ago, the Permian began.

For fifty million years, the Permian was dominated by two groups of large land animals: the amphibians and the synapsids. The diapsids were relegated to small, lizard-like organisms, failing to measure up against the several-metre long amphibians like the Diadectes9, or the pelycosaurs—synapsids that included the apex predator Dimetrodon10.

Dimetrodon NT2 small.jpg
Dimetrodon, an early-Permian syanpsid, by Nobu Tamura

Diadectes, an early-Permian amphibian, by Dmitry Bogdanov (CC BY-SA 3.0, Link)

Towards the end of the Permian, amphibians, synapsids, and diapsids continued to diversify, including two seemingly-unimportant groups—cynodonts, a diverse group of synapsids that could be readily described as ‘small-dog lizards’11; and the archosauriformes, diapsids that superficially represent ‘crocodile-lizards’12. At this time, nothing seemed capable of ending the dominance of amphibians and synapsids over the land.

Until the Great Dying.

Procynosuchus BW.jpg
P. delaharpeae, an early cynodont, by Nobu Tamura

Archosaurus ross1DB.jpg
Archosaurus, a late-Permian archosauriform, by Dmitry Bogdanov (CC BY-SA 3.0, Link)

Feature Picture: Thrinaxodon, an early-Triassic cynodont, by Nobu Tamura

A Tale of Two Skulls: Part 1

Billionaires 2017

Forbes recently released their list of billionaires for this year, and the amount of wealth on the list is staggering: $7.67 trillion USD, roughly 10% of global GDP1 and 18% higher than last year.  This data didn’t really tell me much, though, and in order to understand it I investigated three questions:

  1. are the individual billionaires richer, or are there just more billionaires;
  2. has their wealth increased in real terms, or can this be explained away by inflation;
  3. did they become richer because the world became richer, or because of wealth concentrating?

The first question is the easiest to answer, with the numbers on the list: the wealth of the world’s billionaires increased from $6.5 trillion USD in 2016 to $7.67 trillion USD in 2017 — an increase of 18%— while the number of billionaires grew from 1 810 to 2 043 — a total of 13% — meaning a total per-billionaire growth of 4.5%2.

In order to determine whether this growth is real, in that it represents an actual increase in spending power, we must compare the growth to inflation, which is the measure of how much wealth has devalued; a pound sterling in 1700 was worth considerably more than a pound now. Global inflation from 2016-2017 was 3.28%3, which means their wealth grew 1.22% over inflation, indicating a real gain in wealth of 1.2%. From this we can conclude that, on average, the world’s billionaires have gained wealth in real terms.

Does this increase in wealth indicate they own a bigger share of the pie or, as many in favour of trickle-down economics argue, that they’re growing the pie for everyone and just taking their fair share for themselves? According to the International Monetary Fund, IMF, the global economy grew by 3.4% from 2016-20174, meaning that the billionaires’ wealth is increasing faster than the total wealth of the planet by about 1%.

But the story doesn’t end there: because we’re comparing the wealth on a per billionaire basis, we should compare the global economic growth on a per capita basis, meaning we need to take into account global population growth. In the past year, the world population has increased by 1.11%5, meaning that the average person saw 2.3% more wealth, slightly more than half the rate of billionaires.

We’ve now answered our original three questions:

  1. billionaires have gotten wealthier faster than the number of billionaires has grown;
  2. the wealth growth has been real, rather than a product of inflation;
  3. while some of this growth is due to a global increase in wealth, half is attributable to wealth concentrating; the pie is growing twice as fast for the billionaires as it is for everyone else.
Billionaires 2017

Gender, Sex, and Social Constructs

Gender is a social construct. That’s not to say it’s neither real nor important, especially in a society obsessed with policing gender — money is a social construct, and in a capitalist society its impacts are both very real and very important.

Further, being told what our gender is and means can cause dissonance and distress, and I don’t believe it’s based on conflict with some hidden ‘true’ gender. The way the term is used now is a clunky conflation of numerous factors, from gender-presentation to sex, and as these terms are more rigorously identified and separated, ‘gender’ has less and less meaning.

In a genderless society, trans and non-binary people would still exist, and for those that wished to transition the issue would be treated as an endocrine disorder, rather than a psychiatric one. Why is this? Because the idea of a binary and immutable/innate sex is also a social construct.

While separating ‘sex’ and ‘gender’ is a useful Trans 101 description, I think it reinforces a false dichotomy (the ‘body’ and ‘mind’ being separate entities), and devalues the self-identification of trans/non-binary people (‘your gender is female but your sex is male’ is the ‘politically correct’ way of saying ‘you think you’re a woman but you’re actually a man’).

Beyond this, the way ‘sex’ is used is completely lacking in nuance, and fails to reflect the diversity of humanity. Sex conflates a large number of variables into one title — gonads, chromosomes, genital, hormones, secondary sex characteristics, possibly brain structure — while failing to recognise that these are all distinct and meaningful concepts in and of themselves.

For example, if I am getting an abdominal x-ray, my doctor needs to know where my gonads are, they don’t need to know whether I’m ‘male’ or ‘female’; if I’m growing a distressing amount of hair, my endocrinologist needs to know my testosterone levels are, they don’t need to know whether I’m ‘male’ or ‘female’. Ultimately, ‘sex’ is a categorisation used to enforce social norms far more often than it is to convey useful information about a person.

Gender and sex are social constructs, and upon deconstruction may turn out to be completely useless (and it’s my opinion that they are); however, in a world where both of these constructs exist, they are still real, they are still important, and the identification of individuals on both counts needs to be respected.

Gender, Sex, and Social Constructs

‘Trans’ doesn’t mean ‘Transition’

I’ve recently seen quite a few people use the argument that ‘trans is short for transitioning’, which is used to deny the existence of non-transitioning trans people, and to argue for the legitimacy of sex as a binary — as if etymology of words has the power to alter the reality of what they describe. Still, it’s sufficiently pernicious and irritating that I’ve decided to write this blog post.

Trans as a word is derived from transgender and transexual, which themselves were derived from the German word Transsexualismus (meaning transexual), coined by German psychiatrist Magnus Hirschfeld in 1923. The trans- part of this word is the Latin prefix meaning ‘on the other side’.

Further, the claim ignores the fact that the meaning of trans in its current usage has absolutely nothing to do with the verb ‘to transition’, it’s just a spurious connexion based on vague etymological relations (transition is derived from the Latin transitio, meaning ‘to cross over’, and isn’t an example of ‘trans-‘ as a prefix).

So if you intend to argue about the nuances of sex and gender, the fact that two words look similar does not mean you are free to ignore the vast body of the scientific literature — which includes biology, psychology, and sociology — and ultimately the lived experience of people whose experience differs from your own.

‘Trans’ doesn’t mean ‘Transition’

What is 1 kg of coal?

Bituminous coal, courtesy of Wikipedia

This is a kilogram of coal – okay, so I have no idea how much it actually weighs, but let’s work under this assumption – and its primary use is to be burnt for electricity. What is in a kilo of coal [1]? Primarily, it is made of:

  • 860 g of carbon;
  • 50 g of hydrogen;
  • 70 g of oxygen; and
  • 10 g of sulphur.

Let’s imagine that we have a device that can burn this fully: no energy wasted into forming ash, no incomplete combustion creating carbon monoxide, etc. What would the products be?

  • 3 150 g of carbon dioxide;
  • 900 g of water;
  • 20 g of sulphur dioxide; and
  • 40 MJ of heat.

This estimate is about double the amount of energy usually produced [2], largely due to omitting ash formation, moisture content, and other factors that impede complete combustion. Still, maintaining this generous assumption, and taking into account the 40% efficiency of coal plants [3], and 6% loss from transmission [4], we find that one kilogram of coal can produce about 15 MJ of electricity, about enough to boil 25 kettles of water.

However, there are other trace elements in coal that can be of concern: this kilogram of coal also contains 1 mg of uranium, 1 mg of arsenic, 3 mg of thorium, 5.8 mg of lead, 98 mg of fluorine, 320 mg of chlorine, and 21 μg of mercury [5]. This means that, over an entire day, the average coal power-plant (burning 1.3 kt of coal [6]) will release 520 MBq of uranium & thorium, 1.3 kg of arsenic, 7.5 kg of lead, and 27 g of mercury.

It should be noted that this isn’t an exceptional amount of radiation, but over time it does build up: the area around a coal plant is generally significantly more radioactive than around a nuclear plant, and can be significantly enriched in toxic metals.

Real life, however, is more complicated that this ideal: as noted before, coal only produces half the calculated energy (about 22 MJ of heat per kilogram), many toxic elements remain in the coal ash (making its disposal an issue), and large amounts of contaminants leach from coal stockpiles into the water.

Unlike what the Australian government keeps propounding, coal is not a harmless black rock, and it isn’t good for humanity.

What is 1 kg of coal?

Pokemon Go and Individual Values

In Pokémon Go, each Pokémon has three values that determine how well it will battle: its moveset, its level, and its individual value (IV).

The moveset are the attacks that your Pokémon can use — things like mudshot and fireblast and hydropump — and can’t be changed. Every type of Pokémon has a moveset that is optimal (i.e. gives the highest possible damage per second of attacks available to you), such as Water Gun/Hydropump for the Vaporeon, and this will strongly affect how much damage you do.

The Pokémon’s level is marked by the arc in the background, which stretches from the very bottom left (Pokémon with 10 CP), to the bottom right (Pokémon that have the same level as their trainer does). When you click ‘power up’, you are increasing the Pokémon’s level, which will increase its HP and CP in accordance with its IV.

IV is the only piece of information about your Pokémon that is entirely hidden from you in the game, although it can be calculated using level, HP, CP and the information that your gym leader provides you, through external calculators. IV is broken down into three categories: Attack, Defence and Stamina, each of which take an integer value from 0 to 15, with the total IV simply being the sum of all these values (often presented as a percentage of the maximum value). So, what is a good IV for a Pokémon to have?

Thankfully, this is the same as rolling three sixteen-sided dice from 0 to 15, and we can use familiar maths to calculate both the average roll of m n-sided dice, m\cdot\left(\frac{n+1}{2}\right), and the standard deviation, \sqrt{m\cdot\left(\frac{n^2-1}{12}\right)} . This gives an average IV of 22.5 (50%) and standard deviation of 8 (18%). This means that two-thirds of all Pokémon have an IV between 14.5 and 30.5 (32% and 68%).

To illustrate this graphically, let’s consider every single possible roll of these three dice, written in code here:

for x in 0:15
  for y in 0:15
    for z in 0:15

This results in the bell curve shown in Figure 1, because there is only one way to generate 0 (that is, all dice roll zero), but there are many ways to generate a roll of 22 (192 ways, in fact).

Figure 1: Total IV plotted against the number of possible ways to achieve that IV. This shows a very strong weighting towards the centre.

While it is useful to know how rare your Pokémon is, deciding on whether to keep it should be based on how likely it is to have at least its IV; otherwise, it’s easy to see that 0 and 45 are equally rare. The probability of a random Pokémon having as good an IV or better as your current Pokémon is given by the curve shown in Figure 2.

Figure 2: The probability of finding a Pokemon with equal or greater IV than your current.

This suggests that Pokémon with 80% or 90% IV are incredibly rare, which matches up with what the Gym Leaders say: the top-tier evaluation of a Pokémon places it into this high (80%+ category). Let’s have a look at some particularly interesting IV:

  • 23 (49%) — this is the median IV, or the 50th percentile: half of all Pokémon are equal to and better than it, while half are worse than it;
  • 27 (60%) — this is the tier occupied by the top third of Pokémon;
  • 30 (66%) — the top fifth of all Pokémon have an IV of thirty or higher, meaning 80% of all Pokémon have a lower IV than 30;
  • 34 (76%) — your Pokémon is in the top 10% of all Pokémon;
  • 37 (82%) — at this point, your Pokémon is considered to be top-tier by the Gym Leaders when you select ‘Appraise’, and they are in the 94th percentile;
  • 41 (91%) — this is finally over the 90% IV mark, and represents the top 1% of all Pokémon. Anything with this IV almost has the best base stats of its kind;
  • 45 (100%) — the ultimate Pokémon. Each Pokémon you find has a 0.02% (two in ten thousand) chance of having this IV, making them incredibly rare.

To illustrate how rare these values are, let’s look at Gyarados: you need to catch a hundred Magikarp to make a Gyarados, so what is the highest Magikarp you’re quite sure you can catch (>90% chance)?

For your first Gyarados, you would be expecting an IV of at least 38 (84%). Your second Gyarados should be even higher, with an IV of 40 (88%), but after this, your probability starts falling off sharply. Your third Gyarados should have at least 41 IV (91%), but you can’t be sure of getting a 42 IV Gyarados until your fifth, or a 43 IV one until your tenth! At that point, the chance of you having a 45 IV (100%) Gyarados is 20%, so if you’re lucky you may have a truly vicious sea monster!

For some anecdotal evidence, I have caught 4327 Pokémon, meaning that I should expect to have found about one 100% Pokémon by now. And I have!

A Zubat.



Pokemon Go and Individual Values