How Many Tyrannosaurs Were There?

Suppose you were transported back to the late Cretaceous, what is the probability that you would see a Tyrannosaurus? That depends on a large number of factors, and to simplify, I shall limit myself to T Rex. There were various Tyrannosaurs, but probably in different times and different places. As far as we know, T Rex was limited to what was effectively an island land mass known as Laramidia that has now survived as part of Western North America. In a recent edition of Science, a calculation was made, and it starts with the premise, known as “Damuth’s Law” that population density is negatively correlated with body mass through a power law that involves two assignable constants, plus the body mass. What does that mean? It is an empirical relationship that says the bigger the animal, the fewer will be found in a given area. The reason is obvious: the bigger the animal, the more it will eat, and a given area has only so much food. Apparently one of the empirical constants has been assigned a value of 0.75, more or less, so now we are down to one assignable constant.

If we concentrate on the food requirement, then it depends on what it eats, and what it does with it. To explain the last point, carnivores kill prey, so there has to be enough prey there to supply the food, AND to be able to reproduce. There has to be a stable population of prey, otherwise the food runs out and everyone dies. The bigger the animal, the more food it needs to generate body mass and to provide the energy to move, however mammals have a further requirement over animals like snakes: they burn food to provide body heat, so mammals need more food per unit mass. It also depends on how specialized the food is. Thus pandas, specializing on eating bamboo, depend on bamboo growth rates (which happens to be fast) and on something else not destroying the bamboo. For Tyrannosaurs, they presumably would concentrate on eating large animals. Anything that was a few centimeters high would probably be safe, apart from being accidentally stood on, because the Tyrannosaur could not get its head down low enough and keep it there long enough to catch it. The smaller raptors were also probably safe because they could run faster. So now the problem is, how many large animals, and was there a restriction? My guess is it would take on any large herbivore. In terms of the probability of meeting one, it also depends on how they hunt. If they hunted in packs, which is sometimes postulated, you are less likely to meet them, but you are in more trouble if you do.

That now gets back to how many large herbivores would be in a given area, and that in turn depends on the amount of vegetation, and its food value. We have to make guesses about that. We also have to decide whether the Tyrannosaur generated its own heat. We cannot tell exactly, but the evidence does seem to support the fact that it was concerned about heat as it probably had feathers. The article assumed that the dinosaur was about half-way between mammals and large lizards as far as heat generation goes. Provided the temperatures were warm, something as large as a Tyrannosaur would probably be able to retain much of its own heat as surface area is a smaller fraction of volume than for small animals.The next problem is assigning body mass, which is reasonably straightforward for a given skeleton, but each animal starts out as an egg.  How many juvenile ones were there? This is important because juvenile ones will have different food requirements; they eat smaller herbivores. The authors took a distribution that is somewhat similar to that for tigers. If so, an area the size of California could support 3,800 T. Rex. We now need the area over which they roamed, and with a considerable possible error range and limiting ourselves to land that is above sea level now, they settled on 2.3 + 0.88 million square kilometers, which, at any one time would support about 20,000 individuals. If we take a mid-estimate of how long they roamed, which is 2.4 million years, we get, with a very large error range, that the total number of T. Rex that ever lived was about 2.5 billion individuals. Currently, there are 32 individual fossils (essentially all are partial), which shows how difficult fossilization really is. Part of this, of course, arises because fossilization is dependent on appropriate geology and conditions. So there we are: more useless information, almost certainly erroneous, but fun to speculate on.


You may have heard that the ocean is full of plastics, and while full is an excessive word, there are huge amounts of plastics there, thanks to humans inability to look after some things when they have finished using them. Homo litterus is what we are. You may even have heard that these plastics degrade in light, and form microscopic particles that are having an adverse effect on the fish population. If that is it, as they say, “You aint heard nothin’ yet.”

According to an article in the Proceedings of the National Academy of Science, there is roughly 1100 tons of microplastics in the air over the Western US, and presumably there are corresponding amounts elsewhere. When you go for a walk in the wilderness to take in the fresh air, well, you also breathe in microplastics. 84% of that in the western US comes from roads outside the major cities, and 11% appear to be blowing in from the oceans. They stay airborne for about a week, and eventually settle somewhere. As to source, plastic bags and bottles photodegrade and break down into ever-smaller fragments. When you put clothes made from synthetic fibers into your washing machine, tiny microfibers get sloughed off and end up wherever the wastewater ends up. The microplastics end up in the sludge, and if that is sold off as fertilizer, it ends up in the soil. Otherwise, it ends up in the sea. The fragments of plastics get smaller, but they stay more or less as polymers, although nylons and polyesters will presumably hydrolyse eventually. However, at present there are so many plastics in the oceans that there may even be as much microplastics blowing out as plastics going in.

When waves crash and winds scour the seas, they launch seawater droplets into the air. If the water can evaporate before the drops fall, i.e. in the small drops, you are left with an aerosol that contains salts from the sea, organic matter, microalgae, and now microplastics.

Agricultural dust provided 5% of the microplastics, and these are effectively recycled, while cities only provided 0.4%. The rest mainly come from roads outside cities. When a car rolls down a road, tiny flecks come off the tyres, and tyre particles are included in the microplastics because at that size the difference between a plastic and an elastomer is trivial. Road traffic in cities does produce a huge amount of such microplastics, but these did not affect this study because in the city, buildings shield the wind and particles do not get lifted to the higher atmosphere. They will simply pollute the citizens’ air locally so city dwellers merely get theirs “fresher”.  Also, the argument goes, cars moving at 100 k/h impart a lot of energy but in cities cars drive much more slowly. I am not sure how they counted freeways/motorways/etc that go through cities. They are hardly rural, although around here at rush hour they can sometimes look like they think they ought to be parking lots.

Another reason for assigning tyre particles as microplastics is that apparently all sources are so thoroughly mixed up it is impossible to differentiate them. The situation may be worse in Europe because there they get rid of waste plastics by incorporating them in road-surface material, and hence as the surface wears, recycled waste particles get into the air.

Which raises the question, what to do? Option 1 is to do nothing and hope we can live with these microplastics. You can form your own ideas on this. The second is to ban them from certain uses. In New Zealand we have banned supermarket plastic bags and when I go shopping I have reusable bags that are made out of, er, plastics, but of course they don’t get thrown away or dumped in the rubbish. The third option is to destroy the used plastics.I happen to favour the third option, because it is the only way to get rid of the polymers. The first step in such a system would be to size reduce the objects and separate those that float on water from those that do not. Those that do can be pyrolysed to form hydrocarbon fuels that with a little hydrotreating can make good diesel or petrol, while those that sink can be broken down with hydrothermal pyrolysis to get much the same result. Hydrothermal treatment of wastewater sludge also makes fuel, and the residues, essentially carbonaceous solids, can be buried to return carbon to the ground. Such polymers will no longer exist as polymers. However, whatever we do, all that will happen is we limit the load. The question then is, how harmless are they? Given we have yet to notice effects, they cannot be too hazardous, but what is acceptable?

A Discovery on Mars

Our space programs now seem to be focusing in the increasingly low concentrations or more obscure events, as if this will tell us something special. Recall earlier there was the supposed finding of phosphine in the Venusian atmosphere. Nothing like stirring up controversy because this was taken as a sign of life. As an aside, I wonder how many people actually have ever noticed phosphine anywhere? I have made it in the lab, but that hardly counts. It is not a very common material, and the signal in the Venusian atmosphere was almost certainly due to sulphur dioxide. That in itself is interesting when you ask how would that get there? The answer is surprisingly simple: sulphuric acid is known to be there, and it is denser, and might form a fog or even rain, but as it falls it hits the hotter regions near the surface and pyrolysis to form sulphur dioxide, oxygen and water. These rise, the oxygen reacts with sulphur dioxide to make sulphur trioxide (probably helped by solar radiation), which in turn reacts with water to form sulphuric acid, which in turn is why the acid stays in the atmosphere. Things that have a stable level on a planet often have a cycle.

In February this year, as reported in Physics World, a Russian space probe detected hydrogen chloride in the atmosphere of Mars after a dust storm occurred. This was done with a spectrometer that looked at sunlight as it passed through the atmosphere, and materials such as hydrogen chloride would be picked up as a darkened line at the frequency for the bond vibration in the infrared part of the spectrum. The single line, while broadened due to rotational options, would be fairly conclusive. I found the article to be interesting for all sorts of reasons, one of which was for stating the obvious. Thus it stated that dust density was amplified in the atmosphere during a global dust storm. Who would have guessed that? 

Then with no further explanation, the hydrogen chloride could be generated by water vapour interacting with the dust grains. Really? As a chemist my guess would be that the dust had wet salt on it. UV radiation and atmospheric water vapour would oxidise that, to make at first sodium hypochlorite, like domestic bleach and then hydrogen.  From the general acidity we would then get hydrogen chloride and probably sodium carbonate dust. They were then puzzled as to how the hydrogen chloride disappeared. The obvious answer is that hydrogen chloride would strongly attract water, which would form hydrochloric acid, and that would react with any oxide or carbonate in the dust to make chloride salts. If that sounds circular, yes it is, but there is a net degradation of water; oxygen or oxides would be formed, and hydrogen would be lost to space. The loss would not be very great, of course, because we are talking about parts per billion in a highly rarefied upper atmosphere and only during a dust storm.

Hydrogen chloride would also be emitted during volcanic eruptions, but that is probably able to be eliminated here because Mars no longer has volcanic eruptions. Fumarole emissions would be too wet to get to the upper atmosphere, and if they occurred, and there is no evidence they still do, any hydrochloric acid would be expected to react with oxides, such as the iron oxide that makes Mars look red, rather quickly.  So the unfortunate effect is that the space program is running up against the law of diminishing returns. We are getting more and more information that involves ever-decreasing levels of importance. Rutherford once claimed that physics was the only science – the rest was stamp collecting.  Well, he can turn in his grave because to me this is rather expensive stamp collecting.

Our Financial Future

Interest rates should be the rental cost of money. The greater the opportunities to make profits, the more people will be willing to pay for the available money to invest in further profitable ventures and the interest rates go up. That is reinforced in that if more people are trying to borrow the same limited supply of money the rental price of it must increase, to shake out the less determined borrowers. However, it does not quite work like that. If an economic boom comes along, who wants to kill good times when you can print more money? However, eventually interest rates begin to rise, and then spike to restrict credit and suppress speculation. Recessions tend to follow this spike, and interest rates fall. Ideally, the interest rate reflects what the investor expects future value to be relative to present value. All of this assumes no external economic forces.

An obvious current problem is that we have too many objectives as central banks start to enter the domain of policy. Quantitative easing involved greatly increasing the supply of money so that there was plenty for profitable investment. Unfortunately, what has mainly happened, at least where I live, is that most of it has gone into pre-existing assets, especially housing. Had it gone into building new ones, that would be fine, but it hasn’t; it has simply led to an exasperating increase in prices.

In the last half of the twentieth century, interest rates positively correlated strongly with inflation. Investors add in their expectation of inflation into their demand for bonds, for example. Interest rates and equity values tend to increase during a boom and fall during a recession. Now we find the value of equities and the interest rates on US Treasuries are both increasing, but arguably there is no boom going on. One explanation is that inflation is increasing. However, the Head of the US Federal Reserve has apparently stated that the US economy is a long way from employment and inflation goals, and there will be no increase in interest rates in the immediate future. Perhaps this assumes inflation will not take off until unemployment falls, but the evidence of stagflation, particularly in Japan, says you can have bad unemployment and high inflation, and consequently a poorly performing economy. One of the problems with inflation is that expectations of it tend to be self-fulfilling. 

As a consequence of low inflation, and of central banks printing money, governments tend to be spending vigorously. They could invest in new technology or infrastructure to stimulate the economy, and well-chosen investment will generate a lot of employment, with the consequent benefits in economic growth and that growth and profitability will eventually pay for the cost of the money. However, that does not seem to be happening. There are two other destinations: banks, which lend at low interest, and “helicopter money” to relieve those under strain because of the virus. The former, here at least, has ended up mainly in fixed and existing assets, which inflates their price. The latter has saved many small companies, at least for a while, but there is a price.

The US has spent $5.3 trillion dollars. The National Review looked at what would be needed to pay this back. If you assume the current pattern of taxation depending on income holds, Americans with incomes (in thousand dollars) between $30 – 40 k would pay ~$5,000; between $40 – 50 k would pay ~$9,000; between $50 – 75 k would pay ~$16,000; between $75 – 100 k would pay ~$27,000; between $100 – 200 k would pay ~$51,000. For those on higher incomes the numbers get out of hand. If you roll it over and pay interest, the average American family will get $350 less in government services, which is multiplied by however much interest rates rise. If we assume that the cost of a dollar raised in tax is $1.50 to allow for the depressed effects on the economy, the average American owes $40,000 thanks to the stimulus. Other countries will have their own numbers.I know I seem to be on this issue perhaps too frequently, but those numbers scare me. The question I ask is, do those responsible for printing all this money have any idea what the downstream consequences will be? If they do, they seem to be very reluctant to tell us.