Gravity

Wo! I can't believe it's been 4 years since I posted here. I haven't been that busy! I still have notes on my other 3 climate change posts that I will massage into proper form shortly.  (However, I just saw this from Freeman Dyson which says roughly what I was saying but with more facts and insight and probably more clarity.)  BTW Dyson invented the idea of Dyson Spheres (and many other amazing things) which, if you haven't heard of then you should have.

Anyway the point of this particular post you might consider a little frivolous but it is about the scientific veracity of the movie Gravity.

WARNING: Minor spoiler alert, if you haven't seen the movie.

Gravity (movie)

In brief, I thought the scenery and technical accuracy of this movie were brilliant. The Zero-G effects were perfect even putting "2001, a Space Odyssey" to shame (though that movie did not have access to a lot of new film technology, of course). On first viewing I found a few dubious things but on rumination discovered my own explanations:

1. The three large satellites involved (Hubble?, ISS and Chinese station) all seemed to be in very similar orbits, and even visible from one another, which seems highly unlikely. However, maybe in the future (presumably, in which this is set) the three satellites are parked in a row like this.
2. There seemed to be an invisible force acting in George Clooney's "exit" scene as it seems he is being pulled from the grasp of Sandra Bullock. I thought she should have easily been able to reel him in (if slowly). One explanation is that they were rotating around the ISS/Soyuz and the centrifugal force acting on them was too much for her to pull him in.
3. In orbit things usually move quickly relative to each other so seeing things coming and all this debris just bouncing off things seemed unlikely. However, then I realized that the debris was likely in a similar, but crossing, orbit. (This also explains the 90 minute gap between encountering it.)
4. The accident obviously happened in a low orbit so should not have affected communications satellites in geostationary orbit (at least for a while, if at all). However, perhaps in the future, communications is handled by a network of low orbit satellites rather than geostationary ones (which I think will happen because geostationary is too far away adding to the launch and running costs, and the comms delay).

I have since also read a few other criticisms of the movie.  As one example, someone said that astronauts need cooling systems, "space nappies", etc when using a space suit. All these also can be plausibly explained in terms of technological advances (eg, in-built space suit cooling and water reclamation systems) and maybe a bit of poetic license.

Was it really set in the future? It seems that it was actually in the past as they appeared to be on the Space Shuttle and servicing the Hubble telescope. But the Space Shuttles have been decommissioned and Hubble had its final service years ago. I can only assume that the Shuttle program was resurrected and the use of Hubble extended.

In summary, I found the science plausible compared to some other SF movies I have recently seen (eg The Martian). I especially liked all the Zero-G effects (though The Martian was good in that respect, also).

Dinosaurs and the Himalayas

About 30 years ago I heard of the new controversial theory that an asteroid impact caused the extinction of most dinosaurs.  I immediately embraced this as an interesting and plausible possibility.  However, evidence soon appeared that seemed to contradict the theory.  It appears that many dinosaur species existed for some time after the event.  For example, dinosaur fossils were found in sedimentary layers laid down hundreds of thousands or even millions of years after the boundary that marked the event.  (There is a clear line in sedimentary layers all over the world that has much more Iridium precisely marking the impact of the asteroid about 65 million years ago.)

Recently a new possibility occurred to me.  The idea was triggered by a recent question/challenge on QI (one of my favourite TV shows).  The challenge was to put 4 things in chronological order.  Two of the things were a picture of a dinosaur and a picture of Mt Everest.  (I can't remember the other two.)  This got me thinking that maybe the event that wiped out the dinosaurs also created the Himalayas, as I explain below.

But first I go back to the 1980's....

A Bad Idea

After the abovementioned theory was proposed it was quickly disputed but it still seemed likely to me that the events were linked.  The dinosaurs had been around for hundreds of millions of years.  To suddenly disappear within even a few million years of such a huge event seemed to be more than coincidence.

Now when I began this blog (see Intro) I promised to document some ideas that I had when I was younger.  Some were good.  Here is a bad one.

One idea that occurred to me at the time (1980?) was that the asteroid had hit with such force that it had increased the tilt of the Earth.  With greater yearly fluctuations in temperature this advantaged mammals (and birds) which had hair (and feathers) which could be shed during the warmer months.  So, over the next few million years, dinosaurs lost out to species more suited to the new climatic conditions.   Of course, I now know that the asteroid was too small to affect the tilt of the Earth.  (The tilt was caused by a planetoid almost the size of Mars that hit the Earth more than 4,000 million years ago).

Root Cause

The initial event that, I believe, lead to the demise of the dinosaurs, occurred in the asteroid belt over 70 million years ago.  Apparently there was a major collision event that caused a large rock to be placed in an orbit that intersected the Earth's.  It was just a matter of time before it hit the Earth.  Unfortunately (for them) the dinosaurs were oblivious.

Volcanoes

Another proposal for the extinction of the dinosaurs was the massive volcanoes in India at about the same time.  These resulted in huge amounts of basalt being spewed onto the surface of the Earth, resulting in the feature that is now called the Deccan Traps.

What if all these events are related?

Another Idea

My latest idea is that the asteroid that hit the Earth 65 million years ago was not the only one, and not the largest one, to do so at around that time.  Perhaps the earlier collision event in the asteroid belt placed not one but several rocks in an orbit that intersected the Earth's.  Perhaps the largest such asteroid was 50 km across and hit the ocean just south-west of India.  (At the time India was a true sub-continent languishing in the middle of the Indian Ocean.)  There is actually some evidence of an impact crater of the right size in the ocean bed there.  The asteroid was so large as to puncture a large hole in the Earth's crust which caused the massive volcanic activity that created the Deccan Traps.  This in turn propelled India towards Asia with enough momentum to cause the Himalayas to be formed.

So why didn't this 2nd impact cause another sedimentary layer of Iridium?  Probably the asteroid was so large that most of it went through the thin ocean crust and ended up in the mantle.  Also the fact it landed in the ocean meant that there would be less dust thrown up.

So perhaps the dinosaurs were wiped out not by a single event but by two asteroid impacts which occurred hundreds of thousands (or even millions) of years apart.  The repeated blows to the ecosystem, occurring on different sides of the planet, and perhaps also the subsequent volcanic activity, eventually took its toll.  Perhaps there were even more impacts - I believe the first Hawaiian Islands were also formed about 65 million years ago.

This would explain several things:

• Why the Himalayas could be formed by such a small continent hitting Asia.  Nothing remotely similar happened when even larger continents collided, such as Africa and Europe.
  
• Why there are massive volcanoes at Hawaii, which is far from any plate boundaries.
  
• How the asteroid that killed the dinosaurs happened to hit land rather than the much more likely event that it landed in the ocean.
  
• Why fossils of many dinosaurs are found in layers above the Iridium layer (which marks the time of the impact of the asteroid that hit land).
  
• Why so many big Earth events happened around 65 million years ago.

The Earth Is Safer Now

The good news is that if I am right then the Earth is probably safer than we thought!

To cause something as large as the extinction of the dinosaurs might require a 50 km asteroid to hit the Earth.  The largest object that could possibly hit the Earth in the next few hundred years is not much more than 1 km in diameter.  It's possible that something could come from afar (such as from the asteroid belt), but even then we would probably have a long time to spot something that big and do something about it.

Global Warming - Accuracy

A lot has been written about climate change, especially in the last decade or so.  So what can I add to the debate?  Well I have been following the debate for almost 40 years.  I have read many articles and books on the subject in that time and I think I can present the sort of balanced view that I have not seen presented in anything I have yet read.  I consider this to be the most important topic I have discussed since I have probably read and thought about it more than any other.

I will state from the outset that I have always been a keen proponent of minimising human effects on the environment.  I first began worrying about the effects of increases in atmospheric carbon dioxide in the early 1970's, when I read about predictions that sea-levels could rise up to 10 metres by the year 2000.  Since then I have (with good reason don't you think) become a little more sceptical.  However, just because some predictions have failed to eventuate does not mean that we can ignore them all forever more; after all the boy who cried wolf was proven right in the end.

I also come from a scientific background and have the utmost respect for scientists.  However, scientists are human, and are subject to the foibles that we all have.  History has shown that accepted science is not always correct and that scientists are often not as rational and unbiassed as they would have us believe.

This is a fairly large topic so I have split it according to my four A's, that is:

accuracy - how accurate are the measurements and predictions
avoidance - assuming the predictions are accurate how easily can we avoid the consequences
adaptation - assuming we can't avoid some or all of consequences how can we adapt
acceptance - finally how can we accept what we can't avoid or adapt to

Accuracy

There are two aspects to accuracy.  First, there are reports that the effects of global warming have already been measured, such as rising global temperatures.  Second, there is the accuracy of the predictions to consider.

Temperatures

It is commonly stated that global temperatures have risen by about one degrees Celsius since the start of the industrial revolution based on millions of readings mainly from weather stations.  Any one of these readings could easily be inaccurate for any number of reasons but the hope is that the inaccuracies will average out.  However, there are systematic errors that could mean that the perceived trend of rising temperatures is not real.

One problem is that the thermometers that were used till the middle of the last century tended to give higher readings as they aged.  I believe this means that global temperatures were perceived to have risen until about 1950 after which they were perceived to have fallen for a while, when in fact no such changes took place.

Another problem that I think would have a larger, though difficult to quantify, effect is human activity on local climate.  Most weather stations are *not* located in isolated locations.  I believe human activity in the immediate vicinity of many weather stations means that local temperatures would rise over time.  However, this does not mean temperatures in remote locations have risen or even that global temperatures have risen very much.

For example, in the country town where I went to high school the weather station was located at the airport which was far from the town.  Since then the land around the airport has been cleared (eg for a golf course), there is probably more air traffic at the airport, and there is also a new taxi-way not far from the weather station.  All these factors mean that the air temperature is warmer in the immediate area.

Glacier Retreat

Most of the worlds glaciers are currently retreating.  However, this is mainly due to the fact that the glaciers built up during the "mini ice age" about 200 years ago.

The mini ice age is generally not considered to be caused by any sort of human activity.  I believe it was due to increased volcanic activity at the time.

Due to time-lags most glaciers are still retreating to their natural size for the current global temperature.

There is some evidence that glacier retreat has accelerated in the last few decades.

Sea Level

Rises in the level of the oceans will be the biggest repercussion of global warming.  It is due to reduction in the size of glaciers (see above) and to thermal expansion of water.  Some studies seem to indicate that man-made global warming is causing a rise in sea-levels.

Personally, I think it is very difficult to accurately measure changes in the sea-level except by satellite, since you don't know if your reference point is itself moving.

It is generally accepted that sea-levels have been rising by about 1 mm per year for hundreds of years but this is not due to human-induced global warming.  The best studies indicate that there is little or no acceleration in this trend.

Climate Models

Most predictions of the effect of increased carbon dioxide in the atmosphere are based on very sophisticated computer models.  I believe these models are getting better as computer processing power increases and climatologists begin to understand all the factors involved.  (Certainly weather forecasts are far more accurate than they were 40 years ago.)

I think these models have several problems which I will discuss shortly, but first I will try to give you an idea of how difficult it is to model such complex and chaotic systems.  I believe that the world's climate is at least as complex as the world economy.  Despite all the money spent on climate modeling a lot more is spent on modelling the world economy, given all the cost/benefit involved.  Despite this these models fail to predict risks, as the recent GFC has demonstrated.

There are such a huge number of variables to consider in climate modelling and they involve so many different areas of science (biology, physics, chemistry, geology, etc) it seems likely that there are huge gaps.  Further, it is hard to estimate the exact size of feedback loops, time-lags etc.  Due to the chaotic nature of the systems small variations in one factor can have large an unexpected effects elsewhere.

Another problems is that these models are based on data (such as the global temperatures we saw above) that may be inaccurate.

The main problem I have with these models is that they are not subject to the scientific method - ie make a prediction, test the prediction, then abandon the theory if the prediction is wrong (or else continue making and testing more predictions).  With climate models if a prediction is proved incorrect then it's usually just a matter of tweaking a few variables until the model fits the facts again.  In the best case if a prediction is incorrect then the "scientists" try to find some new factor(s) to explain the results, and then these factors are incorporated into the model until once again the model matches the data.

Never does anyone attempt to disprove the fundamental assumptions on which the model is based.  Scientists should be trying to disprove their theory, not continually changing it to make it work.

Worse still, is that the model may be able to be tweaked in different ways to obtain the same result.  The temptation would be to make adjustments that are more likely to gain more funding or have your latest academic paper pass peer review for publication in the Prestigious Climatologist Journal (not a real publication AFAIK).

Prediction Bias

This brings us to the discussion of whether climatologists tend to exagerate the effects of human-induced climate change.  Unfortunately, recent leaked emails seem to indicate that many have a tendency to distort the facts.  Whether this is purely for personal gain, or with the best of intentions is unclear, but the fact remains that a true scientist always seeks the truth despite personal beliefs or desires.

Their defence is that they are only trying to counter the disinformation being put out there by "skeptics".  While it is true that there is a lot of unscientific nonsense being espoused by all sorts of idiots, I believe this occurs on both sides of the debate and the actual scientists should not get involved in such stupidity.

Why Humans have Little Hair

I have an old diary that I wrote down lots of ideas in when I was a teenager.  Some of the ideas were stupid and obviously wrong.  Some of the ideas are stupid in that they are obviously right.  A few ideas I wrote down that I thought were obviously correct but I had never seen written anywhere.  Now with the invention of the Internet and web sites like Wikipedia it is easy to check whether some of these ideas are prevailing opinion or have even been thought of.

One brief note that I wrote was "humans evolved to have less hair after they invented clothes".  I have always thought this is fairly obvious but I have never seen any discussion of it, so I just did a search on the Internet.  There are many theories on why humans have little hair, but none of them mention the invention of clothes as having anything to do with it.  Here are three of the more plausible that I found.

One theory is that as humans became more sociable they lived in more close-knit groups and were far more susceptible to parasites.  Hair-loss was a way of dealing with the problem.  The problem with this theory is that there are many animals that live in close groups that have not lost their fur - for example chimpanzees preen each other  By the time humans were living this way they would have been intelligent enough to deal with parasites in some way.

Another theory is that at some stage humans became far more aquatic and lost their hair much like other animals have.  (Apparently pigs and elephants had aquatic ancestors which is the reason accepted for them being fairly hairless.)  Hair is not a good insulator in water.  I find it implausible and there is no archeological evidence for it whatsoever.

Perhaps the most plausible theory is that about 3 million years ago we lost our hair in the hot savannah of Africa (see http://www.scientificamerican.com/article.cfm?id=continuum-of-change).  The problem with this theory is that it is an advantage to have less hair in the heat of the day but also a disadvantage in the cool of the night.  Further, other animals in similar conditions have not lost their fur.  Also why when early humans moved into colder areas did they not grow the fur back again?

Clothes

It seems to me that the first humans who started hunting animals were intelligent enough to not only use the meat but also use the pelts of the animals they killed.  At first this might have just been for a bit of extra warmth at night (well before the use of fire).  Later they would have found ways to attach the furs to their torso, so it could be used during the day, but easily removed.  Being able to regulate body temperature by adding or removing clothing would have been a huge advantage over other animals.  To assist the use of clothes in regulating temperature, humans then evolved to have less hair and to use sweat to cool off when the clothing was removed.

When humans migrated into colder areas such as Europe their use of clothes was advanced enough that they did not need to grow their hair back.  With a large brain it is easier to obtain clothes than the extra food required for the skin to produce fur.   Also further from the equator there is a greater range of temperatures throughout the year.  Being able to regulate body temperature by adding and discarding clothes would still be a large advantage.

I am not sure why this is not commonly accepted or at least considered to be a plausible theory.  I am happy to hear any feedback on the subject.

Nature vs Nurture (vs Culture)

When I studied psychology at university I was always amazed at the willingness of people to ascribe things to instinctive behaviour.  I tended much more towards the nurture side of the "nature versus nurture" debate.  That is, I believed that just about all behaviour was learnt.

However, I gradually realized that there was more to it, and finally came to the conclusion that there are not two but three forces that shape an individual, which is part of the source of the confusion in the the first place.  I call these genetic, environmental and extra-genetic.

When we talk about "nature versus nurture", nature basically refers to genetics, and nurture refers an individual's particular environment.  What I call "extra-genetic" is information passed from parent to child but not genetically.  I guess you could think of it as something like culture and hence the debate could instead be decribed as "nature versus nurture versus culture".

This extra-genetic information is in many ways like genetic information and in other ways environmental which is why the whole debate is so difficult to resolve.  I think I need to explain this in more depth.

Behaviour

In the first primitive organisms all behavior was passed genetically.  This is called instinctive behavior.  Of course, though the amount of genetic information that can be passed to an offspring is large it is limited.  Hence, there is a limit to the amount of instinctive behavior.

As organisms became more advanced they developed larger brains for various reasons.  One reason was that a large brain presented a way to bypass the limit on the amount of genetic information.  Parents teach their children things, so that information is passed from generation to generation. The limit on the amount of information is now the size of the brain and the amount of time required to transfer it.  Genes are still involved, of course, to endow the child with a large enough brain and the predisposition to learn from their parents.

Humans

Humans really have taken this to extremes.  They have very large brains and it take many years after birth before they can even begin to function as a fully-fledged person.  This is why children have to be involved and learning from their parents from day one.  Their genetic programming means they are continually learning and processing information.  They have a very strong inclination, especially at a young age, to try to copy their parents' behaviour.

This was brought home to me watching my nephew Alex on my brother's farm.  He must have been about one year old at the time as he was barely walking and not yet talking.  My brother had been using various hand tools and Alex had been watching.  During a break in proceedings he gave a very impressive display of emulating his father using a hammer (though he could barely lift it) and other tools.

This whole process of passing extra-genetic information has been really muddied by humans.  Since human societies are incredibly cooperative information is often not passed from an individual's genetic parents but from many other sources.  With the advent of writing information can even be communicated from someone you have never met or who is long dead.

I will note at this point, though, that you can't learn everything from a book (or a blog).  Many behaviours are only learnt by watching and copying.  This is why young humans, to develop properly, need "role models", preferably their genetic parents.

This has all been evolving (in humans and other animals) and feeding back into itself over millions of years.  Behaviours that were previously instinctive may have changed in some species to being learnt, freeing up genes for other purposes.

Is All Human Behaviour Learnt?

So, I return to my original thoughts.  I still believe that most behaviour in humans is or can be learnt.  However, I now believe that heredity plays a very important part.  I believe genes give people a predisposition to some types of behaviour but that does not mean that if brought up in an atypical environment they will not behave in a completely different way.  I'm trying to think of an example...

I would imagine that people of western European descent would find it easier to learn languages from western Europe than say an Australian aboriginal dialect.  Conversely, an Australian aboriginal would find it harder to learn English than a local dialect.  Obviously, this does not mean it is impossible, just that thousands of years of evolution mean that brains have evolved to be better at using local dialects.

So your genes do not determine your behaviour, which mainly depends on your upbringing, but they do give a tendency towards some types of behaviour.  And I guess the stronger this tendency is the more likely it is to be called instinctive.

This gives rise to the question: Is any human behaviour truly instinctive?  I would have to say yes.  There are some things under the control of the brain that are almost impossible to override - for example, breathing.  But the fact that people can feel so strongly about something to go on a hunger-strike and die from starvation, means that some of even the most basic behaviours can be "unlearnt".

Neutrinos, Photons and Z-bosons

I mentioned last week that I would not be surprised if neutrinos do travel faster than photons (as suggested by the recent highly-publicised OPERA experiment).  But this definitely does not mean that I think Einstein's theory of relativity is wrong or any of the other nonsense that was printed in the papers.  If anything, I think Einstein's mistake was calling the maximum speed the "speed of light".

Are Neutrinos Tachyons?
The newspapers have spouted all sorts of nonsense, that if the result is correct it means that neutrinos are tachyons, sending messages back in time would be possible, extra dimensions, etc.  Let's look at these first.
It is a common misconception that Einstein said that if you can send a message faster than the maximum speed you can send it backwards in time.  I do not believe you can send a message faster than this but if you could the maths does not say that the progress of time becomes negative but in fact it becomes "imaginary" (ie involves the square root of negative numbers).  I believe anything that involves imaginary numbers does not exist in the real world.

Another idea is that there are extra spatial dimensions and neutrinos are somehow taking a shortcut.  Extra dimensions are often used in theories (eg string theory) but people should remember what Einstein himself said - "keep it as simple as possible, but no simpler".  Adding extra dimensions, which we have no proof of, just makes things much more complex.

When people first looked at Einstein's equations they thought that it was possible for particles with special properties to travel faster than the maximum speed and they were called tachyons.  However, I don't believe tachyons exist.  If you look at the mathematics then again the existence of tachyons relies on use of "imaginary" numbers.

My first thought after reading about the OPERA experiment is if neutrinos are tachyons why don't they travel twice as fast or a million times as fast or 10^300 times as fast.  The results of the experiment (if correct) shows they only travel at a tiny fraction more than the speed of photons.  This immediately implies to me that photons travel at less than C, rather than neutrinos travel at more than C.

Problems

In any case, I think a lot of our thinking is clouded by nomenclature.  People equate the maximum speed "C" with the "speed of light" (really meaning the "speed of electromagnetic radiation in a vacuum").  There are other particles, apart from photons, that are also supposed to travel at the maximum speed, among them neutrinos and Z bosons.  To avoid confusion I think we should call the maximum speed simply "C", and distinguish it from the speed of neutrinos, Z bosons, photons in a vacuum, etc, which may possibly be different.

From my understanding there are already problems in this area with current thinking.  Neutrinos are believed to travel at C, but recent experiments have shown that neutrinos must have a rest-mass.  If something has rest-mass then it takes an infinite amount of energy to accelerate it to C (and like "imaginary" numbers I don't think "infinite" numbers have any basis in reality).

The only conclusion is that neutrinos travel at less than C (even if by a very small amount).  If neutrinos travel at less than C I can't see why photons might not also.  Nobody has ever found that photons have a rest mass but this may just mean it is too small to yet be measured.

Another reason I think photons have rest-mass is that they are affected by gravity.  It will be argued that anything that moves through space must be affected by gravity since gravity bends space.  My reply to this would then be that anything that moves through space must have mass.  One day we will understand what it really means to have "mass".

Z-Bosons

The latest reason proposed (by Cohen and Glashow) that there is something wrong with the OPERA experiment results is this: If neutrinos were travelling faster than light they would emit particles until they lost energy causing them to slow down.  This is similar to the way that electrons emit photons (called Cherenkov radiation) when traveling faster than the speed of light in water.

I will explain my understanding of this, in case you have never heard of Cherenkov radiation.  Photons travelling through a medium such as water or glass travel at a significant fraction less than their speed in a vacuum.  (The difference in the speed of light in glass and air is why lenses work.)  If electrons travel through a medium faster than photons would travel through the same medium (but still less than C, of course) then they emit some of their energy as photons till they slow down.  You can think of this as a "sonic boom" but for the speed of light not for the speed of sound.

Electrons only do this because electrons have an electrical charge and photons are electromagnetic particles.  Neutrinos will not do this because they have no electrical (or magnetic) charge.  However, neutrinos do have a "weak force" charge and the weak force equivalent of a photon is a Z-boson.  (I know this is not strictly the full story.)

I think the Cohen & Glashow response does not preclude the OPERA results being valid.  It is only relevant if neutrinos travel faster than Z-bosons.  But I don't think the neutrinos are travelling faster than Z-bosons only faster than photons.  So if the speed of Z-bosons is faster than the speed of light then the neutrinos still do not have to slow down to the speed of light.

I don't believe the speed of Z-bosons has been measured, or at least measured anywhere near as accurately as the speed of light.  My belief is that neutrinos travel slightly faster than light but slower than Z-bosons.  (Again I remind the reader that nothing travels faster than C.)

Cicadas and Prime Numbers

Australian summers are usually filled with the deafening sound of cicadas but there are the occasional years where there seem to be no cicadas.  I remember one summer (1967?) when I was a child there were huge numbers of cicadas.  One weekend, along with two friends (Jimmy and Peter), we collected over one hundred of at least four different varieties.  (Kids had given names to the different types based on their colour, like Black Prince, Green Grocer, etc.)  Not only was this a fun time for kids but the birds were enjoying a feast too.  Many times each day you would hear the monotonous sound of the cicadas interrupted by the intermittent and panicked sound of a cicada that had been caught by a bird.

Someone told me at the time that every seven years there are a lot of cicadas but I do not recall ever having seen so many in any year since.  Several summers later I noticed that were no cicadas at all that year.  This started me thinking about the variation in cicada numbers from year to year and I came across some information on the life-cycle of cicadas.

Life-Cycle of Cicadas

Apparently, the different varieties we had found were different species most of which had different life spans.  (If you don't know, cicadas spend many years underground sucking on the sap from tree roots before emerging and mating for a few months before dying.)  The life span of various species varies from 3 years to as long as 17 years.  I had just learnt of prime numbers at that time and it occurred to me that the life span (in years) of any particular species was always a prime number.  The most common varieties spend seven years in the ground but others spend 3, 5, 11, 13 and even 17 years underground.

Now it was obvious why some years there were few or even no cicadas and very occasionally there were a huge number.  Obviously the numbers of each variety varied from year to year either through some form of collusion or due to different environment factors (weather conditions, prevalence of predators, etc) in certain years.  If a variety has a life-cycle of seven years then the peaks and troughs in their numbers would tend to follow a seven year cycle, though I guess there could be several peaks in one cycle.

Why Prime?

Since different varieties have different cycles then only occasionally would the peaks coincide.  I believe the "year of the cicada" I experienced happened when the peaks of at least three types coincided or at least came close to coinciding.  This probably happens only once, or a few times, every 105 (3 x 5 x 7) years.  By my calculations there may be another peak in 2019 and/or 2020 (1967 + 52/53), though this may be localised to the Lower Blue Mountains area.

But why would the life cycle of cicadas always be a prime number?  I believe cicadas have evolved to have these life spans for the very reason that it makes their numbers unpredictable from year to year.  If there were always the same number of cicadas each year, birds would come to depend on this and the number of birds that hunted cicadas would increase.  The fact that different varieties have different life spans is the key to this strategy working.  I believe that this is an example of inter-species cooperation.  (Inter-species cooperation is something you never hear of and I believe it is far more common than biologists are currently aware.)

Clarification (Oct 11): I should clarify my last comment.  Obviously, symbiotic relationships between species have been extensively studied.  I simply meant that I feel there is a lot of more subtle inter-species cooperation that is yet to be discovered.