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Monthly Archives: March 2020
This example illustrates just how fast exponential growth is. It was proposed on twitter by Charles Arthur (@charlesarthur) who attributes the idea to Simon Moores. The stadium version is a variant of the better known ‘grains of wheat (or rice) on a chessboard‘ problem. The stadium example is better, I think, because the time element gives it a sense of urgency, and that’s what we need right now.
Here’s Wembley Stadium. The watering system develops a fault: in minute 1 one drop of water is released; minute 2, two drops, minute 3 four drops, and so on. Every minute the number of drops doubles. How long will it take to fill Wembley stadium?
The answer is that after 44 minutes, before half-time, the stadium would overflow.
Here’s why.
The sequence is 1, 2, 4, 8, 16, . . . so the nth term in the sequence is 2n – 1. For example, the 4th term is 23 = 8.
Next we need to know how many drops are needed to fill the stadium. Suppose a drop of water has a volume of 0.07 ml. This is 0.00000007, or 7 x 10-8, cubic metres. Wembley Stadium has a volume of 1.1 million cubic metres. So the stadium holds 15,714,285,714,285 drops. Or about 15.7×1012 drops. How many minutes does it take to get to this volume of water?
After n minutes, the total volume of water will be the sum of all the drips up to that point. This turns out to be 2n-1. If this baffles you, check this video (in our case a =1 and r = 2).
We want to solve for n, the number of steps (minutes), 2n = 1 + 15.7×1012. The easiest way to do this is to take the logarithm of both sides.
n log(2) = log(1 + 15.7×1012).
So
n = log(1 + 15.7×1012) / log(2) = 44.8 minutes
At the 43rd minute the stadium would be more than half full: (243 – 1) = 8.80 x 1012, i.e. 56% of capacity.
By the 44th minute the stadium would have overflowed: (244 – 1) = 17.6 x 1012, i.e. 112% of capacity.
Notice that (after the first few minutes) in the nth minute the volume released is equal to the total volume that’s already in, so at the 44th minute an extra 8.80 x 1012 drops are dumped in. And at the 45th minute more than another stadium-full would appear.
The speed of the rise is truly terrifying.
Relationship of this to COVID-19
The rise in the number of cases, and of deaths, rises at first in a way similar to the rise in water level in Wembley stadium. The difference is that the time taken for the number to double is not one minute, but 2 – 3 days.
As of today, Monday 23rd March, both the number of diagnosed cases, and the number of deaths, in the UK are still rising exponentially. The situation in the UK now is almost exactly what it was in Italy 15 days ago. This from Inigo Martincorena (@imartincorena), shows it beautifully.
Boris Johnson’s weak and woolly approach will probably cost many thousands of lives and millions of pounds.
Up to now I’ve resisted the temptation to suggest that Whitty and Vallance might have been influenced by Dominic Cummings. After this revelation, in yesterday’s Sunday times, it’s getting progressively harder to believe that.
We have been self-isolated since March 12th, well before Johnson advised us it. It was obvious common sense.
Please stay at home and see nobody if you possible can.. This cartoon, by Toby Morris of thespinoff.co.nz, shows why.
Some good reading
The report from Imperial College, 16 March 2020, that seems to have influenced the government:
Tomas Pueyo. His piece on “Coronavirus: Why You Must Act Now“, dated March 10th, had 40 million views in a week
Tomas Pueyo. March 19th; What the Next 18 Months Can Look Like, if Leaders Buy Us Time.
“Some countries, like France, Spain or Philippines, have since ordered heavy lockdowns. Others, like the US, UK, or Switzerland, have dragged their feet, hesitantly venturing into social distancing measures.”
David Spiegelhalter. March 21st.
“So, roughly speaking, we might say that getting COVID-19 is like packing a year’s worth of risk into a week or two. Which is why it’s important to spread out the infections to avoid the NHS being overwhelmed.”
Washington Post. Some excellent animations March 14th
Up to date statistics. Worldometer is good (allows semi-log plots too).
The inquiry into UCL’s historical role in eugenics was set up a year ago. Its report was delivered on Friday 28 February 2020.
Nine (the MORE group) of the 16 members of the inquiry commission refused to sign the final report and issued their own recommendations.
The reasons for this lack of consensus included the fact that the final report did not look beyond the 1930s. It failed to deal with the science, and, in particular, it failed to investigate the London Conference on Intelligence, which was one of the reasons the inquiry was set up. That is a topic that I addressed at the time.
Firstly I should say that I agree entirely with all the recommendations, including those of the MORE group.
I’ve thought for a while now that the Galton and Pearson buildings/theatres should be renamed with a prominent plaque saying why.
But I was disappointed by the scope of the inquiry, and by the fact that it failed entirely to engage with the science. This was dealt with much better in the excellent podcast by Subhadra Das which came out at the same time. She had also made an excellent podcast, “Bricks + Mortals, A history of eugenics told through buildings“.
The inquiry did some surveys by email. This was a laudable attempt, but they only got about 1200 responses, from 50,000 UCL staff and students and 200,000 alumni. With such a low, self-selected, response rate these can’t be taken seriously. The author of this report said “I believe some of the ontological assumptions of scientists who researched eugenics are still firmly embedded in the fabric of UCL”. No further details were given and I’m baffled by this statement. It contradicts directly my own experience.
I was also disappointed by some passages in the official report. For example, referring to the ‘London Conference on Intelligence’, it says
“Occurring in the midst of activism to decolonise UCL, it suggested a ‘Janus-faced’ institution, with one face promoting equality in line with its statutory duty of care12 and the other a quiet acquiescence and ambivalence to UCL’s historical role in eugenics and its consequences for those Galton theorised as being unworthy.”
This seems to me to be totally unfair. I have been at UCL since 1964, and in all that time I have never once heard anyone with an “ambivalent” attitude to eugenics. In fact ever since Lionel Penrose took over the Galton chair in 1946, every UCL person whom I have read or met has condemned eugenics. In his 1946 inaugural lecture, Penrose said
“In the light of knowledge of its frequent misuse, inclusion of the term “racial” in the definition seems unfortunate. A racial quality is presumably any character which differs in frequency or which (when it is metrical) differs in average value in two or more large groups of people. No qualities have been found to occur in every member of one race and in no member of another.”
The inquiry stops in the 1930s. There is no acknowledgment of the fact that work done in the Lab for Human Genetics at UCL, ever since the end of WW2, has contributed hugely to the knowledge we now have about topics like genetics and race. They have done as much as anyone to destroy the 19th and early 20th century myths about eugenics.
London Conference on Intelligence
I think the allusion, quoted above, to the London Conference on Intelligence (LCI) was totally unfair. The only, very tenuous, connection between LCI and UCL was that a room was booked for the conferences in secret by a James Thompson. He was an honorary lecturer in psychology. He filled in the forms dishonestly as shown in the report of the investigation of them.
As shown in appendix 5 of this report, the questions about “Is speaker or topic likely to be controversial?” were not filled in. In fact much of the application form was left blank. This should have resulted in the room bookings being referred to someone who understood the topic. They were not. As a result of this mistake by a booking clerk, Thompson succeeded in holding a poisonous conference four times on UCL property, without anyone at UCL being aware of it.
The existence of the conference came to light only when it was discovered by Ben Van Der Merwe, of the London Student newspaper. He contacted me two days before it was published, for comment, and I was able to alert UCL, and write about it myself, in Eugenics, UCL and Freedom of Speech.
As everyone knows, the rise of alt-right populism across the world has given rise to a lunatic fringe of pseudoscientific people who once again give credence to eugenics. This has been documented in Angela Saini’s recent book, Superior. Thompson is one of them. The report on his conferences fails to tell us how and when he came to be an honorary lecturer and whether he ever taught at UCL, and, if he did, what did he teach. It should have done.
Although the honorary title for James Thompson has now been revoked, this has, as far as I know, never been announced publicly. It should have been.
It’s very unfortunate that the Inquiry didn’t go into any of this.
One small problem
I started this blog by saying that I agreed with all of the recommendations of both the main report and that of the MORE group. But there is one recommendation which I can’t understand how to implement in practice.
“Departments must devise action plans for all teaching programmes to engage critically with the history and legacy of eugenics at UCL”
After the question of ‘decolonising the curriculum’ came up, I took the problem seriously and spoke, among others, to UCL’s diversity officer. My teaching at the time was largely about the stochastic theory of single molecule kinetics, and about non-linear curve fitting.
The reason for talking to these people was to seek advice about how I could decolonise these topics. Sad to say, I didn’t get any helpful advice from these discussions. I still don’t understand how to do it. If you have any ideas, please tell me in the comments.
Follow-up
I have just been given some more information about James Thompson, the person behind the London Conference on Intelligence.
“Dr Thompson was made an honorary lecturer in 2007, following his retirement from UCL. As a clinical psychologist he was a member of staff from 1987, joining UCL by transfer when the UCH and Middlesex Hospital departments of psychiatry merged.
We do not have detailed records of Dr Thompson’s teaching at UCL. He was a Senior Lecturer in Psychology with primary responsibility for teaching medical students. He was given honorary status in 2007 as he had agreed to deliver 2 lectures to students on a neuroscience and behaviour module – one in 2007 on the placebo effect and one in 2008 on depression. There is no record of any involvement in teaching at UCL after the second lecture.
His honorary appointment was approved by the Head of Department.”
I hope to have a bit more information soon.