A Day in the Life of a Measurement Scientist (Retired)

October 27, 2020

It is now approaching six months since I retired from NPL, and some friends have been kind enough to express their concern about how I am coping with the transition to senility.

What was I saying?

Oh Yes, the transition to senility. All is going well.

To reassure those friends, I thought I would offer this insight into a typical day in retirement.

The day begins

I generally rise at a leisurely hour and immediately weigh myself. This provides data for one of my longest running data series going back (intermittently) over twenty years.

I then descend to make a cup of tea and download the overnight weather data (yesterday’s average temperature) and data from my smart meter (kWh of gas used).

At weekends I also read the gas and electricity meters manually to confirm the validity of the electronic readings.

Together these temperature/power data pairs form part of series covering more than 700 days. By collecting this data I am able to assess the effect of each change I make such as triple-glazing or external wall insulation. This is at the heart of my efforts to achieve a home with near-zero carbon annual carbon emissions.

In late morning I often travel into the bustling metropolis of Teddington village. Mostly I go for the ‘street buzz’, but once or twice a week I might visit a local artisan baker, or perhaps occasionally indulge in a coffee at Café Mimmo.

The middle of the day 

After returning from Teddington I generally carry out domestic chores, cleaning or preparing experimental food for an evening meal.

Experimental Spanakopita. The Brasso(TM)was used for an unrelated project.

Sometimes I run through the park or take photographs of local items of interest.

Later in the afternoon I incorporate the new data on the Coronavirus pandemic and plot initial graphs and consider whether or not I understand what the data is telling me.

The end of the day  

After dinner, I like to write and experiment.

Experimental projects include verifying the thermal conductivity  of different insulating materials (link) or investigating the physics of the drinking bird.

Experimenting on a ‘Drinking Bird’.

This latter investigation has proved extremely difficult and apparatus has sprawled across the kitchen table for several weeks. I am currently upgrading my temperature control system courtesy of Amazon (link) to meet the rather exacting requirements.

Experimental Apparatus for investigating the ‘Drinking Bird’

I have a number of writing projects, but the blog actually takes a lot of time. I revise each article many times, aiming to make the text as concise as possible because the web is not a good medium for long and complex arguments. But typos and errors always slip through.

And so to bed…

…in the sure and certain knowledge that tomorrow holds new measurements to  surprise and delight.

COVID-19: Day 296: Still bleak

October 23, 2020

Things are still looking bleak.

Using my superpower oflooking on a log graph of the data and drawing a straight line“ I see there has been no let up in the growth of cases, which means that there will be no let up in hospital admissions, and that deaths will follow.

XKCD has summarised the awful reality in a cartoon.

Click for larger version. XKCD cartoon.

Click for larger version. XKCD cartoon.

Let’s take a look at the data.

Data#1. Prevalence

Since late April the ONS prevalence survey has been randomly testing people in England each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

The latest fortnightly data point is highlighted in red. Click for a larger version.

The number of people tested and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 16th October 2020 on average 0.85% of the UK population were actively infected.

The raw count of positive tests was:

  • 1,402 from 179,969 people tested in the two weeks to 8th October,
  • 606 from 138,121 people tested in the preceding two weeks, and
  • 168 from 83,345 people tested in the two weeks preceding that.

Note these are random survey tests (so-called Pillar 4 tests), not clinical tests. Their data – graphed below – suggest that the prevalence is now doubling roughly every 13.5 days – slightly slower than last weeks data indicated.

Estimated prevalence of COVID-19 in England. Click for a larger version.

I have shown two exponential curves on the graph above.

  • The black dotted line (– – –) is the same curve I plotted for the previous four weeks. It is a fit to the 3 black data points and shows what we might expect if viral prevalence were doubling every 15 days.
    • This week’s update lies slightly above the extrapolation.
  • The purple dotted line (– – –) is a fit to the last three data points from today’s data set. It shows what we might expect if viral prevalence were doubling every 13.5 days.

If one considers it likely (which I do) that the viral prevalence has continued on trends similar to the ones shown, then today (23rd October) the prevalence is likely to be around 1.6% i.e. roughly 1 in 63 people in England are infected right now. Regionally it probably exceeds 2.0% in the North West i.e. 1 in 50 people are currently infected.

Regional data (below) makes it clear that considerable complexity underlies the national statistics. In some regions the prevalence was large and still rising (red), in other areas it had peaked (blue) and in other areas it was relatively low, but still rising (green). The purple and black dotted curves on the graph are the same ones drawn on the figure above.

Estimated prevalence of COVID-19 in Regions of England. Click for a larger version. Large and rising prevalences are in red. Prevalences which have peaked are in blue. Prevalences which are small but still rising are in green.

Data#2. Tests and Deaths

The graph below shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined.

All curves are 7-day retrospective rolling averages of the data since July.

Data for positive casesdaily hospital admissions and daily deaths. Click for a larger version.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days.
  • The increasing trends correspond to quantities doubling every 15 days.

We see that the three data sets initially fell with similar time-dependencies. All the quantities are now rising.

  • The rate of positive tests and the rate of hospital admissions seem to be doubling every 15 days.
  • With an optimistic eye one might think that the rate of rise of daily positive tests had slowed over the last two weeks.
  • The rate of deaths appears to be close to doubling every 11 days – this is shown as an additional dotted line on the death data.

What is the most optimistic view I could possibly imagine?

What’s next? As I have said before,’It’s the future’ so nobody knows‘.

But let’s consider the most optimistic view. Let us suppose that the current crop of measures becomes immediately as effective as a lock-down and continues to be so. This isn’t very likely, but let’s suppose it’s the case and see where it gets us.

If that were so then:

  • the number of positive tests per day would be just at its peak now and would fall, halving every 21 days as it did during lock down.
  • the number of people newly admitted to hospital each day would peak in 1 to 2 weeks, and then halve every 21 days
  • the number of deaths per day: would peak in 3 to 4 weeks, and then halve every 21 days.

This optimistic situation is outlined on the graph below where I have drawn dotted lines to indicate the likely trends.

Optimistic projections about the development of positive casesdaily hospital admissions and daily deaths. Click for a larger version.

If this optimistic view were realised, the number of deaths per day would rise to a peak of around 300 people per day in early November, and remain above 100 people per day until early December.

In my opinion this would be a pretty poor outcome.

If we took a less optimistic view and estimated that the current measures would merely stablise the level of viral prevalence in the population (i.e. R ≈ 1), then the current rate of deaths would increase for the next two weeks or so, and then stabilise at roughly 300 people per day indefinitely. This would be a truly terrible outcome.

Like I said, things are still looking bleak.

Stay safe.

COVID-19: Day 289: Looking really bleak…

October 16, 2020

Things are looking bleak.

Twenty days ago on 26th September 2020 I wrote that we appeared to be committed to COVID death rates of around 100 people per day in mid-October. Sadly, yesterday – October 15th – the 7-day average of the daily death rate reached 100.

That prediction is testament to the super-power of “looking on a log graph of the data and drawing a straight line“.

Using the same superpower, I would estimate that we are  probably already committed to more than 200 deaths per day – possibly as many as 300 deaths per day – at the end of October.

Are the new policy responses sufficiently strong to cause a decline in viral prevalence? I would love to be wrong, but personally, I don’t think so. I’ll write more about what to expect at the end of the article.

Let’s take a look at the data.

Data#1. Prevalence

Since late April the ONS prevalence survey has been randomly testing people each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

The latest fortnightly data point is highlighted in red. Click for a larger version.

The number of people tested and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 8th October 2020 on average 0.7% of the UK population were actively infected. They estimated the prevalence was 1.43% in the North West of England and 0.34% in the South East.

The raw count of positive tests was:

  • 926 from 154,664 people tested in the two weeks to 8th October,
  • 250 from 103,220 people tested in the preceding two weeks, and
  • 89 from 68,272 people tested in the two weeks preceding that.

Note these are random survey tests (so-called Pillar 4 tests), not clinical tests.

Their data – graphed below – suggest that the prevalence is now doubling roughly every 11 days.

I have shown two exponential curves on the graph below.

  • The black dotted line (– – –) is the same curve I plotted for the previous three weeks (last week, the week beforethe week before that). It is a fit to the 3 black data points and shows what we might expect if viral prevalence were doubling every 15 days.
    • Last week’s and this week’s updates lie significantly above the extrapolation.
  • The purple dotted line (– – –) is a fit to the last three data points from today’s data set. It shows what we might expect if viral prevalence were doubling every 11 days.

If one considers it likely (which I do) that the viral prevalence has continued on trends similar to the ones shown, then today (16th October) the prevalence is likely to be around 2% i.e. roughly 1 in 50 people in England are infected right now. Regionally it might even approach 3% – roughly 1 in 33.

Estimated prevalence of COVID-19 in England. Click for a larger version.

Data#2. Tests and Deaths

The graph below shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined.

All curves are 7-day retrospective rolling averages of the data since July.

Data for positive cases, daily hospital admissions and daily deaths. Click for a larger version.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days.
  • The increasing trends correspond to quantities doubling every 15 days.

We see that the three data sets initially fell with similar time-dependencies. All the quantities are now rising.

  • The rate of positive tests and the rate of hospital admissions seem to be doubling every 15 days.
  • The rate of deaths appears to be close to doubling every 11 days – this is shown as an additional dotted line on the death data.

What Next?

As I write, our best guess is that roughly 2.0% of the UK population are actively infected with the virus. I am personally alarmed by this figure.

  • Using my super-power of ‘drawing a straight line through the data and extending it‘ I estimate that we are already committed to at least 200 COVID-related deaths per day by the end of October. Nothing can be done about these deaths because the people are already infected and ill.
  • With the prevalence doubling every 11 days then, 100 deaths per day now will turn into 800 deaths per day in 33 days i.e. by mid-November. This would be another national catastrophe.

This week the government have taken action with their 3-tier response. From midnight tonight, households throughout London will be forbidden from visiting each other. In Liverpool and Lancashire the restrictions are even stricter. However, it is likely that adherence to these restrictions will be less perfect than during the spring lock-down. Schools and Universities will remain open.

If the measures achieved R = 1, which I consider very unlikely – then the death rate would stay at whatever level it was when R = 1 was achieved. Because we have acted so late, even achieving R = 1 would simply keep the death rate at it is current high level.

More likely, the measures will not achieve R = 1 but rather something just over 1. This will increase the doubling-time from the present value of (very roughly) 11 to 15 days to something longer – perhaps 30 days. This would then commit us to a death rate of perhaps 400 people per day at the end of November and perhaps 800 people per day at Christmas.

In my opinion…

  • We need to reduce the spread of the virus – not just slow it down. Action on this is long overdue and the current policy response will probably not achieve that, even at Tier 3.
  • ‘Full’ lock downs – as we had in the spring – are the only thing which has been demonstrated to reduce the prevalence of the virus. And even the spring lock-down only halved the incidence of the virus every 21 days.
  • The cost of lock-downs is immense in every dimension, but I personally think when death rates reach many hundreds per day – which is where they are headed – then a full lock down will be politically inevitable.
  • It is better to acknowledge the awful reality we are in and plan a series of lock-downs while the death rate is low than to wait until the rate is high.
  • If this epidemic lasts for a further 6 months before a vaccine arrives, then every extra 100 deaths per day amounts to an additional 18,000 deaths before the end of March 2021.

Like I said, things are looking very bleak.

Stay safe.

Estimated prevalence of COVID-19 in England. Click for a larger version.

Saturday 17th October 2020: Typos corrected

External Wall Insulation: the project begins…

October 15, 2020

I just wanted to take a moment to let people know that amidst the world’s problems, good stuff is happening.

And for me that good stuff is the start of installation of my long-awaited External Wall Insulation.

The idea of insulating a house from the outside is very simple in principle. In fact it is obvious. But in practice there are many steps required to ensure a weather-proof installation that will look smart when finished and last for a long time. That’s why I have hired the professionals at Be Constructive to do it!

Here are some pictures of the project in progress.

The back of my house. Click for a larger view

The picture above shows the general view of the back of the house with the insulation partially applied. Notice the dark red paint on the existing wall which enhances the adhesion of the insulation and the way the insulation is carefully cut out around the windows and the external tap and water drain.

The picture below shows the external tap and drain which have been extended beyond the thickness of the insulation. Expanding foam has been used to keep the system air-tight.

Detail showing the way the external pipes are extended to allow for the insulation. Click for larger version.

The picture below shows more detail of the window including the protective films applied during construction. You can see white ‘webbing’ around the windows which will help give a well-formed corner when the final render is applied.

Details of the insulation around a window. Click for a larger version.

The picture below details of the way the insulation is initially applied to the wall. The insulation consists of two boards of 50 mm thick Kingspan K5 which have been glued together to make a ‘dual-board’ which is 100 mm thick. This ‘dual-board’ is then stuck to the wall using an adhesive mortar. When this is dry – perhaps tomorrow? – the boards will be mechanically fixed to the wall using low thermal conductivity supports.

Details of the way the insulation is initially stuck to the wall. Click for a larger version.

Having considered this for this for such a long time, I am very excited to finally be making progress.

Within a few months I will find out whether or not my calculations were correct! I will keep you updated.

Previous articles on this topic

2020

2019

COVID-19: The effect of a ‘circuit-breaker’ lock-down

October 14, 2020

It is hard to see the future, but with calls for a ‘circuit-breaker’ lock-down ringing around, it is worthwhile to try to anticipate the effect of such a policy.

During the previous lock-down, key indicators of prevalence of the epidemic

  • the rate of daily positive tests,
  • the rate of daily hospital admissions, and
  • the rate at which people were dying

… all fell, roughly halving every 21 days.

We can estimate that a ‘circuit-breaker’ lock-down might be as effective at suppressing the virus as that national lock-down was in May and June.

Based on that assumption, the graph below shows the likely effect on the key indicators of ‘circuit-breaker’ lock-down.

Click for larger version.

The term ‘circuit-breaker’ is mis-leading

The term ‘circuit-breaker’ implies that that it will have an immediate and dramatic effect.

But if the policy is as effective as the spring lock-down, then this will not be the case – the key indicators will halve every 21 days.

If we had a 21 day lock-down, then after it was over, it would take only 15 days for key indicators to return to their current values.

So 36 days down the road – i.e. late November – we would likely be back where we are now.

My Conclusion

  • The only thing that has demonstrably reduced the prevalence of the virus is a lock-down such as we had in May and June.
  • But even that spring lock-down was not very effective, reducing viral indicators with a halving time of 21 days.
  • IMHO we need a series of planned lock-downs – roughly 2 weeks on and then 3 weeks off – which will maintain the viral prevalence at its current level.
  • We would need to live like his until the spring when a vaccine will presumably become available.
  • The cost is terrible. But the alternative – mass deaths and then a lock-down – is worse.

As I pointed out previously (link), the current state of play and the options open to us are similar to what was predicted by Neil Ferguson back in March.

===================================

Details

The graph above has a logarithmic vertical axis and shows the situation in the UK since the start of the opening up at the start of July with regard to:

  • The daily rate of Positive Test Results
  • Hospital Admissions
  • Deaths per day

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined

All curves are 7-day retrospective rolling averages of the data since July.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days.
  • The increasing trends correspond to quantities doubling every 15 days.

 

COVID-19: Time to start using logarithmic plots again…

October 13, 2020

Back in May I wrote about how to decide whether or not to use logarithmic axes when plotting COVID-19 data.

Summarising, the answer is that when the epidemic is in a phase of exponential growth or decline, then one can only see the trends clearly on a logarithmic plot.

I am afraid that we are in that territory again.

In order to understand what is happening, logarithmic graphs – on which exponential growth and decline appear as straight lines – are essential.

Click for larger version.

The graph above has a logarithmic vertical axis and shows the situation in the UK since the start of the opening up at the start of July with regard to:

  • The daily rate of Positive Test Results
  • Hospital Admissions
  • Deaths per day

This logarithmic graph shows three important trends that are not captured in the more dramatic presentations on linear graphs.

Feature#1: The end of the first wave

The graph clearly shows that prior to the July re-opening, the virus was in decline: All measured parameters were declining – halving every 21 days.

Click for larger version. This shows same graph as at the start of the article but highlighting the period from July to September

Feature#2: Re-opening and the summer hiatus

In July and August, hospital admissions and deaths continued to fall – but the daily rate of positive tests were rising.

Click for larger version. This shows same graph as at the start of the article but highlighting the behaviour of the data in August.

  • This shows that the level of societal mixing in the UK since July is too great to suppress the virus.
  • This corresponds roughly to the new base traffic light state: This is evidently not sufficiently restrictive to prevent the viral prevalence increasing.

Initially it seemed like the rate of positive tests didn’t matter: that there might have been some change in the virus or some aspect of its transmission. But this was not the case.

Feature#3: September onwards

Since the start of September, the daily rate of positive tests, hospital admissions and deaths have all shown exponential growth – roughly a straight line on this graph – with a doubling time of around 15 days.

Click for larger version. This shows same graph as at the start of the article but highlighting the period since the start of September

The details of the curves are hard for an amateur to understand but this may be because the distribution of the virus is more in inhomogeneous than in the spring, meaning these national data show the totality of several more local epidemics.

The rate of daily positive tests appears to be rising faster than hospital admissions or deaths at the moment – possibly due to the spread being initially amongst young people.

But hospital admissions and deaths lag the rate of positive tests and the graph makes it clear that further hospital admissions and deaths will inevitably follow the daily rate of positive tests.

My Conclusion

  • The only thing that has demonstrably reduced the prevalence of the virus is a lock-down such as we had in May and June.
  • The cost is terrible. But the alternative – mass deaths and then a lock-down – is worse.

===================================

Details

The graph shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined

All curves are 7-day retrospective rolling averages of the data since July.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days.
  • The increasing trends correspond to quantities doubling every 7, 15, or 30 days as shown in blue text on the graph

Willful Misunderstanding

October 12, 2020

The Daily Mail website consistently has articles which show a deliberate and willful misunderstanding of scientists’ presentations.

Anyway, I just thought I would highlight one case I noticed today.

The Story

On 21st September 2020 Professor Chris Whitty, Chief Medical Officer for England and Sir Patrick Vallance, Government Chief Scientific Adviser gave a televised press conference about the state of the pandemic.

You can read the transcript here or view a video (with someone’s annotations) here (the relevant part starts about 5:00 minutes in).

I have extracted a short section below from Sir Patrick Vallance’s statement which was read while slide 3 (see below) of their presentation (available here) was being shown.

So this is the UK reported cases per day against time and you can see running along the bottom there the number of cases over June, July and August. Up to roughly 3,000 cases per day or so in September, middle of September. At the moment, we think that the epidemic is doubling roughly every seven days. It could be a little bit longer, maybe a little shorter, but let’s say roughly every seven days.

If, and that’s quite a big if, but if that continues unabated and this grows, doubling every seven days, then what you see of course, let’s say that there were 5,000 today, it would be 10,000 next week, 20,000 the week after, 40,000 the week after. And you can see that by mid-October if that continued, you would end up with something like 50,000 cases in the middle of October per day. 50,000 cases per day would be expected to lead a month later, so the middle of November say, to 200 plus deaths per day. So this graph, which is not a prediction, is simply showing you how quickly this can move if the doubling time stays at seven days. And of course the challenge therefore is to make sure the doubling time does not stay at seven days. There’re already things in place which are expected to slow that.

And to make sure that we do not enter into this exponential growth and end up with the problems that you would predict as a result of that. That requires speed, it requires action and it requires enough in order to be able to bring that down. One final word on this section. So as we see it, cases are increasing, hospitalisations are following. Deaths unfortunately will follow that, and there is the potential for this to move very fast. A word on immunity. Next slide, please.

Apologies for the long quote, but I think the context and tone are important. What Sir Patrick Vallance, Government Chief Scientific Adviser said was this:

  • In red he said and emphasised that this was “a big if” i.e. it was hypothetical.
  • In blue he said explicitly that this was not a prediction – but rather an illustration of how dramatically the doubling-time affects things
  • In orange he said that they were working to make sure that what was illustrated didn’t happen.

In addition to his spoken words, on the slide there were three separate indications that this was not a prediction about the likely state of the pandemic in mid-October.

Click for Larger Version. This is Slide 3 from Whitty and Vance’s presentation and contains three separate indications that it is not a prediction.

 

How did the Daily Mail report this?

Over the last few weeks the Daily Mail have persistently stated that this was a terrible prediction with no scientific basis and mocked Whitty and Vance. Here is today’s article (link)

Click for larger version. Extract from Daily Mail on 12th October 2020

The headline reads (my red text)

So much for Prof Gloom and Dr Doom’s scary chart:
Britain’s daily Covid-19 cases are less than HALF
what Sir Patrick Vallance and Professor Chris Whitty’s
predicted they would be by now

And the misleading graphic is shown below:

Click for a larger version.

For someone to hear that presentation, read that transcript (which was quoted from in the article!), look at the slides, and then conclude that this was a failed prediction can only be willful and deliberate misunderstanding.

I can’t understand how anyone could do this with honorable intentions.

Their rationale is – I guess – to undermine the credibility of mainstream scientists in the eyes of their readers.

Why would anyone want to do that? 

COVID-19: Day 282: The trend accelerates…

October 9, 2020

This week’s data shows the prevalence of the virus continuing to increase. However there are now clear differences in the rates of increase of positive cases, hospital admissions and deaths. I’ll comment on possible reasons for this at the end.

It is likely the government will act soon. But no matter what they do, we appear to be already committed to death rates of around 100 people per day later in October. The key question is whether this will be a peak or not.

Let’s take a look at the data.

Data#1. Prevalence

Since late April the ONS prevalence survey has been randomly testing people each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

Click for larger version

The number of people tested and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 1st October 2020 on average 0.5% of the UK population were actively infected. There was considerable regional variations from an estimated prevalence of 1.25% in the North East to 0.1% in the South East.

The raw count of positive tests was:

  • 532 from 127,285 people tested in the two weeks to 1st October,
  • 157 from 81,168 people tested in the preceding two weeks, and
  • 47 from 58,961 people tested in the two weeks preceding that.

Note these are random survey tests (so-called Pillar 4 tests), not clinical tests.

Their data – graphed below – suggest that the prevalence is now doubling roughly every 11 days – a decrease in the estimated doubling time from 15 days.

I have shown two exponential curves on the graph below.

  • The black dotted line (– – –) is the same curve I plotted for the previous two weeks (Last week, the week before). It is a fit to the 3 black data points and shows what we might expect if viral prevalence were doubling every 15 days. Last week’s update was consistent with that extrapolation, but this week’s data point lies significantly above the extrapolation.
  • The purple dotted line (– – –) is a fit to the last three data points from today’s data set. It shows what we might expect if viral prevalence were doubling every 11 days.

If one considers it likely (which I do) that the viral prevalence has continued on trends similar to the ones shown, then today (9th October) the prevalence is likely to be between 0.7% and 1.1%. Regionally (see below) it might even exceed 2%.

Click for larger version.

Data#2. Tests and Deaths

The graph below shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined

All curves are 7-day retrospective rolling averages of the data since July.

Click for a larger version.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days.
  • The increasing trends correspond to quantities doubling every 7, 15, or 30 days as shown in blue text on the graph

We see that the three data sets initially fell with similar time-dependencies. All the quantities are now rising, but there are now distinct differences.

  • The rate of positive tests is increasing more rapidly than in September – doubling roughly every 7 days . This would have been apparent last week except for the Government’s Excel ‘Hancock-up’.
  • In contrast the rate of hospital admissions seems to be increasing rather more slowly doubling every 30 days.
  • The rate of deaths appears to be close to doubling every 15 days.

What Next?

As I write, as many as 1.0% of the UK population may be actively infected with the virus.

This figure is alarming but as I mentioned last week, it is important to note several differences from March.

  • Last week I wrote that “the rate of rise of infection is 5 times slower than it was in the spring – so we have time to act.” In fact the rate of rising is now just 3 times as slowly as in the spring which means we have much less time to act than we did.
  • With current behaviour we are probably already committed to around 100 COVID-related deaths per day in mid-October.
    • In a normal year, 1700 people die each day, so terrible as it may seem, a realistic target for the government might be to prevent the COVID-related death rate significantly exceeding 100 people dying each day – i.e. to bring the second wave to a peak in mid- to late-October.
  • With the current patterns of societal mixing, 100 deaths per day can turn into 800 deaths per day in about 33 days. This would be another national catastrophe.

It seems pretty clear to me that action to reduce the spread of the virus is overdue.

Stay safe.

======================

Additional Thought#1: Geographical variations and extrapolations.

In this analysis I have ignored the geographical variation in viral prevalence and treated the UK as a single population. This is obviously not the best thing to do, but I don’t want to spend my entire life analysing coronavirus data!

The ONS survey does include relevant data. It indicates that at around 1st October, infection rates were probably above 1% in the North East, North West and Yorkshire & Humber (t’North) but only around 0.1% in the South East (t’South).

For the North East, the doubling time was only 9 days and viral prevalence now (9th October) likely exceeds 2%.

Clearly the national prevalence figures will be weighted strongly towards the north of the country and there will likely be different rates of exponential growth in each region, so fitting this complex situation with a single exponential function is simplistic at best.

However, I feel the extrapolations shown do serve as a useful “guide to the eye” as we look back on this data future weeks.

Additional Thought#2: Doubling times.

If a single ‘simple’ process underlies the evolution from cases to admissions to deaths, then an exponential growth in cases should lead eventually to exponential growths in admissions and deaths with the same doubling-time.

The fact that the doubling-times for cases, admissions, and deaths, are different is puzzling. It could arise because the transmission processes are still evolving, or it could arise because the evolution from cases to admissions to deaths is not ‘simple’.

As many have mentioned much of the viral spread seems to be amongst younger people and does not lead directly to hospital admissions.

It may be that complexity in the way a smaller group of vulnerable people are being infected by a larger group of younger infected people may explain this difference in doubling-time.

Or not. I don’t know. At the moment, I am just highlighting it as puzzling.

Click for larger version.

The Last Artifact

October 5, 2020

A long long time ago (May 2018) in a universe far far away (NPL), I was asked to take part in a film about the re-definition of four of the seven SI base units: The Last Artifact

The team – consisting of director Ed Watkins, videographer Rick Smith and sound recordist Parker Brown – visited my lab and I spent a happy afternoon and morning chatting.

I later heard that a version of the film was shown to VIPs in May 2019 when the kilogram, kelvin, candela and ampere were re-defined, and I was told that some my words had made the cut!

But then the film disappeared!

I wrote to director Ed Watkins earlier this year and he shared a version with me privately, and I was impressed. But there was still no version to share.

I am writing this because a set of clips have now emerged which will hopefully be relevant for classroom use.

I don’t think the clips individually make as much sense as the film as a whole because they lack the continuing narrative that the film provides. But they are still beautiful and provide views of otherwise unseen laboratories and artifacts and people.

Personally, I was shocked to see myself on film – so shocked I found it difficult to see the rest of the film clearly. But as my shock subsided, I grew to like the film.

This film is a not made for people like me, and it is not the film I would have made. Rather it is a film for non-scientists and schoolchildren. It is by turns gorgeous, colourful, engaging, and humorous. And when I showed it to a UK Science TV producer they said it worked for them!

The colour and music and sound quality are outstanding and make watching it a simple pleasure. I recall at the time noting that they were shooting at ‘8K’ resolution when I had only ever heard of ‘4k’: Now I know why!

This page contains links to all 12 films or you pick from the list below – the links are in the film’s title: Films with a red asterisk (*) feature me! (sometimes just my voice).Clips

Film 1: (Re)Defining The Universe  (1 miniute 55 seconds)

An introduction to what is meant by an ‘artifact’ ending with a beautiful shot of the international prototype of the kilogram itself.

Film 2 *: What is Metrology? (3 minutes 33 seconds)

An introduction the International Bureau of Weights and Measures and its role in the international measurement system: the SI.

Film 3 *: Metrologists (1 minutes 18 seconds)

Metrologists speak!.

Film 4 *: Measurement: System International (3 minutes 14 seconds)

An introduction the SI.

Film 5 *: The Hunk of Metal (3 minutes 33 seconds)

An introduction the international prototype of the kilogram.

Film 6 *: The History of Measurement (7 minutes 10 seconds)

A nice summary of the history of measurements.

Film 7 *: Redefinition and Fundamental Constants (2 minutes 48 seconds)

The idea of moving away from artifacts..

Film 8 : Avogadro’s Constant  (1 minutes 24 seconds)

One option for re-defining the kilogram

Film 9 : The Avogadro Sphere (2 minutes 37 seconds)

How to make an Avogadro Sphere.

Film 10 : Planck’s Constant (2 minutes 16 seconds)

Some chit chat about the Planck Constant.

Film 11 : Watt Balance (4 minutes 29 seconds)

The concept of weighing with electricity using a Kibble Balance. A chance to hear Ian Robinson speak.

Film 12 *: The Next  Frontier (3 minutes 31 seconds)

What changes after re-definition of the SI units?

COVID-19: Day 275: The trend continues…

October 2, 2020

This week’s data shows the prevalence of the virus continuing to increase with the same 15-day doubling time that emerged last week.

Let’s take a look at the data.

Data#1. Prevalence

Since late April the ONS prevalence survey has been randomly testing people each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

Click for larger version

The number of people tested and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 24th September 2020 on average 0.23% of the UK population were actively infected.

The raw count of positive tests was:

  • 245 from 100,038 people tested in the two weeks to 24th September,
  • 89 from 68,146 people tested in the preceding two weeks, and
  • 36 from 52,117 people tested in the two weeks preceding that.

Notice the extraordinary rise in the number of ONS survey tests carried out: currently more than 50,000 a week. Remember these are random survey tests, not clinical tests.

Their data – graphed below – suggest that the prevalence is now doubling roughly every 15 days.

The exponential curve shown as a dotted line (– – –) is the same curve I plotted last week – a fit to the 3 black data points. From the fact that this week’s update is consistent with the trend line we can conclude that last week’s trend is continuing.

If the trend has continued up to today (2nd October), then the prevalence as I write will be around 0.5% i.e. 1 in every 200 people in the UK is currently actively infected with coronavirus.

Click for larger version.

Data#2. Tests and Deaths

The graph below shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined

All curves are 7-day retrospective rolling averages of the data since July.

 

Click for a larger version.

The graph shows the data alongside exponentially decreasing and then increasing trends

  • The declining trends correspond to quantities halving every 21 days.
  • The increasing trends correspond to quantities doubling every 15 days.

We see that the three data sets rise and fall with similar time-dependences. Given how differently the three datasets are collected, this is powerful evidence that they all arise from the same physical process. This may seem obvious, but it is worth noting nonetheless.

It is hard to see trends clearly, but it looks like the hospital admissions are not rising quite as fast as expected, but this may just be a data-reporting problem.

What Next?

As I write, probably 0.5% of the UK population are actively infected with the virus. In my mind, this seems like a seriously large number of people.

If it takes roughly 7 days for an infected person to spread the virus to one other person, then a further 13% of the population will have been infected with the virus by March 2021 making a cumulative total of roughly 20% of the population. This is still not enough for significant nationwide ‘herd immunity’.

Watching the curves rise is alarming but it is important to note several differences from March.

  • Firstly, the rate of rise of infection is 5 times slower than it was in the spring – so we have time to act.
  • With current behaviour we are probably already committed to around 100 COVID-related deaths per day in mid-October.
    • In a normal year, 1700 people die each day, so terrible as it may seem, a realistic target for the government might be to prevent the COVID-related death rate significantly exceeding 100 people dying each day – i.e. to bring the second wave to a peak in mid- to late-October.
  • With the September level of societal mixing, 100 deaths per day can turn into 800 deaths per day in about 45 days. This would be another national catastrophe.
  • It is not clear if the late September measures taken by the Government will be sufficient to either lengthen the doubling-time and slow the growth, or ideally turn the growth around and begin to reduce the prevalence.

Stay safe.

 


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