Tiling records

I’ve added a static page covering tiling records at Tiling records


CSH pollution evidence follow-ups

Guardian article

Last week I published my attempt to find evidence that cycle superhighways causing pollution. There wasn’t any. This despite numerous members of the Lords saying otherwise. I wasn’t the only one who thought there was a story in Lord Winston being economical with the science – Peter Walker and Laura Laker have published articles in the Guardian covering much the same ground. But because they are good journalists, whereas I had overly dry figures, they have great quotes. The one about Lord Cormack is a ripper:

  • “Lord Patrick Cormack, said his evidence was that his cab journey from King’s Cross station to the House of Lords now took longer.”

That’s right, the guy complaining about pollution in central London, is the guy taking a black cab from King’s Cross to the Houses of Parliament! It was a relief to find out that taxis within central London are not something peers can claim on expenses. You can claim for petrol, parking, trains and the cost of a bicycle though. For July 2017, the most recent month for which data is available and during which peers sat for up to 12 days (most peers sat far fewer than this) the travel allowances claimed by peers were as follows:

Car Rail Air Motorbike Bicycles Taxis and Parking
£31,705 £75,325 £59,496 £0 £2 £8,766

So for the last month available £40,000 claimed for private motor transport, £2 claimed for cyclists. Is it any wonder this second chamber is more-or-less completely clueless what it comes to what a good public policy in relation to cycling might be.

A pollution monitor

Some of the respondents to my last article pointed out that one possible reason for the reduction in pollution on Upper Thames Street since the cycle way opened is that the traffic may now be further away from the sensor than it was before because the cycle lane comes between the two. This could be significant as pollution levels drop away reasonably quickly as you move away from roads. So I went to the pollution monitoring site to find out if this was the case. Here it is:


Pollution monitoring station underneath London Bridge.

 The monitoring station is on the south side of the road. The cycle lane is, at this point on the route, on the north side. So, no, the reduction in pollution is not explained by this factor.

This photo was taken at a random point in time as I walked past – I didn’t wait for a particular set of traffic to come along (as some people offering “evidence” of congestion and/or successful cycle lanes seem wont to do). So I was pleasantly surprised by the fact that by chance there are three cyclists and an HGV in the picture. That old HGV is sure to give its driver a terrible view of his (or her) surroundings, but, thanks to the segregated cycle lane, those three cyclists are at greatly reduced risk of death-by-lorry-left-hook than they were two years ago. Now *that’s* a good reason for segregation.

East-West Cycle Superhighway appears not to be causing pollution

Does re-allocating road space from general use to being a dedicated cycle way increase or decrease pollution?

“Obvious!” say the cabbies and others opposed to cycle ways – the motor traffic gets squeezed into the road space left for them – cars stuck for longer are obviously causing more pollution!

“Obvious!” say the cycle campaigners and others in favour – bicycles don’t cause any pollution and so as modal shift away from motor traffic (including “traffic evaporation”) occurs, there is obviously less pollution!

To my mind, both of these arguments have the broad element of plausibility – without further evidence surely it isn’t possible to say which factor dominates. But some people do seem to be sure… check out this notorious tweet from Professor Lord Robert Winston just a month after the East-West Cycle Superhighway opened:

Despite many requests from enmaddened cycling campaigners, I don’t think Professor Winston ever provided any evidence for this “measurable pollution increase”. He claimed he had spent a morning in City Hall discussing the data behind the tweet … but a Freedom of Information request submitted by David Kahn revealed that no-one at City Hall “can recall such a meeting nor the data which is referenced.”

By January 2018 he had backed down somewhat, merely calling upon the Government to publish figures before and after the introduction of cycle lanes, rather than claiming to know the data himself already. Though we guess what his view might still be as he continued: “The reduction of lanes which traffic can travel down means that there are more cars taking longer journeys than ever before at slower speed. [..] The evidence is that the internal combustion engine is less efficient and pollutes more at slow speed particularly when it’s waiting.” (Full Evening Standard article )

So yes we could wait for official Government figures, but hang on, hadn’t I see Andrew Gilligan’s pinned tweet?

This data is tantalising as. unlike Prof. Winston’s assertions, it looks to have basis in numerical fact. But it is unsatisfying, because the pollution figures are so noisy day-to-day it is hard to tell what is really going on. Also the data ends in October 2016, when the superhighway had only been open for a summer – what if there are seasonal effects.

Fortunately, the source for Gilligan’s data is the London Air Quality Network (LAQN)  who make all their raw data available for download.

I downloaded the raw data for Upper Thames Street – the only pollution measuring site on the superhighway and batched up the data so I got the average pollution level in six-monthly chunks from June 2008 to December 2017. I chose six monthly chunks as the superhighway has now been open for 18 months and this would give me three pieces of data for the open period. Here are the results:


At first look the results are pretty startling, two of the three “best” (i.e. lowest polluting) periods in the last 10 years are since the cycle way has opened. The average PM10 pollution measure prior to the cycle lane opening 35.8 micro-grams per cubic metre. The average after the cycle lane opening is 28.9 micro-grams/m^3 – a fall of nearly 20%.   Surely this is great evidence that the “greenies” are right and Winston is wrong – cycle lanes cause a DROP in pollution?

Well yes I did initially think that. But then stepping back, I realised I was being rather unscientific myself. OK, pollution seems to be lower recently, but it could well be a coincidence that that has happened at the same the cycle way has been open. I needed a control. Fortunately the LAQN also publishes PM10 data for the same period for Marylebone Road, which is largely a cycle-free zone. And here is the data for that location:


The pattern is broadly similar – the last 18 months have seen some record lows for this location too. In fact the average prior to June 2016 was 34.8ug/m^3 and after then was 28.1ug/m^3 – a very similar 20% decrease to the Upper Thames Street location! So the cycleway is not responsible for the pollution drop after all?

Qualitatively, it looks as though the PM10 pollution has been getting steadily better since the peak of 2011 on Marylebone Road, whereas possibly Upper Thames Street shows a bit more a step-change around the time of the superhighway opening. This would be consistent with Marylebone Road benefiting from the ongoing cleanup of buses (see e.g. this Guardian article) but Upper Thames Street less so, because it is not a bus route.

But that’s rather speculative – I think a safe conclusion form the public data is: The East-West Cycle Superhighway appears NOT to have worsened pollution, and may have made it a little better.

Some caveats

  • PM10 pollution (the measure of number of “large” pollutant particles is the only type of pollution discussed here because it is the only one the LAQN produces figures for for Upper Thames Street. Many other pollutants are available.
  • LAQN says that the data for 2017 is still provisional and subject to further ratification.
  • I am not a domain expert. Just an interested bystander.
  • The bucketed sample sizes are small! Do not overdo statistical significance.
  • I wrote a very small Python script to process the data that is available from LAQN. Available on request.

Pretty clusters

It’s been six months since the max cluster metric was developed as a more general way of scoring explorers than the original max square. It’s interesting to see how max clusters are different from max squares. Here are I look at the current top 7 (as recorded at VeloViewer) max clusters.

In the pictures below, blue tiles are part of the max cluster. Red tiles are also visited tiles, but are not part of the cluster.

All the riders listed here have made their data public on VeloViewer so I hope it is ok to showcase it here. If not let me know and I will remove it. The open maps and data are copyright to Thunderforest and the OpenStreetMap contributors

7th: Chris White, Switzerland – Cluster size 4,180 squares


Chris’s max cluster is truly impressive. To appreciate the scale of this map (it is zoomed out compared to the ones below), realise that Lake Geneva in the middle-left of this picture is 70km long! The cluster is well into the French Alps on south-western corner, covers almost the entire Swiss Plateau and touches into Austria, Germany and Liechtenstein. I estimate the width of the cluster to be about 400km.

Zooming in on Chris’s VeloViewer activities page shows many many up-and-down ride – the term plateau does not give justice to the effort required for many of these squares!

I’m not surprised to learn Chris’s own website is called RideFar.info.

6th:  Koos Woestenburg, Netherlands, 5,408 clustered squares


Like Chris, Koos is someone who has benefit from the addition of max cluster alongside max square. Hailing from De Rijp, Koos is trapped by the North Sea to the north and west and the North Holland lakes to the east. This hasn’t stopped him from creating a cluster that snakes deep into Belgium, covering Ghent and Bruges to the west and also hugs the Netherlands/Germany border all the way to Aachen. Northwards, the cluster doesn’t end ’til Groningen. Little pockmarks throughout the thickest part of the cluster suggest that the Netherlands’ famous dykes, canals and dams do make some squares inaccessible.

5th:  Eric Nichols, New England, United States, 5,498 clustered squares


I love how Eric’s cluster follows the shape of the Atlantic seaboard from way up in Maine to the south-side of Boston. A single solitary missing square sullies an otherwise great swathe of blue. I think this is actually a VeloViewer glitch! When I look at Eric’s summary I see a max square of 39×39, but in the overall leaderboard he is credited with 62×62 – the difference being whether this square (mostly an American Air Force Base) is coloured or not. I understand Eric has nabbed this square… the blocker for his max square now is a private game reserve covering multiple squares. Even if this proves impossible to visit, the max cluster can continue to grow.

4th: Phill Cloke, South-east England, 5,673 clustered squares


Phill Cloke’s cluster follows the south coast of England from Southampton all the way to Margate before covering the whole of London and ranging almost to Oxford. What is all the more incredible is that nearly all Phill’s rides are round trips from his home near Sevenoaks (many of his rivals will do one-way rides use transport to another starting point) To achieve this, it becomes normal to see 300km+ rides popping up on your Strava feed if you follow Phill.

3rd: Jonathan France: South-east and Midlands of England: 6,022 clustered squares


Jonathan France has an interesting cluster. He’s clearly aimed at creating a max square centred roughly on south-west London, but then on top of that has another base up towards the source of the Thames. Many century rides between the two bases have covered almost every conceivable route between making a huge band across the whole of Middle England. I know from my own exploring that the area between Basingstoke and Winchester is not too hard to fill; Jonathan is my quiet tip for the first non-Belgian leader in the max square and cluster stakes.

2nd Nils Oudejans: Belgium: 7,742 clustered squares:


Nils’ max cluster shows that he has pretty much covered Belgium. What is scary to me is that the north-west section is so methodically filled it. It is clear that he is not content to sit still at 78×78 in the max square. Ride by ride he is preparing the ground for a huge increase in square size. This square is well over 10,000 square km already!

Leader: Dominique: Belgium: 8,109 clustered squares

DOBut our leader, Dominique, incredibly, has put four hundred more squares into his cluster even than Nils. The pair of them are taking advantage of Belgium’s dense road network and lack of natural boundaries to rack a huge max square. Dominique has poked a little further in all directions than Nils. But Dominique, what happened to that one solitary missing square at Alt Hoeselt?

Ride report: Dog and having the balls

Which roads are dangerous? This ride report shows it is not always the ones you expect.

It was New Years Day 2018 and I was desperate to get a new tiles ride on the board as soon as possible, given that December had more-or-less been a wash-out. Unfortunately I need to be back home by about 10am, so a proper decent length ride featuring new squares was going to be an impossibility. I concoted a plan to ride just 28 miles on the western border of my current square in the M3 corridor south-west of Basingstoke. Here’s the ride. We are now sufficiently far away from London (about a 60 mile ride from Trafalgar Square) that things are reasonably rural and it can be quite difficult to get in a square. The ride features three separate “nubbins” (deviations off the main route which you have to double-back on) because there was no option to do anything else.

I hadn’t expected much drama from the first nubbin – a tarmac-ed road – albeit to a dead-end and full of potholes. It wasn’t even a private road acting as a bridleway or footpath, it was genuine public road and is on the route of the Wayfarer’s Walk to boot. So it should be ok to not be “from round these parts”. I was wrong. With my Garmin showing I had reached the new square, I turned in the road outside Breach Farm (just south of Dummer). I heard a woman’s angry shout and then a black dog came rocketing out of the farm’s open driveway. He was as angry as the woman’s shout. Clipped in with only one pedal and at a standing start, the dog had no bother getting alongside my front wheel.  Although he was in a terrible state – barking and snarling like crazy – he decided not to go under the wheel and I was able to pick up speed. Thankfully the dog also decided not to bite – the worst I suffered was when he pounced his front paws against my SealSkin-coated ankles.

I was almost back at the entrance of the nubbin when he finally gave up. I have no idea whether the angry shout of the unseen woman was at me or her dog. It’s the first time I have had a very close encounter with a properly angry and uncontained dog on UK roads. Got the heart racing!

Later on in the ride, I had another square to visit. The night before the ride, I couldn’t decide whether to do it. At first glance it looks like an easy A303Square

With a road running right through it, this should be an easy square?

one – there is a road running right through the middle of it. But this is the A303 (CBRD description). Most UK people will know this road as a major road that goes right past Stonehenge. And the tile is where the A303 is at its most major – in fact in the extreme right of the picture you can see the road turn dark grey – this is Strava Route Planner colouring for a motorway – the road is just about to merge into the M3. It has two carriageways, slip roads, central reservations, the lot. A bigger and faster road than most American Interstates and many of the motorways of Europe. I would not normally ride roads like this. I’m even scared of riding on roads like because I know from driving on it that vehicle speeds are routinely well in excess of 70mph, even in the inside lane. But, but, it’s the only road I can verify as public in the tile, and this tile will soon be the western edge of my square, so another part of me really wants to go there. And I will be there at about 8.30am on New Year’s Day… how busy can it be?

Whilst vacillating back-and-forth whether it is worth riding down this road just to get a tile, I read about this crash just two days before and found this thread from YACF exhorting me not to ride on this road. (YACF contains some hardcore audaxers who generally won’t be told where to ride). I am opposed to the imposition of laws such as mandatory helmets or hi-viz, or banning cycling from particular roads. This does not mean I forgo a helmet myself, or that I will ride any road that I am legally entitled to. What to do, what to do.

In the end I come to a compromise with myself. I will ride the road but not tell my wife, so she can’t tell me how bloody silly I am.

And, to be honest, the ride is fantastic. I spend five minutes riding two miles of silky smooth tarmac. In that time four cars pass me and they all pretty much move entirely into the outside lane – though they are going fast, I don’t feel buffeted or close passed.

So I guess you just can’t tell which road is going to be dangerous.. an empty dead-end or a near-motorway. Have fun riding every tile!

P.s. this ride took my max square to 52×52

Number of ways to get a nine-dart finish

Off-topic post.

Just as I am gearing to watch the wonder that is the 2018 World Darts, I noticed this puzzle on 538

“In competitive darts, a player starts with 501 points and subtracts the score of each throw. He or she must finish with exactly zero points. (Also, per the rules, the final dart must land in either the bullseye or the outer, doubled segments.) What is the minimum number of throws? How many different ways are there to do it?”

The first part is very easy – the maximum with any one dart is 60 points. Therefore the maximum with eight darts is 480 points, so you can’t score 501 in eight darts or fewer. The combination T20, T20, T20, T20, T20, T20, T20, T19, D12 shows it can be done in nine darts, so this is the minimum. But how many ways are there?

We know the last dart must be a double or bullseye. Call this last value D. Then the first 8 darts must equal 501-D. As above the first 8 darts are worth at most 480 points, so 501 – D <= 480. I.e. D >= 21. Thus the possible  ninth darts are:

[Bull, D20, D19, D18, D17, D16, D15, D14, D13, D12, D11]

So for each of these last darts, we must find how the number of combinations of the first 8 darts give the right score and then add these up to get the total number of combinations.

To prune the search space, note the least possible value of the eight darts is 501-50 = 451 and the most possible value of seven darts is 7*60=420, so at the absolute least each of the first eight dart must be worth at least 451-420=31 points. There is no way to get 31 points (31 is prime) so in fact every dart must be worth 32 points. This leaves the following set of possible darts to consider for the first eight darts:

C = [T20, T19, T18, T17, Bull, T16, T15, T14, D20, T13, D19, D18, T12, D17, T11, D16]

Noting that C is descending numerical order, my recursive algorithm was as follows:

  • Maintain an index into this “consideration array”, C
  • Maintain a remaining target T and remaining number of darts R
  • Maintain a stack starting empty
  • T starts at 501-D and R starts at 8
  • The next value is C[i].
    • if R == 1 and T == C[i] we have found a solution and the stack consists of the darts we need (plus the ninth dart recorded separately)
  • Otherwise If T- C[i] > 0 and R >= 2, then C[i] is potentially part of the solutoin for the current stack, so recurse with T -> T-C[i], R -> R-1, i staying the same, and append C[i] to the stack
  • Otherwise if i < 8 and if C[i+1] * R >= target (i.e. the remaining numbers are big enough to potentially reach the target – this bit relying on the ordering of C), then recurse with T -> T, R->R, i -> i+1 and keeping the same stack.

The algorithm starts with T = 501-D, R=8, i=0 and the stack empty.

Running the algorithm, this way we get all possible solutions, not accounting for re-ordering. Naively there are 8! = 5040 different ways to re-order 8 darts, but if the same dart appears k times in the solution, then the same solution is appearing k! times in this set. In fact each solution can be ordered in  8 Choose{k_1,…k_r} ways where k_i is the number of times a particular dart appears in the solution (i.e. this is just the usual multinomial coefficient formula for counting re-arrangements).

I was taken aback by just quickly these recursive algorithm ran when implemented as a simple Python program. Here are the results:

[T20, T20, T20, T20, T20, T20, T19, D17] , BUL (56 ways)
[T20, T20, T20, T20, T20, T20, T17, D20] , BUL (56 ways)
[T20, T20, T20, T20, T20, T19, T18, D20] , BUL (336 ways)
[T20, T20, T20, T20, T20, T17, BUL, BUL] , BUL (168 ways)
[T20, T20, T20, T20, T19, T19, T19, D20] , BUL (280 ways)
[T20, T20, T20, T20, T19, T18, BUL, BUL] , BUL (840 ways)
[T20, T20, T20, T19, T19, T19, BUL, BUL] , BUL (560 ways)
[T20, T20, T20, T20, T20, T20, T17, BUL] , D20 (56 ways)
[T20, T20, T20, T20, T20, T19, T18, BUL] , D20 (336 ways)
[T20, T20, T20, T20, T19, T19, T19, BUL] , D20 (280 ways)
[T20, T20, T20, T20, T20, T20, T20, T15] , D18 (8 ways)
[T20, T20, T20, T20, T20, T20, T19, T16] , D18 (56 ways)
[T20, T20, T20, T20, T20, T20, T18, T17] , D18 (56 ways)
[T20, T20, T20, T20, T20, T19, T19, T17] , D18 (168 ways)
[T20, T20, T20, T20, T20, T19, T18, T18] , D18 (168 ways)
[T20, T20, T20, T20, T19, T19, T19, T18] , D18 (280 ways)
[T20, T20, T20, T19, T19, T19, T19, T19] , D18 (56 ways)
[T20, T20, T20, T20, T20, T20, T19, BUL] , D17 (56 ways)
[T20, T20, T20, T20, T20, T20, T20, T17] , D15 (8 ways)
[T20, T20, T20, T20, T20, T20, T19, T18] , D15 (56 ways)
[T20, T20, T20, T20, T20, T19, T19, T19] , D15 (56 ways)
[T20, T20, T20, T20, T20, T20, T20, T19] , D12 (8 ways)

Adding them up, there are a grand total of 3944 ways to do a nine-darter… even Phil Taylor hasn’t done all of those!