Algebraic Number Theory

This is an area of mathematics that has fascinated me for some time.

I have written some notes which are my attempt to explain how I have tried to understand one particular branch of the subject. I don’t claim any huge originality or rigour, but students and interested lay persons might be interested.

The notes are constantly evolving and can be found at this link (pdf).

Waterbeach Cycling Campaign questionnaire

Waterbeach Cycling Campaign has recently circulated a questionnaire to all District and Parish Council candidates. Here is the questionnaire with my responses:

Questions for Waterbeach District and Parish Council Candidates standing in forthcoming elections (May 2018)

Waterbeach Cycling Campaign’s mission is to make Waterbeach safe, connected and enjoyable for all types of cyclists and users of non-motorised transport.[1]

Q1: Do you support Waterbeach Cycling Campaign’s mission? If not, please explain why not?

Of course, this is very important, but it is essential that the environment is made safe for all vulnerable road users. Within this category I include all those you have mentioned, plus what in the jargon are called ‘PTWs’ – motorcycles, mopeds and scooters.

Q2: If elected would you be willing to work with Waterbeach Cycling Campaign in order to create a cycling-friendly environment in our area?

Of course, provided that making a cycle-friendly environment doesn’t make life harder for, for example, pedestrians. Conflict between cyclists and pedestrians can be a real issue.

Our supporters would like to see better cycle routes to Cambridge.

Q3: Would you campaign for funding to improve the current main cycle route to Cambridge (the path beside the A10) and if so where would you look to obtain funding?

I am not sure that is the answer if the aims of question 4 are achieved.

Q4: Waterbeach Greenway was the first to have a public engagement event .  What actions would you take to ensure that it is the first to get built?

We all need to work with our County Councillor because that is where the initiative will come from, I believe.

Our supporters would like to see a safe cycle route to the Research Park and Chittering from Waterbeach.

Q5: How would you suggest that a safe cycle route to the Research Park and Chittering could be created?

The obvious answer is through the Barracks site well away from the A10

Our supporters would like to see safer cycling and walking within the village especially for children and the elderly.

Q6: Would you support traffic calming in the village?

Traffic calming is a very wide topic and must be approached with caution since there can easily be unintended consequences. The real issue is a reduction of vehicle speeds. The Parish Council has already looked in detail at this topic and has invested, through the LHI, in staggered speed reduction on the three main entrances to the village. This is something I strongly supported.

The real issue here is what sort of traffic calming and I am aware that road humps, for example, can provoke strong opposition from residents who live close to them. The Parish Council has in the past looked at these issues and I would strongly advocate progress being made.

Q7: Would you support a 20mph speed limit in the village?

There is no point in introducing a 20mph limit in the village if it is not observed and the general advice seems to be that we should look at traffic calming before introduction of a 20 mph limit.

Q8: Would you support parking restrictions to improve safety for pedestrians and cyclists in the village?

I have concerns that, if parked cars are removed, vehicle speeds might well increase. Thus any parking restrictions must be looked at carefully. However, there are clearly some potentially dangerous junctions where parked cars can reduce visibility and cause danger to pedestrians; a particular example is the Cody Road – Bannold Road – Way Lane staggered junction.

Q9: Would you support improvements to footpaths and/or the creation of cycle lanes in the village?

Any improvement to footpaths and / or introduction of cycle lanes would have to be done with caution. It should be done in a coordinated way with traffic calming.

On a more general point, some time ago I got the Parish Council to agree in principle to a village-wide report by a traffic consultant. No progress has yet been made, but I wonder if that would not be the best way forward so that a coordinated and planned approach can be taken? Would you be prepared to support the Parish Council in this?

The development of the new town presents a great opportunity to create an environment which is safe, connected and enjoyable for cyclists, pedestrians and other users of non-motorised transport.

Q10: Do you think that the design of the new town should prioritise walking and cycling over vehicles?

I attended a workshop on the SPD for the new town and I got the impression that these issues were at the forefront of the planners’ intentions. However, things have gone very quiet and no information is coming out of South Cambridgeshire District Council. We all need to keep a very close watch on this process to ensure that priorities for pedestrians and cyclists are kept in the plan.

Waterbeach Cycling Campaign is a non-partisan body. All candidates are given an equal opportunity to submit their views.

[1] Our definition of non-motorised transport is inclusive. It encompasses pedestrians, wheelchairs, mobility scooters (yes – aware that they do have motors..), horse riders and the various devices that children use to get from A to B

Relocating Waterbeach Station – my objections

Here is the objection I have sent to South Cambridgeshire District Council.

The application is premature. Much of the justification for the relocation of the station seems to be on the grounds that the current station can only take 4 carriage trains. However, Network Rail have clearly stated that there are plans to extend the platforms at the current Waterbeach Station and this will significantly help the demand in the short term.

The access for private cars via Cody Road is totally inadequate. Just as commuters will be heading for the new station, residents of the estate that comprises Cody Road, Capper Road, Kirby Road, etc. will be heading in the opposite direction. Similarly, residents of the new houses to the east of the Cody Road junction will be heading along Bannold Road. This will create significant conflict at, in particular, the Way Lane – Bannold Road – Cody Road staggered junction.

It should also be noted that there are significant numbers of parents and children walking along Cody Road and Bannold Road to school in the morning.

I note that the Transport Assessment at paragraph 2.2.3 states that Cody Road is suitable for buses. I would remind the planning authority that Stagecoach have abandoned their bus service serving Cody-Capper-Kirby Roads because of issues relating to residents parking along these roads. I concede that it is not intended to use Capper and Kirby Roads for access, but the already existing issues on Cody Road must be addressed.

Paragraph 6.2.2 at table 11 shows an increase in traffic of 73 vehicles per hour during the 3 hour morning peak (35%). Paragraph 6.2.2 suggests that this is ‘not considered a severe impact’. I would suggest that these figures should be examined for what is the real peak, that is 7am-9 am, since the extra hour from 9 am-10 am must depress the average hourly flow.

I do not understand the quote in the first sentence of 6.4.5 of the Transport Assessment. I thought that it was expected that cycles would use Bannold Drove. If cycles are expected to combine with commuter traffic on the already overloaded Cody Road I would suggest that collisions are inevitable.

Paragraph 6.4.11 assumes that Stagecoach, who as noted above have already abandoned their service to the Capper-Kirby Road estate, will play ball.

In summary of the above, this development should not be approved until there is an adequate link road from the A10 which avoids the village streets and, in particular, Cody Road.

I am concerned about the visual impact of the new station. I note that the proponents have not included in the Landscape Assessment a view from the west bank of the river to correspond with viewpoint 2 from the east bank. It is clear to me that, if a viewpoint immediately west of viewpoint 2 was included, the visual impact of the new station

Relocated Waterbeach station

Well, the planning permission has been submitted and can be found here. Unfortunately quite a few of the documents are unreadable and I have emailed South Cambs to tell them.

My main concern with the application is the proposed access down Cody Road. However, it is difficult to comment on everything since so many of the documents cannot be accessed. I’ll have another go at commenting when these documents are available.


Nothing changes!

17 years ago (in 2000) I was part of a group fighting to get Waterbeach excluded from the County Structure plan as the site of a new settlement. We won the fight then and Northstowe was selected.
I have just found the presentation I gave to the County Council and much of what I said then is still relevant.
CCC Presentation 2000

Waterbeach Station Improvement

I have been told by many people that the existing platforms at Waterbeach Station would definitely be extended fairly soon. Just to make sure, I sent in a Freedom of Information request to Network Rail:

“I should be grateful if you could supply me with details of your plans to
extend the platforms at the existing Waterbeach Station. In particular, whether
this is a definite plan and, if so, when you envisage completion.”

The essence of their response was:

“You can find the requested details in the Control Period 5 Enhancement Delivery Plan.

This was updated in December 2017 and provides as much information as we hold
on the subject of your request at present”

The crucial bit of this plan is on page 31 (click on the image to see it full size):

I must say, this doesn’t appear very definite to me, but maybe those who understand railway-speak can enlighten me,


The South Cambridgeshire Local Plan

I have been looking through the proposals for amendments to the Local Plan which have just appeared. I haven’t looked at them in detail but there are a few points that pop out as being important for residents of Waterbeach who are concerned about the new town.
1 The plan has added the word ‘approximately’ to the size of the development which now reads ‘approximately 8,000 to 9,000 dwellings’
2 The word ‘new’ has been replaced by ‘relocated’ when referring to what will happen to Waterbeach Station.
3 Stronger protection is given to the setting of Denny Abbey and additional protection is given to some of the other heritage assets on the site including ‘World War 2 structures and raised causeways’.
4 A reference to ‘odour … from the Waterbeach Waste Management Park’ is included as something that the site should be protected from.
5 References to separation from Waterbeach have been replaced by ‘Maintaining the identity of Waterbeach village as a village close to the new town is also necessary’
I am sure that there are lots of other things that may be spotted and I leave that to others. You can see most of the stuff relating to Waterbeach at

Waterbeach new station (2)

This map shows the approximate location of the new station as proposed in the GRIP 2 report mentioned in my previous post.

The location is shown in red and the access road from Bannold Drove is shown in dark blue. Some of those points in the village where the walking distance is less to the new station are shown with blue markers; those where the existing station is closer are shown with red markers.

The main point is that, because the access is so far north along Bannold Drove, the walking distance for most residents of Waterbeach will be quite a lot further to the new station than to the old one on Station Road.

I have done a few measurements using Google maps and the walking times (in minutes) look like

Starting point New station Current station Nearer
Jn Cattells Lane, Way Lane 17 10 Current
End of Payton Way 25 13 Current
Jn Bannold Road, Denny End Road 18 14 Current
Jn Cattells Lane, High Street 20 14 Current
Jn Bannold Road, Way Lane 13 15 New
Jn Providence Way, Denny End Road 21 17 Current
Jn Winfold Road, Clare Close 24 17 Current
Jn Capper Road, Cody Road 12 20 New
Jn Way Lane, Spurgeons Avenue 15 12 Current

Thus, unless you live either on Bannold Road north of the Way Lane junction or in the former married quarters, the walking distance will be less to the existing station.

Watch out for further comments on this and keep your eyes skinned for RLW’s outline planning application.

Waterbeach Station

I’ve just found a very interesting document dated last October. I’m quite surprised that it hasn’t surfaced before. It’s called ‘NEW WATERBEACH STATION GRIP 2 REPORT’.

GRIP stands for Governance for Railway Investment Projects and is the process that Network Rail uses to manage developments to enhance or renew Britain’s rail network. The GRIP process apparently has 8 stages and stage 2 is defined as

Feasibility – Defines the investment goals and identifies constraints to ensure that they can be achieved both economically and strategically.

If you would like to read it, you can find it here. I’ll be digesting it over the next few days or weeks, especially since the Parish Council has recently had a presentation on RLW’s plans in this area. Watch this blog for further thoughts.