# Easy algebra: When does HS2 – HS1 = HS3?

In his recent review of the HS2 project Sir David Higgins advocated the removal of the proposed North London Rail link between HS2 and HS1 on the grounds that it would provide a relatively poor return (removing the need for a one stop tube journey) on an apparently unreasonably large proportion (£700m) of the total budget (£42.6bn) .
(Therefore HS2 – HS1 = £41.9bn)

Today, according to the HM Treasury website in the kind of pre-emptive news strike that has now become the norm, George Osborne will propose a third high speed railway for Britain. Depending on who you ask this “keynote speech” or “pre-election waffle” is either a reflection on the success of his government’s long term economic planning or an attempt to deflect attention from a reported six point deficit in the latest polls. The new line, already being referred to as HS3 would link Manchester and Leeds across the Pennines.

I’m not wanting to speculate on the intention of the speech and without knowing who the audience was (apart from all of us) it’s also difficult to speculate on which particular lock his keynotes were meant to open. But the event of the speech is interesting in its own right.

Firstly it allows me to think about the overall news context. Not in any radical way but just to observe how the news game is played. The official press release of this “vision for a northern powerhouse” is published overnight in anticipation of the Chancellor’s and Prime Minister’s “Northern infrastructure tour day”. The speech is backed up by interviews with the traditional media. In one television interview, when pressed to provide a costing of his HS3, Osborne offers a rule of thumb estimate (based on the HS2 cost per mile) of £7bn for his trans-pennine upgrade.
(So HS2 + HS3 = £48.9bn if we were to trust in the Chancellor’s heuristic)

HM Treasury also set about a social media campaign to support their northern tour. Their official storify is here and on twitter their hashtag #northernpowerhouse has already collected some 10,000 tweets and retweets. That’s a lot of words already from Sunday night to Monday morning. Backwards and forwards. Tweets and retweets. The relationship between tweet and retweet is quite similar to the one between press release and news story. But that’s another story.

Back to the speech itself and the way that the HS2 route has been represented. The HS2 route is commonly referred to as a “Y network” . It is proposed to run north from London to Birmingham (as phase 1) where it bifurcates east and west in order to reach Manchester and Leeds without having to negotiate the Peak District. This “Y” network was originally described in a 2009 report from HS2 Ltd as an “inverse A” which included as its bar a high speed link between Manchester and Leeds. So, the answer to my question “when does HS2 – HS1 = HS3?” would appear to be “if Y = 1/A“. The bar was dropped from the initial plan due to the additional cost but it shows that this east-west link across the pennines has been in the government’s back pocket for a while. It’s not the main point of this ramble but the 5 years in between then and now makes my pre-emptive news strike look more like a time bomb.
(and my formula now has a fourth dimension: HS2 – HS1 = HS3 when Y = (1/A x 5))

Shifting slightly from faux algebra to anagrams, and to move towards the point of writing this, it’s also interesting to consider what other letters are in the mix. Alongside the “inverse A” that became a “Y” there were two other options considered. Both of these alternatives were reasoned out of the frame by arguments built around optimal journey times and benefit cost ratios that supported “Y=1/A”. The “reverse S” and the “reverse E” would have provided a single route around the Peak District one way or the other.

Collectively the options for the routes look like this:

And this poses two further questions. Firstly, why and how are these letters being used to signify and explain the alternative routes? Secondly, did they think it was going to be easy?

The first of these questions can be clearly approached from design studies around the use of image and artefact in the design process. I will be thinking about this point as I pursue my current/pending reading of Goldschmidt and the related literature. It’s the second question that’s the real challenge and asking it opens up the design analysis to the wider contexts in which I am looking to apply it. But if I keep asking questions instead of answering them it might turn out to be harder than it should be.