Aidan Stanger wrote:
Stephen Osborn wrote:

John Rowland wrote:

"Stephen Osborn" wrote...


However the contours on an OS map (and AFAIK isobars on a weather chart)
never touch let alone cross.

They can touch, but they can't cross.

I think you are wrong there.

Contours mark places of equal height. If two contours touch at any one
point then, de definito, they have to touch at *all* points, so the two
contours become one contour.


You already have the counterexample of a vertical cliff. I have seen
those in nature - although not all of the cliff was vertical, there were
certainly parts that were, and they were definitely big and vertical
enough for contours to meet on the map.


Whereas, in the example that Mike gave,
the isochrones will have to cross.

No, they won't. It's just the same as a weather map, it's just a map where
every point has a real number associated with it. Draw two isochrones
crossing each other, write various times on the isochrones and on the spaces
between them, and you'll see that it can't happen.

I was accepting Mike's point that "I think it can't be done on a flat
map without rearranging the order of stations on each line."

Using Mike's example, a 'railway straight line' runs Wimbledon, Raynes
Park & Surbiton in that order. The isochrone passes through Wimbledon &
Surbiton (ignoring the 1 minute difference) but not through Raynes Park.

That arrangement is possible on an OS map or weather chart as, say, two
maxima (M) can be separated by a minimum (m) so there will be places
with the same value but they are not linked by a contour / isobar. For
example a1 & a2 in the diagram below:

a b a
a a b b a a

a M a1 b m b a2 M a

a a b b a a
a b a

Here the contours / isobars that a1 & a2 sit on have different centres.

For a travel map to be of use, every point on it has to share share the
same centre.


That statement is absolutely ridiculous! I'd go so far as to say the
converse is true: If they don't share the same centre then the map can
clearly display the information* and is therefore useful. If they do
share the same centre then it's impossible to display sufficient
information clearly, therefore the map would be useless.

They do have to share the same reference point, but that's all. I assume
what you were trying to say was that to be useful for determining the
time it would take to get between any two points on the map, every
contour has to share the same centre. If that is what you mean, I'm not
going to bother disputing it because it's pointless - software could do
the job a lot better than any map!


* The easiest way of doing so would be to set the background colour
according to how long it takes to get to the reference point. I expect
this would be referred to as isochromic isochrones!

That's the way the isochrones I've seen have done it. It makes for a
very clear and interesting picture. Comparing the difference in journey
times to two locations is also done this way (i.e. set the isochrones as
the difference in journey time, +/-, for reaching point B compared to
reaching point A).

--
Dave Arquati
Imperial College, SW7
www.alwaystouchout.com - Transport projects in London