In a message dated 10/21/2010 12:31:46 A.M. Eastern Daylight Time, RichardHenninge@xxxxxxxxxxx quotes: "Their results have varied from 1.02 for the coastline of South Africa to 1.25 for the west coast of Great Britain. However, 'fractal dimensions' of coastlines and many other natural phenomena are largely heuristic" Henninge comments: "make that totally heuristic, essentially, quintessentially heuristic" and continues to quote: "and cannot be regarded rigorously as a Hausdorff dimension. It is based on scaling properties of coastlines at a large range of scales, but which does not however include all arbitrarily small scales, where measurements would depend on atomic and sub-atomic structures, and are not well defined." Henninge concludes his post: "The best prophylaxis to brake these hubristic heuristic tendencies is Wittgenstein's checker: The world is everything that is the case, and that of which we cannot speak, of that we must remain silent. There will be no end to the coast of Britain if we start "finding" programmable patterns in it. Fractals may alter the length of that coastline, as people change people-based impressions, definitions, programs, sentences, but they are not about to make a new coastline in the world about which we can say, lo, it is the case that this coastline is fractal, without being accusable of making a metaphor, giving an illustration, speaking in parables, and being approximate, and human, all too human." Dunno. I for one find it a pity that he (and his associates) limited themselves (or theirselves) to the _west_ coast of Britain, which, in my view, while exciting, is JUST AS EXCITING as the East Coast (of Britain) and the Channel Coast (I HAVE LOADS OF BOOKS on that!). In a way, it reminds one of Carroll in "Sylvie and Bruno" -- that German chartographer who finds that a scale of 1:1 is best to represent the map of England. "But the farmers objected on my spreading the map; their crops would get no sunlight; therefore, they are now using England as her own map". ------ I think Mandelbrot's hypothesis is a good one, and it does not strike me as uselessly Kantian. I can speak of ONE PARTICULAR bit of coast that he however seems to have excluded from his analysis. Cowes Week -- as per Cowes Regatta. I have LOADS of maps of that area, and it's the MOST COMPLEX chart I have ever seen. For one, there's the Isle of Wight. What are we to do with the Isle of Wight. It was a Jutish settlement, and remained thus for centuries. Only LATER it was claimed by Hampshire ("Hants" in the vernacular). Nowadays, since 1974, with the re-distribution of shires, it ceased to be Hants., I think, and got its own status, "I. of W.". That is merely conventional (as in Lewis Carroll, "What's the good of Mercator, just a conventional sign!" -- The Hunting of the Snark). But the problem is SAILING that coast. The Cowes Regatta is varied, but the MAIN regatta is a small stretch FROM Cowes, in the isle of Wight, TO near PORTSMOUTH, indeed in Hants. If you google-map the area you'll see how complex that coast is, and how tricky the currents. Now suppose you take a 'round-the-Isle-of-Wight' regatta as part of the Cowes Regatta. Try to just ANALYSE the 'coast' of the Isle of Wight. It's so COMPLEX. Mineralogically, and other, it is a VERY difficult structure. A coast NEEDS to distinguish between rocky and sandy, say. High tides and low tides. Bays and coves, and rivulets and mouths (so-called, they are literally rear ends rather) of rivers, etc. There are HUMAN extensions of intensions of coasts. The Royal Squadron, for example, in Cowes, where the Regatta originates, cannot claim to be on the "natural" coast of Cowes, since most harbours -- and marinas -- require a lot of draining work, which may modify the coast -- and the coast-line. So, Mandelbrot is INTO something. While he provides 1.25 as the number for the west coast of England -- and which would THIS stretch -- from what to what? --, I would love to have a detailed commentary and corresponding number for the ROUND coast of, say, Great Britain. When I speak of "Great Britain", I speak of Britannia Maior -- as opposed to IRELAND (or Eire), which I refer to as "Britannia Minor". I.e. just the BIG British Isle, and its coast. When I was reading Finnegans Wake I did a LOT of research on the IRISH coast -- also "coast of Britain", if you think of it, and if you want to cover, say, ULSTER. It's SO COMPLICATED. Recall that Joyce starts his work with a description of the coast, as the River Liffey opens to the ocean. THAT area is a bliss, but it's SO COMPLICATED to chart. The usual way of sailing is north, from Liffey, round the coast of Ireland, and back to Liffey from the south. But again, how long is the coast of Ireland (considered "Britannia minor")? In which case, if Mandelbrot knows that the west coast of Britain -- by which he must mean, north of Land's End to Scottish Higlands -- and thus encompassing the whole coast of Wales, the Merseyside -- a VERY COMPLEX area, and the "Cumbria" coast (post 1974) -- is 1.25. I would submit that the WHOLE coast of Gt. Britain may be something like 5.2. If we add that to the fractal for the coast of "Britannia minor" ( Eire-Ulster) -- say, 3.6 we get 5.2 3.6 ---- 8.8 8.8 -- that's hoe long the coast of Britain is. This would have fascinated Kant. The noumenon. When he was teaching in Russia, he was often asked, "You know the riverside of the Thames so well!". His grandfather was a Brit, and he inherited from him this 'marine' extravaganzas. Consider the mouth of the Thames. Kant could recite ALL accidents of the coast in that VERY COMPLEX area (sandy, rather than rocky, and thus providing a very complex fractal to calculate). And when exactly are we going to say, "This is NOT the coast of Britain; this is the INNER THAMES alright". We need a conventional line -- imaginary line. We need to have a line that indicates -- a straight line -- 'this is the Thames' and this is not. Those lines need two points. One would be north of the Thames, the other south of the Thames. Downstream it would be sea, upstream it would be river alright. And we need to measure that imaginary line to add to the fractal, which will be 8.8. Just to do that FOR each mouth of a big river in Britain does require a lot of (Kantian) work: think of the mouth of the Humber, or the mouth of the Tyne. Now, with fractals, we can provide definite 'noumenal' statistics and measures -- and sail along! Speranza ------------------------------------------------------------------ To change your Lit-Ideas settings (subscribe/unsub, vacation on/off, digest on/off), visit www.andreas.com/faq-lit-ideas.html