Talk:How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension/Archive 1

Archive 1

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"Statistical Self-Similarity and Fractional Dimension" is just a subtitle; couldn't we move this page to a shorter title, like "How Long Is the Coast of Britain?", so that the article looks better in lists/categories. ✏ Sverdrup 14:05, 30 Sep 2004 (UTC)

There was already a re-direct from How Long Is the Coast of Britain, and I have just created another one from How Long Is the Coast of Britain?. This can solve the list issue, but not the category issue, I guess. As far as I can see, there doesn't seem to be a consistent practice on whether publications have their main page under their full title or an abbreviation. Picking examples at random, Philosophiae Naturalis Principia Mathematica and The Life and Opinions of Tristram Shandy, Gentleman are main pages, with re-directs from abbreviated titles, whereas Gödel, Escher, Bach: an Eternal Golden Braid and Through the Looking-Glass, and What Alice Found There are re-directs to a main page under an abbreviated title. Gandalf61 10:10, Oct 1, 2004 (UTC)

Length of coastline

I think there should be made a serious issue in Wikipedia on how to state the "length of coastline" of various geographical areas. The claims are often very contradictory and messy, and at least ambiguous. At least I have never seen the data formulated as "coastline length is XXX kilometers on YYY kilometers scale. 80.221.61.8 20:13, 21 April 2006 (UTC)

I agree with the comment above. Many pages describe how long the coast or border of a particular state or nation is. In light of the work done by Mandelbrot in this paper and the work done by Lewis Fry Richardson, I'm a little confused because it seems to me that stating a country's coast or border as being x kilometres means nothing unless it is specified how these things are measured and what scale of measurement is used. How is the standard the measurement done? For example, what does it mean when the CIA World Factbook states that certain country's coastline is a particular length? 18.248.5.226 05:33, 7 November 2006 (UTC)

The CIA World Factbook seems to rely on other primary sources, and suffers from the same confusion of different measurement standards. Its note on "land boundaries" says: When available, official lengths published by national statistical agencies are used. Because surveying methods may differ, country border lengths reported by contiguous countries may differ. In other words, the lenegth of the border with country A as measured by country B may differ from the length of the border with country B as measured by country A. Gandalf61 14:33, 7 November 2006 (UTC)

Layman's terms

"The empirical evidence suggests a rule which, if extrapolated, shows that the measured length increases without limit as the measurement scale decreases towards zero." I'm afraid that this summary still resembles gobbledigook, even after some moments of staring at it bemusedly.

A summary in layman's terms would be exceedingly useful. --Dweller 15:01, 24 July 2007 (UTC)

Okay, let's try to break it down as follows:

• A standard way of measuring the length of a coastline (or a border or a road) on a map is to step along the feature using dividers set to a length that represents a known distance on the map (this process is described in our dividers article). The distance between the ends of the dividers is the measurement scale.
• The measured length of a coastline (or other feature) depends on the measurement scale used. Not surprisingly, a smaller measurement scale gives a longer measured length, because your measurement now includes smaller bays in the coastline, smaller bends in the road etc. This effect is shown in the three illustrations that accompany the article, which show how the length of the coastline of Britain can be measured at three different measurement scales.
• You might expect that as you make the measurement scale smaller and smaller, the measured length will converge to some limit, which we could say was the true length of the feature. The surprising part is that with natural features such as coastlines, this does not happen. Instead, the measured length carries on getting longer and longer as the measurment scale is made smaller and smaller. This "paradox" was first documented in detail by Lewis Fry Richardson.
• Mandelbrot's paper says that Richardson's "paradoxical" observations do indeed make sense if we model a coastline as a geometric object with a non-integer dimension between 1 and 2. Mandelbrot later coined the term "fractal" to decribe such objects. In summary, Mandelbrot says that the measured length of coastlines behaves as if they were fractals over a wide range of measurement scales.

Does that help ? Gandalf61 15:51, 24 July 2007 (UTC)

Erm, sort of. It's not a very concise summary, is it? --Dweller 16:50, 24 July 2007 (UTC)

Umm ... but you didn't like the concise version - you said it was "gobbledigook". You can have it short or simple, but not both. Gandalf61 18:58, 24 July 2007 (UTC)

Something like: "Actually (empirically) trying to measure the length of the coastline with a yardstick of various fixed lengths shows that the measured length of the coastline increases as the yardstick gets shorter; extrapolating these results, the length tends to infinity as the yardstick tends to zero." ? -- !! ?? 14:04, 3 October 2007 (UTC)

Maybe I'll do this myself, but the three illustrations are begging for a concise caption - scale 1, length=x, scale 1/2, length =nx, etc. Yeah, I'll probably do it... Huw Powell (talk) 23:49, 8 April 2009 (UTC)

Origin of the phrase

In James Gleick's book Chaos it says that Mandelbrot got the title from an article by (i think) J.B.S. Haldane. I can't find my copy though. Can anyone help? 82.163.148.31 (talk) 11:20, 6 April 2008 (UTC)

I can't find any reference to Haldane either in Mandelbrot's paper or in Gleick's Chaos. Mandelbrot was inspired by research on the measured lengths of coastlines and other natural geographic borders published by Lewis Fry Richardson. Gandalf61 (talk) 12:08, 6 April 2008 (UTC)

I must have been mistaken then :( 82.163.148.31 (talk) 12:26, 6 April 2008 (UTC)

Length of coastline

From the article: "Note that the paper does not claim that any coastline or geographic border actually is a fractal - that would be a physical impossibility as you eventually get down to atomic scale."

-this makes an assumption that the smallest scale we can view things at is the 'atomic' level. While that statement may be true in a sense, in modern scientific terms this view represents an incomplete model due to the discovery of subatomic particles and the discovery of yet smaller particles within those. It may well turn out that there is no smallest particle - and therefore no smallest scale - and that sub-division is potentially infinite. Humans draw the borders on every map or model, and the conclusion that the coastline is infinite may turn out to not be so absurd afterall.

I therefore suggest this statement be removed or elaborated on - as it stands it is meaningless unless we assume that the 'atomic level' is the smallest scale of geometric space possible which would require a revision of many fields of physical science. —Preceding unsigned comment added by 80.221.34.109 (talk • contribs)

Actually, it's just meaningless if we assume that geometry on a subatomic level is useful in a discussion about coast lines. Yaan (talk) 18:56, 29 March 2010 (UTC)

I came to this discussion page in order to follow out the Mandelbrot article which I feel was lacking in the development of the "how long..." as a seminal work. I see that the "Explaining the Coastline Paradox in layman's terms" conundrum has been recognized here. I suggest that the edits continue in the vain of bays to coves to tidepools. Where the ruler example fails is in both language (Clarify 1 foot ruler versus 3 foot Yardstick, or go metric) and in recognizing the underlying “Fractal-ness” of coastline scale. In other words the yardstick example (and the fine graphics) would be true for measuring the centerline of a coastal highway; A mathematically definable curve which is not infinite. In an absurd reduction it can be used to describe measuring a circle. The article sections could thus describe Newtonian objects. What is needed here is a layman’s definition that captures the “fuzziness”, the hairiness of having to step out and decide if this pebble is to be measured and if this clump of sand on the pebble is included in Her Majesty’s coast. The answer will be found in the words of the master, such as”as even finer features are taken into account, the total measured length increases, and there is usually no clear-cut gap or crossover, between the realm of geography and details with which geography need not be concerned.” that quote should also clarify that the "atomicity" discussion is to be addressed but limited. I hope I’m leaving something helpful here, but can't suggest a solution at this writing. Giving permission to edit by prior discussion contributors. (StowAwayOnTheBeagle (talk) 03:28, 18 October 2010 (UTC))

It may sound overly abstract, but as a web designer, something that came to mind that would make sense to a layman is the 'Magic Wand' tool in Photoshop. You can see a 'selection' (some call 'marching ants') around an object when it is selected, but you can change the 'tolerance' of the 'magic wand' which would expand or constrict the same selection. Perhaps this would be a layman's way of articulating the situation, which would be like selecting the border 'coastline' of an island graphic. — Preceding unsigned comment added by 70.27.1.226 (talk) 01:04, 1 February 2012 (UTC)

Broken link

The link to the pdf on Mandelbrot's homepage is broken. Does anyone know where to find a replacement? 167.127.104.216 (talk) 13:27, 16 May 2017 (UTC)