Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies
by Geoffrey West · 15 May 2017 · 578pp · 168,350 words
Bridge, 61, 64, 65 climate change. See global warming Clinton, Bill, 82 cliques, 298, 305 closed systems, 236 Club of Rome, 231, 239, 416–17 coastline paradox, 136–40, 138, 152 Coleridge, Samuel Taylor, 361–62 commuting time, 332–35 companies, 379–410 as biological organisms, 10–12, 247–53 cities compared
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of stock market, 142, 144 Fractal Geometry of Nature, The (Mandelbrot), 143–44 fractals, 27, 92, 130–45, 315–16 characteristics of, 126–28, 127 coastline paradox, 136–40, 138, 152 Mandelbrot and, 138–45, 152 Richardson and, 131–42, 152 freedom of choice, 56–57 free market economy, 229, 232, 233
The Physics of Wall Street: A Brief History of Predicting the Unpredictable
by James Owen Weatherall · 2 Jan 2013 · 338pp · 106,936 words
. As it turns out, however, the question is more complicated than it appears. There’s a deep puzzle built into it, sometimes known as the coastline paradox. To figure out the length of a coastline, you need to take some measurements, presumably with some sort of ruler. The puzzle concerns how long
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doesn’t have a length, or at least not in the way that simple shapes like a line or a circle do. Mandelbrot addressed the coastline paradox in a groundbreaking paper in 1967. It was one of his first attempts to describe a fractal shape — as, indeed, a coastline turns out to
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drunken firing squad’s shots. When Mandelbrot was looking at the data for IBM, he had not yet invented fractals. His seminal work on the coastline paradox was almost a decade away. But similarly to Pareto half a century before him, something about the pattern struck Mandelbrot. It reminded him of his
Mapmatics: How We Navigate the World Through Numbers
by Paulina Rowinska · 5 Jun 2024 · 361pp · 100,834 words
and zoom in and out on Google Maps to see that. We call this phenomenon of measurements’ dependence on the measuring stick’s length the coastline paradox. We take measurements for granted – when we find a number in a reputable source, why would we question it? The more careful will look for
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field necessitate newfangled techniques, for which the only references are dusty tomes written in French, or even in Polish, or incomprehensible modern monographs?’ In the coastline paradox, Mandelbrot saw a concrete and visual example of the complicated notion of self-similarity he’d struggled to convince people of for a long time
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came as a surprise. The referee behind the positive feedback was the esteemed Polish mathematician, Hugo Steinhaus. Years before Mandelbrot, Steinhaus had already noticed the coastline paradox when measuring the length of the largest Polish river, the Vistula. In his 1954 publication, Steinhaus noticed that ‘the left bank of the Vistula, when
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mathematical community, in Mandelbrot’s paper, he promptly recommended that the paper should be published. He must have seen it as a chance for the coastline paradox, known from ancient times and noticed by multiple prominent mathematicians, to make it into mainstream research. While we don’t know who first noticed this
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access to the coast. The Treaty of Saint Petersburg placed the border fifty-six kilometres east of the coast. But what is the coast? The coastline paradox makes the fjords of the Alaska Panhandle particularly hard to deal with. The treaty didn’t specify the scale of the map on which the
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formulated seven questions that needed answering, including where the border began, how it should be measured, and which mountains the Treaty was talking about.* The coastline paradox caused a major boundary dispute that, as some scholars claim, led to anti-British feelings among Canadians, which contributed to their campaign for more autonomy
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professor, connects from his new home in Louisiana to join me on a Zoom call. After reading his paper on the legal implications of the coastline paradox, I knew I had to talk to him. The Alaskan boundary dispute, it became clear, is just the tip of the iceberg. When I ask
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internal waters, as opposed to the ocean, if the bay significantly cuts into its land territory. By establishing this additional rule, the Conference recognized the coastline paradox without naming it. The agreement from Geneva sparked a decades-long discussion that resulted in the United Nations Convention on the Law of the Sea
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and Norway was taken to the International Court of Justice. The Fisheries Case, as it’s known today, stems from ambiguous sea laws and the coastline paradox. Norway is famous for its beautiful fjords along its long coastline that exceeds 2,500 km even when measured in a straight line. The magnificent
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use a small-scale map. This time, the court stood for Norway, encouraging other coastal nations to follow suit and fight for their territory. The coastline paradox is not just a mathematical curiosity but has a tangible impact on international law. As Stoa tells me, ‘Many times, policymakers or negotiators come across
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the coastline paradox and understand the problem without actually naming it as the coastline paradox or understanding that it is the coastline paradox.’ In other words, people intuitively recognize the ambiguities of the simple word ‘coastline’, without being familiar with
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fractals and dimensions. Mathematics impacts our life whether we’re aware of it or not. The legal implications of the coastline paradox aren’t all happening on an international level. In the US, for example, a significant portion of the funding for coastal management is proportional to
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the local government measures its boundary for tax purposes – the shorter the measuring stick, the longer the coastline, and the larger your tax. Although the coastline paradox impacts who the money and the power belong to, few policymakers or even scholars devote their time to thinking about ways of fixing this problem
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animations and build efficient antennas. Despite their omnipresence, these creatures remain largely invisible, and that invisibility has tangible consequences. The lack of awareness of the coastline paradox leads to lengthy international disputes and misplaced funding of coastal areas, which impacts our day-to-day life. We ignore fractals at our peril. AMONG
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perimeter.* This works well for theoretical district shapes such as squares, but measuring lengths of real-world boundaries is all but impossible due to the coastline paradox. The length of a boundary depends on the length of the measuring stick, which is not ideal when we’re comparing perimeters of different districts
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to Think in Pictures and Its Continuing Influence’. Web of Stories videos, 24 January 2008, https://www.webofstories.com/play/benoit.mandelbrot/8. Coastline Paradox Stoa, Ryan B. ‘The Coastline Paradox’. Rutgers University Law Review 72, no. 2 (Winter 2019): 351–400. 4. Distanced Underground Map Guo, Zhan. ‘Mind the Map! The Impact of
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–1645)’, Internet Encyclopedia of Philosophy, n.d., accessed 23 November 2021, https://iep.utm.edu/grotius/. who these resources belong to: Ryan B. Stoa, ‘The Coastline Paradox’, Rutgers University Law Review 72, no. 2 (2019): 351–400, https://rutgerslawreview.com/wp-content/uploads/2020/11/72_Rutgers_Univ_L_Rev_0351_Stoa
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fishing war between the two countries: Anglo-Norwegian Fisheries, UK v. Norway, Order, 1951 I.C.J. 117 (Jan. 18). the larger your tax: Stoa, ‘Coastline Paradox’. 4. Distanced come up with alternative routes: Shaun Larcom, Ferdinand Rauch and Tim Willems, ‘The Benefits of Forced Experimentation: Striking Evidence from the London Underground
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Cho, Wendy K. Tam ref1, ref2, ref3 cholera ref1, ref2, ref3 circumference, Earth’s ref1, ref2, ref3, ref4n, ref5 Clausewitz, Carl von ref1 Clomedes ref1 coastline paradox ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9 cognitive graphs ref1 cognitive maps ref1 Cold War ref1, ref2, ref3, ref4 collaboration, international ref1, ref2
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of Colorado ref1 circles ref1, ref2 and scale ref1, ref2 straight lines ref1 using logarithmic axes ref1 wiggly lines ref1, ref2, ref3, ref4; see also coastline paradox Literarum latinarum (Kremer) ref1 Livingstone, Ken ref1 logarithmic axes ref1 logarithms ref1, ref2 London, UK Great Stink of London (1858) ref1n Legible London ref1, ref2
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satellite radar altimeters ref1 scale Baltimore phenomenon ref1 and borders ref1 changing ref1 defining ref1 and details included ref1, ref2, ref3 and measuring lines see coastline paradox; lines, measuring representation ref1 Schmidt, Christopher ref1 Schmitt, Otto ref1 school atlases ref1, ref2 school districts ref1 Science ref1, ref2, ref3, ref4 Scott, Natacha ref1
Ways of Being: Beyond Human Intelligence
by James Bridle · 6 Apr 2022 · 502pp · 132,062 words
identified a paradox: the more accurately you try to measure some things, the more complex they become. This surprising observation has become known as the Richardson effect. Imagine taking a kilometre-long ruler and measuring the coast of Britain. Now repeat the exercise with a ruler half as long, then half as
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repeat to infinite complexity. Instead of resolving into order and clarity, ever-closer examination reveals only more, and more splendid, detail and variation.26 The Richardson effect applies to biology, archaeology, evolution and, it seems, to life itself. As our archaeological and biological tools get better, as we unravel the web of
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Europe (Gran Dolina, Sierra de Atapuerca, Burgos, Spain)’, Journal of Human Evolution, 37(3–4), September 1999, pp. 591–622. 25. Richardson explicitly discusses the coastline paradox in Lewis F. Richardson, ‘The Problem of Contiguity: An Appendix to Statistics of Deadly Quarrels’, General Systems: Yearbook of the Society for the Advancement of
New Dark Age: Technology and the End of the Future
by James Bridle · 18 Jun 2018 · 301pp · 85,263 words
realisation that it is in fact impossible to give a completely accurate account of the length of a nation’s borders. This ‘coastline paradox’ came to be known as the Richardson effect, and formed the basis for Benoît Mandelbrot’s work on fractals. It demonstrates, with radical clarity, the counterintuitive premise of the new
Cold: Adventures in the World's Frozen Places
by Bill Streever · 21 Jul 2009 · 302pp · 92,507 words
. Separately, he showed that shoreline length is a function of scale and that shoreline length will increase as finer scales are used. This so-called Richardson effect is often ignored in technical papers attempting to relate shoreline length to various ecological phenomena and political or economic statistics. Some sources suggest that Lorenz
The Food Lab: Better Home Cooking Through Science
by J. Kenji López-Alt · 20 Sep 2015
that weren’t visible from far away. When measured again, these bumps add length to the total perimeter. This is a phenomenon known as the Richardson Effect, which basically says that the more precisely you measure a coastline, the longer the measurement gets. And the more bumpy or irregular the surface is
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in, for deep-frying, 864, 878–79, 879 Garlic-Anchovy, 459 for meat loaf recipes, 528–29 Parmesan, Broiled Asparagus with, 457, 457 and the Richardson Effect, 882 Breadings and batters, for deep-frying, 863–64 Breads. See also Pancake(s) Bacon Parmesan Biscuits, 163 Basic Quick Waffles, 157 best, for stuffings
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Noodles), The Ultimate Chicken Vegetable Soup with, 188, 191 starch molecules in, 750, 753 storing, 79 Vailone Nano, about, 750, 751 Rice cooker, 64–65 Richardson Effect, 882 Ricotta acidic ingredients for, 151–52 best milk for, 153 Classic Baked Ziti, 746, 746, 747 draining, 152 Fresh, in 5 Minutes or Less