Roughness is, among human sensations, just as fundamental as color or pitch, or as heaviness or hotness. But its study had remained in a more primitive state, by far. The reason was that both geometry and science were first drawn to smooth shapes. Thus, color and pitch came to be measured in cycles per seconds, that is, were reduced to sinusoids, in other words to uniform motions around a circle - the epitome of a smooth shape. A study of roughness had necessarily to wait until specific mathematical tools had been discovered and, much later, suitably interpreted. Fractal geometry began when I reinterpreted the flight from nature that had led mathematicians to conceive of notions like the Holder exponent, the Cantor set, or the Hausdorff dimension. They boasted of these notions being 'monstrous' but in fact I turned them over into everyday tools of science. I also added further tools that - taken together - made roughness quantitatively measurable for the first time. Acquiring a quantitative measure is the step that moves a field into maturity. And this move instantly led to a striking conjecture. In 1984, 'Nature' published an article I wrote with D. A. Passoja and A. J. Paullay on metal fractures. We found that the traditional measures of their roughness range all over. To the contrary, their fractal roughness varies very little not only between samples but also between materials. Last time I checked the "universality" had been extended but not explained. The new intrinsic measure created a major intellectual mystery. The first major new tool that I added to those contributed by the likes of Holder, Cantor, and Hausdorff was multifractality, for both measures and functions. I was motivated by the urge to model the intermittence of turbulence but my first full paper (in 1972) also noted that the same techniques ought to apply to the intermittence in the variation of financial prices. An ancient adage claimed that the City of London is as unpredictable as the weather. I found unexpectedly quantitative truth to this adage by showing that both phenomena can be tackled with essentially the same tools. Roughness is everywhere therefore fractal geometry has little fear of running out of problems. This address will sketch the fractal geometry of roughness and explore some new developments relevant to this Congress.
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机译：粗糙度是人类感觉中的，就像颜色或间距一样，或沉重或热度。但到目前为止，其研究仍然是一个更原始的国家。原因是，首先将几何和科学绘制到平滑的形状。因此，在每秒循环中测量颜色和间距，即，换句话说，换句话说，围绕圆形的均匀运动 - 平滑的形状的缩影。对粗糙度的研究必须等到发现特定的数学工具，并以后，适当地解释。当我重新解释出从大自然的飞行时开始分形几何，这使得数学家设想了像持有人指数，唱歌集或豪斯多夫维度的概念。他们吹嘘这些概念是“怪物”，但事实上，我把它们转化为日常科学工具。我还添加了进一步的工具，即在一起 - 使粗糙度首次定量可测量。获取定量措施是将场进入成熟度的步骤。这一行动立即导致了一个引人注目的猜想。 1984年，“大自然”发表了一篇我用D. A. Passoja和A. J.Paullay在金属骨折上写了一篇文章。我们发现，传统的粗糙度范围内的措施。相反，它们的分形粗糙度不仅在样品之间而且在材料之间变化。上次我检查了“普遍性”已经扩展但未解释。新的内在措施创造了一个主要的智力神秘。我添加到由持有人，唱歌和Hausdorff所贡献的人的第一个主要新工具是多重的，用于措施和功能。我受到模拟湍流间歇性的推动的动机，但我的第一个全文（1972年）还指出，相同的技术应该在金融价格的变化中适用于间歇性。古老的格言声称，伦敦市与天气一样不可预测。我发现这种谚语的意外定量真理通过表明这两种现象都可以与基本相同的工具进行解决。粗糙度无处不在，因此分形几何形状几乎没有担心出现问题。这个地址将绘制粗糙度的分形几何形状，并探索与本国会相关的一些新的发展。
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