--- title: "Meaning & Key Takeaway of: Weierstrass, Cantor, or Peano! In…" description: "\"“Weierstrass, Cantor, or Peano! In physics, an analogous development threatened since about 1800, since Laplace’s Celestial Mechanics avoided all illus..." image: "https://sms4smile.com/quotes/i/34f/beno-t-b-mandelbrot-65052_fractals_weierstrass-cantor-or-peano-in-physics-a_3063349.jpg" --- # Weierstrass, Cantor, or Peano! In physics, an analogous… ![“Weierstrass, Cantor, or Peano! In physics, an analogous development threatened since about 1800, since Laplace’s Celestial Mechanics avoided all illustration. And it is exemplified by the statement by P. A. M. Dirac (in the preface of his 1930 Quantum Mechanics) that nature’s “fundamental laws do…” quote by Benoît B. Mandelbrot](https://sms4smile.com/quotes/i/34f/beno-t-b-mandelbrot-65052_fractals_weierstrass-cantor-or-peano-in-physics-a_3063349.jpg) [Download](https://sms4smile.com/quotes/i/34f/beno-t-b-mandelbrot-65052_fractals_weierstrass-cantor-or-peano-in-physics-a_3063349.jpg) [Open image](https://sms4smile.com/quotes/i/34f/beno-t-b-mandelbrot-65052_fractals_weierstrass-cantor-or-peano-in-physics-a_3063349.jpg) > ““Weierstrass, Cantor, or Peano! In physics, an analogous development threatened since about 1800, since Laplace’s Celestial Mechanics avoided all illustration. And it is exemplified by the statement by P. A. M. Dirac (in the preface of his 1930 Quantum Mechanics) that nature’s “fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies.” The wide and uncritical acceptance of this view has become destructive. In particular, in the theory of fractals “to see is to believe.”” Benoît B. Mandelbrot ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. The quote warns that treating mathematical abstractions as literal visual truths can mislead scientific understanding, especially in complex fields like fractals. **In simple terms:** Seeing without questioning can distort reality. Key Takeaway Question assumptions behind visual representations. Themes science philosophy mathematics perception critical thinking Mood skeptical analytical cautious Type philosophical critical scientific When to use this quote - research analysis - education - data visualization - theoretical physics - artistic interpretation Key Concepts abstraction visualization mental models scientific methodology Questions to Reflect On - How do we balance intuition with rigorous analysis? - When should we distrust a visual metaphor? A Different Perspective Visual intuition may oversimplify underlying complexity. ★ ★ ★ ★ ★ No ratings yet [Fractals](https://sms4smile.com/quotes/about/fractals/) [Quantum mechanics](https://sms4smile.com/quotes/about/quantum-mechanics/) ## Related quotes > [The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically…](https://sms4smile.com/quotes/benoit-mandelbrot/the-theory-of-chaos-and-theory-of-fractals-are-separate-but-have-very/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [It has been said that the three great develpments in twentieth century science are relativity, quantum mechanics, and chaos. That strikes me the same…](https://sms4smile.com/quotes/robert-l-devaney/it-has-been-said-that-the-three-great-develpments-in-twentieth/) Robert L. Devaney > [I find enough mystery in mathematics to satisfy my spiritual needs. I think, for example, that pi is mysterious enough (don't get me started!)…](https://sms4smile.com/quotes/tom-lehrer/i-find-enough-mystery-in-mathematics-to-satisfy-my-spiritual-needs-i/) [Tom Lehrer](https://sms4smile.com/quotes/author/tom-lehrer/) > [“My life seemed to be a series of events and accidents. Yet when I look back, I see a pattern.”](https://sms4smile.com/quotes/beno-t-b-mandelbrot/my-life-seemed-to-be-a-series-of-events-and-accidents-yet-when-i-look/) Benoît B. Mandelbrot > [I strongly believe that the fundamental laws of nature are not emergent phenomena.](https://sms4smile.com/quotes/david-gross/i-strongly-believe-that-the-fundamental-laws-of-nature-are-not/) [David Gross](https://sms4smile.com/quotes/author/david-gross/) > [“If magic violates the fundamental laws of nature, they clearly weren't all that fundamental.”](https://sms4smile.com/quotes/ruthanna-emrys/if-magic-violates-the-fundamental-laws-of-nature-they-clearly-weren-t/) [Ruthanna Emrys](https://sms4smile.com/quotes/author/ruthanna-emrys/) > [We lay it down as a fundamental, that laws, to be just, must give a reciprocation of right; that, without this, they are mere…](https://sms4smile.com/quotes/thomas-jefferson/we-lay-it-down-as-a-fundamental-that-laws-to-be-just-must-give-a/) [Thomas Jefferson](https://sms4smile.com/quotes/author/thomas-jefferson/) > [If we had the fundamental laws of nature tomorrow, we still wouldn't understand consciousness. We wouldn't even understand turbulence.](https://sms4smile.com/quotes/steven-weinberg/if-we-had-the-fundamental-laws-of-nature-tomorrow-we-still-wouldn-t/) [Steven Weinberg](https://sms4smile.com/quotes/author/steven-weinberg/) > [The most important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility…](https://sms4smile.com/quotes/albert-a-michelson/the-most-important-fundamental-laws-and-facts-of-physical-science/) Albert A. Michelson > [The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and…](https://sms4smile.com/quotes/paul-dirac/the-fundamental-laws-necessary-for-the-mathematical-treatment-of-a/) [Paul Dirac](https://sms4smile.com/quotes/author/paul-dirac/) > [“In the process, we might remember that the ground state, the vacuum state of our world, doesn't display all the symmetries of the laws…](https://sms4smile.com/quotes/henning-genz/in-the-process-we-might-remember-that-the-ground-state-the-vacuum/) [Henning Genz](https://sms4smile.com/quotes/author/henning-genz/) > [“The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility…](https://sms4smile.com/quotes/albert-abraham-michelson/the-more-important-fundamental-laws-and-facts-of-physical-science/) Albert Abraham Michelson > [“Musical innovation is full of danger to the State, for when modes of music change, the fundamental laws of the State always change with…](https://sms4smile.com/quotes/plato/musical-innovation-is-full-of-danger-to-the-state-for-when-modes-of/) [Plato](https://sms4smile.com/quotes/author/plato/) > [It is disastrous to own more of anything than you can possess, and it is one of the most fundamental laws of human nature…](https://sms4smile.com/quotes/joseph-wood-krutch/it-is-disastrous-to-own-more-of-anything-than-you-can-possess-and-it/) [Joseph Wood Krutch](https://sms4smile.com/quotes/author/joseph-wood-krutch/) > [“indicate that the same fundamental principles, from which the laws of nature derive, lead to many different self-consistent universes, with many different properties. It…](https://sms4smile.com/quotes/alan-lightman/indicate-that-the-same-fundamental-principles-from-which-the-laws-of/) [Alan Lightman](https://sms4smile.com/quotes/author/alan-lightman/) ## More by Benoît B. Mandelbrot > [“My life seemed to be a series of events and accidents. Yet when I look back, I see a pattern.”](https://sms4smile.com/quotes/beno-t-b-mandelbrot/my-life-seemed-to-be-a-series-of-events-and-accidents-yet-when-i-look/) Benoît B. Mandelbrot > [“I found myself in the position of that child in a story who noticed a bit of string and - out of curiosity -…](https://sms4smile.com/quotes/beno-t-b-mandelbrot/i-found-myself-in-the-position-of-that-child-in-a-story-who-noticed-a/) Benoît B. Mandelbrot > [“Too often, an event’s importance is not recognized until it is too late for proper recording.”](https://sms4smile.com/quotes/beno-t-b-mandelbrot/too-often-an-event-s-importance-is-not-recognized-until-it-is-too/) Benoît B. Mandelbrot Explore all 4 Benoît B. Mandelbrot quotes ## More Fractals quotes > [Any issue and any problem, no matter what height you look at it from, no matter how much you extend past the first fractal,…](https://sms4smile.com/quotes/el-p/any-issue-and-any-problem-no-matter-what-height-you-look-at-it-from/) [El-P](https://sms4smile.com/quotes/author/el-p/) > [Enchanting is not the word that would immediately spring to mind when describing a play that deals with fractal geometry, iterated algorithms, chaos theory…](https://sms4smile.com/quotes/lyn-gardner/enchanting-is-not-the-word-that-would-immediately-spring-to-mind-when/) [Lyn Gardner](https://sms4smile.com/quotes/author/lyn-gardner/) > [“Examples of fractals are everywhere in nature. They can be found in the patterns of trees, branches, and ferns, in which each part appears…](https://sms4smile.com/quotes/joseph-p-kauffman/examples-of-fractals-are-everywhere-in-nature-they-can-be-found-in/) [Joseph P. Kauffman](https://sms4smile.com/quotes/author/joseph-p-kauffman/) > [One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining…](https://sms4smile.com/quotes/benoit-mandelbrot/one-of-the-high-points-of-my-life-was-when-i-suddenly-realized-that/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [I fell in love with flora of all types, especially ferns. Loved the sparse structure and repetition of shape - almost fractal.](https://sms4smile.com/quotes/jack-dorsey/i-fell-in-love-with-flora-of-all-types-especially-ferns-loved-the/) [Jack Dorsey](https://sms4smile.com/quotes/author/jack-dorsey/) > [Fractal litigation, whereby the flapping of a butterfly’s wings on one side of the world resulted in a massive compensation claim on the other.](https://sms4smile.com/quotes/steve-aylett/fractal-litigation-whereby-the-flapping-of-a-butterfly-s-wings-on-one/) [Steve Aylett](https://sms4smile.com/quotes/author/steve-aylett/) > [All created forms are fractal, as is their purpose, use, and allotted time for existence.](https://sms4smile.com/quotes/guy-finley/all-created-forms-are-fractal-as-is-their-purpose-use-and-allotted/) [Guy Finley](https://sms4smile.com/quotes/author/guy-finley/) > [Cocoa-buttered girls were stretched out on the public beach in apparently random alignments, but maybe if a weather satellite zoomed in on one of…](https://sms4smile.com/quotes/bonnie-jo-campbell/cocoa-buttered-girls-were-stretched-out-on-the-public-beach-in/) [Bonnie Jo Campbell](https://sms4smile.com/quotes/author/bonnie-jo-campbell/) > [Modern humans became fixated on a collective hallucination of linear time, ignoring the fractal spirals of the surrounding universe.](https://sms4smile.com/quotes/daniel-pinchbeck/modern-humans-became-fixated-on-a-collective-hallucination-of-linear/) [Daniel Pinchbeck](https://sms4smile.com/quotes/author/daniel-pinchbeck/) > [There is no singular 'reason' why Africans use fractals, any more than a singular reason why Americans like rock music. Such enormous cultural practices…](https://sms4smile.com/quotes/ron-eglash/there-is-no-singular-reason-why-africans-use-fractals-any-more-than-a/) [Ron Eglash](https://sms4smile.com/quotes/author/ron-eglash/) > [“My life seemed to be a series of events and accidents. Yet when I look back, I see a pattern.”](https://sms4smile.com/quotes/beno-t-b-mandelbrot/my-life-seemed-to-be-a-series-of-events-and-accidents-yet-when-i-look/) Benoît B. Mandelbrot > [You're a refraction of the one light. You're a waveform of light. You're a fractal, a pattern that continuously changes.](https://sms4smile.com/quotes/frederick-lenz/you-re-a-refraction-of-the-one-light-you-re-a-waveform-of-light-you/) [Frederick Lenz](https://sms4smile.com/quotes/author/frederick-lenz/) > [I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the…](https://sms4smile.com/quotes/benoit-mandelbrot/i-conceived-and-developed-a-new-geometry-of-nature-and-implemented/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [The first of the request prayers in the daily Amidah is a fractal. It replicates in miniature the structure of the Amidah as a…](https://sms4smile.com/quotes/jonathan-sacks/the-first-of-the-request-prayers-in-the-daily-amidah-is-a-fractal-it/) [Jonathan Sacks](https://sms4smile.com/quotes/author/jonathan-sacks/) > [“All high mathematics serves to do is to beget higher mathematics.”](https://sms4smile.com/quotes/ashim-shanker/all-high-mathematics-serves-to-do-is-to-beget-higher-mathematics/) [Ashim Shanker](https://sms4smile.com/quotes/author/ashim-shanker/) [Browse all 59 Fractals quotes ](https://sms4smile.com/quotes/about/fractals/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "“Weierstrass, Cantor, or Peano! 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