--- title: "Meaning & Key Takeaway of: But we must not underestimate the potency…" description: "\"But we must not underestimate the potency of the mathematical process of abstraction. A surprising variety of things happen to have both magnitude and ..." image: "https://sms4smile.com/quotes/i/c00/banesh-hoffmann-70454_abstraction_but-we-must-not-underestimate-the-potenc_21435.jpg" --- # But we must not underestimate the potency of the… ![“But we must not underestimate the potency of the mathematical process of abstraction. A surprising variety of things happen to have both magnitude and direction and to combine according to the parallelogram law; and many of them are not at all reminiscent of journeys.” quote by Banesh Hoffmann](https://sms4smile.com/quotes/i/c00/banesh-hoffmann-70454_abstraction_but-we-must-not-underestimate-the-potenc_21435.jpg) [Download](https://sms4smile.com/quotes/i/c00/banesh-hoffmann-70454_abstraction_but-we-must-not-underestimate-the-potenc_21435.jpg) [Open image](https://sms4smile.com/quotes/i/c00/banesh-hoffmann-70454_abstraction_but-we-must-not-underestimate-the-potenc_21435.jpg) > “But we must not underestimate the potency of the mathematical process of abstraction. A surprising variety of things happen to have both magnitude and direction and to combine according to the parallelogram law; and many of them are not at all reminiscent of journeys.” Banesh Hoffmann ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Abstraction in mathematics reveals hidden structures that behave predictably, like vectors adding via the parallelogram rule, even when they seem unrelated to everyday experiences. **In simple terms:** Mathematical abstraction uncovers universal patterns. Key Takeaway Abstract models can predict diverse phenomena. Themes Abstraction Mathematical structure Universality Vector addition Hidden patterns Mood Curiosity Awe Type Philosophical Scientific When to use this quote - Physics problem solving - Engineering design - Data analysis - Computer graphics Key Concepts Vector spaces Parallelogram law Mathematical modeling Practical Applications - Developing unified theories - Designing algorithms that exploit vector properties Questions to Reflect On - How does abstraction simplify complex systems? - When might abstraction obscure important details? ★ ★ ★ ★ ★ No ratings yet [Abstraction](https://sms4smile.com/quotes/about/abstraction/) [Journey](https://sms4smile.com/quotes/about/journey/) [Law](https://sms4smile.com/quotes/about/law/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Parallelogram](https://sms4smile.com/quotes/about/parallelogram/) [Process](https://sms4smile.com/quotes/about/process/) [Statistics](https://sms4smile.com/quotes/about/statistics/) [Things happen](https://sms4smile.com/quotes/about/things-happen/) [Variety](https://sms4smile.com/quotes/about/variety/) ## Related quotes > [I consider my greatest accomplishment to be lifelong celibacy.](https://sms4smile.com/quotes/isaac-newton/i-consider-my-greatest-accomplishment-to-be-lifelong-celibacy/) [Isaac Newton](https://sms4smile.com/quotes/author/isaac-newton/) > [The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.](https://sms4smile.com/quotes/archimedes/the-centre-of-gravity-of-any-parallelogram-lies-on-the-straight-line/) [Archimedes](https://sms4smile.com/quotes/author/archimedes/) > [The landlady of a boarding-house is a parallelogram - that is, an oblong angular figure, which cannot be described, but which is equal to…](https://sms4smile.com/quotes/stephen-leacock/the-landlady-of-a-boarding-house-is-a-parallelogram-that-is-an-oblong/) [Stephen Leacock](https://sms4smile.com/quotes/author/stephen-leacock/) > [ The vision shared by both \[French utopian\] Charles Fourier and Robert Owen was for an entire town to fit into one structure. 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The potency of forgiveness comes precisely from the fact that it must be…](https://sms4smile.com/quotes/patrick-gale/i-worry-sometimes-that-we-re-apt-to-confuse-forgiveness-with/) [Patrick Gale](https://sms4smile.com/quotes/author/patrick-gale/) > [True, the fragile bodies of his fellows do not weigh down his plane; true, the fretful minds of weaker men are missing from his…](https://sms4smile.com/quotes/charles-lindbergh/true-the-fragile-bodies-of-his-fellows-do-not-weigh-down-his-plane/) [Charles Lindbergh](https://sms4smile.com/quotes/author/charles-lindbergh/) > [Between the idea And the reality Between the motion And the act Falls the Shadow For Thine is the Kingdom Between the conception And…](https://sms4smile.com/quotes/anonymous/between-the-idea-and-the-reality-between-the-motion-and-the-act-falls/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Only an empowered personality can distribute the holy name of the Lord and enjoin all fallen souls to worship Krishna. By distributing the holy…](https://sms4smile.com/quotes/bhaktisiddhanta-sarasvati/only-an-empowered-personality-can-distribute-the-holy-name-of-the/) [Bhaktisiddhanta Sarasvati](https://sms4smile.com/quotes/author/bhaktisiddhanta-sarasvati/) > [Though an atom is invisible, unthinkable, yet in it are the whole power and potency of the universe.](https://sms4smile.com/quotes/swami-vivekananda/though-an-atom-is-invisible-unthinkable-yet-in-it-are-the-whole-power/) [Swami Vivekananda](https://sms4smile.com/quotes/author/swami-vivekananda/) ## More by Banesh Hoffmann > [To pry into the secrets of this world, we must make experiments. But experiment is a clumsy instrument, afflicted with a fatal determinacy which…](https://sms4smile.com/quotes/banesh-hoffmann/to-pry-into-the-secrets-of-this-world-we-must-make-experiments-but/) Banesh Hoffmann > [No longer was light analogous to the discharge of a blunderbuss, but rather to the pulsating flight of birds.](https://sms4smile.com/quotes/banesh-hoffmann/no-longer-was-light-analogous-to-the-discharge-of-a-blunderbuss-but/) Banesh Hoffmann > [Every new discovery in science brings with it a host of new problems, just as the invention of the automobile brought with it gas…](https://sms4smile.com/quotes/banesh-hoffmann/every-new-discovery-in-science-brings-with-it-a-host-of-new-problems/) Banesh Hoffmann Explore all 4 Banesh Hoffmann quotes ## More Abstraction quotes > [Everything in dancing is style, allusion, the essence of many thoughts and feelings. 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But when an abstraction starts to kill you, you have to get to…](https://sms4smile.com/quotes/albert-camus/yes-there-was-an-element-of-abstraction-and-unreality-in-misfortune/) [Albert Camus](https://sms4smile.com/quotes/author/albert-camus/) > [Computer Science is a science of abstraction -creating the right model for a problem and devising the appropriate mechanizable techniques to solve it.](https://sms4smile.com/quotes/alfred-aho/computer-science-is-a-science-of-abstraction-creating-the-right-model/) Alfred Aho > [In 'Self Comes to Mind' I pay a lot of attention to simple creatures without brains or minds, because those 'cartooned abstractions of who…](https://sms4smile.com/quotes/antonio-damasio/in-self-comes-to-mind-i-pay-a-lot-of-attention-to-simple-creatures/) [Antonio Damasio](https://sms4smile.com/quotes/author/antonio-damasio/) > [Don't get stuck on the level of words. A word is no more than a means to an end. It's an abstraction. 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We are for…](https://sms4smile.com/quotes/aldous-huxley/our-perceptions-of-the-external-world-are-habitually-clouded-by-the/) [Aldous Huxley](https://sms4smile.com/quotes/author/aldous-huxley/) [Browse all 562 Abstraction quotes ](https://sms4smile.com/quotes/about/abstraction/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "But we must not underestimate the potency of the mathematical process of abstraction. 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