--- title: "Meaning & Key Takeaway of: The page of my notebook was filled with…" description: "\"The page of my notebook was filled with many messy integrals, but all of a sudden I saw emerge a formula for counting. I had begun to calculate a quant..." image: "https://sms4smile.com/quotes/i/27b/lee-smolin-4171_answers_the-page-of-my-notebook-was-filled-with_819721.jpg" --- # The page of my notebook was filled with many messy… ![“The page of my notebook was filled with many messy integrals, but all of a sudden I saw emerge a formula for counting. I had begun to calculate a quantity on the assumption that the result was a real number, but found instead that, in certain units, all the possible answers would be integers. This…” quote by Lee Smolin](https://sms4smile.com/quotes/i/27b/lee-smolin-4171_answers_the-page-of-my-notebook-was-filled-with_819721.jpg) [Download](https://sms4smile.com/quotes/i/27b/lee-smolin-4171_answers_the-page-of-my-notebook-was-filled-with_819721.jpg) [Open image](https://sms4smile.com/quotes/i/27b/lee-smolin-4171_answers_the-page-of-my-notebook-was-filled-with_819721.jpg) > “The page of my notebook was filled with many messy integrals, but all of a sudden I saw emerge a formula for counting. I had begun to calculate a quantity on the assumption that the result was a real number, but found instead that, in certain units, all the possible answers would be integers. This meant that areas and volumes cannot take any value, but come in multiples of fixed units.” [Lee Smolin](https://sms4smile.com/quotes/author/lee-smolin/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Discovery that physical quantities are quantized, suggesting space and volume come in discrete units rather than continuous values. **In simple terms:** Physical quantities may be fundamentally discrete. Key Takeaway Recognize the role of quantization in physics. Themes physics quantization philosophy of science mathematics Mood curious thoughtful Type analytical philosophical When to use this quote - research labs - academic study - theoretical modeling Key Concepts discrete vs continuous unit theory measurement theoretical insight Questions to Reflect On - How does quantization affect our view of reality? - What evidence supports discrete space? A Different Perspective Quantization may be an emergent approximation, not fundamental. ★ ★ ★ ★ ★ No ratings yet [Assumption](https://sms4smile.com/quotes/about/assumption/) [Integers](https://sms4smile.com/quotes/about/integers/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Notebook](https://sms4smile.com/quotes/about/notebook/) [Values](https://sms4smile.com/quotes/about/values/) ## Related quotes > [Is a woman a thinking unit at all, or a fraction always wanting its integer?](https://sms4smile.com/quotes/thomas-hardy/is-a-woman-a-thinking-unit-at-all-or-a-fraction-always-wanting-its/) [Thomas Hardy](https://sms4smile.com/quotes/author/thomas-hardy/) > [ \[L\]ife ceases to be a fraction and becomes an integer. ](https://sms4smile.com/quotes/harry-emerson-fosdick/l-ife-ceases-to-be-a-fraction-and-becomes-an-integer/) [Harry Emerson Fosdick](https://sms4smile.com/quotes/author/harry-emerson-fosdick/) > [The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one…](https://sms4smile.com/quotes/kurt-g-del/the-development-of-mathematics-towards-greater-precision-has-led-as/) [Kurt Gödel](https://sms4smile.com/quotes/author/kurt-g-del/) > [Integers are the fountainhead of all mathematics.](https://sms4smile.com/quotes/hermann-minkowski/integers-are-the-fountainhead-of-all-mathematics/) [Hermann Minkowski](https://sms4smile.com/quotes/author/hermann-minkowski/) > [In this communication I wish first to show in the simplest case of the hydrogen atom (nonrelativistic and undistorted) that the usual rates for…](https://sms4smile.com/quotes/erwin-schrodinger/in-this-communication-i-wish-first-to-show-in-the-simplest-case-of/) [Erwin Schrodinger](https://sms4smile.com/quotes/author/erwin-schrodinger/) > [I read in the proof sheets of Hardy on Ramanujan: "As someone said, each of the positive integers was one of his personal friends."…](https://sms4smile.com/quotes/john-edensor-littlewood/i-read-in-the-proof-sheets-of-hardy-on-ramanujan-as-someone-said-each/) [John Edensor Littlewood](https://sms4smile.com/quotes/author/john-edensor-littlewood/) > [The gods and their tranquil abodes appear, which no winds disturb, nor clouds bedew with showers, nor does the white snow, hardened by frost,…](https://sms4smile.com/quotes/lucretius/the-gods-and-their-tranquil-abodes-appear-which-no-winds-disturb-nor/) [Lucretius](https://sms4smile.com/quotes/author/lucretius/) > [The series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences.](https://sms4smile.com/quotes/albert-einstein/the-series-of-integers-is-obviously-an-invention-of-the-human-mind-a/) [Albert Einstein](https://sms4smile.com/quotes/author/albert-einstein/) > [Increasing pressure on students to subject themselves to ever more tests, whittling themselves down to rows and rows of tight black integers upon a…](https://sms4smile.com/quotes/leah-hager-cohen/increasing-pressure-on-students-to-subject-themselves-to-ever-more/) [Leah Hager Cohen](https://sms4smile.com/quotes/author/leah-hager-cohen/) > [Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a…](https://sms4smile.com/quotes/gregory-bateson/numbers-are-the-product-of-counting-quantities-are-the-product-of/) [Gregory Bateson](https://sms4smile.com/quotes/author/gregory-bateson/) > [If we can dispel the delusion that learning about computers should be an activity of fiddling with array indexes and worrying whether X is…](https://sms4smile.com/quotes/anonymous/if-we-can-dispel-the-delusion-that-learning-about-computers-should-be/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [God made the integers, man made the rest.](https://sms4smile.com/quotes/leopold-kronecker/god-made-the-integers-man-made-the-rest/) [Leopold Kronecker](https://sms4smile.com/quotes/author/leopold-kronecker/) > [Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next…](https://sms4smile.com/quotes/abraham-robinson/arithmetic-starts-with-the-integers-and-proceeds-by-successively/) [Abraham Robinson](https://sms4smile.com/quotes/author/abraham-robinson/) > [The Good Lord made all the integers; the rest is man's doing.](https://sms4smile.com/quotes/leopold-kronecker/the-good-lord-made-all-the-integers-the-rest-is-man-s-doing/) [Leopold Kronecker](https://sms4smile.com/quotes/author/leopold-kronecker/) > [God made the integers; all else is the work of man.](https://sms4smile.com/quotes/leopold-kronecker/god-made-the-integers-all-else-is-the-work-of-man/) [Leopold Kronecker](https://sms4smile.com/quotes/author/leopold-kronecker/) ## More by Lee Smolin > [“This unification of forces and motion has a simple consequence. In a particle theory, you can freely add all kinds of forces, so there…](https://sms4smile.com/quotes/lee-smolin/this-unification-of-forces-and-motion-has-a-simple-consequence-in-a/) [Lee Smolin](https://sms4smile.com/quotes/author/lee-smolin/) > [“One field Faraday studied was the electric field. This is not a number but a vector, which we may visualize as an arrow and…](https://sms4smile.com/quotes/lee-smolin/one-field-faraday-studied-was-the-electric-field-this-is-not-a-number/) [Lee Smolin](https://sms4smile.com/quotes/author/lee-smolin/) > [“It is interesting to note that the quantum-mechanical revolution was made by a virtually orphaned generation of scientists. Many members of the generation above…](https://sms4smile.com/quotes/lee-smolin/it-is-interesting-to-note-that-the-quantum-mechanical-revolution-was/) [Lee Smolin](https://sms4smile.com/quotes/author/lee-smolin/) > [“In fact, the particle-antiparticle annihilation and the closing of the string is necessary, if the theory is to be consistent with relativity, meaning the…](https://sms4smile.com/quotes/lee-smolin/in-fact-the-particle-antiparticle-annihilation-and-the-closing-of-the/) [Lee Smolin](https://sms4smile.com/quotes/author/lee-smolin/) > [Every string theory that's been written down says the speed of light is universal. But other ideas about quantum gravity predict the speed of…](https://sms4smile.com/quotes/lee-smolin/every-string-theory-that-s-been-written-down-says-the-speed-of-light/) [Lee Smolin](https://sms4smile.com/quotes/author/lee-smolin/) > [“Unfortunately, no one has ever successfully postulated a super-symmetry holding between two known particles. 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