- Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns. [Lynn Arthur Steen, “The Science of Patterns” (1988).]
To understand how something works, we must be able to take it apart and then put it back together. Often this is the only way to see the details and understand the mechanics of operation. Intellectually, this is the process of analysis and synthesis, the best analog to evolution in a static state: evolution examines the details of operation over time, whereas analysis and synthesis examines the details of operation of a fixed entity.
This technique should be a part of standard primary and secondary education, and should be continued throughout every stage of learning and practice. It is as essential to an understanding of the forces that affect our lives as evolution is to biology. Its recognition and assimilation as an established and necessary part of education will mark a major step forward in the intellectual development of cultures. If civilizations are to survive and the people, broadly speaking, are to prosper, given the complexity of our technologies, the question is not whether this will occur but when.
Ernst Mayr was an extraordinary scholar and author on evolutionary theory. Over a long career (he worked until his death at age 100), he analyzed his chosen field of biology, and then was instrumental in bringing about the "modern evolutionary synthesis of Mendelian genetics, systematics, and Darwinian evolution. . ." He will long remain among the great celebrated figures in the biological sciences.
- Ernst Mayr, What Makes Biology Unique?: Considerations on the Autonomy of a Scientific Discipline (Cambridge University Press, 2004).
- Ernst Mayr, The Growth of Biological Thought: Diversity, Evolution, and Inheritance (Belknap Press, 1992).
- Ernst Mayr, This Is Biology: The Science of the Living World (Belknap Press, 1997).
- Ernst Mayr, Toward a New Philosophy of Biology: Observations of an Evolutionist (Harvard University Press, 1988).
Other notable analysts from various fields:
- John Lewis Gaddis, George F. Kennan: An American Life (The Penguin Press, 2011): "The debate in America between idealism and realism . . . played itself out inside (the) soul" of this "brilliant analyst of long-term trends" in foreign policy.
- Stephen Sondheim, Finishing the Hat: Collected Lyrics (1954-1981) with Attendant Comments, Principles, Heresies, Grudges, Whines and Anecdotes (Alfred A. Knopf, 2010). “’Finishing the Hat’ is essentially about . . . the process of writing songs for theatre.”
- Stephen Sondheim, Look, I Made a Hat: Collected Lyrics (1981-2001) With Attendant Comments, Amplifications, Dogmas, Harangues, Digressions, Anectdotes and Miscellany (Alfred A. Knopf, 2011). Stephen Sondheim analyzes his art.
- Samanth Subramanian, A Dominant Character: The Radical Science and Restless Politics of J.B.S. Haldane (Norton, 2020): “Thanks in good part to the insights of Haldane and a few other gifted, mathematically-minded researchers, evolutionary biology became a powerful science that embraces a vast range of temporal and physical scales, from the passage of geological ages to the collision of a single sperm and egg, from the biosphere to the gene.”
- Francesco Fiorani, The Shadow Drawing: How Science Taught Leonardo How to Paint (Farrar, Straus & Giroux, 2020): “Leonardo’s interests were not as dizzyingly disparate as they seem. His mind sought synthesis. He was hunting basic principles, the fundamental laws of all nature.”
History as analysis and synthesis:
- Richard Overy, Blood and Ruins: The Last Imperial War, 1931-1945 (Viking, 2022): “It will help you to grasp and revisit the carnage of 1931-45 as the largest event in human history. No continent, no ocean was spared, and Overy deftly weaves all the subplots into one planetary tapestry of merciless ideology and industrialized extermination.”
Books about analyzing and/or synthesizing:
- Margo Jefferson, Constructing a Nervous System: A Memoir (Pantheon Books): “If Margo Jefferson had gone into another profession — cabinetmaking, let’s say — she’d be the type to draw and redraw plans for a cabinet, build and tinker with the cabinet, stand back to look at the cabinet from every angle, probe the purpose of woodworking, take a break to go examine 2,000 other cabinets, then disassemble her own product and start from scratch with alternative tools, creating an object that no longer resembled a cabinet but performed all the functions of one in startling ways.”
- Gail Rothschild, Difficult Synthesis of Indigo (1961)
- M.C. Escher, Synthesis (1947)
- Wassily Kandinsky, Composition X (The Great Synthesis) (1939)
Music: Composers, artists, and major works
Beethoven knew he was approaching the end of his life when he composed his final opus, the String Quartet No. 16 in F major, Op. 135 (1826). To the untrained ear, or to those who are unaware of Beethoven’s history, this quartet may sound conventional. But others have noted that it is a distillation. This work brings to mind a T.S. Eliot poem, “Little Gidding”: “And the end of all our exploring / Will be to arrive where we started / And know the place for the first time.” However, the value of synthesis is not merely to die in peace or remembrance. The greater message in Beethoven’s music is that we can reflect on all the places we’ve been – physically, emotionally, intellectually – take stock, and move forward renewed and enriched.
- Inspired by the great transcendentalists who thrived in Concord, Massachusetts in the mid-19th century, Charles Ives constructed his Piano Sonata No. 2, “Concord, Mass., 1840-1860”, in the reverse order of complexity from the usual. Each movement is at its most dense at complex in the beginning, then trims down to one or two ideas. Thus, the work is a musical analog to the process of simplification by analysis.
- In Reich/Richter for large ensemble (2019), composer Steve Reich worked off a painting by Gerhard Richter, with whom he collaborated on the project, to create a musical composition that reduced sound to simple components, then expanded it again. This mirrored a process that Richter had used with his work of visual art. Reich explains the process, referencing Richter’s painting: “It starts with one of his abstract paintings from the ’90s. He scanned a photo of the painting into a computer and then cut the scan in half and took each half, cut that in half and two of the four quarters he reversed into mirror images. He then repeated this process of ‘divide, mirror, repeat’ from half to quarter, eighth, sixteenth, thirty-second, all the way up to 4096th. The net effect is to go from an abstract painting to a series of gradually smaller anthropomorphic ‘creatures’ (since the mirroring produces bilateral symmetry) to still smaller ‘psychedelic’ abstractions to very fine stripes.”
- Jóhann Jóhannsson, Drone Mass (2015): “. . . the work represents what the Icelandic composer called ‘a distillation of a lot of influences and obsessions’. As the title suggests, those obsessions include his fascination with the musical device of the drone. This was something Jóhannsson felt as a visceral presence, ‘a fundamental vibration that anchors music and gives you a foundation’. He often used both acoustic and electronic drones – sometimes gently underpinning the music, sometimes drowning out everything else.”
- Frankel, Symphony No. 1, Op. 33 (1958): In the first movement, per the composer, “the tonal debate, between tonic and dominant, is raised to the higher and more complex area of multitonality, and where the constant renewing of thematic elements replaces the notions of 1st subject, 2nd subject, development, etc.”; the second movement presents contrasting textures and a kaleidoscope of scenes [Buxton Orr]; the concluding movement offers a plain melody, which is turned on its head but persists until the work concludes.
- Foulds, Dynamic Tryptich for Piano and Orchestra, Op. 88 (1929): the three movements are titled “Dynamic Mode”, “Dynamic Timbre” and “Dynamic Rhythm”, suggesting the analysis of music through component parts.
- Christian McBride & Inside Straight, "People Music": on this album of swing music, McBride’s aptly-named quintet brings soaring solos together in brilliant synthesis.
- Ran Dank, “Vers le silence”: “By interpreting William Bolcom’s Twelve New Études with works of Chopin, Dank casts provocative light on these composer-pianists, resulting in intriguing juxtapositions.” [Jed Distler, Gramophone magazine, November 2021 issue, p. 58.]
- Ches Smith, “Interpret It Well”: “Throughout the album, subtle sketches are explored and exploded, minimal ideas often turning into cathartic group journeys.”
- Nduduzo Makhathini, “In the Spirit of Ntu”: on this album, Makhathini brings together his previous work.
1831 and 1832, the two years which are immediately connected with the Revolution of July, form one of the most peculiar and striking moments of history. These two years rise like two mountains midway between those which precede and those which follow them. They have a revolutionary grandeur. Precipices are to be distinguished there. The social masses, the very assizes of civilization, the solid group of superposed and adhering interests, the century-old profiles of the ancient French formation, appear and disappear in them every instant, athwart the storm clouds of systems, of passions, and of theories. These appearances and disappearances have been designated as movement and resistance. At intervals, truth, that daylight of the human soul, can be descried shining there. This remarkable epoch is decidedly circumscribed and is beginning to be sufficiently distant from us to allow of our grasping the principal lines even at the present day. We shall make the attempt. The Restoration had been one of those intermediate phases, hard to define, in which there is fatigue, buzzing, murmurs, sleep, tumult, and which are nothing else than the arrival of a great nation at a halting-place. These epochs are peculiar and mislead the politicians who desire to convert them to profit. In the beginning, the nation asks nothing but repose; it thirsts for but one thing, peace; it has but one ambition, to be small. Which is the translation of remaining tranquil. Of great events, great hazards, great adventures, great men, thank God, we have seen enough, we have them heaped higher than our heads. We would exchange Cæsar for Prusias, and Napoleon for the King of Yvetot. "What a good little king was he!" We have marched since daybreak, we have reached the evening of a long and toilsome day; we have made our first change with Mirabeau, the second with Robespierre, the third with Bonaparte; we are worn out. Each one demands a bed. [Victor Hugo, Les Misérables (1862), Volume IV – Saint-Denis; Book First – A Few Pages of History, Chapter I, Well Cut.]
Revolt is a sort of waterspout in the social atmosphere which forms suddenly in certain conditions of temperature, and which, as it eddies about, mounts, descends, thunders, tears, razes, crushes, demolishes, uproots, bearing with it great natures and small, the strong man and the feeble mind, the tree trunk and the stalk of straw. Woe to him whom it bears away as well as to him whom it strikes! It breaks the one against the other. It communicates to those whom it seizes an indescribable and extraordinary power. It fills the first-comer with the force of events; it converts everything into projectiles. It makes a cannon-ball of a rough stone, and a general of a porter. [Victor Hugo, Les Misérables (1862), Volume IV – Saint-Denis; Book Tenth – The 5th of June, 1832, Chapter I, The Surface of the Question.]
- George Saunders, A Swim in a Pond in the Rain: In Which Four Russians Give a Master Class on Writing, Reading, and Life (Random House, 2021): analyzing seven classic Russian short stories.
- Frederic Tuten, The Bar at Twilight: Stories (Bellevue Literary Press, 2022): “. . . full of bittersweet portraits of artists and the places that shaped them.”
Books about poetry: