- 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.
- 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.
- 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.
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.]