Reason's Inclination to Unity and Simplicity: From the Greeks to Einstein and Aquinas on God

Orientation #

He opens by saying the last two Heraclitus fragments were “a beautiful way to end” and that he now stops with the fragments to look at the “secondary reading” handout; the last part of that handout (“moderns on the movers,” from page five) is deferred until after Empedocles and Anaxagoras have been seen. He closes: “next time we’ll start looking at Empedocles.” The previous class worked through Parmenides and Heraclitus and ended with fire as first principle; the next treats Empedocles’ four roots.

The class, in order #

1. The first philosophers and the principle of fewness (“looked for something one, simple and unchanging”) #

Point: Thales, Anaximenes, Pythagoras, Heraclitus all sought one, simple, eternal, unchanging (perhaps also unlimited) beginning of all things, and in doing so were “listening to reason”; the same inclination appears in the great modern physicists.

• The principle of fewness, as Aristotle uses it: fewer causes are better if they suffice; “sometimes called the principle of simplicity.” Einstein will call it the underlying principle of all natural philosophy; for Newton it is the basic principle.
• Shakespeare cited as a reflection of the same inclination: “fewness and truth, ’tis thus”; Troilus: “I am as true as truth’s simplicity, and simpler than the infancy of truth.”
• His selection: three great minds of the opening century of modern science (Galileo, Kepler, Newton) and then the 20th century, to show the tendency at both ends.

2. Galileo led by the hand of nature (“led by hand, as it were”) #

Point: in studying naturally accelerated motion (a stone falling faster and faster) Galileo says he was “led by hand” by nature’s habit of using the most common, simple and easy means.

• “Led by hand” is Thomas’s manuductio (Monsignor Dion “gave many courses on manuductio”).
• Fish and birds: no one thinks swimming or flying could be done more simply than they do it; so why not expect a falling stone to gain speed in the simplest way? Result: equal increments of speed in equal units of time (not equal distances), “the simplest way it could increase its speed.”
• Caution he flags: the word “easy” — the simple is not always easy for us to understand (returned to under Einstein and God).

3. Kepler and Newton (“nature loves simplicity and unity”) #

• Kepler spent ten years looking for a simple geometrical figure to fit the planets’ paths and found the ellipse (with its equation); note he searched ten years convinced something simple would be found: “nature loves simplicity and unity.”
• Newton united terrestrial mechanics (Galileo) and celestial mechanics (Kepler); still calls the whole of natural science “philosophy”; 20th-century physicists call 17th-19th century physics “classical” or “Newtonian” after him.
• Newton’s first rule (read): admit no more causes of natural things than are true and sufficient to explain their appearances; nature does nothing in vain, more is in vain when less will serve, nature “affects not the pomp of superfluous causes.” His comment: this is called simplicity but is better called fewness — fewer are better if sufficient; Aristotle uses the principle many times.

4. Planck: one simple principle; the more general, the simpler (“the more general a natural law”) #

Point: the father of 20th-century physics states the same goal as the Greeks.

• Background as he gives it: December 1900 quantum hypothesis, from black-body radiation where older theories gave absurdities (infinite energies); energy can be given or received only in a smallest amount or its multiples. Heisenberg’s story: Planck told his son on a walk he had found something as great as Newton; Einstein’s Nobel Prize five years later (photoelectric effect, light involves the quantum); Bohr 1913 applied it to the atom; by 1913 nothing in the physical world was without the quantum.
• Planck (read): the highest goal of physical science “as long as it exists” is to embrace all phenomena in one simple principle allowing past and future occurrences to be calculated; the chief purpose of each science “is and always will be” the unifying of its theories into one.
• The line he loves: “the more general a natural law is, the simpler is its form.” This launches the Euclid digression.

5. Euclid II.5: the square has more area for the same perimeter (“the square will always have more area”) #

Point: a simple geometrical fact that anticipates Planck’s line, brevity of wit, and God’s simplicity.

• Aside on statement vs. wonder: Euclid’s statement of II.5 does not arouse wonder, unlike Zeno, whose arguments Aristotle says were put “with a certain tragedy” (quadam tragoedia), Thomas commenting “a certain magnification of words to arouse wonder” (Achilles and the tortoise).
• The theorem as he states it: cut a line into equal and unequal segments; the rectangle of the unequal segments plus the square on the segment between the points of section equals the square on the half.
• What it shows: among rectangles the square has most area for a given perimeter, and the difference is always a square on the difference between the oblong’s side and the square’s side. Examples, perimeter 20: 5×5 = 25; 4×6 = 24 (difference 1 = 1²); 3×7 = 21 (4 = 2²); 2×8 = 16 (9 = 3²). “Same fence, less land.”
• Ancient crooked geometers sold land by perimeter; the “dummies” who estimated an island by sailing time (indentations lengthen the trip).
• The crazy case: 2×10 has perimeter 24 but area 20, less than 5×5 — so the simplest rectangle can have more area for less perimeter. Practical aside: fencing a play-yard for tots, buy the fence “down in Spags,” make it square.
• Analogies drawn: Shakespeare “brevity is the soul of wit”; the wise man says more with fewer words, the Bible’s fool multiplies words; then God: the first thing shown is that He is first cause of all (causality extends to all), the next that He is the simplest thing — the most universal cause is the simplest.

6. Born, Einstein, Jeans, Schrödinger (“believes obstinately in the unity and simplicity”) #

• Max Born (read): “the genuine physicist believes obstinately in the unity and simplicity of nature despite any appearance to the contrary.” His comment: “despite appearance” shows it is a natural inclination, not evidence. Born knew the genuine ones (Einstein, Bohr, Heisenberg — Heisenberg’s hay fever sent him to the ocean). Born’s context: the periodic table, ~92 to nearly 100 elements — “that can’t be 100 first matters”; atoms seemed near-multiples of hydrogen; before electron/proton/neutron reduced 100 to three, the mind was already convinced of more unity.
• Heisenberg: a German physics auditorium has the Latin motto “the simple is the seal of truth.”
• Einstein, Evolution of Physics (read): from Greek philosophy to modern physics, constant attempts to reduce the apparent complexity of phenomena to a few fundamental ideas — “the underlying principle of all natural philosophy.”
• Einstein, Columbia talk (read): the simplest system is not the one a student assimilates most easily but the one with the fewest mutually independent postulates. A fortiori of God: simplest, yet the most difficult to understand.
• Einstein, method lecture in England (Oxford, he thinks; read): the grand object of theory is to make the irreducible elements as simple and few as possible without renouncing any empirical content.
• Bohr’s colleagues said he had the attitude to nature of the early Greeks.
• Student (former programmer): code is honed down, and concise code doing the same thing is admired; DB: his daughter’s small computer with twice the power of his big one.
• Jeans (read): of two hypotheses fitting the facts, we provisionally choose the simpler as more likely to lead to truth — they are led by simplicity even where the facts do not decide.
• Schrödinger, Nature and the Greeks: “science is the Greek way of looking at things”; Einstein’s gravitation could only be found by a genius with a strong feeling for the simplicity and beauty of ideas; attempts to extend it to electromagnetism and nuclear forces hope to get “the clue from the principle of simplicity and beauty.” So the principle is called fewness, simplicity, or beauty (cf. the Pythagorean theorem’s simplicity, and II.5’s difference being itself a square).

7. Heisenberg and Weizsäcker: mathematical simplicity as heuristic (“the highest heuristic principle”) #

• Heisenberg (read): Pythagoreans found strings harmonize when lengths are in simple ratio (like the 2:1 seen earlier); harmony appears to the ear only when mathematical relations are realized; this is one of the strongest impulses of science, and modern science keeps confidence in a simple mathematical basis even for relations not yet grasped. “Mathematical simplicity ranks as the highest heuristic principle.”
• Heuristic: from Greek heurein, to find — the principle of discovery.
• Aside on Heisenberg: invented quantum mechanics, first to say the nucleus is protons and neutrons (after the 1932 neutron), formulated indeterminism, “the greatest change in physics since Newton” (to be treated later).
• Weizsäcker (pupil of Heisenberg; theory of the solar system’s origin and why the sun keeps burning; read): we have no more explanation than Kepler had for the fact that the laws which hold are distinguished by a high degree of mathematical simplicity; economy of thought explains why we look for simple laws, not why we find them.

8. Conservation and the unlimited (“stand on his head to keep the conservation”) #

Point: the moderns’ conservation laws answer to the Greeks’ eternal first matter that remains through change under different forms (cf. Anaximander).

• Heisenberg: any coherent set of physical axioms contains energy, momentum, angular momentum and their conservation; Newton’s three laws reduce to conservation of momentum. Rothman: the conservation laws are the most basic laws of nature, and he begins with the same three.
• Weizsäcker’s example as DB tells it: a cart down and up a hill — height lost is potential energy turned to kinetic, then back; “you dummies” object it doesn’t reach the same height — the warm tracks show heat energy, later made mathematically equivalent to mechanical energy (the locomotive). Height and speed seem to have nothing in common, but the scientist “stands on his head” to make them two forms of one conserved thing.
• The unlimited (not on the handout): Shakespeare’s Mother Earth, “whose womb immeasurable and infinite breast feeds all”; modern equations have something infinite — from F = ma one calculates an infinity of numbers.

9. Thomas’s five attributes; four anticipated (“four of the five, at least in name”) #

Point: the mind naturally seeks something one, simple, unlimited, unchanging; Thomas’s treatise on the substance of God turns on those four plus “perfect.”

• ST I: q. 2 existence; qq. 3-11 substance: 3 simplicity, 4 perfection, 5-6 goodness, then infinite with “everywhere” attached, unchanging with “eternal” attached, finally one. SCG: the same five. Eternity goes with unchangeable, everywhere with infinite, measure of all with one, goodness with perfect.
• Why “perfect” is missing: the Greeks thought of the first cause as matter, which is imperfect; it is added with higher causes. God is not unlimited in exactly their way, but not purely equivocally either.
• Thomas will give reasons; the mind is already inclined that way — “He built that into our mind.”
• Plan restated: Empedocles next; the mover section after Anaxagoras.

10. After class: the mind made for God; simplicity and beauty (“forced by the truth itself”) #

• Student: is the inclination because the mind is itself simple? DB: Augustine’s restless heart made for God; the mind is made for knowing God, inclined toward Him “without realizing it.”
• Aristotle’s phrase about the Greeks, “forced by the truth itself”; Thomas reuses it in SCG I on the infinity of God (about 16 reasons, “crazy number”), then notes the Greeks were forced by truth to an infinite beginning but wrongly took it for a body. Born’s “obstinately” is the same inclination.
• Angels get simpler and more universal in causality as one ascends to God; Teresa of Avila: God is altogether simple, and the nearer one gets, the simpler — the simplicity of saints.
• Poetics: tragedy vs. epic, both represent men greater than us and arouse pity and fear; Homer is greatest, yet tragedy is the higher form — one reason: it achieves the purgation with fewer words and scenes, and has more unity.
• Students: simplicity and beauty in art and music — he prefers Haydn, Mozart, Bach, Handel to modern classical (Haydn’s first symphony on WCRB that day, [unclear in recording] the number); Gregorian chant; plays (Sophocles, Shakespeare) superior to novels, the play “more concentrated.”
• His paper comparing the two Summas’ five attributes; Thomas never says how he arrived at the five, “my number five again.”

11. The two criteria for the end of the mind; the good and beautiful; measure (“the end is called the causa causarum”) #

1. De Anima I: knowledge of a better thing is better; so the end of knowing is knowledge of the best thing.
2. Metaphysics I: we know the way things are but not why; so the end of knowing is knowledge of the first cause.
3. If the first cause is the best thing, all harmonizes (Ethics: “with the truth all things harmonize”). Marxists (“mind is the highest product of matter”) divorce the two — the mind aims at the first cause and at the best, which are not the same: “schizophrenia.”

• Plato, Symposium: the ascent to the beautiful itself, the same as the good itself of the Republic — God. Augustine, Confessions: “too late have I come to know thee, thou ancient beauty.”
• Four causes: the maker is responsible for matter and form (wood and shape of a chair), the end for the maker (sitting); the end is causa causarum. Hence Aristotle shows God is first mover and then first end; if not first end, not first cause; the end being better, God is the best. So the mind tends to something perfect too, which strengthens one to see the reasons later.
• Natural theology fragments: Xenophanes [transcript: “Xenophon”]: no one really knows God, yet “the whole of God sees, the whole of God hears” — no parts, understanding and will one; we too think the soul (most godlike part) finer and thinner, an air-like thing through the body, though it is not spread like air; “nobody thinks the body is more godlike than the soul.”
• Jumping into theology without natural philosophy makes the five attributes seem “out of the blue”; Vatican II on Thomas: not that he says more than the Fathers but that he unifies and orders — Church documents list eternal, simple, unchanging without seeing eternal and unchanging go together. He ordered: existence, substance (the five), operations.
• Suggested addition: a question whether God is the measure of all things (Plato, Laws, against Protagoras’ “man is the measure” — modern humanism), attachable to “one,” since in the Metaphysics being a measure is a property of the One; Thomas attaches nothing to simplicity or oneness. The two Summas differ slightly in order, both instructive.

12. Fragment: the accidental and “carpenters play the violin” (“Do carpenters play the violin”) #

Sophism reported: you know nothing not in your mind; so all you know is in your mind; so you know nothing outside it. Reply: what I know is in my mind when known, but it does not follow it is only in my mind — the mistake of the accidental (first kind outside of words): the definition of square (equilateral right-angled quadrilateral) is in my mind, but “in my mind” is not put in the definition. Distinction: what belongs as such vs. what happens: a carpenter may happen to play the violin, but not as carpenter. Deception comes where the accidental is necessarily found; to return with Aristotle (Plato somewhat involved). [Recording ends mid-sentence.]

His words #

• principle of fewness — fewer causes are better if they suffice; “sometimes called the principle of simplicity” [ed.: parsimony]
• manuductio — being “led by the hand”; Galileo’s phrase, also Thomas’s
• naturally accelerated motion — free fall gaining equal speed in equal times
• classical / Newtonian physics — 17th-19th century physics, named after Newton
• quantum hypothesis — energy given or received only in a smallest amount or its multiples
• quadam tragoedia — Aristotle on Zeno; Thomas: “magnification of words to arouse wonder”
• heuristic — from heurein, to find; principle of discovery
• conservation laws — modern analogue of the eternal first matter remaining through change
• the five attributes of the divine substance — one, simple, unchanging, unlimited, perfect
• forced by the truth itself — Aristotle’s phrase for the Greeks, reused by Thomas
• causa causarum — the end, cause of the other causes being causes
• as such vs. what happens — the per se and the accidental [ed.: per se / per accidens]

Texts #

Read in class

• Galileo, Dialogues Concerning Two New Sciences, on naturally accelerated motion
• Newton, Principia, first rule of reasoning
• Planck, collected papers (three passages, incl. “the more general a natural law…”)
• Euclid, Elements II.5 (stated and exemplified, not proved)
• Max Born, on the genuine physicist (periodic-table context)
• Einstein, The Evolution of Physics; Columbia talk (in Essays in Science); “On the Method of Theoretical Physics” (England, Oxford he thinks)
• Sir James Jeans, on two hypotheses
• Schrödinger, Nature and the Greeks
• Heisenberg, Philosophic Problems in Nuclear Science (Pythagoras; heuristic principle); Heisenberg on conservation
• Weizsäcker, on mathematical simplicity; on energy conservation (retold)
• Milton Rothman, on conservation laws
• Shakespeare: “fewness and truth”; Troilus on truth’s simplicity; “brevity is the soul of wit”; “womb immeasurable and infinite breast”

Mentioned

• Aristotle, Physics on Zeno; Thomas’s commentary
• Aristotle, Poetics (tragedy vs. epic); De Anima I; Metaphysics I (and the One as measure); Ethics (“with the truth all things harmonize”)
• Thomas, ST I qq. 2-11; SCG I (infinity of God, ~16 reasons)
• Augustine, Confessions (restless heart; “ancient beauty”)
• Plato, Symposium, Republic, Laws (God the measure)
• Xenophanes [transcript: “Xenophon”], “the whole of God sees”
• Heisenberg’s lecture on the history of quantum theory (Planck anecdote)
• Teresa of Avila; Vatican II on Thomas; the Bible on the fool’s words
• His own paper comparing the two Summas

His questions #

• As a stone falls, what does its speed do, and how does Galileo conclude it increases? Faster and faster; equal increments of speed in equal times — the simplest way.
• Why is “despite any appearance to the contrary” (Born) evidence of a natural inclination? Appearances would be a reason against; the mind is inclined anyway.
• With the same perimeter of 20, what happens to area as you leave the square? 25, 24, 21, 16 — less and less, always differing by a square.
• Can a rectangle have less perimeter and more area than another? Yes: 5×5 (perimeter 20, area 25) vs. 2×10 (perimeter 24, area 20).
• What do we show about God first, and what next? First cause of all things; then that He is the simplest thing.
• Does “simplest” mean easiest to understand? No — God is simplest and hardest to understand (Einstein: fewest postulates, not easiest for a student).
• Which of Thomas’s five attributes is not anticipated by the Greeks and scientists, and why? Perfect — they thought of the first cause as matter, which is imperfect.
• Which is the greater form, tragedy or epic, and why? Tragedy: the same effect with fewer words and more unity.
• Does it follow from “everything I know is in my mind” that I know nothing outside it? No — the mistake of the accidental (carpenters and violins).
• Where does the deception of the accidental chiefly arise? Where the accidental is necessarily found — left open, to be resumed with Aristotle.