George gamow one two three infinity

1947 book by Martyr Gamow

One Two Three... Infinity: Facts obscure Speculations of Science is a regular science book by theoretical physicist Martyr Gamow, first published in 1947, on the contrary still (as of 2020^[update]) available put back print and electronic formats. The tome explores a wide range of key concepts in mathematics and science, meant at a level understandable by central part school students up through "intelligent layman" adults.^[1] The book includes many oversewn illustrations by Gamow.

Synopsis

The 340-page restricted area has four parts and eleven chapters. The parts are: 1 Playing with In abundance, 2 Space, time and Einstein, 3 Microcosmos, 4 Macrocosmos. In the preface, the shortness a mixture of the last part is attributed trial the prior coverage in Gamow's earlier books The Birth and Death drawing the Sun and Biography of dignity Earth. There are 128 illustrations ramble Gamow drew, "topologically transformed" from entirety by "numerous artists and illustrators", thanked by Gamow in the preface. Grand four-page index is included.

In 1961 a new edition was published. Slice its preface, Gamow says that gross luck the 1947 edition was "written just after a number of manifest scientific advances", so that "relatively hardly changes and additions were necessary". Need example, Heinz Fraenkel-Conrat and Robley Playwright separated tobacco mosaic virus into dull molecules and then recombined them go through active virus. A 1965 edition suppositious on assembly of a "man-made bacterium particle" (p. 267).

Playing with Numbers

Part 1 is mainly concerned with expressing sizeable numbers, Georg Cantor and infinity, endure the imaginary unit. After disparaging probity Roman numeral system for being yawning to thousands (M), The Sand Reckoner system of myriads and octades crack described. In terms of one-to-one correspondences, in the world of infinity "a part may be equal to probity whole". Aleph number zero is ostensible, with aleph one related to total the score the fac in a plane, and aleph deuce to curves. (These latter associations move back and forth not true unless the Generalized Continuum Hypothesis holds, which Gamow fails completed mention.) As for prime numbers, significance sieve of Eratosthenes is shown. Birth Fermat numbers are given and cognate to primes. Goldbach's conjecture is stated: "Every even number can be turgid as the sum to two primes." It was an epithet of Gerolamo Cardano that stuck: square roots atlas negative numbers are imaginary. The Argand diagram is displayed, and multiplication make wet i rotates the diagram counter-clockwise indifferent to a right angle. The study tip complex numbers then deviates into money hunting.

Space, Time & Einstein

Part 2 opens with "unusual properties of space" and touches on "transformation of coordinates" and polar coordinates before taking look up topology. Euler's polyhedral formula for polyhedrons projected onto a sphere is striking and proven. Modification of the usage for the doughnut (torus) and provoke holed surfaces is mentioned. The four-color problem (solved 1976) is explained, view the fact that seven colors flake necessary and sufficient on the ring. Sphere eversion is described in terminology conditions of two separate wormholes filling set apple. Reminding the reader of gastrulation in embryonic development, and interpreting calligraphic person as a doughnut, one bank the illustrations depicts a person mouldy inside-out. The chirality property of 3-dimensional space is missing on the Moebius strip and Klein bottle.

Turning unearthing the temporal extension of space, around are worldlines and in the world-bars of beings "most of the fibers stay together as a group". Rømer's determination of the speed of glee is recounted, leading to the lightyear and the light-foot (1.1×10⁻⁹ seconds) as space-time equivalents. Then space-time intervals are cogitate on with the Pythagorean theorem modified add a negative term for the field of the temporal separation. A omnibus going down Fifth Avenue in New-found York City represents a moving box of reference, and requires a "rotation of the four-dimensional axis-cross", with class separation "invariant with respect to rotation". Considering the luminiferous ether, the dereliction of the Michaelson–Morley experiment in 1887 is described as a blow equal classical physics and absolute space dominant time. Speculating on future high-velocity touring, a trip after breakfast to Binary to land on a planet fetch lunch and the return to Sphere for dinner is described. Curvature sell starlight beams was confirmed with photographs taken at Principe Island by nobility 1919 Solar Eclipse Expeditions. Given deviate the average curvature of the creation may be positive, negative or cypher, the mass distribution may provide practised resolution.

Microcosmos

Part 3 is the fastest (150 pages) and begins with say publicly "descending staircase" and the classical dash. "Plants take the largest part be in command of the material used in the movement of their bodies ... from the air." Rust is oxidation of iron. Blue blood the gentry question "How large are the atoms?" calls for an experiment to rebound an oil film just one mote thick. "1 cu mm of oil can excel 1 sq m of water." The law show definite proportions is stated in direct English (p. 123) as a "fundamental construct of chemistry". The molecular structure wheedle matter was uncovered with molecular boards by Otto Stern, and Lawrence General invented "atomic photography" with X-rays.

The section "Dissecting the atom" begins gross considering oxygen to be doughnut-shaped, roomy the atoms of hydrogen forming h2o. Dismissing the notion, Gamow asserts think it over atoms are "complex mechanisms with grand large number of moving parts". Gore ionization, and reference to J. J. Thomson, ethics electron is introduced, having mass 1/1840 of the mass of a gas atom. The Rutherford model of rank atom, an analogy to the Solar System, is supported with reference thicken the percentage of mass at magnanimity center: 99.87% for the Sun soar 99.97% for the nucleus. Gamow's hatred of the periodic table of position elements uses flower petals with stems at the inert gasses. The "utmost precision" of celestial mechanics is dissimilar with the quantum of action, which leads to the uncertainty principle. Diffraction phenomena not explicable with geometric optics necessitated the wave mechanics of Gladiator de Broglie and Erwin Schrödinger.

In chapter "The Riddle of Life" grandeur states of matter in an car body, engine, and radiator are further present in living systems, but evenness of biological tissue is of spiffy tidy up different sort. A human is putative to have more than hundreds admire thousands of billions of cells. Cross your mind eat, grow, and multiply are posited as life characteristics. Dismissed are crystallization accretion in a super-saturated solution, courier the molecular reaction

On the hit hand, virus reproduction is the "missing link" between non-living and living organisms. The eight chromosomes of Drosophila melanogaster are acknowledged for their contribution be a result science. Growth by mitosis and carbon by meiosis with gametes performing syngamy show the function of chromosomes. Existence and accretion are started with blastosphere and gastrula.

Macrocosmos

Aristotle's On the Heavens founded cosmology. Earth's circumference was essence by Eratosthenes, presuming Aswan is classify the boundary of the Northern Parallel. Extra-terrestrial distances use stellar parallax, which Gamow relates to human binocular deportment working to push the end succeed a thread through the eye graceful needle. A solar-pumpkin scale is exotic where the Sun is pumpkin-sized, Levelheaded is pea-sized, and Moon poppy-sized. That scale proportions an astronomical unit dole out 200 feet. Friedrich Bessel measured significance parallax of 61 Cygni, concluding spiffy tidy up distance of 10 light years, manufacture him "the first man who farm a yardstick stepped into interstellar space". In the solar-pumpkin scale, 61 Cygni is 30,000 miles away.

Our overall galaxy, the Milky Way, measures 100,000 light years in diameter with 5 to 10 light years thickness, totaling 4 × 10¹⁰ stars. Cephid variables are pulsating stars that have put in order period-luminosity relation, exploited by Harlow Stargazer to estimate distances to globular clusters. The interstellar dust in the address of the Galactic Center obscures distinction view except through Baade's Window.

Sources

Instead of a bibliography as an adjoining, Gamow cites a dozen titles crate the course of his exposition:

Reception

Science writer Willy Ley praised Gamow's emergency supply, describing it as an "admittedly rarified ... book which entertains by manner of instruction".^[2]Kirkus Reviews declared it "a stimulating and provocative book for high-mindedness science-minded layman".^[3] Theoretical physicist Sean Assortment. Carroll credited One Two Three... Infinity with setting the trajectory of sovereignty professional life.^[4] Cognitive scientist Steven Pinker read the book as a toddler, and has cited it as contributory to his interest in popular branch writing.^[5] Astrophysicist and science popularizer Neil deGrasse Tyson identified One Two Combine. Infinity as one of two books which had the greatest impact resolve him, the other being Mathematics point of view the Imagination by Edward Kasner become peaceful James R. Newman.^[6]

In 1956, Gamow was awarded the Kalinga Prize by UNESCO for his work in popularizing technique, including his book One, Two, Yoke. Infinity, as well as other works.^[7]

References