Correcting Publisher’s Errors in Einstein’s “Relativity”

In 1916, Albert Einstein (1879-1955) wrote a book in German for the general public about his theory of relativity, and he continued to add to it until its fifteenth edition in 1952. That book is called Relativity, The Special and the General Theory, and its English version is an “authorized translation by Robert W. Lawson.” That fifteenth edition has been in continuous publication since, and its copyright is held by “the Estate of Albert Einstein,” dated 1961.

It is a wonderful book. “The author has spared himself no pains in his endeavor to present the main ideas in the simplest and most intelligible form,” and Einstein’s exposition is a model of what every scientist should strive for in the clarity of their writing, and every journal should seek to publish to serve humanity’s interest in the widest dissemination of knowledge.

The particular edition of this book that I will comment on is published by Three Rivers Press, which is a trademark of Random House, Inc., and this edition of the book has the identification code: ISBN 0-517-88441-0. The publisher (NOT Albert Einstein!) — somewhere between the editor and the typesetter — has introduced errors into the text, and the purpose of this article is to show the corresponding corrections (to the three errors I have noticed). Page numbers are cited for the specific edition noted here.

Page 46 (Theorem of the Addition of the Velocities. The Experiment of Fizeau), footnote, in the second sentence (at the third line of text), a second closing parenthesis is needed for the expression for W, which should then appear mathematically equivalent to:

W = {w + v∙[1 – (v∙w)/c^2]}.

Note that the velocity w (of light in a motionless liquid) is much much greater than the velocity v (of the liquid in a tube). The speed of light in a vacuum is c. W is the “addition of velocities,” of light with respect to a liquid that is itself flowing along a tube, where W is observed from the frame of reference of the tube.

Page 129 (The Structure of Space According to the General Theory of Relativity), footnote, in the second sentence (at the third line of text), the symbol (label) “x” should instead be the symbol (label) “ƙ,” the Greek letter kappa. This makes line 3 consistent with the mathematical expressions in the previous lines of the footnote.

Page 124 (The Possibility of a “Finite” and Yet “Unbounded” Universe), the equation shown in the book is multiply wrong. The equation should be a mathematical statement that the ratio [circumference/surface diameter] = [pi] x [sine(nu/R)/(nu/R)], and this is always less than or equal to pi.

π ≥ π∙{ [sin(nu/R)] / (nu/R) } = [circumference/“radial” arc x 2]

The Greek letter “nu” can look like the lower case script “v,” which appears in the denominator of the erroneous formula on page 124. The first error to correct in that formula is to replace the lower case “r,” which is shown in the argument of the sine function, with the same “v” as in the denominator (and which “v” I will call “nu” further below).

The second error to correct is to replace the equal sign (=) with a multiplication symbol (×, or ∙), or to make that multiplication implicit by eliminating that equal sign and enclosing the entire ratio (corrected as above), to the right of the pi, within parentheses or brackets.

The lower case “r” that Einstein uses on page 125 refers to a quantity (an arc length along a “great circle,” my “radial arc x 2”) that is shown as the product 2x[R]x[theta] in the display that follows.

The following display shows what Einstein is describing on pages 124-125, and how the equation shown above comes about. The quantity (ratio) that should be printed on page 124 is shown within a hatched bean-shaped outline in the display. I leave it to you to enjoy that display, and I hope the trustees of Einstein’s legacy can cause future printings of “Relativity” to be free of textual errors.

Finite Unbounded

Finite Unbounded


The Buried Rainbow

The Buried Rainbow

His mind is a graveyard of memories
of young and beautiful faces,
utopian dreams,
transformative art
unseen in this island world of blind cyclopses
bumbling into each other with hurtling ambition
in the shadowed canyon bottoms.
He tosses pearls of protein, lipids and carbohydrates
on the frozen ground, and they erupt
as fluttering clouds of rock doves
rising into the clear air
to wheel about the shafts of light
streaming onto the canyon walls,
and carrying his gaze up into
the buried rainbow of an undiscovered country,
where fields of energy emanate
from fingertips of generosity
to unfurl a mesh of loving care
that cradles a race of poets.

25 January 2015


DEP Micro-device 2D Electric Field

I used to have the ambition of being an “artistic scientist,” a physicist and engineer aiming to produce scientific findings that were both useful and elegant, and which I would present in as beautiful a manner as I was able. The type of beauty I sought is a combination of logical simplicity, mathematical elegance, some range and depth of insight provided by the ideas, all communicated with visual and literary crispness in my written reports and other presentations.

I achieved this ideal, to my own satisfaction at least, a few times during my scientific career. One of those proud achievements is my model of the electric field in dielectrophoretic (DEP) micro-devices.

My original report “The 2D Electric Field Above A Planar Sequence Of Independent Strip Electrodes” is available below (a link to a PDF file). The report is dated 4 October 1999, and lists two authors; the second author is the patron who paid my salary during the months I worked on this project.

This paper was sent to a journal and subsequently published, but with egregious errors introduced by the journal’s editors, who “simplified” my math for publishing convenience. Months after I pointed this out to them, they issued an errata. The combination of the published paper and the errata (showing correct formulas) did not include many of the illustrations I had produced for my original report (Version 1), and which I think would help anyone actually thinking of using my mathematical model of DEP electrostatics.

So, this blog entry is similar to the case of a former artist who pulls out an obscure and favorite painting of theirs from storage in an attic or basement, dusts it off, and hangs it up on the wall so he can look at it again, and remember how good it felt to make.

A second report (an excerpt in PDF form) describes how use of the electrostatic model could assist in the development of DEP micro-devices (which are used in DNA sequencing technology).

DEP Device Diagram

DEP Device Diagram

DEP 2D Math Beauty

DEP 2D Math Beauty

DEP 2D Model Version-1

DEP 2D Model & micro-devices



Footprints In The River, Handprints On The Sky

Footprints In The River, Handprints On The Sky

My life is as dewdrops on a lotus leaf
spread above the quiet of Walden Pond,
disappearing slowly, inexorably, in the warmth of the sun
birthing an unending present – my unknowable future;
evaporating my sufferings
into the buzz of hummingbird wings
and the laughter of children playing,
no different today than in the days of Pericles and Gautama,
and certainly no different in those days to come
when my forgotten name will be half as old as theirs.
The American Ryokan, the Japanese Thoreau,
how glad I am of their gifts,
examples of living by principle –
content, enlightened, generous, humane, calm, funny,
engaging me with their words
the way their living engaged their neighbors,
waking so many from torpid lives of expediency
by the sheer force of example –
without exhortation,
their tangible traces, now, pure art.
And when I am gone what will be my legacy?:
the impish glee of a child laughing on the swings,
hands furrowing the warmth of the sand,
plunging through sweet air reaching for the higher bar,
watching ripples of light on the water.

24 November 2002

Hello Void, A Thanksgiving Message

This is a country of very ignorant selfish people who are being exploited by very smart selfish people. I can’t do anything to change that, but I don’t have to help it along, either. I can forgo getting the best possible deal at the lowest possible price with the least amount of thought.

I don’t talk politics during the holiday season, at family gatherings, or basically ever. People believe what they want to believe, and facts don’t matter. Challenging people’s beliefs only upsets them and drives them into bunkers of defensiveness. By adolescence, people don’t change, certainly not because of what others tell them. Any change of thinking and attitude is purely a result of responding to life’s traumatic experiences, and such change is rare even when the traumas are regular.

All talk of universal cooperativeness: world socialism, population control, decarbonizing industrialization to prevent climate change, and similar visions of worldwide social justice and economic equity are fantasies never to be achieved. Individual selfishness will always trump social responsibility, satisfying immediate desires will always trump achieving long-term social improvement, confident willful ignorance will always stymie hesitant and deliberate thoughtfulness and understanding.

The fear for human extinction caused by climate change, overpopulation and nuclear war, which is increasingly expressed by intelligent, socially conscious long-range thinkers, is beyond permanent relief. This fear springs from a deep-seated belief that humanity must endure eternally, that it cannot be allowed to pass away. But why? The history of life on earth is one of species emerging, evolving and fading away. Extinction is the rule, the average lifespan of species on earth is a few million years.

A human lifetime is too brief an instant for any individual to have any impact on the course of humanity’s drift toward extinction. It is true that some individuals find themselves in positions of immense temporal power and are able to initiate, or halt, genocidal events. However, the power to cause rapid human extinction is beyond any single individual. The intentional rapid extinction of humanity requires the cooperative madness of many individuals engaged in launching the world’s stockpile of nuclear weapons in one apocalyptic world war. Individual selfishness is one deterrent to the selfless cooperative attainment of this radioactive crescendo of extinction.

A better response by socially conscious people, to the realization of humanity’s drift toward extinction as a mass of insular selfish individuals ensconced in their little logic and fantasy bubbles that are opaque beyond close-in personal horizons, is to make their face-to-face interactions as compassionate, honest, honorable and calming as is reasonable given the circumstances. Obviously, sometimes conflict is necessary and right, but one tries to minimize that. This is “being peace” as Thich Nhat Hanh has written about so eloquently.

You as a living experience are peace for your own well being in the here and now, and as a socially conscious expression of solidarity with whatever individual human being you are dealing with at the moment, because you recognize the same spirit of life in them as in you, and because you realize that every other person is a bundle of largely unseen and unknowable mental fears and psychological conflicts – just as you have, largely unseen by the rest of humanity.

Be peace because that is what you can do. Forget about saving humanity, you can’t do it, it can’t be done, and it doesn’t matter. Before you were here, while you are here, and after you are gone, the universe is.


Siboney — Español-English

Ernesto Lecuona (1896-1963) published his classic Cuban song Siboney in 1929. It has been sung and played by many many performers since, in a multitude of styles.

Ernesto Lecuona was a contemporary of George Gershwin (1898-1937), and both played similar roles in the development of the music of their respective countries, Cuba and the United States. They were each classical musicians, piano virtuosos and brilliant composers, who brought Afro-American strains of folk music characteristic of their countries — son cubano and jazz, respectively — into musical theater works (zarzuelas and musicals, some considered as operas today), piano concertos, works for solo piano, and many songs.

Siboney is a song that has said “Cuba” to the ears and hearts of listeners around the world since 1929, in the same way that George Gershwin’s Summertime has infused listeners with a sense of Mark Twain’s America since 1935. These aren’t national anthems, they’re better, they are the songs of the soul.

Siboney (1929)
(música y letras de Ernesto Lecuona)

yo te quiero,
yo me muero
por tu amor.
en tu boca
la miel puso
su dulzor.

Ven a mí,
que te quiero,
y que todo tesoro
eres tú para mí.

al arrullo
de la palma
pienso en tí.

de mi sueños,
¿si no oyes la queja de mi voz?

si no vienes,
me moriré de amor.

de mi sueños,
te espero con ansia en mi caney,

Porque tú
eres el dueño
de mi amor, Siboney.

Oye el eco
de mi canto
de cristal,
no se pierda
por entre el rudo


(a poetic translation of Ernesto Lecuona’s lyrics)

how I want you,
I would die to
have your love.
honey’s sweetness
from your lips wings
like a dove.

Come to me,
I who love you,
my treasure, and want you
as close to me as can be.

breezes whisper,
as palms murmur
thoughts of you.

my dreams call out,
can’t you hear my voice for you all about?

if you don’t come
I’ll die with your love away.

with tides dreaming
in my hut awaiting you anxiously.

You alone
are that person
who owns all my love, Siboney.

Hear the echo
of my song so
crystal clear.
Don’t lose your way
in the shadows of
swamp night fear.


Eduardo Brito (1931)
[The recording that made Siboney a hit, sung by an excellent baritone; a superb rendition: full, flowing, tuneful, without distracting affectations or showiness. Classic.]

Lecuona plays Siboney (1954)
[Ernesto Lecuona plays Siboney on the piano. Perfection.]

Plácido Domingo (1984)
[The Caruso of our time gives us the ultimate Siboney. Plácido finishes the song at 3:35 (minutes:seconds) but the video continues in silence for another 51 seconds with a slide show of photos of Plácido. (I list it here because the sound is good.)]

Grace Moore (1937)
[Grace Moore unfurls her high soprano voice with a Siboney aimed right at Cary Grant in the 1937 movie When You’re In Love.]

Alfredo Kraus (1982)
[Alfredo Kraus was a lyric tenor with a sparkling and powerful voice. This recording has nice sound and is accompanied by a slideshow of scenes of the Canary Islands — one can imagine Cuba from them — and historical notes on both Lecuona and Kraus, who each had roots in the Canary Islands.]

Xiomara Alfaro (1950s)
[An Afro-Cuban coloratura sings Siboney in this video from a TV broadcast.]

Los Sabandeños (2012)
[A big chorus! A slideshow of photos of the beach called Siboney, in the province of Santiago de Cuba in southeastern Cuba, accompanies the music; there are also historical notes.]

Concha Buika (2013)
[A black Afro-Cuban propulsive jazz rendition with a smokey/raspy?-voiced singer.]

Aurelio Gabaldón (2007)
[A video of Siboney performed at this tenor’s recital (in Spain?). He did a nice job.]

Charlie Musselwhite, with Eliades Ochoa & Cuarteto Patria (1999)
[Charlie Musselwhite riffs harmonica blues on Siboney, in the company of guitarist Eliades Ochoa and his Cuarteto Patria.]


Lessons For Life

Learn how to fail gracefully,
success is rare and failure most likely.

Do not put off what is in you to do.
Do not let death overtake you,
having denied yourself by submission
to obligation.