Adding A Dimension is the third anthology of essays written for Fantasy and Science Fiction, published in 1964.
The essay titles to the right are listed in the order they appear in the book. Because one of the purposes of these critiques is to examine Asimov's growth as a writer, the essays are covered in chronological order in the body of this page.
In his introduction, Asimov states that he hopes to 'add a dimension' to people's understanding of the fact that all scientific discoveries come from what has been discovered before.
"It is my hope that, every once in a while, some vignette of science past may illuminate some corner of Science Present."
Adding A Dimension (1964)
T-Formation
One, Ten, Buckle My Shoe
Varieties of the Infinite
A Piece of Pi
Tools of the Trade
The Imaginary That Isn't
Pre-fixing It Up
The Rigid Vacuum
The Light That Failed
The Light Fantastic
Slow Burn
You, Too, Can Speak Gaelic
The Lost Generation
He's Not My Type
The Shape of Things
Twinkle, Twinkle Little Star
The Isaac Winners
Aug 1963
Dec 1962
Sep 1959
May 60
Sep 1960
Mar 1961
Nov 1962
Apr 1963
Jun 1963
Aug 1962
Oct 1962
Mar 1963
Feb 1963
Jan 1963
Sep 1962
Oct 1963
Jul 1963
Essays listed chronologically
Varieties of the Infinite
A Piece of Pi
Tools of the Trade
The Imaginary That Isn't
The Light Fantastic
The Shape of Things
Slow Burn
Pre-fixing It Up
One, Ten, Buckle My Shoe
He's Not My Type
The Lost Generation
You, Too, Can Speak Gaelic
The Rigid Vacuum
The Light That Failed
The Isaac Winners
T-Formation
Twinkle, Twinkle Little Star
.
September 1959
May 1960
September 1960
March 1961
August 1962
September 1962
October 1962
November 1962
December 1962
January 1963
February 1963
March 1963
April 1963
June 1963
July 1963
August 1963
October 1963
The essays below are discussed as written in chronological order, not as they appeared in the book. The paragraph in grey is the opening lines of each essay.
T-Formation (August 1959)
I have been accused of having a mad passion for large numbers and this is perfectly true. I wouldn't dream of denying it. However, may I point out that I'm not the only one?
For instance, in a book entitled Mathematics and the Imagination (published in 1940) the authors, Edward Kasner and James Newman, introduced a number called the "googol," which is good and large and which was promptly taken up by writers of books and articles on popular mathematics.
Personally, I think it is an awful name, but the young child of one of the authors invented it, and what could a proud father do? Thus, we are afflicted forever with that baby-talk number.
Personal details?
None.
Comments on religion?
None.
Comments on politics?
Makes a comment on taxation (The annual budget of the United States of America is in the neighborhood, now, of $100,000,000,000 (a hundred billion dollars). That means 1,000,000,000,000 (one trillion) dimes.
...
The number 1,000,000,000,000 is roughly equal to the number of dimes taken from your pocket and mine (mostly mine, I sometimes sullenly think) each year by kindly, jovial Uncle Sam to build missiles and otherwise run the government and the country.
Comments on women?
None.
Subject and notes
Isaac Asimov loves playing with large numbers, and in this chapter explains how he made up his own system for writing large numbers (usint trillion, or T, as a base.) From talking about this system he goes back in time to explain how prime numbers were found (Mersenne numbers), and comparing his numbering system with the google and the googleplex.
Terminology
On pg 7, Asimov states: The series (the Fibonacci sequence) is also related to the "golden section" which is important to art and aesthetics as well as mathematics... but he doesn't explain what the "golden section" is. See this webpage of Dr. Ron Knotts for more information.
He also mentions the Recreational Mathematics Magazine. This magazine was only published from 1961-1964.
Quotes?
None.
One, Ten Buckle My Shoe (October 1959)
I have always been taken aback a little at my inability to solve mathematical conundrums since (in my secret heart of hearts) I feel this to be out of character for me. To be sure, numerous dear friends have offered the explanations that, deep within me, there rests an artfully concealed vein of stupidity, but this theory has somehow never commended itself to me.
Unfortunately, I have no alternative explanation to suggest.
You can well imagine, then, that when I come across a puzzle to which I can find the answer, my heart fairly sings. This happened to me once when I was quite young and I have never forgotten it. Let me explain it to you in some detail because it will get me somewhere I want to go.
Personal details?
Since he discusses how he's unable to solve mathematical conundrums, yes, this counts as personal details.
Comments on religion?
None
Comments on politics?
None
Comments on women?
None.
Subject and notes
Asimov explains how the binary system came to be, as well as other numbering systems that have numbers other than 10 as their base.
Quotes?
None
Varieties of the Infinite (November 1960)
There are a number of words that publishers like to get into the titles of science-fiction books as an instant advertisement to possible fans casually glancing over a display that these books are indeed science fiction. Two such words are, of course space and time. Others are Earth (captitalized), Mars, Venus, Alpha entauri, tomorrow, stars sun, asteroids, and so on. And one-to get to the nub of this chapter-is infinity.
One of the best s.f. titles ever invented, in my opinion, is John Campbell's Invaders from the Infinite. The word invaders is redolent of aggression, action, and suspense, while infinite brings up the vastness and terror of outer space.
Personal details?
None.
Comments on religion?
None.
Comments on politics?
None
Comments on women?
His example in attempting to explain this particular number system consists of a "bright boy" and men, no women mentioned.
Subject and notes
Asimov explains infinity - it is not a number. He also explains the mathematic formulas used to indicate infinity, or 'transfinite' numbers and mentions the work of Georg Cantor.
Quotes?
None.
Piece of Pi (December 1960)
In my essay "Those Crazy Ideas" which appeared in Fact and Fancy, I casually threw in a footnote to the effect that [e(pi)i=-1]. Behold, a good proportion of the comment which I received thereafter dealt not with the essay itself but with that footnote (one reader, more in sorrow than in anger, proved the equality, which I had neglected to do.)
My conclusion is that some readers are interested in these odd symbols. Since I am, too, (albeit I am not really a mathematician, or anything else), the impulse is irresistable to pick up one of them, say [pi], and talk about it in this chapter and the next. In Chapter 6, I will dicuss i.
Personal details?
Although Asimov opens his essay with a comment on people's reactions to one of his previous essays, it doesn't really count as 'personal details.'
Comments on religion?
In explaining "pi," Asimov mentions that it was used in the Bible (Chapter 4 of 2 Chronicles).
"There is always the danger that some individuals, too wedded to the literal rules of the Bible, may consider 3 to be the divinely ordained value of "pi" in consequence.
Comments on politics?
Asimov refers to certain politicians as "august legislators" - which is used more as a term of derision. (See notes).
Comments on women?
None
Subject and notes
Asimov discusses the history of "pi", from how it was first discovered to how it is used.
After making his comments about "pi" being called = to 3 in the Bible, Asimov goes on to say, "I wonder if this may not have been the motive of the simple soul in some state legislature who, some years back, introduced a bill which would have made "pi" legally equal to 3 inside the bounds of the state. Fortunately the bill did not pass or all the wheels in that state (which would, of course, have respected the laws of the state's august legislators) would have turned hexagonal.
The only incidence of this I was able to find took place in Indiana way back in 1897. According to Wikipedia: "In 1897, the Indiana General Assembly passed a bill from which it could be deduced that pi was equal to 3.2 or other incorrect values. The Indiana Senate postponed the bill indefinitely, preventing it from becoming law".
This same incident is covered more fully on a page of the website The Straight Dope
Quotes?
None
Tools of the Trade (February 1961)
The previous chapter does not conclude the story of [pi]. As the title stated, it was only a piece of [pi]. Let us therefore continue onward.
The Greek contribution to geometry consisted of idealizing and abstracting it. The Egyptians and Babylonians solved specific problems by specific methods but never tried to establish general rules.
The Greeks, however, strove for the general and felt that mathematical figures had certain innate properties that were eternal and immutable. They felt also that a consideration of the nature and relationships of these properties was the closest man could come to experiencing the sheer essence of beauty and divinity. (If I may veer away from science for a moment and invade the sacred precincts of the humanities, I might point out that just this notion was expressed by Edna St. Vincent Millay in a famous line that goes: "Euclid alone had looked on Beauty bare.")
Personal details?
None.
Comments on religion?
None
Comments on politics?
None.
Comments on women?
None
Subject and notes
Asimov explains that the Greeks were concerned with 'elegance.' The tools they wanted to use to prove various mathematical terms were simply a straight edge and a compass. He then goes on to explain how to 'square a circle' (the classic problem), and eventually gets in to transcendental numbers.
Quotes?
None
The Imaginary That Isn't (March 1961)
When I was a mere slip of a lad and attended college, I had a friend with whom I ate lunch every day. His 11 a.m. class was in sociology, which I absolutely refused to take, and my 11 a.m. class was calculus, which he as steadfastly refused to take-so we had to separate at eleven and meet at twelve.
As it happened, his sociology professor was a scholar who did things in the grand manner, holding court after class was over. The more eager students gathered close and listened to him pontificate for an additional fifteen minutes, while they threw in an occasional log in the form of a question to feed the flame of oracle.
Personal details?
Yes. Asimov talks about his college days and reveals that he 'scores' (or thinks he scores) off of a sociology professor.
Comments on religion?
None
Comments on politics?
None
Comments on women?
None
Subject and notes
Asimov discusses about how and why "negative" or "imaginary" numbers came into use, and how they can be used for scalar quantities and vector quantities - velocity, forces, accelerations, etc.
Quotes?
None.
Pre-fixing It Up (Jul 1961)
I go through life supported and bolstered by many comforting myths, as do all of us. One of my own particularly cherished articles of faith is that there are no arguments against the metric system and that the common units make up an indefensible farrago of nonsense that we keep out of stubborn folly.
Imagine the sobering effect, then, of having recently come across a letter by a British gentleman who bitterly denounced the metric system as beingartificial, sterile, and not geared to human needs. For instance, he said (and I don't quote exactly), if one wants to drink beer, a pint of beer is the thing. A liter of beer is too much and half a liter is too little, but a pint, ah, that's just right.
Personal details?
None.
Comments on religion?
None.
Comments on politics?
None.
Comments on women?
None
Subject and notes
Asimov explains how the metric system came to be, and points out that it is a logical system. "The units are sensibly interelated." Then he goes on to point out the inventors of the system didn't go beyong the "thousand" mark in their prefixes. (The pre-fix" of the title refers to the prefixes to the unit of measurement - meter, centimeter, kilometer) He then discusses how the metric system is used for various measurements, from weight to mass to speed to distance.
Quotes?
None
The Rigid Vacuum (August 1961)
Probably the greatest dilemma facing the man who wants to write science fiction on the grand scale - and who is also conscientious - is that of squaring the existence of an interstellar society with the fact that travels at velocities greater that that of light in a vacuum (186,200 miles per second) is considered impossible.
Personal details?
None.
Comments on religion?
None.
Comments on politics?
None
Comments on women?
None
Subject and notes
Asimov explains how the term "ether" (coined by Aristotle about 350 BC) for space came to be used, and how it was eventually proven that ether did not exist, to be replaced by radio waves, light waves, and the knowledge that light acts sometimes as a wave and sometimes as a particle.
He continues to discuss ether and how it was disproven in the next essay.
Quotes?
One way to establish a theory is to make predictions based upon its tenets and have them turn out to be so.
The Light That Failed (Sept 1961)
In the summer of 1962, a fetching young lady from Newsweek asked permission to interview me; permission which I granted at once, you may be sure. It seems that Newsweek was planning to do a special issue on the space age, and it was this young lady's job to gather some comments on the matter by various science-fiction personalities.
Personal details?
Yes - Asimov being asked to participate in an interivew for Newsweek.
Comments on religion?
None
Comments on politics?
None
Comments on women?
Asimov makes no comments about women in this story except to point out that the reporter is 'fetching.'
Subject and notes
Asimov discusses how the concept of ether was finally disproved by the work of Albert Abraham Michelson. In attempting to measure the velocity of light, he never found the "interference fringes" which should have existed if the light was transmitted to earth via ether.
Quotes?
"Sci-fi is 'a topical fairy tale where all scientist's experiments suceed.'...
Under the proper circumstances, a failure, if unexpected and significant, cando more for the development of science than a hundred routine successes.
The Light Fantastic (Oct 1961)
When I was young, we children used to listen to something called "radio." It's a hard thing to describe to the modern population, but if you imagine a television set with the picture tube permanently out of order, you get the essentials.
On the radio set there was a dial you could turn in order to tune in the various stations and the dial had markings numbered from 55 to 160. As far as I know, nobody I knew had any idea what those numbers meant - or cared.
Personal details?
Not really - merely a comment that in 1964 the younger generation didin't know what a radio was.
Comments on religion?
None.
Comments on politics?
None.
Comments on women?
None.
Subject and notes
Asimov discusses and describes what light and sound waves are (and how these were used to create radio stations). He explains: micropulsations, radio waves, microwaves, infrared waves, visible light rays, ultraviolet rays, X-rays and gamma rays.
He then goes on to cover the frequency of sound waves (as used in the scales of do re mi fa so la ti do) and of the color scale.
Technology
Asimov discusses the creation of the laser (light amplification by stimulated emission of radiation)
Personalities
Asimov points out that Albert Einstein's Nobel Prize in 1921 was not for the theory of relativity (either special or general) but for his work on the photoelectric effect, which is something that I hadn't known!
Quotes?
"These days, whe I watch television here at home, I have my choice of four channels that I can get with reasonable clearness and audibility. Even with only four channels at their disposal, however, the television moguls can supply me with a tremendous quantity of rubbish.
Imagine what the keen minds of our entertainment industry could do if they realized they had a hundred million channels into which they could funnel new and undreamed-of varieties of trash.
Maybe we ought to stop right now!"
---Asimov is foreshadowing the days of cable (1948) and satellite television. See an article on Cable TV in the US at Wikipedia.
Slow Burn (December 1961)
For many years now I have been an inveterate admirer of Sir Isaac Newton. One can, after all, make out a good case for his having been the greatest scientist that ever lived.
What's more, it doesn't displease me one little bit that Newton's first name is Isaac. To be sure, I wasn't named for him, but for my grandfather. Yet the principle remains; we have something in common. And to top it off, the Boston suburb in which I live is named Newton - how do you like that?
Personal details?
Yes - opening para
Comments on religion?
None
Comments on politics?
None
Comments on women?
None
Subject and notes
Asimov points out that Galileo's [apocryphal] experiment on the top of the leaning power of Pisa "destroyed Aristotlian physics and established the modern form of the science."
He then goes on to point out that there is a similar story that can be told about the foundation of modern chemistry, when Henry Cavendish proved that phlogiston did not exist... (although Lavoisier attempted to grab all the credit for it.)
Quotes?
"One conclusion drawn from a particular experiment [can] be shifted to another and much more plausible conclusion by simply becoming quantitative."
You, Too, Can Speak Gaelic (January 1962)
It is difficult to prove to the man in the street that one is a chemist. At least, when one is a chemist after my fashion (strictly armchair).
Faced with a miscellaneous stain on a garment of unknown composition, I am helpless. I say, "Have you tried a dry cleaner?" with a rising inflection that disillusions everyone within earshot at once. I cannot look at a paste of dubious composition and tell what it is good for just by smelling it; and I haven't the foggiest notion what a drug, identified only by trade name, may have in it.
Personal details?
Yes
Comments on religion?
Comments on politics?
None
Comments on women?
"Women, being what they are (three cheers), have for many centuries been shading their eyelashes and upper eyelids and eye corners in order to make said eyes look large, dark, mysterious and enticing."
Subject and notes
Asimov explains that chemistry was almost the sole domain of the Germans during its formative years, which explains why the terms for all the chemicals run together. He also explains what each part of a chemical formula means.
Quotes?
None
The Lost Generation (February 1962)
There are disadvantages to every situation, however ideal it may seem. For instance, by extremely clever maneuvering, I have created the image of one who possesses universal knowledge. This, plus the possession of a magnetic glance, enables me to browbeat editors (present editor always excepted).
Having brought myself to this ideal pass, however, I find myself occasionally asked to speak on some subject far outside my field of competence. When I then protest (very feebly) that I know nothing about it, there is a loud, jovial laugh in response and a hearty slap on the shoulders and someone says, "Good old Asimov! Always joking."
Personal details?
None
Comments on religion?
"Darwin's theory created a terric furor, but the loudest objections were the least crucial, scientifically. Of course, evolution by natural selecton offended the religious sensibilities of many men, since it seemed to deny the version of the creation story found in the first chapter of the Book of Genesis...However, this form of opposition played no great role within the realm of science itself."
Comments on politics?
None.
Comments on women?
Obliquely: "In the same way, a large stallion might very well mate with a small mare, a well-fanged lion with a small-toothed lioness, an intelligent ape with a stupid one." [The male is always first, the female second, so he's saying an 'intelligent' male might mate with a 'stupid' female.]
Subject and notes
The lost generation refers to the 34 years between Mendel's discovery of the 'laws of inheritance' and his subsequent passing on of those laws to Von Negeli, who dismissed them out of hand.
Independent research by Dutch botanist Hugo de Vries. German Karl Correns and Austrian Erich Tschermak came to the same conclusion.
It was the proof provided by Mendel that solidified Charles Darwin's theory of evolution (although Darwin also died 30+ years before this proof had accumulated through testing.
Quotes?
None
He's Not My Type (April 1962)
I seem to be a nonconformist. This is not by any means because I have deliberately set out to be one. On the contrary, nothing would suit me better than to fade into the surroundings. Unfortunately, it turns out that at any gathering I attende I seem, for some mysterious reason, to attract attention.
Sooner or later, some curious stranger is bound to ask, "Who is the loud-mouthed extrovert over there?" And someone else is bound to say, "That's Asimov," and accompany the information with several taps on the forehead, a gesture of whose significance I am uncertain.
Personal details?
Yes, in first paragraph of essay
Comments on religion?
None
Comments on politics?
None
Comments on women?
"An infant quickly learns to tell his mother from other women and a young woman is very likely to be considered by her young man to be not only different from all others, but infinitely superior to all the others put together. I am told that young women (with less reason, no doubt) have similar feelings with regard to specific yung men."
Subject and notes
Asimov discusses the different types of blood and how they were discovered - A, B, O, and combinations therefrom, and then genes of various peoples, including the Rh gene.
He mentions that new blood types are given names like: Duffy, Kell, Kidd, Lewis and Lutheran, named after the person in whose blood the rare gene was first found.
"We can only hope that when the marvels of information retrieval put the right item before a man, it is put before the right man. And for human retrieval, no theory and no machinery exists. We can only hope.
The Shape of Things (May 1962)
Every child comes staggering out of grammar school with a load of mistatements of fact firmly planted in his head. He may forget, for instance, as the years drift by, that the Battle of Waterloo was fought in 1815 or that seven times six is forty-two; but he will never, never forget, while he draws breath, that Columbus proved the world is round.
And of course, Columbus proved no such thing. What Columbus did prove was that it doesn't matter how wrong you are, as long as you're lucky.
Personal details?
None
Comments on religion?
None
Comments on politics?
Obliquely: "In the language of today, they needed an "ocean spectacular" to improve their "world image."
Comments on women?
None
Subject and notes
Asimov explains that the educated gentlemen of Portugal and Spain always knew that the world was round - the only thing that prevented Columbus from getting his funding from Portugal was that they thought the Earth was larger than Columbus thought it was (and indeed, Columbus was wrong and if he hadn't been lucky enough to find the islands that he did, he and his crew would have starved.)
He then points out that the earth is not really a sphere, nor an oblate spheroid, but actually pear-shaped - according to information revealed by Vanguard.
Quotes?
None
Twinkle, Twinkle, Little Star (June 1962)
It came as a great shock to me, in childhood days, to learn that our sun was something called a "yellow dwarf" and that sophisticated people scorned it as a rather insignifficant member of the Milky Way.
I had made the very natural assumption, prior to that, that stars were little things, and everything I had read confirmed the notion. There were innumerable fairy tales about the tiny stars, which (I gathered) must be the little children of the sun and moon, the brightly shining sun being the father and the dim, retiring moon the mother.*
* I had curiously naive ideas about the comparative importance of the sexes in those days.
Personal details?
None.
Comments on religion?
None.
Comments on politics?
None.
Comments on women?
See above.
Subject and notes
Asimov explains how the dark companion of Sirius was found, and from that how the different sizes of suns - from white dwarfs to yellow dwarfs to red giants were found, using spectroscopy.
Quotes?
None
The Isaac Winners (June 1962)
When one looks back over the months or years, it becomes awfully tempting to try to pick out the best in this or that category. Even the ancient Greeks did it, choosing the "seven wise men" and the "seven wonders of the world."
Personal details?
None.
Comments on religion?
None.
Comments on politics?
None.
Comments on women?
See above.
Subject and notes
Asimov lists 72 scientists throughout history, then chooses the top ten who contributed the most to science.
Quotes?
None
The Isaac Winners (July 1962)
When one looks back over the months or years, it becomes awfully tempting to try to pick out the best in this or that category. Even the ancient Greeks did it, choosing the "seven wise men" and the "seven wonders of the world."
Personal details?
Asimov tells the story of Princeton graduate student Hong-Yee Chiu, who was so struck by a comment Asimov made in one of his essays that he changed his field of study from elementary particle physics to astrophysics, in order to investigate maximum possible temperatures.
Comments on religion?
None
Comments on politics?
None
Comments on women?
None
Subject and notes
Asimov then goes on to begin at the beginning (as usual) to study the history of temperature, by beginning with the neutrino.
Finagle's Constant
- designed to prove a wrong term right. An 'ad hoc' device.
That's what Asimov calls and defines it in this essay, and I found a use of it in a 1955 short story by Eric Frank Russell called "Allamagoosa". Wikipedia only has the definition for Finagle's Law:
Finagle's Law of Dynamic Negatives (also known as Finagle's corollary to Murphy's Law) is usually rendered:
Anything that can go wrong, will?at the worst possible moment
One variant (known as O'Toole's Corollary of Finagle's Law) favored among hackers is a takeoff on the second law of thermodynamics (also known as entropy):
The perversity of the Universe tends towards a maximum.
The term "Finagle's Law" was first used by John W. Campbell, Jr., the influential editor of Astounding Science Fiction (later Analog). He used it frequently in his editorials for many years in the 1940s to 1960s but it never came into general usage the way Murphy's Law has.
Eventually the term "Finagle's law" was popularized by science fiction author Larry Niven in several stories depicting a frontier culture of asteroid miners; this "Belter" culture professed a religion and/or running joke involving the worship of the dread god Finagle and his mad prophet Murphy.
Hanlon's Razor (or Hanlon's Law) is a corollary of Finagle's law. Hanlon's Razor says "Never attribute to malice that which can be adequately explained by stupidity."
Asimov finishes with: If his theory is correct, it ought to be possible to detect stars that are about to go supernova by the quantity of neutrons they put out. As supernova-hood is approached, the rate, according to Dr. Chiu, reaches 10 ^53 per second. He quotes Chiu: "Therefore, the establishment of a neutrino monitor station in terrestrial or spatial laboratories may help us predict forthcoming supernovae.
Chiu has had a few books published, including Neutrino Astrophysics (1964)and Stellar Evolution (1972).
Quotes?
None
All quotes maintain their original copyright and are presented here for research, reference and review.
Thanks to Doubleday for permission to use selected quotes.
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