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Anyone who wishes to construct this rectangle from the twelve pentominoes should have no difficulty in matching them with the letters they (sometimes approximately) resemble. It is easy to see that the second of the (only) two solutions is obtained by rotating a seven-element central portion.

Dr. Golomb, who is now professor of Electrical

Engineering and Mathematics at the University of

Southern California, has also invented an ingenious game called Pentominoes@ (distributed in North

America by Hallmark Cards and in Europe by Zimpfer

Puzzles). It has more openings than chess. In an earlier version of 2001: A Space Odyssey, Stanley Kubrick shot Hal playing this game against the astronauts.

I am indebted to Dr. Robert Forward of the Hughes Research Laboratory,

Malibu, for introducing me to the fascinating concept of mini black holes, and for making such encouraging noises about the somewhat outrageous propulsion system of S. S. Sirius that I am almost inclined to patent it…. Dr. Grote Reber, the father of radio astronomy and builder of the world’s first radio telescope, started me thinking about the extent of the heliosphere and, its possible consequences. I am grateful for his comments on cutoff frequencies, but he is in no way responsible for my wilder extrapolations of his ideas. Dr. Adrian Webster, of Cavendish Laboratory’s

Mullard Radio Astronomy Observatory, also gave much vital information, and he too is not to be blamed for my use of it.

I am especially indebted to Dr. Bernard Oliver, vice-president and director of research of Hewlett Packard not only for hospitality at Palo Alto but also for an advance copy of the Project CYCLOPS Design Study NASA Ames CR 114445), which he directed. And I hope Barney will forgive me for the assumption-which in fact I regard as highly improbablo–that CYCLOPS would not have detected intelligent signals, even after two hundred years of operation.

Indignant antenna designers who feel that Argus would not work as specified are invited to contemplate ABM search radars, and to Think Big. All I will say in self-defense is that the Argus elements would be superconducting, active, and divided into many switchable subsections, perhaps with cross-connections between the “spines.” I leave minor practical details (as in the case of the Asymptotic Drive) as an exercise for the student.

The “exasperated” remark in Chapter 21 was made to me at a NASA conference by Professor Neil Armstrong in July 1970. I hope it is the last word on some famous first words.

I am deeply grateful to my old friend William Mac

Quitty, producer of A Night to Remember, for much material concerning the Titanic-including the menu in Chapter 27. Collectors of unlikely

coincidences may be interested to know that just three hours after I had decided to incorporate it in the text, I read in the May 1974 Skin Diver that the

Titanic Enthusiasts of America had served this menu at their Annual

Dinner…. Some readers may feel that the coincidences-or “correspondences”-that play a key part in this story are too unlikely to be plausible. But they were, in fact, suggested by far more preposterous events in my own life; and anyone who doubts that this sort of thing can happen is referred to Arthur

Koestler’s The Roots of Coincidence. I read this fascinating book only after completing Imperial Earth, though that fact itself now seems somewhat improbable to me.

Even more improbable is the fact that when, on July 24, 1975, I appeared as a witness before the House of Representatives Subcommittee on Space Science (in the very building libeled and demolished in Chapter 33!), I was able to quote extensively from Duncan’s address to Congress in Chapter 41. Thus the

House of Representatives’ hearings now contain extracts from the

Congressional Record for July 4, 2276, which should cause confusion among future historians.

The curious acoustic behavior of the spiny sea urchin, Diadema setosum, was observed by me on Unawatuna Reef, off the south coast of Sri Lanka. I have never seen this recorded elsewhere, so it may be my one original contribution to marine biology.

Finally, my speculations about conditions on Titan were triggered by a series of papers that Dr. Carl Sagan was good enough to send me. Needless to say, I am also indebted to Carl for many other stimulating ideas, which any properly designed universe would be very foolish to ignore. “For if not true, they are well imagined…

ARTHUR C. CLARKE Cinnamon Gardens, Colombo January 1974-January 1975

ADDITIONAL NOTE

Several expert readers have accused me of grave error by assuming that

Malcolm would pass on the Makenzie defect to his clones. Though I was well aware of this problem (and tried to avoid it by being carefully unspecific)

I did not go into the matter as seriously as I should have done. I am still hoping that some ingenious geneticist will be able to contrive a solution; unfortunately, I doubt if I will be able to understand it.