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''180'' 〃I never thought about it until we started to get spiral messages。 Harry says its because the thing…the famous it…believes we think in spirals。 But its just as likely that it thinks in spirals and so it assumes we do; too。 The sphere is round; isnt it? And weve been seeing all these radially symmetrical animals。 Jellyfish; squid。〃
〃Nice idea;〃 Beth said; 〃except for the fact that squid arent radially symmetrical。 An octopus is。 And; like an octopus; squid have a round circle of tentacles; but squidre bilaterally symmetrical; with a matching left and right side; the way we have。 And then theres the shrimps。〃
〃Thats right; the shrimps。〃 Norman had forgotten about the shrimps。
〃I cant see a connection between the sphere and the animals;〃 Beth said。
They heard the thumping again; soft; rhythmic。 Sitting in his chair; Norman realized that he could feel the thumping as well; as a slight impact。 〃What is that; anyway?〃
〃I dont know。 Sounds like its ing from outside。〃
He had started toward the porthole when the inter clicked and he heard Barnes say; 〃Now hear this; all hands to munications。 All hands to munications。 Dr。 Adams has broken the code。〃
Harry wouldnt tell them the message right away。 Relishing his triumph; he insisted on going through the decoding process; step by step。 First; he explained; he had thought that the messages might express some universal constant; or some physical law; stated as a way to open conversation。 〃But;〃 Harry said; 〃it might also be a graphic representation of some kind…code for a picture…which presented immense problems。 After all; whats a picture? We make pictures on a flat plane; like a piece of paper。 We determine positions within a picture by what we call X and Y axes。 Vertical and horizontal。 But another intelligence might see images and organize them very differently。 It might assume more than three dimensions。 Or it might work from the center of the picture outward; for example。 So the code ''181'' might be very tough。 I didnt make much progress at first。〃 Later; when he got the same message with gaps between number sequences; Harry began to suspect that the code represented discrete chunks of information…suggesting words; not pictures。 〃Now; word codes fall into several types; from simple to plex。 There was no way to know immediately which method of encoding had been used。 But then I had a sudden insight。〃
They waited; impatiently; for his insight。
〃Why use a code at all?〃 Harry asked。
〃Why use a code?〃 Norman said。
〃Sure。 If you are trying to municate with someone; you dont use a code。 Codes are ways of hiding munication。 So perhaps this intelligence thinks he is municating directly; but is actually making some kind of logical mistake in talking to us。 He is making a code without ever intending to do so。 That suggested the unintentional code was probably a substitution code; with numbers for letters。 When I got the word breaks; I began to try and match numbers to letters by frequency analysis。 In frequency analysis you break down codes by using the fact that the most mon letter in English is e; and the second most mon letter is t; and so on。 So I looked for the most mon numbers。 But I was impeded by the fact that even a short number sequence; such as two…three…two; might represent many code possibilities: two and three and two; twenty…three and two; two and thirtytwo; or two hundred and thirty…two。 Longer code sequences had many more possibilities。〃
Then; he said; he was sitting in front of the puter thinking about the spiral messages; and he suddenly looked at the keyboard。 〃I began to wonder what an alien intelligence would make of our keyboard; those rows of symbols on a device made to be pressed。 How confusing it must look to another kind of creature! Look here;〃 he said。 〃The letters on a regular keyboard go like this。〃 He held up his ''182'' pad。
1234567890
tab QWERTYUIOP
capsASDFGHJKL;
shiftZXCVBNM;。?
〃And then I imagined what the keyboard would look like as a spiral; since our creature seems to prefer spirals。 And I started numbering the keys in concentric circles。
〃It took a little experimentation; since the keys dont line up exactly; but finally I got it;〃 he said。 〃Look here: the numbers spiral out from the center。 G is one; B is two; H is three; Y is four; and so on。 See? Its like this。〃 He quickly penciled in numbers。
12345612711990
tabQWER13T5Y4U101OP
capsASD14F6G1H3J9KL;
shiftZXC15V7B2N8M;。?
〃They just keep spiraling outward…M is sixteen; K is seventeen; and so forth。 So finally I understood the message。〃
〃What is the message; Harry?〃
Harry hesitated。 〃I have to tell you。 Its strange。〃
〃How do you mean; strange?〃
Harry tore another sheet off his yellow pad and handed it to them。 Norman read the short message; printed in neat block letters:
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