Birthday Cantatatata . . One (tine May day, the Tortoise Tortoise and Achilles meet, wandering wan dering in the woods. woo ds. The latter, all decked out ou t handsomely, is doing a jiggish sort of thing to a tune which he himself is humming. On his vest he is wearing a great big button with the words "Today "Today is my irthday!" Tortoise: Hello there, .Achilles. What makes you so joyful today? Is it your birthday, by any chance? Achilles: Yes, yes! Yes it is, today is my birthday! Tortoise: That is hat I had susected, on account of that button hich you are earin", and also because unless I am mistaken, you are sin"in" a tune from a #irthday $antata by #ach, one ritten in %&'& for the fifty(se)enth birthday of Au"ustus, *in" of +aony. Achilles: You-re ri"ht. And Au"ustus- birthday coincides ith mine, so THI+ #irthday $antata has double meanin". Hoe)er, Hoe) er, I shan-t tell you my a"e. Tortoise: h, that-s erfectly all ri"ht. Hoe)er, I ould like to kno one other thin". /rom hat you ha)e told me so far, ould it be correct to conclude that today is your birthday? Achilles: Yes, yes, it ould be. Today is my birthday. Tortoise: 0cellent. That-s just as I susected. +o no, I WI11 conclude it is your birthday, unless Achilles: Yes(unless hat? Tortoise: 2nless that ould be a remature or hasty conclusion to dra, you kno. Tortoises don-t like to jum to conclusions, after all. 3We don-t like to jum at all, but esecially not to conclusions.4 +o let me just ask you, knoin" full ell of your fondness for lo"ical thou"ht, hether it ould be reasonable to deduce lo"ically from the fore"oin" sentences, that today is in fact your birthday. Achilles: I do belie)e I detect a attern to your 5uestions, 6r. T. #ut rather than jum to conc conclu lusi sion onss myse myself lf,, I shal shalll take take your your 5ues 5uesti tion on at face face )alu )alue, e, and and ans anser er it strai"htforardly. strai"htforardly. The anser is: Y0+. Tortoise: Tortoise: /ine! /ine! Then there is only one more thin" I need to kno, to be 5uite certain that today is Achilles: Yes, yes, yes, yes ... I can already see the line of your 5uestionin", 6r. T. I-ll ha)e you kno that I am not so "ullible as I as hen e discussed 0uclid-s roof, a hile back. Tortoise: Why, ho ould e)er ha)e thou"ht you to be "ullible? 7uite to the contrary, I re"ard you as an eert in the forms of lo"ical thou"ht, an authority in the science of )alid deductions. a fount of knoled"e about certain correct methods of reasonin". . . To tell tell the truth, Achilles, you are, in my oinion, a )eritable titan in the art of rational co"itation.
#irthday $antatatata . .
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And it is only for that reason that I ould ask you, ;o the fore"oin" sentences resent enou"h e)idence that I should conclude ithout further u<uess(and Tortoises abhor Wild >uesses. Tortoises formulate only 0ducated >uesses. Ah, yes(the oer of the 0ducated >uess. You ha)e no idea ho many eole fail to take into account all the ele)ant /actors hen they-re "uessin". Achilles: It seems to me that there as only one rele)ant factor in this ri"marole, and that as my first statement. Tortoise: h, to be sure, it-s at least ONE of the factors to take into account, I-d say(but ould you ha)e me ne"lect 1o"ic, that )enerated science of the ancients? 1o"ic is alays a ele)ant /actor in makin" 0ducated >uesses, and since I ha)e ith me a renoned eert in 1o"ic, I thou"ht it only 1o"ical to take ad)anta"e of that fact, and confirm my hunches, by directly askin" him hether my intuitions ere correct. +o let me finally come out and ask you oint blank: ;o the recedin" sentences allo me to conclude, ith no room for doubt, that Today is your #irthday? Achilles: /or one more time, Y0+. #ut frankly seakin", I ha)e the distinct imression that you could ha)e sulied that anser(as ell as all the re)ious ones(yourself. Tortoise: Ho your ords stin"! Would I ere so ise as your insinuation su""ests! #ut as merely a mortal Tortoise, rofoundly i"norant and lon"in" to take into account all the ele)ant /actors, I needed to kno the ansers to all those 5uestions. Achilles: Well then, let me clear the matter u for once and for all. The anser to all the re)ious 5uestions, and to all the succeedin" ones hich you ill ask alon" the same line, is just this: YES. Tortoise: Wonderful! In one fell soo, you ha)e circum)ented the hole mess, in your characteristically in)enti)e manner. I hoe you on-t mind if I call this in"enious trick an ANSWER SCHEMA. It rolls u yes(ansers numbers %, ', @, etc., into one sin"le ball. In fact, comin" as it does at the end of the line, it deser)es the title Anser +chema me"a, =- bein" the last letter of the >reek alhabet(as if Y2 needed to be told THAT! Achilles: I don-t care hat you call it. I am just )ery relie)ed that you finally a"ree that it is my birthday, and e can "o on to some other toic(such as hat you are "oin" to "i)e me as a resent. Tortoise: Hold onnot so fast. I WI11 a"ree it is your birthday, ro)ided on thin" Achilles: What? That I Ask for no resent?
#irthday $antatatata . .
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Tortoise: Cot at all. In fact, Achilles, I am lookin" forard to treatin" you to a fine birthday dinner, ro)ided merely that I am con)inced that knoled"e of all those yes( ansers at once 3as sulied by Anser +chema 4 allos me to roceed directly and ithout any further detours to the conclusion that today is your birthday. That-s the case, isn-t it? Achilles: Yes, of course it is. Tortoise: >ood. And no I ha)e yes(anser D E %. Armed ith it, I can roceed to accet the hyothesis that today is your birthday, if it is )alid to do so. Would you be so kind as to counsel me on that matter, Achilles? Achilles: What is this? I thou"ht I had seen throu"h your infinite lot. Co doesn-t yes( anser D E % satisfy you? All ri"ht. I-ll "i)e you not only yes(anser D E ', but also yes(ansers D E @, D E F, and so on. Tortoise: Ho "enerous of you, Achilles. And here it is your birthday, hen I should be "i)in" Y2 resents instead of the re)erse. r rather, I +2+G0$T it is your birthday. I "uess I can conclude that it I+ your birthday, no, armed ith the ne Anser +chema, hich I ill call Anser +chema 'D . #ut tell me, Achilles: ;oes Anser +chema 'D 0A11Y allo me to make that enormous lea, or am I missin" somethin"? Achilles: You on-t trick me any more, 6r. T. I-)e seen the ay to end this silly "ame. I hereby shall resent you ith an Anser +chema to end all Anser +chemas! That is, I resent you simultaneously ith Anser +chemas D, ' D, @ D, F D, 9 D, etc. With this 6eta(Anser(+chema, I ha)e 26G0; 2T of the hole system, kit and caboodle, transcended this silly "ame you thou"ht you had me traed in(and no e are ;C0! Tortoise: >ood "rief! I feel honored, Achilles, to be the reciient of such a oerful Anser +chema. I feel that seldom has anythin" so "i"antic been de)ised by the mind of man, and I am aestruck by its oer. Would you mind if I "i)e a name to your "ift? Achilles: Cot at all. Tortoise: Then I shall call it Anser +chema D'. And e can shortly roceed to other matters(as soon as you tell me hether the ossession of Anser +chema D' allos me to deduce that today is your birthday. Achilles: h, oe is me! $an-t I e)er reach the end of this tantali
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are yet further Anser +chemas, such as D@J, DF, D9, and so on. It "oes on 5uite a ays, you kno. Achilles: I can ima"ine, I suose it comes to Anser +chema are yet further Anser +chemas, such as J, F, 9, and so on. It "oes on 5uite a ays, you kno. Achilles: I can ima"ine, I suose it comes to Anser +chema DD after a hile. Tortoise: f course. Achilles: And then DDD, and DDDD-, Tortoise: You-re catchin" on mi"hty fast, Achilles. I ha)e a su""estion for you, if you don-t mind. Why don-t you thro all of those to"ether into a sin"le Anser +chema? Achilles: All ri"ht, thou"h I-m be"innin" to doubt hether it ill do any "ood. Tortoise: It seems to me that ithin our namin" con)entions as so far set u, there is no ob)ious name for this one. +o erhas e should just arbitrarily name it Anser +chema Ko. Achilles: $onfound it all! 0)ery time you "i)e one of my ansers a CA60, it seems to si"nal the imminent shatterin" of my hoes that that anser ill satisfy you. Why don-t e just lea)e this Anser +chema nameless? Tortoise: We can hardly do that, Achilles. We ouldn-t ha)e any ay to refer to it ithout a name. And besides, there is somethin" ine)itable and rather beautiful about this articular Anser +chema. It ould be 5uite un"raceful to lea)e it nameless! And you ouldn-t ant to do somethin" lackin" in "race on your birthday, ould you? r is it your birthday? +ay, seakin" of birthdays, today is 6Y- birthday! Achilles: It is? Tortoise: Yes, it is. Well, actually, it-s my uncle-s birthday, but that-s almost the same. Ho ould you like to treat me to a delicious birthday dinner this e)enin"? Achilles: Co just a cotton(ickin" minute, 6r. T. Today is 6Y birthday. You should do the treatin"! Tortoise: Ah, but you ne)er did succeed in con)incin" me of the )eracity of that remark. You ket on beatin" around the bush ith ansers, Anser +chemas, and hatnot. All I anted to kno as if it as your birthday or not, but you mana"ed to befuddle me entirely. h, ell, too bad. In any case, I-ll be hay to let you treat me to a birthday dinner this e)enin". Achilles: Lery ell. I kno just the lace. They ha)e a )ariety of delicious sous. And I kno eactly hat kind e should ha)e ...
#irthday $antatatata . .
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