Metamagical Themas: Sanity and Survival

3 essays by AI researcher Douglas Hofstadter exploring cooperation/game theory/‘superrationality’ in the context of the failure of political coordination to prevent global nuclear war
computer-science, experiments, philosophy, sociology
by: Douglas Hofstadter 2012-04-162019-04-01 finished certainty: log importance: 10

The fol­low­ing 3 es­says were pre­pared from pages 737–780 of an ebook of Meta­m­ag­i­cal The­mas: Quest­ing for the Essence of Mind and Pat­tern (1985) by , an an­thol­ogy of ar­ti­cles & es­says pri­mar­ily pub­lished in “be­tween Jan­u­ary 1981 and July 1983”. (I omit one en­try in “San­ity and Sur­vival”, the es­say “The Tu­mult of In­ner Voic­es, or, What is the Mean­ing of the Word ‘I’?”, which is un­con­nected to the other en­tries on co­op­er­a­tion/de­ci­sion the­o­ry/nu­clear war.) All hy­per­links are my in­ser­tion.

They are in­ter­est­ing for in­tro­duc­ing the idea of ‘’ in , an at­tempt to de­vise a de­ci­sion the­o­ry/al­go­rithm for agents which can reach global util­ity max­ima on prob­lems like the even in the ab­sence of co­er­cion or com­mu­ni­ca­tion which has par­tially in­spired later de­ci­sion the­o­ries like UDT or TDT, link­ing de­ci­sion the­ory to co­op­er­a­tion (eg ) & (specifi­cal­ly, ), and one net­work­ing project.

Sanity and Survival

by Dou­glas Hof­s­tadter


Il­lus­tra­tion of an ab­stract font for the Latin al­pha­bet.


In the four chap­ters of this con­clud­ing sec­tion, themes of the pre­vi­ous sec­tion are car­ried fur­ther and brought into con­tact with com­mon so­cial dilem­mas and, even­tu­al­ly, the cur­rent world sit­u­a­tion. On a small scale, we are con­stantly faced with dilem­mas like the Pris­on­er’s Dilem­ma, where per­sonal greed con­flicts with so­cial gain. For any two per­sons, the dilemma is vir­tu­ally iden­ti­cal. What would be sane be­hav­ior in such sit­u­a­tions? For true san­i­ty, the key el­e­ment is that each in­di­vid­ual must be able to rec­og­nize both that the dilemma is sym­met­ric and that the other in­di­vid­u­als fac­ing it are equally able. Such in­di­vid­u­al­s—in­di­vid­u­als who will co­op­er­ate with one an­other de­spite all temp­ta­tions to­ward crude ego­is­m—are more than just ra­tio­nal; they are su­per­ra­tional, or for short, sane. But there are dilem­mas and “egos” on a suprahu­man level as well. We live in a world filled with op­pos­ing be­lief sys­tems so sim­i­lar as to be nearly in­ter­change­able, yet whose ad­her­ents are blind to that sym­me­try. This de­scrip­tion ap­plies not only to myr­iad small, con­flicts in the world but also to the colos­sally block­headed op­po­si­tion of the United States and the So­viet Union. Yet the recog­ni­tion of sym­me­try—in short, the san­i­ty—has not yet come. In fact, the in­san­ity seems only to grow, rather than be sup­planted by san­i­ty. What has an in­tel­li­gent species like our own done to get it­self into this hor­ri­ble dilem­ma? What can it do to get it­self out? Are we all help­less as we watch this spec­ta­cle un­fold, or does the an­swer lie, for each one of us, in recog­ni­tion of our own typ­i­cal­i­ty, and in small steps taken on an in­di­vid­ual level to­ward san­i­ty?

Dilemmas for Superrational Thinkers, Leading Up to a Luring Lottery


June, 1983

And then one fine day, out of the blue, you get a let­ter from S.N. Pla­to­nia, well-known Ok­la­homa oil tril­lion­aire, men­tion­ing that twenty lead­ing ra­tio­nal thinkers have been se­lected to par­tic­i­pate in a lit­tle game. “You are one of them!” it says. “Each of you has a chance at win­ning one bil­lion dol­lars, put up by the Pla­to­nia In­sti­tute for the Study of Hu­man Ir­ra­tional­i­ty. Here’s how. If you wish, you may send a telegram with just your name on it to the Pla­to­nia In­sti­tute in down­town Frogville, Ok­la­homa (pop. 2). You may re­verse the charges. If you re­ply within 48 hours, the bil­lion is yours—un­less there are two or more replies, in which case the prize is awarded to no one. And if no one replies, noth­ing will be awarded to any­one.”

You have no way of know­ing who the other nine­teen par­tic­i­pants are; in­deed, in its let­ter, the Pla­to­nia In­sti­tute states that the en­tire offer will be re­scinded if it is de­tected that any at­tempt what­so­ever has been made by any par­tic­i­pant to dis­cover the iden­tity of, or to es­tab­lish con­tact with, any other par­tic­i­pant. More­over, it is a con­di­tion that the win­ner (if there is one) must agree in writ­ing not to share the prize money with any other par­tic­i­pant at any time in the fu­ture. This is to squelch any thoughts of co­op­er­a­tion, ei­ther be­fore or after the prize is given out.

The bru­tal fact is that no one will know what any­one else is do­ing. Clear­ly, every­one will want that bil­lion. Clear­ly, every­one will re­al­ize that if their name is not sub­mit­ted, they have no chance at all. Does this mean that twenty telegrams will ar­rive in Frogville, show­ing that even pos­sess­ing tran­scen­dent lev­els of ra­tio­nal­i­ty—as you of course do—is of no help in such an ex­cru­ci­at­ing sit­u­a­tion?

This is the “Pla­to­nia Dilemma”, a lit­tle sce­nario I thought up re­cently in try­ing to get a bet­ter han­dle on the Pris­on­er’s Dilem­ma, of which I wrote


last month. The Pris­on­er’s Dilemma can be for­mu­lated in terms re­sem­bling this dilem­ma, as fol­lows. Imag­ine that you re­ceive a let­ter from the Pla­to­nia In­sti­tute telling you that you and just one other anony­mous lead­ing ra­tio­nal thinker have been se­lected for a mod­est cash give­away. As be­fore, both of you are re­quested to re­ply by telegram within 48 hours to the Pla­to­nia In­sti­tute, charges re­versed. Your telegram is to con­tain, aside from your name, just the word “co­op­er­ate” or the word “de­fect”. If two “co­op­er­ate”s are re­ceived, both of you will get $3. If two “de­fect”s are re­ceived, you both will get $1. If one of each is re­ceived, then the co­op­er­a­tor gets noth­ing and the de­fec­tor gets $5.

What choice would you make? It would be nice if you both co­op­er­at­ed, so you’d each get $3, but does­n’t it seem a lit­tle un­like­ly? After all, who wants to get suck­ered by a nasty, low-down, rot­ten de­fec­tor who gets $5 for be­ing sneaky? Cer­tainly not you! So you’d prob­a­bly de­cide not to co­op­er­ate.

It seems a re­gret­table but nec­es­sary choice. Of course, both of you, rea­son­ing alike, come to the same con­clu­sion. So you’ll both de­fect, and that way get a mere dol­lar apiece. And yet—if you’d just both been will­ing to risk a bit, you could have got­ten $3 apiece. What a pity!

It was my dis­com­fort with this seem­ingly log­i­cal analy­sis of the “one-round Pris­on­er’s Dilemma” that led me to for­mu­late the fol­low­ing let­ter, which I sent out to twenty friends after hav­ing cleared it with Sci­en­tific Amer­i­can

Dear X:

I am send­ing this let­ter out via Spe­cial De­liv­ery to twenty of ‘you’ (name­ly, var­i­ous friends of mine around the coun­try). I am propos­ing to all of you a one-round Pris­on­er’s Dilemma game, the pay­offs to be mon­e­tary (pro­vided by Sci­en­tific Amer­i­can). It’s very sim­ple. Here is how it goes.

Each of you is to give me a sin­gle let­ter: ‘C’ or ‘D’, stand­ing for ‘co­op­er­ate’ or ‘de­fect’. This will be used as your move in a Pris­on­er’s Dilemma with each of the nine­teen other play­ers. The pay­off ma­trix I am us­ing for the Pris­on­er’s Dilemma is given in the di­a­gram [see Fig­ure 29-1c].

Fig­ure 29-1. The Pris­on­er’s Dilem­ma.

Thus if every­one sends in ‘C’, every­one will get $57, while if every­one sends in ‘D’, every­one will get $19. You can’t lose! And of course, any­one who sends in ‘D’ will get at least as much as every­one else will. If, for ex­am­ple, 11 peo­ple send in ‘C’ and 9 send in ‘D’, then the 11 C-ers will get $3 apiece from each of the other C-ers (mak­ing $30), and zero from the D-ers. So C-ers will get $30 each. The D-ers, by con­trast, will pick up $5 apiece from each of the C-ers, mak­ing $55, and $1 from each of the other D-ers, mak­ing $8, for a grand to­tal of $63. No mat­ter what the dis­tri­b­u­tion is, D-ers al­ways do bet­ter than C-ers. Of course, the more C-ers there are, the bet­ter every­one will do!

By the way, I should make it clear that in mak­ing your choice, you should not aim to be the win­ner, but sim­ply to get as much money for your­self as pos­si­ble. Thus you should be hap­pier to get $30 (say, as a re­sult of say­ing ‘C’ along with 10 oth­ers, even though the 9 D-say­ers get more than you) than to get $19 (by


say­ing ‘D’ along with every­body else, so no­body ‘beats’ you). Fur­ther­more, you are not sup­posed to think that at some sub­se­quent time you will meet with and be able to share the goods with your co-par­tic­i­pants. You are not aim­ing at max­i­miz­ing the to­tal num­ber of dol­lars Sci­en­tific Amer­i­can shells out, only at max­i­miz­ing the num­ber that come to you!

Of course, your hope is to be the unique de­fec­tor, thus re­ally clean­ing up: with 19 C-ers, you’ll get $95 and they’ll each get 18 times $3, namely $54. But why am I do­ing the mul­ti­pli­ca­tion or any of this fig­ur­ing for you? You’re very bright. So are all of you! All about equally bright, I’d say, in fact. So all you need to do is tell me your choice. I want all an­swers by tele­phone (call col­lect, please) the day you re­ceive this let­ter.

It is to be un­der­stood (it al­most goes with­out say­ing, but not quite) that you are not to try to get in touch with and con­sult with oth­ers who you guess have been asked to par­tic­i­pate. In fact, please con­sult with no one at all. The pur­pose is to see what peo­ple will do on their own, in iso­la­tion. Fi­nal­ly, I would very much ap­pre­ci­ate a short state­ment to go along with your choice, telling me why you made this par­tic­u­lar choice.


P. S.—By the way, it may be help­ful for you to imag­ine a re­lated sit­u­a­tion, the same as the present one ex­cept that you are told that all the other play­ers have al­ready sub­mit­ted their choice (say, a week ago), and so you are the last. Now what do you do? Do you sub­mit ‘D’, know­ing full well that their an­swers are al­ready com­mit­ted to pa­per? Now sup­pose that, im­me­di­ately after hav­ing sub­mit­ted your ‘D’ (or your ‘C’) in that cir­cum­stance, you are in­formed that, in fact, the oth­ers re­ally haven’t sub­mit­ted their an­swers yet, but that they are all do­ing it to­day. Would you re­tract your an­swer? Or what if you knew (or at least were told) that you were the first per­son be­ing asked for an an­swer? And-one last thing to pon­der-what would you do if the pay­off ma­trix looked as shown in Fig­ure 30-la ?

FIGURE 30-1. In (a), a mod­i­fi­ca­tion of Fig­ure 29-1(c). Here, the in­cen­tive to de­fect seems con­sid­er­ably stronger. In (b), the pay­off ma­trix for a [Bob] Wolf’s Dilemma sit­u­a­tion in­volv­ing just two par­tic­i­pants. Com­pare it to that in Fig­ure 29-1(c).

Two game-the­ory pay­off ma­trixes for vari­ants on the Pris­on­er’s Dilemma by Hof­s­tadter


I wish to stress that this sit­u­a­tion is not an it­er­ated Pris­on­er’s Dilemma (dis­cussed in last mon­th’s colum­n). It is a one-shot, mul­ti­-per­son Pris­on­er’s Dilem­ma. There is no pos­si­bil­ity of learn­ing, over time, any­thing about how the oth­ers are in­clined to play. There­fore all lessons de­scribed last month are in­ap­plic­a­ble here, since they de­pend on the sit­u­a­tion’s be­ing it­er­at­ed. All that each re­cip­i­ent of my let­ter could go on was the thought, “There are nine­teen peo­ple out there, some­what like me, all in the same boat, all grap­pling with the same is­sues as I am.” In other words, there was noth­ing to rely on ex­cept pure rea­son.

I had much fun prepar­ing this let­ter, de­cid­ing who to send it out to, an­tic­i­pat­ing the re­spons­es, and then re­ceiv­ing them. It was amus­ing to me, for in­stance, to send Spe­cial De­liv­ery let­ters to two friends I was see­ing every day, with­out fore­warn­ing them. It was also amus­ing to send iden­ti­cal let­ters to a wife and hus­band at the same ad­dress.

Be­fore I re­veal the re­sults, I in­vite you to think how you would play in such a con­test. I would par­tic­u­larly like you to take se­ri­ously the as­ser­tion “every­one is very bright”. In fact, let me ex­pand on that idea, since I felt that peo­ple per­haps did not re­ally un­der­stand what I meant by it. Thus please con­sider the let­ter to con­tain the fol­low­ing clar­i­fy­ing para­graph:

All of you are very ra­tio­nal peo­ple. There­fore, I hardly need to tell you that you are to make what you con­sider to be your max­i­mally ra­tio­nal choice. In par­tic­u­lar, feel­ings of moral­i­ty, guilt, vague malaise, and so on, are to be dis­re­gard­ed. Rea­son­ing alone (of course in­clud­ing rea­son­ing about the oth­ers’ rea­son­ing) should be the ba­sis of your de­ci­sion. And please al­ways re­mem­ber that every­one is be­ing told this (in­clud­ing this!)!

I was hop­ing for—and ex­pect­ing—a par­tic­u­lar out­come to this ex­per­i­ment. As I re­ceived the replies by phone over the next sev­eral days, I jot­ted down notes so that I had a record of what im­pelled var­i­ous peo­ple to choose as they did. The re­sult was not what I had ex­pect­ed—in fact, my friends “faked me out” con­sid­er­ably. We got into heated ar­gu­ments about the “ra­tio­nal” thing to do, and every­one ex­pressed much in­ter­est in the whole ques­tion.

I would like to quote to you some of the feel­ings ex­pressed by my friends caught in this de­li­ciously tricky sit­u­a­tion. David Poli­can­sky opened his call tersely by say­ing, “Okay, Hof­s­tadter, give me the $19!” Then he pre­sented this ar­gu­ment for de­fect­ing: “What you’re ask­ing us to do, in effect, is to press one of two but­tons, know­ing noth­ing ex­cept that if we press but­ton D, we’ll get more than if we press but­ton C. There­fore D is bet­ter. That is the essence of my ar­gu­ment. I de­fect.”

(yes, I asked Mar­tin to par­tic­i­pate) vividly ex­pressed the emo­tional tur­moil he and many oth­ers went through. “Hor­ri­ble dilemma”, he said. “I re­ally don’t know what to do about it. If I wanted to max­i­mize”


“my mon­ey, I would choose D and ex­pect that oth­ers would al­so; to max­i­mize my sat­is­fac­tions, I’d choose C, and hope other peo­ple would do the same (by the Kant­ian im­per­a­tive). I don’t know, though, how one should be­have ra­tio­nal­ly. You get into end­less re­gress­es: ‘If they all do X, then I should do Y, but then they’ll an­tic­i­pate that and do Z, and so . . .’ You get trapped in an end­less whirlpool. It’s like .” So say­ing, Mar­tin de­fect­ed, with a sigh of re­gret.

In a way echo­ing Mar­t­in’s feel­ings of con­fu­sion, Chris Mor­gan said, “More by in­tu­ition than by any­thing else, I’m com­ing to the con­clu­sion that there’s no way to deal with the para­doxes in­her­ent in this sit­u­a­tion. So I’ve de­cided to flip a coin, be­cause I can’t an­tic­i­pate what the oth­ers are go­ing to do. I think—but can’t know—that they’re all go­ing to negate each oth­er.” So, while on the phone, Chris flipped a coin and “chose” to co­op­er­ate.

Sid­ney Nagel was very dis­pleased with his con­clu­sion. He ex­pressed great re­gret: “I ac­tu­ally could­n’t sleep last night be­cause I was think­ing about it. I wanted to be a co­op­er­a­tor, but I could­n’t find any way of jus­ti­fy­ing it. The way I fig­ured it, what I do is­n’t go­ing to affect what any­body else does. I might as well con­sider that every­thing else is al­ready fixed, in which case the best I can do for my­self is to play a D.”

, whose work proves the su­pe­ri­or­ity of co­op­er­a­tive strate­gies in the it­er­ated Pris­on­er’s Dilem­ma, saw no rea­son what­so­ever to co­op­er­ate in a one-shot game, and de­fected with­out any com­punc­tions.

was brief: “I fig­ure, if I de­fect, then I al­ways do at least as well as I would have if I had co­op­er­at­ed. So I de­fect.” She was one of the peo­ple who faked me out. Her hus­band, Pe­ter, co­op­er­at­ed. I had pre­dicted the re­verse.

By now, you have prob­a­bly been count­ing. So far, I’ve men­tioned five D’s and two C’s. Sup­pose you had been me, and you’d got­ten roughly a third of the calls, and they were 5-2 in fa­vor of de­fec­tion. Would you dare to ex­trap­o­late these sta­tis­tics to roughly 14-6? How in the world can seven in­di­vid­u­als’ choices have any­thing to do with thir­teen other in­di­vid­u­als’ choic­es? As Sid­ney Nagel said, cer­tainly one choice can’t in­flu­ence an­other (un­less you be­lieve in some kind of tele­pathic trans­mis­sion, a pos­si­bil­ity we shall dis­count here). So what jus­ti­fi­ca­tion might there be for ex­trap­o­lat­ing these re­sults?

Clear­ly, any such jus­ti­fi­ca­tion would rely on the idea that peo­ple are “like” each other in some sense. It would rely on the idea that in com­plex and tricky de­ci­sions like this, peo­ple will re­sort to a clus­ter of rea­sons, im­ages, prej­u­dices, and vague no­tions, some of which will tend to push them one way, oth­ers the other way, but whose over­all im­pact will be to push a cer­tain per­cent­age of peo­ple to­ward one al­ter­na­tive, and an­other per­cent­age of peo­ple to­ward the oth­er. In ad­vance, you can’t hope to pre­dict what those per­cent­ages will be, but given a sam­ple of peo­ple in the sit­u­a­tion, you can


hope that their de­ci­sions will be “typ­i­cal”. Thus the no­tion that early re­turns run­ning 5-2 in fa­vor of de­fec­tion can be ex­trap­o­lated to a fi­nal re­sult of 14-6 (or so) would be based on as­sum­ing that the seven peo­ple are act­ing “typ­i­cally” for peo­ple con­fronted with these con­flict­ing men­tal pres­sures.

The snag is that the men­tal pres­sures are not com­pletely ex­plic­it; they are evoked by, but not to­tally spelled out by, the word­ing of the let­ter. Each per­son brings a unique set of im­ages and as­so­ci­a­tions to each word and con­cept, and it is the set of those im­ages and as­so­ci­a­tions that will col­lec­tively cre­ate, in that per­son’s mind, a set of men­tal pres­sures like the set of pres­sures in­side the earth in an earth­quake zone. When peo­ple de­cide, you find out how all those pres­sures push­ing in differ­ent di­rec­tions add up, like a set of force vec­tors push­ing in var­i­ous di­rec­tions and with strengths in­flu­enced by pri­vate or un­mea­sur­able fac­tors. The as­sump­tion that it is valid to ex­trap­o­late has to be based on the idea that every­body is alike in­side, only with some­what differ­ent weights at­tached to cer­tain no­tions.

This way, each per­son’s de­ci­sion can be likened to a “geo­physics ex­per­i­ment” whose goal is to pre­dict where an earth­quake will ap­pear. You set up a model of the earth’s crust and you put in data rep­re­sent­ing your best un­der­stand­ing of the in­ter­nal pres­sures. You know that there un­for­tu­nately are large un­cer­tain­ties in your knowl­edge, so you just have to choose what seem to be “rea­son­able” val­ues for var­i­ous vari­ables. There­fore no sin­gle run of your sim­u­la­tion will have strong pre­dic­tive pow­er, but that’s all right. You run it and you get a fault line telling you where the sim­u­lated earth shifts. Then you go back and choose other val­ues in the ranges of those vari­ables, and re­run the whole thing. If you do this re­peat­ed­ly, even­tu­ally a pat­tern will emerge re­veal­ing where and how the earth is likely to shift and where it is rock­-sol­id.

This kind of sim­u­la­tion de­pends on an es­sen­tial prin­ci­ple of sta­tis­tics: the idea that when you let vari­ables take on a few sam­ple ran­dom val­ues in their ranges, the over­all out­come de­ter­mined by a clus­ter of such vari­ables will start to emerge after a few tri­als and soon will give you an ac­cu­rate mod­el. You don’t need to run your sim­u­la­tion mil­lions of times to see valid trends emerg­ing.

This is clearly the kind of as­sump­tion that TV net­works make when they pre­dict na­tional elec­tion re­sults on the ba­sis of early re­turns from a few se­lect towns in the East. Cer­tainly they don’t think that free will is any “freer” in the East than in the West­—that what­ever the East chooses to do, the West will fol­low suit. It is just that the clus­ter of emo­tional and in­tel­lec­tual pres­sures on vot­ers is much the same all over the na­tion. Ob­vi­ous­ly, no in­di­vid­ual can be taken as rep­re­sent­ing the whole na­tion, but a well-s­e­lected group of res­i­dents of the East Coast can be as­sumed to be rep­re­sen­ta­tive of the whole na­tion in terms of how much they are “pushed” by the var­i­ous pres­sures of the elec­tion, so that their choices are likely to show gen­eral trends of the larger elec­torate.

Sup­pose it turned out that New Hamp­shire’s Belk­nap County and


Cal­i­for­ni­a’s Modoc County had pro­duced, over many na­tional elec­tions, very sim­i­lar re­sults. Would it fol­low that one of the two coun­ties had been ex­ert­ing some sort of causal in­flu­ence on the oth­er? Would they have had to be in some sort of eerie cos­mic res­o­nance me­di­ated by “sym­pa­thetic magic” for this to hap­pen? Cer­tainly not. All it takes is for the elec­torates of the two coun­ties to be sim­i­lar; then the pres­sures that de­ter­mine how peo­ple vote will take over and au­to­mat­i­cally make the re­sults come out sim­i­lar. It is no more mys­te­ri­ous than the ob­ser­va­tion that a Belk­nap County school­girl and a Modoc County school­boy will get the same an­swer when asked to di­vide 507 by 13: the laws of arith­metic are the same the world over, and they op­er­ate the same in re­mote minds with­out any need for “sym­pa­thetic magic”.

This is all el­e­men­tary com­mon sense; it should be the kind of thing that any well-e­d­u­cated per­son should un­der­stand clear­ly. And yet emo­tion­ally it can­not help but feel a lit­tle pe­cu­liar since it flies in the face of free will and re­gards peo­ple’s de­ci­sions as caused sim­ply by com­bi­na­tions of pres­sures with un­known val­ues. On the other hand, per­haps that is a bet­ter way to look at de­ci­sions than to at­tribute them to “free will”, a philo­soph­i­cally murky no­tion at best.

This may have seemed like a di­gres­sion about sta­tis­tics and the ques­tion of in­di­vid­ual ac­tions ver­sus group pre­dictabil­i­ty, but as a mat­ter of fact it has plenty to do with the “cor­rect ac­tion” to take in the dilemma of my let­ter. The ques­tion we were con­sid­er­ing is: To what ex­tent can what a few peo­ple do be taken as an in­di­ca­tion of what all the peo­ple will do? We can sharpen it: To what ex­tent can what one per­son does be taken as an in­di­ca­tion of what all the peo­ple will do? The ul­ti­mate ver­sion of this ques­tion, stated in the first per­son, has a funny twist to it: To what ex­tent does my choice in­form me about the choices of the other par­tic­i­pants?

You might feel that each per­son is com­pletely unique and there­fore that no one can be re­lied on as a pre­dic­tor of how other peo­ple will act, es­pe­cially in an in­tensely dilem­matic sit­u­a­tion. There is more to the sto­ry, how­ev­er. I tried to en­gi­neer the sit­u­a­tion so that every­one would have the same im­age of the sit­u­a­tion. In the dead cen­ter of that im­age was sup­posed to be the no­tion that every­one in the sit­u­a­tion was us­ing rea­son­ing alone—in­clud­ing rea­son­ing about the rea­son­ing—to come to an an­swer.

Now, if rea­son­ing dic­tates an an­swer, then every­one should in­de­pen­dently come to that an­swer (just as the Belk­nap County school­girl and the Modoc County school­boy would in­de­pen­dently get 39 as their an­swer to the di­vi­sion prob­lem). See­ing this fact is it­self the crit­i­cal step in the rea­son­ing to­ward the cor­rect an­swer, but un­for­tu­nately it eluded nearly every­one to whom I sent the let­ter. (That is why I came to wish I had in­cluded in the let­ter a para­graph stress­ing the ra­tio­nal­ity of the play­er­s.) Once you re­al­ize


this fact, then it dawns on you that ei­ther all ra­tio­nal play­ers will choose D or all ra­tio­nal play­ers will choose C. This is the crux.

Any num­ber of ideal ra­tio­nal thinkers faced with the same sit­u­a­tion and un­der­go­ing sim­i­lar throes of rea­son­ing agony will nec­es­sar­ily come up with the iden­ti­cal an­swer even­tu­al­ly, so long as rea­son­ing alone is the ul­ti­mate jus­ti­fi­ca­tion for their con­clu­sion. Oth­er­wise rea­son­ing would be sub­jec­tive, not ob­jec­tive as arith­metic is. A con­clu­sion reached by rea­son­ing would be a mat­ter of pref­er­ence, not of ne­ces­si­ty. Now some peo­ple may be­lieve this of rea­son­ing, but ra­tio­nal thinkers un­der­stand that a valid ar­gu­ment must be uni­ver­sally com­pelling, oth­er­wise it is sim­ply not a valid ar­gu­ment.

If you’ll grant this, then you are 90%of the way. All you need ask now is, “Since we are all go­ing to sub­mit the same let­ter, which one would be more log­i­cal? That is, which world is bet­ter for the in­di­vid­ual ra­tio­nal thinker: one with all C’s or one with all D’s?” The an­swer is im­me­di­ate: “I get $57 if we all co­op­er­ate, $19 if we all de­fect. Clearly I pre­fer $57, hence co­op­er­at­ing is pre­ferred by this par­tic­u­lar ra­tio­nal thinker. Since I am typ­i­cal, co­op­er­at­ing must be pre­ferred by all ra­tio­nal thinkers. So I’ll co­op­er­ate.” An­other way of stat­ing it, mak­ing it sound weird­er, is this: “If I choose C, then every­one will choose C, so I’ll get $57. If I choose D, then every­one will choose D, so I’ll get $19. I’d rather have $57 than $19, so I’ll choose C. Then every­one will, and I’ll get $57.”

To many peo­ple, this sounds like a be­lief in voodoo or sym­pa­thetic mag­ic, a vi­sion of a uni­verse per­me­ated by ten­u­ous threads of , con­vey­ing thoughts from mind to mind like pneu­matic tubes car­ry­ing mes­sages across Paris, and mak­ing peo­ple res­onate to a se­cret har­mo­ny. Noth­ing could be fur­ther from the truth. This so­lu­tion de­pends in no way on telepa­thy or bizarre forms of causal­i­ty. It’s just that the state­ment “I’ll choose C and then every­one will”, though en­tirely cor­rect, is some­what mis­lead­ingly phrased. It in­volves the word “choice”, which is in­com­pat­i­ble with the com­pelling qual­ity of log­ic. School­child­ren do not choose what 507 di­vided by 13 is; they fig­ure it out. Anal­o­gous­ly, my let­ter re­ally did not al­low choice; it de­manded rea­son­ing. Thus, a bet­ter way to phrase the “voodoo” state­ment would be this: “If rea­son­ing guides me to say C, then, as I am no differ­ent from any­one else as far as ra­tio­nal think­ing is con­cerned, it will guide every­one to say C.”

The cor­re­spond­ing foray into the op­po­site world (“If I choose D, then every­one will choose D”) can be un­der­stood more clearly by liken­ing it to a mus­ing done by the Belk­nap County school­girl be­fore she di­vides: “Hmm, I’d guess that 13 into 507 is about 49—­maybe 39. I see I’ll have to cal­cu­late it out. But I know in ad­vance that if I find out that it’s 49, then sure as shoot­in’, that Modoc County kid will write down 49 on his pa­per as well; and if I get 39 as my an­swer, then so will he.” No se­cret trans­mis­sions are in­volved; all that is needed is the uni­ver­sal­ity and uni­for­mity of arith­metic.


Like­wise, the ar­gu­ment “What­ever I do, so will every­one else do” is sim­ply a state­ment of faith that rea­son­ing is uni­ver­sal, at least among ra­tio­nal thinkers, not an en­dorse­ment of any mys­ti­cal kind of causal­i­ty.

This analy­sis shows why you should co­op­er­ate even when the opaque en­velopes con­tain­ing the other play­ers’ an­swers are right there on the ta­ble in front of you. Faced so con­cretely with this un­al­ter­able set of C’s and D’s, you might think, “What­ever they have done, I am bet­ter off play­ing D than play­ing C—­for cer­tainly what I now choose can have no retroac­tive effect on .what they chose. So I de­fect.” Such a thought, how­ev­er, as­sumes that the logic that now dri­ves you to play­ing D has no con­nec­tion or re­la­tion to the logic that ear­lier drove them to their de­ci­sions. But if you ac­cept what was stated in the let­ter, then you must con­clude that the de­ci­sion you now make will be mir­rored by the plays in the en­velopes be­fore you. If logic now co­erces you to play D, it has al­ready co­erced the oth­ers to do the same, and for the same rea­sons; and con­verse­ly, if logic co­erces you to play C, it has also al­ready co­erced the oth­ers to do that.

Imag­ine a pile of en­velopes on your desk, all con­tain­ing other peo­ple’s an­swers to the arith­metic prob­lem, “What is 507 di­vided by 13?” Hav­ing hur­riedly cal­cu­lated your an­swer, you are about to seal a sheet say­ing “49” in­side your en­velope, when at the last mo­ment you de­cide to check it. You dis­cover your er­ror, and change the ‘4’ to a ‘3’. Do you at that mo­ment en­vi­sion all the an­swers in­side the other en­velopes sud­denly piv­ot­ing on their heels and switch­ing from “49” to “39”? Of course not! You sim­ply rec­og­nize that what is chang­ing is your im­age of the con­tents of those en­velopes, not the con­tents them­selves. You used to think there were many “49”s. You now think there are many “39”s. How­ev­er, it does­n’t fol­low that there was a mo­ment in be­tween, at which you thought, “They’re all switch­ing from ‘49’ to ‘39’!” In fact, you’d be crazy to think that.

It’s sim­i­lar with D’s and C’s. If at first you’re in­clined to play one way but on care­ful con­sid­er­a­tion you switch to the other way, the other play­ers ob­vi­ously won’t retroac­tively or syn­chro­nis­ti­cally fol­low you—but if you give them credit for be­ing able to see the logic you’ve seen, you have to as­sume that their an­swers are what yours is. In short, you aren’t go­ing to be able to un­der­cut them; you are sim­ply “in ca­hoots” with them, like it or not! Ei­ther all D’s, or all C’s. Take your pick.

Ac­tu­al­ly, say­ing “Take your pick” is 100% mis­lead­ing. It’s not as if you could merely “pick”, and then other peo­ple—even in the past—­would mag­i­cally fol­low suit! The point is that since you are go­ing to be “choos­ing” by us­ing what you be­lieve to be com­pelling log­ic, if you truly re­spect your log­ic’s com­pelling qual­i­ty, you would have to be­lieve that oth­ers would buy it as well, which means that you are cer­tainly not “just pick­ing”. In fact, the more con­vinced you are of what you are play­ing, the more cer­tain you should be that oth­ers will also play (or have al­ready played) the same way, and for the same rea­sons. This holds whether you play C or D, and it is the real core of the so­lu­tion. In­stead of be­ing a para­dox, it’s a self­-re­in­forc­ing so­lu­tion: a be­nign cir­cle of log­ic.


If this still sounds like ret­ro­grade causal­ity to you, con­sider this lit­tle tale, which may help make it all make more sense. Sup­pose you and Jane are clas­si­cal mu­sic lovers. Over the years, you have dis­cov­ered that you have in­cred­i­bly sim­i­lar tastes in mu­sic—a re­mark­able co­in­ci­dence! Now one day you find out that two con­certs are be­ing given si­mul­ta­ne­ously in the town where you live. Both of them sound ex­cel­lent to you, but Con­cert A sim­ply can­not be missed, whereas Con­cert B is a strong temp­ta­tion that you’ll have to re­sist. Still, you’re ex­tremely cu­ri­ous about Con­cert B, be­cause it fea­tures Zilenko Buz­nani, a vi­o­lin­ist you’ve al­ways heard amaz­ing things about.

At first, you’re dis­ap­point­ed, but then a flash crosses your mind: “Maybe I can at least get a first-hand re­port about Zilenko Buz­nani’s play­ing from Jane. Since she and I hear every­thing through vir­tu­ally the same ears, it would be al­most as good as my go­ing if she would go.” This is com­fort­ing for a mo­ment, un­til it oc­curs to you that some­thing is wrong here. For the same rea­sons as you do, Jane will in­sist on hear­ing Con­cert A. After all, she loves mu­sic in the same way as you do—that’s pre­cisely why you wish she would tell you about Con­cert B! The more you feel Jane’s taste is the same as yours, the more you wish she would go to the other con­cert, so that you could know what it was like to have gone to it. But the more her taste is the same is yours, the less she will want to go to it!

The two of you are tied to­gether by a bond of com­mon taste. And if it turns out that you are differ­ent enough in taste to dis­agree about which con­cert is bet­ter, then that will tend to make you lose in­ter­est in what she might re­port, since you no longer can trust her opin­ion as that of some­one who hears mu­sic “through your ears”. In other words, hop­ing she’ll choose Con­cert B is point­less, since it un­der­mines your rea­sons for car­ing which con­cert she choos­es!

The anal­ogy is clear, I hope. Choos­ing D un­der­mines your rea­sons for do­ing so. To the ex­tent that all of you re­ally are ra­tio­nal thinkers, you re­ally will think in the same tracks. And my let­ter was sup­posed to es­tab­lish be­yond doubt the no­tion that you are all “in synch”; that is, to en­sure that you can de­pend on the oth­ers’ thoughts to be ra­tio­nal, which is all you need.

Well, not quite. You need to de­pend not just on their be­ing ra­tio­nal, but on their de­pend­ing on every­one else to be ra­tio­nal, and on their de­pend­ing on every­one to de­pend on every­one to be ra­tio­nal—and so on. A group of rea­son­ers in this re­la­tion­ship to each other I call su­per­ra­tional. Su­per­ra­tional thinkers, by re­cur­sive de­fi­n­i­tion, in­clude in their cal­cu­la­tions the fact that they are in a group of su­per­ra­tional thinkers. In this way, they re­sem­ble el­e­men­tary par­ti­cles that are .

A renor­mal­ized elec­tron’s style of in­ter­act­ing with, say, a renor­mal­ized pho­ton takes into ac­count that the pho­ton’s quan­tum-me­chan­i­cal struc­ture in­cludes “” and that the elec­tron’s quan­tum-me­chan­i­cal struc­ture in­cludes “vir­tual pho­tons”; more­over it takes into ac­count that all


these vir­tual par­ti­cles (them­selves renor­mal­ized) also in­ter­act with one an­oth­er. An in­fi­nite cas­cade of pos­si­bil­i­ties en­sues but is taken into ac­count in one fell swoop by na­ture. Sim­i­lar­ly, su­per­ra­tional­i­ty, or renor­mal­ized rea­son­ing, in­volves see­ing all the con­se­quences of the fact that other renor­mal­ized rea­son­ers are in­volved in the same sit­u­a­tion-and do­ing so in a fi­nite swoop rather than suc­cumb­ing to an in­fi­nite regress of rea­son­ing about rea­son­ing about rea­son­ing …

‘C’ is the an­swer I was hop­ing to re­ceive from every­one. I was not so op­ti­mistic as to be­lieve that lit­er­ally every­one would ar­rive at this con­clu­sion, but I ex­pected a ma­jor­ity would—thus my dis­may when the early re­turns strongly fa­vored de­fect­ing. As more phone calls came in, I did re­ceive some C’s, but for the wrong rea­sons. co­op­er­at­ed, say­ing, “I would rather be the per­son who bought the Brook­lyn Bridge than the per­son who sold it. Sim­i­lar­ly, I’d feel bet­ter spend­ing $3 gained by co­op­er­at­ing than $10 gained by de­fect­ing.”

, who I’d fig­ured to be a sure-fire D, took me by sur­prise and C’d. When I asked him why, he can­didly replied, “Be­cause I don’t want to go on record in an in­ter­na­tional jour­nal as a de­fec­tor.” Very well. Know, World, that Charles Bren­ner is a co­op­er­a­tor!

Many peo­ple flirted with the idea that every­body would think “about the same”, but did not take it se­ri­ously enough. Scott Bu­resh con­fided to me: “It was not an easy choice. I found my­self in an os­cil­la­tion mode: back and forth. I made an as­sump­tion: that every­body went through the same men­tal processes I went through. Now I per­son­ally found my­self want­ing to co­op­er­ate roughly one third of the time. Based on that fig­ure and the as­sump­tion that I was typ­i­cal, I fig­ured about one third of the peo­ple would co­op­er­ate. So I com­puted how much I stood to make in a field where six or seven peo­ple co­op­er­ate. It came out that if I were a D, I’d get about three times as much as if I were a C. So I’d have to de­fect. Wa­ter seeks out its own lev­el, and I sank to the lower right-hand cor­ner of the ma­trix.” At this point, I told Scott that so far, a sub­stan­tial ma­jor­ity had de­fect­ed. He re­acted swift­ly: “Those rat­s—how can they all de­fect? It makes me so mad! I’m re­ally dis­ap­pointed in your friends, Doug.” So was I, when the fi­nal re­sults were in: Four­teen peo­ple had de­fected and six had co­op­er­at­ed—ex­actly what the net­works would have pre­dict­ed! De­fec­tors thus re­ceived $43 while co­op­er­a­tors got $15. I won­der what Dorothy’s say­ing to Pe­ter about now? I bet she’s chuck­ling and say­ing, “I told you I’d do bet­ter this way, did­n’t I?” Ah, me … What can you do with peo­ple like that?

A strik­ing as­pect of Scott Bu­resh’s an­swer is that, in effect, he treated his own brain as a sim­u­la­tion of other peo­ple’s brains and ran the sim­u­la­tion enough to get a sense of what a “typ­i­cal per­son” would do. This is very


much in the spirit of my let­ter. Hav­ing as­sessed what the sta­tis­tics are likely to be, Scott then did a cool-headed cal­cu­la­tion to max­i­mize his profit, based on the as­sump­tion of six or seven co­op­er­a­tors. Of course, it came out in fa­vor of de­fect­ing. In fact, it would have, no mat­ter what the num­ber of co­op­er­a­tors was! Any such cal­cu­la­tion will al­ways come out in fa­vor of de­fect­ing. As long as you feel your de­ci­sion is in­de­pen­dent of oth­ers’ de­ci­sions, you should de­fect. What Scott failed to take into ac­count was that cool-headed cal­cu­lat­ing peo­ple should take into ac­count that cool-headed cal­cu­lat­ing peo­ple should take into ac­count that cool-headed cal­cu­lat­ing peo­ple should take into ac­count that …

This sounds aw­fully hard to take into ac­count in a fi­nite way, but ac­tu­ally it’s the eas­i­est thing in the world. All it means is that all these heavy-duty ra­tio­nal thinkers are go­ing to see that they are in a sym­met­ric sit­u­a­tion, so that what­ever rea­son dic­tates to one, it will dic­tate to all. From that point on, the process is very sim­ple. Which is bet­ter for an in­di­vid­ual if it is a uni­ver­sal choice: C or D? That’s all.

Ac­tu­al­ly, it’s not quite all, for I’ve swept one pos­si­bil­ity un­der the rug: maybe throw­ing a die could be bet­ter than mak­ing a de­ter­min­is­tic choice. Like Chris Mor­gan, you might think the best thing to do is to choose C with prob­a­bil­ity p and D with prob­a­bil­ity . Chris ar­bi­trar­ily let p be 1⁄2, but it could be any num­ber be­tween 0 and 1, where the two ex­tremes rep­re­sent Ding and C’ing re­spec­tive­ly. What value of p would be cho­sen by su­per­ra­tional play­ers? It is easy to fig­ure out in a two-per­son Pris­on­er’s Dilem­ma, where you as­sume that both play­ers use the same value of p. The ex­pected earn­ings for each, as a func­tion of p, come out to be , which grows mo­not­o­n­i­cally as p in­creases from 0 to 1. There­fore, the op­ti­mum value of p is 1, mean­ing cer­tain co­op­er­a­tion. In the case of more play­ers, the com­pu­ta­tions get more com­plex but the an­swer does­n’t change: the ex­pec­ta­tion is al­ways max­i­mal when p equals 1. Thus this ap­proach con­firms the ear­lier one, which did­n’t en­ter­tain prob­a­bilis­tic strate­gies.—Rolling a die to de­ter­mine what you’ll do did­n’t add any­thing new to the stan­dard Pris­on­er’s Dilem­ma, but what about the mod­i­fied-ma­trix ver­sion I gave in the P. S. to my let­ter? I’ll let you fig­ure that one out for your­self. And what about the Pla­to­nia Dilem­ma? There, two things are very clear: (1) if you de­cide not to send a telegram, your chances of win­ning are ze­ro; (2) if every­one sends a telegram, your chances of win­ning are ze­ro. If you be­lieve that what you choose will be the same as what every­one else chooses be­cause you are all su­per­ra­tional, then nei­ther of these al­ter­na­tives is very ap­peal­ing. With dice, how­ev­er, a new op­tion presents it­self to roll a die with prob­a­bil­ity p of com­ing up “good” and then to send in your name if and only if “good” comes up.

Now imag­ine twenty peo­ple all do­ing this, and fig­ure out what value of


p max­i­mizes the like­li­hood of ex­actly one per­son get­ting the go-a­head. It turns out that it is , or more gen­er­al­ly, where N is the num­ber of par­tic­i­pants. In the limit where N ap­proaches in­fin­i­ty, the chance that ex­actly one per­son will get the go-a­head is , which is just un­der 37%. With twenty su­per­ra­tional play­ers all throw­ing dice, the chance that you will come up the big win­ner is very close to , which is a lit­tle be­low 2%. That’s not at all bad! Cer­tainly it’s a lot bet­ter than 0%.

The ob­jec­tion many peo­ple raise is: “What if my roll comes up bad? Then why should­n’t I send in my name any­way? After all, if I fail to, I’ll have no chance what­so­ever of win­ning. I’m no bet­ter off than if I had never rolled my die and had just vol­un­tar­ily with­drawn!” This ob­jec­tion seems over­whelm­ing at first, but ac­tu­ally it is fal­la­cious, be­ing based on a mis­rep­re­sen­ta­tion of the mean­ing of “mak­ing a de­ci­sion”. A gen­uine de­ci­sion to abide by the throw of a die means that you re­ally must abide by the throw of the die; if un­der cer­tain cir­cum­stances you ig­nore the die and do some­thing else, then you never made the de­ci­sion you claimed to have made. Your de­ci­sion is re­vealed by your ac­tions, not by your words be­fore act­ing!

If you like the idea of rolling a die but fear that your will power may not be up to re­sist­ing the temp­ta­tion to de­fect, imag­ine a third “Poli­can­sky but­ton”: this one says ‘R’ for “Roll”, and if you press it, it rolls a die (per­haps sim­u­lat­ed) and then in­stantly and ir­rev­o­ca­bly ei­ther sends your name or does not, de­pend­ing on which way the die came up. This way you are never al­lowed to go back on your de­ci­sion after the die is cast. Push­ing that but­ton is mak­ing a gen­uine de­ci­sion to abide by the roll of a die. It would be eas­ier on any or­di­nary hu­man to be thus shielded from the temp­ta­tion, but any su­per­ra­tional player would have no trou­ble hold­ing back after a bad roll.

This talk of hold­ing back in the face of strong temp­ta­tion brings me to the cli­max of this column: the an­nounce­ment of a Lur­ing Lot­tery open to all read­ers and non­read­ers of Sci­en­tific Amer­i­can. The prize of this lot­tery is $, where N is the num­ber of en­tries sub­mit­ted. Just think: If you are the only en­trant (and if you sub­mit only one en­try), a cool mil­lion is yours! Per­haps, though, you doubt this will come about. It does seem a tri­fle iffy. If you’d like to in­crease your chances of win­ning, you are en­cour­aged to send in mul­ti­ple en­tries—no lim­it! Just send in one post­card per en­try. If you send in 100 en­tries, you’ll have 100 times the chance of some poor slob who sends in just one. Come to think of it, why should you have to send in mul­ti­ple en­tries sep­a­rate­ly? Just send one post­card with your name and ad­dress and a pos­i­tive in­te­ger (telling how many en­tries you’re mak­ing) to:

Luring Lottery
c/o Scientific American
415 Madison Avenue
New York, N.Y. 10017

You will be given the same chance of win­ning as if you had sent in that num­ber of post­cards with ‘1’ writ­ten on them. Il­leg­i­ble, in­co­her­ent, il­l-spec­i­fied, or in­com­pre­hen­si­ble en­tries will be dis­qual­i­fied. Only en­tries re­ceived by mid­night June 30, 1983 will be con­sid­ered. Good luck to you (but cer­tainly not to any-other reader of this colum­n)!

Post Scriptum

The emo­tions churned up by the Pris­on­er’s Dilemma are among the strongest I have ever en­coun­tered, and for good rea­son. Not only is it a won­der­ful in­tel­lec­tual puz­zle, akin to some of the most fa­mous para­doxes of all time, but also it cap­tures in a pow­er­ful and pithy way the essence of a myr­iad deep and dis­turb­ing sit­u­a­tions that we are fa­mil­iar with from life. Some are choices we make every day; oth­ers are the kind of ag­o­niz­ing choices that we all oc­ca­sion­ally muse about but hope the world will never make us face.

My friend Bob Wolf, a math­e­mati­cian whose spe­cialty is log­ic, adamantly ad­vo­cated choos­ing D in the case of the let­ters I sent out. To de­fend his choice, he be­gan by say­ing that it was clearly “a para­dox with no ra­tio­nal so­lu­tion”, and thus there was no way to know what peo­ple would do. Then he said, “There­fore, I will choose D. I do bet­ter that way than any other way.” I protested stren­u­ous­ly: “How dare you say ‘there­fore’ when you’ve just got­ten through de­scrib­ing this sit­u­a­tion as a para­dox and claim­ing there is no ra­tio­nal an­swer? How dare you say logic is forc­ing an an­swer down your throat, when the premise of your ‘logic’ is that there is no log­i­cal an­swer?” I never got what I con­sid­ered a sat­is­fac­tory an­swer from Bob, al­though nei­ther of us could budge the oth­er. How­ev­er, I did fi­nally get some in­sight into Bob’s vi­sion when he, pushed hard by my prob­ing, in­vented a sit­u­a­tion with a new twist to it, which I call “Wolf’s Dilemma”.

Imag­ine that twenty peo­ple are se­lected from your high school grad­u­a­tion class, you among them. You don’t know which oth­ers have been se­lect­ed, and you are told they are scat­tered all over the coun­try. All you know is that they are all con­nected to a cen­tral com­put­er. Each of you is in a lit­tle cu­bi­cle, seated on a chair and fac­ing one but­ton on an oth­er­wise blank wall. You are given ten min­utes to de­cide whether or not to push your but­ton. At the end of that time, a light will go on for ten sec­onds, and while it is on, you may


ei­ther push or re­frain from push­ing. All the re­sponses will then go to the cen­tral com­put­er, and one minute lat­er, they will re­sult in con­se­quences. For­tu­nate­ly, the con­se­quences can only be good. If you pushed your but­ton, you will get $100, no strings at­tached, emerg­ing from a small slot be­low the but­ton. If no­body pushed their but­ton, then every­body will get $1,000. But if there was even a sin­gle but­ton-push­er, the re­frain­ers will get noth­ing at all.

Bob asked me what I would do. Un­hesi­tat­ing­ly, I said, “Of course I would not push the but­ton. It’s ob­vi­ous!” To my amaze­ment, though, Bob said he’d push the but­ton with no qualms. I said, “What if you knew your co-play­ers were all lo­gi­cians?” He said that would make no differ­ence to him. Whereas I gave credit to every­body for be­ing able to see that it was to every­one’s ad­van­tage to re­frain, Bob did not. Or at least he ex­pected that there is enough “flak­i­ness” in peo­ple that he would pre­fer not to rely on the ra­tio­nal­ity of nine­teen other peo­ple. But of course in as­sum­ing the flak­i­ness of oth­ers, he would be his own best ex­am­ple—ru­in­ing every­one else’s chances of get­ting $1,000.

What both­ered me about Wolf’s Dilemma was what I have come to call re­ver­ber­ant doubt. Sup­pose you are won­der­ing what to do. At first it’s ob­vi­ous that every­body should avoid push­ing their but­ton. But you do re­al­ize that among twenty peo­ple, there might be one who is slightly hes­i­tant and who might wa­ver a bit. This fact is enough to worry you a tiny bit, and thus to make you wa­ver, ever so slight­ly. But sud­denly you re­al­ize that if you are wa­ver­ing, even just a tiny bit, then most likely every­one is wa­ver­ing a tiny bit. And that’s con­sid­er­ably worse than what you’d thought at first—­name­ly, that just one per­son might be wa­ver­ing. Uh-oh! Now that you can imag­ine that every­body is at least con­tem­plat­ing push­ing their but­ton, the sit­u­a­tion seems a lot more se­ri­ous. In fact, now it seems quite prob­a­ble that at least one per­son will push their but­ton. But if that’s the case, then push­ing your own but­ton seems the only sen­si­ble thing to do. As you catch your­self think­ing this thought, you re­al­ize it must be the same as every­one else’s thought. At this point, it be­comes plau­si­ble that the ma­jor­ity of par­tic­i­pants—­pos­si­bly even al­l—will push their but­ton! This clinches it for you, and so you de­cide to push yours.

Is­n’t this an amaz­ing and dis­turb­ing slide from cer­tain re­straint to cer­tain push­ing? It is a cas­cade, a stam­pede, in which the tini­est flicker of a doubt has be­come am­pli­fied into the gravest avalanche of doubt. That’s what I mean by “re­ver­ber­ant doubt”. And one of the an­noy­ing things about it is that the brighter you are, the more quickly and clearly you see what there is to fear. A bunch of ami­able slow­pokes might well be more likely to unan­i­mously re­frain and get the big pay­off than a bunch of ra­zor-sharp lo­gi­cians who all think per­versely re­cur­sively re­ver­ber­ant­ly. It’s that “smart­ness” to see that ini­tial flicker of a doubt that trig­gers the whole avalanche and sends ra­tio­nal­ity a-tum­blin’ in­to—the abyss. So, dear reader . . . if you push that but­ton in front of you, do you thereby lose $900 or do you thereby gain $100?


Wolf’s Dilemma is not the same as the Pris­on­er’s Dilem­ma. In the Pris­on­er’s Dilem­ma, pres­sure to­wards de­fec­tion springs from hope for asym­me­try (i.e., hope that the other player might be dumber than you and thus make the op­po­site choice) whereas in Wolf’s Dilem­ma, pres­sure to­wards but­ton-push­ing springs from fear of asym­me­try (i.e., fear that the other player might be dumber than you and thus make the op­po­site choice). This differ­ence shows up clearly in the games’ pay­off ma­tri­ces for the two-per­son case (com­pare Fig­ure 30-lb with Fig­ure 29-1c). In the Pris­on­er’s Dilem­ma, the temp­ta­tion T is greater than the re­ward R (5 > 3), whereas in Wolf’s Dilem­ma, R is greater than T (1,000 > 100).

Bob Wolf’s choice in his own dilemma re­vealed to me some­thing about his ba­sic as­sess­ment of peo­ple and their re­li­a­bil­ity (or lack there­of). Since his adamant de­ci­sion to be a but­ton-pusher even in this case stunned me, I de­cided to ex­plore that cyn­i­cism a bit more, and came up with this mod­i­fied Wolf’s Dilem­ma.

Imag­ine, as be­fore, that twenty peo­ple have been se­lected from your high school grad­u­a­tion class, and are es­corted to small cu­bi­cles with one but­ton on the wall. This time, how­ev­er, each of you is strapped into a chair, and a de­vice con­tain­ing a re­volver is at­tached to your head. Like it or not, you are now go­ing to play Russ­ian roulet­te, the odds of your death to be de­ter­mined by your choice. For any­body who pushes their but­ton, the odds of sur­vival will be set at 90%—only one chance in ten of dy­ing. Not too bad, but given that there are twenty of you, it means that al­most cer­tainly one or two of you will die, pos­si­bly more. And what hap­pens to the re­frain­ers? It all de­pends on how many of them there are. Let’s say there are N re­frain­ers. For each one of them, their chance of be­ing shot will be one in N2. For in­stance, if five peo­ple don’t push, each of them will have only a 1⁄25 chance of dy­ing. If ten peo­ple re­frain, they will each get a 99% chance of sur­vival. The bad cases are, of course, when nearly every­body pushes their but­ton (“play­ing it safe”, so to speak), leav­ing the re­frain­ers in a tiny mi­nor­ity of three, two, or even one. If you’re the sole re­frain­er, it’s cur­tains for you—one chance in one of your death. Bye-bye! For two re­frain­ers, it’s one chance in four for each one. That means there’s nearly a 50% chance that at least one of the two will per­ish.

Clearly the crossover line is be­tween three and four re­frain­ers. If you have a rea­son­able de­gree of con­fi­dence that at least three other peo­ple will hold back, you should defi­nitely do so your­self. The only prob­lem is, they’re all mak­ing their de­ci­sions on the ba­sis of try­ing to guess how many peo­ple will re­frain, too! It’s ter­ri­bly cir­cu­lar, and you hardly know where to start. Many peo­ple, sens­ing this, just give up, and de­cide to push their but­ton. (Ac­tu­al­ly, of course, how do I know? I’ve never seen peo­ple in such a sit­u­a­tion—but it seems that way from ev­i­dence of re­al-life sit­u­a­tions re­sem­bling this, and of course from how peo­ple re­spond to a mere de­scrip­tion of this sit­u­a­tion,


where they aren’t re­ally faced with any dire con­se­quences at all. Still, I tend to be­lieve them, by and large.) Call­ing such a de­ci­sion “play­ing it safe” is quite iron­ic, be­cause if only every­body “played it dan­ger­ous”, they’d have a chance of only one in 400 of dy­ing! So I ask you: Which way is safe, and which way dan­ger­ous? It seems to me that this Wolf Trap epit­o­mizes the phrase “We have noth­ing to fear but fear it­self.”

Vari­a­tions on Wolf’s Dilemma in­clude some even more fright­en­ing and un­sta­ble sce­nar­ios. For in­stance, sup­pose the con­di­tions are that each but­ton-pusher has a 50% chance of sur­vival, but if there is unan­i­mous re­frain­ing from push­ing the but­ton, every­one’s life will be spared—and as be­fore, if any­one pushes their but­ton, all re­frain­ers will die. You can play around with the num­ber of par­tic­i­pants, the sur­vival chance, and so on. Each such vari­a­tion re­veals a new facet of grim­ness. These vi­sions are truly hor­ri­fic, yet all are just al­le­gor­i­cal ren­di­tions of or­di­nary life’s de­ci­sions, day in, day out.

I had orig­i­nally in­tended to close the col­umn with the fol­low­ing para­graph, but was dis­suaded from it by friends and ed­i­tors:

I am sorry to say that I am sim­ply in­un­dated with let­ters from well-mean­ing read­ers, and I have dis­cov­ered, to my re­gret, that I can barely find time to read all those let­ters, let alone an­swer them. I have been rack­ing my brains for months try­ing to come up with some strat­egy for deal­ing with all this cor­re­spon­dence, but frankly I have not found a good so­lu­tion yet. There­fore, I thought I would ap­peal to the col­lec­tive ge­nius of you-all out there. If you can think of some way for me to ease the bur­den of my cor­re­spon­dence, please send your idea to me. I shall be most grate­ful.

Irrationality Is the Square Root of All Evil


Sep­tem­ber, 1983

The Lur­ing Lot­tery, pro­posed in my June column, cre­ated quite a stir. Let me re­mind you that it was open to any­one; all you had to do was sub­mit a post­card with a clearly spec­i­fied pos­i­tive in­te­ger on it telling how many en­tries you wished to make. This in­te­ger was to be, in effect, your “weight” in the fi­nal draw­ing, so that if you wrote “100”, your name would be 100 times more likely to be drawn than that of some­one who wrote ‘I’. The only catch was that the cash value of the prize was in­versely pro­por­tional to the sum of all the weights re­ceived by June 30. Specifi­cal­ly, the prize to be awarded was , where N is the sum of all the weights sent in.

The Lur­ing Lot­tery was set up as an ex­er­cise in co­op­er­a­tion ver­sus de­fec­tion. The ba­sic ques­tion for each po­ten­tial en­trant was: “Should I re­strain my­self and sub­mit a small num­ber of en­tries, or should I ‘go for it’ and sub­mit a large num­ber? That is, should I co­op­er­ate, or should I de­fect?” Whereas in pre­vi­ous ex­am­ples of co­op­er­a­tion ver­sus de­fec­tion there was a clear-cut di­vid­ing line be­tween co­op­er­a­tors and de­fec­tors, here it seems there is a con­tin­uum of pos­si­ble an­swers, hence of “de­gree of co­op­er­a­tion”. Clearly one can be an ex­treme co­op­er­a­tor and vol­un­tar­ily sub­mit noth­ing, thus in effect cut­ting off one’s nose to spite one’s face. Equally clear­ly, one can be an ex­treme de­fec­tor and sub­mit a gi­ant num­ber of en­tries, hop­ing to swamp every­one else out but de­stroy­ing the prize in so do­ing. How­ev­er, there re­mains a lot of mid­dle ground be­tween these two ex­tremes. What about some­one who sub­mits two en­tries, or one? What about some­one who throws a six-sided die to de­cide whether or not to send in a sin­gle en­try? Or a mil­lion-sided die?

Be­fore I go fur­ther, it would be good for me to present my gen­er­al­ized and non-math­e­mat­i­cal sense of these terms “co­op­er­a­tion” and “de­fec­tion”. As a child, you un­doubt­edly often en­coun­tered adults who ad­mon­ished you


for walk­ing on the grass or for mak­ing noise, say­ing “Tut, tut, tut just think if every­one did that!” This is the quin­tes­sen­tial ar­gu­ment used against the de­fec­tor, and serves to de­fine the con­cept:

A de­fec­tion is an ac­tion such that, if every­one did it, things would clearly be worse (for every­one) than if every­one re­frained from do­ing it, and yet which tempts every­one, since if only one in­di­vid­ual (or a suffi­ciently small num­ber) did it while oth­ers re­frained, life would be sweeter for that in­di­vid­ual (or se­lect group).

Co­op­er­a­tion, of course, is the other side of the coin: the act of re­sist­ing temp­ta­tion. How­ev­er, it need not be the case that co­op­er­a­tion is pas­sive while de­fec­tion is ac­tive; often it is the ex­act op­po­site: The co­op­er­a­tive op­tion may be to par­tic­i­pate in­dus­tri­ously in some ac­tiv­i­ty, while de­fec­tion is to lay back and ac­cept the sweet things that re­sult for every­body from the co­op­er­a­tors’ hard work. Typ­i­cal ex­am­ples of de­fec­tion are:

  • loudly waft­ing your mu­sic through the en­tire neigh­bor­hood on a fine sum­mer’s day;
  • not wor­ry­ing about speed­ing through a four-way stop sign, fig­ur­ing that the peo­ple go­ing in the cross­wise di­rec­tion will stop any­way;
  • not be­ing con­cerned about dri­ving a car every­where, fig­ur­ing that there’s no point in mak­ing a sac­ri­fice when other peo­ple will just con­tinue to guz­zle gas any­way;
  • not wor­ry­ing about con­serv­ing wa­ter in a drought, fig­ur­ing “Every­one else will”;
  • not vot­ing in a cru­cial elec­tion and ex­cus­ing your­self by say­ing “One vote can’t make any differ­ence”;
  • not wor­ry­ing about hav­ing ten chil­dren in a pe­riod of pop­u­la­tion ex­plo­sion, leav­ing it to other peo­ple to curb their re­pro­duc­tion;
  • not de­vot­ing any time or en­ergy to press­ing global is­sues such as the arms race, famine, pol­lu­tion, di­min­ish­ing re­sources, and so on, say­ing “Oh, of course I’m very con­cerned—but there’s noth­ing one per­son can do.”

When there are large num­bers of peo­ple in­volved, peo­ple don’t re­al­ize that their own seem­ingly highly idio­syn­cratic de­ci­sions are likely to be quite typ­i­cal and are likely to be recre­ated many times over, on a grand scale; thus, what each cou­ple feels to be their own iso­lated and pri­vate de­ci­sion (con­scious or un­con­scious) about how many chil­dren to have turns into a pop­u­la­tion ex­plo­sion. Sim­i­lar­ly, “in­di­vid­ual” de­ci­sions about the fu­til­ity of work­ing ac­tively to­ward the good of hu­man­ity amount to a gi­ant trend of ap­a­thy, and this mul­ti­plied ap­a­thy trans­lates into in­san­ity at the group lev­el. In a word, ap­a­thy at the in­di­vid­ual level trans­lates into in­san­ity at the mass lev­el.


, an evo­lu­tion­ary bi­ol­o­gist, wrote a fa­mous ar­ti­cle about this type of phe­nom­e­non, called “”. His view was that there are two types of ra­tio­nal­i­ty: one (I’ll call it the “lo­cal” type) that strives for the good of the in­di­vid­u­al, the other (the “global” type) that strives for the good of the group; and that these two types of ra­tio­nal­ity are in an in­evitable and eter­nal con­flict. I would agree with his as­sess­ment, pro­vided the in­di­vid­u­als are un­aware of their joint plight but are sim­ply blindly car­ry­ing out their ac­tions as if in iso­la­tion.

How­ev­er, if they are fully aware of their joint sit­u­a­tion, and yet in the face of it they blithely con­tinue to act as if their sit­u­a­tion were not a com­mu­nal one, then I main­tain that they are act­ing to­tally ir­ra­tional­ly. In other words, with an en­light­ened cit­i­zen­ry, “lo­cal” ra­tio­nal­ity is not ra­tio­nal, pe­ri­od. It is dam­ag­ing not just to the group, but to the in­di­vid­ual. For ex­am­ple, peo­ple who de­fected in the One-Shot Pris­on­er’s Dilemma sit­u­a­tion I de­scribed in June did worse than if all had co­op­er­at­ed.

This was the cen­tral point of my June column, in which I wrote about renor­mal­ized ra­tio­nal­i­ty, or su­per­ra­tional­i­ty. Once you know you are a typ­i­cal mem­ber of a class of in­di­vid­u­als, you must act as if your own in­di­vid­ual ac­tions were to be mul­ti­plied many-fold, be­cause they in­evitably will be. In effect, to sam­ple your­self is to sam­ple the field, and if you fail to do what you wish the rest would do, you will be very dis­ap­pointed by the rest as well. Thus it pays a lot to re­flect care­fully about one’s sit­u­a­tion in the world be­fore de­fect­ing, that is, jump­ing to do the naively selfish act. You had bet­ter be pre­pared for a lot of other peo­ple cop­ping out as well, and offer­ing the same flimsy ex­cuse.

Peo­ple strongly re­sist see­ing them­selves as parts of sta­tis­ti­cal phe­nom­e­na, and un­der­stand­ably so, be­cause it seems to un­der­mine their sense of free will and in­di­vid­u­al­i­ty. Yet how true it is that each of our “unique” thoughts is mir­rored a mil­lion times over in the minds of strangers! Nowhere was this bet­ter il­lus­trated than in the re­sponse to the Lur­ing Lot­tery. It is hard to know pre­cisely what con­sti­tutes the “field”, in this case. It was de­clared uni­ver­sally open, to read­ers and non­read­ers alike. How­ev­er, we would be safe in as­sum­ing that few non­read­ers ever be­came aware of it, so let’s start with the cir­cu­la­tion of Sci­en­tific Amer­i­can, which is about a mil­lion. Most of them, how­ev­er, prob­a­bly did no more than glance over my June column, if that; and of the ones who did more than that (let’s say 100,000), still only a frac­tion—­maybe one in ten—read it care­fully from start to fin­ish. I would thus es­ti­mate that there were per­haps 10,000 peo­ple mo­ti­vated enough to read it care­fully and to pon­der the is­sues se­ri­ous­ly. In any case, I’ll take this fig­ure as the pop­u­la­tion of the “field”.

In my June column, I spelled out plain­ly, for all to see, the su­per­ra­tional ar­gu­ment that ap­plies to the Pla­to­nia Dilem­ma, for rolling an N-sided die and en­ter­ing only if it came up on the proper side. Here, a sim­i­lar ar­gu­ment goes through. In the Pla­to­nia Dilem­ma, where more than one en­try is fa­tal to all, the ideal die turned out to have N faces, where N is the num­ber of


play­er­s—hence, with 10,000 play­ers, a 10,000-sided die. In the Lur­ing Lot­tery, the con­se­quences aren’t so dras­tic if more than one en­try is sub­mit­ted. Thus, the ideal num­ber of faces on the die turns out to be about 2⁄3 as many—in the case of 10,000 play­ers, a 6,667-sided die would do ad­mirably. Giv­ing the die fewer than 10,000 sides of course slightly in­creases each play­er’s chance of send­ing in one en­try. This is to make it quite likely that at least one en­try will ar­rive!

With 6,667 faces on the die, each su­per­ra­tional play­er’s chance of win­ning is not quite 1 in 10,000, but more like 1 in 13,000; this is be­cause there is about a 22% chance that no one’s die will land right, so no one will send in any en­try at all, and no one will win. But if you give the die still fewer faces—say 3,000—the ex­pected size of the pot gets con­sid­er­ably small­er, since the ex­pected num­ber of en­trants grows. And if you give it more faces—say 20,000—then you run a con­sid­er­able risk of hav­ing no en­tries at all. So there’s a trade-off whose ideal so­lu­tion can be cal­cu­lated with­out too much trou­ble, and 6,667 faces turns out to be about op­ti­mal. With that many faces, the ex­pected value of the pot is max­i­mal: nearly $520,000—not to be sneered at.

Now this means that had every­one fol­lowed my ex­am­ple in the June column, I would prob­a­bly have re­ceived a to­tal of one or two post­cards with ‘1’ writ­ten on them, and one of those lucky peo­ple would have got­ten a huge sum of mon­ey! But do you think that is what hap­pened? Of course not! In­stead, I was in­un­dated with post­cards and let­ters from all over the world—over 2,000 of them. What was the break­down of en­tries? I have ex­hib­ited part of it in a table, be­low:

  • 1: 1,133
  • 2: 31
  • 3: 16
  • 4: 8
  • 5: 16
  • 6: 0
  • 7: 9
  • 8: 1
  • 9: 1
  • 10: 49
  • 100: 61
  • 1,000: 46
  • 1,000,000: 33
  • 1,000,000,000:
  • 11
  • 602,300,000,000,000,000,000,000 (): 1
  • 10100 (a ): 9
  • (a ): 14


Cu­ri­ous­ly, many if not most of the peo­ple who sub­mit­ted just one en­try pat­ted them­selves on the back for be­ing “co­op­er­a­tors”. Hog­wash! The real co­op­er­a­tors were those among the 10,000 or so avid read­ers who cal­cu­lated the proper num­ber of faces of the die, used a ran­dom-num­ber ta­ble or some­thing equiv­a­lent, and then—­most like­ly—rolled them­selves out. A few peo­ple wrote to tell me they had rolled them­selves out in this way. I ap­pre­ci­ated hear­ing from them. It is con­ceiv­able, just bare­ly, that among the thou­sand-plus en­tries of ‘1’ there was one that came from a lucky su­per­ra­tional co­op­er­a­tor—but I doubt it. The peo­ple who sim­ply with­drew with­out throw­ing a die I would char­ac­ter­ize as well—mean­ing but a bit lazy, not true co­op­er­a­tors—­some­thing like peo­ple who sim­ply con­tribute money to a po­lit­i­cal cause but then don’t want to be both­ered any longer about it. It’s the lazy way of claim­ing co­op­er­a­tion.

By the way, I haven’t by any means fin­ished with my score chart. How­ev­er, it is a bit dis­heart­en­ing to try to re­late what hap­pened. Ba­si­cal­ly, it is this. Dozens and dozens of read­ers strained their hard­est to come up with in­con­ceiv­ably large num­bers. Some filled their whole post­card with tiny ’9’s, oth­ers filled their card with rows of ex­cla­ma­tion points, thus cre­at­ing it­er­ated fac­to­ri­als of gi­gan­tic sizes, and so on. A hand­ful of peo­ple car­ried this game much fur­ther, rec­og­niz­ing that the op­ti­mal so­lu­tion avoids all pat­tern (to see why, read ar­ti­cle “Ran­dom­ness and Math­e­mat­i­cal Proof”), and con­sists sim­ply of a “dense pack” of de­fi­n­i­tions built on de­fi­n­i­tions, fol­lowed by one fi­nal line in which the “fan­ci­est” of the de­fi­n­i­tions is ap­plied to a rel­a­tively small num­ber such as 2, or bet­ter yet, 9.

I re­ceived, as I say, a few such en­tries. Some of them ex­ploited such pow­er­ful con­cepts of math­e­mat­i­cal logic and set the­ory that to eval­u­ate which one was the largest, be­came a very se­ri­ous prob­lem, and in fact it is not even clear that I, or for that mat­ter any­one else, would be able to de­ter­mine which is the largest in­te­ger sub­mit­ted. I was strongly re­minded of the lu­nacy and point­less­ness of the cur­rent arms race, in which two sides vie against each other to pro­duce ar­se­nals so huge that not even teams of ex­perts can mean­ing­fully say which one is larg­er—and mean­while, all this mon­u­men­tal effort is to the detri­ment of every­one.

Did I find this amus­ing? Some­what, of course. But at the same time, I found it dis­turb­ing and dis­ap­point­ing. Not that I had­n’t ex­pected it. In­deed, it was pre­cisely what I had ex­pect­ed, and it was one rea­son I was so sure the Lur­ing Lot­tery would be no risk for the mag­a­zine.

This short­-sighted race for “first place” re­veals the way in which peo­ple in a huge crowd er­ro­neously con­sider their own fan­cies to be to­tally unique. I sus­pect that nearly every­one who sub­mit­ted a num­ber above 1,000,000 ac­tu­ally be­lieved they were go­ing to be the only one to do so. Many of those who sub­mit­ted num­bers such as a googol­plex, or a ‘9’ fol­lowed by


thou­sands of fac­to­r­ial signs, ex­plic­itly in­di­cated that they were pretty sure that they were go­ing to “win”. And then those peo­ple who pulled out all the stops and sent in de­fi­n­i­tions that would bog­gle most math­e­mati­cians were very sure they were go­ing to win. As it turns out, I don’t know who won, and it does­n’t mat­ter, since the prize is zero to such a good ap­prox­i­ma­tion that even God would­n’t know the differ­ence. Well, what con­clu­sion do I draw from all this? None too se­ri­ous, but I do hope that it will give my read­ers pause for thought next time they face a “co­op­er­ate-or-de­fect” de­ci­sion, which will likely hap­pen within min­utes for each of you, since we face such de­ci­sions many times each day. Some of them are small, but some will have mon­u­men­tal reper­cus­sions. The globe’s fu­ture is in your hand­s—and yes, I mean you (as well as every other reader of this colum­n).

And with this per­haps sober­ing con­clu­sion, I would like to draw my term as a colum­nist for Sci­en­tific Amer­i­can to a close. It has been a valu­able and ben­e­fi­cial op­por­tu­nity for me. I have en­joyed hav­ing a plat­form from which to ex­press my ideas and con­cerns, I have—at least some­times—en­joyed re­ceiv­ing the huge ship­ments of mail for­warded to me from New York sev­eral times a mon­th, and I have cer­tainly been happy to make new friends through this chan­nel. I won’t miss the monthly dead­line, but I will un­doubt­edly come across ideas, from time to time, that would have made per­fect “Meta­m­ag­i­cal The­mas”. I will be keep­ing them in mind, and maybe at some fu­ture time will write a sim­i­lar set of es­says.

But for now, it is time for me to move on to other ter­ri­to­ry: I look for­ward to a re­turn to my pro­fes­sional work, and to a more pri­vate life. Good-bye, and best wishes to you and to all other read­ers of this mag­a­zine, this is­sue, this copy, this piece, this page, this column, this para­graph, this sen­tence, and, last but not least, this “this”.

Post Scriptum

What do you do when in a crush­ingly cold win­ter, you hear over the ra­dio that there is a se­vere nat­ural gas short­age in your part of the coun­try, and every­one is re­quested to turn their ther­mo­stat down to 60 de­grees? There’s no way any­one will know if you’ve com­plied or not. Why should­n’t you toast in your house and let all the rest of the peo­ple cut down their con­sump­tion? After all, what you do surely can’t affect what any­one else does.

This is a typ­i­cal “tragedy of the com­mons” sit­u­a­tion. A com­mon re­source has reached the point of sat­u­ra­tion or ex­haus­tion, and the ques­tions for each in­di­vid­ual now are: “How shall I be­have? Am I typ­i­cal? How does a”


“lone per­son’s ac­tion affect the big pic­ture?” Gar­rett Hardin’s ar­ti­cle “The Tragedy of the Com­mons” [] frames the scene in terms of graz­ing land shared by a num­ber of herders. Each one is tempted to in­crease their own num­ber of an­i­mals even when the land is be­ing used be­yond its op­ti­mum ca­pac­i­ty, be­cause the in­di­vid­ual gain out­weighs the in­di­vid­ual loss, even though in the long run, that de­ci­sion, mul­ti­plied through­out the pop­u­la­tion of herders, will de­stroy the land to­tal­ly.

The real rea­son be­hind Hardin’s ar­ti­cle was to talk about the and to stress the need for ra­tio­nal global plan­ning—in fact, for co­er­cive tech­niques sim­i­lar to park­ing tick­ets and jail sen­tences. His idea is that fam­i­lies should be al­lowed to have many chil­dren (and thus to use a large share of the com­mon re­sources) but that they should be pe­nal­ized by so­ci­ety in the same way as so­ci­ety “al­lows” some­one to rob a bank and then ap­plies sanc­tions to those who have made that choice. In an era when re­sources are run­ning out in a way hu­man­ity has never had to face hereto­fore, new kinds of so­cial arrange­ments and ex­pec­ta­tions must be im­posed, Hardin feels, by so­ci­ety as a whole. He is a dire pes­simist about any kind of su­per­ra­tional co­op­er­a­tion, em­pha­siz­ing that co­op­er­a­tors in the birth-con­trol game will breed them­selves right out of the pop­u­la­tion. A per­fect il­lus­tra­tion of why this is so is the man I heard about re­cent­ly: he se­cretly had ten wives and by them had sired some­thing like 35 chil­dren by the time he was 30. With genes of that sort pro­lif­er­at­ing wild­ly, there is lit­tle hope for the more mod­est breed­ers among us to gain the up­per hand. Hardin puts it blunt­ly: “Con­science is self­-e­lim­i­nat­ing.” He goes even fur­ther and says:

The ar­gu­ment has here been stated in the con­text of the pop­u­la­tion prob­lem, but it ap­plies equally well to any in­stance in which so­ci­ety ap­peals to an in­di­vid­ual ex­ploit­ing a com­mons to re­strain him­self for the gen­eral good—by means of his con­science. To make such an ap­peal is to set up a se­lec­tive sys­tem that works to­ward the elim­i­na­tion of con­science from the race.

An even more pes­simistic vi­sion of the fu­ture is proffered us by one Wal­ter Brad­ford El­lis, a hy­po­thet­i­cal speaker rep­re­sent­ing the views of his in­ven­tor, Louis Pas­cal, in a hy­po­thet­i­cal speech:

The United States—in­deed the whole earth­—is fast run­ning out of the re­sources it de­pends on for its ex­is­tence. Well be­fore the last of the world’s sup­plies of oil and nat­ural gas are ex­hausted early in the next cen­tu­ry, short­ages of these and other sub­stances will have brought about the col­lapse of our whole econ­omy and, in­deed, of our whole tech­nol­o­gy. And with­out the won­ders of mod­ern tech­nol­o­gy, Amer­ica will be left a grossly over­pop­u­lat­ed, ut­terly im­pov­er­ished, help­less, dy­ing land. Thus I fore­see a whole world full of wretched, starv­ing peo­ple with no hope of es­cape, for the only coun­tries which could have aided them will soon be no bet­ter off than the rest. And thus un­less we are saved from this fu­ture by the bless­ing of a nu­clear war or a truly lethal


pesti­lence, I see stretch­ing off into eter­nity a world of in­de­scrib­able suffer­ing and hope­less­ness. It is a vi­sion of truly un­speak­able hor­ror mit­i­gated only by the fact that try as I might I could not pos­si­bly con­coct a crea­ture more de­serv­ing of such a fate.

Whew! The cir­cu­lar­ity of the fi­nal thought re­minds me of an idea I once had: that it will be just as well if hu­man­ity de­stroys it­self in a nu­clear holo­caust, be­cause civ­i­liza­tions that de­stroy them­selves are bar­baric and stu­pid, and who would want to have one of them around, pol­lut­ing the uni­verse?

Pas­cal’s thoughts, ex­pressed in his [1978] ar­ti­cle “Hu­man Tragedy and Nat­ural Se­lec­tion” and in his [1980] re­join­der to an [1980] ar­ti­cle by two crit­ics called “The Lov­ing Par­ent Meets the Selfish Gene” (which is where El­lis’ speech is print­ed), are strik­ingly rem­i­nis­cent of the thoughts of his ear­lier name­sake Blaise, who in an un­ex­pected use of his own cal­cu­lus of prob­a­bil­i­ties man­aged to con­vince him­self that the best pos­si­ble way to spend his life was in de­vo­tion to a God who he was­n’t sure (and could­n’t be sure) ex­ist­ed. In fact, Pas­cal felt, even if the chances of God’s ex­is­tence were one in a mil­lion, faith in that God would pay off in the end, be­cause the po­ten­tial re­wards (or pun­ish­ments) if Heaven and Hell ex­ist are in­finite, and all earthly re­wards and pun­ish­ments, no mat­ter how great, are still fi­nite. The fa­vored be­hav­ior is to be a be­liev­er, Pas­cal “cal­cu­lated”—re­gard­less of what you do be­lieve. Thus Blaise Pas­cal de­voted his bril­liant mind to the­ol­o­gy.

Louis Pas­cal, fol­low­ing in his fore­bear’s mind­steps, has opted to de­vote his life to the world’s pop­u­la­tion prob­lem. And he can pro­duce math­e­mat­i­cal ar­gu­ments to show why you should, too. To my mind, there is no ques­tion that such ar­gu­ments have con­sid­er­able force. There are al­ways points to nit­pick over, but in essence, thinkers like Hardin and Pas­cal and Anne and Paul Ehrlich and many oth­ers have rec­og­nized and in­ter­nal­ized the nov­elty of the hu­man sit­u­a­tion at this mo­ment in his­to­ry: the mo­ment when hu­man­ity has to grap­ple with dwin­dling re­sources and over­whelm­ingly huge weapons sys­tems. Not many peo­ple are will­ing to wres­tle with this beast, and con­se­quently the bur­den falls all the more heav­ily on those few who are.

It has dis­turbed me how ve­he­mently and staunchly my clear-headed friends have been able to de­fend their de­ci­sions to de­fect. They seem to be able to di­gest my ar­gu­ment about su­per­ra­tional­i­ty, to mull it over, to be­grudge some cu­ri­ous kind of va­lid­ity to it, but ul­ti­mately to feel on a gut level that it is wrong, and to re­ject it. This has led me to con­sider the no­tion that my faith in the su­per­ra­tional ar­gu­ment might be sim­i­lar to a self­-ful­fill­ing prophecy or self­-sup­port­ing claim, some­thing like be­ing ab­solutely con­vinced be­yond a shadow of a doubt that the sen­tence “This sen­tence is true” ac­tu­ally must be true—when, of course, it is equally de­fen­si­ble to be­lieve it to be false. The sen­tence is un­de­cid­able; its truth


value is sta­ble, whichever way you wish it to go (in this way, it is the di­a­met­ric op­po­site of the “This sen­tence is false”, whose truth value flips faster than the tip of a happy pup’s tail). One differ­ence, though, be­tween the Pris­on­er’s Dilemma and odd­ball self­-ref­er­en­tial sen­tences is that whereas your be­liefs about such sen­tences’ truth val­ues usu­ally have in­con­se­quen­tial con­se­quences, with the Pris­on­er’s Dilem­ma, it’s quite an­other mat­ter.

I some­times won­der whether there haven’t been many civ­i­liza­tions Out There, in our galaxy and be­yond, that have al­ready dealt with just these types of gi­gan­tic so­cial prob­lem­s—Pris­on­er’s Dilem­mas, Tragedies of the Com­mons, and so forth. Most likely some would have sur­vived, some would have per­ished. And it oc­curs to me that per­haps the ul­ti­mate differ­ence in those so­ci­eties may have been the sur­vival of the meme that, in effect, as­serts the log­i­cal, ra­tio­nal va­lid­ity of co­op­er­a­tion in a one-shot Pris­on­er’s Dilem­ma. In a way, this would be the op­po­site the­sis to Hardin’s. It would say that lack of con­science is self­-e­lim­i­nat­ing—pro­vided you wait long enough that nat­ural se­lec­tion can act at the level of en­tire so­ci­eties.

Per­haps on some plan­ets, Type I so­ci­eties have evolved, while on oth­ers, Type II so­ci­eties have evolved. By de­fi­n­i­tion, mem­bers of Type I so­ci­eties be­lieve in the ra­tio­nal­ity of lone, un­co­erced, one-shot co­op­er­a­tion (when faced with mem­bers of Type I so­ci­eties), whereas mem­bers of Type II so­ci­eties re­ject the ra­tio­nal­ity of lone, un­co­erced, one-shot co­op­er­a­tion, ir­re­spec­tive of who they are fac­ing. (No­tice the tricky cir­cu­lar­ity of the de­fi­n­i­tion of Type I so­ci­eties. Yet it is not a vac­u­ous de­fi­n­i­tion!) Both types of so­ci­ety find their re­spec­tive an­swer to be ob­vi­ous—they just hap­pen to find op­po­site an­swers. Who knows—we might even hap­pen to have some Type I so­ci­eties here on earth. I can­not help but won­der how things would turn out if my lit­tle one-shot Pris­on­er’s Dilemma ex­per­i­ment were car­ried out in Japan in­stead of the U.S. In any case, the vi­tal ques­tion is: Which type of so­ci­ety sur­vives, in the long run?

It could be that the one-shot Pris­on­er’s Dilemma sit­u­a­tions that I have de­scribed are un­de­cid­able propo­si­tions within the logic that we hu­mans have de­vel­oped so far, and that new ax­ioms can be added, like the par­al­lel pos­tu­late in geom­e­try, or Godel sen­tences (and re­lated ones) in math­e­mat­i­cal log­ic. (Take a look at Fig­ure 31-1, and see what kind of logic will ex­tract those two poor dev­ils from their one-shot dilem­ma.) Those civ­i­liza­tions to which co­op­er­a­tion ap­pears ax­iomat­ic—­Type I so­ci­eties—wind up sur­viv­ing, I would ven­ture to guess, whereas those to which de­fec­tion ap­pears ax­iomat­ic—­Type II so­ci­eties—wind up per­ish­ing. This sug­ges­tion may seem all wet to you, but watch those su­per­pow­ers build­ing those bombs, more and more of them every day, help­lessly trapped in a ris­ing spi­ral, and think about it. Evo­lu­tion is a mer­ci­less pruner of ill log­ic.

Most philoso­phers and lo­gi­cians are con­vinced that truths of logic are “an­a­lytic” and a pri­ori; they do not like to think that such ba­sic ideas are grounded in mun­dane, ar­bi­trary things like sur­vival. They might ad­mit that


“The prob­lem is how to turn loose with­out let­ting go.” FIGURE 31-1. One pow­er­ful metaphor for the ab­sur­dity we have col­lec­tively dug our­selves in­to. The sym­me­try of the sit­u­a­tion is acutely por­trayed in this car­toon drawn by Bill Mauldin in 1960. Note that if ei­ther per­son re­leases his rope, thus chop­ping of his coun­ter­part’s head, that per­son’s hand will go limp, thus re­leas­ing his rope and caus­ing the other blade to fall and chop of the head of the in­sti­ga­tor. That idea is a cen­ter­piece of our cur­rent nu­clear de­ter­rence strat­e­gy: Even if we are wiped of the globe, our trUSty mis­siles will still wreak di­vine re­venge on the evil em­pire of Sa­tanic Uglies who dared do harm to US.

nat­ural se­lec­tion tends to fa­vor good log­ic—but they would cer­tainly hate the sug­ges­tion that nat­ural se­lec­tion de­fines good log­ic! Yet truth and sur­vival value are all tan­gled to­geth­er, and civ­i­liza­tions that sur­vive cer­tainly have glimpsed higher truths than those that per­ish. When you ar­gue with some­one whose ideas you are sure are wrong but who dances an in­fu­ri­at­ingly in­con­sis­tent yet self­-con­sis­tent ver­bal dance in front of you, your one so­lace is that some­thing in life may yet change this per­son’s mind, even though your own best logic is help­less to do so. Ul­ti­mate­ly, be­liefs have to be grounded in ex­pe­ri­ence, whether that ex­pe­ri­ence is the or­gan­is­m’s or its an­ces­tors’ or its peer group’s. (That’s what Chap­ter 5, par­tic­u­larly its


P.S., was all about.) My feel­ing is that the con­cept of su­per­ra­tional­ity is one whose truth will come to dom­i­nate among in­tel­li­gent be­ings in the uni­verse sim­ply be­cause its ad­her­ents will sur­vive cer­tain kinds of sit­u­a­tions where its op­po­nents will per­ish. Let’s wait a few spins of the galaxy and see. After all, healthy logic is what­ever re­mains after evo­lu­tion’s mer­ci­less prun­ing.

I was de­scrib­ing the (Chap­ter 24) to physi­cist , and I gave him our canon­i­cal ex­am­ple: “If abc goes to abd, what does xyz go to?” After we had dis­cussed var­i­ous pos­si­ble an­swers and set­tled on wyz as the most com­pelling for rea­sons of sym­me­try, he sur­prised me by say­ing this: “You know, the root of the world’s deep­est prob­lems is the tragic in­abil­ity on the part of the world’s lead­ers to see such ba­sic sym­me­tries. For in­stance, that the U.S. is to the S.U. what the S.U. is to the U.S.—that is too much for them to ac­cept.” Oh, but how could Weis­skopf be so sil­ly? After all, we’re not try­ing to ex­port com­mu­nism to the en­tire world!

Lo­gi­cian , who first heard about the Pris­on­er’s Dilemma from me and who was ab­solutely de­lighted by it, also sur­prised me, but in a differ­ent way: He ve­he­mently in­sisted on the cor­rect­ness of de­fec­tion in a one-shot sit­u­a­tion no mat­ter who might be on the other side, in­clud­ing his twin or his clone! (He did wa­ver about his mir­ror im­age.) But just as I was giv­ing up on him as a lost cause, he con­ceded this much to me: “I sus­pect, Doug, that this prob­lem is a lot knot­tier than you or I sus­pect.” In­deed, I sus­pect so, Ray­mond.

The Tale of Happiton


June, 1983

Hap­pi­ton was a happy lit­tle town. It had 20,000 in­hab­i­tants, give or take 7, and they were pro­duc­tive cit­i­zens who mowed their lawns quite reg­u­lar­ly. Folks in Hap­pi­ton were pretty healthy. They had a life ex­pectancy of 75 years or so, and lots of them lived to ripe old ages. Down at the town square, there was a nice big cour­t­house with all sorts of relics from WW II and mon­u­ments to var­i­ous he­roes and what­not. Peo­ple were proud, and had the right to be proud, of Hap­pi­ton.

On the top of the cour­t­house, there was a big bell that boomed every hour on the hour, and you could hear it far and wide-even as far out as Shady Oaks Dri­ve, way out nearly in the coun­try­side.

One day at noon, a few peo­ple stand­ing near the cour­t­house no­ticed that right after the noon bell rang, there was a funny lit­tle sound com­ing from up in the bel­fry. And for the next few days, folks no­ticed that this scratch­ing sound was oc­cur­ring after every hour. So on Wednes­day, Curt Demp­ster climbed up into the bel­fry and took a look. To his sur­prise, he found a crazy kind of con­trap­tion rigged up to the bell. There was this me­chan­i­cal hand, sort of a ro­bot arm, and next to it were five weird-look­ing dice that it could throw into a lit­tle pan. They all had twenty sides on them, but in­stead of be­ing num­bered 1 through 20, they were just num­bered 0 through 9, but with each digit ap­pear­ing on two op­po­site sides. There was also a TV cam­era that pointed at the pan and it seemed to be at­tached to a mi­cro­com­puter or some­thing. That’s all Curt could fig­ure out. But then he no­ticed that on top of the com­put­er, there was a neat lit­tle en­ve­lope marked “To the friendly folks of Hap­pi­ton”. Curt de­cided that he’d take it down­stairs and open it in the pres­ence of his friend the may­or, Jan­ice Fleen­er. He found Jan­ice eas­ily enough, told her about what he’d found, and then they opened the en­ve­lope. How neatly it was writ­ten! It said this:


Grotto 19, Hades
June 20, 1983

Dear folks of Hap­pi­ton,

I’ve got some bad news and some good news for you. The bad first. You know your bell that rings every hour on the hour? Well, I’ve set it up so that each time it rings, there is ex­actly one chance in a hun­dred thou­sand-that is, -that a Very Bad Thing will oc­cur. The way I de­ter­mine if that Bad Thing will oc­cur is, I have this ro­bot arm fling its five dice and see if they all land with ‘7’ on top. Most of the time, they won’t. But if they do-and the odds are ex­actly 1 in 100,000-then great clouds of an unimag­in­ably re­volt­ing smelling yel­low-green gas called “Retch­goo” will come ooz­ing up from a dense net­work of un­der­ground pipes that I’ve re­cently in­stalled un­der­neath Hap­pi­ton, and every­one will die an aw­ful, writhing, ag­o­niz­ing death. Well, that’s the bad news.

Now the good news! You all can pre­vent the Bad Thing from hap­pen­ing, if you send me a bunch of post­cards. You see, I hap­pen to like post­cards a whole lot (e­spe­cially post­cards of Hap­pi­ton), but to tell the truth, it does­n’t re­ally much mat­ter what they’re of. I just love post­cards! Thing is, they have to be writ­ten per­son­al­ly-not typed, and es­pe­cially not com­put­er-printed or any­thing phony like that. The more cards, the bet­ter. So how about send­ing me some post­card­s-batch­es, bunch­es, boxes of them?

Here’s the deal. I reckon a typ­i­cal post­card takes you about 4 min­utes to write. Now sup­pose just one per­son in all of Hap­pi­ton spends 4 min­utes one day writ­ing me, so the next day, I get one post­card. Well, then, I’ll do you all a fa­vor: I’ll slow the cour­t­house clock down a bit, for a day. (I re­al­ize this is an in­con­ve­nience, since a lot of you tell time by the clock, but be­lieve me, it’s a lot more in­con­ve­nient to die an ag­o­niz­ing, writhing death from the evil-s­melling, yel­low-green Retch­goo.) As I was say­ing, I’ll slow the clock down for one day, and by how much? By a fac­tor of 1.000011. Okay, I know that does­n’t sound too ex­cit­ing, but just think if all 20,000 of you send me a card! For each card I get that day, I’ll toss in a slow-up fac­tor of 1.00001, the next day. That means that by send­ing me 20,000 post­cards a day, you all, work­ing to­geth­er, can get the clock to slow down by a fac­tor of 1.00001 to the 20,000th pow­er, which is just a shade over 1.2, mean­ing it will ring every 72 min­utes.

All right, I hear you say­ing, “72 min­utes is just barely over an hour!” So I offer you more! Say that one day I get 160,000 post­cards (heav­en­ly!). Well then, the very next day I’ll show my grat­i­tude by slow­ing your clock down, all day long, mid­night to mid­night, by 1.00001 to the 160,000th pow­er, and that ain’t chick­en­feed. In fact, it’s about 5, and that means the clock will ring only every 5 hours, mean­ing those sin­is­ter dice will only get rolled about 5 times (in­stead of the usual 24). Ob­vi­ous­ly, it’s bet­ter for both of us that way. You have to bear in mind that I don’t have any per­sonal in­ter­est in see­ing that aw­ful Retch­goo come rush­ing and gush­ing up out of those pipes and caus­ing every last one of you to per­ish in grotesque, mouth-foam­ing, twitch­ing con­vul­sions. All I care about is get­ting post­cards! And to send me 160,000 a day would­n’t cost you folks that much effort, be­ing that it’s just 8 post­cards a day just about a half hour a day for each of you, the way I reckon it.


So my deal is pretty sim­ple. On any given day, I’ll make the clock go off once every X hours, where X is given by this sim­ple for­mu­la:

X = 1.00001N

Here, N is the num­ber of post­cards I re­ceived the pre­vi­ous day. If N is 20,000, then X will be 1.2, so the bell would ring 20 times per day, in­stead of 24. If N is 160,000, then X jumps way up to about 5, so the clock would slow way down just un­der 5 rings per day. If I get no post­cards, then the clock will ring once an hour, just as it does now. The for­mula re­flects that, since if N is 0, X will be 1. You can work out other fig­ures your­self. Just think how much safer and se­curer you’d all feel know­ing that your cour­t­house clock was tick­ing away so slow­ly!

I’m look­ing for­ward with great en­thu­si­asm to hear­ing from you all.

Sin­cerely yours,
De­mon #3127

The let­ter was signed with beau­ti­ful me­dieval-look­ing flour­ish­es, in an un­usual shade of deep red … ink?

“Bunch of hog­wash!” splut­tered Curt. “Let’s go up there and chuck the whole mess down onto the street and see how far it bounces.” While he was say­ing this, Jan­ice no­ticed that there was a smaller note clipped onto the back of the last sheet, and turned it over to read it. It said this:

P. S.—It’s re­ally not ad­vis­able to try to dis­man­tle my lit­tle set-up up there in the bel­fry: I’ve got a hair trig­ger linked to the gas pipes, and if any­one tries to dis­man­tle it, pssssst! Sor­ry.

Jan­ice Fleener and Curt Demp­ster could hardly be­lieve their eyes. What gall! They got straight on the -phone to the Po­lice De­part­ment, and talked to Offi­cer Cur­ran. He sounded pop­pin’ mad when they told him what they’d found, and said he’d do some­thing about it right quick. So he high­tailed it over to the cour­t­house and ran up those stairs two at a time, and when he reached the top, a-huffin’ and a-puffin’, he swung open the bel­fry door and took a look. To tell the truth, he was a bit gin­ger in his in­spec­tion, be­cause one thing Offi­cer Cur­ran had learned in his many years of po­lice ex­pe­ri­ence is that an ounce of pre­ven­tion is worth a pound of cure. So he cau­tiously looked over the strange con­trap­tion, and then he turned around and quite care­fully shut the door be­hind him and went down. He called up the town sewer de­part­ment and asked them if they could check out whether there was any­thing funny go­ing on with the pipes un­der­ground.

Well, the long and the short of it is that they ver­i­fied every­thing in the De­mon’s let­ter, and by the time they had done so, the clock had struck five more times and those five dice had rolled five more times. Jan­ice Fleener had in fact had her thir­teen-year-old daugh­ter Saman­tha go up and sit in a


wicker chair right next to the mi­cro­com­puter and watch the ro­bot arm throw those dice. Ac­cord­ing to Saman­tha, an oc­ca­sional 7 had turned up now and then, but never had two 7’s shown up to­geth­er, let alone 7’s on all five of the weird-look­ing dice!

The next day, the Hap­pi­ton Ea­gle-Tele­phone came out with a fron­t-page story telling all about the pe­cu­liar go­ings-on. This caused quite a com­mo­tion. Peo­ple every­where were talk­ing about it, from Lid­den’s Burger Stop to Bixbee’s Drug­gery. It was truly the talk of the town.

When Doc Hazelthorn, the best pe­di­a­tri­cian this side of the Cornyawl River, walked into Ernie’s Bar­ber­shop, cor­ner of Cherry and Sec­ond, the at­mos­phere was more somber than usu­al. “Whatcha gonna do, Doc?” said big Ernie, the jovial bar­ber, as he was clip­ping the few re­main­ing hairs on old Doc’s pate. Doc (who was also head of the Hap­pi­ton City Coun­cil) said the news had come as quite a shock to him and his fam­i­ly. Red Dulkins, sit­ting in the next chair over from Doc, said he felt the same way. And then the two gen­tle­men wait­ing to get their hair cut both added their words of agree­ment. Ernie, sum­ming it up, said the whole town seemed quite up­set. As Ernie re­moved the white smock from Doc’s lap and shook the hairs off it, Doc said that he had just de­cided to bring the mat­ter up first thing at the next City Coun­cil meet­ing, Tues­day evening. “Sounds like a good idea, Doc!” said Ernie. Then Doc told Ernie he could­n’t make the usual golf date this week­end, be­cause some friends of his had in­vited him to go fish­ing out at Lazy Lake, and Doc just could­n’t re­sist.

Two days after the De­mon’s note, the Ea­gle-Tele­phone ran a fea­ture ar­ti­cle in which many res­i­dents of Hap­pi­ton, some promi­nent, some not so promi­nent, voiced their opin­ions. For in­stance, eleven-year-old Wally Thurston said he’d gone out and bought up the whole sup­ply of pic­ture post­cards at the 88-Cent Store, $14.22 worth of post­cards, and he’d al­ready started writ­ing a few. An­drea McKen­zie, sopho­more at Hap­pi­ton High, said she was re­ally wor­ried and had had night­mares about the gas, but her par­ents told her not to wor­ry, things had a way of work­ing out. An­drea said maybe her par­ents weren’t tak­ing it so se­ri­ously be­cause they were a gen­er­a­tion older and did­n’t have as long to look for­ward to any­way. She said she was spend­ing an hour each day writ­ing post­cards. That came to 15 or 16 cards each day. Hank Hoople, a jan­i­tor at Hap­pi­ton High, sounded rather glum: “It’s all fate. If the bul­let has your name on it, it’s go­ing to hap­pen, whether you like it or not.” Many other cit­i­zens voiced con­cern and even alarm about the re­cent de­vel­op­ments.

But some voiced rather differ­ent feel­ings. Ned Fur­dy, who as far as any­one could tell did­n’t do much other than hang around Simp­son’s bar all day (and most of the night) and but­ton­hole any­one he could, said, “Yeah, it’s a prob­lem, all right, but I don’t know noth­in’ about gas and sta­tis­tics and such.”


“It should all be left to the mayor and the Town Coun­cil, to take care of. They know what they’re doin’. Mean­while, eat, drink, and be mer­ry!” And Lulu Smyth, 77-year-old. pro­pri­etor of Lu­lu’s Thread ’N Nee­dles Shop, said “I think it’s all a ruckus in a teapot, in my opin­ion. Far as I’m con­cerned, I’m gonna keep on sell­in’ thread ‘n needles, and playin’ gin rummy every third Wednes­day.”

When Doc Hazelthorn came back from his fish­ing week­end at Lazy Lake, he had some sur­pris­ing news to re­port. “Seems there’s a de­mon left a sim­i­lar set-up in the church steeple down in Dway­nesville”, he said. (D­way­nesville was the next town down the road, and the arch-ri­val of Hap­pi­ton High in foot­bal­l.) “The Dway­nesville de­mon is­n’t threat­en­ing them with gas, but with ra­dioac­tive wa­ter. Takes a lit­tle longer to die, but it’s just as bad. And I hear tell there’s a de­mon with a sub­ter­ranean vol­cano up at New Athens.” (New Athens was the larger town twenty miles up the Cornyawl from Dway­nesville, and the re­gional cen­ter of com­merce.)

A lot of peo­ple were clearly quite alarmed by all this, and there was plenty of ar­gu­ing on the streets about how it had all hap­pened with­out any­one know­ing. One thing that was pretty uni­ver­sally agreed on was that a com­mis­sion should be set up as soon as pos­si­ble, charged from here on out with keep­ing close tabs on all sub­ter­ranean ac­tiv­ity within the city lim­its, so that this sort of out­rage could never hap­pen again. It ap­peared prob­a­ble that Curt Demp­ster, who was the mov­ing force be­hind this idea, would be ap­pointed its first head.

Ed Thurston (Wal­ly’s fa­ther) pro­posed to the Jaycees (of which he was a mem­ber in good stand­ing) that they do­nate $1,000 to sup­port a post­card-writ­ing cam­paign by town kids. But Enoch Swale, owner of Swale’s Phar­macy and the Sleep­good Motel, protest­ed. He had never liked Ed much, and said Ed was propos­ing it sim­ply be­cause his son would gain sta­tus that way. (It was true that Wally had re­cruited a few kids and that they spent an hour each after­noon after school writ­ing cards. There had been a small ar­ti­cle in the pa­per about it once.) After con­sid­er­able de­bate, Ed’s mo­tion was nar­rowly de­feat­ed. Enoch had a lot of friends on the City Coun­cil.

Nel­lie Doo­bar, the math teacher at High, was about the only one who checked out the De­mon’s math. “Seems right to me”, she said to the re­porter who called her about it. But this set her to think­ing about a few things. In an hour or two, she called back the pa­per and said, “I fig­ured some­thing out. Right now, the clock is still ring­ing very close to once every hour. Now there are about 720 hours per mon­th, and so that means there are 720 chances each month for the gas to get out. Since each chance is 1 in 100,000, it turns out that each mon­th, there’s a bit less than a 1-in-100 chance that Hap­pi­ton will get gassed. At that rate, there’s about 11 chances in 12 that Hap­pi­ton will make it through each year. That may sound pretty”


“good, but the chances we’ll make it through any 8-year pe­riod are al­most ex­actly 50-50, ex­actly the same as toss­ing a coin. So we can’t re­ally count on very many years …”

This made big head­lines in the next after­noon’s Ea­gle-Tele­phone—in fact, even big­ger than the plans for the County Fair! Some folks started call­ing up Mrs. Doo­bar anony­mously and telling her she’d bet­ter watch out what she was say­ing if she did­n’t want to wind up with a puffy face or a fat lip. Seems like they could­n’t quite keep it straight that Mrs. Doo­bar was­n’t the one who’d set the thing up in the first place.

After a few days, though, the nasty calls died down pretty much. Then Mrs. Doo­bar called up the pa­per again and told the re­porter, “I’ve been cal­cu­lat­ing a bit more here, and I’ve come up with the fol­low­ing, and they’re facts every last one of them. If all 20,000 of us were to spend half an hour a day writ­ing post­cards to the De­mon, that would amount to 160,000 post­cards a day, and just as the De­mon said, the bell would ring pretty near every five hours in­stead of every hour, and that would mean that the chances of us get­ting wiped out each month would go down con­sid­er­able. In fact, there would only be about 1 chance in 700 that we’d go down the tubes in any given mon­th, and only about a chance in 60 that we’d get zapped each year. Now I’d say that’s a darn sight bet­ter than 1 chance in 12 per year, which is what it is if we don’t write any post­cards (as is more or less the case now, ex­cept for Wally Thurston and An­drea McKen­zie and a few other kids I heard of). And for every 8-year pe­ri­od, we’d only be run­ning a 13% risk in­stead of a 50% risk.”

“That sounds pretty good”, said the re­porter cheer­ful­ly.

“Well,” replied Mrs. Doo­bar, “it’s not too bad, but we can get a whole lot bet­ter by dou­blin’ the num­ber of post­cards.”

“How’s that, Mrs. Doo­bar?” asked the re­porter. “Would­n’t it just get twice as good?”

“No, you see, it’s an ex­po­nen­tial curve,” said Mrs. Doo­bar, “which means that if you dou­ble N, you square X.”

“That’s Greek to me”, quipped the re­porter.

“N is the num­ber of post­cards and X is the time be­tween rings”, she replied quite pa­tient­ly. “If we all write a half hour a day, X is 5 hours. But that means that if we all write a whole hour a day, like An­drea McKen­zie in my al­ge­bra class, X jumps up to 25 hours, mean­ing that the clock would ring only about once a day, and ob­vi­ous­ly, that would re­duce the dan­ger a lot. Chances are, hun­dreds of years would pass be­fore five 7’s would turn up to­gether on those in­fer­nal dice. Seems to me that un­der those cir­cum­stances, we could pretty much live our lives with­out wor­ry­ing about the gas at all. And that’s for writ­ing about an hour a day, each one of us.”

The re­porter wanted some more fig­ures de­tail­ing how much differ­ent amounts of post­card-writ­ing by the pop­u­lace would pay off, so Mrs. Doo­bar obliged by go­ing back and do­ing some more fig­ur­ing. She fig­ured out that if 10,000 peo­ple—half the pop­u­la­tion of Hap­pi­ton—­did 2 hours a day for


the year, they could get the same re­sult—one ring every 25 hours. If only 5,000 peo­ple spent 2 hours a day, or if 10,000 peo­ple spent one hour a day, then it would go back to one ring every 5 hours (still a lot safer than one every hour). Or, still an­other way of look­ing at it, if just 1250 of them worked ful­l-time (8 hours a day), they could achieve the same thing.

“What about if we all pitch in and do 4 min­utes a day, Mrs. Doo­bar?” asked the re­porter.

“Fact is, ’t­would­n’t be worth a damn thing! (Par­don my French.)” she replied. “N is 20,000 that way, and even though that sounds pretty big, X works out to be just 1.2, mean­ing one ring every 1.2 hours, or 72 min­utes. That way, we still have about a chance of 1 in 166 every month of get­ting wiped out, and 1 in 14 every year of get­ting it. Now that’s real scary, in my book. Writ­ing cards only starts mak­ing a no­tice­able differ­ence at about 15 min­utes a day per per­son.”

By this time, sev­eral weeks had passed, and sum­mer was get­ting into full swing. The County Fair was buzzing with ac­tiv­i­ty, and each evening after folks came home, they could see loads of fire­flies flick­er­ing around the trees in their yards. Evenings were peace­ful and re­laxed. Doc’ Hazelthorn was play­ing golf every week­end, and his scores were get­ting down into the low 90’s. He was feel­ing pretty good. Once in a while he re­mem­bered the De­mon, es­pe­cially when he walked down­town and passed the cour­t­house tow­er, and every so often he would shud­der. But he was­n’t sure what he and the City Coun­cil could do about it.

The De­mon and the gas still made for in­ter­est­ing talk, but were no longer such big news. Mrs. Doo­bar’s lat­est rev­e­la­tions made the pa­per, but. were. rel­e­gated this time to the sec­ond sec­tion, two pages be­fore the comics, right next to the daily horo­scope col­umn. An­drea McKen­zie read the ar­ti­cle avid­ly, and showed it to a lot of her school friends, but to her sur­prise, it did­n’t seem to stir up much in­ter­est in them. At first, her best friend, Kathi Hamil­ton, a very bright girl who had plans to go to State and ma­jor in his­to­ry, en­thu­si­as­ti­cally joined An­drea and wrote quite a few cards each day. But after a few days, Kathi’s en­thu­si­asm be­gan to wane.

“What’s the point, An­drea?” Kathi asked. “A hand­ful of post­cards from me is­n’t go­ing to make. the slight­est bit of differ­ence. Did­n’t you read Mrs. Doo­bar’s ar­ti­cle? There have got to be 160,000 a day to make a big differ­ence.”

“That’s just the point, Kathi!” replied An­drea ex­as­per­at­ed­ly. “If you and every­one else will just do your part, we’ll reach that num­ber—but you can’t cop out!” Kathi did­n’t see the log­ic, and spent most of her time do­ing her home­work for the sum­mer school course in World His­tory she was tak­ing. After all, how could she get into State if she flunked World His­to­ry?

An­drea just could­n’t fig­ure out how come Kathi, of all peo­ple, so


in­ter­ested in his­tory and the flow of time and world-events, could not see her own life be­ing touched by such fac­tors, so she asked Kathi, “How do you know there will be any you left to go to State, if you don’t write post­cards? Each year, there’s a 1-in-12 chance of you and me and all of us be­ing wiped out! Don’t you even want to work against that? If peo­ple would just care, they could change things! An hour a day! Half an hour a day! Fifteen min­utes a day!”

“Oh, come on, An­drea!” said Kathi an­noyed­ly, “Be re­al­is­tic.”

“Darn it all, I’m the one who’s be­ing re­al­is­tic”, said An­drea. “If you don’t help out, you’re adding to the bur­den of some­one else.”

“For Pe­te’s sake, An­drea”, Kathi protested an­gri­ly, “I’m not adding to any­one else’s bur­den. Every­one can help out as much as they want, and no one’s obliged to do any­thing at all. Sure, I’d like it if every­one were help­ing, but you can see for your­self, prac­ti­cally no­body is. So I’m not go­ing to waste my time. I need to pass World His­to­ry.”

And sure enough, An­drea had to do no more than lis­ten each hour, right on the hour, to hear that bell ring to re­al­ize that no­body was do­ing much. It once had sounded so pleas­ant and re­as­sur­ing, and now it sounded creepy and omi­nous to her, just like the fire­flies and the bar­be­cues. Those fire­flies and bar­be­cues re­ally bugged An­drea, be­cause they seemed so nor­mal, so much like any other sum­mer—only this sum­mer was not like any other sum­mer. Yet no­body seemed to re­al­ize that. Or, rather, there was an un­der­cur­rent that things were not quite as they should be, but noth­ing was be­ing done …

One Sat­ur­day, Mr. Hobbs, the elec­tri­cian, came around to fix a bro­ken re­frig­er­a­tor at the McKen­zies’ house. An­drea talked to him about writ­ing post­cards to the De­mon. Mr. Hobbs said to her, “No time, no time! Too busy fix­in’ air con­di­tion­ers! In this heat wave, they been break­in’ down all over town. I work a 10-hour day as it is, and now it’s up to 11, 12 hours a day, in­clud­in’ week­ends. I got no time for post­cards, An­drea.” And An­drea .saw that for Mr. Hobbs, it was true. He had a big fam­ily and his chil­dren went to parochial school, and he had to pay for them all, and …

An­drea’s older sis­ter’s boyfriend, Wayne, was a star half­back at Hap­pi­ton High. One evening he was over and teased An­drea about her post­cards. She asked him, “Why don’t you write any, Wayne?”.

“I’m out life­guardin’ every day, and the rest of the time I got scrim­mages—­for the fall sea­son.”

“But you could take some time out just 15 min­utes a day—and write a few post­cards!” she ar­gued. He just laughed and looked a lit­tle fid­gety. “I don’t know, An­drea”, he said. “Any­way, me ’n Ellen have got bet­ter things to do—huh, El­len?” Ellen gig­gled and blushed a lit­tle. Then they ran out of the house and jumped into Wayne’s sports car to go bowl­ing at the Hap­pi-Bowl.


An­drea was puz­zled by all her friends’ at­ti­tudes. She could­n’t un­der­stand why every­one had started out so con­cerned but then their con­cern had fiz­zled,, as if the prob­lem had gone away. One day when she was walk­ing home from school, she saw old Granny Sparks out wa­ter­ing her gar­den. Granny, as every­one called her, lived kit­ty-corner from the McKen­zies and was al­ways chat­ty, so An­drea stopped and asked Granny Sparks what she thought of all this. “Pshaw! Fid­dle­sticks!” said Granny in­dig­nant­ly. “Now An­drea, don’t you go around be­liev­in’ all that malarkey they print in the news­pa­pers! Things are the same here as they al­ways been. I oughta know—I’ve been liv­in’ here nigh on 85 years!”

In­deed, that was what both­ered An­drea. Every­thing seemed so an­noy­ingly nor­mal. The teenagers with their cruis­ing cars and loud mo­tor­cy­cles. The usual bor­ing hor­ror movies at the Key The­ater down on the square across from the cour­t­house. The band in the park. The pa­rades. And es­pe­cial­ly, the damn fire­flies! Prac­ti­cally no­body seemed moved or affected by what to her seemed the most over­whelm­ing news she’d ever heard. The only other truly sane per­son she could think of was lit­tle Wally Thurston, that eleven-year-old from across town. What a ridicu­lous irony, that an eleven-year-old was saner than all the adults!

Long about Au­gust 1, there was an ed­i­to­r­ial in the pa­per that gave An­drea a real lift. It came from out of the blue. It was writ­ten by the pa­per’s chief ed­i­tor, “But­tons” Brown. He was an old-time jour­nal­ist from St. Jo, Mis­souri. His ed­i­to­r­ial was real short. It went like this:

The Dis­obe­di-Ant

The story of the Dis­obe­di-Ant is very short. It re­fused to be­lieve that its pow­er­ful im­pulses to play in­stead of work were any­thing but unique ex­pres­sions of its very unique self, and it went its merry way, singing, “What I choose to do has noth­ing to do with what any-ant else chooses to do! What could be more self­-ev­i­dent?”

Co­in­ci­den­tally enough, so went the rea­son­ing of all its colony-mates. In fact, the same re­frain was in­de­pen­dently in­vented by every last ant in the colony, and each ant thought it orig­i­nal. It echoed through­out the colony, even with the same melody.

The colony per­ished.

An­drea thought this was a ter­rific al­le­go­ry, and showed it to all her friends. They mostly liked it, but to her sur­prise, not one of them started writ­ing post­cards. All in all, folks were pretty much back to daily life. After all, noth­ing much—seemed re­ally to have changed. The weather had turned real hot, and folks con­gre­gated around the var­i­ous swim­ming pools in town. There were lots of bar­be­cues in the evenings, and, every once in a while some­body’d make a joke or two about the De­mon and the post­cards. Folks would chuckle and


then change the top­ic. Most­ly, peo­ple spent their time do­ing what they’d al­ways done, and en­joy­ing the blue skies. And mow­ing their lawns reg­u­lar­ly, since they wanted the town to look nice.

Post Scriptum

The atomic bomb has changed every­thing ex­cept our way of think­ing. And so we drift help­lessly to­wards un­par­al­leled dis­as­ter.

–Al­bert Ein­stein

Peo­ple of every era al­ways feel that their era has the sever­est prob­lems that peo­ple have ever faced. At first this sounds sil­ly. How can every era be the tough­est? But it’s not sil­ly. Things can be get­ting con­stantly more dan­ger­ous and fright­ful, and that would mean that each new gen­er­a­tion truly is fac­ing un­prece­dent­edly se­ri­ous prob­lems. As for us, we have the prob­lem of ex­tinc­tion on our hands.

Some­one once said that our cur­rent sit­u­a­tion vis-a-vis the So­viet Union is like two peo­ple stand­ing knee-deep in a room filled with gaso­line. Both hold open match­books in their hands. One per­son is jeer­ing at the oth­er:.. “Ha ha ha! My match­book is full, and yours is only half full! Ha ha ha!”

The re­al­ity of our sit­u­a­tion is about that sim­ple. The vast ma­jor­ity of peo­ple, how­ev­er, refuse to let this re­al­ity seep into their sys­tems and change their day-to-day be­hav­iors. And thus the va­lid­ity of Ein­stein’s gloomy ut­ter­ance.

I re­mem­ber many years ago read­ing an es­ti­mate that the fa­mous ge­neti­cist had made about nu­clear war. He said he fig­ured there was a 2% chance per year of a nu­clear war tak­ing place.1 This amounts to throw­ing one 50-sided die (or a cou­ple of sev­en-sided dice) once a year, and hop­ing that it does­n’t come up on the bad side. How Wald ar­rived at his fig­ure of 2% per year, I don’t know. But it was vivid. The fig­ure has stuck with me for a cou­ple of decades. I tend to think that the chances are greater nowa­days than they were back then: maybe about 5% per year. But who can say?

The fea­tures a clock on its cov­er. This clock does­n’t tick, it just hov­ers. It hov­ers near mid­night, some­times get­ting closer, some­times re­ced­ing a bit. Right now, it’s at three min­utes to mid­night. Back at the sign­ing of , it was at twelve min­utes be­fore mid­night. The clos­est it ever came was two min­utes be­fore mid­night, and I think that was at the time of the Cuban mis­sile cri­sis.

The pur­pose of the clock is to sym­bol­ize the cur­rent dan­ger of a nu­clear


holo­caust. It’s a lit­tle like those “Dan­ger of Fire To­day” signs that Smokey the Bear holds up for you as you en­ter a na­tional for­est in the sum­mer. It is a sub­jec­tive es­ti­mate, made by the mag­a­zine’s board of di­rec­tors. Now what is the mean­ing of “dan­ger”, if not prob­a­bil­ity of dis­as­ter per unit time? Sure­ly, the more dan­ger­ous a place or sit­u­a­tion, the faster you want to get out of it, for, just that rea­son. There­fore, it seemed to me that the Bul­let­in’s num­ber of min­utes be­fore mid­night, B, was re­ally a coded way of ex­press­ing a Wald num­ber, W—a prob­a­bil­ity of nu­clear war per year. And so I de­cided to make a sub­jec­tive table, match­ing up the val­ues of B that I knew about with my own best es­ti­mates of W. After a bit of ex­per­i­men­ta­tion, I came up with the fol­low­ing table:

Bul­letin Clock (min­utes be­fore mid­night) Wald’s per­cent­age (prob­a­bil­ity per year)
1 min 20%
2 mins 10%
3 mins 7%
4 mins 5%
5 mins 4%
7 mins 3%
10 mins: 2%
12 mins 1.5%
20 mins 1%

A fairly ac­cu­rate sum­mary of this sub­jec­tive cor­re­spon­dence is given by the fol­low­ing sim­ple equa­tion:

This es­ti­mates for you the holo­caust dan­ger per or­bit of the earth, as a func­tion of the cur­rent set­ting of the Bul­let­in’s clock.

W and B may not be es­timable in any truly sci­en­tific way, but there is a defi­nite re­al­ity be­hind them, even if not. so sim­ple as that of N and X in Hap­pi­ton. Ob­vi­ously it is not a “ran­dom” dice-like process that will de­ter­mine whether nu­clear war erupts in any given year. Nonethe­less, it makes good sense to think of it in terms of a prob­a­bil­ity per year, since what ac­tu­ally does de­ter­mine his­tory is a lot of things that are in effect ran­dom, from the point of view of any less-than-om­ni­scient be­ing. What other peo­ple (or coun­tries) do is un­pre­dictable and un­con­trol­lable: it might as well be ran­dom.

If ten­sions get un­bear­ably high in the Mid­dle East or in Cen­tral Amer­i­ca, that is not some­thing that we could have pre­dicted or fore­stalled. If some ter­ror­ist group man­u­fac­tures and uses or threat­ens to use—a nu­clear bomb, that is es­sen­tially a “ran­dom” event. If over­pop­u­la­tion in Asia or star­va­tion


In Africa or crop fail­ures in the So­viet Union or oil gluts or short­ages cre­ate huge ten­sions be­tween na­tions, that is like a ran­dom vari­able, like a throw of dice. Who could have pre­dicted the crazy flareup be­tween Britain and Ar­gentina over the silly Falk­land Is­lands? Who knows where the next hot spot will turn out to be? The global tem­per­a­ture can change as swiftly and capri­ciously as a bright sum­mer day can turn sul­try and men­ac­ing—even in Hap­pi­ton.

It is the vivid im­agery be­hind the Wald num­ber and the Bul­letin clock that first got me think­ing in terms of the Hap­pi­ton metaphor. The story was pretty easy to write, once the metaphor had been con­coct­ed. I had to work out the math­e­mat­ics as I went along, but oth­er­wise it flowed eas­i­ly. It was cru­cial to me that the num­bers in. the al­le­gory seem re­al­is­tic. The most im­por­tant num­bers were: (1) the chance of dev­as­ta­tion per year, which came out about right, as I see it; and (2) the amount of time per day that I think would be­gin to make a sig­nifi­cant differ­ence if de­voted by a typ­i­cal per­son to some sort of ac­tiv­ity geared to­ward the right ends. In Hap­pi­ton, that thresh­old turned out to be about fifteen min­utes per day per per­son. Fifteen min­utes a day is just about the amount of time that I think would be­gin to make a real differ­ence in the real world, but there are two ways that one might draw a dis­tinc­tion be­tween the sit­u­a­tion in Hap­pi­ton and the ac­tual case.

First­ly, some peo­ple say that the sit­u­a­tion in Hap­pi­ton is much sim­pler than that of global com­pe­ti­tion and po­ten­tial nu­clear war. In Hap­pi­ton, it’s ob­vi­ous that writ­ing post­cards will do some good, whereas it’s not so ob­vi­ous (they claim) what kind of ac­tion will do any good in the real world. Work­ing hard for a freeze or for a re­duc­tion of US-SU ten­sions might even be harm­ful, they claim! The sit­u­a­tion is so com­plex that noth­ing cor­re­sponds to the sim­plis­tic and sure-fire recipe of writ­ing post­cards.

Ah, but there is a big fal­lacy here. Writ­ing post­cards in Hap­pi­ton is not sure-fire. The gas could still come ooz­ing up at any time. All that changes is the odds. Now in the real world, we must fol­low our own best es­ti­mates, in the ab­sence of per­fect in­for­ma­tion, as to what ac­tions are likely to be pos­i­tive and what ones to be neg­a­tive. You can only fol­low your nose. You can never be sure that any ac­tion, no mat­ter how well in­tend­ed, is go­ing to im­prove. the sit­u­a­tion. That’s just the way life is.

I hap­pen to be­lieve that the odds of a holo­caust will be re­duced (per­haps by a fac­tor of 1.0000001) by writ­ing to my rep­re­sen­ta­tives and sen­a­tors fairly reg­u­lar­ly, by at­tend­ing lo­cal freeze meet­ings, by con­tribut­ing to var­i­ous or­ga­ni­za­tions, by giv­ing lec­tures here and there on the top­ic, and by writ­ing ar­ti­cles like this. How can I know that it will do any good? I can’t, of course. And it’s no differ­ent in Hap­pi­ton. The best of in­ten­tions can back­fire for to­tally un­fore­see­able rea­sons. It might turn out that lit­tle Wally Thurston, by mov­ing his pen­cil in a cer­tain grace­ful curlicue mo­tion one


after­noon while writ­ing his 1,000th post­card to the De­mon, stirs up cer­tain air mol­e­cules which, by bounc­ing and jounc­ing against other ones hel­ter-skel­ter, wind up giv­ing that tiny last push to the car­oming icosa­he­dral dice atop the bel­fry, and bang! They all come up ‘7’! Wal­ly, oh Wal­ly, why such fol­ly? Why did you ever write those post­cards?

Those who would cau­tion peo­ple that it might be coun­ter-pro­duc­tive to work against the arms race—un­less they be­lieve one should work for the arms race—are in effect coun­sel­ing paral­y­sis. But would they do so in other ar­eas of life? You never know if that car trip to the gro­cery store won’t be the last thing you do in your life. All life is a gam­ble.

The sec­ond dis­tinc­tion be­tween Hap­pi­ton and re­al­ity is this. In Hap­pi­ton, for fifteen min­utes a day to make a no­tice­able dent, it would have had to be do­nated by all 20,000 cit­i­zens, adults and chil­dren. Ob­vi­ously I do not think that is re­al­is­tic in our coun­try. The fifteen min­utes a day per per­son that I would like to see spent by real peo­ple in this coun­try is lim­ited to adults (or at least peo­ple of high­-school age), and I don’t even in­clude most adults in this. I can­not re­al­is­ti­cally hope that every­one will be mo­ti­vated to be­come po­lit­i­cally ac­tive. Per­haps a highly ac­tive mi­nor­ity of 5% would be enough. It is amaz­ing how vis­i­ble and in­flu­en­tial an ar­tic­u­late and vo­cal mi­nor­ity of,that size can be! So, be­ing re­al­is­tic, I limit ’my de­sires to an av­er­age of fifteen min­utes of ac­tiv­ity per day for 5% of the adult Amer­i­can pop­u­la­tion. I sin­cerely be­lieve that with about this much work, a kind of turn­ing point would be reached—and that at 30 min­utes or 60 min­utes per day (ex­actly as in Hap­pi­ton), truly sig­nifi­cant changes in the na­tional mood (and hence in the global dan­ger lev­el) could be effect­ed.

I think I have ex­plained what Hap­pi­ton was writ­ten for. Trig­ger ac­tiv­ity it may not. I’m grow­ing a lit­tle more re­al­is­tic, and I don’t ex­pect much of any­thing. But I would like to un­der­stand hu­man na­ture. bet­ter, to un­der­stand what it is that makes us so much like stu­pid gnats dully buzzing above a free­way, un­able to see the on­rush­ing truck, 100 yards down the road, against whose wind­shield we are about to be smashed.

One last thought: Al­though to me it seems that nu­clear war is the gravest threat be­fore us, I would grant that to other peo­ple it might ap­pear oth­er­wise. I don’t care so much what kinds of efforts peo­ple in­vest their time in, as long as they do some­thing. The ex­act thing that cor­re­sponds to the threat to Hap­pi­ton does­n’t much mat­ter. It could be nu­clear weapons, chem­i­cal or bi­o­log­i­cal weapons, the pop­u­la­tion ex­plo­sion, the U.S.’s ever-deep­en­ing in­volve­ment in Cen­tral Amer­i­ca, or even some­thing more con­tained, like the en­vi­ron­men­tal dev­as­ta­tion in­side the U.S. What it seems to me is needed is a healthy dose of in­dig­na­tion: a spark, a flame, a fire in­side. Un­til that hap­pens, that cour­t­house clock­’ll be tick­in’ away, once every hour, on the hour, un­til …


Post Post Scriptum

Two mag­a­zines are de­voted to the pre­ven­tion of nu­clear war. They are: the Bul­letin of the Atomic Sci­en­tists and Nu­clear Times. The Bul­letin, founded in 1945, aims to fore­stall nu­clear holo­caust by pro­mot­ing aware­ness and un­der­stand­ing of the is­sues in­volved. It de­scribes it­self as “a mag­a­zine of sci­ence and world affairs”. Its ad­dress is: 5801 South Ken­wood Av­enue, Chicago, Illi­nois 60637.

Nu­clear Times is a more re­cent ar­rival, and calls it­self “the news mag­a­zine of the an­ti­nu­clear weapons move­ment”. Its ar­ti­cles are shorter and lighter than those of the Bul­let­in, but it keeps you up to date on what’s hap­pen­ing all over the coun­try and the world. Its ad­dress is: Room 512, 298 Fifth Av­enue, New York, New York 10001.

The fol­low­ing or­ga­ni­za­tions are effec­tive and im­por­tant forces in the at­tempt to slow down the arms race and to re­duce global ten­sions. Most of them put out ex­cel­lent lit­er­a­ture, which is avail­able in, large quan­ti­ties at low prices (some­times free) for dis­tri­b­u­tion. Need­less to say, they can al­ways use more mem­bers and more fund­ing. Many have lo­cal chap­ters.

The Council for a Livable World
11 Beacon Street Boston,
Massachusetts 02108

711 G Street, S.E. Washington,
D.C. 20003

Nuclear Weapons Freeze Campaign
4144 Lindell Boulevard, Suite 404
St. Louis, Missouri 63108

The Center for Defense Information
303 Capital Gallery West
600 Maryland Avenue, S.W.
Washington, D.C. 20024

Physicians for Social Responsibility,
639 Massachusetts Avenue
Cambridge, Massachusetts 02139

International Physicians for the Prevention of Nuclear War
225 Longwood Avenue, Room 200
Boston, Massachusetts 02115

Union of Concerned Scientists
1384 Massachusetts Avenue
Cambridge, Massachusetts 02238

  1. Pos­si­bly this refers to Wald’s 1969 speech, “A Gen­er­a­tion in Search of a Fu­ture”. In it, Wald does­n’t make the es­ti­mate him­self but at­trib­utes it to an­other Har­vard pro­fes­sor:

    A few months ago, Sen­a­tor , of Geor­gia, ended a speech in the Sen­ate with the words “If we have to start over again with an­other Adam and Eve, I want them to be Amer­i­cans; and I want them on this con­ti­nent and not in Eu­rope.” That was a United States sen­a­tor mak­ing a pa­tri­otic speech. Well, here is a No­bel lau­re­ate who thinks that those words are crim­i­nally in­sane.

    How real is the threat of ful­l-s­cale nu­clear war? I have my own very in­ex­pert idea, but, re­al­iz­ing how lit­tle I know, and fear­ful that I may be a lit­tle para­noid on this sub­ject, I take every op­por­tu­nity to ask re­puted ex­perts. I asked that ques­tion of a dis­tin­guished pro­fes­sor of gov­ern­ment at Har­vard about a month ago. I asked him what sort of odds he would lay on the pos­si­bil­ity of ful­l-s­cale nu­clear war within the fore­see­able fu­ture. “Oh”, he said com­fort­ably, “I think I can give you a pretty good an­swer to that ques­tion. I es­ti­mate the prob­a­bil­ity of ful­l-s­cale nu­clear war, pro­vided that the sit­u­a­tion re­mains about as it is now, at two per cent per year.” Any­body can do the sim­ple cal­cu­la­tion that shows that two per cent per year means that the chance of hav­ing that ful­l-s­cale nu­clear war by 1990 is about one in three, and by 2000 it is about fifty-fifty.

    I think I know what is both­er­ing the stu­dents. I think that what we are up against is a gen­er­a­tion that is by no means sure that it has a fu­ture.