Noesis

The Journal of the Noetic Society
Number 58
February 1991

EDITORIAL
IQ TESTS AND SMUT
Rick Rosner
5139 Balboa Blvd. #303
Encino, CA  91316-3430

I was exposed to pornography and IQ tests in a similar manner.  In elementary school, I happened upon soft-core stuff--naked playing cards and pre-pubic hair Playboy, Iowa Tests and the Lorge-Thorndike.  In secondary school, administrators and other students presented me with racier material--Penthouse and beyond, the SAT and its accomplices.  Later, I found the hard stuff--videos, the LAIT, the Mega, the Titan.

At each rung in the ladder of debauchery, I experienced an initial blast of revulsion, followed by a perverse thrill and gradual descent into jaded disinterest.  Each novel exposure inoculated me against the next level of outrageousness.  Had I been exposed to nudie pix and mental tests in anything but a sequence of increasing potency, I might have been permanently scared away.

As it is, I must fight firmly-rooted temptations to boggle and blister my brain.  My fiance has a copy of a Kevin Langdon test which I've instructed her to hide from me.

I get a raunchy rush when IQ is mentioned in conversation, on TV or in print, though I know that psychometrics has a grim history.

Trying to avoid feminist sins of exploitation and objectification, I went a year without looking at pictures of naked women.  I ran out of fantasies.  Without a constant undercurrent of sexual agitation, I felt myself turning into a wimp. 

 I try not to take sex and IQ too seriously.  I try to limit my exposure, to suffer a little for my perversity.  Fellow Noesis members, how about you?

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Many, many thanks to all of you who sent letters, checks, and even cash.  I was super pleased to receive your correspondence.  Those who haven't sent ten bucks to cover the next several months of Noesis will find that this is their last issue until a new editor takes over.  My address and phone number remain Rick Rosner, 5139 Balboa Blvd., #303, Encino, CA  91316-3430, (818) 986-9177.  Call between 8 a.m. and 11 p.m., Pacific time.  Don't be surprised if I'm groggy and disoriented.

I've written that less-than-scintillating submissions will be edited savagely, but it's an idle threat.  However, here are some very strong and practical suggestions:

Ron Hoeflin and other editors have been able to print material as it is received, assorted typefaces, drawings and all.  But, due to the present publishing set-up, almost everything for Noesis has to be entered through my keyboard.

My keyboard and I have serious limitations.  We can't handle exponents, subscripts, or symbols such as sigma.  I know it's ridiculous to expect you to avoid such notation, but please try to express formulas so that they don't lose too much clarity if some math symbols must be replaced with verbal phrases.  (Mr. Langan, sorry about the replacement of symbols in your marble problem discussion.)

Please double-space your stuff.  I must retype everything you submit, and I get lost in densely-spaced copy.

Thanks for your consideration.  My 90%-sincere apologies to those offended by my masquerade as Richard Sterman and by my slatternly writing.

FAKE ID--AN APPRECIATION
by Rick Rosner

If you're like me, you'd like your whopping IQ to mean something, to make some difference in your everyday life.  But, if you're like me, you actually find yourself rather stupid, prone to moronic behavior under dopey circumstances.  You might find other people even more stupid, except for their occasional flashes of cunning that serve mainly to make you feel bad for judging them so harshly.  And other people's stupidity doesn't seem to give you any advantage, but instead is a cornucopia of ridiculous situations in which you find yourself pointlessly struggling.

Well, by working in bars (a primary locale for mentally deficient behavior), I've found a way to get paid for being smarter than certain people, to catch them lying, to catch them using fake ID.

I have the unnatural advantages of being much older and less intoxicated than my underage victims, but for each fake ID user I catch, my bosses pay me ten bucks, and I reap the additional spiritual rewards of feeling clever and being mean to attractive people who would have snubbed me had we attended high school together.

My fiance read this article, and she said, "Why would Noesis readers be interested in this?  I think you'd better add some math."  Besides the satisfaction of abusing my social superiors, catching fake ID's gives the pleasure of watching probability in action.  Of the people whose ID's I check, around one third are, in my initial estimation, possibly underage.  (The rest are too old and wrinkly.)  About one in twelve possibly underage people has a fake ID.

After getting an ID in my grubby, grasping hand, I go to work, comparing the person to his or her ID, asking questions, trying to make my internal ID gauge, which is wavering between REAL ID and FAKE ID, pick a definite value.  Much of the excitement for me is in feeling the gauge swing wildly back and forth as I ask questions, trying to decide, "Is this person using fake ID or is he just a total idiot?"  No casino game or imaginary urn problem offers the same type of elusive value determinations.

There are two types of ID-checking errors, which I call alpha and beta errors.  An alpha error is when a person uses fake ID successfully.  A beta error is when we decide wrongly that an ID is fake.

I don't worry too much about alpha errors.  When it comes to fake ID, I'm such a vicious asshole that anyone who gets past me will probably also fool any liquor control cops who check out our bar.  L.A. fake ID's can be so good that a trained, conscientious doorperson might not catch more than 40% of the fake ID's he or she examines.  I like to think that I catch 80% of the fakes I encounter.

I worry more about beta errors, where we turn away people who should have been admitted, just because they're brainless and don't remember personal facts such as their age and their birthdate.  I try to catch at least 50 actual fakes for every beta error.

An additional justification for telling Noesis readers about fake ID is that it's not a very speculative subject and I can hope that it won't lead to the circular, perpetual debates that ensue when Noesis members present revolutionary new cosmologies.

At Mom's Saloon, I catch an average of 7 ID's each night I work, and at The Oar House, an average of 12.  At the Sagebrush Cantina, where I just started, I hope to catch up to 30 in a single shift, if none of the violence-prone customers or other staff members incapacitate me.  Many of the underage visitors to Mom's come from Beverly Hills, and I get the additional satisfaction of confiscating ID's from especially affluent and snotty people.

California is the golden state for fake ID's.  From over 170 DMV offices, the state of California annually issues at least five million ID's.  Between .1% and .4% of these are fake.  The person pictured on the ID is not the person whose name and birthdate appear on the ID.

Official-but-fake ID's are obtained by people who have the guts to go to the DMV and get a driver's license or state ID while posing as someone else.  Between 20 and 80 thousand official-but-fake California ID's are in use, most by underage people trying to pass for 21.  An official but fake driver's license is the best readily-available fake ID.  Over 95% of these will never be detected, which makes catching them challenging and fun.

The next best type of fake ID is one borrowed from someone who looks like the user and shares their approximate physical dimensions.  Perhaps one fourth of 18, 19, and 20-year-olds have access to some type of fake ID.  Many of the millions of tourists visiting L.A. have fake ID.  Most out-of-state fake ID users aren't as sophisticated and are easier to catch.

Between one and five percent of people trying to enter most popular bars are underage.  The exact percentages vary with the time of year, the strictness of doorpeople, and other factors.

Here are some characteristics found in people using fake ID, arranged from most to least indicative:

SERIOUS GIVEAWAYS

Has same name and birthdate as another patron
Doesn't know or can't spell name
Doesn't know birthdate
True eye color disagrees wildly with color given on ID
ID user fabricates immediately falsifiable information (i.e. says he's wearing colored contacts but isn't wearing contacts, says she went to high school in Albuquerque but names a high school and a street which don't exist)
Has an overstuffed wallet but nothing that matches the name on the ID
True height disagrees with height on recently-issued ID by more than four inches
Doesn't know zodiac sign

SOMEWHAT SERIOUS SCREWUPS

True eye color somewhat disagrees with ID eye color
Signature differs wildly from signature on ID
Doesn't know his/her age
True height disagrees with height on recently-issued ID by two or more inches
Says he/she drove, but has nothing in car with name that matches ID
Has a facial characteristic that doesn't match that in picture, most commonly:
            Arc of eyebrows
            Distance between eyes
            Prominence and shape of chin, nose, head, or ears
Doesn't know year she/he graduated high school
Has two friends with questionable ID's
ID user's apparent age is five years less than age on ID
Friends don't know ID user's name

MIDDLING OBJECTIONS

Signature differs somewhat from signature on ID
ID has expired
ID isn't a driver's license
ID user doesn't know his/her state's capital, area code, or prominent landmarks (i.e. Someone with an ID apparently issued in St. Louis says the Connecticut River runs through her town.)
Female user doesn't know birth stone
Has one friend with dubious ID
ID user's apparent age is three years less than age on ID

QUIBBLES

ID says "Duplicate"
ID user has no other ID
No middle name is listed on ID
ID is less than a year old
ID user has no idea when ID was issued
Signature on recently-issued ID is childish and unpracticed
ID user or friends are wearing Greek insignia (Fraternity/sorority members often find it easy to get fake ID.)

Some fake ID users pretend not to speak English so they don't have to answer questions.  Some say they're very religious and don't have pagan knowledge of their zodiac sign.  The occasional user will claim plastic surgery or a bad car wreck to explain away differing facial features.  Some people will claim they lost height when they lost weight.  Others will say they're models and must claim to be taller in order to get work.

The first half of George Dicks's

NOESIS 49 REBUTTAL

ran in the previous issue.  Here's the second half.

George W. Dicks, Jr.
198 Sturm St.
New Haven, IN  46774
(219) 749-8511

Rebuttal--Point 3 (CTMU solution unsatisfactory)

As any member of our society journal probably realizes, the only reason I felt compelled to write my paper was because I found the CTMU solution unsatisfying in some way or another.  Let me explain my reasoning at this time.

You see, when I read Chris Langan's original paper I was actually quite impressed.  Those of you who know me know that I am a computer person myself and can therefore figure out the rest on your own.  I have spent tremendous time using the computer to simulate a wide variety of processes, physical, economic, and otherwise and can therefore appreciate the assertion that because we can model almost anything on a computer why not simply assume that the theory of computation is the dominant theory of the universe?

It is here that I met with my biggest obstacle.  In modeling the universe in this fashion, we have simply replaced one formalism, Logic and Mathematics, for another one, CTMU.  At this point we are led to ask what we have gained.  In my estimation, there is nothing describable in the old formalism which is not describable in the new one.  However, it also seems apparent that the new formalism really has nothing much new to add either.  It does, however, serve to neatly render all previous results into one meat and tidy formalism.  This benefit must not be discounted.

The problem, as I saw it, with the Noesis 44 solution was simply that it was like using a B2 for crop-dusting.  This formalism is simply too general and too powerful to claim it as the solution to any specific problem.  At the high level represented by the theory, the most which may be said is that the problem is computable which, given the fact that the theory can handle any conceivable situation, is not terribly helpful.  The author of the Noesis 44 solution does attempt to focus on the problem somewhat but the end result is that without knowing many of the parameters to each of the presumed automata we simply cannot make any kind of prediction as to the particular dynamics of any particular instance of the Newcomb Problem.

Because we aren't given these parameters I felt it necessary to factor this computational process out of the problem in order to have any chance of solving the problem for a given Predictor in a given situation.  I realized that such a factoring could be easily handled with probabilistic methods and I also realized that such a method does carry an attendant loss of ability to predict any particular trial.  The result of the concerns is the Noesis 49 paper.  As the editor of Noesis 49 correctly pointed out, the Noesis 49 solution can be tricked by playing games with the experimental data.  However, the editor failed to mention two very important facts.  First, we don't know the parameters to the automata so we cannot make a prediction from them. Also, the Noesis 49 solution admits that it may be fooled, but it also learns pretty quickly from its mistakes.

Rebuttal--Point 4 (It is reasonable to distinguish Predictor and Chooser)

I actually find this point kind of ridiculous but I will contain myself.  The entire problem is presented from this standpoint. Namely, that the entire reward structure is determined by the actions of one of the players.

The editor argues from the standpoint that each of the two players is trying to ascertain the choice made by his opponent in order to maximize his own personal gain from the situation.  This having been said, we must realize that within the context of the problem one of the two players must eventually dominate in order to avoid an infinite computational regression.

Also, please understand that the names chosen are purely arbitrary and that Fred and Barney, Tweedle-Dee and Tweedle-Dum, or any other pair would serve our purposes equally well.  The whole purpose to using this type of name was to sterilize the problem.  Names like Demon, God, Super-Being, and Alien tend to force possibly unwarranted assumptions about Predictor's ability.  Also, names like Human, You, Guinea Pig might lead to similar unwarranted assumptions about the abilities of Chooser.  This was the whole reason for changing the names, to rid the problem of superfluous intellectual baggage.  I'm sorry.  I didn't quite meet my objective in this regard because Predictor and Chooser also lead to unwarranted assumptions.  I will try not to lead you astray like this in the future.

Better names would be Aleph and Alpha, Beth and Beta, or some similar pair of non-loaded, equally rooted pair of identifiers.

Rebuttal--Point 5 (Certainty theory is reasonable)

Let me preface my remarks by saying that I nearly omitted the entire section on certainty theory because the Noesis 49 solution basically doesn't require it because any type of empirical induction would suffice.

The basic premise of the Noesis 49 solution is quite simple.  It isn't any different from the basic premise of all of science.  Namely it is the assertion that given sufficient data about the past and given sufficient information about the present, we can predict the future.

The method which I developed to handle this type of situation I titled Certainty Theory.  I have since learned that this isn't a completely original idea and in fact that it is the inverse of Sampling Theory.  However, for me it was original.  The only reason I included it in my paper is because I understood the audience who would receive my paper.  I knew that if I had made a mistake that this audience could easily point it out and I could correct my thinking.  That the only criticism I received was philosophical and not mathematical made me feel reasonably good.

The idea began in response to a question which one of Marilyn's readers posed about the lottery.  I believe the question dealt with which numbers should the reader bet on or some related subject.  Marilyn's response was correct as far as it went, being the classic probability response that the outcome of given game is in no way determined by the preceding games.  I had read this explanation many times before, but each time it never felt right.  That's when I realized that classic probability is based solely on the assumption that a randomizer is not biased in any way.  Unfortunately, we live in a physical world and all of our randomizers are biased, just ask the dungeon master we caught playing with shaved dice!

I then set out to determine how these biases may be determined and how the attendant probabilities may be estimated.  I realized that actual probabilities are the result of an infinite number of trials and also that each trial would slightly reduce the amount of doubt which we have about a given estimate.  This is why I set out to produce a method which can learn from experience and therefore can correct itself.  Also, I knew that the rashness of simply doing a certain number of trials and basing the probability upon the result is rife with peril and therefore I wanted some method of keeping track of how sure I was of my estimate of the probability.  The result is certainty theory.

I understood quite well the problems which the review in Noesis 49 points out such as the blindness to bluffing, etc.  However, I realized that even these problems could be reduced to a probability estimate.  In other words, if the other player is bluffing, this will show up as erratic play which means that his probability of a correct play is determinable for his actual skill level and the odds of a bluff.  Since we assume that any trial is like any other trial, this probability may be used th calculate the expected value of it.

The Noesis 49 review then proceed to indicate by means of several other paradoxes and problems to show that certainty theory is blind.  However, the simple fact is that without complete knowledge about the situation, a certainty 1 estimate of the probabilities involved, we must infer from past data an estimate of the probability.  This is what certainty theory attempts to do.  In fact, to dispute the empirical basis for probabilistic methods such as this is to dispute the entire basis for science.  This leaves us with nothing but a chaotic mess of unprovable hypotheses with completely convinced adherents.  Consider the long, irrational history of religious struggles if you consider this tolerable.  Let me close this tirade by saying if you can't prove your assertions to an open-minded critic, then you can't prove them to anyone.  Faith isn't proof.

Conclusions

Let me say in closing that I appreciate your patience in allowing me to defend some of the points which were made in my paper published in Noesis 49.

I have attempted with varying degrees of success to make the following points:

1) That the Noesis 49 solution was more general to the presented Noesis 44 solution while the Noesis 44 solution is potentially more general.
2) That the Noesis 49 solution is complete as to all facets of the problem.
3) That the CTMU solution is too general for the problem.
4) That the Predictor and Chooser should be treated as separate entities.
5) That certainty theory is not essential to my paper but is reasonable.

Also, let me reiterate that the entire purpose of this rebuttal is simply to defend certain points and to clarify others.  It was not intended to step on any toes and absolutely not intended to humiliate or criticize anyone.

Also, let me repeat my appreciation to all members involved in working on this problem. It's been interesting and I think I've learned a lot. I would especially encourage Chris to continue work on his CTMU and I would appreciate the opportunity to see the entire thing at some time in the future.  As I told him in a letter, I find it very interesting and believe there's quite a bit there for those who look.

Let me close by encouraging any and all of you to send me any correspondence you find appropriate on this or any other matter.  I truly enjoy hearing from each and every one of you.  My phone is always on the hook and my mailbox is always open.  It's up to you.

Sincerely,
George W. Dicks, Jr

ASSORTED SIMPLE-MINDED PUZZLES

In the previous issue, I presented two problems--one, to find a 13-letter word for the desire to eat clay, and the other, to find the velocity relative to earth of the eleventh of a string of eleven spaceships, with each spaceship traveling half the speed of light faster than the one preceding it (and with each ship containing a member of The Brady Bunch).

MARSHALL FOX, of Atlanta, Georgia, totally kicked butt by coming up with TWO 13-letter words for the desire to eat clay!  He unearthed chthonophagia, which was my answer, as well as allotriophagy, a synonym for pica, which is a less specific term expressing an abnormal craving for unnatural foods.

I don't know how Mr. (Dr.?) Fox discovered these words.  But here's a set of questions that sent me rooting through over a dozen Elvis biographies:

1.  What was Elvis's nickname for himself?
2.  What was Elvis's nickname for his penis?
3.  Minutes after he was born, Elvis found himself in what home appliance?
4.  Elvis liked to watch women wearing only panties wrestle.  What color panties did he prefer?
5.  What does Cybill Shepherd say she liked most about dating Elvis?
6.  Beaver Cleaver's TV mother Barbara Billingsley shares what self-perceived physical flaw with Elvis?

Marshall Fox also figured out how fast the eleventh spacecraft was moving relative to Earth, 88573/88574 the speed of light, and that the formula for the relative speed of the nth spacecraft is (3n-1)/(3n+1) the speed of light.  The velocities of each member of The Brady Bunch are as follows:

Mike Brady                                          1/2 c
Carol Brady                                         4/5 c
Alice the Maid                          13/14 c
Sam the Butcher                                   40/41 c
Greg Brady                                          121/122 c
Marsha Brady                                      364/365 c
Peter Brady                                          1093/1094 c
Jan Brady                                             3280/3281 c
Bobby Brady                                        9841/9842 c
Little Cindy Brady                                29524/29525 c
Tiger Brady (winner of the Patsy award for excellence in animal acting)
                                                            88573/88574 c

Here's one last Brady Physics question: BOBBY BRADY, WEIGHING 40KG, SHAKES HANDS WITH HIS ANTI-MATTER DOUBLE. EXPRESSED IN MEGATONS, HOW BIG IS THE RESULTING EXPLOSION?

[I have only an approximate idea of the correct answer.  To solve this a few years ago, I called several federal agencies to find the appropriate conversion factors, which I've since forgotten.  I don't want to end up under FBI surveillance, so call Los Alamos yourself.  (If this was 1944, would a bunch of Noesis members be working on the Manhattan Project?)]

In his letter, Marshall Fox also offers a rigorous rule of thumb for the probability of encountering a novel situation.  If there is a finite number of possible situations, and one situation occurs each day, then the probability of encountering a novel situation on day x is [(n-1)/n]x-1, where n is the number of possible situations.  Fox estimates that for his job, n=10, which, considering his problem-solving ability, must force him to develop intricate distractions.  Fox says his autobiography is in the October, 1990 issue of Telicom, and that he's been involved with high-IQ society stuff for two years.

For my hapless attempts at employment, I still prefer my half-assed formula, if only because I keep getting surprised at work. Fox has his hypothetical employee pulling ping pong balls from a barrel; I prefer to think of my hypothetical self wandering blindfolded in an occupational cornfield.

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

You know those repeatedly-Xeroxed cartoons and humorous statements that show up pinned to office bulletin boards?  Such as "Answers 15 cents, Correct Answers $5, Blank Looks are still free," or the one with Snoopy hung over on Monday, still dazed on Tuesday, dancing on Friday?  As with last year's Richard Gere rumor (Still haven't heard it?  It can't be printed, but I suppose it's O.K. to send a summary if you write and ask.), no one knows where these things originate.  The most recent notorious Xerox is an obscene cartoon in which Bart Simpson says to his mom, "Don't have a cow, she just lost her pacifier."  A Denver liquor store had its liquor license revoked for circulating it.

Anyway, my mom came to L.A. last week to attend my fiance's wedding shower, and she brought a mystery Xerox with her.  I like it 'cause it's not so tough my ears bleed from overthinking.  Here it is verbatim:

This test does not measure your intelligence, your fluency with words, and certainly not mathematical ability.  It will, however, give you some gauge of your mental flexibility and creativity.  In the many years since the test has been developed, we have found few people who could solve more than half of the questions on the first try.  Many, however reported getting answers long after the test had been set aside--particularly unexpected moments when their minds were relaxed. Some reported getting all of the answers over a period of several days.  Take this as a personal challenge and have fun!

Instructions:  Each question below contains the initials of words that will make it correct.  Find the missing words; for example--12 M in a Y (12 months in a year).

1.  26 L of the A
2.  7 W of the W
3.  1,001 A N
4.  12 S of the Z
5.  54 C in a D (with the J)
6.  9 P in the S S
7.  88 P K
8.  13 S on the A F
9.  32 D F at which W F
10. 18 H on a G C
11. 90 D in a R A
12. 200 D for P G in M
13. 8 S on a S S
14. 3 B M (S H T R)
15. 4 Q in a F G
16. 24 H in a D
17. 1 W on a U
18. 5 D in a Z C
19. 57 H V
20. 11 P on a F T
21. 1,000 W that a P is W
22. 29 D in F in a L Y
23. 64 S on a C
24. 6 S on a C
25. 100 B of B on the W
26. 2 H in a W
27. 90 D same as C
28. 101 a S M L
29. 2 M in O
30. "M C to A and to A a G N"

Here're a couple more of my own:

101 D, by W D
96 T, by ?

ccccccccccccccccccccccccccccccccccccccccccccccccccc

In Noesis 56, December, 1990, George Dicks submitted a new short form of the Mega Test, designed to take about an hour, involving problems such as the construction of a crossword puzzle that fills Hilbert Space and running an ant around the vertices of 25 maximally-intersecting cubes.  (Member Eric Erlandson, by the way, is working on a means of determining the maximum intersection of n cubes.) 

I think that the Dicks Mega Test is an admirable effort, but might involve too much bias toward test takers with classical educations.  Therefore, I'm submitting two additional problems, designed to favor people whose preferred reading matter is People magazine and The National Enquirer.

11a. List the members of the Kennedy family and their in-laws in order of the number of sexual partners each has had.  (Don't forget Joe Senior.)  b. List the Kennedys in order of the combined assets of their sexual partners.  c. List those zany Kennedys in order of the total number of words written about each of their sex partners.

12. Imagine an S-chain, the end points of which are two celebrities.  In between the celebrities are a minimum number of people arranged so that there is a chain of sexual contact joining the celebs.  (Ignore temporal factors--contact doesn't have to flow directly from one end point to the other.)  S is the number of links joining the celebrity end points.  For Marc Gastineau and Brigitte Nielsen, S is 1.  For Sylvester Stallone and Marc Gastineau, I hope S is 2.  What is S for Madonna and Tip O'Neill?  (For half credit, is S even or odd?)

 

IN CLARIFICATION OF THE CTMU AND ITS APPLICATIONS IN
NOESIS
by Chris Langan

The following enumerated remarks are in response to those of Chris Cole and George Dicks in Noesis 57 (Sections I and II resp.).

SECTION 1

1) The CTMU is a theory of reality as mind, not "the universe as a computer".  The latter analogy was given advisedly as a conceptual aid and as a means by which to apply mechanistic and computational formalisms to the model.  It does not encapsulate the whole theory.

2) The components of the CTMU are not all new.  The idea as a whole is new.  Technically, there are no new ideas, just new combinations of old components.  The CTMU is more deeply rooted in analytical philosophy and the foundations of mathematics than in practical computer science, which nonetheless plays a large part in it.

3) I know of the late physicist Richard Feynman.  But who is Ed Fredkin, and where can his ideas be sampled?  If Chris means to give him credit for the CTMU, where are the applications?  Given the current mania for computer simulation of natural processes, it would be incredible if no writers or scientists had latched onto the general notion of a computational universe.  However, we don't give those who make mathematical conjectures automatic credit for proving them as theorems, we don't give Michelson, Morley, or Lorentz credit for Special Relativity, and we don't give Jules Verne credit for the deep-sea submarine.  Credit is reserved for those who display greater understanding of the ideas in question--for example, by application to problems like Newcomb's paradox, quantum wave-function collapse, and logical and empirical induction.  Those are the rules; I'm only following them.

4) Anyone who thinks I'm an "incautious thinker" has a responsibility to point out some specific flaw in my reasoning.  No matter how "general" my reasoning is, it is either right or wrong, and if it is wrong, then it contains an identifiable flaw.  This group has had a standing invitation to locate such a flaw, but has not done so.  For example, if my reasoning is too general to solve the (very general, but very important) problems I claim to have solved with it, such a fact is demonstrable; my claim could be falsified.

5) The CTMU is a theory of the codeterminate relationship between reality and the intellect.  The empirical evidence offered so far includes the many experiments now confirming EPR-Bell quantum non-locality and Heisenberg uncertainty.  These are hard, physical facts which were fundamentally unexplained prior to the CTMU.  The logical evidence presented in favor of the CTMU has been nothing short of overwhelming.  Resolutions of paradoxes are evidence for logical theories as surely as predictions and explanations of anomalies are evidence for physical theories.  Because physical theories necessarily have logical structures, logic has priority.  A single unresolved paradox of the general form x = ~x invalidates the entire logical system containing it, and thus every semantical theory formulated within that system; it renders determinations of truth and falsity impossible for every statement the system and theory contain.  In principle, I can thus claim every confirming instance of every logically consistent scientific theory as evidence of the CTMU, making it the best-confirmed theory in history.  In point of fact, this is precisely what I've already done.

6) Even if CTMU were a definition rather than a theory, definitions are necessary components of theories.  There is an inclusory relation, not a total distinction, between the two.  In fact, the CTMU can be characterized as a THEORY of how the mind DEFINES and IS DEFINED by the universe.  If you must, re-read Noesis 46 and 47.

7) That some details of CTMU were omitted in my presentation was quite deliberate.  I used only what I had to use to solve the problems I attacked.  The size and scheduling of Noesis imposed severe restrictions on me; even so, I was simultaneously accused of being overly general and excessively technical.  This is a paradox that even I find hard to resolve.

8) I have a razor-fine dissection of the original marble problem (#26, Trial Test B, Insight 10) in the form of a dialogue so clear and amusing that even an average high schooler could understand it.  However, the current editor--despite what I'm sure are his many virtues--shows an apparent preference for scatological humor over this kind of material, and threatens to "edit like crazy" anything not completely to his liking.  That naturally precludes further extensive discussion of the marble problem, towards which he professes antipathy.  This is unfortunate, since the dialogue is illuminating on Bayesian paradox in general.  Had anyone expressed any real encouragement, I'd have printed and mailed it myself.  But supporters are apparently few.  So for now, I'll just reiterate my former assertion: there is one and only one way to solve the problem as presented.  In a nutshell, the reasons are:

a) Observation is all you have to go on, and the 1<=(r)<=10 marbles you observe display just one color.  The number of possible colors is critical information, so you can't just guess it or make it up.  It has to come from observation.  The way you refer to the electromagnetic distinctions on which color is defined is also important, but only as an upper limit on what may be observed.  I.e., if you can discern only n colors, you can observe no more than n.  Letting your chromatic sensitivity or vocabulary play a greater part than this implies that you are controlling the sample by observing it, a ridiculous assertion.  You are not a "demon". . . or are you?

b) Since you can't make up the number of colors, you're entitled to just two, the one you've observed and a generalized complement to symmetrize (remove imbalances in) the initial information necessary for Bayes' rule to work.  This is the direct negation of the observed color: white ---> nonwhite.  Failure to add this complement imbalances the calculation and makes whiteness "axiomatic" for marbles on the basis of just one observation . . . an absurdity, given that the formulation requests a "probability" and thus implies an exhaustive and disjunctive set of at least two nonzero colors.  The idea of "color" does not exist for monochromatic observers.

c) You must not only symmetrize color (i.e., white-nonwhite), but also the possible distributions in terms of color alone.  Otherwise you're imparting phony confirmation to information you can't legitimately claim . . . the information embodied in any asymmetry among allowed colors or initial distributions.  Thus, the white nonwhite ratio n/(10 - n) is equally probable for all n from 1 to 10.

Let me explain.  The method by which marbles were colored and put into the box can be known to you only through the actual distribution.  Unequal probabilities among possible (initial) distributions would imply that you have a priori information on this method and so on the actual distribution itself.  But the problem formulation gives you no such information.  If such information emerges over repeated experiments, the problem changes and Bayesian inference is relativized to new data.  But until then, you're more limited.

These conditions--that only two colors may be used, and that all distributions in these two colors are initially assumed to be equiprobable--plug directly into Bayes's rule and yield a probability of .67 that all ten marbles in the box are white, given that sampling with replacement has produced ten white marbles in a row.  This is a very specific determination which should be easy for all to follow.  There is nothing "ambiguous" about it.  But just to make sure, let's run the computation one more time.

BAYES'S RULE: p(a|b) = [p(b|ai)p(ai)] / [p(b|ai)p(ai) + . . . + p(b|an)p(an)]

where p(a|b) means "the probability of a, given b", and the ai are exhaustive independent alternatives defining a random variable A.

Let A = {a0 or . . . or a10} be the actual distribution of marbles in the box, and let an be the possible distribution with n white and (10 - n) nonwhite marbles.  The symmetry condition on possible distributions means that p(a1) = . . . = p(a10) = .1 (since at least one white marble has been observed, p(a0) = 0).  Let b represent the evidential data, a sample-with-replacement of 10 white marbles in a row.

Then

                   1                                1
p(a|b)= _________=    ____________________= 1/1.49 = .67
       sigma(n/10)10         0 + .110 + .210 + . . . + 1
       n=0 to 10

        The original marble problem has now been solved more explicitly than any other problem on any Ronald Hoeflin test.  So, unlike most of them, it can now be cautiously used to measure intelligence.

SECTION II

8) Regarding George Dicks's criticisms, I'm forced to reiterate a crucial distinction that makes all the difference in the world.  He has solved Newcomb's PROBLEM; I resolved Newcomb's PARADOX.  George is one of many who have solved the problem in essentially the same way. I didn't solve it at all except as a "side effect" of resolving the paradox between the arguments that George and Chris employed.  This can only be done in one way, as defined with great precision in Noesis 44.  The Resolution of Newcomb's Paradox represents the first and only time that this has been done in print.  While I've already congratulated George on writing a fine paper with some original features, his entire "rebuttal" is virtually irrelevant in view of the foregoing distinction.  But I'm going to go over a couple of things I'm afraid he and Chris might have missed in Noesis 44-49, just to make sure that nobody backs himself into a corner he can't pitch his tent in.

9) Computative regression is the essence of Newcomb's paradox. The regression is defined by the conventional formulation which George changed to get his own version of the problem.  Trying to avoid a computative regression in resolving Newcomb's paradox is like trying to avoid the idea of viruses while searching for an AIDS vaccine.  It can't be done with any hope of success.

10) The arguments used to solve Newcomb's problem fall into two general classes, mathematical expectation and temporal directionality. The former class is probabilistic and statistical; the latter is intuitive.  Both classes involve subjective utility or self-interest, and both claim an empirical basis.  Chris Cole argues from physical intuition grounded in his experience of reality.  George Dicks argues from numerical data.  But it's easy to see that Bayes's rule, the proper use of which I outlined above, can easily be adopted to Newcomb's problem in lieu of the method he employed.  The way I've used it to avoid "false axioms" in the marble problem applies as well to Newcomb's problem, and yields a numerical determination comparable to his.  The point is, CTMU principles cover all numerical methods in this class while depending on none.  The CTMU is determinant over all of them in kind.

11) "Empiricism works" is a statement with which I fully agree. However, it does not work by itself.  Empirical induction is to theorization what observation is to recognition; one is of no use without the other.  The CTMU is primarily a theory of induction.  To claim that it was used to resolve Newcomb's paradox at the expense of empiricism is a non sequitur.  The CTMU resolves the paradox because, unlike certainty theory and standard numerical statistics, it accounts for the means by which empirical data--like the perfect success of Newcomb's Demon and quantum nonlocality--can violate intuitive (and observationally-confirmed) assumptions about time and space.  These means involve the relationship of mind to reality, not just mind or reality alone.

"Anything less is just theology" is a statement which I find impenetrable.  Your past experiences and disappointments with what has traditionally passed for theology have nothing whatever to do with the CTMU, which realizes Kant's dream of a "theology" derivable from the union of mind and reality.  If you mean to challenge that, you'd better gear up for a whole new game.  CTMU "theology" owes nothing to the history of religion, and whatever arguments you use against it had better not either.  That includes any idea you might have that the theological implications of the CTMU are "unverifiable" or mere "wishful thinking".

12) The Resolution of Newcomb's Paradox allows for any arrangement of chooser and predictor.  These designations are meaningful only relative to each other.  That particular arrangement in which the predictor dominates the chooser happens to be set by the canonical formulation.  In Noesis 45, the theory of metagames was incorporated into the CTMU.  This theory, by merging the best interests of the players, allows them to cooperate in nondominative situations where "choosers" and "predictors" are indistinguishable. This idea was further developed in Noesis 48.  The bottom line is, if neither player is "predictive" relative to the other, then there exists a jointly accessible algorithm which lets them cooperate to achieve mutual benefits (the theory of metagames).  This prevents what George calls a "chaotic exchange of move and counter-move," provided both players know of it.  But if one is dominant, as the formulation stipulates, then the situation is identical to that of The Resolution.  These possibilities are exhaustive and mutually exclusive, so no further explanation is necessary.  George's attention to specific arguments is commendable, but unnecessary resolve the original version of Newcomb's paradox.  It can't be used to justify a claim of superiority or priority, particularly when it completely ignores the theory of metagames.

If, despite the ubiquity of computative regressions in every aspect of our mental lives, you doubt their possibility, you still can't use your doubt as an objection to the CTMU or its resolution of Newcomb's paradox.  If you deny it, then you also deny the validity of mathematical achievements like nonstandard analysis, which itself uses an "incredible" model--a nonstandard universe containing "infinitesimal" (nonzero but subfinite) quantities--to resolve inconsistencies in the infinitesimal calculus.  The CTMU is on even firmer ground, and you will ultimately find it harder to avoid than death and taxation.  It is a fait accompli.

My remarks are numbered.  If you disagree with anything I've said, please refer to it by number and line.  The exchange has thus far been circular, and I can't waste time on circular objections.  You supposedly have I.Q.'s in the vicinity of 180 and vocabularies to

match.  If you find these comments "stultifying", "unreadable", or anything but crystal clear, don't blame me.  I'm just the one who tentatively bought your PR.

This is not to say that I don't hold your intellects in high regard despite your lack of encouragement.  I only wish that some of you could forget about defending your special views long enough to recognize that you have witnessed a remarkable development.  I expect only what is reasonable and seek nothing that is not mine by right. One supposed benefit if a high IQ is knowing when to cut your losses and reinvest in new concepts, and you've all had an adequate prospectus since early 1990.

Chris Langan

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EDITOR'S COMMENTS

I believe in matter and space as information held in some vast awareness, which doesn't seem so far from CTMU.  I also think that the increasing prevalence of such belief is part of the zeitgeist of the near future.  I agree with Langan that quantum nonlocality is consistent with such belief, and I think that Langan makes a strong, often clear presentation of his position.  (I'd rather read scatological material than arguments about CTMU, but I am a slimeball.)

I don't believe in Langan's solution of the marble thing or in anyone's solution to Newcomb's paradox.  (Newcomb's paradox is not only an imaginary situation, but an insufficiently-imaginable situation of the irresistible force/immovable object variety.  It demands a short-story writer, not a game theorist.)  With regard to the marble thing, here are two similar problems of my own:

1. Ten numbers are chosen.  The average of nine of the numbers is 75.  What is the probability that the average of all ten numbers is less than 100?

2. An urn is filled with ten marbles, nine of which are white. The remaining marble has been randomly selected from a box containing x marbles, only one of which is white.   After ten random samples with replacement from the urn, all of which turned up white marbles, what is the probability that all marbles in the urn are white?

Answers:

Problem 1-- Pi squared divided by 17

Problem 2-- Standard Monty Hall/Marilyn Savant/Chris Cole/Marshall Fox/Bayesian probability theory says that the probability of all white marbles in an urn is 1/{(n-1/n)sx + [1-(n-1/n)]s}, where n is the number of marbles in the urn (and n-1 is the number of definitely-white marbles), s is the number of samples, and x is the number of marbles in the box.  For a ten-marble urn sampled ten times, the probability of all white marbles is approximately 1/(.34868x + .65132).  Unfortunately, the problem doesn't specify what x equals, so we're basically screwed, even though in this problem we know that nine of the urn's marbles are for sure white!  For white marble fans, this is a more favorable situation than in the original, troublesome marble problem, where we only know with certainty that at least one marble is white.  Our buddy Bayes can give us only so much assistance.

CTMU inspired me to do some sloppy mathematical speculation.  If the universe is a vast information-manipulating array, can a number be assigned to its level of complexity?  How about assigning the cosmos the number 80, as in 10 to the 80th, which, I think, is Eddington's estimate of the number of elementary particles in the universe.  Given the outrageous assumption that the universe is an info array of complexity 80, what number can be assigned to the info array in a typical human head?  My guess is 14, plus or minus 3 (a compromise between the number of neurons and the number of molecules in Joe Bob's brain).  I further flailingly speculate that, given an average complexity level of 14, people can still adequately function with levels of 11 or 12, and that catastrophic brain damage aside, complexity level and IQ are virtually uncorrelated.  (That is, people  perceive and feel with about the same intensity regardless of any manifestations of apparent intelligence or even sanity.)

Given a human complexity level of 14, I'd guess that analogues of what we consider emotions can be seen in animals down to levels 8 or 9, that what we consider thought can be seen down to levels of 3.  I can't imagine our universe containing any local intelligence larger than planet-sized, with a complexity level of around 40.

What do y'all think?

Langan suggests problems in verifying perceptual frameworks in his discussion of Newcomb's paradox.  (Are we real, or are we disembodied simulations in some information system, and is there even any difference?)  I'd like to recommend the novels of science fiction author Philip K. Dick, whose characters often must confront the breakdown of simulated reality, and who frequently find that there is no paradox-free perceptual frame.  Dick's novel Ubik is my favorite.

from Richard W. May--

Here is some humorous (perhaps) material for Noesis. Regrettably I omitted consideration of the universe as a quantum vacuum fluctuation, i.e., as a "free lunch", and its relation to Kashrut!  Members may have my phone number.  (716) 886-5982

A Prolegomenon To An Enchiridion--
AUTOANTHROPOPHAGY:  THE EUCHARIST OF THE GODS,
A Seven Level Allegorical Encryption

(c) 1988 R. W. May

The biological basis of the Socratic imperative "know thyself."  The meaning of the ouroboros:  the self-devouring dragon-snake, which bites its own tail.  Kafka's story "A Hunger Artist" provides and intimation.  Autoanthropophagy:  A scientific methodology and spiritual practice for the Age of the Apotheosis of Scum.

Complete autoanthropophagy as an unreachable esthetic, moral and spiritual ideal, which can only be approached.  Partial autoanthropophagy as attainable; the oracle at Delphi's injunction: "Everything in moderation."  The attained percentage reduction in corporeal volume as a quantitative measure of moral development to be used in an ethical calculus, which will yield a mathematical science of true virtue.  May spiritual autoanthropophagy be total?  The ultimate self-immolation.  May it be asked whether He also ate of the Last Supper?  The symbolism of the phoenix which consumes itself "in fire," only to regenerate itself; the actual nature of the phoenix-fire:  "Autoanthropophagy."  Relation to cosmology:  the collapse of all mass-energy into a black hole during implosion phase of the cyclic universe theory as autocosmophagy.  The universe consumes itself gravitationally.  The relevance of the hermetic principle:  "As above, so below."  Implications for the biological food chain and the concept of a higher being incorporating a lower being?  The necessity of the seduction of breakfast.  Prolonged fasting and the digestion of one's own protein as the traditional, indirect/internal form of autoanthropophagy.  Fasting preceded the enlightenment of the Buddha.  Monastic austerities, asceticism, and "starvation" diets, etc.  On the superiority of the "direct method" of autoanthropophagy for the modern age.  Autoanthropophagy:  the missing culmination of seppuku?  The moral superiority of autoanthropophagy to cannibalism of the nuclear family.  Beyond becoming one's own mother: becoming one's own breakfast.  Self-actualization:  you are what you eat and you eat what you are.  Intellectual autoanthropophagy:  eating one's own words.  "An Immodest Proposal":  autoanthropophagy and its twofold relation to world famine.  Autoanthropophagy:  an American approach to self-sufficiency.  Eating closer to home:  why eat cows? The ultimate practice of macrobiotics.  The problem for vegetarians.

A psychoanalytic view:  the unconscious meaning of such idiomatic phrases as "Eating one's heart out," "Eating one's words," etc.  The cryptic significance of fingernail biting.  Are certain human sexual practices sublimations of autoanthropophagy with respect to object and aim?  Kamikaze autoanthropophagy contra the suppression of women's flatus by the patriarchy:  the solution to the immemorial problem of the liberation of the flatus of ideological lesbians.  Autogynecophagy and the political and spiritual aspects of the liberation of women's flatus by lesbian, matriarchal amazons.  Autogynecophagy:  anorexic and bulimic aspects.  Autolobotomy and its relation to autoanthropophagy.