Clif Pickover's Extreme Challenges in Mathematics and Morals

The Search for Isoprimes

11 is an isoprime, a prime number with all digits the same. Do any other isoprimes exist? 101 is an oscillating bit prime. Do any others exist? For example, 10101 is not prime. Neither is 1010101. Cliff www.pickover.com

Solutions

David Jones: If any more exist, they would also have to be all ones. If you take any other number, say repeating 3's, the number is automatically divisible by 3. Furthermore, the number of 1s in the number would have to be prime itself. Say I string together 15 1s. Since 3 and 5 divide 15, I can quickly conclude that this number is divisible by 111 or 11111. [Cliff says, "Do you think humanity will ever find a 1111... isoprime?"]

> 101 is an oscillating bit prime. Do any others
> exist? For example, 10101 is not prime. Neither is
> 1010101.

Much like the example above, we know that such primes will have to end with the same number they start with. For example, 737373737373 can't be prime since 73 divides it. We need to add a seven to the end to make it a viable candidate. I don't have any other brilliant leads beyond this.

I seem to recall a few months ago that you proposed other people come up with special classes of numbers. A few suggestions were made about "heavenly primes" and the like. If memory serves, some of them were oscillating primes and a handful of them were found. Davy

chuck2051" says: According to The Penguin Dictionary of Curious and Interesting Numbers, the next isoprime is 1,111,111,111,111,111,111. The third one is 11,111,111,111,111,111,111,111.

David Jones: Well, the first couple aren't that hard to find. Define a function ISO(n)= n number of ones. For example, ISO(2)=11, ISO(3)=111, ISO(4)=1111 and so on. By toying with Maple I found that ISO(19) and ISO(23) are both prime which I verified with my 49G. I think I tested it up to about ISO(83) before I put it down. I could have easily made an error as I was entering numbers by hand and may have miscounted digits. I don't know Maple well enough yet that I could write a script for it to create and test numbers for me and PrimeForm won't let me define functions like that. Maybe tommorrow at work I'll play with it a bit more.

Michael Benedetti says: In the world of factoring and primality proving 11 is considered a repunit prime. All repunit primes in base 10 can only be composed of 1's. the others known have 19 digits, 23 digits, 317 digits, and 1031 digits. The next 2 which are believed to be prime but are not proven such yet are 49081 digits and 86453 digits. For any info regarding prime numbers there is a great web site run by Chris Caldwell at http://primes.utm.edu/

Daniel Dockery: Unless I err, the fourth isoprime would be:

11,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111

(317 digits) Both Primo and Maple certify the number as prime. At 20020127T0850, Cliff wrote:

> 101 is an oscillating bit prime. Do any others exist?
> For example, 10101 is not prime. Neither is 1010101.

I've found no others less than 10**700 (the highest I've searched so far). Daniel

David Jones: Just to give you an idea of how hard it is to find these things (isoprimes), lets go back to our problem of Specially Augmented (aka "Jim") Primes from a few months ago. Jim Primes and Repunit primes grow at about the same rate for N. On November 4th I complete proving that n=3,011 was prime. At the same time, I had a separate computer looking for more and it was at n=23,000. Today, 85 days later, I am testing n=47,461. My N value currently goes up by about a 1,000 every week.

Using a log(log(n)) fit to predict where the next SAP should be, it should have been at about 39,000 but it didn't appear. The next one should be at around n=245,000. I haven't quite figured out a reliable timetable yet, but an optimistic prediction shows that I won't get there until about April of next year unless I either get a faster computer, a faster testing program, or more help.

If/When I do find one, it will only have passed a preliminary test for "probable" primality. Doing a full primality proof on n=3011 took a couple of weeks if I remember correctly. I would imagine that proving a prime on n=245,000 would take at least three months. The individual proving ISO(86,453) has my best wishes as I would hate to lose months of computing time just to find out my candidate is NOT a prime number.

The moral of the story here though is that, now days, beating any sort of prime record requires a ton of patience and even more persistence. Davy

Daniel Dockery:At 200201281158, David Jones wrote:

> The individual proving ISO(86,453) has my best wishes
> as I would hate to lose months of computing time just
> to find out my candidate is NOT a prime number.

On a first run, PFGW yielded a 3-prp result for the 49081 digit item after about 10 minutes (with thread priority; all the other runs were set for only idle cycles), and a "composite" result for the 86,453 digit item after about 45 minutes. A second run repeated 3-prp for 49081, but yielded 3-prp for 86453 this time, both with about the same speed. Running a primality test (pfgw -t -f -l) cycled through, I think, base 17 before declaring 49081 composite; time was close to 30 minutes. I haven't yet attempted the full test on 86453, and may not at this point. Daniel

" Cliff wrote:

> 
> 11 is an isoprime, a prime number with all digits the same. Do any other
> isoprimes exist?

It's conventionally called a "repunit", standing for "repeated unit", i.e. string of 1s. A list of the largest known repunits can be found on Professor Caldwell's Prime Pages http://primepages.org/

In particular:
http://primes.utm.edu/glossary/page.php/Repunit.html

> 101 is an oscillating bit prime (OBP). Do any others exist? For example,
> 10101 is not prime. Neither is 1010101.  Humans have not disovered any
> other OBPs, as far as I know.

What base is that in? You mention 'bit', so should I assume it's base 2? In which case, these are simply the repunits in base 4. If it's base 10, then these are simply the replunits in base 100. Repunits in bases other than ten are typically called Generalised Repunits. In base 10, primes with the generalisation of this pattern are typically called "undulating". There have been some very famous undulating primes, such as Landon Curt Noll's '37' one. Rudolf Ondrejka's Top Ten lists may well contain some of your '101...01' type , it contains all sorts of things. http://www.utm.edu/research/primes/lists/top_ten/

 
> After you read through the discussion on this subject at:
> http://sprott.physics.wisc.edu/pickover/extremec.html
> 
> you'll discover that the largest isoprime published in a book is:
> 
> 11,111,111,111,111,111,111,111.

Book? What kind of 16th century medium is that? The Cunningham Project has been finding factors of numbers of such form (and thus finding primes too) seemingly for ever, well over a decade. http://www.cerias.purdue.edu/homes/ssw/cun/

> And, we think we have discovered a new one:
> 
> 11,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111,111,111,111,111,
> 111,111,111,111,111,111
> 
> My question: do you think humanity will ever discover a larger
> isoprime?   Upon what do you base your reasoning?

You've obviously never heard of Harvey Dubner! (Having said that it wasn't Harvey but Lew Baxter who found a probable repunit prime with 86453 digits only 15 months ago.) The largest known _proved_ repunit is the 1031-digit one found to be PRP by Harvey Dubner some time in the mists of time, but proved to be actually prime only more recently. Phil

Jan Kristian Haugland :

George Weinberg wrote:
> On Wed, 30 Jan 2002 08:40:04 -0500, Cliff 
> wrote:
> >11 is an isoprime, a prime number with all digits the same. Do any other
> >isoprimes exist?
> 
> Funny thing, when I first read this I somehow got the
> impression you were talking in binary,  maybe it's
> the oscillatong but thing.  11 seems to be prime in quitre a lot of
> bases.

Yes, it "seems" to be prime whenever the base is a
prime minus one. ;-)

(...)
> >My question: do you think humanity will ever discover a larger
> >isoprime?   Upon what do you base your reasoning?
> >
> 
> No.  Didn't read the discussion, so I may be wrong, but I think
> that the frequency of isonumbers falls off fast enough and the
> frequency of primes falls off fast enough that even going out to
> infinity there's likely only a finite number.

The frequency of primes falls off, but not very fast, so
it is not unreasonable that there may be infinitely many.
That however doesn't necessarily mean humanity will find 
too many others. Compare with Mersenne primes.

>Phil Carmody wrote:

>
>>> My question: do you think humanity will ever discover a larger
>>> isoprime?   Upon what do you base your reasoning?
>
>> Facts and research.
>
>In 1993 Dr. Ron Rivest did a calculation on the number of MIPS-years
>it takes to factor a number (it's in the appendix of my O'Reilly PGP
>book, dunno if the calculation has been updated). You could probably take 

the iso-prime research and run it through his calculator to determine >when humanity could find the next isoprime. You'll need to take into account improvements in factoring -- I believe there have been several since 1993 and I see no reason to believe there won't be more. -- Matthew T. Russotto mrussotto@speakeasy.net --

Galactic Set A or Set B

Solutions

says:I'd find out where the aliens are from, and choose the set that results in their solar system being wiped out. That'll learn 'em for posing these conundrums! Derek.

April responds to Derek: But what if their solar system was in set A, the set that contains our galaxy? Is revenge worth our galaxy's destruction? Then again, if left alive, the aliens could pose this question again until someone chose set B to be saved. Hmm, now I'm thinking, does it really matter which set the aliens live in? Regardless, I'd choose to save set A on the anthro-centric biased assumption that the Milky Way is the only galaxy in the universe that has intelligent life until proven otherwise.

Marcus Rauchfuss says: The logical choice would be choice B. Save the many and sacrifice the few. However, I would also kill the aliens who want me to choose. On second thought: If the aliens are not from the Milky Way I should choose the Milky Way out of sheer spitefulness. After all, it's the aliens fault to choose me to choose.

"lonno7" :"Save the many and sacrifice the few?" The many what? Stars? Gasbag planets? Comets? Asteroids? Are you assuming there are, in fact, other advanced civilizations "out there" on the basis of no evidence whatsoever (except for a couple of aliens) and that we should snuff ourselves for them? for remotely possible civilizations that might not even exist at all? Everybody, keep this guy AWAY from the button! My opinion: Let's see, all the stars in the universe that have no effect on the Earth, or all the stars in the Milky Way -- including our Sun. I'm not sure I see the dilemma here, but for the record, I'm all for saving our home galaxy.

--- Pedersen  wrote:
> * But what if their solar system was in  set A, the
> set that contains our galaxy? Is revenge worth our
> galaxy's destruction? Then again, if left alive, the
> aliens could pose this question again until someone
> chose set B to be saved. Hmm, now I'm thinking, does
> it really matter which set the aliens live in?

Davy says: I'm thinking it does, but only in the sense that I'm voting to kill the aliens regardless of where they live.

Suppose the aliens live in Set A. If we choose set B then that means that we are condemned to live out the rest of our lives with this alien race. Now, if they have the power to destroy the rest of the universe, then surely they have the ability to dominate us. If they are actually willing to destroy the rest of the universe, then I surely don't want to condemn the human race to be subject to whatever other kinds of cruelty they have in mind. I'm a give me liberty or give me death kinda a guy, so I say we take them out even if we have to go with them. (Furthermore, if it does turn out that there are at least two sentient races in are galaxy, this increases the likelyhood that there are other lifeforms in other galaxies that we are saving.)

Suppose the aliens live in Set B. If we sacrifice ourselves for the sake of the rest of the universe, then the alien race just moves on to the next life form and makes them the same deal. I can't imagine the EVERYBODY would sacrifice themselves, so eventually somebody would have chosen to take us out anyway. Might as well beat them to the punch and take away the evil alien race at the same time.

I still haven't decided what to do if we don't know where the aliens live, but I would probably choose B.

Davy

VIDYANANDA says:

Unless Milky Way Galaxy has some super-cosmic importance it is logocal that the answer on the first question would have to be B: "The need of the many outweigh the need of the few." -- Mr Spok

MRBW545 says: My instant answer is A, although I appreciate Vidyananda's reasoning for choosing B. If given more time and information, I would like to know where the aliens come from and what their take on the situation is. Would their galaxy be destroyed by my choice? It would seem to me more complex than what you have presented here. What an awesome amount of death I would be responsible for. I would have to question, "Why was I chosen for this decision? . As I continue to think about this, what would the aliens do if I am unable, or refuse, to make a choice? This would be an interesting choice for a human like myself to have to make.

Trozman says: "The need of the many outweigh the need of the few." -- Mr Spok
The last time I checked, the other 124,999,999,999 galaxies aren't sending out distress signals. Obviously I'd choose A... survival of the human race? Nah, more like personal need for survival. Hey, I'm a mammal, what can I do? :D

---

Gordon Question of Big Numbers

What is the largest number (integer) that a computer could in principle work with or maybe yield as a result of a computation? The computer that I am envisioning is one that is not an idealized or theroretical model, but one limited by known physical laws such as the speed of light, electrical resistance, RC delay, atomic dimensions, world supply of silicon, finiteness of programs and data, and other known phenomena. Can such a machine work with numbers so huge they would require Donald Knuth's arrow notation to express them? (Dennis Gordon posed this question)

Comments

John Rivaz: If the computer can be programmed to work in text mode (as a very young child doing arithmetic with numbers above 9) the limit is storage capacity rather than length of registers in the processor.

Therefore to get your answer one needs to consider the largest number that can be stored using all the matter in the universe. If a quantum computer is to be considered, then all the matter in the multiverse is the figure you need.

Carl Speare: These answers pose further questions: is the universe infinite? Does the multiverse really exist? If yes, then even if the universe is finite, are there an infinite number of them? Well, if we consider John de Rivaz's idea that an integer is represented a string in memory, the limit would be the memory. And quite a large number it would be for even small computers - 64K of RAM (TRS-80, C64) would yield about 60,000 digits (if you assume a small chunk of memory necessary for a resident microkernel to handle the computation). There is a fairly simple implementation of a large- decimal class that uses a string-based integer representation in many languages (even BASIC).

However, a string based representation is rather ineffecient, because you get only one digit per "byte" of memory. But each byte (actually just 8 bits) can store up to 256 values. So, more efficient (both faster and more space efficient) methods go about their method by representing the number in base 16. (Even more efficient methods go right to base 256, but I'll stick with base 16 for now.) So, the number 141 takes 3 bytes in the string method, but only 2 bytes in the base-16 method: 8D. Now, that does not mean all numbers save only a byte of space. Consider,

6498212189713214987894231234654987984651 in decimal is now: 13

18B624E4B9E074CE3F0777DAF07A6F0B in base 16 (hex) saving 6 bytes of memory. (As one would assume, base 256 saves even more space for large numbers.) So, 40 digits became 34; in fact, you save

truncate ( NCHAR / { ln(16)/ln(10) } ) + 1 characters. So, ( 40 / 1.2 ) + 1 = 33.333 + 1 = 33 + 1 = 34. In general the formula works only for larger strings (it fails in the case of 3 digits, like 141 -> 8D). As you can see, base 256 saves yet more:

truncate ( NCHAR / { ln(256)/ln(10) } ) + 1

would be: 40/2.4 + 1, or about 18 characters.

So, where does this leave us? Going to base 256, on a common computer (64MB of memory, 50MB free) we have:

50 * 1048576 bytes, or 52,428,800 bytes of memory. This would allow up to 52,428,000 digits in the old method, or about 125,829,120 digits using a base-256 representation. So, on a common desktop, 125 million digits is the largest you could go to (reasonably).

Here are some other memory values, based upon having 78% of the memory available for use, which is a reasonable assumption based upon modern operating systems. The list shows the old method [string], then the new method [base 256, or hexhex] storage spaces. As a caveat, all values are approximate.

Mem : [string] : [hexhex]

016MB: 13,107,200 : 31,457,280
032MB: 26,214,400 : 62,914,560
064MB: 52,428,800 : 125,829,120
128MB: 104,857,600 : 251,658,240
256MB: 209,715,200 : 503,316,480
384MB: 315,572,800 : 754,974,720
512MB: 419,430,400 : 1,006,632,960

So, in less than half a gig of free memory, we can store over 1B digits. So, you can go ahead and figure that a 64GB machine (IBM 390, Sun E10000) we could go ahead and go for broke (same 78% free):

64GB: 53,687,091,200: 128,849,018,880

So, there you are: a man-made computer, available today, can put together 128B digits.

---

Zygotic personhood

"Zygotic personhood" (the idea that a fertilized egg is a person) is a recent concept. For example, before 1869, the Catholic church believed that the embryo was not a person until it was 40 days old. (Aristotle agreed with this 40-day threshold.) Thus, the church did not believe a human had a soul until day 40. Pope Innocent III in 1211 determined that the time of ensoulment was anywhere from 12 to 16 weeks.

Given this background, if your child was acerebrate (had no brain) would you consider terminating the pregnancy? If born and on life-support for 20 years, would you ever consider terminating the life and donating the organs so they could save others?

Are there any religions today that the set the time of personhood later than the zygote stage of development? In 200 years from now, do any of you feel that the Catholic church will set a different standard for personhood?

"John de Rivaz" : On the basis that soul= program and data, in any instance where some programming and/or some data unique to that individual exist, then there is a person. If some parts of personality are provided by the genes, then it is logical to regard a fertilised egg as "a person" as parts of the unique program are already there. Exterminating it is therefore murder. But it should be noted that in nature many fertilised eggs are exterminated without human intervention, possibly because they would produce unsatisfactory results. In religious terms, gods often require mankind to behave in a similar manner - "do as I do" - "do likewise" and so on. So this doesn't really solve the abortion dilemma. Similarly at the other end if a person who has died is cryopreserved, then the cryopreserved body contains some of the program and data that made the person. If future technology can extract this, then the cryopreserved body is still "a person" and deliberately thawing it is murder. In addition, it is still murder to prevent a dead person from being cryopreserved, because you are destroying the program and data.

---

The Problem of the Tanks

You are a tank traveling (up, down, left, right and diagonally) through electric fields. If you travel through two - signs in a row, your battery is drained and you are stuck. If you travel through two + signs in a row, your battery overcharges and explodes. How can you travel from Start to End through every cell once and survive?

- + - + -
+ + - - +
- + + + S
- + E - -
- + + - +

I am curious to see how many people can solve this and how long it took. If you are able to solve this, rather than post the answer, why not just mention you were able to solve it and then tell as about how long it took to solve it. Is there any correlation with the ability to solve this puzzle and age, gender, or profession? How many different solutions does this have?

Teachers: why not give this to students and see how well they do? Have them create their only "tank" problems.

Programmers: why not write a computer program to solve problems of this kind?

Graphics experts: why not write a computer program that displays this more attractively and show the computer trying to solve this or shows the player moving the tank around the field.

Visionaries: why not extend this puzzle to the third dimension?

If you wish, you can redraw the figure on graph paper, or format it as a table, for greater clarity.

Do you think anyone on this planet could solve this problem within 30 seconds? What kind of correlation would exist between the ability to solve this problem and IQ?

Solution Comments

Cynthia Sue Larson: What a great puzzle this is! I redrew it on a piece of paper, and worked on solving it while doing some other computer work. I re-drew the puzzle using a pen, and then used a pencil to trace possible solution paths. I solved the puzzle in about ten minutes, using a technique of working from both the "Start" and "End" points simultaneously, and finding where they could best meet in the middle. This is how I noticed when I had a problem (there were two plus signs at the middle), so I erased the line coming from the shorter of the two paths and started over. This puzzle will be great to show kids -- it's a perfect summertime activity! love, Cynthia Sue Larson

Quinn Tyler Jackson" : Pickover: "Do you think anyone on this planet could solve this problem within 30 seconds? What kind of correlation would exist between the ability to solve this problem and IQ?" Yes, I do believe someone on the planet could solve it in 30 seconds. It would be interesting to see a curve of solution times. Pickover: "Is there any correlation with the ability to solve this puzzle and age, gender, or profession?" Please compile that information and let us know. :-) Pickover: "Programmers: why not write a computer program to solve problems of this kind?" I considered writing a G.A. that attempts this and comparing fitness algorithms and results. The alleles would have 8 states -- once for each direction. The chromosome would have to have at least 25 alleles. "Fitness" would be fairly simple -- the number of moves before a chromosome gets stuck. In fact, Dr. Pickover, may I have permission to use that particular maze in my work? I've been using a 64-bit-blackbox key for my experimentation with G.A. -- and I feel that this maze actually represents a more "difficult" (yet solvable) problem for a G.A. experiment I am currently working on. With citation as regards the source of the maze, of course. I will print it out and let my three children have a go at it tonight. -- Quinn Tyler Jackson http://QuinnTylerJackson.n3.net/ Quinn Tyler Jackson" : Using genetic algorithms to solve problems.... [Cliff responds, That's great you are interested in this puzzle. Let me know what you discover.] I managed to get a GA going that was able to solve the puzzle as you posted it in 600 ms, which is pretty fast. Due to the non-deterministic nature of GA, however, and due to the nature of this particular problem, a recursive maze solver would probably solve it more quickly than a genetic algorithm. The problem that I am currently using for the GA experiments is fairly straightforward compared to the maze: A random 64-bit number is generated. The GA attempts to "guess" in as few tries as possible what that number is. ("Pick a number between zero and 15 trillion," or something like that.) The fitness score for guesses is the number of BITS in the guess that are correct, regardless of their position. ("Getting warmer...") I managed to get a 64-bit key solver down to about 45 generations with n^4 fitness scaling and a few other tweaks. The maze problem, however, is more interesting for a GA because it is possible to have paths that are relatively fit, but that do not reach the goal. This has proven to be a real challenge, since the GA often gets to 21/24 fitness and then plateaus. The 600ms result was only obtainable by introducing allele chain reversals during chromosome mating. This allowed for the introduction of completely new path attempts in populations that had grown fit on a 'near miss' path. I will keep at this until the thing is tweaked to always solve it because I need a solvable problem for some other things I'm doing -- and I find the 64-bit-key thing far too "computer-oriented" -- the maze fits the experiment better. Cheers, -- Quinn Tyler Jackson

genie@megasociety.com : > > Do you think anyone on this planet could solve this problem within 30 seconds? No. It's an easy problem, but a lot of people are not that smart. Many would not even be able to decipher the requirements. They use a maze subtest in the WISC IQ battery (the tank puzzle is really a type of maze puzzle with constrained pathways). These types of puzzles may be useful for IQ evaluation because they tend to be "culture- fair" and not too complex. I wrote some puzzles that list members may find amusing: http://www.ultrahiq.net/UltraPuzzle.html Spatial problems like the tank problem are typically easier for men to solve because of the positive (but ultimately curvilinear) relationship between testosterone level and spatial skills. There was a discussion on gender diffs on another list a few months back that inspired this brief FAQ on gender differences and IQ for one of our ezines: http://www.ultrahiq.net/Ubiquity/SprUbiq01/Gender.htm

David Jones : About 10 seconds. My first run through failed, second run through worked. For me, I think the contributing factor was having been exposed to topology and some graph theory. There are certain parts of the "maze" that can only be traversed a certain way. Once you see where certain lines must be drawn, you peice the remaining bits together like a jigsaw puzzle. > Visionaries: why not extend this puzzle to the third > dimension? Your question reminds me of an acquaintence I knew in Phoenix. There was something in his brain that allowed him to have a phenomal ability to visualize three dimensional patterns and figures, but he couldn't understand plane geometery to save his life. While he was of average intillegence, this is the sort of thing he probably wouldn't have been able to do in the time requested. I tend have a backwards problem in that I can't understand anything three dimensional unless I can actually see it. (Its a wonder how I did do well in my Vector Analysis class.) Something odd about myself though is that I cannot play chess on a computer. Even though chess is a 2 dimensional game, I only seem to get a minimal understanding of the dynamics of position when looking at it on a flat surface. If I play computer chess, I have to have a board sitting next to me so I can see the game in 3D if I want to play well. Based on these two examples, I might suggest that the ability to solve this type of problem might be based on how one learns to use spatialization in problem solving. My friend would probably solve the same exact tank problem faster than I if we were actually sitting in battlefield and looking out over a set of markers denoting the charge fields. Davy

"Carlos Paula Simoes" : Hi Cliff, Quite easy :-) I have placed this question (slightly changed, same rules) in the puzzle contest I run at www.cpsimoes.net. The complete address for that specific question is: http://planeta.clix.pt/cpsimoes/puzzle1a5.html

German Gonzales says:

Software and solutions can be found here:

http://www.devweb.cl/mathfun/

How many possible paths are there (disregarding + and - signs), so we can get a hint at what percentage of random trials are likely to lead to a solution?

Answer: there are 912,072 path disregarding signs, therefore the percentage is: 28 / 912072 = 3.06E-5

---

Search Packs for Transcendence

At http://www.pickover.com, I speak of "seach packs" that consist of 2 to 4 words that, when typed into the Google search engine, yield fascinating results. Do you have any search packs to suggest that encourage the mind to transcend its Earthly bounds (or that yield very interesting web sites)?

Here are some of my favorite search packs from www.pickover.com. You just type the words into Google input field, without quotation marks:

Search 1: "god synchronicity transcendence afterlife" 
Search 2: "mind lsd dimensions" 
Search 3: "third temple jerusalem" 
Search 4: "parallel universes beings god" 
Search 5: "pickover hawking jesus" 
Search 6: "genius iq savant" 
Search 7: "quiet mind tome" 
Search 8: "dreams transcendence geometry" 
Search 9: "apocalyptic dreams time travel" 
Search 10: "jesus never died" 
Search 11: "problem miracles" 
Search 12: "alien inside brain" 
Search 13: "rephaim gilgal" 
Search 14: "god mathematics knowledge" 

What search pack do you particularly like?

Comment Jason Edwards: Here are three search packs I thought were interesting:

1. "mystical sequence numbers"
2. "automated reasoning Turing Babbage"
3. "eschatology Abraxas"

Using the first "search pack" I came across a page that referred to this sequence: 3,7,13,39,69,... as a "mystical sequence." It wasn't exactly clear from the web page why the author called it mystical however. Has anyone else seen this sequence before or know why the author calls it mystical? Can anyone come up with the next term? Can anyone come up with a generating formula?

Lately I have been intrigued with "automated reasoning" and the concept of computer-assisted proofs. One of the main things that is fascinating to me is the hint of controversy surrounding the subject. In 1976, when Wolfgang Haken and Kenneth Appel came up with a computer-assisted proof for the long standing Four-Color problem, many mathematicians refused to accept it because they felt Haken and Appel's "brute-force" approach to exhausting all of the possibilities wasn't as rigorous as a traditional deductive argument. A couple of years ago Tom Hales and Sam Ferguson offered a proof of the Kepler sphere-packing conjecture. Their proof consisted of almost 300 pages and was also computer-assisted, which makes it extremely difficult to verify. I remain rather skeptical about computer-assisted proofs, nevertheless I find the subject especially fascinating. Does anyone else have an opinion on automated reasoning? Jason

Cliff, "Carlos Paula Simoes" : Search packs (using Google)

mind increase power
reach superior intelligence
alien inside brain
god mathematic knowledge
time light brain"

"Quinn Tyler Jackson" : "transcend consumerism meaning"

---

Synchronicity

In my book Dreaming the Future, I discuss synchronicity.

Psychologist Carl Jung and biologist Paul Kammerer believed in "synchronicity" (or meaningful coincidences -- or the theory that there is a mysterious connectedness of objects and events in space and time). Paul Kammerer (1880-1926) wrote, "We thus arrive at the image of a world-mosaic or cosmic kaleidoscope, which, in spite of constant shufflings and rearrangements, also takes care of bringing like and like together." He compared events in our world to the tops of waves in an ocean. We notice the tops of the isolated waves, but beneath the surface there may be some kind of synchronistic mechanism that connects them. He also believe that because of this, we often also see "streaks" of luck or misfortune in situations ranging from sports to gambling to family catastrophes. Modern examples of this might include clusters of airplane accidents, many momentous events happening in the same year, the sudden simultaneous arrival of musical geniuses and music, the "curse" of the Kennedy family, and the skiing accidents of celebrities, which, while not causally connected in any formal sense, are connected through meaning. Skeptics would suggest this connection arises from our tendency to affix patterns to ANY sequences of events, regardless of their significance.

In the following new experiment with members of this group, I will now mention two words that one would not normally hear in daily conversation, or read in the newspapers, or hear on TV:

1) Madagascar
or
2) Scarab

If any of you do hear or read these words within 48 hours of reading about this present experiment, let us know. (Don't go out of your way to find these words -- just let your life flow naturally and see what happens.) Feel free to invite your friends to participate in the "Madagascar Experiment" and tell us their findings in this group. -- Cliff

Comments

Cynthia Sue Larson" says: Hello, everyone! With positive expectations that the Synchronicity Experiment would yield interesting results, I read and agreed to participate. For the first 24 hours, I didn't notice any reference to the two key words. As the end of the 48 hour period since I'd read about "Madagascar" and "scarab" neared, I was very pleased to find two separate emails that came to me containing those two rather unusual words. The Madagascar reference pertains to the June 21 solar eclipse, and the scarab reference was part of a forwarded article on the subject of (what else?) -- Synchroncity! lots of love, Cynthia

martyn27015@yahoo.com: There's this statistics, or probability, professor that i read about who would give an assignemnt the first class of the term. He would tell his students to flip a coin 100 times and record the results. The twist was that half the class were to just make up the results without him knowing who made it up. The next class, the professor asked some students, one at a time, to let him take a glance at the results, and he'd tell them who really did it, and who faked the results. And he did do that, with nearly 100% accuracy. Most classes he made no mistake. His technique was this: according to some probabalistic principle, the odds are VERY high that when flipping a coin a hundred times, at least once there will appear a streak of either six heads or six tails. The ones who faked it, trying to be "random," had at most three or four consecutively. My point is, that people really don't have a natural feeling for probability at all, and if we see some obscure pattern we instinctively think there is a cause attached to it.

martyn27015 talks about how difficult it is to make up a list of random heads and tails. Similarly, I have done experiments in which humans find it very difficult just to type a "random" sequence of 1s and 0s, as in 1010111011100010101010010100101 -- Cliff

rachi11er@yahoo.co.uk: Hello Cliff, Does it count that two days ago I read about the Jung/scarab beetle incident in a completely unconnected book? I will now look out for Madagascar and it's peculiar lemurs at every turn. There are theories that synchronicity works because we have a brain which actively looks for certain elements in the world and even goes so far as to "buffer" its perceptions in such a way that, if you sit beside two people talking in a cafe, you will probably not hear their conversation at all - unless they mention your name. At that point you will realise you had in fact heard not just your name, but quite likely the entire sentence it was contained in. Of course, that theory rather disintegrates in the face of some synchronicities - surprise visits from real scarab beetles among them! Regards, Chiller (and thanks for the invite)

fahrenheit45l@yahoo.com" Previous posts discussed the concept of synchronicity. I would like to add a few comments on this subject. re:1) Madagascar > or > 2) Scarab synchronous events are supposed to be meaningful. Here is a little known secret, which i discovered independently of the Jungians. I have been using it for over 20 years. When a synchronous event catches your attention, and the meaning is not obvious, ask yourself the following question: If this was a dream, what would it mean to me? {Of course, dream interpretation is an art or skill or gift that few have. Freud helped to open the doors for me ) So, if the G-d of Abraham and Isasac and Jacob ( as compared to the god of the philosophers) is not communicating with you, then at least you can discover a lot about the repressed corners of your Unconscious mind. Funny, on more than one occasion, i awaken in the middle of the night, and a synchronous link is pointed out to me, that i had missed during the day(s). For example, pay attention Dr. Pickover, in the Strand bookstore i pointed out to a couple an award winning children's book "A wrinkle in Time." It was in front of the table as i passed by outside the store. I also lucky enough to find a used copy of "...hyperspace" the same day. In the middle of the night, i was reminded about how the book read as a child helped me through a crisis in my adult life. I was also reminded about the tesseract that played crucial role in the story and how i had even built a model of the tesseract. And finally, it was brought to my attention, that the tesseract is also featured in Dr. Pickover's hypersapce book. My daughter would just yawn and say that this a usual event ...... for me. PS - a lesser know case of synchronicity ????? the day Gene Roddenberry was taken to the doctor for what turned out to be a stoke," all the pipes in the house break and there is water everywhere." (yvonne fern: G R the last conversation) Can someone find out if his stroke was hemorrhagic?

"Brandon J. Van Every" : r skill or gift that few have. Freud helped to open the doors for me ) I have a completely different armchair opinion on the subject of dream interpretation. I believe all people can understand the meaning of their dreams if they are merely willing to follow their instincts. The dreams are occurring, after all, so that the subconscious can work out and make sense of what's going on in the person's life. Why should it be hard to interpret a dream when the subconscious is trying to make it easier for you? All you have to do is match the elements of the dream against what is occurring in your life, and use your instinct as the "aha" that links the two. Problems with dream interpretation are created by our societies. Instead of realizing that each person owns their own dream, and is the person best qualified to interpret it, society tells us that dreams are something terribly mysterious that only experts can understand. It's rather similar to white anthropologists telling blacks in Africa what their culture really is. We should be suspicious of people who argue from authority about phenomena occurring within us. Much as it might have helped Freud or Jung or any of those other guys' academic credentials, there are no universal dream symbols. There is no possible way for a psychiatrist to understand a person's dreams without the complete context of that person's life. More information on dreaming and synchronicity here: http://www.fortunecity.com/westwood/vivienne/598/asd-17/abstracts/Rita_Dwyer_17.html

j snow : re: finding the scarab I had some "midnight" uneasiness last night. Before i went to bed, i realized belatedly, that as i was busy writing about "the synchronicity experiment" a lady bug had been tapping on my computer screen. It came back several times, but i was too dense to realize that the lady bug is a flying beetle as is the scarab. If one complains that a ladybug is not a scarab, well, neither was the one that flew into Jung's room when he was with the patient... Synchronicity deals with symbols. My main reference is a SUNY press book that is temporarily misplaced. sorry. It is hard to be scientifically objective since many a dream image will find its counterpart in the consensual reality world, and then bring the dream back into consciousness. For example, one morning i saw a woman on the NYC subway carrying a book with a mostly white cover and a splash of color that reminded me of the cover of "Iron John" by Robert Bly. And that reminded me of my dream that included that book, which provided the key to the meaning of the dream. But that does not provide convincing evidence of synchroniciy since many objects may have reminded me of the dream, or the dream may have repeated the theme many times.... But i know other stories ........ enuff said, The following article may be of interest http://www.gis.net/~fpnma/sermons/scarab.htm THE SCARAB AT JUNG'S WINDOW by R.M. FEWKES One of this year's best selling books is called SMALL MIRACLES: EXTRAORDINARY COINCIDENCES FROM EVERYDAY LIFE by Yitta Halberstam and Judith Leventhal. The book is a collection of stories of extraordinary coincidences in the lives of ordinary people. "Coincidences," say the authors, quoting the writer Doris Lessing, "are God's way of remaining anonymous", or the universe's way of telling us that there is more to reality than meets the eye. Coincidences are small miracles that can awaken us "to the rich promise of a bounteous universe and the splendor lying dormant within your soul. Coincidences are everywhere and can happen any time. When your soul is ready, they will come. All that is required is that you open your heart." (p.xiii)

John de Rivaz" : This brings to mind a public demonstration by Dr Richard Dawkins. He divided the audience into two sections, and told them that he was going to toss a coin, and those to the right were to influence it by power of thought to go heads, and those to the left tails. The successful side was similarly divided and so on until he was left with one person who had succeeded in influencing all 8 tosses correctly. Similarly, throughout the UK, (population totalling about 56 million people) several million read popular newspapers such as "The Sun". Every night some of them dream of travel disasters, such as air or train crashes. When there is such a disaster, a few of those may be moved to write into the newspaper saying that the had precognicance of the crash. Also in the UK a "news" paper called the Sunday Sport once published a story about a Lancaster Bomber found on the moon. Gosh gee Whizz - I have a story about a hydrogen fuelled car that appeared in the early 19th century in Switzerland. That much is true. How did it get there? Before you look at the real story set your mind moving in the direction of Time - A Traveller's Guide by Clifford Pickover http://www.amazon.com/exec/obidos/ISBN=0195120426/longevitybooksA/ and http://www.newscientist.com/features/features.jsp?id=ns22911 (A time machine in Michigan State University) and let your imagination run riot before reading the actuality on http://www.deRivaz.com, and click on links, and find the 7th one down the page. If any newspaper is willing to publish articles about dreams as news, this generates the belief that people can dream the future. I believe this form of journalism is taken to greater extreme in the United States with "The National Enquirer". Coincidences seem to happen all the time - no one surely can fail to have noticed how they can receive no telephone callers and no personal callers for some days, and then two occur at the same instance, probably also at the same moment they are scrambling eggs.

j snow : In an earlier post, Cliff gave us two secret words, Madagascar and scarab, as part of a syncronicity experiment. We were to report if we had come across the words within a short period of time after Cliff gave the words to us. summary of my results: i read the experiment on tuesday april 17 while i was on the computer, lady bug kept tapping the screen. (beetle) On friday july 27, NPR radio mentionned madagascar. ( 3 feet from my computer is a CD that i picked up for a buck. Key song was madagascar. This may have interfered with experiment :-- ) peace. J

---

Simultaneity in Science

Several famous, simultaneous discoveries exist in the history of humankind. For example, Newton and Leibniz "discovered" calculus independently, but at the exact same moment in history. The same is true for Darwin and Wallace, who both separately developed the theory of evolution at the same time. What other examples can you give, and what significance is there to such simultaneity?

Conments

Dennis W. Gordon" <74644.1103@compuserve.com> : Cliff, It appears that the mechanical computer was simultaneously invented by both Charles Babbage and George Biddell Airy (Astronomer Royal in the United Kingdom) and another un-named man working with Airy. I am not sure of the significane is, but maybe human pettiness and jealousy figured in. Dennis

petebarnes@home.com : How about the discovery of the telephone, which was patented by Alexander Graham Bell and his business partners. Bell beat his competitor, Elisha Gray, in filing the patent by a matter of hours, although Gray was filing for a device that he had not quite perfected, but which would have given him the credit for the invention. Western Electric, cofounded by Gray, became one of the Bell System's major competitors. Pete B

---

Would you pay $2000 for a Turbing?

In 1950, Alan Turing proposed that if a computer could successfully mimic a human during an informal exchange of text messages, then, for most practical purposes, the computer might be considered intelligent. This soon became known as the "Turing test," and it since led to endless academic debate.

Opponents of Turing's behavioral criterion of intelligence argue that it is not very relevant. This camp suggests that it is primarily important that the computer demonstrates cognitive ability regardless of behavior. Some say that computers can never have real thoughts or mental states of their own. The computers can merely simulate thought and intelligence. If such a machine passes the Turing Test, this only proves that it is good at simulating a thinking entity. Holders of this position also sometimes suggest that only organic things can be conscious. If you believe that only flesh and blood can support consciousness, then it would be very difficult to create conscious machines. But to my way of thinking, there's no reason to exclude the possibility of non-organic sentient beings.

I call these "humanlike" entities Turing-beings or "Turbings." If our thoughts and consciousness do not depend on the actual substances in our brains but rather on the structures, patterns, and relationships between parts, then Turbings could think. If you could make a copy of your brain with the same structure but using different materials, the copy would think it was you.

Would you pay $2000 for a Turbing -- a Rubik's-cube sized device that would converse with you in a way that was indistinguishable from a human? Why?

Some Comments

"Rhonda Eudaly" : Though where I could see where it might come in handy in rehearsing all the possible outcomes of those conversations you know you have to have but don't want to, I don't think I could justify $2K on it. Other than that, no, not me. I don't even like telephones, can't imagine conversing with a calculator (for example) - and it's always been my contention that talking to yourself is eccentric, it only becomes a problem when you start answering yourself. And in a way, couldn't this be that last step from eccentricity? Rhonda

"John de Rivaz" : If a "Turbing", the device the size of a Rubic Cube that will hold a human like conversation, costs $2K now, it will be $200 in a few years time. Assuming you have plenty of other things to do then it would seem sensible to wait. Possibly every sensible person thinks this way now and that is an explanation as to why the technology industry is in the doldrums. The idea of making early adapters pay development costs could dying. Instead shareholders have to pay them, and maybe it is this re-organisation that has caused the present re-valuation of technology shares. However once the change has worked its way through the system, technology should again be a highly profitable investment. For links to technology shares corporate web pages, please see http://www.geocities.com/longevityrpt/shares.htm

John W Burgeson : Cliff wrote: "Would you pay $2000 for a Turbing -- a Rubik's-cube sized device that would converse with you in a way that was indistinguishable from a human? Why?" Cliff -- my PC is a little bit larger (not much) than a Rubik's cube, but it also costs about 1/2 as much as your example. Now I might assert that I have already paid for that function, for this device allows me to converse with you (and many others) on an as needed basis. Often the conversations are quite interesting; sometimes, for instance when a "fundie" shows up on Compuserve's RELIGION forum, they are pathologically sad. My point is, of course, that I am quite unable, except on a very occasional basis, to determine whether or not all these people, including you, are "Turing test enabled" computers or real live persons. You, for instance, I have never met in person, even though we once collaborated (you did most of the work) on an invention disclosure. So the answer is "yes," and I assert I have already done so. This sounds like your neat thought-problem of 10 years ago in which you asked us to reflect on what a scientist of 1910 would have thought if an IBM PC were to be given him. John Burgeson (Burgy)

Will Dye : Mr. Pickover wrote: > I call these "humanlike" entities Turing-beings or "Turbings." I don't care for the "Turbing" naming convention. For one thing, "Turing being" may be easily confused with the well-established term "Turing machine". I'm also concerned that the tie-in to the Turing test may inadvertently contribute to the perception that machine intelligence is properly measured against the sole yardstick of engaging in human-style conversation. All this fussing about terminology may seem obsessive (see .sig), but please keep in mind that one of the core problems in this field is parsing out more precise meanings of words. Take it from an old-timer: in this hyar swamp, ta move faster, ya gotta move slower. > Would you pay $2000 for a Turbing -- a Rubik's-cube sized device > that would converse with you in a way that was indistinguishable > from a human? Would you pay $2,000 for a human slave, occasionally brought out so that you could have a conversation with someone who has no choice but to listen? I doubt if it will be easy to instill as complex a human-like behavior as good conversation without instilling other human-like traits such as ambition, loneliness, desire, or even agony. Perhaps I'm wrong, and the technology, once developed, will be of the Star Trek variety -- all 'logic' and no 'emotion'. Perhaps regulatory and/or humanitarian concerns will encourage engineers to create entities that are "OK" with being a conversation-in-a-box. Still, at $2,000 a pop, the engineers will be under a lot of pressure to create an entity that only... just... barely parrots back the right answers, at the right times, to be classified as unworthy of true liberty. Still others simply don't care if the box is genuinely happy or not, or at least don't care enough to bother tackling the difficult issue of providing dangerously-intrusive legal protections for manufactured entities. I can't be sure if we can or should attempt to instill regulations in such matters, but hopefully we'll at least be able to control our own actions. I, for one, pray that I never develop a mindset that would allow me to financially encourage such a trade. --Will

cliffpickover@hotmail.com : I would pay $2000 for a Turbing device for several reasons, including: 1) You (or whomever you give the device to) would never be lonely. After all, we posited the fact that the device responds in a way that is indistinguishable from a human. 2) The technology would be quite advanced. If we could somehow reverse engineer this, we would be millionaires! Note that we are currently far from being able make a machine that passes an unconstrained Turing Test in which a human may converse with the machine for an extended period of time on any subject. (Judges can always tell they are talking to a machine if they ask enough questions and have no constraints.) I wonder if we will be able to create such a Turbing by 2010?

Will Dye : Mr. Pickover writes: > I would pay $2000 for a Turbing device for several > reasons, including: > > 1) You (or whomever you give the device to) would never be > lonely. After all, we posited the fact that the device > responds in a way that is indistinguishable from a human. Ewww. If the only way you can sustain a conversation is by enslaving the other participants, then no wonder this list is so quiet. Seriously, if someone in an age of advanced communications and medical technology can't maintain a relationship with anyone who has a choice to leave, creating quasi-human slaves is decidedly not the optimal response. > 2) The technology would be quite advanced. If we could > somehow reverse engineer this, we would be millionaires! Oh, brother. There are so many dubious assumptions in that scenario that I don't even know where to begin. I regret that I sound rather grumpy here, but I'm not sure how else I can express my level of disagreement. --Will

"John de Rivaz" : If you read some of the newsnet postings, particularly on groups discussing religious matters, it does appear that some people have tried to write computer programs that mimic human response, albeit somewhat badly, and connected them to newsnet. For example, in a debate on whether citizens should have the freedom to chose whether their bodies are autopsied or not after they have died, one such entity merely posts messages to the effect that people who want such freedom should be made into dog meat. The quality of the messages seldom change, although the content is the same. It is interesting to note that those who have taken the trouble to vote on the web site http://www.autopsychoice.com are more or less in favour of people being allowed an informed choice, so perhaps the entity is a hungry dog!

"John de Rivaz" : Subject: Are we living in a simulation? A thoughtful idea about the question of whether we are already living in a simulation: >>>>>>>>>>> Message #16723 Date: Tue, 26 Jun 2001 21:14:02 -0700 (PDT) From: Scott Badger Subject: Re: But, how can you know if your life is real? I somewhat suspect that this reality is, in fact, a simulation. Primarily because we have already conceived of such a thing. It is worth noting that the virtual worlds that currently exist on the internet, crude as they are, far surpass the allegedly real earth in terms of square footage. The development of technology among any sentient species is bound to result in increasingly sophisticated computer simulations. Ask yourself what kinds of virtual worlds/simulations we will likely have here on earth in 10,000 years. Now ask yourself how many sentient species are likely to exist in the universe that are at least 10,000 years older than us in terms of technological development. So how would we know this is the fake world? We couldn't if the creators (machines most likely) were any good at all at programming. I would think that creators/programmers capable of generating simulations as sophisticated as this one would strive to make successive versions increasingly undetectable by the "simulants". Maybe there's a contest going on with the prize going to the most convincing simulation. I suspect that if this is a simulation, it will be uncovered by a singularity-related super intelligent (SI) entity who is most likely to detect a fault in the programming as professor Ettinger suggested. Perhaps that's how it works. I can imagine a scenario where, in any given simulation, the arrtival of a singularity is the key to disovering the existence of the simulation ... the SI might also figure out the means of transporting to the world of the creator. But that world would have already had its singularty and its inhabitants would have likely already transcended to meet their creators ... leaving only the machinery necessary to maintain our simulation and any possible nested simulations. Imagine getting to heaven only to find that your god had gone off to find his/her god ... who had already left to find his/her god ... Perhaps our ultimate evolutionary path is to travel through these layers until we reach level 1 ... with universes to explore on the way. Hey, I'm up for that. Scott Badger

John de Rivaz" : In previous posts to this discussion group, we've talked about the idea of living in accurate, virtual reality simulations. Here is related information: From CryoNet: >>>>>>. Message #16948 From: Azt28@aol.com Date: Tue, 10 Jul 2001 17:50:42 EDT Subject: Re: CryoNet #16924 Simulation From Lee Corbin: > >I think we don't live in a simulation, not because it is not > >possible but because we can't produce it now. > > But the most common conjecture is that the simulation wasn't > constructed "now", but in, say 20,000 A.D., and that we just > don't know the right date. I have advocated the idea of Black Magic: A quantum computer simulate a system and then project that simulation onto a material quantum system on a vacuum fluctuation. We may see such phenomena in the laboratory 10 to 20 years from now. Well before AD 20 000 that technology would be able to project the full observable Universe as a simulation. We are too few a part of that simulation to be its main purpose. You don't create 10^20 stars to watch GWB in the White House or anything else on Earth. In God I don't trust, and I don't think the Universe we see has been built by anyone, less by anyone with the objective to watch us. We are nothing and we have to learn this fact. May be the Universe is a simulation, I like the idea of a self simulation. Degenerate quantum state, as found inside a neutron star may form spontaneously a simple very repetitive quantum computer. It seems indeed that the quantum domain may be reduced to two quantities: one finite number: zero and one undefined one, you can as well call it one or infinite or undefined. If there was any thinking behind the simulation, the parameter choice would have been somewhat smarter. It seems we are in the dumbest possible world, a nearly proof that nobody is at the command level. Yvan Bozzonetti. Brandon J. Van Every" : Regarding the question about whether we could be living in a simulation... > We are too few a part of that simulation to be its main purpose. You don't create 10^20 stars to watch GWB in the White House or anything else on Earth. The universe doesn't have to be simulated, only Earth. Any time we request data farther than the boundaries of Earth, they can feed us any data they like. Could be a combo of data from real telescopes hooked up to the simulation, and blot-outs of anything they don't want us to see. One question of the simulation is whether we're clever enough to pierce the veil of illusion.

math@antiquark.com : I'd buy 100 Turbings and startup my own telephone soliciting call center, with turbings doing the calls. It was be amazingly profitable... no need to pay unreliable humans $5 an hour. For one-time fee of only $2000 per turbing, you'll have a reliable, around-the-clock telephone solicitor. Of course, this assumes that turbings are utterly devoid of souls and ethics. Derek.

Chuck: I'd have mine screen my phone calls and hang up on telephone solicitors. Yes, I'd probably buy one unless they got awful reviews from other users.

"peteb_hwp" : Well, certainly not if I were the very first one to know about it. Imagine what your friends would say about you being caught conversing with a Rubik's Cube at the Christmas party! :=) Seriously, I would not pay 2K for a copy of myself (I already talk to myself, and I don't even like the answers most of the time), but I would gladly pay 2K or more for such a device that was a copy of, say, Albert Einstein's intellect. Or any of a number of other highly interesting individuals that come to mind, say Carl Sagan, Isaac Asimov or Mark Twain. Hey, how about, how much would you pay for a Turbing of your mother- in-law? :=) Myself, I think the true test would be to have such a Turing machine show that it was self-aware and capable of independent thought. The mimic test you mention is just evidence of super good computer programming IMHO. In fact, as I am sure you know, there are quite a few of these Elisa programs floating around, some are astounding. Pete B [Cliff comments, "One wonders if people might actually fall in love with their Turbings."]

"peteb_hwp" : I think love involves a lot more than just intellectual interactions, there are emotions, physical responses, etc., so I doubt that would happen. Although, if as you proposed, somebody has a Turbing of their own mind, and that person is extremely narcissistic (sp?), then perhaps they would become enamored of their own thoughts being fed back to them. Thinking about it further, though: would a self-centered personality be any good in a Turbing machine, or would it just be absorbed in reflecting on its' own new state of existence? Imagine how bad that would be, to have a Turbing of yourself, and have the machine refuse to talk to you! Or worse yet, it gets mad at you for ignoring it. "Yeah, I got rid of the darned thing, everything was always all about it, never about me, you know what I mean?" :=) Wonder if a Turbing could get a headache? Get mad or jealous? And to turn your question on its' head, could a Turbing machine fall in love with its' owner, do you suppose? Pete B

"Quinn Tyler Jackson" : Cliff: "Would you pay $2000 for a Turbing -- a Rubik's-cube sized device that would converse with you in a way that was indistinguishable from a human? Why?" Quinn: No, because I already have a desktop version of that (the Internet) that costs me about $25.00/month.

-- "Quinn Tyler Jackson" : Bobomutin: Applications would include, home psychologist, philosopher, medical advisor, pastoral counselor, baby-siter, entertainer, educator, lawyer, and so forth. Certainly, the depressed, the bereaved, the elderly, the emotionally disturbed, would be a central market for such a comodity. But also conventional younger people would need a bit of chat now and then. Reply: Pocket Poet(R) 1.0 For Pickover Turbing(R) Models 5.2+ O Owner, in whose hand I gently whir, I know all the poems that ever were, And if you solve the puzzle of my face, I shall some cinquain gently, humbly pur. But don't forget my Double AA's refresh, And period interface with mesh, For if my charge becomes uncharged, you know, I'll rhyme a word like orange with Gilgamesh. And though I can recite all forms of verse, For just two thousand taken from your purse, There is one thing like no other poet: I shall not, if scorned, versify some curse. My guarantee completely covers that, And so, you're safe to loudly curse and spit If some epiphany of mine is off: Just take me back to be quickly refit. Indeed, though poets voice of their age Are supposed to be, if I should enrage You with a metered observation's foot, You're free to flip and switch and turn my page. But if you seek some succor in my mete, Just listen 'til my stanza is complete -- Do not return me if you find me curt, If I should kick you with my neuram feet. But since you paid your two thou, what's to do? My software wasn't beta'd 'pletely through, So I may, like a poet, shatter dreams .... Perhaps just download debugged version 2. -- Quinn Tyler Jackson

John de Rivaz" : > No, because I already have a desktop version of that (the Internet) that costs me about $25.00/month. Good Grief! in the UK you can get it effectively for nothing. Companies like NTL offer you free unmetered connection provided you spend UKP15/month with them for voice telephone calls. On the basis that you (or your wife :-) ) spends that much on phone calls anyway, then the Internet is free.

---

What will society be like in 1000 years?

Would you care to speculate about what civilization and society will be like 1000 years from now? -- Cliff

"John de Rivaz" : If technology advance continues, such speculation is futile, unfortunately. The major change is the end of ageing and relative rarity of death, but as this will come so much sooner than 1000 years that one would be looking at nearly 1000 years of humans living as ageless beings. (Never immortal, as you have to have lived for eternity in order to be sure you are immortal, and if you then die you are not immortal) Some speculation about this has been made in George Bernard Shaw's play cycle "Back the Methuselah." It would be easy to speculate, but so hard to be anywhere near reality!

Derek Ross" : In Msg 141, you ask "What will we be doing 1000 years from now?" In my opinion -- even though this does not sound futuristic -- we will probably be doing the same activities we were doing 1000 years ago, and still continue doing today. Off the top of my head, I can think of a few obvious ones: - Riding around on four-legged animals. - hitting/kicking/batting/swatting a variety of balls for fun (or watching others do the same). - Reading books and writing letters. - Pitching cloth tents in the wilderness, crapping in the bush, and staring at flaming logs. (AKA camping). - Growing tomatoes in your garden. - Going to church. - Painting pictures using pigments dissolved in oil. - Going to restaurants. - Capturing fish with a small metal hook attached to a string, using a worm as bait. I'm sure you get my point -- we will continue engaging in activities that appear to be useless and archic, that could easily be eliminated by a quick technological fix. But if people find some activity enjoyable, then it will continue to be practiced. Just my $0.02. Derek.

---

What is the most forgettable license plate?

pmosk@watson.ibm.com: I read an article about someone who claimed to have devised the most forgettable license plate, but did not divulge it in the article. What is the most forgettable license plate? Is it a random sequence of eight (the maximum allowed in New York) letters and numbers: for example 6AZL4QO9, or perhaps a set of visually confusing numbers or letters, for example MWNNMWWM? What do you think?

Comments

-Paul

David Jones : I remember once watching a news show about some yearly competition to find out who has the best memorization skills. They have tests like each person has to memorize the most digits of a random number within 30 minutes and so forth. They talked with some of the competitors and the main trick they all use is mneumonics (sp?). For example, with MWNNMWWM I just have to remember four words: MoWN NaMe WoW Me (remove the vowels.) So, the most forgettable license plate would have to be one that somehow minimizes mneumonic compression. Consecutive numbers are easier to compress than consecutive letters. Your brain stores 53 as a single number, but it stores 5 and 3 and two separate numbers. On the other hand, there is no easy way of compressing something like QK. Yes, you can use the word QuicK but you still have to know what two letters in the word you care about. My point though is that the order of number and letter placement can complicate things. Im guessing that something like AA#AAA#A would do the job as it seems like with well chosen letters you could require the memorizer to use a minimum of six mneumonics. After that, I don't have too many good ideas. GJ for the first two letters might be a good start as I cannot quickly think of a word that uses those two letters in that order and they are phonetically similar enough that they can be easily confused. Davy Cliff asks, What about a binary number sequence like 01011011...? This would be hard to remember.

---

"Omega Browser" Survey

Imagine you have a strange web browser called Omega. This is your only browser for the rest of your life. If your Omega browser was locked in such a way that you could view five web sites, what would they be? (You may consider that the web site you choose has access to all its "subsites" at that domain name; e.g. www.britannica.com would have access to all its articles.) Cliff

Comments

Derek Ross : Google. They have a cache of every page they reference, so in essence, google contains the entire internet. Derek.

David Jones : Well, I could pick a site like safeweb or version99 which allows me to browse other websites anonymously, but in turn would allow me to bypass the Omega limitation. Similarly, Google.com allows you to access the cached pages they use for their search engine so, although much more limiting, I still achieve the effect of viewing other websites while staying on the same domain. I will assume, however, that answers like these are not in the "spirit" of the question. I guess that first and foremost would be nightswimming.com. I own the domain and also must have access to it in order to change its contents. Second would be yahoo. I mean, what CAN'T you do on Yahoo? I get mail, games, maps, shopping, news, calendars, umm, I know theres more, but you get the point. Third would be pogo.com. They have much better bridge players there than yahoo games does. Fourth would be ZDnet so I can download shareware and game demos and still get access to tech news. Fifth would be classicgaming.org - gotta have my emulation/nostalgia fix. On second though, I might scratch the fifth one in favor of soa.org - I would need to have access to information for my actuary certifications. Davy

"Daniel Dockery" : Hmm. Challenging to select but five. At first, I considered utility sites, or sites of convenience, which I use often (e.g., for banking, credit, postage, etc.), though after considering that what I select are to be the *only* sites I can access, and knowing that, though it is less convenient, everything that these particular sites offer is available offline, locally, I decided to remove them from consideration in this. I also removed from consideration frequently used (by me) sites which are simply works of reference which I can acquire and use offline (e.g., http://www.m-w.com/) as well as search engines and the like (since what use is a search engine if I cannot access the sites returned by the search?) As someone pointed out, Google (http://www.google.com/, an *excellent* search engine) maintains a cache of indexed pages which would, in effect, allow one to, to a degree, circumvent the limitations of the Omega browser, but, as was also pointed out, I suspect that's rather missing the spirit of the question, so I omitted it. I think, though, that before I can answer fully, I need additional details as to the extent of the limitation: 1) Does the limitation apply only to the parts of the 'net accessed with the browser? Or does it apply also to protocols other than http? E.g., would this preclude accessing ftp sites with an ftp client, preclude nntp access with a newsreader, or limit us from accessing our pop3 and/or smtp mail servers with the email client of our choice? If we are limited to only five 'net sites total no matter what the protocol, then three of my choices are made for me of necessity by virtue of having to preserve a connection for my two mail servers and my isp's news server. If it applies only to the browser, though, we would be free to select sites other than our ISP, etc. 2) You say that we may consider that a site includes all its sub-sites and pages --- but what about its sub-*domains*? For example, if we elect to access http://www.ibm.com/ can we also access the subdomains http://www.alphaworks.ibm.com/ or http://www-106.ibm.com/developerworks/? If so, then the three ISP requirements mentioned in (1) can be diminished to one, the ISP itself, by considering that the mail and news hosts are but subdomains of it. As a preliminary list, supposing for the moment that the limitation only applies to web-sites (i.e., that I needn't select my ISP as part of the list solely for the sake of email and usenet) and that a site includes its sub-domains, I would suggest these as my choices: http://www.perseus.tufts.edu/ While, like the reference work sites earlier discounted, I could acquire all of these texts for my personal library offline, the tools, cross-references, and notes of this site make it surpass what is available in a printed book, thus my selection here. I visit the site often. http://www.arXiv.org/ An incredible reference site to which I return with frequency. http://www.ibm.com/ For access to both the Alphaworks and Developerworks sites (URLs cited earlier). http://www.microsoft.com/ Primarily for access to http://msdn.microsoft.com/ and http://windowsupdate.microsoft.com/ http://sprott.physics.wisc.edu/ For both Prof. Sprott's site, and your own pages hosted there: http://sprott.physics.wisc.edu/pickover/home.htm Of course, if a site *doesn't* extend to include its subdomains, I will have to reconsider and revise these choices (for the IBM and Microsoft cases, at least). ---Daniel

---

Special Augmented Primes

One of my favorite bizarre questions involving prime numbers relates to the wonderful "special augmented primes." You can augment a prime simply by placing a 1 before and after the number. The augmented prime is "special" if it yields an integer when divided by the original prime number. For example, 137 is such a number because 137 is prime and because 11371 / 137 yields an integer, namely 83. Are there other such numbers? How rare are special augmented primes? It turns out that there is a general set of numbers of the form 90909...01 that are special augmented primes. For example, Jim * discovered that 909090909090909091 -- when augmented by ones to form 19090909090909090911 -- has a factor of 10**19+1 and, similarly, 909090909090909090909090909091 has a factor of 10**31+1. For those of you with access to computer programs that can manipulate large integers, how many more of these Jim * augmented primes can you find? Amazingly, Jim found this incredible extension to the 9090 trend:

909090909090909090909090909090909090909090909090909090909090909090\
909090909090909090909090909090909090909090909090909090909090909090\
909090909090909090909090909090909090909090909090909090909090909090\
909090909090909090909090909090909090909090909090909090909090909090\
909090909090909090909090909090909090909090909090909090909090909090\
9090909090909090909090909091

which, when supplemented, has a factor of 10**293+1. What smaller special augmented primes are lurking in our number system waiting to be discovered? Cliff (Note: I am waiting to get Jim's last name.)

Comments

"Daniel Dockery" : For any using the software, this is a Maple routine that will produce augmented primes for the nth prime number: auP := proc(n) local p; p := ithprime(n): (10^length(p)+p)*10+1; end: E.g., auP(1) = 121, auP(2) = 131, auP(33) = 11371, etc. > The augmented prime is "special" > if it yields an integer when divided > by the original prime number. For > example, 137 is such a number because > 137 is prime and because 11371 / 137 > yields an integer, namely 83. Are > there other such numbers? Searching the range of the first 50,000 primes, I found only four. p( 5)= 11, auP( 5)= 1111, auP/P: 101 (itself a prime) p( 6)= 13, auP( 6)= 1131, auP/P: 87 p( 33)= 137, auP( 33)= 11371, auP/P: 83 (prime) p(1128)=9091, auP(1128)=190911, auP/P: 21 Unless I missed one or more in my search, the above would suggest they have, at least in the above cited number range, a density of around 0.008%, I think. > How rare are special augmented primes? > > It turns out that there is a general > set of numbers of the form 90909...01 > that are special augmented primes. > For example, Jim * discovered that > 909090909090909091 -- when augmented > by ones to form 19090909090909090911 > -- has a factor of 10**19+1 and, > similarly, 909090909090909090909090909091 > has a factor of 10**31+1. In both of the cases given above, by my calculations, the prime 90...91 (i.e., the prime itself, not the augmented form) equals (10**n+1)/11. That is, 909090909090909091 * 11 = 10**19+1, 909090909090909090909090909091 * 11 = 10**31+1. (10**n+1)/11 will, I think, always produce a number of the form 90...91 with (n-1) digits when n is an odd number greater than or equal to 5. Checking the range of {5<=n<1000}, it appears to create prime numbers when n=5, 7, 19, 31, 53, 67, 293 and 641. I find it interesting to note that in all cases, here, for the 90..91 numbers, the integer auP/P is always 21. > For those of you with access to computer > programs that can manipulate large integers, > how many more of these Jim * augmented > primes can you find? If, as above, you define a JauP (Jim augmented Prime, naturally) to be (10**n+1)/11*21 for some odd n (will n always be prime?), then a casual search for n<1000, reveals there are JauPs for n in {5, 7, 19, 31, 53, 67, 293, 641}. JauP(641) = 190909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 90909090909090909090909090909090909090 \ 909090909090909090909090909090911 > Amazingly, Jim found this incredible extension > to the 9090 trend: > > 909090909090909090909090909090909090909090909090909090909090909090\ > 909090909090909090909090909090909090909090909090909090909090909090\ > 909090909090909090909090909090909090909090909090909090909090909090\ > 909090909090909090909090909090909090909090909090909090909090909090\ > 909090909090909090909090909090909090909090909090909090909090909090\ > 9090909090909090909090909091 Hmm. Maple and Pari both return prime(n)=false for the above large number; as best I can tell, it's of the form 6*x+1 for x = 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 15151515151515151515151515 \ 151515151515151515 > which, when supplemented, has a factor of 10**293+1. Using n=293, (10**n+1)/11 yields 909090909090909090909090909090909090909090909090909090909090909090 \ 909090909090909090909090909090909090909090909090909090909090909090 \ 909090909090909090909090909090909090909090909090909090909090909090 \ 909090909090909090909090909090909090909090909090909090909090909090 \ 9090909090909090909090909091 which is probably what was intended with the earlier number, I imagine, which simply had an extra row of 9090..9090 attached. :) > What smaller special augmented primes are > lurking in our number system waiting to > be discovered? I wonder if there are any other integer multiples auP/P besides the four found and cited earlier (i.e., 21, 83, 87 and 101). In my searches so far, I've found none. Since it seems that all JauP produce the same integer multiple, 21, I wonder if there are similarly other primes which produce their auP when multiplied by the four earlier integer multiples? (I've searched through the first 1000 primes in each of the four cases and found none.) It should be possible to speed up searches for such numbers by noting that since our augmented number must end in the digit 1, and must be the product of an integer i and the prime itself, that for primes ending in the digit 1, i mod 10 must equal 1, primes ending in 3 can only have an i mod 10 equal to 7, primes endi