I received a welcome comment from a reader — a mathematician who had submitted an incorrect answer, then reconsidered it — concerning my philosophy about experimenting with you puzzle-solvers in regard to your particular fields of expertise, and showing how we are often led to apply that special knowledge when far simpler solutions are available. He wrote:
I didn't do the puzzle this week, but I can certainly attest to the problem last week relating to lightbulbs and switches. You see, my first answer was submitted after viewing the problem from the pure mathematics standpoint. I read the problem, did some quick calculations in my head revolving around binary permutations, and sent it in. It wasn't until my drive to work in the morning when I realized my mistake: I used mathematics to solve a problem that didn't require it. This error locked me into trying solutions that only mathematics were able to provide. This overlooked the obvious answer that required examination of the physical properties of the lightbulbs (heat), which I re-submitted and got right.
The grin on my face couldn't be contained when I realized what I had foolishly done, so I immediately began trying the problem on other like-minded (i.e. programmers) people at work. All of them fell into the same manner of thinking: "Well it's three switches with a binary operation..." and all of them got it wrong, as well.
First of all I wanted to thank you and add a couple things about your comment this week with respect to the pair-of-socks puzzle. On the site you said: "The mathematical possibilities, the permutations and combinations, the percentages, all tended to mislead a good number of readers."
Here he relates an anecdote that I've often told about the performance of conjuring tricks. I'm in complete agreement with his magician friend.
I think lessons like this are always worth re-learning. Sometimes you need a problem like the one presented, to put your thinking back in check and that's what the lightswitch problem did for me. It was a lesson long forgotten and I'm happy to remember it once again.
I was speaking with a local magician (with 40+ years of experience) once about getting some tips on performing magic. He explained that his toughest audiences were not adults, but children. When I asked why, he explained that adults always over-analyze the performance and the effect. They come up with elaborate reasons, for example, on how a coin can jump between his hands: "They think I have a cloth tube running in my jacket with a string on the coin to pull it through to the other hand. The children just say 'You have two coins,' which is exactly what is going on."
I usually add another aspect to this matter of children being difficult to deceive. They are simply not sophisticated enough to be easily fooled. Let me explain what I mean by that. The "palming" move — when a small object appears to vanish after being passed from one hand to the other — is accomplished not only by the actual retention of the object in the first hand that holds it, but by subtle gestures that convince the observer that the second hand actually holds the object. When the second hand is then opened and shown to be empty, the desired result is obtained: bafflement, astonishment, stupefaction, surprise, amazement, wonder, awe, bewilderment, and delight are all sought-after elements. Look at the video clip attached here to see what I mean. This is a few seconds of direct, unprocessed, tape.
Click here to view the video.
Please note that you will need Real Player to view the video. Click here to download the player.
The movement of the hands relative to one another — the second hand taking up the motion of the first to imply that the object follows along with it, the dropping away of the first hand as if its function has ceased and has been taken over by the second hand, the pointing finger (which also allows that hand to remain closed and to thus securely retain the object!) and the purposeful direction of the performers gaze, which the observer assumes will follow the location of the object, all contribute hugely. But here's the point I'm making: adults recognize the simple move of transferring an object. They've seen or experienced similar situations many times, and they react to the implications and suggestions being offered. Children have not had that world experience, and since they do not actually see the object changing hands, they are often not convinced of the reality of the exchange. As I said, they do not have the sophistication that adults have. Adults need such an ability to make assumptions, as shortcuts in their lives, and they are usually only poorly served by this device when someone purposely sets out to deceive them.
We magicians are a cunning lot, and I even suspect that perhaps the so-called "psychics" often resort to these techniques, too. It's just possible.
A comment came in from a reader, one that I think you should see. I may have created a monster....:
One note about the "moving compass trick." I've done it to several co-workers, all with engineering backgrounds and enjoyed 100% success. Not one guessed "magnet." I have the magnet under my wristwatch. I tell them "it takes two people" and demonstrate that it does not move when I do it alone. My watch is far enough away so the field isn't strong enough to affect the magnet. Then I get the two of us waving our hands around the compass and it moves. Naturally I get my watch closer than before. The magnet is far enough away that the field is weak and the compass needle lags behind. The "it takes two" part has thrown everyone so far.
There you have it. Highly-trained engineers missing an obvious solution....
We've long discussed the matter of acupuncture, pointing out that it is best described as a form of "sympathetic magic," a process of relating a map to the actual terrain, as we also see in palmistry and in "reflexology." This chart of the human body's "meridians," as you'll observe, shows just how remote the actuality is from these imaginary lines that quacks claim control body functions, and which they say can be blocked or opened by sticking needles along the paths for "qi," that mysterious spiritual "fluid" that is said to course through living things. I find it not surprising that this poor woman looks unhappy. And as you might suspect, the quacks assign all this magic to pets and farm animals, too, which interests those responsible for the well-being of these critters.
Though not an "MD," a veterinarian acquaintance of mine certainly has the training and expertise to examine quack claims made in reference to human medical matters. Dr. Robert Imrie, DVM (Doctor of Veterinary Medicine) has been in the forefront of those who question certain aspects of medical claims that are — to say the very least — doubtful. I have long been alarmed at the use of acupuncture, "therapeutic touch," and homeopathy to treat pets and farm animals, and I welcome this news. He writes:
Not only does this constitute a major victory for proponents of medical rationalism, I believe it is also an extremely important "first." So far as I'm aware, to date there have been no analogous "showdowns" between proponents of science-based medicine and "everything-else-based medicine" at the level of a national medical professional association — in the U.S., or for that matter, anywhere else in the world. Certainly there has been no similar confrontation within the AMA (American Medical Association), ADA (American Dental Association) or the ANA (American Nurses Association). I hope and expect that our successful efforts to induce the AVMA to courageously and proactively identify and address the issues attendant to unproven and disproved medical therapies, will eventually "boil over" into controversy among the other healthcare professional associations on a state, national, and even international basis.
While the posted guidelines are described as merely "proposed," they have already generated a storm of protest from alternative medicine "true believers." Though it seems unlikely to me that the staunch advocates of genuine science on the nine-person review committee will be swayed by purely political pressure, the AVMA House of Delegates which must accept the new guidelines, might be. Alternative medicine skeptics, science-based medicine advocates, and those concerned about animal welfare need to offer all the support they can. As the AVMA message states:
Written comments postmarked by February 15, 2001 will be forwarded to the AVMA Alternative and Complementary Therapies Task Force for its consideration. No e-mail or fax comments will be accepted. Mail comments to:
Dr. Craig A. Smith, AVMA
I'm pleased to report that after nearly three years of effort, medical skeptics have won a substantial victory for the cause of science and reason in healthcare. The proposed AVMA (American Veterinary Medical Association) Guidelines for Complementary and Alternative Veterinary Medicine have just been posted to the AVMA Website at: www.avma.org/compaltmed.asp. They will remain available on line only until January 31, 2001. Veterinary practitioners and members of the general public have been invited to comment on them. (The vastly different and highly "promotional" 1996 Complimentary and Alternative Veterinary Medicine Guidelines are available on line at www.seanet.com/~vettf/Guidelines.htm).
1931 N. Meacham Road
Schaumburg, IL 60173-4360.
Though this appeal by Dr. Imrie is directly primarily to AVMA members, I urge you, too, to please write Dr. Smith to offer your support as a layperson for the revised guidelines. All of us should have an active interest in this situation, since it affects human treatment modalities, as well. A few minutes to write Dr. Smith will be well invested, I believe. Quackery in veterinary practice passes over to regular medicine, as we've seen. Please help to avoid this happening. The response we obtained from you folks recently to the Presidential Commission through this web page, was very impressive. I hope that readers will respond as generously to this appeal.
Organizing some library material, I came upon a large folder that I'd put aside for a less busy time. This came to the JREF along with the letters of Sir Arthur Conan Doyle and a box of lantern-slides once toured by a believer in fairies, Leslie Gardner, a Theosophist who eagerly embraced the photographs produced by the two little girls who fooled Sir Arthur — and a hefty portion of British society — with their tricks. We've discussed the letters here and they can be found in the archives of this web page. In fact, our colleague Dr. Massimo Polidoro is ready to come out with a book discussing the Conan Doyle correspondence.
The folder is a treasure indeed. It is a catalogue and a collection of letters written by and to persons who vigorously supported belief in fairies. This material was collected by Mr. Gardner. When I have the time to look into this mass of material properly, I'll feature it here in summary. It provides an excellent view of the social atmosphere of England during World War I, with its enthusiasm over spiritualism and even more incredible beliefs such as fairies and angels.
Harrison Bauer was the first with a correct answer to the geometrical-shapes puzzle. Apparently this was a pretty easy one, though some of you had a tough time sending the answer in. It really needed a modified graphic — as you see here — to express it. I must mention that one unhappy reader complained that I didn't say what the shapes were required to be identical to, nor congruent to. There's one in every crowd.... Here's the solution:
Incidentally, reader Tom Salinsky had a very efficient approach to his solution. He wrote:
I found the solution by looking for a second 2 x 2 square to match the one at top right. This was intended to answer the question, "Do I have to divide the big square at top right?" However, shading the second available square revealed the answer.
I'm just as interested in the methods used for solutions, the approaches and reasoning involved, as I am in the actual answers. Thanks, Tom.
Try this new problem: The two bolts shown in the illustration have regular helical grooves. If you move the bolts around in the direction indicated, and as shown — the way you would "twiddle" your thumbs — what is the result, aside from the strange looks you'll get from friends and family? You don't rotate either bolt around its own axis, and you keep them closely in contact with one another. Will the heads move toward one another, will they retreat from one another, will they remain the same distance apart? No fair scraping around in the toolbox for a pair of bolts to try it. Think it out. It has a really cool analogy that explains it nicely, which we'll give you next week.
You may have observed that the year 2001 got started without any part of the USA falling into the ocean, no world leader was taken to Valhalla on a cloud, and Paris was not consumed in an earthquake or conflagration. Nor has spoon-bending made any major changes in our lifestyle; it's still just a silly profession. I'm not at all surprised. Next week, you'll be able to do spoon-bending just like the pros do it. I mean the professional magicians, of course. The psychics use divine powers to do this, as we all know. Watch for this mind-boggling exposé here next Friday. Until then, think about writing Dr. Smith, will you? Thanks!
And let me know what you think of the new page format, which will go up next week. Go to the home page and click on "What Do You Think?" to make comments.... Thanks!
