There was a recent UFO conference held in a University of Colorado auditorium. Some 600 UFO enthusiasts were there to see a 2-hour video of "testimony" from former government and military employees about the existence of extraterrestrial beings and the government's monitoring of them. It's all part of Dr. Steven Greer's "Disclosure Project." The North Carolina physician is trying to get Congress to hold official hearings on the government's claimed interaction with aliens — the kind who regularly visit us from space. Greer says that as a child he saw a "disc-shaped craft" at close range and as a result began studying such matters. He thinks people from outer space are monitoring Earth, in part to scope out our weapons technology.

Some of the audience weren't too enthusiastic about the video, but for reasons you might not suspect. Maureen Murphy of Boulder handed out fliers inviting people to attend another nearby meeting, "The Alien Cover-Up," sponsored by the Allies of Humanity, a group with a somewhat different view. "We don't disagree with Dr. Greer on the disclosure agenda," she said, "we just disagree on the aliens' agenda. They're taking women against their will, they're taking the eggs, they're creating a race that will have an allegiance to the visitors." Either way, it's the end of the world as we know it, folks.

The UFO bunch is staggering from recent blows to its quaint stock of stories that is flaunted to scare us into believing that the aliens are underfoot and overhead. One of the most-flaunted stories is now not brought up much anymore. The famous 1947 Roswell case, in which a balsa-wood-and-mylar space craft is said to have plummeted to Earth outside of the small New Mexico town, has been pretty well discredited now, even in the UFO community. They needed a colorful conference to stay in business, and nothing gets more enthusiastic support that a conspiracy theory in which the evil U.S. government is concealing cosmic facts from us.

Commenting on the Greer conference, George A. Filer, the director of the Mutual UFO Network Eastern Division (MUFON), wrote in his report:

The testimony of over twenty government employees for the first time provides real evidence of the reality and existence of the phenomenon [UFOs and visitations]. I have attended dozens of conferences and most of the speakers had no real evidence, and often they had wild stories that made me wonder if they were part of a counter intelligence plot to confuse. If you want to understand what is going on, I suggest www.disclosureproject.org. These persons have indicated they are willing to swear under oath in front of Congress that they are telling the truth. If they perjure themselves they can go to jail and forfeit all retirement pay and allowances. I wonder if most speakers at conferences are prepared to do likewise?

Here we have the tired old notion that if someone really believes something to be true, and/or will swear that it's true, it is true. This is rather flying in the face of reality, but serves the purposes of the believers very well. Mr. Filer continues:

In almost every field of endeavor speakers are required to have credentials but the field of Ufology often takes the wildest claims as a reason to give the speaker top billing. I would think the minimum requirement would be to have passed a test as a field investigator or to have worked in a sensitive government position. . . . Remember in our nation one or two witnesses can convict and send a man to prison or death.

This is nonsense, but typical of the shallow statements of these "investigators." Yes, "one or two witnesses" can give testimony to what they say they think they saw, but a jury and/or a judge has to decide whether these witnesses are reliable — not based entirely upon their employment or position! — and the jury or judge then makes an appropriate decision. Any top government official, with security clearance, and a Phd., in any "sensitive government position," can go to see David Copperfield at work, and then appear in a court of law and swear that David sawed a woman in two pieces with a buzz-saw. And they can really mean it. That does not mean that David sawed a woman into two pieces. It only means that a well-educated, honest, good observer with serious government credentials, sincerely believes what he or she saw. It says nothing about that person's expertise in other fields, their honesty, nor their eyesight.

This week, a story in the Australian newspaper, The Age, put into the shade the items I've been featuring here on such patents as that awarded to the peanut-butter-and-jelly sandwich, and the making of toast. According to The Age, a freelance patent lawyer in Melbourne has patented the wheel! John Keogh was awarded an Innovation Patent for a "Circular Transportation Facilitation Device" within days of a new patent system being invoked back in May. Now, an "innovation patent" only has to show an "innovative step" and can be prepared without professional legal help. Lawyers Down Under are obviously all a-tremble.

In Australia, standard patents have to be crafted by a registered professional patent lawyer who has engineering and/or science qualifications. Patents must also show an inventive step — a significant advance — as they do here in the USA. Mr. Keogh said that he patented the wheel to prove that the "innovation patent" system was flawed. He said that the impetus for this perhaps unwise move came from the Federal Government. Constituents had claimed that the cost of obtaining a patent was too high, so the Australian government decided to find a way to issue a patent more easily and more cheaply.

Obtaining a patent for a wheel would require that the person applying show that he/she originated the invention, a false claim in this case, and a very serious matter. This would invalidate the Wheel patent as well as amount to a misrepresentation on the part of the applicant. But Mr. Keogh, reports The Age, is unrepentant. He said that the Federal courts would have to decide the fate of the new system when infringement suits were inevitably brought. Sounds probable to me....

But, concludes The Age, Mr. Keogh has no immediate plans to patent fire, or crop rotation, or other fundamental advances in civilization. Whew! That was close!

But I'm way ahead of Keogh. I'm applying for patents on the axle, and on the circle. In effect, he has already infringed on my patents..... Hah! Send in the lawyers!

Reader David Deutsch contributes this astounding discovery:

You've heard of Crop Circles? Well, here's something even stranger which I have seen with my own eyes, and have personally photographed:

Crop Cylinders! Moreover, I will stake my scientific reputation on the proposition that these cylinders not only existed, but were no accident: they were placed there by intelligent beings — and later removed to a destination I can only guess at.

A news item last week reported that a British scientist studying heart attack patients says he is finding evidence that suggests that consciousness may continue "after the brain has stopped functioning and a patient is clinically dead." He bases this on the fact that a "dead" patient can recall things heard and felt after the brain has stopped producing its characteristic electrical wave pattern, and this discovery has led to celebration among those who have been seeking evidence for the elusive "soul" factor, and proof of survival after death. Might I suggest that this is more likely to be an indication that the brain has not "stopped functioning," and goes on for a bit doing its regular duty, until it eventually loses function? Parsimony rears its ugly, rational, head once more.... At least, those who do come out of this state report only pleasant memories of it, so we probably need not fear being buried alive or experiencing decomposition. That's a relief. But, we'll all find out.

Won't we....?

A stunning Bay Watch actress with eyes wide in astonishment, and a psychic who calls up the dead: what better combo for an episode on an "Extra" TV show? Actress Traci Bingham declared on the program recently:

Something just recently happened to me in my life, and I want to see if he [Gary Quinn, "Psychic to the Stars"] knows about it.

Quinn didn't disappoint her. In the same cold-reading procedure that they all use, he stunned Traci — who appears to stun easily. Said the "Extra" commentator, "Quinn astonished Traci with one poignant question." Stunned her with a question? I would expect a statement, not a question, but maybe I'm just demanding too much. Asked Quinn:

Is there someone who passed, in your immediate family?

Traci verified that there was, and that it was her father. Then she asked:

I want to know if he suffered before he died?

This is Quinn's "stunning" answer:

No, he's with us and he wants you to know that he's there with you all the time and that for you not to worry because the message I'm getting for you is that he really loves you, and he wants you to know that, and not to worry.

Well, that convinces me. Mr. Quinn could not possibly have know that, unless he were speaking directly with Dad. I'm converted. My only question is, couldn't "Extra" have found something in the entire session that was a bit more evidential? That did it for Traci, obviously, and for me, of course, but there just may be some out there who would need a bit more to be totally convinced....

A reader, James Forsyth, offers this interesting observation. I've changed some U.K. spelling:

I am writing as a skeptic who thoroughly enjoys your website/project.

I have recently read your column regarding Christopher Bagley's intent "to disprove astrology shapes people's lives or determines their personality and psychology in any way." I noticed that you quite sensibly modified this statement into an "investigation" and it is following this modification that I would like to provide a number of statistical possibilities through which astrology may in fact determine psychology/personality in some (albeit extremely remote and unintentional) way.

Astrology at its base level is predicated upon the date of birth. Furthermore, star-signs can be read as a measure of birth within the seasons. Looking at it this way, we can substitute the question to read: "does the season of birth determine psychology or personality in any way?" The gestation period of the human is approximately nine months. During this period, the developing fetus is subject to a number of factors which may potentially modify growth. Two minor instances of these are diet (via umbilical cord) and sunlight (through womb). Anecdotally, a packet of potato chips or crackers may contain the words on the nutrients list SUBJECT TO SEASONAL VARIATION. This is pretty obvious, but the nutrients within most food will change according to season. Any nutrients which the mother eats across this period is in turn passed to the fetus. Is the nutrition presented during the gestation period from January until Sept/October (JFMAMJJAS) the same nutrition as provided to the fetus with the gestation period from May until Dec/Jan (MJJASOND)?

There is almost certainly going to be some difference between these — and potentially between a fetus which develops across any different nine-month timespan. (NB: with increased transport and food technology, particularly in relation to prepackaged foodstuffs, these seasonal differences are likely to be increasingly minimized.) Similarly, the amount of sunlight that the developing fetus receives will be different between JFMAMJJAS and MJJASOND.

Both of these factors may play a part in the growth and development of a fetus. These are obviously not major growth factors, although a difference in development may in fact lead on to a slight statistical difference in development of the personality and/or psychology to that of a fetus with different nutrient growth.

Another minor factor could be the development after the birth of the baby. Given that the human baby develops so rapidly across its first year, and more importantly its first few months, it is not absurd to suggest that there may in fact be a difference between a developing infant whose first out-of-womb year cycles Summer-Autumn-Winter-Spring as opposed to the infant who cycles Winter-Spring-Summer-Autumn. These two different experiences continue the nutrient/sunlight through an important developmental stage of the infant.

In counter-argument, it could be stated that these are such slight occurrences (compared with other major growth influences) that it is on the whole insignificant to the development of personality. To this I would suggest that if these factors can be shown to affect growth (a proof which is beyond my personal means to provide but a conclusion which is in the realm of possibility) then across a large enough sample (say 5 billion people) then there would possibly be slight statistical differences in development between a group of people who are born in January and those who are born in June.

The substitute question: does the season of birth determine psychology and/or personality in any way? As I stated above, I have not performed either research or proven or disproven anything in this writing. I have merely suggested the possibility for further study and research through which my (untested) hypothesis may hold ground, that is, that the season of birth may determine psychology and/or personality in some way. It follows that if the season of birth does determine these characteristics in any slight way, that an arbitrary division of births across the year will have slight differences between them when taking a large enough sample size.

I do not in any way think that astrology or star signs are anything more than arbitrary divisions. Therefore I do not think there is any form of "truth" to astrology. However, the blanket statement of "in any way" seems to me to go too far and it is that sort of statement which may be counter-productive to the sceptics cause.

Mr. Forsyth, thank you for your comments. This is a very old argument re astrology, and has been outlined many times before, down through the years. And it is certainly a proper proposition. You wrote: " . . . it could be stated that these are such slight occurrences (compared with other major growth influences) that it is on the whole insignificant to the development of personality." Agreed. An examination of astrological claims, however, shows that the radical differences in character and personality that are stated, could not possibly be accounted for by the seasonal variations.

Your bottom line here appeals to me: "The substitute question: does the season of birth determine psychology/ personality in any way?" Exactly. And that's just the sort of research I'd like to see done, properly, and definitively.

A chap who offers the infamous Tice Clock for sale (see archived reference) responded to a note I sent him asking why, despite Mr. Tice's reluctance to apply for the JREF million-dollar prize, he himself did not apply and simply snap up the award:

I find it hard to believe that any one person can speak from their high horse, judge whomever they please, attempt to denigrate their reputation, chastise anyone associated with them, accept money for doing it and then choose to ignore their own closet full of skeletons. What gives you the right? You sir, have not been ordained by anyone but yourself, and your efforts mean nothing to me. I am intelligent enough to know what is and what is not, and so are our customers. Don't bother me again.

Perhaps this fellow suffers from chronic indigestion, but for some reason he is infuriated that I offered him a million dollars! This response of his certainly does not address the question: if this thing works, and he's convinced that it does work, and he offers it and sells it to his customers, why won't he put it to the test and take the million-dollar prize? Hello?

I find these "skeletons" being referred to, I've looked in all my closets, and there's nary a bone in there to be found. And I don't remember any ordination taking place, ever. What is this money that I "accept" for calling the bluff of the fakers? I've not seen any of it. Is there a fortune to be made here that I'm not aware of? Surely, Tice and his vendor are doing well, selling an expensive device that does not work — at all.

Gee, we put our money where our mouth is. Now come and take the money....!

Before we get any further away from the "ten triangles" puzzle, one reader, Michael P. Allen — and one reader only! — discovered an interesting omission:

The solution from Jaime Arbona, as posted June 29, 2001, appears to have eleven triangles rather than ten. The small triangle in the middle right is highlighted as an individual triangle in the diagrams presented. Thanks for a great web page!

Yes, you're right, Michael! This was quite a surprise to Martin Gardner, who was titillated to learn of it. We'll call this the Arbona-Allen solution. Jaime didn't spot it, either! I didn't spot it, and no one else did. Everyone go and stand in the corner. I'll be there in a minute.

Reader Shuhang Deng also comments on this puzzle. It had been proposed that perhaps any two lines that were not parallel and did not pass through the vertices of the triangle, would give ten triangles. Mr. Deng opines:

Actually, that is the case. We have total 5 lines to work with, and it takes 3 lines to make a triangle, given that no lines are parallel and no 3 or more lines go through the same point. So, this puzzle turns into a mathematical question: a combination of 3 out of 5, regardless of order, is 10!

Comments on this comment....?

Last week was perhaps a slightly more interesting problem, since I was asking for two distinctly different methods of arriving at the solution. Many of you solved it, first, merely by drawing in the other diagonal of the rectangle, DC, and since that is also a radius of the circle, which is also AC, and the two diagonals AF and DC are equal, DC is equal to AC. Easy enough. But remember, I said this was a "unique" solution, one which is good for all values. That means that if we move D along the arc almost to B, then actually to meet B, the diagonals become identical (equal) to BC, and we have a solution by general means. Both solutions are shown here. But there were algebraic, trigonometrical, and simple Pythagorian solutions offered, too

One reader offered:

DE = sin DCA
DF = EC
EC = cos DCA
sin² DCA + cos² DCA = 1 (AC)

It can also be done algebraically — I solved for (EF)² — (AC)² and found it equal to (AC)² — (EF)². Hence, AC = EF again.

Sean Ellis wrote:

Consider the angle subtended at C by the arc AD, and label this angle "a". It follows from trigonometry that DE = r sin a, where r is the radius of the circle. Also, DF = r cos a. These are two sides of a right triangle with EF as its hypotenuse, so by using Pythagoras' theorem we can show that the length of EF will be the square root of (r sin a)² + (r cos a)². This reduces to simply r, since cos² a + sin² a = 1. The length of AC, being a radius of the circle, is also r, therefore the lengths are again shown to be equal.

Matthew Gillie offered:

The length of EF is given by Pythagorus as the square root of (EC² + CF²). As point D tends towards point A, EC tends to AC and CF tends to zero. Therefore EC + CF = AC. Therefore length EF = square root of AC². i.e. EF = AC.

Okay, I guess, but mine was easier....?

Back to matches once more.... Here we have a triangle formed from 12 matches. We'll use one match-length as one unit of measurement, okay? By moving just two matches, make the area of the figure — no longer a triangle! — 5 square units. Then by moving two more matches, reduce the area to 4 square units. Finally, move two more matches, and reduce it to just 3 square units.....