Why isn’t this one of the most amazing thing’s ever? (Updated)
Please note, I have changed my mind on the below and summarised this at the end of the post:
Introduction
Suppose I found a theorem that pertained to Euclidean geometry; the kind of geometry which we did at school. I would be the first person to discover such a theorem in over two millennia. I might well win a cash prize and maybe a couple Nobel's. It would be pretty big news...
"Hey are you that guy who found the first new Theorem applicable to the Euclidian 2 space in over twenty five centuries?"
"Sure am."
"You like the maths version of Bono."
"Thanks."
But allow this day dream of maths geniuses (I'm bad at maths) and suppose that I then showed you three new theorems that, like the first, were also utterly new to human mathematics. At that point, I think we might both agree, my discoveries would be pretty huge; I would probably be up there with Alan Turing or or maybe even Carol Vauderman.
But I could go higher!
Suppose I tell you, and many other mathematicians, that there is a fifth theorem. I explain that this fifth theorem is related to the other four theorems and then, with this big head start, I ask you all to find it. For the sake of overkill, suppose I arrange have a competition in a maths magazine and I give the world a year to try to find this Theorem.
Time passes...
A year later nobody has found the fifth theorem that I claim to have found. When you all give up, and I make sure your fingers weren't crossed behind your backs, I let loose with the big gun, the Fifth Theorem.(Actually it’s not actually the big gun, that comes next, but you wouldn't know this yet...)
You look at the Fifth Theorem and say something like, "OMFG Doh! That's so obvious...," as do all your other maths buddies.
But...
Just when y'all all think I can't go any higher, I lay down the cherry-on-top-big-gun-guitar-solo... Very simply I point out how the ratios in the theorems’ elements are all perfect diatonic notes; they correspond to each other as do keys on a piano. Naturally you appreciate that not on is this pretty nifty in its own right it’s also the first time in history that such a geometrical relationship has been discovered.
I think, at this point, the beers would be on you....
While Euclid wept, Jimmy played guitar.
The above really happened.
In the mid 1990's an Astronomy Professor at Boston university called Gerald Hawkins discovered these five new geometry Theorems and, in addition, he discovered the musical relations within them. None of this is in any dispute (as I currently understand it).
It is monumental, but I suspect that the reason it is so unknown is that Professor Hawkins demonstrably discovered all of this new human knowledge within fifteen crop circles dotted around southern England in the early nineties
I have been a huge crop circle skeptic since a friend’s dad was into them twenty years ago. He had loads of books on them and I, like most, thought it was all hogwash. These thoughts remained so until last week when I heard about Hawkin's theorems. They do seem to me to be pretty special evidence that some cropcircles really are not made by any known intelligence.
What should we think?
Should we, like the Guardian’s Obituary of Hawkin’s or the media at large, just ignore this strange revelation or should we at least try to see what it could possibly be and mean?
Here is how I see it...
What is special about this case is not the fact that the messages were in crop circles it is the fact there seems to be in existence items of anachronous foundational information.
The information is foundational because these theorems do belong to an ancient set of mathematical information that hasn’t been faulted and is consistent with the corps of mathematics. The information is anachronous because it doesn’t seem to belong in this time, or, unexpectedly, Euclid’s time.
Let’s get even finer grained and forget about the geometry and images and claims and focus on one theorem, say, the first. Hawkin’s First theorem states that:
The ratio of the diameter of the triangle's circumscribed circle to the diameter of the circles at each corner is 4:3.
Let’s label this statement H. It doesn't matter what H says, the point is that H is true and it has been true for all points in human history.
So the unexplained core of this issue can be reduced to down to the path of humanity’s knowledge of H throughout history.
I can see three reasonable possibilities:
- H was discovered by Euclid but lost or for some reason suppressed until for some reason, possibly hoaxing, it was publicized in cropcircles in the early 1990's
- H was discovered at some point since Euclid but lost or for some reason suppressed until for some reason, possibly hoaxing, it was publicized in cropcircles in the early 1990's
- H was never discovered (in human history) until Gerald Hawkins discovered it 1995.
As you can see, even if you want to dismiss H’s revelation as part of a long term complex and very unusual hoax that for at least twenty years hasn’t had any whistle blowers or debunking (The hoax would have had to have started before 1990) you still have an awful lot of explaining to do.
The “planks and string” response doest work here because what’s important and really mysterious is the existence of H not its medium of conveyance. We would have the same essential anomalies if Hawkins had been emailed the diagrams rather than stumbling upon them by chance.
So trying to explain 1 and 2 isn’t an easy task that you can glibly shrug off, there is a real mystery here whatever way you look at it.
I think it is very reasonable to assume that 3 is true, that H and its kin were put in those circles for a reason by an intelligence civilization is not aware of. For sure this view deserves ridicule and sceptical denial, but so do the alternatives and moreover the alternatives involve complities and conspiracies that the simple “some unknown intelligence” doesn’t.
Conclusion
Perhaps someone will drop me a mail saying “Dude, there are thousands of theorems like this found every year” or “Hey, you know these five theorems were known about by Islamic/Chinese/Indian mathematician for millennia?” And that would be great, one of the good things about a sceptical outlook is that there is reward in your convictions either way.
But there is no clear way to be convinced here, unlike, as far as I am aware, all other mysterious phenomenon and information.
I look forwards to your debunking and shall leave with a thing to ponder...
Imagine you were some other, higher, intelligence (God, Alien, Time-traveller, intradimensional funk being...). Imagine for whatever reason you were trying to communicate with Humanity en mass, the planet as a whole. After trying books, patterns on toast, voices in the heads of madmen and all that jazz you decide to use your powers (technology or magic) to message humanity using big symbolic displays that all can see. The best method for this you determine to be flattening huge areas of plant life in intricate advanced patterns that convey your message.
Annoyingly for your divinity we “stoopid humans” can’t seem to get past the conclusion that as some cropcircles were hoaxes, therefore all must be, and so we humans never reay get your message. Rather than give up on us just yet you decide to do something... irrefutable ( As opposed to "IRRESPRESSIBLE!").
You decide to send messages that contain information that we humans do not have and that when we get we cannot doubt as being true and external to our knowledge sphere. This way you know that we just won’t be able to rationally conclude your messages are hoaxes.
What information would you send?
Relevant Links
- This is a detailed and reputable essay from the Mathematical Association of America on the Theorums.
- This is a transcript of a 1992 Share International Magazine interview with professor Hawkin's about these Theorums.
- This is maths heavy but has some nice photos of the actual crop circles Hawkin's used.
- For a final puzzle ask yourself what's strange about Hawkins obituaries in The Independent, The Guardian, The NY Times, The Telegraph - they either don't mention the Theorems or misquote him from this interview. Perculiar!
- This PDF looks super maths heavy. It is a proof of the theorems and more...
Update
