**Chalices everywhere!**

I’ve had a couple of comments on this story that may be borderline spam, but since they have to do with chalices they’re certainly right up our alley.

They point to this site, which is peddling a theory that Leonardo da Vinci’s paintings are full of hidden images.

Briefly, the argument is this: that when you flip one of Leonardo’s paintings, and place the reversed image next to the original, you see shapes. Especially you see chalices, or closely related forms of stemware.

“We asked a probability expert [to] form a proper hypothesis and to do a calculation relative to the probability of the discoveries being random or coincidental based on these facts.” Not surprisingly, the probability expert decided that there was no possibility that the discoveries were random.

I think the probability expert is all wrong.

First of all, let me say that I know very little about statistics. Let me also say that, for the purposes of this argument, I don’t have to know a whole lot about statistics. No complicated mathematics will be involved. A bit of multiplication, but we have calculators for that.

So, first, what’s the probability of finding a *random* image (not stated beforehand) in a rich and complex painting flipped and set beside the original? About 1 in 1, I’d say. You *will* find something if you keep looking. You will also find an image in the wood grain on your desk if you keep staring at it, or in a marble floor.

Now, on to the probability of finding a *particular* image at random. Here is where it gets a little more complicated, because there’s an enormous difference between declaring what the image will be *before* you find it and declaring what it was *after* you’ve found it.

Suppose I have a room ten feet long by ten feet wide, and suppose I have the floor marked in one-inch squares. That makes 14,400 squares, which we’ll number according to their positions along the length and width of the room. For example, one corner will be square L=1, W=1; the square next to it will be L=2, W=1; and so on.

Now, if I close my eyes, spin around three times, and throw a penny into the air, the odds of its landing on any *particular* square are 1 in 14,400—a pretty high number. So if I tell you that the penny is going to land on square L=83, W=29, and then it does land on that square, you’ll be suitably amazed. I must be psychic, you’ll say. If I can do it again and again, I’ll be rushing to apply for the Amazing Randi’s million-dollar prize before it’s too late.

But suppose I don’t tell you before I throw the penny. Instead, I wait till it lands and then announce that it fell on square L=14, W=111. Amazing! The odds of its hitting that one *particular* square were 1 in 14,400! That can’t *possibly* be chance! Well, now you think I’m not really the brightest bulb on the Christmas tree. You patiently explain to me that the penny had to land *somewhere,* and although it’s true that there was a 1 in 14,400 chance of its landing on any *particular* square, it’s only amazing if I called L=14, W=111 *before* I tossed it.

You’re perfectly right, of course. Yet this basic error in statistics underlies more than half the conspiracy theories and supposed amazing discoveries you read about on the wonderfully weird web. It underlies the statistical argument against evolution.

The question gets more complicated when you start to have sequences of events—more complicated in the sense that the numbers get bigger. That’s really all.

Here’s an example: five random lines of text. I generated them at Random.org, so they should be random enough for our purposes.

icpbyldwcgbmsyogyljb

tteqvcckaihnrbyqyvgt

sgnmbgswbswdafgkbunk

jnmqzmclymnrdxhspocp

jbulylikiourtlpfbakc

Now, the odds of finding any one letter in any particular position are 1 in 26, since there are 26 letters in the alphabet. So, right off the bat, there’s only a 1 in 26 chance that the first line would begin with *i,* which it does.

The odds of finding any particular two-letter sequence in a particular position are 1 in (26 x 26), or 1 in 676, so it’s beginning to look extremely unlikely that the first two letters would be *ic,* and yet there they are.

Looking at the third line, I can see that the word “bunk” is spelled out at the end. What are the odds of that? The odds of finding any four letter sequence in any particular spot are 1 in (26 x 26 x 26 x 26), or 1 in 456,976. It simply can’t be random chance. Some invisible hand must have written that word as some sort of message to me.

Once again, if you thought I was serious, you’d be either amused or dismayed, depending on how well you liked me. Yet this is the sort of argument we’re facing in this comment.

Here is a general rule of statistical interpretation: whenever someone tells you that something can’t be random chance because the odds against it are astronomical, suspect a misunderstanding of statistics. The higher the stated odds, the more you should suspect a misunderstanding. Pretty much *every* event is extraordinarily unlikely if you use the ex-post-facto method of applying statistics, but that’s what we expect in a rich and varied universe.

All right, now for some fun. Part of our correspondent’s argument from probability hinges on this statement: “We searched a minimum of over 5000 paintings of the period and were unable to locate any use of the Perpendicular Mirror Process outside Leonardo da Vinci’s works.” In other words, 5000 paintings and no mirror chalices.

So I went to the wonderful Web Gallery of Art and looked at paintings of the Renaissance period. I picked the paintings as randomly as I could, which is to say I just started at the beginning of the As. Then I took a few paintings and subjected them to the Perpendicular Mirror Process. I didn’t look at 5000 paintings. More like a few dozen.

Here are some images I came up with. Note the prominent chalice shape in the center of each picture.

Andrea del Sarto: *Portrait of His Wife*

Andrea Del Sarto: *St. John the Baptist*

Bergognone, *St. Agnes*

(in this one, note also what appears to be the ghostly outline of a smiling mask!)

So I had no trouble finding chalice shapes. They’re all over the place.

After a while, I began to wonder just how easy it is to find chalices this way in pictures where human bodies are concerned. So I tried the same technique on a photograph of me, because I’m the only one I know who doesn’t object to being manipulated this way.

Christopher Bailey: *Self-Portrait*

Wow! Spooky, huh? This is starting to freak me out.

January 28th, 2008 at 7:39 pm

Chalices everywhere! Interesting follow up you write about the link provided in the previous comment on Chalices, so I went back to the original link http://www.lionardofromvinci.com/index.html provided and found that Mr Domoretsky and his research team were talking about a Chalice with a top and bottom to it and not what you present with your pictures above.

I also found that the research team was talking about a planned intersection within a sketch by Lionardo called The Virgin and Child with St. Anne and the infant St. John sketch:

Note: The Link is provided:

http://www.lionardofromvinci.com/Summary.html

Also is the link page to the Chalice found traced out for viewing purpose.

http://www.lionardofromvinci.com/Chalice1a.html

(Note:One of the keys to the encryption process is in identifying the location,angle and position of the line of planned intersection. Without

understanding the process by which the line is determined a viewer cannot place the mirror in the proper position to create the encryption plane and hence construct the hidden images. Determining how to locate the intersection lines is a tedious process, one that took 4 years of

trial and error to understand and apply.)

I also would like to mention that both pictures of Lionardo’s that the research team are pointing out in there study show a clear top and bottom to there “Chalice” and that the images you have represented in your process above “Don’t” at all.