I’ve found stereograms entrancing ever since I first managed to “see” one. If you can’t see them, try viewing these images on one of those shiny new LCD monitors and focus on your own reflection. Be sure the monitor is perfectly level, and your head is perfectly vertical. Then use your peripheral vision to search the image for a hint of 3D structure but keep your face in focus. With any luck the image should simply *pop* into view. (Unless your eyes point in slightly different directions… right?).

These images fascinate me because they’re essentially tricking my binocular vision into hallucinating objects when I look “through” a pattern of (almost) random noise. I used to make my own stereograms using a program called Surface 3D R2 by Andreas Moll (Traxxdale Software) but it no longer seems available so try these two free Win XP programs if you want to do this too.

The background pattern for these two stereograms comes from the Hubble Deep Field image which was developed by some of the oldest light in the universe. They’re puzzles with two-digit answers. Can you solve them?

Oooo! I’ve always loved these. When I was a kid, my family bought me three or four books of them. I even taught my gramma to see them, and that took some doing. To me, though, it’s always been really easy to see the images. I know some people need to hold the paper really close to their faces and then pull back, but I’ve never had to use any such trick. It’s just a matter of unfocusing your eyes so that they’re looking “behind” the paper rather than at it.

Anyhow, I particularly liked the first puzzle you posted — since it really was a puzzle and not just a matter of being able to see the image and recognize pi. Actually, the first puzzle still has me stumped. It APPEARS to be a sequence problem, starting in the bottom right with the answer blank in the top left, but I haven’t yet figured out the answer! I can think of several possibilities from the first four boxes (those on the bottom), but the next box (top right) keeps breaking my rules!

…WAIT. Just now, sitting here and looking at it again, I’ve figured it out. The thing is, I was spending too much effort trying to puzzle out the pattern to the FORMATION of the dots in each box (how many rows by how many columns) to lock onto the TOTAL number of dots in each box. Well, plus I’ve always thought 1 should be considered a prime number! (I mean, the only numbers 1 is divisible by is 1 and itself, right???)

Anyhow, the answer is thus 13 dots. In any (pyramid-stacking) order. Which is LAME. I would make it three rows of 5 dots, 5 dots, 3 dots, but that’s just me. :)

Thanks for the entertainment! Now stop distracting me from my dissertation writing! I need to get that done before AGU or I won’t have any time to play!

HA! I was starting to worry that I was the only one who could see them because I know what they’re supposed to look like.

And, you’re right– the second puzzle was basically a test to see if you could see the stereogram and recognize the number (not to mention reading the text, which was a real pain to make even remotely legible).

Oh, and 1 is kind of a lame prime. Screw 1.

(Actually, I forgot about 1. Gotta live up to my name, after all…)

Haha! One is AWESOME! It’s the RULER OF PRIMES!

After all, it’s the only number that ALL the other primes can be divided by. King of Primes!

I just found out that wikipedia claims 1 isn’t a prime number. Apparently this change happened in the mid 1900s. News to me!

If 1 were prime, the fundamental theorem of arithmetic wouldn’t be true: “each number has a

uniquefactorization (excluding the order of the factors) into primes.”If 1 is prime, 15 = 1*1*1*3*5 is just as valid as 15 = 3*5, which means unique factorizations aren’t possible.

If 1

isn’tprime, 15 = 3*5 is the only possible factorization, thus saving the fundamental theorem of arithmetic. Apparently there’s another obscure difference involving something called Euler’s totient function.Frankly, I’m surprised that I never ran into this2017 update: “Goldbach’s original conjecture (sometimes called the “ternary” Goldbach conjecture), written in a June 7, 1742 letter to Euler, states “at least it seems that every number that is greater than 2 is the sum of three primes” (Goldbach 1742; Dickson 2005, p. 421). Note that here Goldbach considered the number 1 to be a prime, a convention that is no longer followed.” Backup link: http://archive.is/NMvJ before. I certainly didn’t leave “1” out of that puzzle for any good reasons.

Bah! The silliness of mathematicians shows through! :) This is why I’m an engineer.