Category Archives: Rants and Musings

A Card “Force” Using Unintuitive Mathematical Odds

“A card force is one of any number of methods used in close-up magic to apparently offer a subject a free or random choice of card, when in fact the magician knows in advance exactly which card will be chosen. This can then be revealed later in the trick.”

Premise: We have a set of three cards, all of which are known to us. We attempt to force a specific card on the unsuspecting participant by instructing them to randomly point at one of three cards, which are all laying face down. Theoretically, they have a one in three chance of picking the correct card randomly. If they point at the desired card, we immediately instruct them to flip it, effectively “forcing” the card on them in one try. If this works on the first try, the trick will be especially impressive. However, if it doesn’t work on the first try, we still have a fall-back method:

If they point at one of the other cards, instead of telling them to flip the card, we pretend that they’re playing a game of elimination and we simply remove the card, instructing them to point again. If they point at the next incorrect card, we instruct them to remove it, leaving one final card: the correct one.

Potential downside: If they point at the desired card on the second step, then the “force” fails,
because when we remove it, the end card will actually be the incorrect one.

Cards used: Ace of Hearts (the desired card), Queen of Clubs, and 8 of Spades

Approximate Results After 2000 Simulations:
Times ended on Ace of Hearts: 1322 (0.661)
Times ended on Queen of Clubs: 339 (0.1695)
Times ended on 8 of Spades: 339 (0.1695)

Click here to run the simulations yourself using javascript

Odds of picking the right card during the first step: 1/3. If incorrect card is chosen on first step, we pretend it’s an elimination game and remove the card, leaving only two cards, the desired card, and the incorrect card. At this point, you might think there is an even 50/50 chance they will choose the correct card, but in reality, the odds of them choosing and eliminating the desired card are still 1/3 because it hasn’t been touched. The odds of them choosing and eliminating the second incorrect card, however, have increased to 2/3. This is unintuitive, but the simulation shows it to be true.

Because of the fact that we know which cards are which, we can effectively double our seemingly low 33% odds all the way to 66% simply by using this card force method.

The only unsolved problem is, how do you handle a dead end where someone chooses the wrong card, and then the right card on the second step?

Litmus Test for Door to Door Sales

If I ever get down on my luck, I’m totally going to start a business selling “No Soliciting” signs from door to door.

The way I see it, it’s practically a guaranteed sale…

“Sorry, we’re not interested in whatever you’re selling! In fact, we hate door to door sales people!”

“Well in that case, you’ll love this sign!”

The best part about it is that if they don’t buy the sign, you can just come back every week until they do. After all, they don’t have a sign saying you can’t!

Backwards Alphabet

As I was laying in bed last night, looking up at the ceiling and trying to fall asleep, a revelation came to me: I don’t know the alphabet backwards.

Now, this is a real problem. I mean, what would I do if a cop pulled me over for an impromptu alcohol test? I can imagine it now, “Mr. Chapin, please stand on one leg, touch your nose with your index finger, and recite the alphabet backwards for me”. To which I would reply, “err… uh… but I can’t!”, and would end up in jail even though I was sober as could be.

These are the kind of thoughts that go through my head whenever my body is inactive and my mind refuses to shut off (usually when I’m either attempting to go to sleep, or when I’m taking a shower). Yup. Some of my best insights take place while I am washing my hair.

So anyways, I immediately set about to teach myself the alphabet backwards. To make it interesting, I resolved to do it all entirely in my head without using a piece of paper or writing device even once. This may be ridiculously easy for some of you, but I’m one of those people who can only recite the alphabet in sing-song. Take away the song, and I’m lost even when I’m going forward! Whenever I’m indexing things in alphabetical order (like a file cabinet, for instance), I end up singing the alphabet song in my head every time I need to figure out whether “e” comes before “f”. This usually means that the alphabet song gets sung in my head a couple hundred times before I’m finished.

Ah. The dangers of learning things in sing-song…

Here’s the method that I contrived and used to re-teach myself the alphabet both forwards and backwards while I was laying in bed:

1. Sing the alphabet in my head to find the first three letters, “abc”.
2. State the three letters in my head to myself again, but this time in normal tone, “abc”.
3. Reverse the three letters and state them to myself again, “cba”.
4. Mentally draw the shapes of the letters in forwards order.
5. Mentally draw the shapes of the letters again, but this time in reverse order.
6. Repeat until it feels “natural”.
7. Repeat steps 1 through 6, over and over, making three letter sequences for all the letters in the alphabet: abc, def, ghi, jkl, mno, pqr, stu, vwx, yz
8. Practice chaining together the first couple of sequences in my head, “abc, def”.
9. Practice chaining together the same sequence, but this time in backwards mode, “fed, cba”.
10. Repeat until it feels “natural”.
11. Repeat steps 8 through 10 to chain together the remaining sequences.
12. Haltingly practice saying the alphabet backwards, one sequence at a time, “zy, xwv, uts, rqp, onm, lkj, ihg, fed, cba”.
13. Repeat over and over until it feels “natural”.
14. Speed up recitation and attempt to find the sing-song rythm, “zyxwvut srqponmlk jih gfe dc b and a”.
15. Go to sleep and let my subconscious mind ponder the changes to my brain.
16. Wake up in the morning and recite the alphabet forwards and backwards while taking a shower.
17. Recite forwards and backwards both before sleeping and after waking up, for an entire week.

Satellite Imagery/Video of the USA from space

Satellite Image

What would you think if the government was recording live satellite video imagery of the entire USA, up close? What if a crime was committed but wasn’t discovered till later on? The government could literally rewind time and track the entire path of the escape vehicle, leading to the arrest of the perpetrator.

According to the wikipedia, the USA is approximately 3,718,711 square miles in size.

Using these numbers, if you were to take the USA and squeeze it into a flat, square shape,it would be approximately 1,928 miles in width and 1,928 miles in length.

If you were to photograph the USA at 431,309,824 pixels per square mile (approximately three times higher resolution than current internet satellite/aerial imagery gives you), then you would use 1,603,257,976,815,616 pixels to photograph the entire USA.

If we saved this image off without compression as a 2 bytes per pixel image, then the file size would be 3,206,515,953,631,232 bytes, or around 2,917 terabytes in size.

With a typical compression algorithm, you could theoretically get it down to around a third of that size… probably around 960 terabytes.

Now, let’s theoretically record this area at 30 frames per second. At first glance, you’re probably thinking, “whoa! 28,878 terabytes a second???”. But you have to remember that this would be video you’re dealing with. A good video compression algorithm would only record the differences between frames. And trust me, a TON of those pixels aren’t going to change noticeably in that small space of time. Pretty much all you’d be recording would be people and vehicles moving across the face of an otherwise static and unchanging image. So let’s just say that less than 1% of that square mileage would appear to have moved at all.

Which means you’d probably have less than 5 terabytes worth of image differences per frame. At this estimate, 1 second of video would only take up around 150 terabytes (not 28,878). This means that we could record the USA at 540,000 terabytes per hour. Assuming that we took a complete snapshot of the entire USA every single hour (960 terabytes), then 24 hours of the USA would take up around 12,678 petabytes.

This may sound like a completely absurd size, but it’s not so mind-numbing when you think about the new holographic data storage technologies that are being developed right now. Terabytes will be cheaper than megabytes are now.

What if they only recorded major cities for now, and they were to do it at only, say, 5 frames per second? Or even just one frame per second for starters? They could still track vehicles and do basic surveillance.

In the mean time, check out this massive 18,000×18,000 pixel image that was taken by the Hubble telescope!