Transmission impossible

Your will can create the future, one step at a time. Impossible as it seems, in this astounding display of your ability to control the future actions of others, you take a freely shuffled pack of playing cards, letting your volunteers freely select pairs of cards, it might be a red pair, a black pair or a mixed pair, when the experiment is over you show that what they believed were free choices were in fact controlled by your will, you predicted exactly what they do! To prove these reality altering skills aren’t just luck, you repeat the experiment, and again show your inhuman ability to correctly manipulate their free choice.

It's all in the cards (and the card box)

First the secret set up. Remove 4 red cards from the pack and place them in the card box, without letting anyone know you've done this. You explain that you can control future events. Give the volunteer the cards (that’s 52 minus the 4 reds). The pack will look and feel normal – people wont notice that the pack is missing the 4 cards secretly hidden in the box.

You need to predict the future. It's simple – get a sheet of paper and a pen, and write 'there will be 4 more black cards' on it. Fold this and place it in clear sight so that no-one can see your prediction. Than start the acting. Have the spectator shuffle the (incomplete) deck. Shuffling reinforces the idea in the spectator's mind that what's about to happen is the triumph of magic over chance.

Two by two it’s up to you

Retrieve the shuffled pack, then start to turn over cards two at a time. If they are both red put them to one side. If they are both black, put them to the other side. If you get one red and one black, then pop them out of the way into the card box. (Make sure that when you put the first mixed pair in, you don’t reveal the hidden red cards). Here's where you can really play with the spectator. let them shuffle the pack again if they want, or spread the cards and have them select any two. Just remember to stack up the red-only and black-only pairs, and discard the mixed red and black pairs into the box.

Prediction one is full of fun

Once all the cards in the pack are finished, you prepare for the first reveal. Remind your specatator that you wrote the prediction before they started, and that they selected pairs of cards absolutely freely, a 'random' number of red pairs, black pairs and mixed pairs. Now get them to count the red pairs on show, and then count the black pairs, and open your prediction. It will be spot on: there will be exactly 4 more red cards!

Prediction two, is because of you

Tell your spectator that normally you can never have the psychic energy to repeat your amazing feat, but this time you will make an exception for them (people like to feel special). Put all the cards together in a pile, including the ones you put away in the card box. As your spectator shuffles this (now complete) pack you make your second prediction. You write 'same number of red cards as black cards'. Do the random selections, shuffles and so on as before, placing red pairs to one side, black pairs to the other and mixed pairs in the card box. After this, have the punter count the red pairs and black pairs and then read your prediction. Again, incredibly, it's correct! You’ve proven twice that you have the mind powers to force their choices.

Mind powers, what’s the theory?

If you take a full deck of cards, half are red and half are black. Selecting any two at random they can be both red (RR), both black (BB) or mixed (RB or BR). Let’s get theoretical, and think about one situation that could happen, but probably wouldn’t. Suppose, for argument's sake, that you never select any mixed pairs. At the end the total number of red pairs would need to equal the number of black pairs, as there are the same number of reds and blacks in the pack, and we assumed no mixed pairs are selected. Suppose you now secretly removed 4 red cards, as in the first prediction, then again if we assume there are no mixed pairs chosen, at the end counting the all the cards in the RR and BB pairs, there will always be 4 more black cards. It has to be this way, as four red cards have been secretly removed.

Mind powers in reality?

Now consider the case in real life. There will fairly certainly be some mixed pairs chosen. Each mixed pair RB or BR, will equally prevent a future RR or BB pair from happening, so as mixed pairs occur the number of red and black cards remaining in the pack reduce by one card each – one less red, and one less black. If it’s a full deck, like in prediction 2, then each mixed pair will equally reduce the final number of any red and black pairs selected. Each mixed pair selected and removed is like using a deck with one card of each colour removed. At the end the total number of cards in the red pairs pile and in the black pairs pile needs to be equal. But of course exactly the same reasoning as before applies if you’ve secretly removed the 4 red cards first. Any mixed pair will reduce the number of possible future RR and BB pairs by one each, but the cards remaining in the deck have 4 less reds, so at the end, after all the selections, you will have two more BB pairs, which means 4 more black cards.

Things can only get better

We've just started with a theoretical situation which, while not very likely, let us form ideas about things work. We then refined our theory to reflect real life. Scientists (and especially computer scientists) use this form of reasoning a lot. Mathematical theories often need to be modified when they are applied to real situations. But understanding how to make the right changes to account for the workings of the real world can often allow us to correctly predict the future mathematically, and create interesting new software.