The Clairvoyant Penny

Mathematician Thomas Storer offers a foolproof way to foretell the future: Flip a penny and ask it a yes-or-no question. Heads means yes, tails means no.

How can you be sure the answer is accurate? Simple: Flip it again and ask, “Will your present answer have the same truth value as your previous answer?”

Suppose the answer is yes. This is either true or false. If it’s true, then the original response was true. If it’s false, then the truth value of the original response is not false, i.e., it’s true.
If the answer to the second question is no, this too is either true or false. If it’s true, then the original response was true. If it’s false, then the original response was not false, i.e., true.

Since all the outcomes agree, the penny’s original response is guaranteed to be correct.

January 18, 2009September 15, 2010 | Science & Math

Logical

Raymond Smullyan doesn’t believe in astrology.

When asked why, he says, “I’m a Gemini.”

January 17, 2009January 17, 2009 | Science & Math

A Cosmic Coincidence

Light travels 186,000 miles per second. The average diameter of Earth’s orbit is 186 million miles.

So, on average, sunlight reaches us in a neat 500 seconds.

January 16, 2009 | Science & Math

Digit Acrobatics

digit acrobatics

January 13, 2009September 18, 2010 | Science & Math

Quine’s Paradox

“Yields a falsehood when preceded by its quotation” yields a falsehood when preceded by its quotation.

January 8, 2009January 8, 2009 | Science & Math

Easy as Pie

Now I will a rhyme construct,
By chosen words the young instruct.
Cunningly devised endeavour,
Con it and remember ever.
Widths in circle here you see,
Sketched out in strange obscurity.

Count the letters in each word.

January 7, 2009January 6, 2009 | Poems · Science & Math

One Solution

The Professor brightened up again. ‘The Emperor started the thing,’ he said. ‘He wanted to make everybody in Outland twice as rich as he was before — just to make the new Government popular. Only there wasn’t nearly enough money in the Treasury to do it. So I suggested that he might do it by doubling the value of every coin and bank-note in Outland. It’s the simplest thing possible. I wonder nobody ever thought of it before! And you never saw such universal joy. The shops are full from morning to night. Everybody’s buying everything!’

— Lewis Carroll, Sylvie and Bruno

December 28, 2008 | Science & Math · Society

Couch Logic

Your vote will make a difference only if it breaks a tie or creates one.

This is very unlikely to be the case.

So why vote?

December 27, 2008 | Science & Math · Society

Math Notes

9⁹ + 1⁹ + 2⁹ + 9⁹ + 8⁹ + 5⁹ + 1⁹ + 5⁹ + 3⁹ = 912985153

December 26, 2008December 26, 2008 | Science & Math

The Mpemba Effect

When University College physicist Denis Osborne visited Mkwawa Secondary School in Iringa, Tanzania, in 1963, he little expected the question he got from student Erasto Mpemba:

“If you take two similar containers with equal volumes of water, one at 35°C and the other at 100°C, and put them into a freezer, the one that started at 100°C freezes first. Why?”

The other students derided Mpemba, but he was right — in cooking class he’d noticed that hot ice cream mixes froze more quickly than cold ones.

Osborne confirmed the effect and shared a publication with Mpemba in 1969. What’s behind “the Mpemba effect” is still something of a mystery — it seems to be a combined result of supercooling, convection, evaporation, and the insulating effect of frost. (If you want to conduct your own experiment, start with containers at 35°C and 5°C.)

December 20, 2008March 19, 2010 | Science & Math