The Zebra Puzzle

There are five houses.
The Englishman lives in the red house.
The Spaniard owns the dog.
Coffee is drunk in the green house.
The Ukrainian drinks tea.
The green house is immediately to the right of the ivory house.
The Old Gold smoker owns snails.
Kools are smoked in the yellow house.
Milk is drunk in the middle house.
The Norwegian lives in the first house.
The man who smokes Chesterfields lives in the house next to the man with the fox.
Kools are smoked in the house next to the house where the horse is kept. [should be “… a house …”, see discussion below]
The Lucky Strike smoker drinks orange juice.
The Japanese smokes Parliaments.
The Norwegian lives next to the blue house.

Now, who drinks water? Who owns the zebra? In the interest of clarity, it must be added that each of the five houses is painted a different color, and their inhabitants are of different national extractions, own different pets, drink different beverages and smoke different brands of American cigarets [sic]. One other thing: in statement 6, right means your right.

Zebra Puzzle – Wikipedia, the free encyclopedia

Return to free will

The following is a comment I made on the “Infant Power” post in response to Bobmo’s question “Do you suspect that humans have free will?”

I suspect that humans do not have free will, but I am open to the possibility that we do.

But here is my question. How do you go about testing humans to find out if they have free will?

I suppose the opposite of free will is determinism. In a deterministic world if you know all of the variables and rules you can work out what will happen in the future.

We don’t know all the variables and rules and we are not very good at working out what will happen in the future in a very specific way. Does that mean free will exists in this world? I don’t know.

Even mechanisms that are relatively simple can produce behavior that is hard to predict. For example, the Chaos Wheel is a simple water wheel that will spin in one direction for a while and then begin to spin in the opposite direction. As time goes by it changes direction many times and at odd intervals. Does it have a brain and does it choose it’s direction? No. But nevertheless it exhibits complex behavior.

IBM’s Watson is much more complex than the Chaos Wheel and it exhibits even more complex behavior. Watson was designed to play the quiz game Jeopardy and is quite good. Deep Blue was a computer built to beat humans at Chess and it succeeded. Deep Blue analyzed many possible chess moves and then “chose” what it “thought” to be the best move. Did Deep Blue really make choices?

Could it be that humans are highly complex machines made of organic molecules? I think it is possible. The Human Connectome Project is working on mapping all the connections in a human brain. Even after the project has mapped a brain we will still not understand everything about how the brain works. But this project will move us forward in our learning. Sebastian Seung gave a presentation at the TED conference on this subject.

With so many questions unanswered how can anyone say definitively if humans have free will. Is it possible? Yes.

Art Benjamin: Mathemagician

Arthur Benjamin: Lightning calculation and other “Mathemagic”

In this video Arthur Benjamin calculates squares of 2, 3, and 4 digit numbers faster than you can do it on a calculator. I know. I tried to keep up while watching the video. Audience members give him their birth date and he tells them what day of the week they were born. Wait until you see what he does for his grand finale.

[Edit: Fixed YouTube link]

Millions more

Because I am fascinated by large numbers, I present here a paraphrased version of the story of the rice on the chessboard.

A man who lived in a wealthy kingdom had performed a great deed. When the King learned of this he decided to reward the man and asked him what he would like as his reward. Seeing a chessboard (8 squares on a side) in the King’s chamber he asked for one grain of rice to placed on the first square, 2 on the second square, 4 on the 3rd, 8 on the fourth and so on, to the last and 64th square. The King, not fully understanding the implications of this request, said that he would gladly reward the man as he stipulated and ordered that the rice be brought in. Things began nicely, but the amount of rice required for each square quickly became enormous. The 21st square required more than a million grains rice. The 41st square required more than a trillion grains and the ruler exhausted all the rice in all the land before he reached the 64 square.

I have created 21 images, each with twice as many pixels as the previous one, to demonstrate visually exponential growth. I have assembled them on a separate page because they are too large (2,000 x 2,000 pixels, but only 32 kilobytes) to fit the format of this blog. If I had created all 64 images the largest one would have been over 4 trillion pixels wide. On most computer screens there are 72 pixels in an inch so it would require a screen 941 miles wide to view the image at full resolution.

See my visual representation of geometric or exponential growth here. It is much more dramatic than a simple line on a graph.

One trillion

I’m sure you’ve seen this before, but I liked it so much I thought I’d pass it on:

1,000 (thousand) seconds = 17 minutes ago
1,000,000 (million) seconds ago = December 7, 2008
1,000,000,000 (billion) seconds ago = 1976
1,000,000,000,000 (trillion) = 29,702 B.C.

Feel free to check my numbers.
86,400 seconds = 1 day
31,536,000 seconds = 1 year