Have you met Linda?

Here's an interesting factoid you probably didn't know about yourself. Let me introduce you to Linda.

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

Go ahead, pick one.

If you're like most people, you picked the second one. However, that's not correct. Why? Answer this similar question.

Consider of a room containing 100 people.

How many of those people are:

1. bank tellers?
2. bank tellers who are also active in the feminist movement?

Which set of people is larger? Of course, option one contains all bank tellers, both feminist and non-feminist.

This is an example of the conjunction fallacy, in which people answer the probability question by instead thinking of plausibility. But when you're asked the same question in terms of concrete numbers (instead of percentages), you are more likely to answer correctly.

I got this from Thinking Fast and Slow, by Daniel Kahneman.

Phase precession

This amazing video has something to do with phase precession in magnetic resonance imaging (MRI). Discuss...

Are chimps closer to humans or gorillas?

This question occurred to me recently. Which species do chimps share a more recent ancestor, humans or gorillas? So I looked it up. According to the paper

Rannala, B. and Yang, Z, "Probability distribution of molecular evolutionary trees: A new method of phylogenetic inference", Journal of Molecular Evolution, 43(3): 304-311, 1996.

the most likely phylogenetic tree (based on genetic nucleotide sequencing data) looks like this,

Hominidae is the family of great apes, containing us (genus Homo), chimpanzees (Pan), gorillas (Gorilla), and orangutans (Pongo). As you can see, the chimps share a more recent ancestor with us than with the gorillas. In other words, chimpanzees are more closely related to humans than they are to gorillas.

Neural Adaptation

This is a demonstration of neural adaptation. When a neuron is continuously excited by a stimulus, its firing rate decreases after a while; this is called adaptation. But when you remove the stimulus, the neural adaptation affects your perception.  Here are two demonstrations of the effect.

Colour Adaptation
Stare at the red nose on the left for about 30 seconds. Then shift your gaze to the white panel. What do you see?

Motion Adaptation
Click on the image below and follow the instructions.

Nerd jokes

A Mathematician, a Biologist and a Physicist are sitting in a street cafe watching people going in and coming out of the house on the other side of the street. First they see two people going into the house. Time passes. After a while they notice three people coming out of the house.
The Physicist says, "The measurement wasn't accurate".
The Biologists says "They have reproduced".
The Mathematician says, "If a person enters the house, then it'll be empty again."

Three statisticians went duck hunting and they saw a duck flying.
The first statistician fired his gun, but the shot went a metre too high.
The second fired his gun but the shot went a metre too low.
The third statistician cried, "Bullseye!"

Timecube

If you think the brain is infalible, check out the Time Cube web page. Dr. Gene Ray, the author, is the self-proclaimed "greatest philosopher" and "greatest mathematician", and I think even his title of "doctor" is self-assigned. Enjoy.

Yes... I mean, No.

You might have seen this optical illusion. Step back from the screen and determine which side is angry, and which is happy. Then approach your computer, and ask the same question.

How do they do that?

Your visual system is tuned to certain spatial frequencies, so you tend not to notice image content of frequency higher or lower. I did an experiment and created my own version of this optical illusion. I started with these images.

Then I applied a lowpass filter to YES, and a highpass filter to NO. That gave me these images.

Adding them together gives this image...

Yes, your visual system acts as a filter (as does every optical system).