Episode 13: Vectors, matrices and hearing

This week the topic was vectors and matrices. We interviewed Dave Langers, who studies the human brain, and how it processes hearing signals. We talked about how Dave uses matrices and vectors to store information from brain scans, which allow him to manipulate the information more easily.

Interesting links:

• Matrices, on Khan Academy
• Matrices at Maths is Fun
• Matrix multiplying at Maths is Fun
• Auditory system on Wikipedia

Puzzle: Using the vectors (1,3,1,3), (2,2,6,6) and (4,8,8,12), by taking multiples of each and adding them together, find a combination which adds up to (0,0,0,0). You must use all three vectors at least once.

Solution:

2 × (1,3,1,3) - (2,2,6,6) - (4,8,8,12) = (0,0,0,0)
This can be achieved using other combinations too - for example, if you multiply all the vectors on the left of this equation by the same number, you’d also get a zero vector.