Professor Harold Thimbleby gives many talks to school audiences and science festivals. He has given talks at the Royal Institution, British Association annual conferences, Edinburgh Science Festivals, and at many schools around the country. |

Lecture at the Royal Institution: Harold looks on while a student (white shirt) turns the prop shaft of a Land Rover 90 rear axle. The closer student (dark top) grips the near wheel, and we can see how the differential handles slip. |

*Mud and Maths* take the lids off
differentials and explains the maths behind how cars stay on roads, and how four wheel drive cars stay in control in mud.

When a car goes round a corner, all its wheels go at different speeds. If they went at the same speeds, some of them would slip and the car could skid out of control, or if they didn't slip it'd be impossible to steer. In mud all the wheels slip, and they go at different speeds even when driving in a straight line! How does a single engine drive the wheels at different speeds so that they each grip? Mathematically, the car solves some equations. Mechanically, it uses differential gears. Ordinary cars have a single differential, which gives them good performance on the road, but a car like a Land Rover has three — and the maths gets muddier and the driving more exciting or is it that the driving gets muddier and the maths more exciting?

- The lecture is typically illustrated with various Lego models, but if the lecture can be given near my home in Hertfordshire, I can bring some real differentials — they are too heavy to carry otherwise!
- This lecture can be aimed at any level; from "
*a*+*b*=*c*" maths (which car differentials do) to vector arithmetic. A little knowledge of Newton's Laws (*F*=*ma*) and friction (*F*<µ*N*) will be useful but not essential.

Calculators have been around for centuries, and they were one of the first handheld computerised gadgets. They are now to be found inside mobile phones, on desktop computers, even in wristwatches. This lecture demonstrates, with participation, that current everyday calculators can easily give wrong and misleading answers. They also have surprising and severe mathematical problems, which can catch people out. They are much harder to use than they need be. The talk reviews the straight-forward maths behind calculation and calculators, and provides a solution to the surprising range of problems identified. A calculator will be demonstrated and compared with commercial systems (which are all worse).

*Please come with your own calculator.*

The talk will be of interest to **anyone** who uses calculators.

Computers are used everywhere, and we are all supposed to be "computer literate." Yet most computer literacy is about plugging in computers and getting them to do boring office work. There is a lot more to computers that is fun and interesting, and has nothing to do with work. Let's unplug them, look at their principles and see what computers really can and can't do.

The hands-on talk discusses the successful (and fun) educational approach, which has been used for motivating people from children through to undergraduate and postgraduate computer science students.

There was a craze about 3D pictures (autostereograms or "magic eye" pictures) a few years ago. How do they work, and how do computers draw them? The talk will also cover how 3D (binocular) vision works and will show off several very interesting optical illusions.

See my other web page on autostereograms.

Keeping secrets is one of the earliest inventions of civilisation, and has become the science of cryptography. The World War II Enigma machine was just lots of scrambling, done in ways that could be understood in principle by a school child — though it took daring and powerful computing to crack it. This talk introduces the key ideas behind conventional cryptography, and explains why it is not good enough for modern applications such as international commerce on the Internet.

This 'home made' model Enigma is used to send and decode secret messages. Real Enigmas have 26 keys; this one has 4 to make everything much easier to understand. |

Pressing buttons on a mobile phone chooses various functions, as if the phone's functions are controlled by a code. Mobile phones are conceptually difficult to use almost entirely because their code is difficult to use. We can design a new code systematically, and using Huffman codes, we can find one that is much faster and simpler than the manufacturer's original code.

*Please bring your own mobile phones, and race Harold's programs.*