Mathematical Conversation Starters: Talk Monday, April 7

Mathematical talk 2Prof. John DePillis

Department of Mathematics, University of California, Riverside, author of  777 Mathematical Conversation Starters   and   Illustrated Special Relativity Through Its Paradoxes

WHERE:  Health and Public Affairs Building I, Room 112

WHEN:    Monday, April 7, 2014, 3:40 – 4:40pm


USING BASIC LINEAR ALGEBRA as a natural language of special relativity, and assuming very little knowledge of physics, we present a novel linear-algebraic derivation of the Lorentz transformation. Through the geometry of Minkowski diagrams, we analyze properties and paradoxes of special relativity.

A BASIC ASSUMPTION of special relativity (SR) is that the speed of light in a vacuum is the same for all observers regardless of their speeds or the speed of the light source. Consequences of this simple axiom are profound. For example, rods in motion shrink in the direction of motion, and clocks in motion always run slower than stationary clocks.

One twin leaves Earth in a fast rocket ship and after fifty years, say, returns to Earth, having aged only 30 years. But if each twin is in symmetric motion relative to the other, why do the twins age at different rates?

Rigid systems are incompatible with SR usually because the motion of some rigid systems force certain particles to travel faster than the speed of light. However, we show in the bug-rivet paradox that rigidity can also cause time reversal in the sense that effect occurs before its cause.


Talk will address the following questions:

How does mathematics conflict with our notion of free will?

Did Aristotle assert that women have fewer teeth than men do?  And if he did, how did he get away with it?

Can it be that Sherlock Holmes never deduced anything?

How does our mind “do” algebra on its own without our realizing it?

Does Infinity deserve a semi-mystical status?

Does the fourth dimension deserve a semi-mystical status?   Are three dimensions necessary for our existence?

Can a quart of ink paint an infinite area?

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