About Fuzzy Logic   

The Fuzzy Logic of A   
Loan Application   

The Fuzzy Logic of   
Crossing The Street   

The Mathematics of Getting a Speeding Ticket

Will the caller get a speeding ticket while getting there "as fast as I can"? Like all speeding tickets, it depends.

There are many scenarios possible based on different combinations of factors. Some factors are quantitative - the speed of the car, the posted speed limit, the time of day. Some are qualitative - the type of road, the color and make of the car, and the mood of the traffic officer. Sometimes the factor is luck - nobody is on patrol. Each scenario can spin into many different stories.

We will look at two scenarios around speeding tickets, and use graphs to show how the possible spins or stories on each can be pictured mathematically. The first spin is the story "according to the letter of the law". The second spin is one of the many stories that can actually happen in practice.
The first scenario has our driver in a school zone during the day. First the mathematical story is told using precise numbers and Boolean logic. This is the simplest, easiest solution and the least likely.

IN A SCHOOL ZONE

The Mathematical Story According to the Letter of the Law

According to the letter of the law only two things need to be considered - the speed of the car and the posted limit. Even if the driver is only driving slightly over the limit in a school zone, the yes/no of Boolean logic dictates that he should get a speeding ticket. 30 is an exact number, and assuming the radar reading is accurate, either he is over 30 KPH or he is not. There is only one story, and one ending.

In practice, the "spirit of the law" kicks in, and many stories and many endings become possible. Qualitative factors enter the calculations - the color and make of the car, the type of driver, and the mood of the cop with the radar gun. The boundary between "OK" and "TOO FAST" blurs.

A gray area appears on the graph. In this gray area the traffic cop makes a judgement call.

The Mathematical Story in Practice

In practice, the story depends on the call of the cop with the radar gun. She has lots of choices, and, at this moment in time, she is in the mood to make allowances for an elderly gentleman in a black Volvo who is slightly over the speed limit. The driver driving 34 KPH in a school zone does not get a speeding ticket.
In our next scenario, the driver is on the Don Valley Parkway late at night. Will this driver get a ticket? Again, it depends.

ON THE DVP

Again, according to the letter of the law, and Boolean logic, there is only one story. Even if the driver is only .2 KPH over the limit he should get a ticket.

Again, in practice, qualitative factors enter the calculations - the color and make of the car, the type of driver, and the mood of the traffic cop. The gray area appears on the graph.

The Mathematical Story in Practice

The traffic cop in the car parked under the bridge makes a judgement call. Even though the driver is only 9 KPH over the limit and the gray discretionary area is fairly wide, the flashing lights go on and the teenager in the red sports car is pulled over.

Very little in any of these stories has to do with statistics, calculus, or, for that matter, any mathematics. Instead, they spin out of the decisions that people make using some combination of qualitative and quantitative factors, and their own "judgement".

The mathematics of the speeding ticket has an analogue in the mathematics of approving a loan application.

decydeWARE™
Lorna Strobel Stewart Ph.D.
2/10/03