Threesology Research Journal
3buses (9K)

(The Study of Threes)

The title of this page is from a book "Why Do Buses Come in Threes: the hidden Mathematics of everyday life," by Robert Eastaway & Jeremy Wyndham.

While many of us who have had the aggreeable opportunity (or unmitigated displeasure) of riding in a public bus who have noticed (muchless acknowledged) that buses do frequently arrive in groups of three, there are some public transit riders who have not recognized this occurrence with any regularity and might be quick to offer the view if asked, that buses tend moreso to come in groups of two or in singles. Others might argue that this is not a world-wide phenomena as is described in the following comments:

Why do buses come in threes, math book.
--- Buses in Threes ---

Buses in Threes:

Mexican buses don't come in threes

Friday 23 June 2000

Bus drivers in Cuernavaca, Mexico are giving their customers a more reliable service than their British counterparts by following quantum chaos theory. Research published today in the Institute of Physics publication, Journal of Physics A: Mathematical and General, describes how the people of Cuernavaca rarely say, 'you wait for hours, then three come at once', because bus drivers own their own vehicles and therefore have to compete for business. This competition means that buses do not cluster as they do in the UK, [or U.S.] and act as a quantum chaotic system. Quantum chaos is the chaotic way sub-atomic particles are distributed in space and time.

Milan Krbalek and Petr Seba, researchers from the Czech Republic, say that this unusual distribution essentially results from bus ownership. No company is responsible for their wages, and there is no timetable either. To maximise their income, the drivers need to pick up as many people as possible, leading to stiff competition for fares. To prevent clusters of buses, drivers go so far as to employ people at checkpoints along their route to tell them when the last bus left the area. Drivers can then speed up or slow down to increase the chance of picking up more passengers.

By looking at the bus distribution in Cuernavaca, Krbalek and Seba found that the solution to the model is a distribution from random matrix theory, a solution that has previously been applied to quantum chaos theory. 'Although this system is far from being of quantum origin, the fluctuations in the time intervals between subsequent buses arriving to a given bus stop display exactly the same features as observed in the chaotic quantum transport', said Seba. For the first time, the universal nature of quantum chaos theory is demonstrated.

The surprising similarity of bus distribution to quantum chaos theory is explained by coherence – having the same energy. In the quantum case the coherent propagation of the quantum particles through the system leads to complicated interference phenomena and finally to the observed universal properties. In the case of buses in this Mexican city the coherence is a certain synchronisation between buses operating on the same line. Such a distribution is not found in London or even UK cities with deregulation, because bus drivers are not competing with each other in the same way.

This interesting research opens the possibility to extend quantum chaos theory to other coherent systems. Preliminary results from further research already show that similar behaviour is found when looking at the distances between cars on German highways.

--- Mexican Buses Don't Come In Threes ---

Here is another view which strives to answer the question:

Buses (why they come in threes)

Bus operators offer a lot of plausible explanations why you wait an hour for a bus and then three come along at once. They largely involve blaming traffic and/or passengers, the surprising existence of which apparently hamper the efficient running of a bus service. This is just a cover story. The real reason why buses arrive in threes is that they set off, from the bus station, in threes. There's little attempt to conceal it. A bus conductor nips out of the garage, looks shiftily left and right, and then shouts back 'Bob! Fred! Jimmy! GO! GO ! GO!' Three double deckers then steam out, racing towards their destination in a competition to see who can arrive first and with least passengers.

--- Buses (why they come in threes) ---

Whether you agree or disagree with the view that buses tend to run in groups of three on a frequent basis, such comments as those above will make many more people aware of the phenomena to the extent of concluding that the occurrence is frequent enough to be noticed by several observers. We must also ask why buses leave the bus station in groups of three, and why there is a difference with bus services (with respect to buses arriving in groups of three) in Indo- European related countries and those that are not considered to be traditionally associated with the Indo-European groups of peoples. Is it economics, or is economics merely a part of an underlying difference in brain computation with respect to preferential cognitive grouping behaviors that are expressed in a multitude of forms such as developing a theory that there are three families of fundamental particles?

While I refer to the phenomena of threes in buses as a grouping, you might prefer to use other words such as bunching, associating, pattern, organization, etc... By using such a word as "bunching," for example, we might adopt a framework of correlation which brings to mind such things as a bunch of grapes, a bunch of kids, a bunch of money, etc... However, such words may tend to influence a wider berth of generalization that detract from the intended focus of specificity that was intially observed. Such a detraction may or may not provide a means to discuss a larger issue of a recurring similarity of phenomena in other areas.

In considering the grouping of buses, let us take a moment to make a comment about groupings of people. Specifically, when people are observed walking along a street or road or path. However, it must be understood that my references are with respect to my own observations within the context of areas I have experienced while living in a few places in the United States. Other readers living elsewhere (including elsewhere in the U.S.) may have different experiences. These differences should be noted and catalogued for future reference... if not by the initial observer, then those who come across their record having an interest in this circumstance.

Most often, I observe people walking alone, or with one other person, or with two others... This is a 1, 2, 3 pattern. There are a few instances of four or more amongst school kids walking home together, but this grouping is not as frequent as the single, pair, or triple variety. On some occasions I have seen a "four grouping" in terms of either 3 boys and 1 girl or 3 girls and 1 boy instead of either four girls, four boys, or two girls and two boys.

Image for the title of this page was adapted from:

--- Example: Why do Buses Come in Threes? ---

Some readers might also like to read the following article:

-Theorem of Threes-

--- Of Buses and Bunching: Strangeness in the Queue ---
by Dr. Neil Gunther

Your Questions, Comments or Additional Information are welcomed:
Herb O. Buckland