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Reinventing a Square Wheel

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Riding a square-wheeled bicycle can be a lot of fun, but inventing it is even more exciting! More on this below.

Since we all know, or rather should know, that " ... there is nothing new under the sun ...", it is obvious that many of the inventions around us are actually ... reinventions. There is nothing wrong with that.

But how about the reinvention of a square-wheeled theory? For instance, how about the reinvention of a theory that is actually quite old and well established and misappying it, that is using it outside its domain of applicability?

Naturally, this does not happen very often, but ... it does happen!

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Recall that according to the bible (קֹהֶלֶת Ecclesiastes 1:9):

That which has been is that which will be,
And that which has been done is that which will be done.
So there is nothing new under the sun.

The complete (original Hebrew) text is in fact more depressing:

This is the English text of Ecclesiastes 1 in the New International Version:

  1. The words of the Teacher,a son of David, king in Jerusalem:
  2. "Meaningless! Meaningless!" says the Teacher. "Utterly meaningless! Everything is meaningless.”
  3. What does man gain from all his labor at which he toils under the sun?
  4. Generations come and generations go, but the earth remains forever.
  5. The sun rises and the sun sets, and hurries back to where it rises.
  6. The wind blows to the south and turns to the north; round and round it goes, ever returning on its course.
  7. All streams flow into the sea, yet the sea is never full. To the place the streams come from, there they return again.
  8. All things are wearisome, more than one can say. The eye never has enough of seeing, nor the ear its fill of hearing.
  9. What has been will be again, what has been done will be done again; there is nothing new under the sun.
  10. Is there anything of which one can say, “Look! This is something new”? It was here already, long ago; it was here before our time.
  11. There is no remembrance of men of old, and even those who are yet to come will not be remembered by those who follow.
  12. I, the Teacher, was king over Israel in Jerusalem.
  13. I devoted myself to study and to explore by wisdom all that is done under heaven. What a heavy burden God has laid on men!
  14. I have seen all the things that are done under the sun; all of them are meaningless, a chasing after the wind.
  15. What is twisted cannot be straightened; what is lacking cannot be counted.
  16. I thought to myself, “Look, I have grown and increased in wisdom more than anyone who has ruled over Jerusalem before me; I have experienced much of wisdom and knowledge.”
  17. Then I applied myself to the understanding of wisdom, and also of madness and folly, but I learned that this, too, is a chasing after the wind.
  18. For with much wisdom comes much sorrow; the more knowledge, the more grief.

The second and third verses set the scene: it is not just that all that you ever invented, or are about to invent, or will ever invent, is not new. Worse, much worse: all human effort is pointless, meaningless, purposeless, because in the GRAND SCHEME OF THINGS, it all comes to naught .... The second verse is more poignant in Hebrew.

And yet ... for all these verses' glory, and ... for all our accepting (in our heart of hearts) their truth, our effort is relentless and we never lose our appetite for invention.

So, if you happen to come up with an idea of what appears to you as a new product, a new service, and so on, or, if it strikes you that you have worked out a new theory, before you rush out to announce it to the world, you would do well to stop and ask yourself: is this really new? Or am I reinventing the wheel?

For instance, consider this (color is mine):

Some questions and answers on Community Music Therapy

New name, old game?

There is of course nothing new under the sun, and a common response to CoMT is to ask whether it is just re-naming an established international practice — and, moreover, re-naming from a eurocentric and ill-informed basis. Are we, then, re-spraying an old car to sell it as new? David Aldridge said to one of us that it might be more useful to re-name narrower music therapy practices 'clinical music therapy' rather than re-branding the broader practices of most of the world's music therapists 'CoMT'. These are fair and urgent questions. Are we just reinventing the wheel?

Community music therapy (2004, page 18)
By Mercédés Pavlicevic, Gary Ansdell

My point is that the unremitting pressure (especially on academics) to constantly come up with "new" technologies, "new" theories, "new" applications, and so on, has given rise to a situation where the term "new" itself is under siege. So much so that it is constantly being stretched (beyond recognition) to allow its use as a descriptor of ideas, theories etc. that do not actually warrant this designation!

Indeed, the current tendency to label anything one arbitrarily chooses to as "new", has given rise to a situation where as a descriptor the term "new" no longer seems sufficiently powerful, or expressive, to adequately convey the idea of "newness". So, superlatives such as "breakthrough", "radically different" and "revolutionary", are added to the presumably weakened term "new" in order to infuse it with extra oomph.

That this opens the floodgates to an avalanche of spin and empty rhetoric is obvious. Because, if one cannot justifiably show (prove) that one's idea, theory, or what have you, are new, chances are that this fact will be dressed up with layers of verbiage replete with effusive language that will go to great length to explain (away), and compensate for the missing substance.

What is the wonder then that one of the Ten Natural Laws of Operations Analysis makes an explicit reference to the invention of the wheel?

The Ten Natural Laws of Operations Analysis

Bob Bedow
DELEX Systems, INC.
8150 Leesburg Pike
Vienna, VA 22180
  1. Ignore the problem and go immediately to the solution, that is where the profit lies.

  2. There are no small problems only small budgets.

  3. Names are control variables.

  4. Clarity of presentation leads to aptness of critique.

  5. Invention of the wheel is always on the direct path of a cost plus contract.

  6. Undesirable results stem only from bad analysis.

  7. It is better to extend an error than to admit to a mistake.

  8. Progress is a function of the assumed reference system.

  9. Rigorous solutions to assumed problems are easier to sell than assumed solutions to rigorous problems.

  10. In desperation address the problems.

Source: Interfaces 7(3), p. 122, 1979.

But let us examine this point more closely, because there may well be more than one way to reinvent the wheel:

The American Heritage® Dictionary of the English Language,
tr.v. re·in·vent·ed, re·in·vent·ing, re·in·vents
  1. To make over completely: "She reinvented Indian cooking to fit a Western kitchen and a Western larder" Irene Sax.

  2. To bring back into existence or use: reinvented the concept of neighborliness.
reinvent the wheel
  1. To do something again, from the beginning, especially in a needless or inefficient effort: "School districts need not reinvent the wheel every time they try to improve their schools" Washington Post.

  2. To recast something familiar or old into a different form: "Call it reinventing the wheel or recasting old ideas, but these contemporary versions have a spirit and style all their own" New York Times.

So one reading of the term "reinventing the wheel" has a "positive" connotation. In this sense it means "thinking out-of-the-box", extending, altering, or even replacing the "old" and "ordinary". A good example of such a reinvention is the famous Segway Personal Transporter.

The story behind this re-invention of the wheel is told in the best-seller Reinventing the Wheel: A Story of Genius, Innovation, and Grand Ambition (2005) by Steve Kemper. This invention has gained notoriety when on June 12, 2003, the former President G.W. Bush fell off his Segway PT on the front driveway of his parents' summer home in Kennebunkport, Maine.


And if you happen to be in Australia, you can take Segway Tours to all sort of places, eg a 2-hrs tour of Sydney's Olympic Park.

But, it goes without saying that certain re-inventions of the wheel are without any merit and should therefore be avoided. For, what is the point of reinventing an existing, well-known, well-understood, commonly used idea, theory or device, if they do not "extend the old", or "throw more light on it", or "endow it with greater capabilities", or "alter it", or what have you?

Of course, it is even less commendable to reinvent a square wheel especially if such an invention is presented to the world as "a land mark" invention, and if what is needed for the job is in fact the good, old ... circular wheel.

According to WIKIPEDIA,

Reinventing the square wheel is the practice of unnecessarily engineering artifacts that provide functionality already provided by existing standard artifacts (reinventing the wheel) and ending up with a worse result than the standard (a square wheel). This is an anti-pattern which occurs when the engineer is unaware or contemptuous of the standard solution or does not understand the problem or the standard solution sufficiently to avoid problems overcome by the standard. It is mostly an affliction of inexperienced engineers, or the second-system effect.

This is not to say that one would necessarily lack explanations showing that the "reinvented square wheel" works, or that one would want for arguments justifying its invention (see discussion on spin and rhetoric).

And, of course, there are those rare occasions where a square wheel is exactly what is needed for the job at hand! For example, take a look at Prof. Stan Wagon riding his famous specially designed square-wheel-bike.

And consider Prof. Wagon's comments on this invention:

My square-wheel bike, on permanent display at Macalester College. This construction, believe it or not, earned me an entry in "Ripley's Believe It or Not"; beats standing in a block of ice for three days or growing three-foot long fingernails. This version is our second such vehicle, built in 2004. The first, from 1995, was a little less refined and the ride on the catenary road less smooth. The new version rides very very smoothly.

And here is a live demonstration of the Texas A&M Physics Department's square-wheeled bike, built by the machine shop. The bike rides on a road of repeated pieces of an inverted catenary:

There is a nice animation of the process by bryceguy72 on Youtube.

Math education

Conventional wheels naturally play an important role math education. But how about square wheels? And how about using actually using square wheels, say riding a square-wheeled bicycle?

Obviously, for the ride to be smooth, the surface cannot be flat, and this may cause some serious difficulties in balancing the wheels. So how about a square-wheeled tricycle


The pictures show Glen Whitney, Executive Director of the Museum of Mathematics, riding a a square-wheeled tricycle at the Math Midway traveling exhibition, created as part of the new Museum of Mathematics.

Square-wheeled theories

But the point remains that square wheels generally have no rhyme or reason.

So, the question is: how is it that scholars keep on reinventing square wheels in situations where the circular wheel is all that is required, indeed a circular wheel is available and doing a perfectly good job?

Good question!

I wish I had a definite answer.

I submit, though, that more interesting are the related questions:

  • How is it that articles proposing square-wheel theories are published by refereed journals?

  • How is it that square-wheel theories are embraced and promoted by scholars and academic institutions?

These questions are relevant to my Info-Gap Campaign whose objective is to contain the spread of Info-Gap decision theory in Australia.

This theory is hailed as "novel", "revolutionary", and "radically different", but it is in fact a classic case of the reinvention of the wheel — it is an instance of Wald's Maximin model (circa 1940) — and a square one at that!

The square wheel aspect is manifested in Info-Gap's case in its flawed deployment of a Maximin analysis in the treatment of severe uncertainty. Indeed, this flawed deployment of the Maximin analysis makes Info-Gap decision theory the precise antithesis of what a theory that is aimed at tackling severe uncertainty ought to be. For this reason I argue that Info-Gap decision theory is a voodoo decision theory par excellence.

Some wheels have extra ordinary illusory power.

Theorem: The wheels shown below are static.

Proof. Stare intensely at one of the black dots!

You can, of course, argue that the wheels are in fact not static, that their motion stops when gazed at intently, only to resume when one's gaze is relaxed. You certainty can!

For other interesting optical illusions visit the web site of the National Institute of Environmental Health Sciences and the website of New Optical Illusions from which the above picture is downloaded.

Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.

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