The Gradient: April 1, 1988

From 1987 to 1994, Professors Kevin Mitchell and David Eck published a departmental newsletter known as The Gradient. During the first year of publication, they put out an April Fools edition. Several articles from that issue are shown below. You could also check out the

complete issue in PDF format

(Note: Although in reality, the field house was built, there was a new science center a few years later -- but still with no new space for Math/CS.)

Reagan Announces Linearization Policy

Mathematics To Be Deregulated;
Pythagoras Spins In Grave;

President Ronald Reagan today unveiled a program to deregulate mathematics. The policy is widely perceived as another step in the Reagan agenda to streamline the rules and regulations governing certain areas of the economy. Previously, the airline industry has been deregulated and as a result has become more competitive. Currently the financial services sector is undergoing deregulation, though the process has been slowed by the stock market `meltdown' of last October. What differentiates the new policy from earlier forms of deregulation are the effects that the policy will have beyond the economic sector, in particular on the education of students in the mathematical sciences.

Linear Algebra is the Model

Reagan began the conference by denouncing the current state of mathematics as being too complicated for the average layman to understand. He said, ``What Americans need are a few simple rules to govern all mathematical processes and manipulations.'' Reagan described linear algebra as a model which all branches of mathematics should emulate. He said, ``Recall that if $ V$ and $ W$ are real vector spaces, then a function $ T:V\to W$ is called a linear transformation if $ T({\bf u+v})=T({\bf u})+T({\bf v})$ and $ T(k{\bf v})=kT({\bf v})$ for all vectors u and v in $ V$ and all real numbers $ k$. What could be simpler than that? Whether you add or scalar multiply before or after the transformation you get the same answer! There's no way to get it wrong. Mathematics needs more of that.'' With this model in mind, the President then went on to describe in general terms the government's new policy, which he has called linearization.

Reagan's Lemma

While the details of the linearizartion program have not been completely worked out, these facts are known. In algebra and trigonometry the following definitions will now apply:

$\displaystyle \frac{1}{a}+\frac{1}{b}$ $\displaystyle \equiv\frac{1}{a+b};$    
$\displaystyle a^{1/n}$ $\displaystyle \equiv\frac{1}{a^n};$    
$\displaystyle \cos(a+b)$ $\displaystyle \equiv\cos a+\cos b;$    
$\displaystyle \sqrt{a+b}$ $\displaystyle \equiv\sqrt a+\sqrt b.$    

This last statement greatly simplifies the calculation of the hypoteneuse of a right triangle; we now have $ \sqrt{a^2+b^2}=a+b$. Vice President Bush, standing at Reagan's side, has proposed that this result be called Reagan's Lemma. It would, of course, replace the Pythagorean Theorem.

Getting to the Root of the Problem

Reagan, in fact, observed that a lot of the problems in mathematics are directly attributable to the Pythagoreans, a secretive mathematical society in ancient Greece. Before the Pythagoreans, geometry was understood through numbers and their ratios. A major tenet of this belief was that any two line segments were commensurable. That is, for any two line segments it was believed possible to find a unit small enough so that each segment would be an exact integral multiple of that unit. But the Pythagoreans discovered that certain familiar lengths such as the side of a square and its diagonal are inherently incommensurable and hence could not be evenly measured by a common unit no matter how small. This discovery was a major setback for a philosophy which had postulated number as the central key to all understanding. So embarrassing was this situation that according to one legend the discoverer was thrown overboard and members were forbidden from revealing the secret of these inexpressible quantities to outsiders. Reagan asserted, ``Ever since that time, the rules and formulas of mathematics have been made overly complex in order to hide such inadequacies. It is time to get to the root of this problem.''

Goodybye Chain Rule

The policy of linearization would have a dramatic effect on the calculus. Centuries of work by Newton, Leibniz, Lagrange, and Cauchy were wiped away with a stroke of Reagan's pen this morning in the Oval Office. For example, the product rule for derivatives now becomes:

$\displaystyle (f(x)g(x))'=f'(x)g'(x),$

and the companion integration by parts formula would be

$\displaystyle \int (uv)\,dx=\left(\int u\,dx\right)\left(\int v\,dx\right).$

The chain rule, which computes the derivative of a composite function, now reads:

$\displaystyle \big(f(g(x)\big)'=f'(g'(x)).$

It was not immediately clear what the repercussions would be for integration by $ u$-substitution.

`A Piece Of Cake'

Reagan noted for years students have been requesting such changes in mathematics. ``Just look at the answers on any of their math exams. Students have been way ahead of their teachers on the issue of linearization. In fact, I'd like to go back to ninth grade and take Mr. Anton's algebra final. It would be a piece of cake now!'' Reagan also went on to suggest that mathematical research would be stimulated as problems that were once insurmountable now become trivial by using the algebra and calculus of linearization.

`I Before E'

In a related issue, the President announced he would soon be proposing legislation to Congress to simplify spelling in English. He noted that deregulation does not mean there will be no rules, but rather there will be fewer and simpler rules. Reagan cited an example of one of the changes under discussion. ``Currently we have: `q always followed by u.' We would like to adopt the position: `i before e' without exception.'' A reporter from this newspaper asked Reagan, ``How would this affect the famous mathematical formula ` $ e^{i\pi}=-1$.' Will it now have to be written as ` $ i^{e\pi}=-1$'?'' Reagan responded with a hoot, ``There you go again, more of that Greek nonsense!''

Plans for Field House Scrapped;
Sciences Complex Approved

In a surprise move, the Board of Trustees of Hobart and William Smith Colleges announced today that plans for a new field house are being dropped. The funds released by this decision will be used instead for a multi-million dollar natural sciences complex. In their statement announcing the decision, the Board said, ``While recognizing the importance of recreational and athletic facilities, we must not forget that our primary institutional goals are academic. Thus, when the need for improved science facilities was brought to our attention, we of course felt that our first priority must be to satisfy that goal.''

The Gradient has learned that in fact, the new sciences complex will house a Cray 3 supercomputer. Reliable sources, speaking under the condition that they not be identified, have informed The Gradient that the agreement to build the sciences facility was the last condition that the Colleges had to fulfill to obtain government funding for the computer. Federal and State governments were reportedly eager to place Cray's newest model in a location where it would be accessible to major universities in the area. According to one source, the agreement has not yet been announced because of fears that the large-scale construction necessary would meet with community opposition. As New York Governor Mario Cuomo is reported to have put it, ``Those environmentalist know-nothings killed the supercollider and they killed the incinerator, and we're not going to give them a chance at this one.''


Views and Reviews:

Standard Mathematical Tables, Sixteenth Edition,
Published by The Chemical Rubber Co.

Every so often, one comes across a book that has been available for some time but has somehow failed to achieve the attention it deserves. Standard Mathematical Tables is a prime example of such undeserved obscurity, and it is about time that this extraordinary collection of mathematical gems be given the attention it is due.

The treasures to be found in this collection include the remarkable long work, Table of 574 Integrals, which opens with the hauntingly simple ``$ \int a\,dx=ax$'' and then goes on to develop its theme through a number of variations of increasing complexity and subtlety. The editors have cunningly placed this work just after the shorter and superficially simpler Derivatives, thus illuminating the deep and unsuspected symmetries in these two pieces.

Another example of the skill of the editors is their assemblage of the classical oral epic, Natural Trigonometric Functions to Five Places and a number of modern variations on it, including Natural Trigonometric Functions for Angles in X Radians, Natural Trigonometric Functions for Angles to Five Tenths of a Degree, and the daring and sublime Common Logarithms of the Trigonometric Functions.

The collection also includes some shorter and lighter works, such as the familiar Metric Conversion Table and the less familiar Numbers Containing $ \pi$, which turns out to be the source of such well-known epigrams as ``$ 1/\pi=0.3183099$'' and ``$ \pi^2=9.8696044$.''

But the only way to really appreciate Standard Mathematical Tables is to read it yourself. You are guaranteed many hours of pleasure.