Math – Page 3 – Sean Carroll

Maharishi Mathematics

March 15, 2007 / 34 Comments

It’s that time of year when eager young students are deciding where to embark on, or to continue, their higher educations. You can see our advice-giving posts on choosing an undergraduate school and choosing a graduate school.

But there are a lot of options out there, and it would be a shame to overlook any of them. So we’d be remiss not to mention the unique opportunities offered by the Maharishi University of Management. Founded by the Maharishi Mahesh Yogi, spiritual advisor to the Beatles, and led by John Hagelin, highly-cited theoretical physicist and occasional Presidential candidate, the MUM offers a — did I already mention “unique”? — set of experiences to the enthusiastic student. And that’s not even counting the Yogic Flying!

Here, for example, are some of the course descriptions for the undergraduate major in mathematics.

Infinity: From the Empty Set to the Boundless Universe of All Sets — Exploring the Full Range of Mathematics and Seeing its Source in Your Self (MATH 148)

Functions and Graphs 1: Name and Form — Locating the Patterns of Orderliness that Connect a Function with its Graph and Describe Numerical Relationships (MATH 161)

Maharishi Vedic Mathematics: Mathematical Structure and the Transcendental Source of Natural Law (MATH 205)

Geometry: From Point to Infinity — Using Properties of Shape and Form to Handle Visual and Spatial Data (MATH 267)

Calculus 1: Derivatives as the Mathematics of Transcending, Used to Handle Changing Quantities (MATH 281)

Calculus 2: Integrals as the Mathematics of Unification, Used to Handle Wholeness (MATH 282)

Calculus 3: Unified Management of Change in All Possible Directions (MATH 283)

Linear Algebra 1: Linearity as the Simplest Form of a Quantitative Relationship (MATH 286)

Calculus 4: Locating Silence within Dynamism (MATH 304)

Complex Analysis: Transcending the Real Numbers to a Simpler and More Unified Numbering System (MATH 318)

Probability: Locating Orderly Patterns in Random Events to Predict Future Outcomes (MATH 351)

Real Analysis 1: Locating the Finest Impulses of Dynamism within the Continuum of Real Numbers (MATH 423)

Set Theory: Mathematics Unfolding the Path to the Unified Field — the Most Fundamental Field of Natural Law (MATH 434)

Foundations of Mathematics: The Unified Field as the Basis of All of Mathematics and All Laws of Nature (MATH 436)

Now, sure, any old university will be offering courses in real analysis and set theory. But will they learn about the unified field, and locate the finest impulses of dynamism? “Vector calculus” sounds kind if dry, but “Unified Management of Change in All Possible Directions”? Sign me up!

Nobody ever said the Maharishi wasn’t a good salesman.

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N Bodies

This will be familiar to anyone who reads John Baez’s This Week’s Finds in Mathematical Physics, but I can’t help but show these lovely exact solutions to the gravitational N-body problem. This one is beautiful in its simplicity: twenty-one point masses moving around in a figure-8.

The N-body problem is one of the most famous, and easily stated, problems in mathematical physics: find exact solutions to point masses moving under their mutual Newtonian gravitational forces (i.e. the inverse-square law). For N=2 the complete set of solutions is straightforward and has been known for a long time — each body moves in a conic section (circle, ellipse, parabola or hyperbola) around the center of mass. In fact, Kepler found the solution even before Newton came up with the problem!

But let N=3 and chaos breaks loose, quite literally. For a long time people recognized that the motion of three gravitating bodies would be a difficult problem, but there were hopes to at least characterize the kinds of solutions that might exist (even if we couldn’t write down the solutions explicitly). It became a celebrated goal for mathematical physicists, and the very amusing story behind how it was resolved is related in Peter Galison’s book Einstein’s Clocks and Poincare’s Maps. In 1885, a mathematical competition was announced in honor of the 60th birthday of King Oscar II of Sweden, and the three-body problem was one of the questions. (Feel free to muse about the likelihood of the birthday of any contemporary world leader being celebrated by mathematical competitions.) Henri Poincare was a favorite to win the prize, and he submitted an essay that demonstrated the stability of planetary motions in the three-body problem (actually the “restricted” problem, in which one test body moves in the gravitational field generated by two others). In other words, without knowing the exact solutions, we could at least be confident that the orbits wouldn’t go crazy; more technically, solutions starting with very similar initial conditions would give very similar orbits. Poincare’s work was hailed as brilliant, and he was awarded the prize.

But as his essay was being prepared for publication in Acta Mathematica, a couple of tiny problems were pointed out by Edvard Phragmen, a Swedish mathematician who was an assistant editor at the journal. …

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