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In the Big Picture, our Sun is but one star of hundreds of billions in
the Milky Way Galaxy. |
My interests are wide ranging and eclectic enough that a brief introduction of my intellectual philosophy
is the best way to begin.
My interests involve mostly everything, from top to bottom and back up to the top. That is, understanding
the Big Picture of any given phenomenon by going down to understanding the Details that make up the Big
Picture, and then back up to assessing the situation as a whole. I'm drawn to understanding the processes
and evolution of Whole Systems, dealing with the Details as necessary to accomplish that goal.
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If we had considered only data points near the arrow,
we would have missed the pattern of the Big Picture. |
The biggest portion of understanding any phenomenon is looking for Patterns. Frequently, there are many
interrelated Patterns at different time and distance scales. The trick is finding Patterns that are really
there without perceiving those that are not. Apparently, I have that talent, and I take advantage of
it.
One of my own favorite sayings is "If it can't be said as a Differential Equation, I'm not interested.
Everything can be said as a Differential Equation." What I mean by that is that all things can be
described analytically, at least at the basic scientific level, as a Differential Equation, even if
that equation cannot be solved completely. Once that is done, then remarkable similarities can be
seen between very different phenomena. For example, the equations that describe the Fluid Flow in
a water basin are similar to those for certain aspects of Galaxy Motion: Understanding one can lead
to understanding the other. This approach is better than mere analogy, it's analytical. I do this
kind of comparison all the time.
The quote also describes my interest in everything. (Well, a tiny fraction of everything, but that's still a
lot!) And that I view everything through the filter of Mathematics. It's Mathematics that organizes my
thoughts, processes, and conclusions. In order to understand any given thing, the Details have to be
understood also, but they can be so numerous and complicated that it is easy to lose track of the Big
Picture while plowing through the details: The "can't see the forest for the trees" problem. Mathematics
helps me from getting "lost in the forest." And promotes my interests in so many diverse things:
Atoms, quarks, automobiles, inventions, planets, galaxies, economics, war, peace, love, law, ....
Some are simple enough that mere Algebra will suffice (law), others so complicated that
integro-differential stochastic Mathematics is needed (global economies). It's all good.
Mathematics is the one Universal Language. Although it is a written language, not a spoken language,
it is good everywhere in the Universe. Algebra is Algebra, Calculus is Calculus. Residue Theory is as
good on the far side of the Galaxy as it is here, means the same thing there, and is used by alien
civilizations the same way. When the Vulcans land in Montana in April 2061, the only way we will be
able to talk to each other initially is through Mathematics. (Yes, I'm a Star Trek fan.) Seriously,
though, there are several professional Astronomers that have predicted First Contact with intelligent
alien life by 2030. You might want to work on your Mathematics skills if you wish to take advantage
of the entrepreneurial opportunities that will arise.
From an analysis perspective, Applied Mathematics can be broken into Linear Phenomena and Nonlinear
Phenomena.
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An electromagnetic wave packet, also called a photon. The red undulations
represent the electric field, the black the magnetic field. It is propagating to the right. |
Linear Mathematics is relatively "easy" to understand (for me, anyway) and covers about 85% of all
physical processes. It can still be quite involved and time consuming, and can lead to surprising
results. The Universe smiled upon us by allowing Quantum Mechanics and Electromagetism to be
fundamentally linear. Good thing, too. They are difficult enough as it is.
Nonlinear Phenomena, however, are generally extremely difficult to even model, let alone understand
and interpret. But that 15% is the truly interesting part of Nature for me because my attraction to
it arises from there being are no general solution techniques for solving and interpreting Nonlinear
Phenomena: The challenge of cracking a nonlinear problem is it's attraction. Let others tackle the
easy stuff. I'll take on the hard things.
Having said all that, the following is a list of my present, past, and potential future interests,
professional and personal:
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Two colliding solitons. Click for animation. |
Wave Theory: Specifically, nonlinear waves, including solitary waves, shock waves, and solitons.
A soliton is a solitary wave with particle properties. A high amplitude soliton catches up with a slower low
amplitude soliton, collides wth it by exchanging identity with it and proceeds on ahead. The behavior is
remarkably similar to billiard balls colliding but for the exchange of identity and a phase shift. This
particle-like behavior comes from a purely wave mechanism! Click on the figure to the right to see
a simple animation. [Alex Kasman]
Nonlinear Differential Equations: Generally, fluid mechanics contains the most horribly nonlinear equations.
I love it!
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Complex contour |
The Calculus of Residues: One of the mathematical solution methods of last resort, where functions
and variables take on complex (real and imaginary) values.
Complex Functions and Variables: Specifically, pole vaulting, going around otherwise impassible
singularities on the complex plane.
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The coast of Norway. Click for large image. |
Lagrangian Mass Variables: A very different perspective of fluid flow.
Self-Similarity: A class of phenomena described by the character of being scale-independent.
Chaos: The science, not the college student mind. Sometimes this is called stochastic determinism.
Fractals: Objects that have fractional dimension; e.g., the coast of Norway has a dimension of
1.52. Really.
Infinitesimal Lie Group Theory: Umm, don't ask.
Plasma Physics, Plasma Engineering, and Space Physics: It's all Plasma Physics (nothing to do with
blood). A plasma is an ionized gas; 99% of the matter in the universe is in this so-called fourth
state of matter.
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A star cluster of at least 100,000. Click for large image. |
Inertial Confinement: Controlled nuclear fusion.
Acoustics: Linearized waves in a fluid; sound.
Astronomy: Specifically, the dynamics of star clusters and galaxies.
Electrophotography: Photocopying machines.
Meteorology: What are the local weather effects of a medium size lake at high lattitude? I'm trying to answer
that question.
Computer Simulation: When Mathematics "fails" to allow an exact result.
Alternative Voting Methods: Instant Runoff Voting is a good first improvement on the standard
First Past The Post, but there are better (Ceiling N/2 is my favorite; I invented it).
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North shore of Lake Bemidji.
Click for large image. |
Music: Specifically, presently singing in the Bemidji Chorale. I've been singing in public since junior
high school; A Capella, madricals, and barber shop quartets.
Bicycling: Every day in the summer if good weather. Look for a fat man on a bicycle circumnavigating
Lake Bemidji.
Camping: But the hard ground is getting harder and harder for sleeping. A trailer may be in my future.
Hiking: Best hike I ever had was up the Grand Tetons. Of course, I was younger then.
Weight Lifting: Started lifting at 46. It's never too late.
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The home farmstead. The full resolution photograph is five feet
wide. This was my first successful attempt at creating a panorama. It was constructed
from 15 individual overlapping exposures. Click for large image. |
Photography: Specifically, nature panoramae (sunrises, sunsets, mountain ranges, ...), where
individual frames are digitally stitched together to create 120° to 270° vistas.
Writing: I have several fiction ideas yet to take concrete form.
Reading: Newspapers, books, manuals, comics.
Law: Specifically, intellectual property law; patents, copyright, and trademarks, most particularly
patent prosecution. Patents have a dual purpose: To reward the efforts of the inventor, and to teach the
public about the new invention. After 20 years from filing for a patent, ownership reverts to the public
domain.
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Isaac Newton |
History of Science, Engineering, and Mathematics: Newton, Franklin, Maxwell, Gauss, Archimedes, Gutenberg,
Euclid, ....
Different Cultures: The customs of others is fascinating.
Alternative Perspectives of Ordinary and Common Phenomena: There is rarely only one way or
explanation.
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Sudoku
Click for large image. |
Rewriting Lyrics: Creating science lyrics to popular and classic tunes or soundtracks. So far, The
Physics Song uses the Banana Boat tune (Day-O) and the theme to the old TV series
Mr. Ed. In the works, the Beach Boys.
Nature Sound Recording: Someday, we may miss hearing birds and insects. My first recording (before
reading the manual for the digital recorder, unfortunately; too much shot noise) has crickets and trains
at 4 am in the Iowa countryside; Playing the CD on a home stereo sounds like a locomotive crashing through the
living room! Could make for an excellent practical joke on someone. (But you didn't hear it from me.)
You can listen to the 70 minute mp3 file here
(64 MB). There are crickets, highway noise from US 30, four "locomotive events" from the old Chicago
Northwestern dual railroad tracks (more than four trains), and echos. The highway and tracks are a
tenth of a mile away, located in the distant far left of the farmstead panorama above. It's recorded
in stereo using the built-in condensor microphones. CAUTION: Keep your playback volume low.
Sudoku: A daily fix. Sudoku is an excellent way to hone your logic and problem solving. For those
of you who just have to peek, here is the solution to the
puzzle displayed above.
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Last Updated November 13, 2009.
© 2009 Stevens F. Johnson and the Dept. of Physics/Science, Bemidji State University.
All rights are reserved unless explicitly stated otherwise.
