A PDF of some general equations, useful on a physics qualifying exam. Also included is the latex source.
For explanations, see
http://math.ucr.edu/home/baez/physics/
Factors in evaluating the quality of a science paper
what is the conclusion, stated in one or two sentances?
evaluate whether the conclusion violates conservation of energy, laws of thermodynamics, occam's razor
what are the assumptions?
are all the mathematical steps between assumption and conclusion valid operations?
Assuming these three criteria are met, we can then step back:
where is the paper published? Popular new outlet, personal website, arxiv, PRL?
is the publication peer-reviewed? You may not be an expert in the specific field, so how is it reviewed by people who are?
how often do other papers cite this work?
From the Congressional Joint Committee on Atomic Energy, April 17, 1969, regarding the justification for funding the then-unbuilt Fermilab:
Senator John Pastore: Is there anything connected with the hopes of this accelerator that in any way involves the security of the country?
Robert Wilson: No sir, I don't believe so.
Pastore: Nothing at all?
Wilson: Nothing at all.
Pastore: It has no value in that respect?
Wilson: It has only to do with the respect with which we regard one another, the dignity of men, our love of culture. It has to do with: Are we good painters, good sculptors, great poets? I mean all the things we really venerate in our country and are patriotic about. It has nothing to do directly with defending our country except to make it worth defending.
http://www.its.caltech.edu/~dg/crunch_art.html
Note: the following was written prior to reading
http://www.phys.uu.nl/~thooft/theorist.html
which gives an overview of the necessary learning for a physicist
Establishing a education dependency diagram.
Quantum field theory {Quantum mechanics, Electrodyamics}
Atomic{multivariable calculus, partial differential equations}
Electrodynamics {multivariable calculus, partial differential equations}
Special and General relativity {multivariable calculus, partial differential equations}
Classical mechanics{multivariable calculus, partial differential equations}
Quantum mechanics {multivariable calculus, partial differential equations}
Fluid mechanics {multivariable calculus, partial differential equations}
general physics {algebra, geometry, trigonometry}
-note: in physics, many things are based on the Simple Harmonic Oscillator (SHO). It may seem trivial in this class, but in the future, everything is either and SHO, asymptotic behavior, or perturbation theory.
Combinatorics {algebra}
-summary: algorithmic counting, instead of brute force counting
Linear algebra {algebra}
multivariable calculus {calculus single variable} Note: calculus is usually broken into three courses
calculus single variable {algebra,trigonometry,geometry}
partial differential equations {algebra}
-summary: "smart guesses" for the solution form, then apply boundary conditions
Geometry {algebra, trigonometry}
algebra {numerics}
numerics {counting}
For example, one needs to take algebra in order to get into quantum mechanics.
As another example, pure mathematicians can scrape by in Quantum mechanics, even though they haven't taken general physics.
This doesn't apply to someone who wants to saturate a subject (take all the courses).
This dependency idea is not present in other fields, such as literature, socialogy, and history. I don't need to understand 1923 in order to learn about 1961. However, learning about any specific subfield will help the overall understanding (human tendencies and patterns in history.)
metric system conversion
Why is the United States, one of the most technologically advanced societies on Earth, not using the metric system?
Benefits:
easy to manipulate and remember base 10 system. Who thought, "hmm, 5280 feet in a mile, 12 inches to a foot, and inverse powers of two for fractions of an inch SOUNDS LIKE A GREAT MEASUREMENT SYSTEM TO ME" ?
Science already uses metric system. Students would no longer have to memorize conversion tables!
Sources of resistance:
fear of conversion
economic costs of conversion
trans-national corporations will save money by being able to produce a single product
NASA won't lose satalites due to metric conversion factors
difficulty converting HOGSHEAD TO LITERS and BARRELS TO LITERS !
Q. Can metrics go too far?
A. Well, the French tried to implement a metric clock.
Accessibility of peer-reviewed journal articles
Journal articles are not written in plain English. Any given sentence in a journal will contain English words, but when read as a sentence, will not be comprehensible. Whereas military articles contain abbreviations, journal articles are purely jargon. This is acceptable to the reader base as long as the jargon is commonly understood (the same as the need for abbreviations to be understood). The purpose of jargon (and abbreviations) is to condense explanation by hiding behind a phrase. Jargon works only when the reader is able to extrapolate the meaning of the condensed explanation.
New readers in a field will, by definition, not understand the jargon (since they are new). Another flaw is miscommunication. That is, when the author uses jargon, and that jargon means something else to the reader. Lastly, and most importantly, accidently glossing over something that the author thought they understood, but actually was ill-defined. New physics is hidden in the supposedly condensed explanation, or the leap in logic is off a cliff.
Stereoscopic images from a small (13") crappy telescope by taking images separated in time, like 6 months apart. Would anything be usable by parallax?
Why use Latex?
Human readable source
100 times smaller source file than equivalent Microsoft Word document
better formatting
easier to input
cross platform compatibility
relative ease of notation input. See attached example. [The .tex file opens in notepad.] For very messy math, the input in latex notation is straight forward to do, once you pass the initial learning curve
free. Latex and its compilers are free. And open source
temporal compatibility: invented by Knuth in 1977, finished in 1989, a document created since then is still readable, and something I create now will still be readable in 20 years
Q: If you were a blind scientist, how would you read journal articles?
A: LaTeX, plus "AsTeR"
http://www.cs.cornell.edu/home/raman/aster/aster-toplevel.html
http://people.rit.edu/easi/itd/itdv01n4/article3.htm
Math notation is in Nemeth
http://www.duxburysystems.com/nemeth.asp
http://www.brailleauthority.org/nemeth_1972.pdf
http://www.tsbvi.edu/math/math-nemeth.htm
Idea: can physics be constructed as a set of formal proofs?
I haven't seen this in peer-reviewed articles, so either
it hasn't been done
too hard (too much investment for too little return)
mathematical frame not ready to support operations
not worth doing
it has been done, I just haven't found it / heard of it
it should be important enough that the idea would be introduced at a low level (undergraduate?)
not possible
Plan:
Start with experimentally-based relation
perform mathematically rigourus step
arrive at new useful, experimentally verifiable (verified in most cases) relation
Example: starting with Maxwell's equations, derive charge conservation
"It's basically hard to distinguish, purely from citation data, a vibrant community of legitimate research from a vibrant community of crackpots."
Idea: free, open networked peer-reviewed journal articles
I want to be able to have a few papers and then ask, "what else should I read?"
The problem is that each article will cite 20-40 other references, and each article will
possibly be cited by newer articles. In bibliometrics, the importance of a paper can be
judged on how many newer articles cite a given paper. However, the software used
for bibliometrics is not widely available (AFAIK). Second, the database of citations for
all journals is not easily accessible. Probably the best way to solve this problem
would be to use the doi database API. However, I don't have the time to do this.
Even with the doi database and API, the citations of a given article are not in doi
format. This means that the current list of citations would need to be converted to
a networkable format.
Lastly once all the information is useful, it could be analyzed using a visual output
language like processing, as in HTMLgraph
see this site as a visual graph: http://www.aharef.info/static/htmlgraph/?url=http%3A%2F%2Fwww.eipiplusone.com
However, as plotted these graphs are not that useful, as they don't allow the end user
to ask, "which page is that?"
Applicable to the citation question, one the plot is produced, it would be easy to pick
out which papers are important, based on their connectivity.
Note that this service is available through XX, but only as a paid service. Additionally,
the number of journals may be limited.
(even better than I suggested). The problem now will be to build a knowledge base.
Physics as a form of hacking is more difficult, rigerous, respected, rewarding and consequential.
What are the physics of higher (N>3) space dimensions?
For example, what happens to the cross product?
http://en.wikipedia.org/wiki/Seven_dimensional_cross_product
how does this affect the Maxwell equations?
--> Tensors
http://mathforum.org/library/drmath/view/52011.html
levi-civita still works in 4 dimensions