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Perhaps the cause of "rejection" of science is that the so-called scientific culture tolerates stuff like over-diagnosis, or changing definitions as part of the cost of communicating scientific information. I don't think it has to be that way, but unfortunatly, it is a cancer that pervades the sciences and the policy wonks that distribute scientific information...

I refer you to this historical piece of wisdom...

In summary, the idea is to try to give all of the information to help others to judge the value of your contribution; not just the information that leads to judgment in one particular direction or another...

If more people communicating science would practice this, I'll bet there would be more trust in the sciences (by all folks)...

No, they are not. There are nucleosynthesis limits that show that baryonic matter (us, stars, planets) are only a small fraction of the total dark matter (somewhere in the 4 to 10% range).

Now, there also is "missing" baryonic matter (about a 50% difference between what we can see and what nucleosynthesis indicates), so it must be part or even all of that. Note that stars etc are only about 10% of the baryonic matter, so I would be surprised if the planets were more than another 5% or 10% to that total, and thus maybe 1% to the total mass of the universe.

When you write "denies", or "disbelieves", or "holds", you are essentially expressing some sort of qualification on believe. So, to be more straight forward, and I think accurate:

Atheist - A person who believe there is no god, or supreme beings.
Agnostic - A person who believes we don't know or can't know if god or supreme beings exist.

Once confronted with the question, "Does God exist?", there are pretty much three options: Yes, No, I don't know.

Saying no, means you believe that God doesn't exist, since you can't really prove that in any rigorous, universal way. Realistically you can't know that.

"Atheism is the most daring of all dogmas, for it is the assertion of a universal negative." - G.K. Chesterton

Richard Dawkins: I can't be sure God does not exist

There was surprise when Prof Dawkins acknowledged that he was less than 100 per cent certain of his conviction that there is no creator.

The philosopher Sir Anthony Kenny, who chaired the discussion, interjected: “Why don’t you call yourself an agnostic?” Prof Dawkins answered that he did.

An incredulous Sir Anthony replied: “You are described as the world’s most famous atheist.”

Prof Dawkins said that he was “6.9 out of seven” sure of his beliefs.

“I think the probability of a supernatural creator existing is very very low,” he added.

Collins: Why this scientist believes in God - Dr. Francis Collins

THE RELATION OF SCIENCE AND RELIGION - Some fresh observations on an old problem - by RICHARD P. FEYNMAN

The Public Face of Religion in America

Matthew Parris: As an atheist, I truly believe Africa needs God

what puzzles me more is a) why kites where not used more excessively for lifting objects, especially since the sail was known (perhaps they just dinae think of it?)

Kites were probably not used because wind is a very inconsistent source of power, and when you want to move something you want to move it *now*, not in 3 weeks when the wind is strong enough, or at night when the wind picks up, or whatever depending on where you are and what season you're in.

That's a bit of wordplay- same story as to when the boat was invented: it was whenever someone had wood, and noticed that it can take a load (and still float)

Now a shaft going through a firm hole that stays in place while it rotates and has a wheel attached yes, it is a different kind of invention, but the concept of "wheel" was there already- heavy things were carried by rolling them onto logs. True, not the most elegant solution, but beats the hell out of having your slaves die of exhaustion.

Puns aside, what puzzles me more is a) why kites where not used more excessively for lifting objects, especially since the sail was known (perhaps they just dinae think of it?) and b) why there was no industrial revolution after Ancient Greece since they had steam engines

Evolutionists seem to think any non beneficial mutation results in a non reproducing/ non viable entity.
No we don't.

The satellite, which could be something everybody in America gets a chance to use, is going to become the private property of not several, not a network or a special organization devoted to the satellite, but just one single university. A very expensive university in California. Why should they get it? Why not MIT? "Why not" a hundred other universities and colleges? It shouldn't be given to Caltech.

Caltech already runs it, and has since the start.

Just what one needs to image the black hole at the center of the Milky Way. If they can get the timing right, between this set of 4 telescopes operating as one, the Keck telescopes in Hawaii, and the Spitzer IR Space Telescope, we could have a virtual telescope in the IR band that is easily 30,000 km wide.
http://www.keckobservatory.org/
http://www.spitzer.caltech.edu/

Btw: This idea increased spatial resolution using very long baseline interferometry is why it would be worth a few billion dollars to send multi-spectral moderate aperture telescopes to the L4 & L5 points, IMHO.
http://en.wikipedia.org/wiki/Lagrangian_point

I have sympathy for the authors of the letter to the WSJ because of the attitudes of people like you. I'm an free thinking, rationally minded, individual. I value my right and capacity to evaluate arguments on their merit and to question the factual basis of other people's assertions. When people jump down my throat and call me a sophist, a "denier", and imply that anything I say must be preconceived notions that I have swallowed whole from some fossil fuel industry shill, all because I presumed to point out something that appears to be erroneous in someone else's statement, it irritates me.

The proposition I was testing (in a totally back of the envelope way) was that the temperature record of the past decade shows evidence of warming. I tested this particular proposition, not because I was hand picking data, but because the poster I responded to had suggested that the truth of this proposition was blatantly obvious. It did not seem so to me, and I believe that my quick calculation verified that intuition. Other than that I did not deny anything.

I specifically said "your argument provides good evidence that the past decade has been significantly warmer than other decades in the past 130 years". That is, a clear longer term warming trend exists. I also noted that "one could definitely argue that this does not constitute evidence against global warming". Which is exactly what you are doing.

I would argue however that the vehemence of your reply displays an attitude that is both characteristic of many people who urge action on reducing carbon emissions (something I support) and antithetical to the scientific mindset. There is much evidence that a person's preconceptions can have a significant impact on the outcome of their research, even with seemingly cut and dried empirical work like measuring the charge of the electron. The potential for bias induced error is undoubtedly much greater in a theoretical and speculative investigation like climate modeling, in which many important variables can only be roughly estimated. Combine with that potential the very real and evident passion displayed by many people who are involved in the research and you have a formula for bad science.

I have degrees in physics and economics. Physics draws conclusions from repeated experiments under carefully controlled conditions. Economics must rely on theory and limited data run through sophisticated econometric models, because the systems under consideration are not subject to control and repetition. Economists try to tease answers from our limited data. Answering a question like "Was the recent stimulus bill effective in promoting economic growth?" is not easy. Ideally we would set up the exact conditions of the U.S. in 2008 and try several runs with the stimulus bill and several without, then compare the results. That, unfortunately, is not possible. One can try to answer the question using mathematical models and computer simulations but the conclusion depends on how you handle your data and set up your model. Indeed, none of the models are able to predict the future trajectory of the economy with accuracy. Which is what I think the authors were getting at. If the climate models are so completely accurate that no reasonable person could possibly question them, then why did none of them predict flat global average temperatures over the past decade? If they're not that accurate, then why are people who ask seemingly reasonable questions about them insulted and shouted down?

I would suggest that climate modeling is much more similar to modelling the economy than to modelling, say, the trajectory of a space capsule. The problem of studying global warming is far more complicated than that of studying the impact of smoking on cancer rates. If we had data on the fates of thousands of Earth-like planets, some of which had been inhabited by carbon emitting civiliz

People start off being able to reason, school stomps it out of most of them:
http://www.alisongopnik.com/TheScientistInTheCrib.htm

Well-rounded (or rather, healthy, which does not always mean being perfectly rounded) human beings are more likely to come out of healthy communities and healthy families...

Some other links;

"The Underground History of American Education" by 1991 NYS Teacher of
the Year John Taylor Gatto
http://www.johntaylorgatto.com/underground/toc1.htm

"The Seven Lesson Schoolteacher" also by John Taylor Gatto
http://www.newciv.org/whole/schoolteacher.txt

"State Controlled Consciousness" also by John Taylor Gatto
http://www.the-open-boat.com/Gatto.html

"The Big Crunch" by David Goodstein, Vice Provost, Caltech
http://www.its.caltech.edu/~dg/crunch_art.html

"Disciplined Minds" by Jeff Schmidt
http://www.disciplined-minds.com/

"What Makes Mainstream Media Mainstream" by Noam Chomsky
http://www.chomsky.info/articles/199710--.htm

"University Secrets:Your Guide to Surviving a College Education" by
Robert D. Honigman
http://web.archive.org/web/20060707100524/www.universitysecrets.com/us.htm
http://web.archive.org/web/20060710145531/www.universitysecrets.com/table.htm

"The Kept University"
http://www.theatlantic.com/issues/2000/03/press.htm

"In Defense of Childhood: Protecting Kids' Inner Wildness " by Chris
Mercogliano, who spent thirty-five years teaching at the Albany Free School
http://www.chrismercogliano.com/childhood.htm

"Teach Your Own" by John Holt (and other books)
http://www.holtgws.com/

"The Teenage Liberation Handbook" by Grace Llewellyn (and other books)
http://gracellewellyn.com/

"The Emergence of Compulsory Schooling and Anarchist Resistance" By Matt Hern
http://web.archive.org/web/20071014123355/http://www.social-ecology.org/article.php?story=20031028151034651
http://www.mindfully.org/Reform/2003/Compulsory-Schooling-AnarchistMar03.htm

"Sustainable Education" by Jerry Mintz
http://www.greenmoneyjournal.com/article.mpl?articleid=195&newsletterid=1

"Federated Learning Communities"
http://www.ericdigests.org/2000-1/learning.html
http://www.

Sorry, but Sagan turned out to be, well, wrong:

Pope John Paul II - "Faith can never conflict with reason"
an interview with the gent who runs the Vatican Observatory
Why Catholics Like Einstein
A small peek into the whole controversy
a bit of insight

Everyone points at Galileo (quite a few centuries back) and screams, but turns a blind eye towards everything else that's been going on ever since.

Reading your comment, I have to think back to that lolcat picture "IZ NOT GUD WITH COMPUTERZ".

If you can prove the data exists, then there is away to access the data programatically. Or how do you think you just accessed it? Without a computer? Without a program? Is your browser not a program on a computer??

Crude example based on looking at it for five seconds:
Just use CURL or wget, to loop through the whole range for all parameters in http://nesssi.cacr.caltech.edu/cgi-bin/getcssconedbvo_release.cgi , (use a delay so to avoid flooding the server), then parse the results, piece the data together and load into your favorite database on your box,using a small script.
Done.

It might take some time due to the primitivity of the interface (the multi-cone search may be quicker), but there's nothing preventing you from accessing it programmatically.

Kids these days... If they don't get everything pre-chewed and padded in 3 feet of colorful but non-frightening foam, they run away and cry like babies.

As Gatto points out, schooling is segmented, with 1% or so of students receiving an education intended for them to be part of a top elite, and then about 10% or so more receiving a somewhat different education to be part of a managerial/professional class (doctors, lawyers), and then the rest intended for worker class status.

Whatever the level of "interactivity", there is still the issue of who sets the agenda, who tells whom what to learn and when, and so on. Is the situation learner-directed (like a public library) or is it state-directed (or employer-directed) like in a public school or private workplace?

If you think about what most businesses want, whatever they say, it is not "curiosity" but "assignable curiosity", which is a big difference. It is not critical thinking, but it is thinking critically about business problems within business assumptions while not rocking the boat where it matters. See also Jeff Schmidt's "Disciplined Minds" book which goes into that:
http://www.disciplined-minds.com/

The primary function of top 50 schools is not really "education" so much as "filtering". See Goodstein or Chomsky:
http://www.its.caltech.edu/~dg/crunch_art.html
http://www.chomsky.info/articles/199710--.htm
"People within them, who don't adjust to that structure, who don't accept it and internalize it (you can't really work with it unless you internalize it, and believe it); people who don't do that are likely to be weeded out along the way, starting from kindergarten, all the way up. There are all sorts of filtering devices to get rid of people who are a pain in the neck and think independently. Those of you who have been through college know that the educational system is very highly geared to rewarding conformity and obedience; if you don't do that, you are a troublemaker. So, it is kind of a filtering device which ends up with people who really honestly (they aren't lying) internalize the framework of belief and attitudes of the surrounding power system in the society. The elite institutions like, say, Harvard and Princeton and the small upscale colleges, for example, are very much geared to socialization. If you go through a place like Harvard, most of what goes on there is teaching manners; how to behave like a member of the upper classes, how to think the right thoughts, and so on."

It can take a long time to accept all this, especially after one has been through decades of schooling where the number one thing taught is how much you need schooling... It took me a long time to accept that... It can be especially hard for those who get the best grades in school...

When I was in high school (1970s) and we had just gotten Commodore PETs, I was thinking how this mean everyone could get cheap-to-copy tapes with content and programmed instruction so they could learn all sorts of stuff. I saw the big issue as being the cost of textbooks. I did not see then that such a thing would have violated the basic idea of schooling, that you are learning what the school system wants you to learn when it wants you to learn it, and what it already had was sufficient to that task. Schools were not interested in having their routines disrupted by people learning what they wanted when they wanted in as much depth as they wanted and without much oversight and tracking.

That is why educational computing has gone pretty much nowhere within most schools, except when it has been very narrowly crafted to essentially be just like a text-book (maybe just a bit better) and when it has been linked into a pervasive system of monitoring and evaluation and fine-grained control. Some of that is changing, but it is changing despite what schools are, not because of what schools are. Any change is from some few dedicated educators who often are risking everything to try something that would actually help kids a lot (like Gatto).

Th

I see a serious flaw in your reasoning.

My reasoning? If only I were so smart! The reverse demand slope of wine is an old, well-worn theory not of my making. I know there is a hot low-end wine category right now, but that doesn't change people's brains.

Even if you take exception to my wine example, the point still stands that many times people avoid more inexpensive products because they believe them to be inferior.

I'm not confused at all. Engineering and science have different goals. Science seeks to discover facts. Engineeering seeks to design systems which work, even in the face of uncertainty about facts.

I did not claim that climate science had no place in estimating fresh water supply. I merely pointed out that if you choose to do so, you must change your assumptions to reflect your change in goal: Discovery of physical phenomena, vs. construction of a system which will operate under the influence of those physical phenomena.

My studies as an undergraduate concentrated on construction of earthquake-resistant structures. Seismologists at the time were reasonably certain that the maximum vertical acceleration possible in an earthquake was typically (far) less about 0.6g and never more than 1g. There had never been an earthquake in recorded history which exceeded 1g peak vertical acceleration. Engineers designed structures with those figures as maximums. Then the Northridge earthquake hit and several seismograph measured a peak vertical accelerations in excess of 1g (the greatest being something like 1.6g). The I-5 freeway overpass which collapsed near downtown L.A. is thought to have failed because the vertical acceleration exceeded its design maximum.

While it feels comfy and safe to take refuge in historical statistical evidence, as engineers we should have realized that if an earthquake can produce horizontal accelerations in excess of 1g, then it's not that farfetched to think that some freak underground geologic structure could somehow reflect those movements in the vertical direction. Engineers accepted the "conservative" estimates of seismologists without question, and forgot that our "conservative" estimates frequently err in the opposite direction. Science strives for accuracy. Engineering strives for handling the worst case.

Depending on your route, it might make sense to either visit LIGO Livingston Observatory in Louisiana or LIGO Hanford Observatory in Washington state. The former is preferable because of their cool "science education center", but both of these facilities have public outreach staffs and hold public events regularly. Call ahead and ask about the public tour schedule. They are in the middle of a huge upgrade and their instruments are not in operation, but I think it's still worth your time.

Depending on your route, it might make sense to either visit LIGO Livingston Observatory in Louisiana or LIGO Hanford Observatory in Washington state. The former is preferable because of their cool "science education center", but both of these facilities have public outreach staffs and hold public events regularly. Call ahead and ask about the public tour schedule. They are in the middle of a huge upgrade and their instruments are not in operation, but I think it's still worth your time.

The text may be misleading, but that is how people actually talk about this sometimes.

I think I just have not been clear about the key issue.

People have for decades fought any kind of funding for "cold fusion" on the argument that it violates established laws of physics. The people arguing most heavily for that are people getting lots of funding for "hot fusion", despite the conflict of interest. This has serious ethical complications.

Physicist David Goodstein wrote, in another context: http://www.its.caltech.edu/~dg/crunch_art.html
"Peer review is usually quite a good way to identify valid science. Of course, a referee will occasionally fail to appreciate a truly visionary or revolutionary idea, but by and large, peer review works pretty well so long as scientific validity is the only issue at stake. However, it is not at all suited to arbitrate an intense competition for research funds or for editorial space in prestigious journals. There are many reasons for this, not the least being the fact that the referees have an obvious conflict of interest, since they are themselves competitors for the same resources."

For example, related to Cold Fusion, see:
http://nextbigfuture.com/2011/10/dr-george-miley-replicates-patterson.html#comment-341890693
"Third, theory that is institutionally immune to experimental falsification is the sine qua non of pseudoscience so it was the American Physical Society that was engaging in mass pseudoscience. Indeed, theory that is INSTITUTIONALLY immune to experimental falsification is theocracy."

If there is not funding for research, for the most part, it is not done. If things can't be published no matter how carefully and well done the research is, that is a disincentive for professional scientists to work in that field. That is what has been going on for decades with cold fusion. A few people have persisted anyway. But institutionally, cold fusion was never given a fair hearing.

What I'm talking about is the way that people are all essentially religious about some supposed physical law (like the second law of thermodynamics as an example, which basically is at the core of saying energy can not come from anything we do not make an exception about by calling it some kind of battery or reaction). People can cite such laws with the highest moral tone as to why something won't work because it does not fit into known approaches. Then time after time again something does not fit, and then suddenly it is OK because some new exception to the law is invented related to some new theory. But, do people learn much from that?

A true scientist is both intensely skeptical and yet also open to new ideas. Pathological 100% skepticism about anything new generally doesn't help anyone (except maybe those already getting grant funding). Scientists are not supposed to be theologians, but it seems many are (and poor ones at that, too). Also related: http://en.wikipedia.org/wiki/Scientism#Religion_and_philosophy

You're probably thinking of The Mechanical Universe hosted by a CalTech prof. I used to get up on Saturday mornings, eat breakfast, watch cartoons for 90 minutes, then watch TMU. Meant I had a good background before I even got to high school Physics.

Much as I enjoyed Bill Nye as an adult, it was still too much aimed at the ADD crowd IMO. Never watched Beakman's World. Mr. Wizard was better paced for the pre-MTV crowd.

I still don't understand math. I can manipulate the symbols but I don't understand what the symbols represent.

Spoken like a true algebraist! "The symbols" represent anything you want them to, subject only to whatever "ground rules" the desired algebraic manipulations require.

I believe that as a student in any discipline, understanding the things that the symbols represent is far more essential than being able to decode the symbols without comprehension.

I'd go further and question what it means in the first place to "learn" something without understanding it. In this sense, what one needs to "understand" is that the value of algebra is precisely that the symbols are "meaningless." This extends directly to C.S., and, for that matter, bookkeeping — using one set of symbols and procedures to enumerate, say, sheep, and another for, I don't know, ice cream cones, would be a major PITA.

Sure I have basic concepts down such as whole numbers, but more complex functions are completely lost on me.

If you take a nonzero complex number to be a positive "scale factor" and an angle (i.e., taking "polar coordinates"), you can think of them as geometric transformations, namely, rotation and uniform scaling about some fixed point in the plane. Then "complex multiplication" is simply "composition of transformations," which, as you can easily see from the geometry, happens to be commutative. Incidentally, quaternions are heavily used in computer graphics for similar reasons in three dimensions.

And addition of complex numbers is just "vector addition" in the plane, a.k.a. "adding arrows," a.k.a., adding pairs of numbers "componentwise." But you can do that in exactly the same way for triples, quadruples, quintuples, . . ., n-tuples of numbers; what's special about complex numbers is that they also have multiplication that follows the exact same rules as "ordinary" multiplication. And again, what they "represent" is entirely up to you — they're often used in physics and engineering to represent a great variety of phenomena. What do these phenomena have in common? The simple and seemingly bone-headed, but nevertheless true answer really does seem to be, "similar equations." This is no different, conceptually, than what counting sheep and counting ice cream cones have in common, namely, 1, 2, 3, 4, 5, . . . whatever these "mean."

I would be ever grateful to a math educator who could teach understandable concepts first, followed distantly by symbolic notation. Now that you understand what I'm taking about, I'll give this concept a name: "numbers vs numerals"

Highly recommended reading.

While I wholeheartedly agree with your sentiments, I tend to feel the problem is less one of "notation" per se and a more fundamental one of poor communication — funny symbols are just shorthand for (lots and lots of typically tedious and quite repetitive) words, after all. The main purpose of mathematical speech, including, without limitation, the sort used in the classroom, is communication. While this is no different than any other subject, I'm amazed at the number of students and teachers, "good" and "bad" alike, who seem to think it is.

In an unrelated nod to the article, how is this "news"? I'm 33 years old, and the Count has been around for 1, 2, 3, 4, 5, 6 years longer than me! (cue laughter and lightning)

"No, I think you'll find what's "hard" is actually making things that other people talk or dream about :-)"

True, but that is also hard to do when most of the social resources to do that are diverted into "me, too" redundant competition, paperwork related to that like patents, or, alternatively, military arms races.

I would have been happy to work on the details of all sorts of neat socially-useful devices. (I've ended up do mostly software because it was cheaper to do that as a small independent compared to stuff like robotic hardware or things requiring lab chemistry.)

Essentially, there is little support for fundamental or basic civilian research anymore, including at places like IBM Research. The few slots to do that are intensely fought for these days, meaning the best social infighters tend to get them (not saying some of them are not good scientists, too).

So, what is really hard is actually making things with essentially no budget while also having to do something else so you can get ration units to pay your bills and also trying to be a nice person. :-)

Still, the scale of our society is so big that fundamental stuff happens anyway here and there. But it is such a lie compared to the picture I was painted in the 1970s when I was in school. Part of the reason:
http://www.its.caltech.edu/~dg/crunch_art.html
http://disciplinedminds.com/

That's one reason much better fundamental science will flourish with something like a "basic income".

Here is a 12 minute YouTube video I just made that talks about a balance between five interwoven economies that shifts with cultural change and technological change:
      http://www.youtube.com/watch?v=4vK-M_e0JoY
A PDF file of the presentation is here:
      http://www.pdfernhout.net/media/FiveInterwovenEconomies.pdf

Also indirectly related to life in big organziations:
"Smile or Die"
http://www.youtube.com/watch?v=u5um8QWWRvo
"Have Fun at Work"
http://infohost.nmt.edu/~shipman/org/hfaw.html
"It is dangerous, and often fruitless, to try and solve problems without considering the underlying social system. ... On a purely practical level, this book is an excellent survival manual for results-oriented engineers who have developed attitude problems about the structural barriers to success in their work environments. Livingston discusses how to evaluate your social structure's potential for success, ways to get working projects out the door in spite of these barriers, and how to tell when you're wasting your time even working there."

I started with a different weight for the earth, which I got from here: http://coolcosmos.ipac.caltech.edu/cosmic_kids/AskKids/earthweight.shtml

Otherwise, I'm in the same ballpark that the AC got:

13,170,000,000,000,000,000,000,000 Earth, in pounds
6.585E+21 Earth, in tons ( / 2000)

5000000 Rate of decay per second, in tons
1.317E+15 Seconds to eradicate Earth ("in tons" / "rate of decay per second")
2.195E+13 Minutes ( / 60)
3.65833E+11 Hours ( / 24 )
15243055556 Days ( / 365)
41761796.04 Years

Where are we off?

This book chapter, by Kip Thorne and others, plus a heavy does of vector calculus, will get you there: http://www.pma.caltech.edu/Courses/ph136/yr2004/0424.1.K.pdf

Ohh... I did find class notes for 236. I assume that the prof will be happy you're learning too so here's a link:
http://www.pma.caltech.edu/~ph236/yr2010/index.html [caltech.edu]

by the way... learn to use google, and Amazon... Slashdot is full of old hosers, and now even Cmdr Taco has left!

Ohh... I did find class notes for 236. I assume that the prof will be happy you're learning too so here's a link:
http://www.pma.caltech.edu/~ph236/yr2010/index.html

by the way... learn to use google, and Amazon... Slashdot is full of old hosers, and now even Cmdr Taco has left!

You've made an admirable attempt to define your question clearly, but you didn't quite succeed. General relativity can be understood at a variety of mathematical levels, so saying you want to understand "the mathematics of general relativity" doesn't really pin it down.

The other issue is that you haven't defined your physics background. If you really want to understand GR, you need to be fairly sophisticated in physics.

The first thing I'd suggest is that you build a solid foundation of understanding in special relativity. The best intro to SR is Taylor and Wheeler, Spacetime Physics, and you already have the math background to understand that.

Physically, GR is a field theory. The first field theory was electromagnetism. E&M is a lot easier to understand than GR, because it takes place on a fixed background of flat spacetime, and it also connects directly to everyday experience. The more intuition and technical skill you can build up in the context of E&M, the better prepared you'll be for GR. For someone ambitious about going far in physics, the best intro to E&M is Purcell, Electricity and Magnetism. Purcell uses vector calculus, and he tries to teach you all the vector calc you need as he goes along. However, you will want some of the preparation provided by a second-semester calc course, and you will probably also have an easier time if you can also study from a separate book on vector calculus. Here is a free online calc book that I like, and here is a free vector calc book you could use. When you're learning second-semester calc, I'd suggest you skip the integration tricks that form the bulk of such a course; they're largely irrelevant to your goal, and nowadays you can use Maxima or integrals.com for that kind of thing.

With that background, you're more than prepared to start studying GR at the level of Exploring Black Holes, by Taylor and Wheeler.

If you want to go on after that and understand GR at a higher mathematical level, you could try an upper-division undergrad book such as Hartle or my own free book, and then maybe move on to a graduate-level texts. The mathematics used in graduate-level texts is typically introduced explicitly in the text itself; basically tensors and calculus on a manifold. You don't need any more math prerequisites than vector calculus before diving in. The classic graduate text is Misner, Thorne, and Wheeler. I would still recommend it wholeheartedly, except that it's now decades out of date. A more modern alternative is Carroll; there is a free online version, plus a more complete and up to date print version. Other GR books worth owning are General Relativity by Wald and The Large-Scale Structure of Space-Time by Hawking and Ellis.

Accidental means unintentional, usually with undesirable outcomes. Their intention was clearly to find supernovae therefore it was in no way an accident. An accidental discovery would be Hubble taking a picture of the galaxy for other reasons and just happening to catch the supernova. The PTF survey looks at a large part of the sky and has found 858 type Ia supernovae so far.

Simple fix. Pre-compute curvature, tessellate based on curvature. I.e. anisotropically remesh.

Yeah. I've had LHC@Home on my specific BOINC project manager since 2004. It hasn't had much available work, though. Mostly I work on Einstein@Home (processes LIGO and other gravitational wave observatory data).

A hamiltonian cycle in a connected, locally connected triangular grid graph (not isomorphic to D) can be found in polynomial time.

D is the linearly-convex hull of the Star of David. A polynomial time algorithm which is not exactly simple is available in [2]. It can be applied to solid grid graphs.
This approximately means if your lawn is not shaped like the Star of David and does not enclose any trees, bushes or ponds, you can implement the algorithm from [2] and get an perfect mowing path in polynomial time.
[1] Gordon, Orlovich, Werner. COMPLEXITY OF THE HAMILTONIAN CYCLE PROBLEM IN TRIANGULAR GRID GRAPHS
[2] W. Lenhart and C. Umans. Hamiltonian Cycles in Solid Grid Graphs

Thank you too, in return. I just used that point on fish and water writing to someone else today, coincidentally.

I've been trying to get Richard Stallman and the FSF to consider supporting a campaign (suggesting maybe run by me for pay, so I'm biased, but OK if it was someone else) for fostering the cataloging, creation, and discussion of free software that explores conventional and alternative heterodox economics for a 21st century of abundance for all, based on this appeal:
http://www.responsiblefinance.ch/appeal/
"The authors of this appeal are deeply concerned that more than three years since the outbreak of the financial and macroeconomic crisis that highlighted the pitfalls, limitations, dangers and responsibilities of main-stream thought in economics, finance and management, the quasi-monopolistic position of such thought within the academic world nevertheless remains largely unchallenged. This situation reflects the institutional power that the unconditional proponents of main-stream thought continue to exert on university teaching and research. This domination, propagated by the so-called top universities, dates back at least a quarter of a century and is effectively global. However, the very fact that this paradigm persists despite the current crisis, highlights the extent of its power and the dangerousness of its dogmatic character. Teachers and researchers, the signatories of the appeal, assert that this situation restricts the fecundity of research and teaching in economics, finance and management, diverting them as it does from issues critical to society."

Also related indirectly:
"RSA Animate - 21st century enlightenment "
http://www.youtube.com/watch?v=AC7ANGMy0yo

So, it is more than a lack of visionaries. The world has no shortage of would-be visionaries, like Paul Hawken documents:
http://www.blessedunrest.com/
"Paul Hawken has spent over a decade researching organizations dedicated to restoring the environment and fostering social justice. From billion-dollar nonprofits to single-person dot.causes, these groups collectively comprise the largest movement on earth, a movement that has no name, leader, or location, and that has gone largely ignored by politicians and the media. Like nature itself, it is organizing from the bottom up, in every city, town, and culture. and is emerging to be an extraordinary and creative expression of people's needs worldwide."

The problem is more like visionaries are filtered out or bought off or changed or isolated or starved or turned into wage slaves doing unrelated stuff to survive. Example:
"The murdering of my years: artists & activists making ends meet"
http://books.google.com/books/about/The_murdering_of_my_years.html?id=iBA7vACOwngC

Related articles on how dissent in academia is systematically suppressed:
http://disciplinedminds.com/
http://www.chomsky.info/articles/199710--.htm
http://www.its.caltech.edu/~dg/crunch_art.html

Yet, things progres anyway, as a tribute to the better side of human nature. Here are examples of GPL'd software that could serve as a base for moving further into exploring alternative economics:
http://p.seppecher.free.fr/jamel/
http://freeciv.wikia.com/wiki/Main_Page
http://www.ryzom.com/en/

There is also a lot of other softwar

For a long time I thought a balanced approach to renewable energy was the best strategy but I've recently changed my opinion to favoring solar heavily. Specifically, solar to various hydrocarbons. Even though it's not as efficient as other solar storage techniques, such as pumping water uphill, it directly generates a portable, energy dense medium. The lecture that really changed my mind came from Cal Tech professor Dr. Nathan Lewis. He talked about limits of every energy source and broke down the numbers in terms of potential energy from each. Nothing even came close to solar. And even though solar to hydrogen is cleaner, realistically, solar to hydrocarbons are much easier to use in our current economy.

Scientist code is usually a giant JUST-SO story, sufficient to derive the results they need for the task at hand.
They either don't have, or avoid putting in data that will crash the program so limit checking is not necessary.
Crashes are fine if they do nothing more than leave a trail of breadcrumbs sufficient to find the offending line of code.

Funny — this could as easily describe how physicists often write mathematics.

In this paper (the paper itself is here), Feynman notes that

The mathematics is not completely satisfactory. No attempt has been made to maintain mathematical rigor. The excuse is not that it is expected that rigorous demonstrations can be easily supplied. Quite the contrary, it is believed that to put the present methods on a rigorous basis may be quite a difficult task, beyond the abilities of the author.

Feynman's "exoskeleton" nevertheless led him to some reasonably well-respected work in quantum electrodynamics. But my point is simply that the problem isn't with "scientists," it's with intelligent people confusing 'ability, in principle to understand X' with 'actually understanding X in practice' —a fallacy that is very common in IT, and one Feynman quite consciously worked to avoid. Life is short, "all one surveys," quite long. Besides, it cuts both ways: it's not at all clear that developers who don't understand the underlying science would do a better job with scrupulous documentation, because even if they bothered to RTFM, they wouldn't have the necessary background to understand it. The net result might be a loss stemming from a "false sense of comprehension."

Finally, it is not unusual for engineers to "understand how hard it [will be] to turn [a given] exoskeleton into [the required] self-sufficient robot" only in retrospect, thus it seems quite silly to expect anyone else to understand this at the outset —here I did not say "believe one understands."

For "turning an exoskeleton into a robot," write "double-entry bookkeeping," "plumbing," "formal mathematical proof," "horseback archery," or "dating," and nothing much changes— it's hard to have a good working knowledge of something one has no experience doing.

Dariusz's name is Lis (fox in Polish), not Lisused. second group used

http://www.submm.caltech.edu/~dcl/

Yes, it certainly is too bad that NASA doesn't do anything anymore.

(Sorry if I left out your favorite misson; there's just so many.)

http://patapata.sourceforge.net/WhyEducationalTechnologyHasFailedSchools.html
"Ultimately, educational technology's greatest value is in supporting "learning on demand" based on interest or need which is at the opposite end of the spectrum compared to "learning just in case" based on someone else's demand. Compulsory schools don't usually traffic in "learning on demand", for the most part leaving that kind of activity to libraries or museums or the home or business or the "real world". In order for compulsory schools to make use of the best of educational technology and what is has to
offer, schools themselves must change. ... So, there is more to the story of technology than it failing in schools. Modern information and manufacturing technology itself is giving compulsory schools a failing grade. Compulsory schools do not pass in the information age. They are no longer needed. What remains is just to watch this all play out, and hopefully guide the collapse of compulsory schooling so that the fewest people get hurt in the process."

I wrote that essay after working towards some FOSS tools to make it easier for kids to get into programming.

Also related:
http://www.johntaylorgatto.com/chapters/16a.htm
"I'll bring this down to earth. Try to see that an intricately subordinated industrial/commercial system has only limited use for hundreds of millions of self-reliant, resourceful readers and critical thinkers. In an egalitarian, entrepreneurially based economy of confederated families like the one the Amish have or the Mondragon folk in the Basque region of Spain, any number of self-reliant people can be accommodated usefully, but not in a concentrated command-type economy like our own. Where on earth would they fit? In a great fanfare of moral fervor some years back, the Ford Motor Company opened the world's most productive auto engine plant in Chihuahua, Mexico. It insisted on hiring employees with 50 percent more school training than the Mexican norm of six years, but as time passed Ford removed its requirements and began to hire school dropouts, training them quite well in four to twelve weeks. The hype that education is essential to robot-like work was quietly abandoned. Our economy has no adequate outlet of expression for its artists, dancers, poets, painters, farmers, filmmakers, wildcat business people, handcraft workers, whiskey makers, intellectuals, or a thousand other useful human enterprises -- no outlet except corporate work or fringe slots on the periphery of things. Unless you do "creative" work the company way, you run afoul of a host of laws and regulations put on the books to control the dangerous products of imagination which can never be safely tolerated by a centralized command system."

And, speaking as someone who has been using computers for thirty years, and while thinking everyone should ideally have a baisc computer literacy to be an informed citizen, how many programmers does the world really need? Kids are smart. They know there are fewer and fewer "good" jobs in technology for all sorts of reasons.
http://philip.greenspun.com/careers/women-in-science
http://www.its.caltech.edu/~dg/crunch_art.html
http://community.dice.com/t5/Tech-Market-Conditions/Alice-Dice-s-claim-of-4-Unemployment/td-p/235866

From:
http://www.eetimes.com/electronics-news/4209831/Engineering--The-next-generation
"We often hear from readers who are engineers that they try to dissuade sons and daught

Professional Neuroscientist here... In fact, I'm recording from a sensory neuron that is partially responsible for the conciousness of an awake behaving mouse right now while browsing slashdot.

There is no reason to think that quantum physics has anything to do with the nature of conciousness. It is not useful to explain free will, or the illusion of free will, of the qualia of objects, or the steadyness of perception on a background of constantly varying spike rates in the brain.

Perhaps the best, short, free, relatively recent summary of the field was written by Christof Koch and Francis Crick, A Framework for Conciousness, and is available here :
http://papers.klab.caltech.edu/29/1/438.pdf

I also have a little essay on the nature of free will on my blog here, if interested.
http://brainwindows.wordpress.com/philosophy/philosophy-the-science-of-free-will/

One other concept that I never see in these debates - if we had some mechanism whereby microtubules could propagate information in the ways suggested, presumably this would happen at c. If this was the case, the speed advantage over the feet-per-second velocity of action potentials would ensure that we would all have evolved to use this mechanism (or been eaten by organisms that did).

Enjoy

Try NASA/IPAC Infrared Science Archive, for NASA's Infrared and Submilimeter Data all of the data is there, 277 columns by a little over 257 million rows. It should be trivial to write a Perl script to massage the data and feed it into POVRAY for the 3D representation, might take quite a while to get your output.

Here you go. Dipshit.

Professional Neuroscientist here... In fact, I'm recording from a sensory neuron that is partially responsible for the conciousness of an awake behaving mouse right now while browsing slashdot.

There is no reason to think that quantum physics has anything to do with the nature of conciousness. It is not useful to explain free will, or the illusion of free will, of the qualia of objects, or the steadyness of perception on a background of constantly varying spike rates in the brain.

Perhaps the best, short, free, relatively recent summary of the field was written by Christof Koch and Francis Crick, A Framework for Conciousness, and is available here : http://papers.klab.caltech.edu/29/1/438.pdf

I also have a little essay on the nature of free will on my blog here, if interested. http://brainwindows.wordpress.com/philosophy/philosophy-the-science-of-free-will/

By conservative estimates, bin Laden cost the US at least $3 trillion over the past 15 years,

It's great the way our problems with Al Qaeda, Taliban, Afghanistan, Pakistan, Iraq, Iran, Saudi Arabia, etc. can all be lumped on Bin Laden.

By that same logic, the butterfly that set off Hurricane Katrina was one hella expensive insect. Never mind the decades of poor decisions that came before, to make it what it was...

Hell, I wanna get on that bandwagon too! If it weren't for bin Laden, the USA would still have the wonderful warm relationship with the Arab world it previously enjoyed. The bastard!

Look up, for example, the work of Alcubierre, Van Den Broek, and others.

Yes, those would be the applications of General Relativity that require "exotic matter", which doesn't actually exist in our universe. If we had fairy dust we could also build a theoretically plausible Peter Pan Drive, if we had some fairies.

Also consider that warp (on a small scale) is what makes gravitational lensing possible.

Fun science fact: even in Newtonian gravity light beams are deflected by gravity wells (just with a slightly different deflection to what General Relativity predicts), so gravitational lensing in itself is not a particularly good example of GR-type spacetime warping.

Of course the dirty little secret of GR is that Einstein never considered it his final theory or even a fully satisfactory one - but after 1915, his program of building a classical relativistic theory of unified force fields increasingly diverged from where quantum mechanics was headed, and his deep disagreements with Bohr and other QM gurus are well-documented.

Everyone likes to remember Einstein as "the genius" who invented relativity - and pretend that he both invented E=MC^2 and that this led to the atomic bomb - yet pure Einsteinian relativity did not produce Quantum Electrodynamics (which really DID make atomic fission weapons possible) and in fact the failure of classical unification suggests that the foundations of GR (and by extension, SR, because GR was necessary to make SR compatible with gravity) are likely flawed, or at the very best, incomplete.

Many of the best minds have tried to make GR compatible with QED and failed. John Wheeler, for example. String Theory was our last, best hope for making sense of the incompatibility, but that seems to be rapidly falling out of fashion now as "not even wrong". So on the one hand we have the "beauty and simplicity" of Einstein's geometrical approach, and his SR is considered beyond debate - yet his later development of SR appears to lead into nothing but dead ends. So perhaps it wasn't strictly correct itself?

We "know" that SR is "absolutely correct", but we also know that it doesn't account for gravity without GR, and we also know that GR doesn't account for electromagnetism, let alone the strong and weak forces - and that things like parity violation in the strong force and the microwave background radiation ought to raise serious questions about whether the anisotropy of spacetime and the relativity of velocity addition are as fundamental principles as they appear at the local, electromagnetic level. Or whether Lorentz' ideas about the contraction being merely a local illusion of a global, absolute "ether frame" process might not have some validity.

But that's not something people like to talk about. In science, we like our unassailable saintly intellectual heroes, regardless of whether they were entirely self-consistent.

The Big Picture should also be mentioned:

http://bigpicture.caltech.edu/

and in porcelain form:

http://www.griffithobs.org/exhibits/bbigpicture.html

Others have also made the point that really cool astronomy projects are within the reach of "citizen scientists" with a modest budget.

No one at Caltech has to use Bose, they can build their own that are better.

Curiously enough, there used to be a Caltech project class based on pretty much exactly that, although it's unfortunately no longer offered:

http://www.its.caltech.edu/~musiclab/

As a bit of trivia, Caltech alum Bill Gross actually ended up founding GNP Audio based on an engineering project he did as a student. He later went on to co-found, like, a gajillion other companies.

Caltech physicist David Goodstein has been talking about PhD overproduction for nearly twenty years, and that it actually started twenty years before that. Worth reading. http://www.its.caltech.edu/~dg/crunch_art.html

http://www.marketwatch.com/story/imf-bombshell-age-of-america-about-to-end-2011-04-25?pagenumber=2
    "Commentary: China's economy will surpass the U.S. in 2016 [based on PPP] ...
    This is the result of decades during which China has successfully pursued economic policies aimed at national expansion and power, while the U.S. has embraced either free trade or, for want of a better term, economic appeasement.
    "There are two systems in collision," said Ralph Gomory, research professor at NYU's Stern business school. "They have a state-guided form of capitalism, and we have a much freer former of capitalism." What we have seen, he said, is "a massive shift in capability from the U.S. to China. What we have done is traded jobs for profit. The jobs have moved to China. The capability erodes in the U.S. and grows in China. That's very destructive. That is a big reason why the U.S. is becoming more and more polarized between a small, very rich class and an eroding middle class. The people who get the profits are very different from the people who lost the wages."
    The next chapter of the story is just beginning. ..."

See also:
    http://www.its.caltech.edu/~dg/crunch_art.html
    http://www.johntaylorgatto.com/chapters/16a.htm
    http://www.historyisaweapon.com/defcon1/zinncomrev24.html
    http://peswiki.com/index.php/OS:Economic_Transformation

What tinkerers related to science and technology can do though?
    http://www.treehugger.com/files/2009/09/surface-area-required-to-power-the-whole-world-with-solar-power-wind.php
    http://pesn.com/2011/01/17/9501746_Focardi-Rossi_10_kW_cold_fusion_prepping_for_market/

http://disciplinedminds.tripod.com/
"Upon publication of Disciplined Minds, the American Institute of Physics fired author Jeff Schmidt. He had been on the editorial staff of Physics Today magazine for 19 years. ...
    Who are you going to be? That is the question.
    In this riveting book about the world of professional work, Jeff Schmidt demonstrates that the workplace is a battleground for the very identity of the individual, as is graduate school, where professionals are trained. He shows that professional work is inherently political, and that professionals are hired to subordinate their own vision and maintain strict âoeideological discipline.â
    The hidden root of much career dissatisfaction, argues Schmidt, is the professionalâ(TM)s lack of control over the political component of his or her creative work. Many professionals set out to make a contribution to society and add meaning to their lives. Yet our system of professional education and employment abusively inculcates an acceptance of politically subordinate roles in which professionals typically do not make a significant difference, undermining the creative potential of individuals, organizations and even democracy.
    Schmidt details the battle one must fight to be an independent thinker and to pursue oneâ(TM)s own social vision in todayâ(TM)s corporate society. He shows how an honest reassessment of what it really means to be a professional employee can be remarkably liberating. After reading this brutally frank book, no one who works for a living will ever think the same way about his or her job."

Also by a physicist:
    http://www.its.caltech.edu/~dg/crunch_art.html

More links collected by me:
    http://www.pdfernhout.net/to-james-randi-on-skepticism-about-mainstream-science.html#Some_quotes_on_social_problems_in_science
    http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-October/005379.html
  http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/005584.html
    http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/006005.html

http://philip.greenspun.com/careers/women-in-science
"Summers was deservedly castigated, but not for the right reasons. He claimed to be giving a comprehensive list of reasons why there weren't more women reaching the top jobs in the sciences. Yet Summers, an economist, left one out: Adjusted for IQ, quantitative skills, and working hours, jobs in science are the lowest paid in the United States. ..."

But, see also on money as a bad motivator for creative work:
    http://www.youtube.com/watch?v=u6XAPnuFjJc

Some deeper issues:
    http://disciplinedminds.tripod.com/
    http://www.its.caltech.edu/~dg/crunch_art.html

My own saga: :-)
    http://www.pdfernhout.net/princeton-graduate-school-plans.html
    http://www.pdfernhout.net/reading-between-the-lines.html

Help yourself.