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While the theoretical model has been carefully studied (See for example, http://epubs.siam.org/doi/pdf/... ), I'm not aware if any entity ever validated the model by actually flying an aircraft along one of the potential flight paths and comparing the ping times and doppler offsets from the theoretical model with an actual flight path. Does anyone know if that was ever done? Second best would be to compare the metadata from some other known flight with that flight's actual path.

Well, I found the original article here. After skimming the PDF, it looks like they spent a whole bunch of time playing around with complex diffusion equations to model a very basic drip coffee setup. As they note in their conclusion, actually applying this model to actual drip coffee machines (which have various input methods for water), not to mention the varying geometry of drip coffee brewing apparatuses, would require a lot more complexity.

So, I still don't quite get what the big deal is, since this just models one not-quite-common-in-the-real-world scenario apparently with idealized geometry and other parameters... though I just skimmed the article. Perhaps someone else will find something more interesting from looking at this actual article link more closely.

You've successfully done the exact same thing that food-scientists have been doing for decades! That or the BBC managed to completely miss the point of the original publication.....Just checked. Yeah, BBC didn't get this at ALL. http://epubs.siam.org/doi/abs/...

People often forget that the first A in NASA stands for aeronautics. They have been hard at work at fully computerizing air traffic control. However as you can imagine this requires lots of testing given the potentially fatal consequences. NASA has held several competition rounds among contractors for the next air traffic control system, providing feedback to all candidates for the next round.

Here is one such paper. There are many others, from various academia and industry consortia. The work they are doing is rather cool.

Citeseer and google scholar contain a large amount of scientific papers freely accessible. Many journals have open access policies. Many researchers publish their result on arxiv before sending it anywhere else. IEEE and ACM let their members access papers (IEEE policy at http://www.ieee.org/publications_standards/publications/subscriptions/prod/mdl/mdl_overview.html . ACM's policy at https://campus.acm.org/public/qj/profqj/qjprof_control.cfm?form_type=Professional . SIAM's policy http://www.siam.org/membership/individual/benefits.php ). So ok, it is not free, but that's not really expensive either if you are actually interested. Most researchers publish preprint on their website. If they don't, drop them an email they'll send you a preprint (if I had not put it on my website, I would send a preprint.)

Assuming you could not find it. And the author is a jerk. And you don't want to pay for it. You can still stop by a university libray where you will be able to download it using university subscription or photocopy it if the library has a paper edition.

Finally, we are not looking to send our papers to the most expensive journal. To the most prestigious certainly, but the price has nothing to do with it. Arguably, one of the most prestigious journal in CS is ACM Computing Surveys. It is an ACM journal, so all ACM members can read it online for the price of their subscription. Hardly the most expensive journal.

That being said, I'd rather we only publish in openaccess journal et we ditch the publishers out. But that's not realistically going to happen anytime soon.

I haven't seen anything mentioned here in this discussion that isn't mentioned in the career pages of SIAM or the MAA.

I really don't see what the problem is. Algorithms are all around controlling everything we do. Like any technology, it is how they are used by humans that determine if their use is good or bad.

Look at the list of the greatest algorithms in history, as selected by SIAM (Society of Industrial and Applied Math) in 2000. Our lives would be completely different and worse without them.

• Monte Carlo method
• Linear programming solutions via the Simplex method
• Krylov subspace iteration methods
• Decomposition approach to matrix computations
• Compiler optimization for FORTRAN
• QR algorithm for computing eigenvalues
• Quicksort
• FFT
• Integer relation detection
• Fast multipole

Since this paper was written in 2000, I would guess that the Google founders' PageRank should be included in there as well.

http://www.siam.org/careers/thinking/work.php

The conference proceedings are not online yet. So I am not sure. I could not even find the title of the talk on the conference web page

I know people who are at SIAM PP and they are all : "why are they talking about PP on slashdot ?". There was no major anouncement. I'll check the proceedings again next week, but I believe there is no major improvement. IBM is probably just trying to get some more light.

We can find the following IBM talks in yesterday page :
http://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=9507
The paper have the same author and name than this paper published last year :
http://portal.acm.org/citation.cfm?id=1645413.1645421

So they are probable publishing an improvement on their 2009 work.

SIAM (Society for Industrial and Applied Mathematics) has several special interest groups related to computing/programming problems. The other major math and stat groups have excellent articles on computing problems from time to time as well like the AMS, MAA, or AMSTAT, but SIAM probably provides the most of these groups and a lot of coverage that compliments IEEE and ACM. Also depending on if you're working in a specific industry or if you're furthering your studies in a graduate program there may be other professional societies that deal with informatics or computational issues related to that focus.

Knuth's maxim is sufficiently pithy to have become, over time, self referential, as evidenced by your misunderstanding.

The root of all evil used to be deep and singular, now it is broad and shallow. I guarantee you that Knuth did not include choosing the best fundamental algorithm under the label "premature" unless it involves squabbling over log log N terms or stray digits in the exponent term.

http://www.siam.org/pdf/news/174.pdf

An unpacked (deoptimized) version of Knuth's maxim is that the transition from program structure and notation which maximizes readability, comprehension, and conviction (concerning its correctness and merit) to one which favours performance should be delayed as long as possible. Ideally until performance becomes the sole remaining success factor.

(Taking into account the human mind's special capacity to imprint upon evil, Knuth's formulation remains the better one.)

Originally Knuth meant manually hoisting loop constant expressions (often in ways that later turn out to not be fully general) or manually evaluating constant expressions or manually fusing nested function calls and the kind of rot that a good compiler these days will do on your behalf. Anyone used the "register" keyword lately? Once upon a time it seemed like a good idea.

While the principle remains the same, the temptations have changed. Such as parallelizing a bad implementation of a poor algorithm in the misguided belief that the underlying task is not sequentially bound.

That said, projects which do *no* evil typically fail to impress anyone. The ideal is to wrap large amount of cleanly structured and accessible source code around a nugget of pure, smoldering evil, coked to the last clock cycle.

Perversely, the worst example of this is TeX itself. The smoldering nugget of pure evil is the single pass parsing regime and data packing eight bit character values.

I suspect the literature on parallel programming would roughly equal the literature on electro-chemical storage cells. Sheesh, if only those guys were paying attention, we'd have watch batteries powering small cities by now.

On second thought, how much literature could there really be if you can summon the majority of it onto your screen in 4/10'ths of a second for any combination of keywords?

Parallel programming is a lot like fuel cells. You get some pretty impressive results on selected applications involving pristine apparatus in a controlled setting, dating back to the Apollo program (in both cases).

Reality on the ground is rarely so forgiving.

If we hadn't already achieved a pixel processing speed-up between 1980 and 2008 best approximated by a sideways 8, Javascript wouldn't even have entered the conversation.

It boils down to this: ignoring everything you guys have already accomplished, you've pretty much done nothing. I worked for that kind of company once. The guy in charge put on a Cirque du Soleil of intestinal recursion. That's how I feel about the claim that software developers haven't been paying attention to parallelism for elephant years.

Only for purchase linked except this one which has more detail (under News)
http://sinews.siam.org/old-issues/2008/januaryfebruary-2008/breakthrough-in-conformal-mapping

Just today, I sent in my annual membership renewal to SIAM even though the president this year is Cleve Moler who invented matlab(TM), the secret language of crippled users of matrix algorithms. http://www.siam.org/election/president_letter.php

Chan, dean of physical sciences at UCLA and a member of the SIAM [Society for Industrial and Applied Mathematics] Board of Trustees, was the math consultant for the NUMB3RS pilot.

(from http://www.siam.org/news/news.php?id=926)

In the same article they discuss how they work to get Numb3rs integrated into high school curricula:

About three weeks before an episode airs, CBS sends a synopsis of the mathematical topics involved to three NCTM teams (writers and reviewers, from both the high school and the university level). How large a part a topic will play is a matter of guesswork, says Karen Longhart, who coordinates the preparation of materials for NCTM; the actual plot is a closely guarded secret. The teams parcel out the themes and then go to work preparing materials for use by igh school teachers (see www.cbs.com/primetime/numb3rs/ti/activities.shtml). An estimated 20,000 teachers have worked the materials into lesson plans, says NCTM president Cathy Seeley, who expresses delight that this "wonderful opportunity" arose during her term.

I'll agree that the math seems overly simplified but it's done to a reasonable level for high school or early undergrad motivation for the topics. Certainly anyone with a good background in math can come up with better approaches than they use but judging from the half hour conference presentations I've seen they'd be hard pressed to present the solution plus the plot in an hour. It's also nice to see mapping work done that's more analytical than Google Maps and most commercial GIS.

People in general have no clue about the math behind floating point.

In my opinion, it should be an error to compare two floats values for equality or inequality.

--jeffk++

If we think back to the good old days of the first Gulf War and all that, we might remember the Patriot missile and what a dismal failure that was. Part of the problem there was that the missile's clock values were such that they would not convert to base 2 (and hence to float) accurately and so the tracking was off and lots of expensive misses happened. If you recall, lots of US soldiers died when a Scud that theoretically ought to have been shot down hit their barracks.

As usual, it's not just one thing that screws everything up, not even in the narrow confines of the Patriot's software problem. Here's a short write-up on that math/software part of it. There were other issues with the Patriot but that'd be blatant off-topic flamebait. ;)

If you want to figure out how to boost your ratings, why not get the advice from the horse's mouth?

Brin and Page's original paper about PageRank (Google) : the original Google paper

Another PageRank paper Inside PageRank

The problem is that PageRank isn't the end-all-and-be-all of Google. Allow me to quote from this SIAM News article

While Google relies heavily on PageRank for ranking its search results, it uses at least a hundred other metrics as well, making use of such things as the content of "anchor text," the highlighted description a user clicks on to follow a link. Such methods are powerful heuristics for sharpening the relevance of link analysis, but they also leave Google more vulnerable to spammers. A search on the term "miserable failure," for instance, returns a Web page about George Bush as the top result, a type of mischief known as "Google bombing." To help thwart spammers, Google keeps its exact ranking methods secret and changes them frequently.

Any doofus can look up the details of PageRank; therefore, that information is useless if you want to do better than everyone else. Trying to figure out those "hundred other metrics" is where SEO comes in. Trying to discern hidden logic is a tough problem and that's why those SEO companies can charge an arm and a leg. I have been told that the mathematics involved in SEO algorithms is non-trival.

GMD

Have you ever heard of Reed Solomon Error Correcting Codes?
You should check them out.
I'm thinking they allready built them into the design, and the 1TB is accounting for them allready.

[Please exuse me if this is what the article is about, I didn't feel up to sacrificing my first male child to the Times.] The newsletter for the Society for Industrial and Applied Mathematics has an interesting article about postage. from the article (link goes to page with link to PDF Read "Math 1, Spam 0")

The Penny Black Project instead uses "proofs of work," a concept first introduced in 1992 by Cynthia Dwork and Moni Naor of the IBM Almaden Research Center. The idea is simple: "If I don't know you, you have to prove to me that you spent ten seconds of CPU time just for me, and just for this message," says Dwork, who now works at Microsoft Research. For legitimate senders, spending ten extra seconds to send an e-mail message is no problem. Most of the time, you spend more time than that simply composing the message. But for spammers, those ten seconds are the kiss of death. The one thing that no one can steal is more seconds than there are in a day. For a single computer, the CPU time available in a day amounts to 86,400 seconds; a spammer who wanted to put electronic postage on millions of messages would thus need hundreds of computers. Dwork is betting that most spammers cannot afford that kind of expense. Spam costs almost nothing for a spammer to send, but a recipient who looks at the message and manually deletes it incurs a perceptible cost in lost time.

Dislaimer: I write software for Mars missions, including the 2007 Pheonix mission.

I hope they haven't recycled the imperial to numeric conversion code.

I must say I'm really tired of hearing about this every time there's an article about a mars misson. I mean, no one says "I hope they haven't recycled those overflow errors" every time an Ariane 5 rocket is lauched! Was it a stupid problem? Yes, however people seem to forget how rediculously hard it is to successfully launch a mission like this. Yes it's very easy to prevent a single mistake, but thousands of potential mistakes? Our track record with Mars probes is twice as good as the nearest competitor (Russia) and it's looking to continue that way.

Somebody want to contribute an open source alternative to them?

Look. The people working at NASA know how to write this stuff. That's not the problem. The problem is that on large scale projects like this, it's entirely possible for things like this to be overlooked... People tend to worry about the "hard" stuff rather than the easy stuff. And as for why they even have to convert units, as far as I understand NASA generally uses metric, it is the american aerospace companies that generally insist on using imperial units.

Also, Open Source is *NOT* the catch-all answer for everything! The development team I'm on uses linux for our development, and our software will be running on a lot of linux (and windows) boxes during the mission. We love open source, and even use some open libraries (such as castor) in our code as allowed (we are not allowed to link to GPL code of course).

However, I would cringe if the flight software was some open source deal... I mean, looking at the linux kernel sources, (some say it is the gem of open source) I wouldn't want to have to depend on anything written like *THAT* to handle flying in space. Great for on the ground where we can fix/replace/patch if there's a problem but... It's not cleanly designed and implemented like, say, QNX, etc. Few people alive have experience writing software for spaceflight systems, and I expect they they know just a little bit more about it than even the best of linux hackers do.

I guess I just don't understand why the parent post was modded insightful. Nothing personal, in7ane, but really!

Authors of accepted papers are encouraged to submit their TEX files to SIAM for typesetting.

It is because of expectations like this that I require graduate and undergraduate students write up assignments in LaTeX for my scientific computing course.

Authors of accepted papers are encouraged to submit their TEX files to SIAM for typesetting.

It is because of expectations like this that I require graduate and undergraduate students write up assignments in LaTeX for my scientific computing course.

It covers various ethical dilemmas (as I imagine Engineers do), and as someone else mentioned, goes over some of the more disastrous software creations. If you're interested, such lists usually include the Therac 25 (rollover bug, improper software re-use), the London Ambulance Service (Their newly-ordered, lowest-bidder Computer Aided Dispatch system caused massive problems), and the Ariane 5 rocket (overflow/improper error handling).

OTOH, I agree with you that people should know the conseqences (and likelyhood) of failure, as they clearly don't. There are loads examples on RISKS of people having laser surgery, needing some computerized medical device, and seeing gross examples that those using them have literally no idea the devices are misconfigured, warning of possible malfuctions, etc.

You can definitely do the FFT in integer arithmetic. I'm not sure of the details. Fixed point arithmetic is something I don't think about very much. It would be more work than floating point and it doesn't sound very fun to me. But then I'm very lazy, as my presence goofing off here proves. Still, I wish you good luck. A good integer FFT is a noble goal.

Concerning your attempt to get rid of multiplications, the Winograd FFT reduces the number of multiplications to O(n) but the number of additions increases (to O(n^2) if I remember correctly.) For large n this is obviously not useful unless multiplication is much slower than addition (which is not the case on todays computers.) It is however sometimes used for short length modules in mixed radix FFT algorithms.

If you are interested in efficient FFT, a web search turned up the following, which seems to have a ton of references (including the Winograd paper): burrus-notes There is also a good general reference book by Charles Van Loan published by the Society for Industrial and Applied Mathematics: SIAM It's amazing how much work is done in this area. The FFT is very important.

As it turns out, a lot of the best modern origami artists (in my opinion) are somehow technical: John Montroll and Peter Engel are mathematicians, and Robert Lang is an engineer. Even Dr. David Huffman (of Huffman compression fame) was into origami.

Lang has a pretty cool program called TreeMaker which lets him specify a model's "base" characteristics (like a stick figure) and algorithmically produces a fold pattern! Lang also has some of the most fiendishly complex origami I've ever attempted. (And yes, I have to say "attempted" on most of his insect models, not "completed".)

Of course, SIAM is a nonprofit research and teaching professional organization. All journals are peer-reviewed, at very little cost to the society. However, since I completed my Ph. D., I have been strongly considering refusing to submit my original research to any journals that do not offer similar non-exclusive copyright transfers. While I was working on my Ph. D., my advisor had a great deal of say as to which journals we submitted.

It may seem like an obvious thing to do (i.e., submit to an "open" peer-reviewed journal). However, most young researchers are looking for tenure, and get tenure (at predominantly research oriented schools) by having many of their articles published in top-tier journals. Unfortunately, this openness is rare among the top-tier journals. (SIAM is an exception.)

As far as the middle east goes, there is one major source rock and one minor one for the entire region.
The Late Callovian ocean floor? Gold thinks the rocks in the area are simply reservoirs which are capturing the upward flow. The Middle East has been greatly disrupted by tectonic activity (90 degree rotation is somewhat drastic), and obviously there are many faults to deeper areas. So the search for "source" rock has actually been the search for rock which met expectations near the reservoirs.

Gold seems to be under the impresion that oil has to form in situ; it does not. The composition and age of the reservior rock and caprock have nothing to do with oil formation. And it's not 'rotting'; it's thermal decomposition under a known range of parameters.
He agrees that oil is formed elsewhere, but dozens of kilometers further down than the 3 km which you expect. How does this thermal decomposition cause molecules to replace iron with nickel atoms, and reach the 700C+ temperature and pressure of 60 km down? (Two Sources...)

He also is ignorant of the fact that surface structural trands are invariably controlled by pre existing old trends. he also seems to think that island arc volcanoes are the result of deep heat sources and not subduction, ignoring a huge amount of evidence.
I haven't found reference to his belief on the origin of volcanoes themselves. He does state that they do emit much more gas than gas biogenic origin can explain. He's well aware of subduction and the tectonic faults, but points out that the resulting fractures offer routes for hydrocarbons to pass upward. So the same weak points along the Southeast Asia plate edges which cause volcanoes also cause hydrocarbons to become available near the surface. This is a different cause of volcanoes than one such as the Hawaiian "hot spot", whose cause I have not seen him mention (except that they also emit flammable gases...I don't know what possible biogenic source is there).

And he forgets that the earth has been completely molten and outgassed.
He didn't forget, he states that the Earth cold-formed with partial melting (see The Formation Process of the Earth). His specialty in astronomy might help him with that conclusion, as planetary accretion is studied in the field of astronomy more than it is in geology. We can also see that Venus retained a lot of carbon during its formation -- that atmosphere certainly didn't get boiled away.

And no, you can't see oil moving on 3D seismic, whatever the wall street journal says.

Try Google with "4D technique oil flow".
"4D seismic monitoring is the process of repeating 3D seismic surveys at a given site in time-lapse mode. This technique allows us to make 3D images of changes in dynamic subsurface properties as a function of time. In particular, images of heterogeneous fluid flow can be obtained that show spatial and temporal variation in fluid saturation, pressure and temperature."

All the above IIRC of course.

OK, I may be biased (I work for one of them) but they can be quite helpful. Most if not all have reduced rates for students. I know that SIAM has activity groups focusing on different areas of Mathematics. (Anyone care to guess who I work for?).

I am a 2nd year undergrad at a local university studying Computer Science, and I work tech support here. I can't form a real accurate opinion of what we do for our members, as I'm not all that interested in it, or do I work with members much. But I know we have conferences all over the country and have Job listing and such. Plus it's a good way to network with other geeks... Umm... I mean Mathematicians.

I suggest you check out some websites, see what you like, and perhaps pose the question towards some of them.

Society for Industrial and Applied Mathematics
American Mathematical Society
Association for Women in Mathematics
Mathematical Association of America

Also, here is a direct link to the AMS's link page

Good Luck, and feel free to email me with questions.

If you overwrite something with all zeros (or ones), it's almost guaranteed to still be there later because all you did was weaken (strengthen) the signal, the variation between two signals with the same current value represents the original value.

Since we're looking at the level of the magnetic domains and not the data bits directly, we must consider that we're looking at the coded version of the bits -- most likely encoded with a Reed-Solomon code. That is, for every N data bits, a codeword of N+M bits is stored on the medium, where M << N (typically). Since RS codes are linear, all 0s in the data would indeed give all 0s in the encoded representation, assuming that there are no additional constraints (e.g., such as a maximum run constraint). But, all 1s in the data will not in general (and perhaps not ever -- I'd have to refresh my memory on the details to be sure) give all 1s on the medium.

In general, the RS code and a good decoder will allow recovery of old data if most of the old bits can be recovered. This is why a CD can play back error-free despite a small number of scratches. If certain bits are much more suspect than others, a good RS decoder can make use of that information (a deletion is less costly than an incorrect bit).

The Ubiquitous Reed-Solomon Codes by Barry Cipra gives a concise and mostly non-technical introduction to RS codes.

One should realize that the most fundamental numerical algorithms do not change very rapidly. The most common numerical algorithms (sorting, linear algebra, differential equations, etc., both in serial and parallel) have been the subject of intense research by an army of applied mathematicians over the last half-century. All you have to do to take advantage of that work is to call your friendly local numerical library.

Of course, sophisticated 3D graphics methods are still the subject of intense research.

So in sum, I would argue that as far as "serious" numerical methods go, excellent solutions usually exist. (These methods are "open source", indeed open source before the term existed! They are usually published in the scientific literature. The main gains that remain are in "entertainment" applications. Bob

Since I didn't have the exact details right at the fingertips, I quoted the details from the paragraphs from those two weblinks in my article. I guess even the internet can be wrong! [smile]

Now you get to write a nastygram to the

Society for Industrial and Applied Mathematics for errors in a 1993 article,
(my story link was http://www.siam.org/siamnews/mtc/mtc193.htm)

and the European Patent Office for accepting data in a patent that erroneously describes the operation you are so angry about. (My original link here was http://swpat.ffii.org/vreji/pikta/txt/ep/0241/081/ desc.html)

Gee, I would have thought them reliable sources of information, but....

Check out the Vinny the Vampire comic strip

Agreed.

The technology takes advantadge of the error correcting technology built into every audio CD. This technology is what allows the CD to play well even with hundreds of minor scratches. I think that the error correction will try to compensate for loss of data up to a tenth of a second or something like that. What they do is they put hundreds of minor glitches that are able to be corrected for by the technology. The error correction technology works really well, and is no way even close to being similar to a wave file.

If I recall correctly, compact discs use a version called cross-interleaved Reed-Solomon code, or CIRC. The basic level of error correction provided for Audio CD is one uncorrectable bit out of every 10^9. CD-ROM provides additional protection for data (ECC/EDC ) reducing the error rate to one bit in 10^13 For those interested, there is this detailed description, along with this basic introduction.

The coding system is based on groups of bits--such as bytes--rather than individual 0s and 1s. That feature makes Reed-Solomon codes particularly good at dealing with "bursts" of errors: Six consecutive bit errors, for example, can affect at most two bytes. Thus, even a double-error-correction version of a Reed-Solomon code can provide a comfortable safety factor. Current implementations of Reed-Solomon codes in CD technology are able to cope with error bursts as long as 4000 consecutive bits.

Thus it is possible to put in a couple hundred bytes of junk data every second or that would be the basis of the copy protection, all without compromising audio quality.

That said, I can record any sound playing through my computer with the software I have. The Audio Quality will be very good, then I can burn direct to CD, or convert to MP3, or whatever. Of course, all that I use this for are the music tapes I have from when I used to record certain local bands in clubs professionally.

Check out the Vinny the Vampire comic strip

...the task of proving optimality seems impossible. No, I take that back, it is impossible

Actually, you're wrong. It is possible to prove in some cases that a given algorithm is optimal, and that a given implementation is optimal. You can discover this from a mathematically-based analysis of optimality, so that you can't use better hardware or loop unrolling, etc., to get a better solution.

Optimality is multi-faceted, since optimal solutions may exist for time constraints, space constraints, or both. Optimality is tied to computational complexity theory, since for some problem domains you can show that any solution must have a given complexity bounds, especially a theta-bound since that is the tightest bounds of a problem. Then you can show for a given machine set (abstracted assembly), with certain types of operations, that an implementation of the algorithm is in some sense optimal.

For some examples of proven optimal solutions to computational problems, see the following: static dictionary membership queries; generating minimal perfect hash functions; monte carlo estimation; scanning spanning trees of undirected graphs; hyperplane depth; simultaneous buffer and wire sizing (with implementation); maximum independent set of a circular-arc graph. The list could go on, but this gives you some idea of the breadth of solutions available. Sometimes, as with the halting problem, you can show that no solution exists, optimal or not.

As a final note, however, optimal solutions exist in algorithmics for well-defined computational problems. It is an entirely different thing to solve most real-world problems, where many non-theoretical issues enter the fray, such as how quickly can the code be written, is the design easily understood, how well can your code be maintained, does it do what the user or customer wants, does it have a good human interface, etc. These issues, rather than theoretics, dominate most of the actually programming that goes on in the world (despite what your professors may have taught you! ;-). In that sense, the language/optimality/editor/UI/paradigm flame wars will still go on for as long as people are using computers.

But it is still fun, on the rare occasion, to point out to your boss that your implementation of merging accounting transactions is theoretically optimal. Not that they really care, they just want it done by Friday. ;-)

...the task of proving optimality seems impossible. No, I take that back, it is impossible

Actually, you're wrong. It is possible to prove in some cases that a given algorithm is optimal, and that a given implementation is optimal. You can discover this from a mathematically-based analysis of optimality, so that you can't use better hardware or loop unrolling, etc., to get a better solution.

Optimality is multi-faceted, since optimal solutions may exist for time constraints, space constraints, or both. Optimality is tied to computational complexity theory, since for some problem domains you can show that any solution must have a given complexity bounds, especially a theta-bound since that is the tightest bounds of a problem. Then you can show for a given machine set (abstracted assembly), with certain types of operations, that an implementation of the algorithm is in some sense optimal.

For some examples of proven optimal solutions to computational problems, see the following: static dictionary membership queries; generating minimal perfect hash functions; monte carlo estimation; scanning spanning trees of undirected graphs; hyperplane depth; simultaneous buffer and wire sizing (with implementation); maximum independent set of a circular-arc graph. The list could go on, but this gives you some idea of the breadth of solutions available. Sometimes, as with the halting problem, you can show that no solution exists, optimal or not.

As a final note, however, optimal solutions exist in algorithmics for well-defined computational problems. It is an entirely different thing to solve most real-world problems, where many non-theoretical issues enter the fray, such as how quickly can the code be written, is the design easily understood, how well can your code be maintained, does it do what the user or customer wants, does it have a good human interface, etc. These issues, rather than theoretics, dominate most of the actually programming that goes on in the world (despite what your professors may have taught you! ;-). In that sense, the language/optimality/editor/UI/paradigm flame wars will still go on for as long as people are using computers.

But it is still fun, on the rare occasion, to point out to your boss that your implementation of merging accounting transactions is theoretically optimal. Not that they really care, they just want it done by Friday. ;-)

Are you self-aware at all? Can you prove it to another person?

The most enjoyable Computer Science course I took at Cornell asked questions like this. It was a "fun" class with a survey of programming in lots of different environments. Every day the professor would put up a maxim for discussion, basically an interesting theory. They were usually quite provocative. One of my favourites goes like this:

19. Eventually mankind will solve the problem of consciousness by deciding that we are not conscious after all, nor ever were.

An expanded list of Professor Trefethen's maxims is at SIAM in case anybody's interested.

I'm subscribed to a few journals, and I figure the open-source method of having journals would reduce the cost of journals (paying in upwards of $200 a year for a journal is crap).

However, I'm not so sure that we should open it up to people outside the discipline. This is my major concern. I don't want non-mathematicians reviewing SIAM, as I'm sure that non-physicians should have no right to review medical journals.

Most hip journals post their articles, or most of their articles online already. SIAM, the Society for Industrial and Applied Mathematics. Mathematics publications aren't that sexy, so that attracts a limited amount.

My major concern is that if we start pushing biomed articles, it'd be a good idea for academics to push open discourse. However, I do agree with the major concerns for health care providers. If a research article takes one position on a health condition and this is open to the public, this could damage health care treatment. An example of this is if there was some new fangled cancer treatment and it got published in a journal online and if I was a cancer patient, knowing this could present problems with dealing with your health care provider. What if the published research is wrong and incorrect? What if it's misleading to the untrained eye?

Another topic that we have to talk about is whether or not most people would a) be interested and b) can understand topics in journals. I realise that the Slashdot reader is more intelligent than your average web surfer, but realistically, would your average AOL user be able to adequately understand stuff published in the NEJM (New England J. of Med)? Would they really care?

All I'm saying is that we can't go nuts and start open-sourcing everything. Patience...