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And, using perl and Math::BigInt, I did, and it checked out. Also useful is to verify that the number really was RSA200, as other anonymous Wiki-troll-edits were changing the number like a flickering flame.

And the source of the original Anon-Wiki edit was an email from the academic ring-leader, available on FactorRecords on FactorWorld.

IAAAM,

Bill N1VUX
I Am An Apostate Mathematician
I prostitute my math degree sorting ones from zeroes

And, using perl and Math::BigInt, I did, and it checked out. Also useful is to verify that the number really was RSA200, as other anonymous Wiki-troll-edits were changing the number like a flickering flame.

And the source of the original Anon-Wiki edit was an email from the academic ring-leader, available on FactorRecords on FactorWorld.

IAAAM,

Bill N1VUX
I Am An Apostate Mathematician
I prostitute my math degree sorting ones from zeroes

FWIW: ANY factorization of a number into two primes is unique, as any number is uniquely factored into primes.

For a second source, see Mathworld.

Yes, I should be modded -1 sexist.

It's unclear whether the newborn is a boy or a girl, but what is known is that it has no hair.

Perhaps you're thinking of tachyons , which (if they exist) go faster than the speed of light.

He's absolutely right http://mathworld.wolfram.com/NormalNumber.html

Eh? If one can be determined from the other, then it's a pretty reasonable assumption that they should be equally random. Or that the difference in their randomness is related to the base in which you're performing the computation (ie, base 10) which wouldn't be interesting at all.

Actually, it's because pi is not random at all. It is believed to be normal (http://mathworld.wolfram.com/NormalNumber.html, that's the third time I've posted that here). The reason their method worked is because they knew the sequence of numbers: as soon as they figured out where they were in the sequence, there were online databases of which numbers would come up next.

Actually, formally speaking, it doesn't mean a thing. Nobody has yet been able to prove that pi or e is normal (http://mathworld.wolfram.com/NormalNumber.html), although both are believed to be. Just because they show up in the same function doesn't make them more or less random.

HOWEVER, somewhere, someplace way WAY down the sequence, it will certainly start repeating the ENTIRE sequence again, like 3.14159....3141592653589793....

No, Pi will never repeat itself. Substrings will, but the entire number of Pi will never be repeated inside itself. This is because it is an irrational number.
For more information: http://mathworld.wolfram.com/IrrationalNumber.html

For example, lots of large numbers follow Benford's Law. Excerpt: "Benford's law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability ~= 30% , much greater than the expected 11.1%" The probability distribution is logarithmic; the probability of a digit D is log10(1 + 1/D). This is a way the SEC checks filings for fraud. If the numbers are too evenly distributed, there's a good chance of fraud. Obviously if you know about this law you can spoof it to some degree, but it was an effective tool for a while (still probably is for some not so smart firms).

http://mathworld.wolfram.com/NormalNumber.html has a good description

(I believe this is proven)

Pi has not been proven normal.

http://mathworld.wolfram.com/NormalNumber.html

http://www.wolfram.com/products/gridmathematica/

Mathematica product (by Wolfram Research) for running Mathematica on a Grid.

It runs on a very wide range of platforms too apparently.

I wonder, is there a second Serre's Conjecture, or do people not do research any more to see if their work has already been done? Every link I can find for Serre's Conjecture or Quillen-Suslin Theorem indicates that it has already been proved (Quillen got the Fields medal in 1978).

that Serre's Conjecture was already proven?

Pretty exciting stuff! (Relatively speaking, of course :-)

Mathworld says hendecagon is to be preferred over undecagon, as it is formed of Greek roots rather than a mix of Latin and Greek.

How many Slashdotters would buy a computer case shaped like a D20?

D20? Eh. Now, an icosahedron, there's something worth buying. Even better, a tetrahedron 5-compound.

(yeah, let's see you out-nerd that! ;)

Since most computer scientists are mathematicians at heart, they'll solve the problem by saying: ``Assume a network of super-luminal communications devices.''

Hint: after Trillion, the next is Quadrillion, and then (hold you breath) Quintillion. Gosh it's, like, a pattern!

With bulbs, it gets more complex because it's not just a function of the temperature of the white

It is exactly a function of the temperature of the white.. in fact, it's exactly function of the temperature of the filament. (minus a few absorption bands)

The function is given by Planck, Planck's Law of Blackbody Radiation

The 'temperature' in your presets is an approximation to the Blackbody spectrum at those temperatures. Warmer and Cooler are, however, reversed when people discuss the whites of pictures etc. I suspect it's because for much of our history light would be either the sun or a fire - and everyone knows a fire is warm. (even though it is much cooler than the sun)

Regardless, given enough complexity, leds could surely approximate a solar spectrum, but it would be very difficult for incandescents to reach the temperature required to actually emit a solar spectrum. (first you have to find a filament material that won't melt/vaporize at solar temperature.)

All cost of production determines is whether or not the good is offered in the first place. If the market price is higher than the cost of production, the good will be offered; if not, then it won't.

The price itself is determined simply by supply relative to demand, period. The notion that cost of production affects price is nothing more than a remnant of the long-ago debunked "Labor Theory of Value"

As I noted, the curve describing total costs ($) of production versus number of items produced determines in turn the curve for marginal production cost ($/widget)-- the latter being the derivative of the former. Furthermore, this marginal production cost curve not only affects, but IS the supply curve. And market price is dictated by the interaction (and curve intersection) of this with with consumer demand. Thus, production costs not only dictate whether the good will be offered (by whether there is an intersection of the curves for production greater than zero), but also helps determine what the market price will be (by exactly where the curves intersect).

Or, in syllogism form:

Production costs determines marginal production costs.
Marginal production costs is another name for the supply curve.
The supply curve (together with the demand curve) determines price.
Ergo, production costs affect price.

(The more obsessively anal economist will note that the marginal production cost curve is actually the cause for the production cost curve, not the effect; and that the marginal production cost curve is only the short term supply curve, with the average production cost being the long term supply curve. On the one hand that's irrelevant here, and on the other hand all three curves are still a specific instances of production costs, so nyah-nyah-nyah to the hypothetical Mr. Obsessive.)

--
Why can't we moderate posts incoherent?

Now if they were able to distinguish prime numbers from a random list of very lengthy primes and non-primes, then that would be something.

There is an efficient algorithm for primality testing already.

And, seriously, being able to come up with twenty digit prime numbers off the top of your head like the twins did *is* something. And it poses quite a challenge to the reductionist approach to the mind , which is basically to map cognitive impairments with damage to specific parts to the brain. The two twins had serious brain defects, yet possesed abilities not found in people with undamaged brains.

• I guess I'm just finding it difficult to imagine what I would ever need, say, 32Ghz for, other than gaming--which would be what my ultra-hip game console would be for.

1. Speech recognition. Not the easy kind, where a user sitting at his laptop controls the mouse cursor, but the hard kind, which listens to a room full of people and nails the transcript in real time.
2. Robots. Not the easy kind, that do a few simple preprogrammed maneuvers, but the hard kind, which do what you would have told them if you'd thought of it first. Then they take over and hunt us down like rats to use as an energy source, but that's a different story (or two stories).
3. There is a whole class of problems (computer scientists call them "NP-hard") which essentially take as much computing power as you have. Examples include completing the timetable for a university's class schedule based on which students want which class at which time, etc. (a form of the "Traveling Salesman Problem").
4. Three-dimensional interfaces. Bitmap images currently use only 2-D; imagine how much more horsepower it will take to manipulate and display 3-D bitmaps. And that's just the bitmaps themselves, not the a whole 3-D space that the user manipulates instead of this little flat thing you're looking at now.
5. Real-time cartoons. It's currently impractical to generate realistic animation from a script. With enough computing power, you could do all the sprite movement and ray-tracing in something like Display Postscript.
6. Whatever is next. We'll always find things to do with more processor cycles.

Yes... though it blows up for non-positive integers. See mathworld for details.

I probably HBT, but anyway - your "waste of time" statement is just not true. Many, many articles on Wikipedia are excellent: informative, detailed, and well-written. In particular, I often have occasion to look up information about mathematical topics, and have usually found the maths articles to be highly useful.

For example, compare the Wikipedia entry for "Lie group" with the Mathworld entry. There are many other pages of a similar, or higher, level of quality.

Of course, you have to take everything on Wikipedia with a pinch of salt - but that applies to every online resource! And, in fact, every source of information in the world.

I hope the take the history of Mathworld as a warning as what can happen in the publishing world.

Using the so-called "miraculous" BBP Formula you can derive an algorithm for quickly determining the Nth hexadecimal digit of pi without -- get this -- without computing any of the 0...N-1 digits. The formula was determined with heavy reliance on Mathematica, though oddly Mathworld doesn't mention this (and Mathworld is hosted at Wolfram!).

Doesn't the story go that the Feigenbaum constant was discovered because he moved away from computers, not onto them? Or was that Lotfi Zadeh and fuzzy logic?

I think you don't understand what Pi or what a circle is.

Pi is the ratio of the circumference of a circle to its diameter. A circle is not a physical object. It exists only in the mind. Therefore, it is impossible to physically "measure" pi; just like it is impossible to find the weight of linux. Linux is software, it doesn't have a weight. Likewise, Pi is not a physical quantity, but a mathematical one. So it doesn't have a physical measurement.

However, you might be interested in this method for finding the digits of Pi that uses a physical experiment along with probability theory:
http://mathworld.wolfram.com/BuffonsNeedleProblem. html

Of course the experiment suffers from the same fundamental problem that trying to directly measure a drawn circle suffers from. That is that the physical situation is not the same as the mathematical one. Physical lines will never be perfectly parallel and the needle will not be a perfect needle. You need a way to correct for the fact that your lines aren't parallel.

I would say that the best physical method for measuring Pi is with a computer. That way you can ensure that the differences between the physical situation and the mathematical one are corrected. That is the beauty of digitizing things. You can guarantee error free results.

I refer you to http://scienceworld.wolfram.com/physics/Photon.htm l.

"10 to the 22nd, 10 to the 23rd, 10 to the 24th... fuck this.. infinity. . goodnight"

Not to disturb you sleep or anything, but once you hit that basic infinity, you're far from done.

Here's a good jumping off point.
Pleasant dreams ;-)

But 1/0 is very close to infinity, because:
lim |1/x| as x->0 = Infinity

This will continue until Google figure out a way to provide transfinite mail storage.

You're missing arguably the most useful subtraction: -blog. Blogs are fine for what they are, but the extremely high clique numbers in blogspace seem to give them ridiculously high page ranks. In the cases where I need information that may be best found in blogs (e.g. new web design tricks), I can remove the exclusion.

Check your facts. A pyramid can have any polygon for a base. The Egyptian pyramids (among others) happen to have square bases.

No, again we bump up against reading comprehensions I think.

"The folks who do the averaging happen to use the arithmetic mean over the field with specific sets of weights"

"rather than, say, the geometric mean "

What he is saying is that the folks who do arithmetic mean and weights, take sample data that is unevenly spread, and attempt to adjust it so as to give a smooth average. I.e they weight the numbers, for example, they take 500 Monitoring stations in NY City, each individual monitoring station has less weight than say the 5 monitoring stations in Provo Utah.

Alternatively one could take an average of the different locals and then use the one average as the local mean temperature.

i.e. there is more than one way to do such a thing.

For the readers at home, doing a search on Geometric Mean shows a host of people using it as perfectly valid science. In fact another term for geometric mean is "Weighted Mean" as in using the arithmetic with weights being equivalent to geometric mean.

gee a lot of math people talking about the benefits of geometric mean
You would find it hard to believe that no one used this convention normally
Geometric means are often useful summaries for highly skewed data

I'll agree that in first year Physics they might only teach one method of averaging, but it is well known, even outside of mathematical circles, that there is more than one way to average a series of complex variable numbers.

Might I suggest, assuming UNSW offers it, that you take some higher Physics courses, and possibly some mathematics courses. I'm sure those will go into these areas in more detail.

Now I know you primarily use Java (spit) but you do use Matlab, I do believe Geometric mean is included within that, maybe you could play around with it a bit.

Hardy-Ramanujan partition function is a direct formula and gives an easy asymptotic estimate. The series form for this was proven by Hans Rademacher.

Partition function from Mathworld.

More on Ramanujan at St. Andrews
Also at physorg.
It all deals with the Partition function.

Actually, grand parent is right. Two parts with a MTBF of, say, an hour, used in the same system at the same time, sum to a MTBF of (slightly) less than 1 hour. Not directly, which would imply an MTBF of 1/2 an hour, but they sum.

Look at the space shuttle: No single part has an failure rate worse than once in 100K launches (IIRC; it may have been one in a million. It's in the design specs)*

Now, there are some odd million parts. WHOA! No, you don't get a failure every launch, but the failure rate is WAY higher than on in a million -- think the RFP/design specs 'required' a one in 10K chance of failure.

The reason for the discussion was based on some of the 'design requirements' floated about for the next-gen 'shuttle replacement' -- one of which was a 1 in a million chance of failure -- thus necessitating a piece-wise failure rate of around 1 in a billion.

And what in the world does the Monty Hall problem have to do with this?

Try: Math World

and:
NASA

And the most directly applicable:
Hotwire article

Or just consider how they test for MTFB: Take 1000 parts. Run them until all of them die (not really for hard-drives, but this is how you do it for REALLY IMPORTANT things:~} ). Now plot the distribution and take the mean.

Cheers,

* yes, I am a rocket scientist, and this was discussed in classes I took years ago.

Here's an explaination to those of you who are wondering why the you would put puncutation between the upper and lower case letters.

Regular expressions operate on the ascii table. Thus the letters are encoded as numbers (duh). Anyway, they have it so that the upper and lower case letters are exactly 0x20 or 32 away. This is to be able to flip one bit to upper or lower the case letters so that it's a very efficient operation.

A = 0x41 = 0100 0001
a = 0x61 = 0110 0001

In pseudo code A xor 0x20 -> a.(for those that know what xor is)

I relize that explaining this in an article about regexs may not find any readers who didn't already know it. But hey, I though it was cool when I learned it.

First off, IANAP (I am Not a Physicist)

However, I have taken some more advanced undergraduate courses in electromagnetics and optics. Caveat emptor, so hopefully, this doesn't come off as being too condescending, and is, in fact, more or less accurate :)

First off, it's necessary to understand the difference between group velocity and phase velocity. Basically, a pulse of light can be thought of as a sum of many perfect sinusoids, each of which travels through space with a particular phase velocity. The superposition (sum) of all of these waves appears to travel with the group velocity (note that in almost all media save for vacuum, the phase velocities are not equal and so distortion of the wave packet, the shape of the pulse, takes place as the pulse propagates). Got it? Good.

For the easy problem: slowing the speed of light is nothing new (though the degree to which they managed to slow light down is quite impressive!) The index of refraction is the ratio of the phase velocity in a medium to the phase velocity in a vacuum. As a very simplistic explanation, this difference is due to the delaying of light when a photon hits an electron, is absorbed, and gets released some infinitesimal amount of time later. Almost all materials have indices of refraction greater than 1 for all wavelengths of light. For those that don't, e.g. x-rays in certain crystals driven at frequencies near their resonance, phase velocities are greater than the speed of light, but the fact that they cannot be modulated implies that Relativity remains safe since no INFORMATION is travelling faster than the speed of light. As a neato application of the slowing of light, optical delay lines for fiber optics currently consist of diverting signals into spools of optical fiber, where they're held until signals can become resynchronized. Work is currently being done in using these really high n materials to create optical delays.

As for the slightly harder problem of the laser pulse apparently travelling faster than the speed of light... When the researchers sent the pulse of light into the medium, this pulse consisted of the multiple sinusoidal waves mentioned above. These sinusoids cancel out at the front of the pulse and towards the end of the pulse, and produce the pulse (typically a Gaussian) in the middle. Remember what I said about the index of refraction being the ratio of phase velocities to vacuum phase velocities? Some of the sinusoids will travel faster than others, with the result that the sinusoids at the beginning of the pulse that previously cancelled out no longer do so, and so the group velocity appears to be faster than the speed of light. If you were to physically block the laser until just a few moments before the pulse of light was generated, and then detected the pulse a little down the road, you'd find that the maximum speed (the distance from laser to receiver divided by the time from unblocking to receiving the pulse) would be the speed of light. Once again, information does not travel faster than the speed of light (though the group velocity appeared to do so).

So old theory, though it's really cool to see it applied. You'll also note that both of these experiments made use of a Bose-Einstein Condensate (BEC) which is a really hard to prepare state of matter in which quantum effects are readily observable. A lot of really cool (no pun intended) physics is being/will be done involving BECs.

Agreed on the fractals! Fractals are cool!

A Sierpinski Sieve not only looks cool, but there is a very simple algorithm you can use to generate it:

- Pick 3 corner points. They need not be arranged in a perfect triangle (if they aren't, you will get a warped version of the fractal.. useful for illustration!)
- Start at any point inside the shape formed by the three corner points.
- Pick one of the 3 corner points at random. Your new point is half-way between your old point, and your chosen corner point. Plot a dot there.
- Repeat the above step indefinitely.

This is VERY simple code, it only uses very simple graphics intructions and changes to things like colors and corner points (moving them further apart, closer together, use equilateral or isoceles triangles...) give instant gratification..

As homework for the "Advanced" (curious) students, maybe let them try to make one (or more) of the three corner points interactive and move at runtime.

Asperger's syndrome is a very specific kind of autism, that has become a buzzword but relatively few people have.

There's a very broad definition of autism something like "parts of the brain normally used to handle day-to-day activities are instead used for other things" - IANAP, and my interpretion could be off base here, but that's what I'm getting at. There are plenty of folks who would not be diagnosed as 'autistic' because the degree to which they are affected is not disabling, but the way in which they are affected is just the same.

Asperger's syndrome is one example of this that's well described - to quote the autism.org page "Sometimes people assume everyone who has autism and is high-functioning has Asperger's syndrome. However, it appears that there are several forms of high-functioning autism, and Asperger's syndrome is one form.". There are probably dozens of related high-functioning conditions. The "absent minded profesor" is more than a cliche.

Sometimes the "other things" the brain is wired for are quite useful for mathmatics. As far as I know there has only been one person like Srinivasa Ramanujan, but there are plenty of other ways in which a differently wired brain helps in math-related fields, especially superior 3D visualization and th ability to hold large amounts of state about a problem in your head.

You make an excellent point. If I were the head of IRS, I'd use this very point as an argument to Congress allow IRS to propose a normalized (consistent) ruleset, and adopt the changes. Once they accomplish that (yeah, right!!), then whenever a proposed new law would violate consistency, then IRS could inform Congress so they could revise it prior to adoption. There are reasonable ways to deal with objections by taxpayers and filers who like the existing ambiguity, which I own't go into here.

Of course, this raises the question of whether the tax code is not just complex and inconsistent, but a complete axiomatic system per Goedel's Incompleteness Theorem. If so, then it is literally impossible to "fix it". Nevertheless, a reference application would be a great tool to study the problem.

(Godel's theorem says, informally, that any consistent axiomatic system has undecidable propositions. For example, "This sentence is false.") (For a good read, try Hofstader's book Godel, Escher, Bach: An Eternal Golden Braid.)

PS - My ex also worked for H&R Block for a few years. According to her, H&R Block returns tend not to get audited as often, because they tend to be correct more often. I know that shortly after we met, she found almost $10,000 in errors by my expensive tax accountant over the previous three years!

All you need is the ability to trap all the energy from both stars. Some kind of container whose inside is it's outside. I predict this will give rise to a whole new industry in Dyson-Klein Bottles.

Mathematically compliment is opposite sides of an angle

No. Mathematically complement is "oposite sides of an angle". Actually, the angle up to 180 degrees (so you have a lne extending from one side) not 360 (just the outside of the angle). And also some other things

I guess we can't expect more from someone who actually believes in yin and yang and can't even spell yin correctly

THis is different from the compliment that sings the praise of someone else.

Yeah, it's spelled differently :)

Mathematically compliment is opposite sides of an angle

No. Mathematically complement is "oposite sides of an angle". Actually, the angle up to 180 degrees (so you have a lne extending from one side) not 360 (just the outside of the angle). And also some other things

I guess we can't expect more from someone who actually believes in yin and yang and can't even spell yin correctly

THis is different from the compliment that sings the praise of someone else.

Yeah, it's spelled differently :)