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I think you have your units skewed. 2(pi)r would be the area of a circle. Because this is a pot, and not a sphere, you would multiple 2(pi)r by the height of the pot.

No. The area of a circle is (pi)r^2. The circumference of a circle is (pi)d, or 2(pi)r. Don't believe I know my 5th grade math? Check it out.

Not true. I purchase quite a lot of closed source software for Linux. Some of it I run under Wine, but where possible, I buy Linux versions.

When I was working on my CS degree I purchased copies of Matlab and Mathematica, I also would have purchased Maya (went to the lab instead) if it had been less than $400 for the student version. All my windows friends found them on irc/p2p.

I used to purchase my copies of Redhat, I have the boxed sets (other than those I gave away) for every release between 5 and 7.3. However, I quit using Redhat since I received the exact same benefits for buying it as someone that downloaded it for free. I would have stuck with them if they had allowed me a year of priority access to up2date with the box set purchase. They didn't. I left. I now use Debian and am much happier with it. It isn't because I want something for free, but because I when I pay I want something more than is given away for free. If I get something better for a few dollars than I could get for nothing then I'll pay a few dollars. That is why my display is running Accellerated X. The display drivers in Xfree86 could not handle my laptops screen/videocard (1400x1050 lcd with an intel i830M graphics card) and left a nasty black border around the screen. I tried the Accellerated X demo and it worked perfect.

There IS software available to purchase for Linux. Much of it is better than the free stuff, and lots of us use it. Many people have no idea that some of it even exists. I think that many of the companies that sell Linux software and have superior products just need to spend a little more on marketing so they get some name recognition (this means you XIG). The companies also tend to get "stuck" on a distro. Many of them only release RPMs and refuse to provide instructions for other non-RPM distros, even when it works perfectly on the distro (this means you again XIG).

Okay, quick Google search to verify my education, and you get this:
http://scienceworld.wolfram.com/physics/Pound.html

which agrees with me, and this:
www.sizes.com/units/pound_force.htm
which agrees with you. You also get some discussion, and some confusion. I think the dicussion supports my understanding, but I'm biased. I don't know where to look for a clear answer (OED isn't written by physicists).

How about this: The official unit of mass in the Imperial system is the slug. The slug is defined by: 1 lb = 1 slug * 1 ft/sec^2 . The pound was already standard, and a force, so they derived the official mass from it, much as the Newton is derived from the kilogram. If the pound was a mass that equation would not give slug as a mass, and, more to the point, there would be a derived force unit, instead of a derived mass unit. Convinced?

In reality, since there is confusion, we just always use lbm and lbf where it isn't blatantly obvious. I actually do prefer SI units (just MKS and some electrical stuff, not Joules, Newtons, etc), but since I work in American industry, I have become rather familiar with the "old ways".

In practice, many, many natural statistics are normally distributed, and it would be a reasonable guess that penis length is. Therefore, the mean and the median will be the same.

In practice, many, many natural statistics are normally distributed, and it would be a reasonable guess that penis length is. Therefore, the mean and the median will be the same.

Notice that the conjencture "any significant number - other than 0 - is between 0 and 1" is unfalsifiable, because if the number is not between 0 and 1, its _reciprocal_ is!

For example, the continued fraction of pi shows no obvious patterns, but 4(1/pi) has.

The problem is the question: do we accept the "significance" if the number is not in 0-1? If we don't accept, it is an "inverse Texas sharpshooter fallacy". The "Texas sharpshooter" shoots into the wall of a barn and then draws a target around the position where most of the bullets hit. We name a target (0-1) and blame the gunsights if they don't hit. (Blaming systematic precision errors for accuracy problems.) Like this: it is the _reciprocal_ of pi that is the significant number, not pi itself!

If a conjencture is unfalsifiable, it is meaningless. This conjencture is: we can always say the reciprocal is the significant number.

I was about to reference Wolfram in a conference paper I'm submitting tomorrow. Unfortunately, I hadn't heard the bit about Matthew Cook until today, and I find that I can't in good conscience reference a man who operates in complete opposition to the way academia is supposed to work.

Instead, I'll just go back to the primary literature and cite von Neumann.

BTW, mentioning Eric Weisstein's book conjures up the complete screw-job CRC gave him: they more-or-less stole the entirety of his work.

the suggestion that any number of a truly fundamental significance besides 0 and 1 would be not only rational but an integer seems improbable

Why not? What if it's a Goedel number? What would that program be?

What about the Monster?
This is the largest "simple" group which doesn't fit into any group category. What this means is rather hard to explain in simple terms, but this group has lots of mysterious connections to other maths. The order is 2^46 * 3^20 * 5^9 * 7^6 * 11^2 * 13^3 * 17 * 19 * 23 *29 *31*41*47*59*71.

Anyone who is a visitor of Wolfram MathWorld or ScienceWorld will recognize the invaluable contribution that Wolfram has made to the scientific community. From a personal perspective without MathWorld sometimes I would be completely lost...

Anyone who is a visitor of Wolfram MathWorld or ScienceWorld will recognize the invaluable contribution that Wolfram has made to the scientific community. From a personal perspective without MathWorld sometimes I would be completely lost...

I could have sworn that the use of limits in calculus was fairly recent (50s or 60s). Without that formalism calculus was hazier back then.

But we don't live in a three body Solar system.

That's exactly what the Mac does, once you understand that part of that window (viz. the menu bar) is conveniently placed at the top of the screen. What they did, you see, is go past your preconception that a "window" has to be connected.

Actually I do believe that is was the Indians who gave up the concept of zero. However, the Arabs are responsible for countless mathematical innovations including algebra (thanks mostly to Mr. al-Khwarizimi), the concept of tha alogrithm (thank again Mr. al-Khwarizmi) and arabic numerals. Find out more about Mr. al-Kwarizimi.

IANAM, is there a mathematical term for the shape of a Pringle?

Yes, it's a saddle point, specifically one for which d^2[f]/dx^2 and d^2[f]/dy^2 differ in sign, where the surface is described by z = f(x,y).

You are so completely misguided in your attempts to understand the Nyquist theorem that it's almost comical to anyone that has ACTUALLY TAKEN A SIGNAL PROCESSING CLASS IN COLLEGE. Please, stop before you embarrass yourself further.

1. Every signal can be composed of a series of sinusoidal waves. It's a mathematical fact. Yes, even your precious trangle wave can be represented *precisely* by a series of sine waves.

2. Nyquist's theorem states precisely that you sample at regular periods. I don't know where you're getting this notition that it requires you to sample at irregular intervals.

You need to stop thinking about this in terms of the time domain and learn something about the frequency domain. There is a LOT of mathematics that a LOT of very smart people have worked on for a great deal of time before you were even born. And they completely prove your "theories" wrong.

Take any signal. Any arbitrary signal you want. Sine wave, square wave, etc. Now bandlimit it. It's physically impossible for frequencies to extend out to infinity, so every signal that is physically producable in nature is band-limited. Now sample that signal at some frequency. So long as that sample frequency is twice the band limit, you can reconstruct that signal EXACTLY. Not almost, not partially, not with some distortion, but EXACTLY. You may not understand why this is, but you can prove this mathematically.

Finally, about your little triangle wave diatribe. First of all, a perfect triangle wave is impossible in nature. Notice I said perfect. The reason is that to accomplish that would require and infinite number of harmonics, and thus frequency components out to infinity. YOu can see this from its fourier series. Now, a sine wave, on the other hand, represents a single frequency, or an impulse function in the frequency domain. Anyway, the point here is that if you have a triangle wave of frequency 'n' and a sine wave of frequency 'n', the triangle wave is going to have many, many higher harmonics of 'n', whereas the sine wave does not. Therefore OF COURSE you cannot represent a triangle wave of frequency 'n' by sampling it at '2*n'. To think that you can shows a complete understanding of how the frequency domain works. HOWEVER, if you took that triangle wave, and band-limited it at some cutoff frequency (sufficiently high enough to approximate a perfect triangle wave) and then sampled it at twice that frequency, then you would be able to perfectly reconstruct that waveform.

exactly. that sampling rate is simply overkill. take a look at an application of the nyquist sampling theorem. human hearing maxes out around 20kHz. 44.1kHz is plenty (and with some breathing room) to sample stuff that humans can hear.

now, the increased resolution offered by 24 bits of accuracy per sample could help. but increasing the sampling rate beyond 44.1kHz does nothing: "No information is lost if a signal is sampled at the Nyquist frequency, and no additional information is gained by sampling faster than this rate."

Some are just real good at math.
They have a Fields Medal for that
Some of those peeps work on bio, nuclear, and chemical weapons.
Encryption software can be readly by individuals of lesser moral standing for devious purposes. By no means does this mean that there should not be research undertaken in cryptology and made freely available
However, I do think that software could have a signifigant impact on humanity. For instance, look at Linux, OpenOffice etc... Individuals from impovreished areas can use software such as this to greatly improve their life.

"Bolexes, Panasonigs, and Bomegas"

The root of the problem was apparent when I had it calculate Pi and it got a slightly wrong answer.

Cool. If you've fixed that problem, the Fields Medal that's in store for you comes with a big-enough cash prize to buy any CPU they sell down at CompUSA.

However, I'll assume that you were speaking in the context of serious science. A theory doesn't become "truth" until the amount of existing corroborating evidence and fruitless searches for refutative evidence is appropriate for the strength of the claim.

It is true that scientists measure the strength of a prediction by asking, "What is the probability that random chance could produce this level of agreement between theory and experiment?" But nobody does this by dividing the number of successful experiments by the number of possible unconducted experiments. This is as it should be because scientists assume that the universe is subject to understandable rules. If a repeated experiment has been devised and carried out carefully enough, it is safe to assume that the outcome of that experiment will always be the same.

Now, a theory basically says, "The relationship between parameter X and parameter Y is Z." So an experiment varies parameter X and looks at parameter Y. To evaluate how close the prediction is to the outcome, scientists use the Chi-Squared Test, which returns a probability that random chance could produce such a good fit. So when you read a paper describing some study and it reports something like "p=0.03", that's saying that there's a three per cent chance that the positive outcome was just lucky. In general, a publishable study should achieve p<0.05.

I'd be vastly surprised if any serious philosopher put that argument forth. I'd be even more surprised if anyone who knew something about the philosophy of science had trouble trying to answer it. I'd be even more surprised if anyone bothered to write about it in a book except to comment about how surprising it is that any serious philosopher put that argument forth.

there are things out there in space with radii of 10-20 km completing approximately 45 rotations per second?

that's simply amazing. or, as the dude would say, "far out. far fucking out!"

Actually the reference provided in the story claims that the "gravitational waves have been observed indirectly from several projects since the 1960s". I fail to understand though why the ./ story states no such waves have not been detected.

Anybody know why Jocelyn Bell received no credit for actually discovering pulsars, yet her thesis advisor, who actually seemed to do nothing, did?

Looking for an integer value in a real number continuum is an irritating thing to do.

It may be an irritating thing to do, but it is important to to emphasize when demonstrating that the "Law of Averages" (if I toss 20 heads in a row, there is more than a 50% chance that the next toss will be a tail, in order to force convergence toward the expected mean) is utter bunk.

It also helps one understand situations where the expected mean is zero, and all one is left with is the divergent spreading of the probability density function. I am, of couse, describing the diffusion of gas particles away from a point of high concentration, via Brownian random walks. In the latter case, the mean square displacement of an ensemble of particles is given by <r^2> = A t, where A is a constant depending on the temperature and other variables, and t the time (see here for the exact expression, it's right down at the bottom of the page). The standard deviation of the particle distribution obviously varies as sigma = SQRT(<r^2>) = SQRT(A t), and interpreting t as equivalent to the number of coin tosses N then demonstrates the equivalence between the random walk and my arguments above, where sigma varies as SQRT(N).

Also from math world, the edges of a polygon a line segments, which are straight lines, so the 50p coin isn't a heptagon.

Also from math world, the edges of a polygon a line segments, which are straight lines, so the 50p coin isn't a heptagon.

giga: SI prefix meaning 10^9 NIST (that's a govt website, but I'm assuming you might accept it as a valid source.)

ton: non-SI metric unit meaning 1000 kg ref
Non-SI metric units are commonly used in the scientific community. The SI itself is restricted to a very small set of units, and everything else is derived from those. Even common metric units like the liter aren't part of the SI.

So anyway, a gigaton is a perfectly valid and commonly used unit of mass.

Again quoting from Wolfram, which I consider a reasonably authoritative source:

There are several statistical quantities called means, e.g., arithmetic-geometric mean, geometric mean, harmonic mean, quadratic mean, root-mean-square.

The quantity commonly referred to as "the" mean is the arithmetic mean, also called the average.

In the absence of further specification, in particular in a conversation involving average bandwidth usage, I think it's clear that "mean" indicates arithmetic mean.

Huh? A great many things are described by Gaussian distributions which have no values less than zero.
A Gaussian distribution is simply a normal distribution or a bell curve. See here.

Quoting from the site: Normal distributions have many convenient properties, so random variates with unknown distributions are often assumed to be normal, especially in physics and astronomy. Although this can be a dangerous assumption, it is often a good approximation due to a surprising result known as the central limit theorem. This theorem states that the mean of any set of variates with any distribution having a finite mean and variance tends to the normal distribution. Many common attributes such as test scores, height, etc., follow roughly normal distributions, with few members at the high and low ends and many in the middle.

Depending on the test, it might be possible to have a negative test score. However, I'm quite certain it isn't possible to have negative height!

From what I gather computers can help. I am not a pure math major, however from what I gather Hales used a computer program to prove by exhaustion Kepler's Conjecture. While Hales did not use a pocket calculator, he did use a machine to perform the proof, no?

Actually, the median in your example would be 5.

http://mathworld.wolfram.com/StatisticalMedian.htm l

I never said it was a regular heptagon :-)

A polygon is a closed plane figure with n sides. The sides don't have to be straight, nor does the figure even have to be convex. It has seven sides, so it's a heptagon.

In fact as you point out, the curvature of the sides gives it the property that the centre of curvature is the opposite apex of the coin, which allows it to roll - although in my experience it's more likely to roll down a drain than actually be accepted by the ciggy machine in my local.

Here endeth the lesson on the ten bob bit :-)

Oi, I did not turn up much, then again I did not search long. Here is a quick thread which talks briefly about it. It is mainly due to the fact that the Nobel committee was, as they are now, very anal about experimental backing. Although we had the Michelson-Morley experiment to disprove the existence of the ether and a slew of other experiments that seemed to jive with the theory of relativity the comitte did not view it as enough evidence. There is speculation that a few memebers did not even have a remote belief in the theory's validity (as mentioned in the thread). Yet they had to give him a Nobel for something, he did publish three powerhouse papers, so he got a Nobel for the photo-electric effect. At least this is all to my best understanding.

> the software was legal iff you bought the film

Did you mistype if or do you really mean iff? If this is true, that's pretty interesting. You can't use the software (look at it? read the code? what?) if you haven't bought a film.

Anyone care to elaborate?

wrong

From Mathworld

The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical (and was known to 19th century mathematicians), n = 3 (the original conjecture) remains open, n = 4 was proved by Freedman (1982) (for which he was awarded the 1986 Fields medal), n = 5 was demonstrated by Zeeman (1961), n = 6 was established by Stallings (1962), and n>=7 was shown by Smale in 1961 (although Smale subsequently extended his proof to include all n>=5).


So, to answer your question, the proof for higher dimensions doesn't hold if n10 or something (where 10 is a random number depending on the proof). Sometimes, the argument in one case relies on properties that just aren't present for smaller n. It just means you have to go hunting for a more elegent proof!

According to Wolfram's MathWorld site, Perelman's proof is described in two papers, located online here and subsequently, here.

Of course, I'm pretty sure the reason they're not mentioned in the article is because the most people reading the article would probably have some difficulty trying to understanding them. ;)

I recently had to implement code to convert terrestrial time (TT) to martian solar day (MSD). Some interesting tidbits in that research follow.

As you might guess, the extra days in leap years help keep our calendars synchronized with our actual position about the sun (heliocentric longitude). This is called intercalation, and the general rules governing the gregorian calendar cover 400 year periods. Other methods exist which are in a sense more "accurate," but less useful for predicting future dates. Fortunately, the earth is pretty regular in its movement around the sun.

The 0 degree mark for heliocentric longitude occurs at the vernal equinox, an event that can be easily determined from earth, and has been for centuries. In the Iranian calendar, the new year begins on the day of the vernal equinox. Since this event occurs later in the day each year, eventually an extra day must be added. Such calendars are based on observation rather than rule-based model and consequently are implicitly self-calibrating.

Leap seconds, as pointed out, are an entirely different beast, and are meant to shore up the discrepency between our actual rotation and the atomic clocks we use. The current offset is 22 seconds slow officially. Oddly enough, a NASA document from 1997 uses a value of 63 seconds as the offset between TT (terrestial time) and UTC (Greenwich Mean Time). Another from 2000 shows a 32.184 second offset from TT to TIA (atomic). It doesn't exactly correlate or add up, and I'm not precisely sure why that is. Perhaps someone could enlighten me on the matter.

Curiously, our leap years follow the mathematical model while our leap seconds follow the observation method of calibration. Consequently, you can determine the correct date in the future, but not the correct second.

-Hope

There is a very comprehensive reference of currently used time standards over at wolfram research site. It came up yesterday while I was trying to figure out the difference between Universal Time (UT) and Coordinated Universal Time (UTC). In the last link I believe you will find that "Earth's rotation is irregular at the 0.1 second level" along with a diagram of the errors so far.

There is a very comprehensive reference of currently used time standards over at wolfram research site. It came up yesterday while I was trying to figure out the difference between Universal Time (UT) and Coordinated Universal Time (UTC). In the last link I believe you will find that "Earth's rotation is irregular at the 0.1 second level" along with a diagram of the errors so far.

There is a very comprehensive reference of currently used time standards over at wolfram research site. It came up yesterday while I was trying to figure out the difference between Universal Time (UT) and Coordinated Universal Time (UTC). In the last link I believe you will find that "Earth's rotation is irregular at the 0.1 second level" along with a diagram of the errors so far.

Can you explain to me why it really is exponential?

It isn't.

I can see that it might be quadratic (n sets of wires to n people = n*n wires), but how do you get exponential?

The folks over at Wolfram tell us that a complete graph, that is, one where every node is connected to every other node, has n(n - 1)/2 edges. Which is quadratic.

Best: Finding Nemo

Worst, by miles: either ep of the Matrix frantschise.

How about Mathematica?

The Michelson Morley experiment attempted to do this over a hundred years ago, but it didn't work. Subsequent experimentation has confirmed that "velocity relative to the universe" is not a meaningful idea.

It concerns certain types of differential equation systems where the solutions can approach a number of "attractors" (basically just complicated sets of points) and circulate around them periodically. The problem is classifying the maximum number of these periodic attractors (it has been shown to be a finite number) and their relative position in the vector field.

The Lorentz attractor is an example of a system which has two periodic attractors (you can see a Java-implementation here) and was the result of an attempt to predict the weather during the 60's.

Punishments too light. Expect life jail sentences, extension of liability to family, friends, and unlimited fines, all to be determined by the copyright holders.

You owe the media companies the Skewes Number of dollars. No, 10^that. No, 10^10^10^10^10^10^10^10^10^10^10^10^10^10^that. No, wait...

Ah, what the hell. They own all possible Universes. Get SETI going, we have fines to collect.

>You don't have to test every number between 1 and sqrt, just the primes.

Oh yeah.. know any formula which will tell me if a number is prime or not? (joke..)

Seriously though, the most popular method is the Elliptic Curve method.. which is significantly better than simply testing all possible primes.

The thing is, it's not sufficiently better to make decryption practical for large keys.