Cap'n Refsmmat

I take it every amateur astronomer on the planet has noticed how the sky suddenly appears very different?

Or possibly the end of the freemasons video.

I can't think of any situation when you could measure a particle's position infinitely accurately.

Not sure what "incoming links" you're referring to; if you point to some of the other sites you've found, I might be able to work it out. http://blogs.scienceforums.net/Moontanman/ I guess we ought to integrate that better.

No, in your case you have both a and b negative, since [math]e^{i \pi} = -1[/math]. So my example applies.

What you've shown is that the identity [math](a b)^x = a^x b^x[/math] does not hold when a and b have complex values. It also does not hold when they have negative values; for instance, [math]1 = 1^{1/2} = (-1 \times -1)^{1/2} = (-1)^{1/2} (-1)^{1/2} = i \times i = -1[/math] which is clearly false. This is because exponentiation of a complex number is requires a choice of branch cut, since it is defined as [math]w^z = \exp(z \log w)[/math], and the logarithm of a complex number is a multi-valued function. (Similarly, the property fails for negative bases because the ordinary real definition of the logarithm doesn't extend to negative numbers.) In short: the rules of math are just fine. You just broke one.

How did you derive the equation?

Michel is right. All the content is there, but IPB by default restricts My Content searches to more recent content. You can search your name in the Advanced Search and ask for oldest posts first and everything will appear.

Not true. You can change the value of e and still get the right answer -- so long as you change the base of the natural logarithm to be whatever new value you chose.

I recently read a discussion on the Invision company forums about their approach to automated software testing, which was to say "our software is too complicated to undergo automated tests." So they just have a big complicated post they paste into the editor to make sure it works right. Because clearly complicated software needs to be tested far less than simple, easily-testable software.

http://community.invisionpower.com/resources/bugs.html/_/ip-board/delete-first-row-in-quote-r40935

Two six-inch diameter pontoons could support about 200 pounds; eight-inch pontoons would handle 350 pounds, and ten-inch pontoons 550. Here, have a table. On the left is diameter in inches, and on the right is how much payload could be carried by two eight-foot pontoons with that diameter: Be sure to give yourself extra capacity -- this is the maximum payload with the pontoons fully submerged, and you probably don't want that.

So let's suppose the two pontoons are perfect cylinders. The force of buoyancy is [math]F_B=\rho V[/math] where [imath]\rho[/imath] is the density of water and V the volume displaced by the pontoons. (For those of you about to complain about the missing g: I'll use a density in pounds, giving me a buoyant force in pounds.) Now, the volume of a cylinder is [math]V = \pi r^2 h = \frac \pi 4 d^2 h[/math] where r is its radius and h the length. Since you want diameter, I converted that to be in terms of d, the diameter. Let's put that together and multiply by two, for two pontoons: [math]F_B = \frac \pi 2 \rho d^2 h[/math] Now, some numbers: [math]\rho = 62.5 \; \frac{\text{pounds}}{\text{foot}^3}[/math] [math]h = 8 \text{ feet}[/math] So, for example, suppose your pontoons are two feet in diameter. The maximum buoyant force they can provide is [math]F_B \approx 3140 \text{ pounds}[/math] On the other hand, if you know the boat weight and you just need to know pontoon diameter, just solve for d: [math]d = \sqrt{\frac{2 F_B}{\pi \rho h}}[/math] You said you need to support 700 pounds; add in the weight of the pontoons themselves, plus a fat margin of error (you don't want the pontoons to be fully submerged underwater, after all) and say you want a maximum load of 3000 pounds, and you can plug in the numbers and get close to two feet.

Good point. I had set the backup time based on some guesswork about when people are likely to be online, but I just compared that to the real statistics. The backups should now run a few hours later, when fewer members are online.

Looks like there's not much we can do about it. We may upgrade to a new server in a few months, in which case there are things we can do to limit the effect of backups (e.g. have a separate disk drive to write backups to), but until then we're stuck. I've made a couple changes but I don't know how much help they'll be.

500 errors aren't browser related; only the server can give them. Backups. I wonder if I can make them less painful on the server.

I think it would be interesting if we all did research to find out what is known about the points raised, rather than speculating about their stupidity. One might not be able to prove or disprove them directly, but we could at least shed light on the subject.

You can. http://www.scienceforums.net/index.php?app=core&module=search&do=user_activity&mid=84431 It's the "Find content" button in your profile.

No, his result shows that letting 1/0 be infinity creates inconsistencies in mathematics. A number n cannot simultaneously be one and not-one.

If it happens around the time you posted this thread, that's backups running. If it happens other times, there's something wrong I should fix. Do you know when you experience the problem?

It looks like you keep overwriting inside your loop, so the only data left after the loop exits will be the last call to intensity(). My MATLAB knowledge is minimal though, so I may be entirely wrong.

kristalris, you may be interested in reading Paul Feyerabend's book Against Method, which argues that historically science has not followed any scientific method at all, and that any scientific method you could force upon scientists would prevent any progress from being made.

I do have an option to switch the up-down reputation system to a simple "Like" button.

You seem to think math is some ethereal thing which we merely discover facts about. That's not the case. Math is a set of rules. We define what it means to divide two numbers, and if our definition doesn't handle the case of 1/0, then it has no value. You could propose a new way to define division, of course.

What do you mean "there's no way to actually prove something is equal to infinity using math because it's not a real number"? Mathematics is a set of rules relating made-up mathematical objects; mathematicians define new rules and new objects and explore their properties. If one can construct a set of rules that describe when some expression evaluates to infinity, then one can prove that an expression is equal to infinity.