Kyrisch

Since general use light sources (such as lightbulbs and flames and such) produce incoherent or not-all-in-phase light, and since only coherent light sources can completely destructively interfere (and produce said shadow) it will be difficult to make a flashlight "emit a shadow". Even with a laser, the wavelengths of visible light are so tiny that it is extremely difficult to make two light beams completely interfere using everyday stuff. The closest you can get is light and dark bands by shining a single coherent source through a number of slits spaced very close together.

So, it is commonly accepted that the first three dimensions are those that we experience every day (e.g. length, width, and depth). And that the first dimension is linear, the second to do with area, and the third to do with volume. The fourth, however, is sometimes called duration, meaning that it represents "time". Often it is conceived as also linear (such phrases as "timeline" exemplify just that). So my question is as follows; is this "cyclical" nature of dimensions inherent or conceived? I imagined at first that it would be like [math]\i^n[/math] in that it repeats every four integral values but then I realised that this conception was probably largely fabricated by human thought. Is there any mathematical basis in this?

I love the magnetic 'mood maker' for impotence -- "Fits discreetly in your underwear"

Earth magnets slowly become apolarised. Electromagnets are extremely energy inefficient.

I used to have an idea for a perpetual motion machine because that was before I learned the concept of Conservation of Energy. The energy content of a system never changes. Therefore, since SOME energy will be lost to heat (due to friction, imperfect vacuum, etc.) it will EVENTUALLY stop, even if it runs for a while.

I guess. This isn't that far-fetched... It is reminiscent of quantisation which is observed in nature already.

You'd yo-yo back and forth through the tunnel, really.

It could be. Too bad we don't know much about that one either xP.

I've seen Darwin Fish bumper stickers xD http://www.northernsun.com/images/thumb/2214.jpg

Nothing actually gives it shape. It just sort of exists, just a property of the universe. In order to describe it, the metaphor of the 'fabric' of space-time is used in order to conceptualise gravitation wells as 'bending of the fabric and stuff' but I doubt its actual nature is much like that at all.

Not true. The process of cooling the residual heat just moves it. Heat energy doesn't go away. Again you are just moving the information. Not if you're far enough away that you have apparatus ready by the time the light reaches you. And the point is not that you would have to "travel faster than the speed of light to retrieve the information". The point is the information still exists in the direction, wavelength, intensity, et cetera of the light waves produced. That is, knowing the laws of physics and collecting all the relevant information will allow one to theoretically figure out the original birthdate information.

Didn't you post this someplace else?

In the first case, as the beads slide down they will transfer the information of their former position into a heat signature on the shafts that, with the right instruments, can be used to determine exactly how many beads had fallen because of energy conservation. The energy is transferred, not destroyed. In the second case, whatever method you used to "rearrange the spins randomly" will leave traces that will be the information of the former spins transferred into another form. Spin, charge, location, and velocity are all forms of information.

Such is the basis of the philosophical viewpoint called "solipsism", the main tenet of which is that the only thing that can truly be known to exist is one's own mind.

At this point I'm not even sure if he's faking this, really...

The index of refraction of air is so close to 1 that it is usually estimated to be that in calculations which just goes to show how much closer to 1 the index of refraction would be for a near-vacuum.

So it is obviously not the Casimir Effect, though it could be related. Virtual particles are the hypothesised culprits of the force, but I am proffering another possible reason for its existence.

Well, the integral of distance is a sort of concept space-time, able to be expressed in meter-seconds. For instance, an object at rest will still have a different "time-coordinate" after five seconds, but say during that five seconds the object moved two meters. After this, the object is 10 m-s from the origin.

Well of course there are relative velocities within the universe, but it is commonly said that, in reference to the expansion of the universe, as opposed to things moving away from each other, space itself is expanding. I am in no way suggesting that all relative motion is caused by expansion of space.

Nothing is 'moving away' from anything else. Space itself is expanding.

Obviously. Thoughts are electrical, emotions are chemical, and improbable speeds are, well, improbable. Please.

Information cannot be destroyed. This is a commonly accepted tenet. What the problem is here is that the definition of information has not been standardised in this thread. Of course if you write something down on the piece of paper, and then you burn the piece of paper, you can't get back what was on the paper without the proper equipment. But WITH the proper equipment, you could. Information is less words and sentences and more so everything in the universe that is not mass or charge or something physical. For instance, placement (think x,y,z,t coordinates) is information. And with the proper tools, one could actually retrace the movement of the matter, knowing the variables and the laws of physics, and figure out what was written on that piece of paper in the same way (though in a much more complicated manner) that someone can tell someone has been someplace because of footprints. In specific, the 'information' contained in your brain is manifest in, quite simply, its physical structure. When you die, nothing changes; there is no loss of information, there is no violation of physical law.

Actually any differentiable function can be defined using infinite Taylor or Maclaurin series: [math] f(x) = \frac{f©}{0!} + \frac{f'© (x - c)}{1!} + \frac{f''© (x-c)^2}{2!} + \frac{f^n©(x-c)^n}{n!} ... [/math] for any c. The series is actually, conversely, defined by the function.

How about my old Algebra II teacher puzzling over a problem in which "the rational function achieves the value of its asymptote" to another teacher within my earshot. I was interested, so I listened a bit longer and they kept discussing, in utter confusion how this function could "possibly ever attain the value of its horizontal asymptote" and how "the textbook must be wrong" and "that can't have an asymptote there." This is the point whereat I spoke up and explained (to the ALGEBRA II TEACHER, mind you) what is the definition of end behaviour.

From trigonometry it can be found that [math] x = -l[/math] and [math] a = g [/math] which makes the period for a pendulum [math] T = 2\pi\sqrt{\frac{l}{g}}[/math] but that doesn't help with that actual derivation of the general formula for period ([math]T = 2\pi\sqrt{\frac{-x}{a}}[/math]).