Bignose

I don't know about changing science, but clearly spelling is changing...

The difference is that every time a door without a prize is opened, you get a new piece of information you didn't have before. And that extra information changes the probabilities. It isn't simply: P(door picked = car) it is P(door picked = car | door x_1 does NOT have the prize) where the "|" denotes "given that" or "on condition that". The vertical bar is used for conditional probabilities. Sometimes the conditions won't always add extra information. For a random variable that is truly random, e.g the probability of heads coming up when flipping a fair coin is completely independent of any of the previous flips, then the conditions don't mean anything. But, many variables are not independent. For example, if on Saturday there is a 30% chance of rain on Wednesday, and it rains on Tuesday, the condition that it rained on Tuesday probably changes the probability of precipitation on Wednesday.

The differential to a power means repeated operations of the differentiation operation: [math]\frac{d^n}{dx^n}=\frac{d}{dx}(\frac{d}{dx}(\frac{d}{dx}...))) [/math] where there are n total differentiations performed. for example [math]\frac{d^3 f(x)}{dx^3} =\frac{d}{dx}(\frac{d}{dx}(\frac{df(x)}{dx})) [/math] You should be able to start taking derivatives of the function you have there and a pattern emerge after repeated differentiation.

The theory that all available energy is split evenly among all the different forms (translational, rotational, vibrational, etc.) is known as the equipartition of energy theorem. http://en.wikipedia.org/wiki/Equipartition_theorem Like a lot things in thermodynamics, under the right circumstances, equipartition of energy is very, very accurate. Reference 3 in the above Wikipedia article for one ("On the specific heat of mercury gases", Kundt and Warburg, 1876). Of course, there is a lot of interesting physics not in the "right circumstances", and when quantum effects start to become important, then equipartition doesn't hold as well anymore. Nevertheless, the point remains that the forms of energy can be transferred from one form to another. The amounts of transfer from one form to another can be calculated -- see the (excellent) book The Mathematical Theory of Non-Uniform Gases by Chapman and Cowling, Section 13.31 in the 3rd edition. I have significant doubts that you can just take away rotational energy, because while there will be a lag, eventually the transitional and vibrational energies will be converted to rotational energy again. So, I guess what I'd like to see is some results that contradict what is published in the literature. The Chapman and Cowling book is a true classic in the kinetic theory of gases. It's going to take some very strong evidence to change my mind about what is written in C&C.

But, is there any evidence at all that these "forbidden transitions" are gravity waves? Just because there is a "penchant" for rarefied atoms for absorbing "certain" waves (care to be any more specific than "certain"?) doesn't mean that they automatically do the same for your gravity waves. There are waves on the ocean surface and light behaves as a wave, but the two are very, very different despite their both being waves. Just because rarefied atoms absorb "certain" waves really doesn't say much at all about their ability to absorb gravity waves.

gravity waves? If not gravity waves, then what does this have to do with this topic?

If you haven't learned the chain rule yet, applying the definition of the derivative should yield some good results.

Kedas, One more time, while I agree that in physical reality there is no such thing as a solely 2-D object, that in no way whatsoever hinders the development of the mathematics of a 2-D object. The definition of MOI involves a triple integral over 3 space dimensions. Mathematically, if the object is only 2-D, then it acts just like it is a Dirac delta function in that third dimension. And, one more time, treating an object that is very nearly purely 2-D, as in a 1m circle made of sheet metal, that is approximating that very small thickness of the sheet metal as a delta function, can be very accurate. The difference between the two is almost negligible. It is a difference between mathematics and physical reality, but very often the mathematical shortcut is exceptionally good. Other examples is treating the atoms of an ideal gas a point particles yields the perfect gas law, which can be very accurate under specific conditions. When launching a probe from the Earth to Mars, the gravitational influence of Pluto isn't negligible, but treating Pluto as a point mass is accurate enough. The real art of physics is very often in finding the approximations that make the math significantly simpler, but don't affect the answer a great deal. Physics is replete with examples if you just look for them.

But I'm not just "making up a mass that has no meaning". Consider if I made a square and a circle out of very thin sheet metal. Sure, technically, that is a very squat cylinder or a parallelepiped with a very thin depth, but if you use an MOI calculation for a 2-D object with a given mass per unit area, the answer between the 3-D and the 2-D calculations will be negligibly different -- implying that the 2-D approximation is very, very good. Let's even look at your list of moments of inertia. Specifically, the one for a solid cylinder: [math]I_z = \frac{m r^2}{2}[/math] where [math]I_z[/math] is the MOI about the axis, [math]m[/math] is the mass of the cylinder, and [math]r[/math] is the radius. Note that the height, [math]h[/math] isn't even part of the equation! That means that it doesn't matter if the height is 1 cm, 1 million cm, or even infinite or zero centimeters! The answer is the same! Even further proving my point is that the formula for the cuboid and the formula for the "thin rectangular plane" are the same! The depth doesn't matter at all! You don't even have to perform the 3-D calculations to get the same answer as the 2-D ones, meaning that you don't have to do the extra work of the full 3-D calculation. And, the fact is, you can define densities not just as mass per unit volume. In the sheet metal example above, it is perfectly reasonable to define a mass per unit area. For a long thin rod or chain, it is perfectly reasonable to define a mass per unit length -- and is done so often to predict the shape a hanging chain or rope will take. Sure, mathematically, a line is only 1 dimensional, but the math of that 1 dimensional object can be used to predict with incredible accuracy the behavior of a true 3 dimensional object such as a rope or chain. Just like the math for a 2-D object like a circle or square can be used to predict very accurately the behavior of a true 3-D object like a circle or square cut out of sheet metal. Of course in reality there is that 3rd dimension, but it isn't important for the math. It is definitely possible to find the moment of inertia of a circle or square.

Kedas, while physically being merely a 2-D object a circle or square wouldn't have any mass in the real world, it doesn't prevent us from mathematically talking about a circle or square's MOI. If you want to start down that road, why not just say that a circle or square can't have an MOI because there is no such thing as a perfect circle or perfect square? Mathematically we can assign an area density or mass per unit area and make it mathematically have mass. Just like mathematically we can and do use point masses and point charges all the time, despite there being no such thing in the real world. It is a simplifying assumption made primarily to make the math easier and get a result that is going to be very close to the real world. To a very large extent, it doesn't really matter at all that no 2-D object has mass, or that there is no such thing as a perfect circle, mathematically such objects do exists and we can perform mathematics on them.

Not to be too pedantic, but it definitely depends on the size of the circle and the square, as well. It very much depends on whether you are talking about the circle that circumscibes the square, or the circle the inscribes the square. Or maybe the circle with the same area as a given square (assuming constant density)? Each of these has a potentially different answer, the specific situation needs to be made clearer. And, what will help answer the question is the equation of moment of inertia... like moo said.

It is an old one, but a very well studied one: http://en.wikipedia.org/wiki/Monty_Hall_problem Short story, for all problems like this (for any number of doors), you stick with your original choice as the host opens "goat" prizes until the very last time you are offered a chance to switch (i.e. only two doors left) and then always switch. The reason you always change has to do with the conditional probabilities and with the extra information you have received by the host revealing what doors the prize definitely is not behind.

This is the big one that came to my mind. It is one of the primary reasons so much of the scientific knowledge was conducted by monks and the church -- members of the clergy who were supported by their communities for food, clothing, etc. had the spare time to sit around thinking about stuff rather than spending 100% of their waking time keeping themselves alive. Similarly, only the aristocrats and rich had the means a little later in history to pursue scientific inquiry. Heck, I suspect that you can make a really similar argument today. A significant majority of people in this world today still have to spend most of their time keeping themselves alive. The next Einstein may be living in the heart of Africa right now, though no one will ever know because they are far more concerned about where their next meal will come from than the intricacies of space-time. In a larger point-of-view, I actually think the more compelling question might be: given human that we know it today, how have we actually done such a good job learning the amount of science we have to date? Because, really, it wasn't too long ago mankind was exceptionally primitive. Just as one example from Greg Easterbrook that there is wine available in gas stations all across the US that would have been considered among the finest wines by Medieval kings and queens. Heck, even 15 years ago or so it was an impossibility to communicate with people all across the globe in a public forum like this (maybe not impossible, but certainly not very easily). More to the point, up to about 100 years ago or so, you could honestly give your title as a "scientist" and have significant knowledge about the cutting edge in almost all of the different disciplines. Today, it would probably take a lifetime just to read the entire amount of scientific publication that will occur in calendar year 2009. Several lifetimes to not just read it all, but understand it all. It may even be cranking at a rate fast enough it might take a lifetime just to read a current month's worth of output. There are no "scientists" per the old definition anymore, and not very many true "biologists" or "chemists" or "physicists" any more, either. To keep up to date, you have to pick a small specific sub disciple and keep up with that and hope to catch the big waves from the other parts of your chosen discipline. There just isn't enough time to stay up-to-date with all the little discoveries of each part of an entire branch of science anymore. The actual amount of information that we have and are generating today is almost unbelievable -- well at least to me.

I'd look it up in a table of integrals, personally, though that may not be the non-calculator answer you were looking for...

OK, but then you haven't actually shown anything that I've asked. I asked how gravity and time as the same, how you would use this in an equation, and all you did was say... "gravity and time are the same." If I said, "bananas and strawberries are the same" and then just said "b=s, therefore bananas=strawberries" , that doesn't prove my first assertion at all. It is just a repetition of my first point and doesn't actually prove anything. What I am looking for is actual evidence that supports the first statement, not just re-iteration of it. For example... what is "time-density"?!? How can you measure time-density? How can this be a constant for all masses, when the acceleration due to gravity (g) is definitely different for different masses and the t in your equation is meant to replace the g? Any chance at all these will be any evidence to support your assertion forthcoming?

You have to be joking at this point. OK, this did it. I'm out. It has become obvious that you are simply a troll, and have no true intention of actually discussing things.

No! The formula you write is NOT on that page you cite. You cannot just replace a term in an equation because you want to. Please either justify your equation, or find a citation for it. Preferably in a peer-reviewed scientific journal, or else we are just going to be going in circles again because then the question is going to be to justify your equation. As near as I can tell, you made up these numbers. Any chance (a snowball's in hell maybe) that you can actually show how you got these numbers?

This conflicts directly with the experimental results that the speed of light is a constant. Please provide evidence that the speed of light is slower here on Earth.

Please show me an example. Explicitly. With real numbers and everything. Please show me the formula to calculate the force of movement time. (While you're at it, you might want to define exactly what "movement time" is)

Fine -- leaving aside your changed mind about disintegration -- care to explain anything at all about how black holes "burn the hell out of something" and just what the heck "super-gravity" is?

This is a truly unfair statement right here. Because quite simply -- neither do you. And you know how I know that you don't either? Because you haven't published any papers in any scientific journals explaining the concepts. If you did truly understand gravity, you would have been able to publish numerous papers and won the Nobel prize by now -- because uncovering the true mechanism of gravity is an ongoing topic of research right now. Like I wrote above, there is a proposed graviton at the carrier particle for gravity, but existence of the graviton has not been proved yet, so in reality no one truly understands gravity. So quit acting all arrogant like you do.

Then unconfuse it for me. How can something with the units of length per time squared (gravitational acceleration) or with the units of force (mass time length per unit squared) be "indistinguishable" with something with the units of time? If they were indistinguishable, why can't I use the same measurement device to measure both exactly the same way? Why can't I use a stopwatch to measure the local gravitational acceleration? Why can't I use a spring scale to measure time? And finally, why are the "mechanics of time within the universe" different from time on my wall clock? My wall clock is clearly within the universe, so I would think that the same rules should apply. The space my wall clock occupies is clearly a subset of the space of the entire universe. Edited for grammar & spelling.

Wow, just.... wow. Black holes don't "burn the hell out of something" and their gravity isn't "super-mode" (whatever the heck that is supposed to be?!?). Black holes are the result of regular ol' normal gravity around a very large amount of mass. And how does the result that black holes -- which would be extremely dense matter -- prove the result that when you destroy something so thoroughly that nothing exits anymore that the result is a temperature of absolute zero? In a black hole, that is pretty much the opposite of nothingness.

It took me 37.1 seconds to write this reply. Meanwhile my body experienced a consistent 9.8 m/s/s acceleration due to gravity. My body did not experience 37.1 seconds of gravity, because the acceleration due to gravity is a length per unit of time squared, not a unit of time. I have successfully distinguished between time and gravity. How do you remedy this with your statement that I quoted?

Ok. Let's discuss this specifically then. How is this possible? What does "time is actually the foundation of the forces behind gravity" even mean? Because current theory has particle exchange (i.e the photon exchange is the electromagnetic carrier particle) as the foundation of the forces. While its existence hasn't been confirmed, it is currently suggested that the graviton is the force carrier particle for gravity. How does time enter into this as the "foundation"?