Bignose

The "air moves faster" approach implicitly assumes one thing -- that the air on the top of the wing and the air on the bottom of the wing have to rejoin. That a volume of air that was split in half by the leading edge reforms into the same volume as the two halves slide off the back of the trailing edge. That actually isn't true. Yes, the air on the top does move faster, but it isn't because it has a farther distance to go and has to "catch up" to the bottom air. In practice, the way things like life on an airfoil are calculated usually involves the circulation http://en.wikipedia.org/wiki/Circulation_%28fluid_dynamics%29 The circulation is calculated on a wide circle around the wing (usually nowhere near the surface itself to make the calculations/measurements easier). So long as the integration is performed along a continuous closed loop, you can choose any path you want.

No, you can derive [math]\frac{d}{dx}\sin{x}=\cos{x}[/math] just from the definition of the derivative and the angle sum formulas. i.e. using [math]\frac{df(x)}{dx} = \lim{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}[/math] and [math]\sin{a\pm b} = \sin{a}\cos{b}\pm\cos{a}\sin{b}[/math] and [math]\cos{a\pm b} = \cos{a}\cos{b} \mp \sin{a}\sin{b}[/math]

It's funny, Halls, because once I got used to RPN (Reverse Polish Notation), I almost couldn't work a "regular" calculator anymore. I found the RPN to be very intuitive once I got used to it. And, I found it much easier to put in more complicated expressions than the standard way of entering numbers. These days, I don't use either. I still have my HP calculator, and I know it still works, but I haven't used it other than to open it up to see if it still works for many years now. I actually just use Excel if it is just numbers, or open MathCAD if I have to do some symbolic math. I've found that I am always close enough to a computer that Excel is never more than a few seconds away.

Ah, but no library has "everything" and even then, the information about complex analysis would be spread around in many different books and journals. It isn't all collected into one single spot. It's an impossible task, I tell ya.

have you tried MathWorld? Wikipedia or any other encyclopedia? But, seriously, I have my doubts that there could ever be a "one place" where you could have everything. I mean, just on this one topic of imaginary numbers (complex analysis), there are several multi-hundred page books listed as still being in print on Amazon.com. Add to that all the journal articles and out of print texts on complex analysis, and we're talking hundreds of thousands of pages. And, all that on just one small part of mathematics. Collecting it all together is probably an impossible task.

BAC+ BCA+ ACB+ CAB This can be re-written B(AC)+ B(CA)+ (AC)B+ (CA)B and if you save the terms in parenthesis, you should be able to save some extra multiplications there. Matrix multiplication is associative. But, just like your other thread, I don't see the potential for much savings.

What with New Science and Motor Daddy starting numerous threads that ended up nowhere, I would just like to point out that we did have one thread that actually ended up with some significant success: http://www.scienceforums.net/forum/showthread.php?t=33756 Klaynos and I were able to show the OP in that thread that his use of scientific terms was either plain wrong or ambiguous. And the OP came to understand his mistakes and planned to go off and work on learning how these terms are defined and used what their limits are. Really and truly a success story if there has ever been one. I think that it got lost amongst all the NS and MD clutter, however.

I am absolutely crying. Hubble's constant does NOT, NOT, NOT have units of meters per second which is a length per time. I don't know how much clearer anyone can make that. Hubble's constant has units of velocity per length, or length per (length * time) or inverse time. If you have an expression with units of m/s, because you have multiplied Hubble's constant by something else, then it is no longer Hubble's constant! I can't multiply [math]\pi[/math] by 2 and still call it [math]\pi[/math]!

I still get the sense that there is a disconnect between the mathematical concept of a space and what is commonly thought of as space. An "object" in a Hilbert space is a mathematical expression, one that obeys certain rules so that it can be a member of the Hilbert space. For example, something like [math]\sin{x}[/math] or the Hermite polynomials [math]H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n}e^{-x^2}[/math] or any other function/mathematical expression that the inner product exist for. Nothing about a Hilbert space is connected to objects in space, like a baseball, a planet, or an electron. Now, physicists use the properties of a Hilbert space to mathematically describe some problem in "actual" space. But, the Hilbert space is just a collection of mathematical expressions. Nothing more. No connection to any actual physical object.

There is nothing sacrosanct about any unit of length. They are just conversion factors from each other. If Hubble expansion is spread out over megaparsecs, then it is also spread out over microns. A different number of micros -- determined by the conversion factor -- but one length is just as good as any other length. If Hubble expansion is spread out over megaparsecs, then it is also spread out over Angstroms, astronomical units, cubits, chains, fathoms, feet, furlongs, inches, leagues, light-days, microns, miles, nautical miles, parsecs, and yards, not to mention any of the even more esoteric units of length like finger or palm or cable length or telegraph mile. And when dealing with a constant, you can't just "not include" of a unit if you don't want it there. If you want something to last a second, you have to multiply by that second. You have to explicitly state that, and keep track of the units. In this case, if you multiply Hubble's constant by a period of time, then you're going to be left with a dimensionless number. Look, if you're trying to calculate something, you have to keep track of the units. There is no ifs, ands, or buts about this. You know this, whether you've consciously thought about it or not. If someone gave you a rope with a length of 22 inches and tied another rope that had a length of 2 meters to the end of the first one, you'd convert one or the other to get the total length. You wouldn't just sit there confused wondering what good a rope of 2 m and 22 inches is. You'd figure out that it is 100 3/4 inches long or 2.55 m long. As another example, if you had a 1000 US dollar bill, a 1000 Canadian dollar bill, a 1000 Euro bill, and 100 000 yen bill, you traveled to the UK, you would find it very hard to spend that money in its current form. You'd convert it to British pounds. You know what conversion factors are. You wouldn't be able to live daily life without them. This calculation is the same thing. When a constant has units of inverse time, you can't just "not include" the unit of time. Anymore than I can describe the length of rope using units of brightness like the lumen or anymore than I can describe how much money you have in gallons. You can't just change the units. The units are what give the number meaning. If you were trying to build a table and you asked how long the legs are supposed to be, and i just said "1", you'd have to ask "1 what?". It is supposed to be 1 foot tall like a coffee table or is it supposed to be 1 yard tall more like a dining table? Or 1 meter? Just saying "1" is completely meaningless. Just like not including the units on Hubble's constant, or the speed of light, or Planck's constant or the gas constant or the gravitational constant or any other physical constant is meaningless. You don't get to change or "not include" a unit because you don't like it in there. You can use the constants in a calculation -- where you multiply, divide, add and subtract other physical qualities also with units -- and then try to interpret the results. But if the units don't match in the calculations, you have nonsense again. You have to observe very detailed bookkeeping with the units to ensure that your calculations are correct. Just like you check your paycheck to ensure you were paid the correct amount, and you check your bank statement to ensure that no errors were made. You have to check the units to make sure that they come out correctly. There is no other choice. NS, I have tried to be very patient, but this is some very basic stuff. Like I wrote above, you know how important conversion factors are -- you wouldn't survive day to day life without some knowledge of them. Conversion factors are just as important in physics calculations. Now,let's this simple question: before doing any calculations with it, before using it at all -- what are the units of Hubble's constant? Not just the specific units in any one version of them, but what does each specific unit represent, i.e. a yard is a length. So is a km. So is a furlong. A min is a time. So is an hour, or a day. A kg is a mass. etc. What are the fundamental units of Hubble's constant? I'll give a few examples to build up to answer my question. 60 miles per hour is the speed of a car. What are the fundamental units of 60 mph? A mile is a length, and an hour is a time. So 60 mph is a length per time. Here's a more complicated example. I fill a tank from a hose at a rate of 3 gallons per minute, what are the fundamental units of gallons per minute? Well, a gallon is a volume, and volume is a length cubed. And a minute is a unit of time. So, 3 gallons per minute is a length cubed (length^3) per time. Now let's look at an even more complicated example. Let's say I own a farm and I am using a sprayer to put insecticide on my crops. Based on the speed I drive the sprayer and the speed I set the flow rate of the sprayer, I find how many gallons of insecticide I out in the crops per acre. Let's say it 5 gallons per acre. Now, let's look at the fundamental units. We saw above that a gallon is unit of length cubed. An area is a unit of area, which is a length squared. A length cubed divided by a length squared is just a length. The fundamental unit of 5 gallons per acre is a length. Now, you may ask, well why don't we just express all things in terms of fundamental units? Well, if your neighbor farmer and you were talking and you neighbor asked how much insecticide you put down and you said "oh, about 4.6 microns" the other guy would look at you very strangely. But, if you told him "oh, about 5 gallons per acre" then he'd know exactly what you are talking about. Sometimes keeping the numbers in non-fundamental units carries a lot more meaning. In the same way, you should be able to find that the gravitational acceleration at sea level, 9.8 m/s/s had fundamental units of length per time squared. Now, finally, let's look at Hubble's constant. 72 km/mps/s. A km is a length. A megaparsec is also a length. A s is a unit of time. Just like the above example of the sprayer, you have a length in the numerator and in the the denominator, so they cancel. And you are left with just time in the denominator. Therefore, in fundamental units, Hubble's constant has fundamental units of inverse time. It doesn't matter if you express it in inverse seconds or inverse millenia. It is inverse time no matter what unit of time you pick. It also doesn't matter if you express Hubble's constant in terms of meters, or yards or miles, or furlongs or cubits. There is a length on the top and length on the bottom so they cancel out. The reason Hubble's constant is still expressed as km/mpc/s is because, just like the sprayer example, boiling it down to the fundamental units loses some of it's intuitive meaning. But, finally, you can't change what fundamental units a number has, just because you want to. A speed is a length per time. It is wasn't length per time, it isn't a speed. If it was a length per time squared, then it is an acceleration. If a number doesn't have fundamental units of inverse time, then it cannot be an expression of Hubble's constant. Hubble's constant is inverse time. There is no other choice. I hope that you'll take this long post under advisement. I don't have much hope that you will, but I do have some small kernel of hope. I hope that maybe, this time, it'll get through why your calculation here where you just change the units haphazardly is wrong, and your calculations in your other threads where you change units is just wrong. The units are a necessary part of any physical calculation, you cannot just change them however you like. You end up with completely meaningless nonsense unless you keep the units.

I don't know quite where you got that interpretation of a Hilbert Space. A mathematical space doesn't really have anything to do with matter. A space is just some collection of members that obey certain rules. A Hilbert space is one where its collection of members have an inner product [math]<f,g> [/math] and they have a norm defined by [math] |f| = \sqrt{<f,f>} [/math] which forms a complete metric space. That's pretty much it. Nothing about "hidden properties of matter". So, I'm not sure where you got that idea from... maybe you could elaborate some?

What does this + notation even mean? I don't even know how to interpret this. Anywho... The constant is 72 km/mpc/s. This can also be written as: [math] 72 \frac{km}{mpc \cdot s}[/math] Now, 1 megaparsec is 3.08*10^19 km So, if you multiply the above fraction by that conversion you get: [math] 72 \frac{km}{mpc \cdot s} \cdot \frac{1}{3.08 \cdot 10^{19}}\frac{mpc}{km} = 2.34 \cdot 10^{-18} \frac{1}{s}[/math] the length units (the km and the mpc) and you get units of inverse time. This isn't even physics 101, this is high school stuff. Haven't you ever had to convert a mile into a kilometer? Or a U.S. gallon into a Liter? I have serious, serious doubts about your claim of working as a scientist when you cannot even get simple unit conversions correct.

Part of the problem is that the water and ethanol interacts, so it isn't going to be linear. A reference like the CRC Handbook of Chemistry and Physics should have some water/ethanol mixtures.

right. A km (kilometer) is a unit of distance. And a mpc (megaparsec) is a unit of distance. Therefore, 72 km/mpc/s has units of inverse time. Period. The math you posted doesn't have the right units and it therefore 100% wrong. If you can't even get the units correct when performing a calculation, any interpretation of that calculation is completely wrong and meaningless and useless. Start getting the units right (on this particular calculation, and in your your thread about the "MAJOR" discovery) and then maybe we can talk slightly intelligently about the interpretation of those calculations. But, without the correct units on your calculations, you are spouting nonsense. I might as well say "I have to drive 47 Kelvin in my car to get to work every day, and my car gets 26 amperes per mole. I get paid 0.0812 deciliters per lumen squared. On the way home, I buy dinner at the grocery store and pay an average of 14.87 hair follicles." Do you see how ridiculous this gets? Without correct units, I might as well be talking in a foreign language.

Ha! that's what happens when my fingers outrace my brain! (and now everyone can laugh derisively at my "Maths Expert" title! I know I am!)

This is pretty easy. Is 2+3*4 = 24 or 20? (2+3)*4 = 20 2+(3*4) = 24 It is picked so that there is a convention. So that even when someone fails or forgets to put the ()'s in, there is a definitive answer. I don't think that any one method is intrinsically superior to the other ... I don't think that 20 is a better or worse answer than 24 to the above question -- except that my brain goes with the established convention and so in that respect part of me does prefer the 24. I think that the rules are there to make it as unambiguous as possible. Maybe someone else will know more about the history or rationale behind them, because I don't...

Actually, the big, giant, overwhelming point that you are completely missing here is that while the specific value of Hubble's constant is not agreed upon, every single source has the same units -- a velocity divided by a length or equivalently inverse time. Is there any possibility that you could cite any source whatsoever that calls a number Hubble's constant in said constant doesn't have the units of inverse time?

Treating a bubble as a sphere would be a decent 1st approximation. But, a bubble, being a fluid, actually will form circulation zones inside the bubble, breaking that assumption for rigidity. I have some books that give appropriate drag coefficients for bubbles. I'll try to look them up for you later today or tomorrow.

Just to echo what swansot said, but just in a different way, a deceleration is an acceleration with just the opposite sign. The math works out either way.

If it is true probability, then no "system" would work "all the time". If the probabilities are uneven, there may be certain betting systems that come out ahead in the long run -- i.e. over many, many races. But, nothing that is truly random works "all the time". If he truly is winning many times consecutively, then I would suspect that he's figured out how the computer picks the winners each time and knows which one the computer is going to next. p.s. he's also kind of a fool if you guys are really putting for money. "You can shear a sheep many times, but you can skin it only once." -- Amarillo Slim. The point being that even if he has figured out which horse the computer will pick each time, he should have still thrown a significant number of races toy keep up appearances. He should have only won slightly more often than pure luck would have dictated. Enough to consistently win money, but not enough that you guys would start to suspect something and so keep playing.

I don't know what Hubble's constant you could be talking about. http://scienceworld.wolfram.com/physics/HubbleConstant.html http://en.wikipedia.org/wiki/Hubble's_law http://science.nasa.gov/newhome/headlines/ast25may99_2.htm http://www.thefreedictionary.com/Hubble's+constant Every single one of these sources (and many others) states that Hubble's constant is a velocity (km/s typically) divided by a length (parsecs or megaparsecs, typically) which would have units of inverse time. Is there any way you could post a source that lists Hubble's constant in any other units? Such as this distance you seem to think exists?

Not that I expected you to learn from the previous discussions of dimensions, but your math is "ludicrous" H0 = hubbles constant = 70.1 km/s/Mpc (I took the number from wikipedia, there is a margin or error, but the exact number itself is unimportant) Note that since km and Mpc are both units of length, this can also be expressed in units of inverse seconds (1/s or s^-1) and is about 2.5*10^-18 s^-1 c = speed of light = 300 000 km/s Now, in your own words here "Divide 'c' by the Hubble constant" c/H0 = 300 000 km/s / 2.5*10^-18 s^-1 = 1.2*10^23 km It has units of kilometers. And, I have no idea what that number may mean. But the point is it does NOT NOT NOT have units of time!!! Wherever you got 4000 seconds from, it certainly wasn't from the division you said because the division you talk about only has units of length in it. The units of time cancel. Learning how to ensure that your calculations have the right units is day 1 Introduction to Physics stuff. Until you get these things right, I don't know how you can think your "calculations" can be taken seriously.

Solarist, this is an incredibly refreshing attitude here. I think if you poke around a few of the other recent threads here in the Pseudoscience and Speculations section, especially recent ones by Motor Daddy and New Science, you'll see all too often the defender of a new idea be deliberately obtuse or simply refusing to accept that anything but their world view is correct. It is never embarrassing/shameful/sad to have to admit that you made a mistake. What makes it sad is when someone refuses to admit a mistake. No one (of sound mind) can say that 1) they know everything and 2) that they have never made a mistake. Einstein, Newton, Gauss, etc. as great as they were, and as great as their contributions to modern science/physics/math are, they made tons of mistakes. Solarist, there is a lot of learn out there, and if you need any help, please ask questions on the forum. We, the members, may have the answers or we may not. We certainly aren't immune from making mistakes either. But, we all enjoy learning and discussing science and enjoy helping other people learn and discuss it as well. Stick with it. You've got some interesting ideas, and they may turn out to be right. But, you need to build your theory on a solid foundation. A theory is a lot like a house. A house is built on rock, or on concrete for a reason -- to make it a sturdy as possible. If you build it on sand, the house is at risk. In the same way, when a theory is build on shaky ground, it can be toppled easily. As an example in this case, poor use of the concept of kinetic energy. But, if you learn how to use the terms correctly, what the physics concepts can and cannot do, then you'll have a theory built on a solid foundation -- a theory that will stand up to much tougher scrutiny. Maybe one of the biggest things that need to be said here is that if you want to overturn or improve an existing theory, you need to be very well versed in the current state of a theory before you bring about changes. You have to know what current theory says, what it's assumptions are, what it's successes and failures are, basically everything. And that is going to take time to get up to speed. As another analogy, you have to learn to walk before you can run. So, in order to prevent some of the more basic mistakes from happening, you will need to know the current theory as well as possible before trying to fix what you perceive as its failures. Like I said, this forum is really pretty good about helping if we can, so I will hope that you'll stick around and ask questions if they come up. Again, this attitude is almost unbelievably refreshing, so I hope that you'll become a long-time member.

No Solarist, please re-read exactly what you wrote before: In this statement, you say, kinetic energy creates a magnetic field. This is what I am objecting to. Not to the fact that planets have a kinetic energy. Not to the fact that planets have a magnetic field. But to your statement that the kinetic energy creates the magnetic field. This extraordinary statement which is contrary to much of basic physics requires extraordinary proof. Or you have to drop the claim. Provide some evidence that what you say is true, or admit that it was wrong. Or, if I am mis-interpreting the statement, please clarify it. Because as it is quoted right there -- you say that kinetic energy creates a magnetic field, which just isn't supported by facts. ---------------- Still objects have magnetic fields all the time. My magnets on my refrigerator are still (in my reference frame) and obviously have a magnetic field because that it what is holding the magnets up. Earth has a lot of iron which is inherently magnetic, and it would still have a magnetic field whether it was spinning or not. It is a property of the material, not of its spin or velocity. Certainly the movement of magnetic and electric fields are related. But, look at Maxwell's equations ( http://en.wikipedia.org/wiki/Maxwell's_equations ): you've got the movement of the electric field and magnetic fields -- but where is the movement of the obejct? There is no velocity of the magnet itself in the equations. The magnetic and electric fields can change without the obejct itself moving -- pushing more current through a wire, for example. The resistance of a resistor changing due to temperature effects, as another example. As a battery dies and less and less power can be drawn from it as a third example. In those examples the fields change without any movement of the objects themselves. There is no spot where the kinetic energy of an object changes an electric or magnetic field -- this is the concept you presented above and this is the concept that you need to provide evidence for.

Even if items are charged, and even if item have a specific kinetic energy (in any frame), how are the two linked? There is nothing that necessarily links them together except in a sort-of trivial manner. I.e. if an item is being moved due to an electro-magnetic field, then it has kinetic energy, but that is just the result of any force. Gravity, internal combustion engine, and human power are all also good as getting things moving and thus giving an object KE. An object can have an electro-magnetic field without it necessarily having kinetic energy and an object can have kinetic energy without it necessarily having an electro-magnetic field. Unless you can cite some proof otherwise? and, in which case, I'll repeat my question then -- how hard (interpret as how fast) do I have to hit a golf ball to create a magnetic field?