Bignose

The proof is in the Speculation section. Just read a couple of dozen, they almost always end up with the speculator ignoring or leaving in a huff. The figure is my estimate. I don't participate in speculations a great deal, not like some of the other members here. But, I can only remember 1 time when a thread I participated in, the speculator publicly said "I see now that I have much more learning to do, and I am going to go do that". It is times like that that make that section worth it, in my opinion. But, as I wrote above, they are all-too-rare.

[math]\pi[/math] in base [math]\pi[/math] is 10, not 1. [math] 1\cdot\pi^1 + 0\cdot\pi^0[/math]

Where better than a forum to attempt to show someone why their speculation goes against current theory and observations? Where better than a forum to show someone that the logical consequences of their speculation is self-contradictory or contradictory to known observations. Unfortunately, it rarely happens that way. Once in a while, we do get someone with an open mind who learns from what other members say. But, it is all-too-rare; something in the neighborhood of 1 to 2%.

at the end there, you forgot your factor of 1/2 which would then correctly make the last expression [math]\frac{\sqrt{3}}{4}[/math]

This probably isn't the right place for this (and mods, feel free to cut off to another thread as necessary). But. The universe is expanding, many, many measurements tell us this. I think that it is fine that you don't care for 'dark energy', but nonetheless, unless you can argue why all the data observed is wrong, you cannot ignore that the universe is indeed expanding. To expand, there is a certain energy balance. From what we can observe today, it doesn't balance -- so that unknown lump that must be present to balance the energy is called 'dark energy'. There are a few ways to go about this, if you want to eliminate it. 1) Find the missing energy. 2) Show why the current measurements of the observable energy are wrong so that when they are corrected, the balance is restored. 3) Show that the universe isn't expanding, and hence we don't need that extra energy. etc. Just saying "there is no such thing as dark energy" isn't enough, you have to provide alternatives and be able to show how it fits into current knowledge or show where current knowledge is wrong. Though a post may be speculative, the rules of this forum are that you still have to be following the rules of science. Black holes are largely a mystery. Scientists take what is known with current observations and theory (theory that has been shown correct via experimentation) and tries to make them fit. Sure, there are several open questions about them, but again, if you want to speculate on them, you need to be able to show why the current understanding is incorrect, or how your speculation doesn't trample on what is known. If the logical consequences of your speculation are contrary to what is known, then the speculation needs to be refined or dropped. I don't think that any real scientist anywhere is going to tell you that they know what was before the Big Bang. I know that simulations can simulate conditions seconds after a Big Bang -- and when ran forward in time agree with the conditions observed today. But, they don't say anything about pre-BB. Again, unless you can show where these simulations have gone wrong, you can't just not like them. You have to show why, and present alternatives that work as well if not better than the current simulations. Similarly, no good scientist can definitively tell you that a meteor strike killed the dinosaurs. We have evidence that fits into that idea -- from a large crater to a layer of the same kind of rock found all across the globe -- but it isn't definitive. Other ideas can fit in as well. There have been other extinctions not apparently caused by meteor strikes that have also occurred. Maybe the biggest point here is that with any bit of science, it is okay to speculate something else. But, it is not okay to just not like it. The current knowledge has undergone a very rigorous process to become the current understanding. There are many, many issues that are still open, and hotly debated; read almost any cutting edge journal or attend any convention, and you will see disagreements among the scientific community. But, the big point is that there isn't a scientist that just sits there and says "I don't like that hypothesis" and nothing more. If a scientist disagrees, he'll say things like "your idea doesn't fit with the data of X and Y taken last year" or "how does this data fit with the theory of Z?" or something similar. A scientist disagrees because it disagrees with the current knowledge, or doesn't quite fit in right, or similar. If a scientist's intuition tells him it is wrong, but he doesn't know why, he holds his tongue; he may go back and try to work out why his intuition is telling him it is wrong, but he also knows that intuition is not the only thing. And THAT is what speculations ends up being full of. People whose intuitions are saying "that doesn't seem right". But, intuition is not enough -- that's why science is such a useful tool. Science doesn't give a wit about intuition -- it wants to know how well does the observations fit the predictions. Something can be very unintuitive -- but if the predictions it makes fit the observations the best -- then it is right. You have every right to your intuition and to your opinion. But, unless that opinion is backed up by evidence -- it is NOT science. Science MUST be backed up by evidence. Without evidence, it is NOT science. And finally, the rules of this science forum are that the scientific method be followed everywhere, even in the speculations section. It doesn't matter what it is called. It could be called "Bananas and Ice Cream" or "Rabid Orangutan" or "Cocktails at Dawn". Whatever it is called, the rules say that the scientific method will be respected and followed in there. And, the admins and mods enforce that rule -- if someone is not following the scientific method, then they get disciplined. They can do this because it is a private forum. They make the rules. If they banned the letter "e" one day, then they can do it. Similarly, we don't have to come here. I suspect that if the mods started banning anyone who did use the letter "e", that this would pretty quickly become a very dead forum, because the number of visitors and posters would diminish very quickly. That is our choice, as visitors an posters. At this time, I choose to participate here; I personally like the rules and how they are enforced. If I didn't, I wouldn't participate here. It really is that simple. So, and I do hope that you don't take this as being overly rude because tone does not convey over the written word on a forum well, but if you don't like the rules here, then you are free to leave and post somewhere that has rules that you like more. Or start your own forum. This is not to say suggestions aren't welcome. There has been much discussion about what exactly to name the Speculations section. And, the suggestion to have a politics forum and a religion and philosophy forum have been taken -- these are now part of this community. So, suggest away -- but "right" and "wrong" is wholly determined by the site owner. It is his site, he can do with it what he wants. So, unless you can convince him that the name is wrong, then it is what it is.

The difference to what has very typically ended up in the speculations forum and this example was that, indeed, the issues with the understanding of gravity were known at the time. And, Einstein was proposing mechanisms to fix the known errors, including making mathematical predictions that turned out to be quite good when the associated experiments were performed. If someone want to speculate about the holes that are in the current theory, they are more than welcome. There are plenty of holes, today, and I suspect for a long time. However, the speculation still has to be science. Again, it really is a good example, that speculating quark are tiny fairies may be a good story, but it is not science. Secondly, any speculation that tries to fill current known holes, can't just trample all over what is not currently a hole. That is, if someone speculates a mechanism that is different that what is currently accepted, it has to match all known observations at least as well as the current theory, otherwise why get rid of the current theory? And, that leads to another big chunk of threads that end up in speculations, people with ideas that completely ignore or break the current knowledge. It is not that we don't want to encourage speculation, it is that we want to encourage speculation in a learning environment. Say someone shows up and says that all gravity is just magnetism. That's all well and good, until you start applying what we know about magnets and gravity today. When you apply today's knowledge -- knowledge that has been confirmed by thousands to millions of experiments -- you can see the flaws in such thinking. Unless the speculator proposes mechanisms by which gravity acts like gravity sometime, and like magnets others, the current knowledge refutes the speculation. And, the posts in that Speculations thread are directed at helping the speculator improve their knowledge and see why the current knowledge refutes that speculation. All too often, the speculator refuses to listen to anything except support for his ideas, and then criticize members to "have an open mind", when they are typically the worst at following their own advice. There is a good group of knowledgeable members here. For the most part, they are posting suggestions and improvements in the speculations section. But, the speculators are not listening -- so things get pretty heated. When someone continuously makes the same mistake that has been pointed out to them, or continuously ignores the results of thousands of experiments -- it is easy to get frustrated. There are a few threads going on now with exactly this same pattern -- a mistake has been pointed out, the the speculator refuses to acknowledge the mistake. Sometimes it is a result of not enough schooling or training -- but just as often it is a result of stubbornness. And, in the end, those threads end up looking like a disaster.

Have you taken a Philosophy of Science course? Or read one of the many good books about it? Because your replies show an ignorance of what some of your peers in philosophy have written. Karl Popper's The logic of scientific discovery immediately springs to mind. Popper's main point is one of falsifiability. Without the ability to falsify an idea, the idea is NOT science. It is story telling. http://en.wikipedia.org/wiki/Demarcation_problem Let me copy a block from the above link: Threads that end up in Speculations are because they have failed multiple of these bullet points, and hence are closer to story-telling than science.

Mooey, did you read "Will Humans Swim Faster or Slower in Syrup?" by Gettelfinger and Cussler, AIChE Journal, 2004? That article had univeristy swim team members perform laps in water and in a guar gum solution with about 10 times the viscosity of water, and found that times were pretty darn close to the same. The major conclusion was that competitive swimming wasn't really in the laminar flow regime, and that surface drag was only a tiny factor. Of course, the recent Olympics and all the records that fell seems to point differently, but I remember that article. I think that the authors won an Ig Nobel Prize for it, if I am not mistaken.

Moved to Homework Help as this is the more appropriate section.

That doesn't address any of my questions about adding terms with unlike units (T & P), or having an equals sign inside of parentheses and thus not having a meaningful equation/expression. How soon can these be addressed?

How can you add T + P? Per your graphic, T has units of kJ (energy) and P has units of kJ/s (energy per time)! This is like saying 4 bananas plus 2 scissors = a quantity of tables. Everything you add together has to have the same unit, or at least the same kind. i.e. 1 km + 5 km = 6 km. Or 1 km + 50 inches = 1.00127 km. The two things being added are both lengths. If they don't have the same unit, they can't be added. 1 km + 5 gallon = something that is completely nonsensical. Dimensional consistency is an absolute necessity for a meaningful equation. It isn't a guarantee of meaningfulness, because an equation can have correct units but still be nonsensical, but it is necessary. Also, I still don't understand how there is an equal sign INSIDE a parentheses. Can you please write it in a more conventional notation? I cannot understand it at all unless you put it into a notion I can understand. If Q = MS(T+P), then what is -P + Q equal to? If it isn't equal to anything, then all you have is an expression, not an equation, and again, not terribly meaningful. Also also, you cannot directly convert temperature into an energy. Because temperature is an intrinsic properly, and energy is extrinsic. That is, temperature is independent of the quantity of mass of an substance. You can have 1 mg of a substance at 500 K or 1000 kg, and the temperature is the same. However, energy does depend on the mass of the substance. If 1 mg of a substance has 5 kJ of energy in it, that is significantly different than 1000 kg or a substance with 5 kJ. You will need to know the mass of a substance at a certain temperature to estimate energy and vice versa.

OK, two problems immediately jump out. 1) Why is the equals sign INSIDE the square brackets? This is meaningless in a mathematical sense. An equation has one group of symbols, which can include brackets, but every open bracket is closed before you get to the equals sign, set equal to another group of symbols, again with the brackets closed before the end of the term. This same equation has been posted several times, so I don't think that it is just a typo. So, please explain it further. 2) If I ignore the brackets per my issue #1, it reads -P + Q = MS(T + P), right? But, if so, there is a units error, because if the left hand side is energy (per your descriptions of the terms) then the right side has to have units of energy as well. But, the terms inside the parentheses have units of energy, and MS isn't unitless (mass times a frequency). Hopefully, fixing my issue #1 will remedy this issue as well, but at the moment, this expression isn't even dimensionally consistent.

I went ahead and moved this to Homework Help to hopefully get quicker response if you reply back to the tree. And, yes, I completely concur with the tree that we will help you if you show us the work you've done up the point where you are stuck. Spoon feeding answers doesn't really help anybody, though, so it isn't done on this forum.

Another recent thread talked about this to a certain extent. The inner product or dot product between two vectors in 2 or 3 dimensions can have a be thought to determine the angle between them. [math]\mathbf{u}\cdot\mathbf{v}= \sum_i u_i v_i = \lVert\mathbf{u}\rVert \lVert\mathbf{v}\rVert \cos \theta[/math] The exact same thing can be done for any i>1, however. I.e. you can use i=4 in the same equation, and find a [math]\cos\theta[/math] that makes the equation true. That can be defined as the cosine of the angle between the 4-vectors.

What does any of what I wrote have to do with the big bang? I was trying to use "time as a constant" per Double K and got stuck, and was hoping he'd explain it. All it is is physics 101, the time integral of velocity gives the position. Merged post follows: Consecutive posts merged I don't see any dilemma with using time as a variable to integrate over. Integrating velocity with time has been supremely successful at predicting position as a function of time. Taking the derivative of position with respect to time has been supremely successful at predicting velocity. Every prediction of things moving (at a speed significantly slower than the speed of light) is based on these equations that treat time as a variable. If they didn't work, we wouldn't be able to predict solar and lunar eclipses, how to put satellites into orbit, even how far a golfer hits a golf ball. And since these are all things we can do, I don't see any dilemma at all.

All I can say is: huh? (the smart alec is me says time is so non-constant that it changes from being a constant to being not constant in just a few days!)

All righty, let's give this a try. An object's velocity is equal to the derivative of its position with respect to time. Let v = velocity, x = position, and t = time. or in equation form: [math]\frac{dx}{dt} = v[/math] To find an object's position at a certain time, you integrate the above: [math]x = \int dx = \int v dt [/math] time is a variable to integrate over.... if time were a constant, the above would be meaningless. I.e. plug in pi.. [math] \int v d\pi [/math] has no meaning. Any more than [math]\int v d2[/math] does. But, if we treat time as a variable (not as a constant), then we get right answers. I.e. if a ball is moving at +2 m/s, and at time t=0 was at x=0, where will the ball be at t=7 seconds? [math] \int^7_0 v dt = 7*2 - 0*2 = 14 m [/math] and you get the right answer. As I wrote above, integrals treating t as a constant don't even have meaning. How do you resolve this? How can mathematical equations "work" by treating time as a constant? Because I don't know how to make the above work with a constant. Hopefully you can resolve this for us.

when a payment is made, does it go to paying off the accrued interest first, or does it go to paying off the principal first? Or some split thereof? I think that that is what you are a really asking for -- and the answer may very well be in the same law that states interest only accrues on the principal.

What would be wrong would be claiming that you beat the game, and failing to mention the aids you received. I think an a similar analogy would be people who claim they broke 80 golfing when they allowed themselves 1 mulligan per 9, fluffed their lie, and didn't assess themselves the proper penalties. They may have broke 80 at whatever game they are playing, but it wasn't golf. It was golf-like, but golf itself involves following all the rules. I think that the same applies. If you use cheat codes and the like, you may be playing a game similar to the original, but it isn't quite the same. As with Pangloss, it is "wrong" only if it hurts someone else, which is rather unlikely. Gambling on the result is about the only thing wherein someone else gets hurt unfairly, though if everyone goes into the gamble accepting a few rules allowed to be broken (again, a group of golfers that give each other mulligans), then it is fair. Otherwise, it is only you who actually knows what you did.

The random motion of the atoms and molecules ensures that if available, they will always spread out into an equilibrium configuration. And, in the absence of other forces, equilibrium is typically uniform distribution. For example, you can put a drop of food coloring in a glass and let it sit. In time, the coloring will be evenly distributed over the entire glass. The drop, that was very concentrated in color, will eventually be spread out into and the entire glass will be a very pale color. The molecules of the blue dye and moving in all random directions, and this randomness causes them to eventually fill the entire available volume evenly.

If you're going to insist on using a fractional representation (for whatever reason) why not use 335/113, it is accurate to 7 digits.

May I suggest you read: http://relativity.livingreviews.org/Articles/lrr-2001-4/ It is an excellent collection of experimental evidence that supports general relativity. As general relativity is the extension of special relativity, experimental evidence that supports GR also supports SR. In order to defend your idea, you better be able to show why every single piece of evidence in that paper is incorrect.

In what way is the word "type" significantly different than "manifestation"? They really seem like synonyms to me, when used in this context.

Oh come on. Really? Exactly what conclusion did I write that was wrong? Please quote it directly. And you really don't need to write so insultingly. I didn't insult you. And if "correctness is paramount", why aren't you paying attention to everyone else that is telling you how to correctly perform integrations? Follow your own words here, ambros, and everyone will be a lot happier here.

It doesn't matter what specific units are used, metric, English, etc. That's I used the generic t for time unit, l for length, and m for mass. Heck, look at the chart about SI units: http://en.wikipedia.org/wiki/International_System_of_Units, the "symbol" category of the chart under the heading Units. The answer should be the same no matter what units you use, too. F=ma doesn't care if the force is in the Newtons, kilograms-force, or pounds-force; doesn't care if the mass is kilograms, grams, slugs, or pounds-mass; doesn't care if a is in meters per time squared, nautical miles per year squared, or light years per picosecond squared. In the end, the quantity on the right hand side will always be a mass times a length over a time squared. The bigger point is that you can come up with an infinite number of combinations of dimensional quantities to result in a mass times a length over a time squared. [math]F_{wrong1} = mvd [/math] where v is a velocity and d is a displacement will also have the same units, but this equation will not give the right answer except by coincidence. [math]F_{wrong2} = mjt [/math] where j is the jerk (derivative of acceleration with respect to time) and t is the elapsed time is also wrong, but has the right units. [math]F_{wrong3} = \frac{\rho d^4 j}{v} [/math] where [math]\rho[/math] is the density. Again, correct units in the end, but way wrong equation. The moral of this story is that dimensional analysis is a great 1st step, but it is no where near the end. It weeds out all equations that have the wrong dimensions, but it doesn't tell you anything about how correct any of the many different equations with the right dimensions are.