Tom Mattson

OK, change it to "no basis in the picture of reality that is painted by our observations". No, my position is really the opposite: That reality cannot be prescribed by some a priori argument. All we know of reality is through our observations, and a brainless, disembodied super intelligence is not compatible with any of them, and that is my point. There is no reason to believe that such a thing exists.

I made some suggestions at Physics Forums for a snappy title, but they were rejected. "We do more physics before 9:00 AM than your forum does all day." "Our forum can beat up your forum." "The next best thing to university." "Physics from alpha decay to Z bosons."

Actually, the real question would be, "Why would you expect the orbit to be circular?" In order to get a perfectly circular orbit, the initial conditions have to be so precise as to make it highly unlikely to ever happen in practice. So, most orbits are elliptical. Planets aren't attracted to it. They are attracted to the sun and follow elliptical orbits. The definition of an ellipse is a curve that is such that the sum of the distances from each of two foci to any point on the curve is constant. In the case of the Earth's orbit around the Sun, one focus is at the attracting center and the other focus just happens to not have a body located at it.

Don't know if you're still around, but here goes. Usually, I ask students to post what they have so far, and where they got stuck (me doing the problem for you doesn't help you at all). So, I'll speak in generalities. OK Well, he gets 8.05% on the principal (P) every month, so the relation for the total amount of money (T) at a rate ® and for a time (t) is: T=Prt They ask you for P, and you know everything else. Use the same equation. Just change the rate.

MSN Physics. You two will get along great.

I didn't read through most of this, so forgive any repeated information. It is true that GR cannot be "The Theory of Gravity", but this hardly had anything to do with Bohr. The only quantitative work that Bohr did in QM is the (long-defunct) model that bears his name. It was Schrodinger and Heisenberg who did the bulk of the work in nonrelativistic QM; Dirac, Klein, and Gordon who are most famous for relativistic QM; Feynman, Schwinger, Tomonaga, who are most famous for relativistic QFT. Ever hear of the Dirac equation? How about relativistic quantum field theory? Indeed! ??? Neils Bohr 1. The Bohr model. 2. Correct interpretation of quantum mechanics. Albert Einstein 1. Special relativity. 2. General relativity. 3. Brownian motion. 4. Photoelectric effect. 5. Bose-Einstein statistics. This is just plain stupid. Let me ask you something. Are you a member of the MSN Physics message board, and do you listen to a guy named Starship? If so, then STOP!

I don't know of any branches of mathematics that aren't used in physics! Here's a brief (and incomplete) rundown of what you need to know for the various subjects in physics: Classical Mechanics calculus, vector arithmetic, ordinary differential equations, partial differential equations, calculus of variations Classical Electrodynamics calculus, vector calculus, some tensor calculus, ordinary differential equations, partial differential equations Relativity linear algebra, tensor calculus, some group theory Quantum Mechanics calculus, linear algebra, ordinary differential equations, partial differential equations, group theory, some operator theory Thermodynamics calculus, ordinary differential equations (with Legendre transformations) It gets even more complicated with Quantum Field Theory, SUSY, String Theory, and Loop Quantum Gravity.

Is anyone still following this thread? In any case, a just a note on this post... You are correct in saying that fj is not an operator, but you are incorrect in saying that |ej>fj is not allowed. If you read my last post, you will see where I deduced that fj=<ej|f>. So, fj is just a complex number, and as such is allowed to stand on either the right or left hand side of a bra or ket.

Fav character: Homer, and I have a strange affinity for Milhouse too. Fav episode: That's a lot tougher. I like those 2-part episodes that they show at opposite ends of the season, such as "Who Shot Mr. Burns?". I also look forward to the Halloween special every year. And who doensn't like a "Patty Gets Married" episode? Sorry, I can't do it. I can't pick one. Stop looking at me like that, because it won't help. I mean it.

Nicely done.

The best way for you to get help with homework is for you to show how you start, and where you got stuck. I will make some comments that will help you start. Look up the geometrical formulas for the area and the volume of an open top cylinder. (The volume is the same as that of a closed top cylinder, and the area is the same except you have to subtract off the area of one cap). You are fixing the volume to some constant, and trying to minimize the area. So, at some point you are going to be taking the derivative of the expression for area and setting it equal to zero. From that, you will solve for the ratio of h:d. This problem is similar to the first one. Set up an expression for the cost of the tank in terms of the diameter and height, and minimize. You can reduce this problem to that of finding the maximum area under a circular arc for a fixed arc length. Set up the expression for the area, and minimize. I would do this with analytic geometry, because you know that the cylinder has to touch the surface of the cone in a circle. You will need to write an expression for the volume of the cylinder using that information. Try to start these, and I will help you through the rough spots.

:slaphead: I forgot, you get to use a calculator. I also taught courses for the GRE and GMAT, and you don't get to use one there.

I know you guys are already way past this first one, but I have to point something out that everyone missed. There is a glaring mistake above, and it has to do with units. When you square (0.1$), you get (0.01$2), or 0.01 "square dollars".

Ah, yes, I should have guessed it was a grid-in question. I hope you didn't do the full multiplication. There's no need. Check it out. When I multiply the first two digits below, I get: ...103 x.103 ----------- ......9 That's all I need! For success on the SAT, only do as much work as you need to get the answer. That will save you loads of time. ETS deliberately does not give you enough time to solve each problem fully, so if you always do things the long way you will not finish.

It means: If you take this unknown 'x' and put it into the formula 1032x (I assume you meant it to be an exponent), the result can have which of the following digits in the one's place? When you do SAT Math, the answer choices are just as important as the problems. Post the answer choices and I'll tell you what I mean. This looks like a marathon problem, but I promise you it is not.

That's what everybody struggles with. The key to success in Critical Reading is... 1. Read the Blurb This is the 1-3 sentences in italics at the top of the passage. It gives you the main idea of the passage. 2. Skip the Passage That's right, skip it. Go straight to the questions. 2. Don't Do the Questions in Order There are three basic question types here: I. Specific Questions. II. Vocabulary In Context Questions III. Main Idea Questions Do types I and II first, skipping over type III until the end. Treat type II quesions exactly as you would Sentence Completions. For type I questions, see the following. 4. Read What You Need Don't read the whole passage and then try to answer the questions. You won't remember the answers. ETS knows that most test takers are going to dive right into the passage, and they have written the passage to be mind-numbingly boring just so that method will fail. It always results in you reading the same material again. So, if you're going to read parts of the passage while answering the questions anyway, why do the first reading to begin with? All it does is waste time. Instead, treat the passage as an open book exam. Read the questions first, then go to the passage and find the answers. You'll do a lot better that way. For the Specific Questions, the line number is usually given, so you know right where to go. Go to the line and read 5 lines up to 5 lines down. The correct answer is something that you can point to in the passage. You should be able to underline it. The correct answer choice will be a rewording of the answer you find in the passage. If the line number is not given, that's OK because... 5. The Specific Questions Appear in Roughly the Same Order as in the Passage Say questions 23, 24, and 25 are all specific questions. Say #23 refers to line 41 and #25 refers to line 65, and #24 doesn't give you a line number. You can be sure that it is between lines 41 and 65. So you're all set in that department, then.

You should get at least one more: 10 Real SATs, a big red book published by the same people who write the test (ETS). You can time yourself and score the exam with the instructions in the book. By the time you go through the whole thing, you should know what score to expect on the real thing. I would also recommend getting a Princeton Review study guide. I used to teach for them, and with their materials and methods, together with the 10 Real SATs book, my students went up over 100 points per section on average. Tom

Yes; the thing is that, in general, you need an infinite number of sines and cosines to represent the function. That is why you see the infinite sums. There is really nothing on those websites that is beyond basic calculus and trigonometry, so with some instruction and study you should be able to get it. What specifically is giving you trouble? You learn the first in trigonometry, the second in calculus.

Nah; if you look at my first post in that thread, you'll see my secret trick: Get other people to do it for you!

I didn't say that. What I am saying is that, in order for me to be convinced that something has been designed, I would need some evidence for the designer other than the thing in question. I can determine that a car was designed by meeting the designer, who presumably documented his work. I can visit the production plant and observe how human hands were involved in each step of the process. Tom

Superman, Check this out: http://www.physicsforums.com/showthread.php?threadid=204 Math sites are 2 posts down. Tom

A designer label, like Calvin Klein's. That's right, I will not be convinced of Intelligent Design until I see untampered-with newborn babies with "God" stamped on their asses. OK, seriously now. The thing that would convince me is not seeing the craftwork, but having some other evidence of the craftsman. People who propose that some "super intelligence" created everything are operating under the assumption that a "super mind" exists, and this assumption has no basis in reality. How do you know that any mind other than your own exists? You know because of observing certain behaviors in other bodies. When you are sad, you cry. When others are subject to conditions that would make you sad, and you observe them cry, then you infer that they are sad. The inference goes from: (my mental states)-->(my behavior)-->(others' behavior)-->(others' mental states) The last step is the inductive leap, as you do not have access to the mental states of others. So, to propose a mind in the absence of any behavioral observations is to propose 'god', which makes ID just another name for "Creation Science", which is a true contradiction in terms. "Thumbs down", I say. Tom

The leap from the first step to the second step is done by expanding |f> as a linear combination of the basis states |ej>. You can always expand an arbitrary vector in terms of basis states (that is the definition of basis states). So, you get: |f>=:sum:fj|ej>..........(1) where fj are complex numbers. The leap from the first to the third step is done with the projection operator. For a complete set of orthonormal basis states |ej>: :sum:|ej><ej|=1 where 1 is the unit operator. So, in this step: |f>=:sum:|ej><ej|f> all you are doing is multiplying |f> by 1, so the above is an identity. Since the <ej|f> are inner products of a bra-ket, they are complex numbers and can be moved to the left of the kets |ej>, like so: |f>=:sum:(<ej|f>)|ej>..........(2) (1) and (2) can be equated, and upon comparison it is seen that: fj=<ej|f> Tom

By all means, if anyone comes into a hospital needing treatment, they should get it. The answer to this problem is not to pass a law that forces doctors to let people die in front of them. The answer is to be found in taking steps to get our neighbors (*cough Mexico cough*) back on their feet. If we grant some assistance to get their economy self-sufficient on the condition that they clean up their government (especially their police department, one of the world's most corrupt), then the citizens might actually want to stay there. The basic problem with that is that if medicine were socialized, it would not be as advanced as it is today. Things like MRI, PET scan, CAT scan, EEG, EKG, advanced surgical procedures and medications, etc. are only possible because of American capitalism. In the large scale, socialization stifles the spirit of invention, because people want to get paid for their ideas. So if we did live in a world in which everyone gets what they need, you would probably be getting treated with leeches. My $0.02. Tom

General relativity is not required to understand the twin paradox. While it has been correctly noted that the difference between the two twins is that one of them accelerated, Special Relativity is perfectly capable of dealing with accelerations. This should make sense, because if you have a 4-velocity vu and take the time derivative of it, you get the 4-acceleration. Simply taking this derivative does not change the metric from flat to curved, so we are still working with SR. Here is a document that shows how to deal with accelerated frames, and the twin paradox is specifically treated: http://xxx.lanl.gov/pdf/gr-qc/0006095 Tom