Tom Mattson

FWIW, that was a typo. It should have been [imath]x=b[/imath].

Well you originally asked how to get the problem started, and you have been given plenty of clues as to how to do that much. Honestly if your teacher isn't teaching you then you can't rely on an internet forum to do the job. People post here for fun, not to do your teacher's job. You and your classmates should go at once to your school's administration and explain the situation. If it is as bad as you say then that is unacceptable.

Can you explain what you don't understand about what we said? This is basically a problem in stoichiometry. For starters, since you have 1 mole of [imath]C_xH_yO_z[/imath] on the left side and you have [imath]a[/imath] moles of [imath]CO_2[/imath] on the right side, it is clearly the case that [imath]x=a[/imath]. You need to do a similar analysis to find [imath]b[/imath] and [imath]c[/imath].

See my response to your thread in Organic Chemistry.

This article explains it nicely: Wikipedia: Combustion. Scroll down to the heading "Chemical Equation". Now your compound isn't a hydrocarbon, because it also contains oxygen. So you will start with the following equation: [math]C_xH_yO_z + aO_2 \longrightarrow bCO_2+cH_2O[/math] You will need to determine [imath]a,b,c[/imath] in terms of [imath]x,y,z[/imath]. Once you have that it should be easy, because you know the mass of the organic compound, so you should be able to figure out how many moles of [imath]C,H,O[/imath] you are starting with.

The sample space is sufficiently small that you should be able to list out the possible outcomes, no?

Try to make use of the following identities: [math]log_b(x)+log_b(y)=log_b(xy)[/math] [math]log_b(b)=1[/math]

The main point of this thread (esp. in Post #20) is not that you can get a measurement apparatus to spit out an 'i'' date=' but rather that observables of the form [imath']z=x+iy[/imath] aren't any more dubious than observables of the form [imath]\vec{r}=x\hat{i}+y\hat{j}[/imath]. For some reason people reject the former as observables while readily accepting the latter. But, as you noted, in both cases one is just measuring 2 real components and putting them together in a formal linear combination. But some people do make that statement. As an example, take the entry from Math World entitled Hermitian Operator. It says: This thread is in response to remarks such as that.

I'm not sure I follow you. In one sense [imath]\hat{X}[/imath] and [imath]\hat{Y}[/imath] both operate on the same vector space, in that they both operate on the same type of vector space, namely [imath]\mathbb{R}[/imath]. In another sense the two operators act on different vector spaces, because you could say that they operate on their own private, disjoint copy of [imath]\mathbb{R}[/imath]. I think you already said it yourself: We take a formal combination of the components. What is it that you think is missing? This thread is about the definition of the word "observable". That is, do we define "observable" to be "that which corresponds to a Hermitian operator? Or do we define it as "that which corresponds to a normal operator? I would say that the former is acceptable, but too restrictive and that the latter is to be preferred. I haven't seen it either, nor would I expect to. Loosely speaking, the index of refraction is a macroscopic property of a material, applicable when you can ignore the details of its structure. If you are considering the (quantum mechanical) dynamics of a particle through a medium, then I cannot imagine that you would ever find the notion of a refractive index useful. Of course, I could be wrong, as I don't know much about solid state physics.

In the physics community, a raging wiki-battle is waged over the articles on Bell's theorem. There is a semi-famous "local realist" named Caroline Thompson whose contribution causes no small amount of controversy. Other than that you can surf Wikipedia for any article that has a "biased POV" tag, and then step in and help out.

Another, more far-reaching approach is to look up the proof of the Integral Test (if it's not in your book then I'm sure you will have no trouble finding it on the internet). Then you can apply the integral test to the summand in the harmonic series and show that it diverges. I say that this approach is more far-reaching because you can apply the Integral Test to many more series than just the harmonic series.

I thought about that very same thing. But until SFN adopts a policy of silencing cranks, and as long as I hold this position, I am going to expose people such as this for what they are, to the best of my ability.

Physics is the science that has as its ultimate objective as complete an accounting of the observed phenomena of the natural world as possible. By my inclusion of the word "science" in that definition, I am implying that prediction of the outcome of experiments is part and parcel of this discipline. I have made it obvious to anyone who has at least a pair of brain cells to rub together that I do not think that physics is merely the study of any set of equations. In case you have forgotten, my comments on this point can be found in Posts 36 and 38 of this thread. In short: Mathematics is necessary but is not sufficient to understand physics. Once again for the hard-of-caring: I have already made this obvious to all but the most simple. The only level of training about which I have ever elluded (For the record, I do not "spout". I leave that to the cranks.) is that level of training that qualifies one to state what is and what is not required to understand physics. I would say that a necessary condition is the completion of a degree in Physics, and that the higher the degree the greater the qualifcation in this regard. This is a telling symptom of that arrgance I mentioned. Saint, you apparently have yet to reach the zero level of education in phyiscs. And yet you brazenly think that your ill-informed, ill-reasoned opinions are worthy of "equal time" on SFN, despite the fact that there are people here who know much better than you do about scientific issues. There are two rough categories of people who read these boards who concern me most. There are people who have completed a scientific education, and there are those who have yet to embark on that journey and who would like to know what is needed to do it. When some ignorant fool starts posting that a knowledge of mathematics is not necessary for an understanding of physics, those two groups of people will absorb and react to that in two different ways. The people who do not know what is necessary to become a physicist will be mislead. The people who do know what is necessary to become a physicist will know that said ignorant fool is talking out of his arse, and will step up to call said ignorant fool on it. In either case, the ignorant fool would be doing a great service to the community by knocking it off, and he would be doing a great service to himself by shutting the hell up an listening to those who have actually taken the time to study physics.

From the "Incommensurability" paper: OK, since we are quoting authorities without making any justification, how about a quote from an authority who actually works as a scientist? No less an authority than Steven Weinberg said the following regarding Kuhn's claim: ... Nor do scientific revolutions necessarily change the way that we assess our theories, making different paradigms incommensurable. Over the past forty years I have been involved in revolutionary changes in the way that physicists understand the elemntary particles that are the basic constituents of matter. The greater revolutions of this century, quantum mechanics and relativity, were before my time, but they are the basis of the physics research of my generation. Nowhere have I seen any signs of Kuhn's incommensurability between different paradigms. http://www.cs.utexas.edu/users/vl/notes/weinberg.html (color added for emphasis) As for Newtonian and Einsteinian mechanics not contradicting each other, that seems easy enough to prove wrong. Consider a particle of mass [imath]M[/imath] which is subjected to a constant acceleration [imath]a[/imath] relative to Earth. Now use both Newtonian and Einsteinian mechanics to predict the speed of the ship as measured by an observer on Earth at a later time [imath]t[/imath]. You will get two different answers, and they cannot both be correct. Hence, it seems clear that the two theories contradict each other. I'm not sure how you arrive at that conclusion, or even of how you define "compatible", but it's simple enough to analyze the logic of Newtonian's "if...then" proposition. The Newtonian regards the following two statements as logically atomic: [imath]D:[/imath] The diameter of the ball is smaller than the diameter of the hole. [imath]F:[/imath] The ball will fall in the hole. From these he forms the compound proposition [imath]D \longrightarrow F[/imath] The Einsteinian does view [imath]F[/imath] as atomic, but not so for [imath]D[/imath]. Rather, he regards [imath]D[/imath] as a compound proposition with infinitely many conjuncts. Explicitly: [imath]D:[/imath] [imath]\bigwedge_{\alpha}D_{\alpha}[/imath] [imath]D_{\alpha}:[/imath] The diameter of the ball is smaller than the diameter of the hole as determined by an observer in reference frame [imath]\alpha[/imath]. Where [imath]\alpha[/imath] is a continuous index that labels all reference frames. Back to compatibility: As I said, I am not sure of what definition you are using. But if by "compatible" you mean that one point of view can be understood in terms of the other, then I say that this can be done. Einstein affirms the differences among the various [imath]D_{\alpha}[/imath] while Newton denies it. Newton says that the [imath]D_{\alpha}[/imath]'s are all the same. On to your next gedanken. FYI, this exact thought experiment has been worked out relativistically by Rindler in Am. J. Phys. I have the article at home and I will certainly post the complete reference when I find it. For now I will just say that the following contradiction that you "derived" is dead wrong: No, this is just a mistake that stems from a misunderstanding of the relativity of simuntaneity. Going back to my logical analysis of [imath]D \longrightarrow F[/imath]: While the Einsteinian denies that [imath]D[/imath] is logically atomic, he affirms that [imath]F[/imath] is logically atomic. If the ball falls in one frame, then it falls in every frame, and the same is true of the rod. As you will see if you read the Rindler article, this is accomodated in relativity by admitting that the rigidity of an object is relative, and as he demonstrates this is a direct consequence of the relativity of simultaneity. Finally: Not true. As discussed at length above, relativistic assertions regarding measurements of relative quantities must refer to a frame of reference, as I schematized in my indexed statements [imath]D_{\alpha}[/imath] above. No relativistic assertion [imath]D[/imath] is accompanied by [imath]\neg D[/imath]. Rather, every relativistic assertion [imath]D_{\alpha}[/imath] regarding relative quantities is accompanied by [imath]\neg D_{\beta}[/imath], [imath]\beta\neq\alpha[/imath]. Since [imath]D_{\alpha}[/imath] is not necessarily equivalent to [imath]D_{\beta}[/imath] when [imath]\alpha\neq\beta[/imath], this is not a contradiction.

Mart, I've read your post, and I am afraid that you just don't get it. The argument by Saint clearly concludes with a statement on the necessity of mathematics in understanding physics (specifically, it denies the same). That was not Saint's argument. But even if that were Saint's argument' date=' so what? That argument isn't valid either. ??? I made comments that directly addressed the logic of the argument. I also made comments based on experience that directly addressed the truth value of the conclusion. I don't know it is possible that one could read my attack on the value of the message and miss those things, but unfortunately you did.

"Mathematics=Reality" is not the issue at hand, which is rather "Is an understanding of mathematics necessary for an understanding of physics?" I think you mistake authority for arrogance. It is not arrogant to speak on what one knows. It is arrogant to presumptuously peddle misinformation on subjects on which one is completely ignorant. It would be just as bad if I were to go to a message board on neuroscience and start telling professional researchers and educators in that field what is and what is not required to understand their subject. It would not only be arrogant, it would be positively obnoxious. That "the world can be understood outside of mathematics" is not the issue. It is whether physics can be so understood. Physics is a discipline that requires formal training. Without that training, one is not in any position to say what is and what is not required to understand it. I am calling it like I see it.

Of course it's an analogy. I stated it as a counterexample to Saint's argument, which is: P is used to build Q. Therefore, P is not necessary to achieve Q. Finding counterexamples is a standard, textbook way to show the invalidity of an argument. Of course, it's obvious that the above syllogism is invalid, but I stated the counterexample anyway in case Saint hasn't studied logic, which I am inclined to think is likely.

Nonsense. Your conclusion simply does not logically follow from your premises. But we don't even need to resort to formal logic here because common sense is enough to debunk your argument. Cars are built with tools, and yet a car is not 'tools'. Does that mean that tools are not necessary to build cars? If you tried to convince any auto builder of that he would laugh you out of the room. And it doesn't sound any more sensible when you apply the argument to physics. There's a difference between my curiosity and your opinions: I am open to learning new things, whereas you just want to tell people 'how it is', despite the fact that you have never so much as lifted a finger to see 'how it is' for yourself. The claims I have seen you make both in this thread and elsewhere are marked by having equal parts ignorance and arrogance. That is why, to the extent that you make those claims, your contribution to this thread in particular and SFN in general is rubbish, and should be exposed as such. Anyone can have an opinion. But in order for that opinion to not be meaningless at best or misleading at worst, then the required level of study is far higher than you have bothered to undertake.

I think that you did not understand my point about necessesity vs. sufficiency. Neither theory nor experiment alone can serve as the basis for understanding physics. Both are required' date=' and if either one is missing then understanding is not taking place. Not by any normal usage of the word "understanding" it isn't. It is not enough to simply observe that things that are thrown upwards eventually fall downwards (and even this is not always true). To understand what is happening it is necessary to know when, where, and how fast the object falls downwards, or if it will fall downwards at all. This requires mathematics. Just out of curiosity, on what do you base your remarks? You obviously aren't basing them on your studies or research. That leaves one wondering what you are basing them on.

They do experiments. So? What does that have to do with the point at hand? The assertion is that physics cannot be understood apart from mathematics. That statements asserts the necessity--not the sufficiency--of mathematics in understanding physics.

What I don't understand is why anyone would come to a site called "Science Forums Network" for help with an assignment in English. Isn't it common knowledge that scientific types aren't no good at English?

It's not good to be committed to a position without knowing why you hold that position... Anyway, if I were doing this project from scratch I would first investigate how the sedimentary and metamorphic rocks would be impacted and why that would pose a problem. Then I would investigate why the MTA feels a tunnel is needed. It could be necessary to sustain commerce. After that I would weigh the pros and cons and only then take a position on it.

Why do you have to be against tunneling? Why can't you be for tunneling?