Iggy

I wouldn't trust a megalomaniac dictator's reasonable desire to avoid rationally predicted consequences. The desires may not be reasonable, or the predictions all that rational. That's the problem with totalitarian autocracy -- the country publicly plays out the private delusions of the dictator. I wouldn't put delusions of war past the Dear Leader. Someone could have told Saddam in 1991 that invading Kuwait was a bad idea because Iraq would effectively be betting everything on a war they would certainly lose. But, Saddam may not have been thinking clearly, and in an authoritarian regime nothing is more powerful than, and everything is subject to, the leader's thoughts -- even if they are confused thoughts that might lead the country to its own destruction. Kim Jong Il may wake up a couple years from now and believe like you said, the US can't afford another war. He could take out the South's largest military installations and population centers with a few nukes and a few hundred sarin or VX missiles. Occupying the south within a week could seem like an obtainable goal. If he isn't worried about China intervening, or the UN issuing sanctions and sternly-worded letters of resolution, I wouldn't put it past him. I wouldn't say it's impossible. He could hold Japan hostage to be doubly sure nobody intervened, "Anyone gets any ideas and I take out Tokyo [evil laugh]". Saddam did say that the only mistake he made in '91 was invading Kuwait before he had the bomb. Kim Jong Il could be doing it just a bit smarter. Or, the Dear Leader could wake up tomorrow and decide he's got nothing left to lose. I think the danger that the South faces from the North, and that Israel faces from Iran, is very real and far worse than people typically imagine.

It takes into account Newton's universal law of gravity and the centrifugal force. It assumes uniform density and slow rotation. That is all. Then let's move on. Would you agree that this calculation, should be 6.2 km instead, and would that difference affect your results?

Right. Sorry about the imprecise language. I also meant the equatorial radius. The equatorial column of water in the thought experiment would be 1/229 longer where the ratio of centrifugal force to gravitational force at the equator is 1/289. That was the result Newton got. -------------- I'm reading onward in the article. Sorry I'm so slow. I don't have much time. I believe it would be 1/299 precisely.... ...yes, because the volume of a sphere is [latex]4/3 \pi R^3[/latex] and a spheroid is [latex]4/3 \pi {R_1}^2 R_2[/latex], if [latex]R_2[/latex] is larger than [latex]R_1[/latex] by 1/300, the volume of the spheroid would be 300/299 times the volume of the sphere. It would increase the volume by 1/299. Ok, the gravitational potential should be, [latex]\phi = \frac{GM}{(R^2 + X^2)^{1/2}}=-\frac{GM}{Y}[/latex] where X is the distance from the center to the point under consideration along the polar axis and Y is the distance along the hypotenuse that you've labeled [latex]\sqrt{2}R[/latex]. At X=R (i.e. at the north pole) it has, [latex]\phi = -\frac{GM}{\sqrt{2}R} = -\frac{(6.67 \times 10^{-11})(2 \times 10^{22})}{\sqrt{2}(6378100)} = -1.478 \times 10^5 J/kg[/latex] due to the ring. At X=0, Y=R, (at earth's center) it has, [latex]\phi = -\frac{GM}{R} = -\frac{(6.67 \times 10^{-11})(2 \times 10^{22})}{6378100} = -2.0900 \times 10^5 J/kg[/latex] due to the ring. Mass gains 61,367 Joules per kilogram by moving from the north pole to the center due solely to a ring at the equator having a mass 1/299 of the earth. The gravitational potential of a sphere is [latex]\phi = -\frac{GM}{R}[/latex], so we have: [latex]-\frac{GM}{R_2} - -\frac{GM}{R_1} = 61367[/latex], solving for R2 gives, [latex]R_2 = - \frac{R_1GM}{61367 R_1 - GM} = 6384370 \ m[/latex] so that, [latex]R_2 - R_1 = 6384370 - 6378100 = 6270 \ m[/latex] So, the energy gained from dropping down a polar shaft from a ring of mass at the equator alone would be enough to lift the same quantity of mass roughly 6.3 km off the surface of the equator. Why do you suppose we differ here? I'm still not seeing where you got that 11.035. It is clearly half of the centrifugal force at the equator divided by the gravitational force at the equator times the polar radius... but why does half have any meaning? EDIT--> To be precise and consistent, we might establish: Rpolar = 6356.7 km Requator = 6356.7 + 21 = 6377.7 km Since you used 21 km and earth's actual polar radius is 6356.7 this would make sense. This makes the equatorial radius longer by 1/304. The volume of the spheroid would then be larger by 1/303. In other words, a spheroid with r1 = 6356.7, r2 = 6377.7 would be 304/303 times the volume of a sphere with r = 6356.7. The volume would be 1/303 larger. If we both reasoned with those numbers I think we'd come out alright. If I recalculate with those numbers I get a slightly different 6151 m, or roughly 6.2 km. Might using those same numbers give you the same?

Ok. I'll be interested to see the valid method, but it'll have to wait till tomorrow. To be clear, the correct answer to that first thing would be 27.9 km, not 11.035 km. With uniform density, following your thought experiment, the equatorial radius is longer by 1/229, not 1/578 as you suspect. Newton correctly calculated this. The equation that compares the ellipticity, [latex]\delta[/latex] (the factor by which the equator is longer) to the ratio between centrifugal and gravitational force, [latex]\phi[/latex] (1/289 -- as we found) is: [latex]\frac {\delta}{1/100} = \frac{\phi}{4/505}[/latex] Newton gave this equation in the Principia book 3 and it was later proved by Clairaut and other mathematicians correct for slowly rotating bodies of uniform density. As you can see, the equatorial column isn't longer in the same amount (i.e. [latex]\delta[/latex] isn't equal to) the ratio of centrifugal and gravitational force ([latex]\phi[/latex]). Nor is it equal to half phi. It is 1.26 times [latex]\phi[/latex]. Where [latex]\phi = \frac{1}{289}[/latex], [latex]\delta = \frac{1}{229}[/latex]. The equator is longer by 1/229 where the ratio of centrifugal force to gravitational force at the equator is 1/289. Roughly 28 km.

You might be confusing me with Ahmad. I didn't answer his question because I'm not him. I've never experienced Ahmad's "strange self-induced feeling" so I obviously can't know how much, or answer why, it is similar to an aggravated sympathetic nervous system. Are these two mutually exclusive? If self-hypnosis can cause a stimulated sympathetic nervous system then why would you suggest studying the one rather than associating the feeling with the other? That wouldn't make any kind of sense.

Good deal. I was looking more for a summary of your method, but I suppose we can start at the beginning and take things piecemeal. I have a question/problem with the first thing: Both the centrifugal and gravitational force of a rigid body of uniform density changes linearly with r, so I don't think you're making good sense. To put that another way.... you say "at the center of the earth, there is no centrifugal force". That is true enough, but there is also no gravitational force at that spot either. I don't believe the ratio of centrifugal force divided by gravitational force changes with r in the way you say... it should stay constant since they are both linear. For example, at r=3189050m (half of the equatorial radius) the gravitational force [you can calculate with gm/r2] is 4.90 m/s2. The centrifugal force is 0.01696 m/s2. The ratio there is the same as at the surface: 0.003. At r=637810m (10% of the equatorial radius) you get 0.00339 m/s2 for the centrifugal force and 0.98 for the gravitational field. Again the ratio is 0.003. The average of the ratio is not 1/578 because the ratio doesn't change from 0 to 1/289 with r. The ratio stays a constant 1/289 with r (from the center to the surface), and that's how much lighter the equatorial column of water would be (1/289) if the earth were spherical and of constant density. Do you agree, and how would this affect your reasoning?

Are those two mutually exclusive?

I completely agree. That's actually what I meant when I said "ontology doesn't like that answer". Without math or an understanding of physics and geometry, a person is somewhat stuck trying to understand theories by analogy His position (i wouldn't call it an ontology) is not consistent (either internally consistent or consistent with real world data).

I agree -- very true, but Mississippichem was saying it's immature to demand a non-mathematical ontology. I think that's a really good point. Ontology tries to answer questions about the true nature of things, like "what is spacetime?". That is an ontology question. Here are a couple different answers: Spacetime is a Lorentzian manifold populated with events having a form determined by energy and momentum content Spacetime is like a rubber sheet The first one is correct and ontology likes it because it truly explains the nature of spacetime. It conveys the meaning of the concept. Ontology doesn't like the second answer. People who don't have the requisite knowledge to understand spacetime may like the second answer and may be looking for other answers like it, because they can understand better what it means, but that doesn't make it good ontology any more than "an airplane is like a bird" is good ontology because some people don't understand concepts of lift and drag. Physicists practice ontology. To develop relativity Einstein had to ask "What is spacetime?", "Is it background independent?", "What is its metric signature?", "What relationship does it have with matter, and what equations must it obey?". And, he used philosophy, like mach's principle and the hole argument to help him answer those questions and develop relativity. To approach the ontology of spacetime and the ontology of relativity a person would have to know what those concepts are, what they do, and how they do them, which requires math. Because Owl avoids the math, he can't help but fail in the ontology and philosophy. It's like a stone mason who refuses to use any building material except Jello. It's bound to fail

Good point. I was just thinking about how Einstein's system and Newton's system made different predictions about light deflection. When observation agreed with Einstein and rather than Newton (1919), I'd rather science agree with him too even though the majority of physicists were slow and/or reluctant to accept the validity of the new theory. In other words—if honest, diligent, and fair observations falsify one theory and support another, I don't think it should matter if there is a consensus with rejecting the old theory and accepting the new or not. Science, to put it simply, should be indifferent to consensus. That's what I was thinking.

I agree. Schizophrenia is a good example. But, what has this to do with the cogito being inconsistent or wrong? All of these are true: I perceive (though the perception could be misled) a book, therefore I exist I perceive (though the perception could be misled) Natalie Portman, therefore I exist I perceive (though the perception could be misled) my own thoughts, therefore I exist I perceive (though the perception could be misled) music, therefore I exist So, I can't find the inconsistency. I can't figure how it matters that perceptions (or "sensations" as you say) are mentioned in all of them. The problem comes when person says, "I perceive (though the perception could be misled) Natalie Portman, therefore Natalie Portman exists." That would be non sequitur because if I perceive her, and the perception is misled, then the perception of her could be entirely mistaken. The conclusion relies on the validity of the perceptions. Perhaps I was really looking at a cat and I was misled into believing the perception involved Natalie Portman. In that case she may not exist at all. On the other hand — if I perceive something, and the perception is misled, I may be wrong about the nature of the thing perceived but I couldn't be wrong that "I perceived". "I exist" is not non sequitur — "I perceive" and "I exist" have the same subject. I don't get this idea that if the proof of existence involves the perception of one's own thoughts, it is inconsistent. Descartes' idea that perceptions may not be reliable doesn't imply that they are unperceived or that they don't exist, or that the thing perceiving them doesn't exist.

No, I see what you mean. It seems tied to the ontological argument and makes similar conclusions. I don't find that bit convincing (the second part of the first quote to be exact). But, I would just stress that it really doesn't matter as far as the 'cogito ergo sum' goes. His musings about a deity are superfluous when it comes to that. My memory serves the same purpose. I rely on my memory of Descartes' argument as if that is the thing being talked about. It would be better to have a rereading first, but like you said, "I don't quite care enough to trawl through it myself" If I am in the mind of God or in a holodeck simulation then my thoughts will exist as part of God's intellectual imagination or part of the holodeck computer. But, I think that doesn't matter in the least. Wherever my thoughts reside, they exist. After reading on the subject, I'm sure that's the point Descartes was trying to prove.

Because "my perceptions" references "me". "Book" doesn't reference "me". Why would you assume that his proof applies equally to both. His proof relies on the self-reference. Descartes, by the way, wasn't inept -- despite how any matchbook cover summary of his proof might make him appear. Sure, I may be a cat named "princess anastasia" being convinced that I'm human, but this doesn't imply that *I don't exist* I haven't seen any reasonable justification for why that might be. If a book says "John perceives" then John does exist as a character in a book. It would be a rather dull and unenlightened character, but what can we do? Perhaps we make the book more sophisticated. If you watched star trek the next generation you might know what I mean. Books were played out on the holodeck and it did eventually happen that a character in a book (Professor Moriarty as it happened) became self-conscious and questioned his own existence. Even though Moriarty existed in the form of a simulation on a computer he would nevertheless correctly conclude that he exists, simply because he is able to question his own existence. Descartes' isn't saying "I exist, and not in a simulation or some predetermined and prewritten form". He was just saying "I exist", by which he meant that he could logically doubt the existence of other things, but it would be illogical to doubt his own existence. -------------------------- I may well be the imaginings of an extremely adept being who is able to simulate, in his own mind, every thought I am capable of having. But, this doesn't matter. Descartes' proof doesn't involve the nature of the universe. We may exist in a universe accountable only to itself, or we may exist in a universe simulated in some Deity's head. When I say "I exist", it doesn't matter. I exist whatever the circumstances of my existence. Sorry, i wrote my paragraph above before reading this. I think you have a very distinct possibility there. Right. That is why I said "extremely adept being". If I have consciousness enough to contemplate my perceptions (rather complex ones at that) and question my own existence then any entity dreaming me up must be just as intelligent as me and even more capable. This is why Tres Juicy's example of "how do I know I'm not a character in a book" falls apart and why I moved on the example of a holodeck. A book just isn't capable of simulating consciousness. He was refuting the same points brought up here. Also, I would take his use of "God" and "Devil" to mean very powerful and capable beings. Those words represented a very recognizable allegory at the time is all. No, he really isn't saying that. He is midway through saying "maybe my perceptions are wrong". His example is that... just perhaps... some being is purposefully deceiving him. This is only an example to illustrate some way by which perceptions could be mistaken... and it is an analogy commonly used in his time just because a lot of people in that time were quite comfortable imagining a God or a Devil doing that sort of thing. He goes on to examine the necessary attributes of that being, but I'm sure he doesn't try to imply "...therefore the being exists". The other quote does seem to be an extension of the ontological argument. I'd never seen it or imagined that line of reasoning. It does, like you said, seem superfluous.

Can you explain that? It seems very confused. Descartes would agree with both these statements: I perceive books, therefore my perception of my own thoughts exist. I perceive my own thoughts, therefore my perceptions of my own thoughts exist. Descartes' point (that perceiving books doesn't imply that books exist) isn't inconsistent with the above two statements. They are inherently different because "I" and "book" are not self-referential, but "I" and "my perceptions" are. If my perception of a book is misguided then it may well mean that the book doesn't exist. If my perception of my own thoughts is misguided it doesn't follow that my perception of my own thoughts doesn't exist... obviously. Wow! Can you quote Descartes saying this? Sensory information exists otherwise one wouldn't be able to question their own senses. That is the first thing. Now, sensory information may either be misguided or not. No way to know -- that's Descartes' point. If it is misguided, does that imply that the misguided sensory information could possibly not exist? No, clearly not.

no, we don't. Perhaps everything related to Descartes was added to our current literary cannon by people or a powerful being or who knows what for whatever end. It isn't impossible. You can't prove that Descartes existed. and his existence is something he could prove to himself at the time he said it and that's the whole point. I think you've missed the point of the cogito. EDIT: by the way, what does "it is circular" mean? The cogito is tautological, and tautologies are circular in a sense, but what does that have to do with "proves nothing"

Could you summarize your approach so that one isn't forced to wade through all the finer points to determine where a potential error might lie? It's common practice to start with an abstract, then an introduction which is usually filled with statements like "section 2 will calculate "______" using "_____" and show why that implies "______" before getting into all the gory details. If your link had more of that type of format it would be much more approachable.

I'd disagree with the bolded part. Don't you think science should be indifferent to consensus?

Anthropologists take the idea seriously that things we ingest can affect the whole mentality of a culture. The most recent example I remember reading is how toxoplasmosis might be responsible for some cultural aspects of Brazil and other countries where it is prevalent. But, there is obviously no evidence that ancient people were less stupid than us. All of the evidence is against it, so I think you might look closer at how you got to that particular conclusion.

He doesn't say "I am not an illusion". He wouldn't be able to prove that. All he can prove is that he exists -- either in an illusion or however else. What do you think about the example Descartes gives with the devil tricking him? What could a devil trick you into believing? If it were powerful enough it could trick you into believing most any mistaken notion. But it could never trick you into thinking you exist when you do not, because that would be a self contradiction.

Inescapable deductive fact, and no truer words... Owl's disbelief might just be related to his displayed difficulty in understanding the deductive reasoning moving from the "if" to the "then".

And since heavier things don't fall faster, there is an upper limit on the amount of deflection a corpuscular theory of light can give.

H0 means "the Hubble constant today". Only one type of Friedmann universe has a Hubble constant that remains constant over time: It is [latex]\Omega_M = 0[/latex]. An empty universe. See Carroll 1992 for an example of that graph explained before the discovery of acceleration. By the way, the hubble constant is called a 'constant' because it is a proportionality constant between distance (at some point in time) and velocity (at the same point in time) -- not because it is constant over time. I understand how that could be confusing, but that's exactly why websites bother to say: The value of the Hubble parameter changes over time -wikipedia ...the Hubble "constant" is not really constant because it changes with time and therefore should probably more properly be called the "Hubble parameter"... -Hubble Law It's a simple misunderstanding . The big bang has never been about constant expansion. You won't find any sources saying that. It is not, as they say, a freely coasting model.

Not only does that link fail to support what you are saying, it repeats precisely what I said, Before the discovery of acceleration, everyone assumed that the deceleration parameter was positive (that's why it's called deceleration and not acceleration parameter) I can quote wikipedia if that would help, http://en.wikipedia.org/wiki/Hubble%27s_law#The_.E2.80.98ultimate_fate.E2.80.99_and_age_of_the_universe It is impossible to be competent in cosmology while not knowing that the rate of expansion changes even without lambda. Anyone who has used the friedmann equation would have to know that. People used to think the universe was decelerating, now they think it's accelerating. Sorry you believed otherwise.

If you would say this is true: A person can know that an object is at a time in the past (t) [at that space-time coordinate] if it is at a distance of c times t where c is the speed of light? then what about this: A person can know that an object is at a time in the past (t) [at that space-time coordinate] if it is at a distance of s times t where s is the speed of sound? The person could be in a submarine for example

So a person can know that an object is at a time in the past (t) [at that space-time coordinate] if it is at a distance of c times t where c is the speed of light?