Michael J.

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  1. Does ethics allow for the existence of Ellsworth Toohey?

    Mr. Laughlin, Sorry to jump in here; from what I've read of this forum, you are usually very clear but I do not understand the above paragraph at all. Are you saying there is some contradiction in the presentation of the character of Toohey in Atlas Shrugged? If not, how could the above consideration preclude the existence of such a character in "real life"? Or are you simply saying that a character like Toohey is _unlikely_ to arise in real life?
  2. Dimensions

    It should be noted that the word dimension has a usage in mathematics that needn't imply any direct physical interpretation. To be very informal the dimension of an abstract mathematical space is the number of "degrees of freedom" it has. For example the Hilbert space specifying the set of possible states of a quantum system is infinite dimensional but these dimensions don't have the same physical interpretation that the three dimensions of our everyday space do. I'm not an expert on Objectivism but from what others have said I believe this usage of the word dimension is what most Objectivists would call a "concept of method" or an "epistemological device". As far as physical dimensions go, according to the theory of special relativity time is indeed a physical dimension along with the three spatial dimensions. One way of thinking about this is as follows. One of the key facts about special relativity is that the theory is invariant under the Lorentz group - this is the transformation corresponding to a change in speed. If T is a time coordinate and X is a spatial coordinate then a Lorentz boost in the direction of the X axis takes the form: T' = (cosh r)T + (sinh r)X X' = (sinh r)T + (cosh r)X where r is some parameter. Physically this is the transformation between two reference frames that have relative motion along the X-axis. (I've suppressed the other two spatial dimensions Y,Z for simplicity.) The key thing to take away from these transformations is that it mixes up the spatial and temporal coordinate. In order to know the new coordinate T' you have to know both T and also X. And similarly to know the new coordinate X' you have to know not only X but also T. Or to put it another way: the Lorentz group is only a symmetry on spacetime (space and time considered together) not individually on space (X) or time (T). Explaining it in different terms: how would you answer someone who claimed that left/right and back/forth were dimensions but up/down wasn't a dimension and thus the world is 2-dimensional? Well one answer would be that to exclude up/down is arbitrary because after all what one considers up/down is dependent on your orientation. If you choose an up/down axis then rotate your system then the notion of up/down changes. There is no rotation invariant way of choosing up/down so to exclude one direction from being a dimension is arbitrary, given that the laws of physics are rotation invariant. Well exactly the same argument holds for time in the context of special relativity. If you tried to consider only X,Y,Z as dimensions and exclude time T then doing so would require an arbitrary choice for T, which would change after you Lorentz boosted the system. (One should contrast this with Galilean relativity, a theory that preceeded special relativity. In this theory transforming between frames in relative motion is governed by Galilean transformations not Lorentz transformations and it turns out it _is_ possible to choose a time axis that is Galilean invariant. So it made sense to separate time from space in this context.) Hence T is properly considered a dimension along with X,Y,Z in the context of SR, essentially because the laws of SR are Lorentz invariant. The "extra dimensions" in the context say of String Theory are highly speculative. I'm not personally completely dismissive of such theories, because of a number of technical reasons, but one can't go wrong by remaining very skeptical of such possibilities at the present state of knowledge.
  3. Regarding the mathematical aspect of this, overall I don't think it's a good idea to overload the notation. I think that, in general, the exact status of an equality (i.e. whether it's an assertion, a condition we're demanding, or a mere assignation, etc.) should be determined from the context of the statement in the mathematical argument in which it appears, and it's not reasonable to always expect to convey this information by using a special equality symbol (especially in more complicated arguments). To me the really important thing is that equalities appear interspersed in a coherent, well reasoned mathematical argument (which uses both words and mathematical symbols where necessary) instead of presenting a string of equations as if that constitutes a mathematical argument (as is sometimes done).
  4. Thank you for the kind words, and for your point of view in this thread.
  5. Thank you for your reply. While the existence of extra dimensions *within String Theory* is not really arbitrary (it emerges by requiring Weyl invariance at the quantum level) it is undoubtedly a problem with the theory, since the methods of extracting a 4-d theory from the extra-dimensional theory are highly non-unique, so in that sense I agree. This is, of course, what has led to the landscape problem. I still have some hopes though that this problem is resolvable.
  6. While I don't have much knowledge of the observational status of the Big Bang theory, I do believe I have enough theoretical knowledge of the Big Bang theory and String Theory to disagree with that. Everything I know points to the fact that these theories are well motivated by sound theoretical principles, and a good attempt to integrate established physical ideas. The Big Bang theory is based on a natural class of solutions of the theory of General Relativity, the best theory of gravity we have (and if I remember correctly from a previous thread, you have expressed strong support for this yourself). String Theory is an attempt to integrate the hugely successful General Relativity theory with the (arguably even more) successful theory of Quantum Mechanics, which is a notoriously difficult task since standard quantum field theory techniques don't work. The way Einstein's equations pop out of the calculation for the one-loop conformal invariance of the string sigma model is strikingly beautiful and a strong pointer that the study of String Theory is, at the very least, relevant to the subject of quantum gravity. Thus, in my opinion, the underlying premises of these theories are very far from arbitrary. I also don't understand the part about contradicting philosophical axioms of identity and causality. When we were discussing Dr. Woit earlier, I should have mentioned to anyone interested that his personal views on the best ideas for going beyond the standard model can be found in his expositionary paper "Quantum Field Theory and Representation Theory: A Sketch": http://arxiv.org/abs/hep-th/0206135 A somewhat technical paper, but quite lucid. There is some non-technical discussion at the end.
  7. I respect Peter Woit's arguments, but I mostly disagree with him (except for his opinions on the landscape, which seem essentially correct to me, and some of his broader sociological points certainly have merit). I will note however that Dr. Woit has never argued (and I'm not saying you've suggested this either) that String Theory is of no value and shouldn't be studied; his criticism is that, in his judgement, it has failed as an attempt to unify gravity and the standard model, and that the way it is dominanting theoretical high energy physics research (apart from phenomenology) is problematic. I have the UK edition of his book, which was published earlier this year. Very nice book, disagreements aside. I believe the US version is actually already available, as announced on his well known blog: http://www.math.columbia.edu/~woit/wordpress/?p=449
  8. Artificial Intelligence

    It is this last sentence that I still don't get, but I'll leave it for now. Thanks for the explanation. Michael
  9. Artificial Intelligence

    Thanks, but that's precisely the link I'm not seeing at the moment. The consciousness of a particular brain clearly has causal efficacy over certain matter (though not over all matter). Why would that preclude the consciousness itself being a physical/chemical process involving some of the matter of the brain?
  10. Artificial Intelligence

    A basic question. According to Dr. Leonard Peikoff in p.33 of Objectivism: The Philosophy of Ayn Rand, materialism is described as follows: I suppose this is the meaning of the word "materialism" that most Objectivists use. My question: suppose someone thinks that consciousness exists, but is entirely reducible to matter - more precisely, the process of cognition exists but is essentially a physical/chemical process involving the matter of the brain. Would such a person be a materialist (under the above meaning), and if so why? Thanks, Michael
  11. Parents & Ideas

    I _think_ that by this she meant that this is more than a rational person can _necessarily_ absorb, by virtue of the fact he is rational. In other words she wasn't saying that if a parent does manage to absorb this then he is irrational (a claim that would be pretty hard to defend) but that the sole fact that a parent is rational isn't enough, in itself, to entail that he can absorb this. This seems reasonable. That being said, I too find this quote, as a whole, pretty hard to understand. I have had many good intellectual discussions with my parents and have persuaded them on many issues over the years (and vice versa of course) and I don't see any reason not to try and convince them about my views even if they strongly disagree. A more general comment: I don't think teaching is best viewed as a unilateral experience. The best teachers I have had in general don't take the point of view that their knowledge is infinite in comparison with their students and that they can't possibly learn anything from their students that they don't already know. Instead they are receptive to insights their students offer, and this allows a stimulating two-way exchange of ideas that, in the long run, allows the student to learn much more from the teacher. I'm not saying that the relationship between teacher and student is symmetrical of course, and in the case of a parent and a young child it's very, very much skewed; however I would guess that the relationship usually gets closer and closer to being symmetrical as the child grows up, and when the child is grown up the parent may look on him/her as an intellectual equal. (Though, as I think AR implied, if a parent doesn't ever reach this view, this doesn't necessarily reflect on his/her rationality.)
  12. Favorite Einstein Paper

    No slight was perceived, and thanks for the additional information about Minkowskian geometry.
  13. Favorite Einstein Paper

    The issue of measuring the speed of light is quite a subtle one - one reason is that a background theory is required to _interpret_ any experimental results obtained as being such a measurement. (This issue is quite familiar - usually when one measures physical constants one is assuming other physical facts, e.g. pertaining to how the apparatus works, in order to interpret the result as indeed measuring the relevant constant.) With no fixed theory in the background it is quite impossible to measure the one way speed of light, because there are ether theories that give precisely the same experimental results as SR while assuming different one way speeds of light to SR. What is true however is that if you _assume_ SR (i.e. you take SR as your background theory, which is reasonable given its exceptional agreement with experiment) then it is possible to measure the one way speed of light in any particular frame, and you find it does indeed equal c in any frame. This sounds vacuous at first - by assuming SR isn't one already assuming the one-way speed of light is c? Not quite. In modern formulations SR is usually taken only to postulate that there exists a frame independent finite speed c and is agnostic about whether light (or anything else) actually travels at that speed. To be precise, SR predicts that massless particles move at the invariant speed c and massive particles move at speeds lower than c, but that leaves open the question of whether photons are massive or massless. It is then an experimental question whether light itself travels at c, and it is in this sense that my previous paragraph was intended - yes the experiments show that the one-way speed of light is indeed c, given SR as a background theory. This agrees with Maxwell's theory of electromagnetism, which predicts that electromagnetic radiation moves at the invariant speed c.
  14. question about fields

    That's basically the reason I don't find ether theories very interesting - they have the feel of being a step in the wrong direction. It's not too surprising that one can start with some physical assumption like the ether and then adjust the model to agree precisely with SR, but that kind of approach is unlikely to lead to physical insight in the long run.
  15. question about fields

    Thanks for the reply. OK agreed - it was a modification. I think that regarding E,B as real probably does suffer from the problem you raise regarding Lorentz transformations. My current picture of classical electromagnetism is as follows: the tensor field F_uv and the charged particles are both real and fundamental, and these fundamental existents can each have a causal effect on each other (as described by Maxwell and the Lorentz force law). (Of course there are other interesting issues/problems - like the self-energy problem for charged particles. However I didn't want to address these as it seems non-essential to the issue of whether the fields can be regarded as real, in principle at least.) Thanks.