[Objectivist Values In Popular Movies?]

I too saw this in Minority Report.  Also note the the pro-gun stance in the movie.

I'll third the recommendation for Minority report. There's definitely a free will stance in the movie, as well as a "knowledge is power" theme.

But I don't recall anything that pointed to a pro-gun stance. What makes you think that?

I can't comment on Incredibles or Hombre, having seen neither. But for anyone looking for a good children's movie, I recently caught most of "Matilda" on television and thought I'd mention it here.

The title character is a little girl gifted with genius-level intelligence, who's life is an unfortunate hell thanks to her unloving, slime-ball parents and her school's militant, child-hating psycopath of a principal (who runs the place more like a prison than an educational facility). Her only real adult ally is one of her teachers. Eventually she discovers that she has powerful telekinetic abilities, which she masters and uses to make things right.

The movie was surprisingly good. There was no moral equivocation that I could see; her parents were clearly shown as unscrupulous car-part thieves and rotten parents (ignoring Matilda except when punishing or demeaning her), and the principal was so over-the-top it's surreal. Matilda herself, on the other hand, comes across as confident in her own judgement and being quite courageous in following her sense of right and wrong, even before she discovers her powers. And once she does discover them, she doesn't hesitate to use them (quite creatively) to make things better for herself and the people she cares about; she doesn't waste any time hand-wringing or being afraid of her own abiities.

The bad guys are ultimately undone by their own vices; the principal is superstitious, and Matilda eventually breaks her by playing on her irrationality. Her parents are forced to flee the country to avoid getting caught by the law. And Matilda is able to arrange it so that she can stay with her teacher. The movie ultimately comes across as very pro-intelligence, pro-happiness and pro-justice.

The only complaint I can think to make is that the law is not favorably portayed; the two agents after Matilda's father turn out to be just as terrible as the man they're trying to bust. But I don't see that as a major theme; more like a continuation of the theme that Matilda is stuck with no good adults around (except her teacher).

Other than that, stick this one in the same file as Harry Potter and rent it for your kids.

[Creating Fonts/smilies]

So the same (non-animated) .GIF files will work for both the fonts and the forums? That's what I wanted to know.

Thanks.

[A Thanksgiving Story]

BEAUTIFUL!!!

Which teacher?

P.S. At this point, John should just slowly let an evil grin cross his face and tell the truth: "nothing, I was just planning on being hungry later."

[Creating Fonts/smilies]

Here's one for you gurus out there.

I eventually plan to set up a webpage with a forum, and I want to know how to create graphic symbols that can be inserted into posts (like smilies). But here's the catch: I also want to be able to use those same symbols as a font in Microsoft Word (thus killing two birds with one stone).

What software tools are out there that will let me create symbols that can be used both ways? The symbols won't have to be animated, but I'd prefer a tool that costs nothing.

[Mathematics: Reality And Infinity]

I don't know what else you have in mind for how to make your project work, but based on this opening description, it sounds dubious. Human thought and consciousness cannot be reduced to an algorithm and reproduced in software.

Not all aspects of it, no. I realize that I can't recreate volition that way. But then again, I'm not interested in things like volition.

That principle isn't new, but a recent good article on it from an Objectivist perspective is in the April 2004 issue of Rob Tracinski's monthly journal, "The Intellectual Activist": "Mindless Intelligence: Machine Thinking and Contemporary Philosophers' Rejection of the Mind". Have you seen this?

I'm not subscribed. I know that they have a free trial, but since it only lasts 30 days I want to wait until the semester is over and use the trial period over the break.

People may "get away" with not having clear definitions of their concepts, but only at their peril. To think properly (and therefore also to understand proper thinking) requires requires that concepts be defined explicitly by the subject...

...It is true that much of the details of what we learned are forgotten at the conscious level and that much of the mental processing that goes into writing and speaking is at the subconscious level, but even at its best, the subconscious is not infallible; the results it gives you have to be validated consciously.

We don't consciously validate - or even define - everything our subconscious gives us to infinite precision. For example, you walk into a room and see a patch of color that you identify as a man. Do you stop and consciously start taking measurements and comparing them to your concept of "man?" Could you even give a mathematical description of what a man looks like? Of course not. And even if you could, stopping to consciously confirm that every bit of sensory data that comes your way is exactly what you think it is would take so much time that you would starve to death if you tried to function that way.

Past a certain point, we don't stop to analyze in that kind of detail unless we have reason to.

Furthermore, the process used by the subconscious is not the same as the conscious process of validation. A software implementation of the subconscious, even if it could be done, would not account for human intelligence and thinking.

Why would it have to? I don't need my calculator to account for human mathematical thinking, I just need it to come up with useful answers faster than I can myself.

What do you mean by "irreducible"?

There are a finite number of concepts in my mind at any one time. Some are primary, or "atomic." They can't be broken down further. Concepts of sensation (like "blue") fall into this category, for example. Other concepts result from combining these atomic concepts according to certain rules.

I'm trying to identify which concepts are atomic and the rules for their combination, and apply that. Think of it as "linguistic housecleaning," if you will.

First level concepts based on perception? All the ones you listed are higher level abstractions.

We'll see, eventually. I can only tackle one level at a time.

Do you expect a program to compute all higher level abstractions and structure them hierarchically in a (mathematical) lattice? If so, under what "motivation" for the formation of specific concepts?

Under whatever motivation I decide to program into it. You don't expect a calculator to be self-motivated, you expect it to do what you tell it to do. Unit-reduction, as described by Rand in ITOE, would be a good use.

To know how the subconscious works, which no one now does, will take a lot more than defining concepts "programmed" into it.

Doubtless. But while that may not be the only step, it is a step. One thing at a time.

How is this different than Logicism (one of the traditional and not very successful modern attempts at the foundations of mathematics)? You haven't described how you "derive" mathematical concepts from logic, but based on the traditional history alone it sounds dubious.

Of course not. I would have to write a paper, not a short post. And I only accomplished this in the last week. I'm still proving properties. I'm keeping notes in a text file (call it the bastard love child of an outline and a rough draft), but it's going to be a while before I can turn that into a full essay.

And every new discovery or invention defies "traditional history." So that doesn't worry me.

Partially. Presuming that your project is feasible at all, why do you need to incorporate definitions of advanced mathematical technical concepts that the vast majority of people do not know and get along without very well in their thinking?

...More relevant to understanding the nature of concepts is the whole topic of "open-endedness" already mentioned in the post above and emphasized in Ayn Rand's IOE. What else do you need the "mathematically infinite" for?

First off, I'm not so sure that it's going to prove to be all that "advanced." I realize that this claim won't mean anything to you since I haven't posted/published anything yet, but the definitions of the basic mathematical concepts I cited (one, plus, etc.) were far simpler than I expected them to be and I have reason to suspect that "infinity" will follow the same pattern. Simply put, the complexity lies in defining the unit, not the quantity.

Second, the plan is to use the concepts and processes of my own mind as the model for AI. To do that, I first have to understand the model. Hence the linguistic housecleaning. If I can't define the concept precisely enough in my own mind, I can't replicate it in software.

[Linguistics: Minimal Rules For Language]

Hmm... This topic hasn't really helped me. Let me try asking something more specific and see if that shakes anything loose.

I mentioned in my opening post the need for both a subject and a verb (even if one is only implied) to express a complete thought in English. To put it in broader, philosophical terms, my understanding is that any complete thought must both refer to an existant (even if it's only a mental existant with no physical counterpart, like "gremlin") and say something about the nature of that existant (like "gremlins are green" or "I am thinking").

In other words, the pattern here is "some existant A," along with "some attribute B which is possessed by A." My impression is that any meaningful statement in any language must either already be in this form ( A is B ) or must be grammatically or implicitly equivalent to that form.

So, here's my question: can anyone think of any exceptions in any language? Or am I correct in believing this to be an inescapable law of rational thought?

[Mathematics: Reality And Infinity]

You raise this question in the context of Objectivism, but it is not clear what you are trying to find out.  To ask for a definition and explanation of the technical concept of infinity within mathematics is like asking about any other technical concept in a science.  It can only be addressed directly knowing the context and purpose of the question and the extent of knowledge that can be relied on in a technical explanation.

Perhaps my opening comment was misleading. I should clarify.

I am not using objectivism as a context. But I do realize that my audience consists largely of objectivists and I anticipated that the first response of many of them would probably be to mention that infinity is valid as an epistemological concept only. I simply wanted to forstall that and avoid wasting everybody's time (including my own).

As for my purpose in asking... That's a little complicated. My long-term goal is the creation of true artificial intelligence; computer programs that can take sense data and organize and theorize about it in the same way that a human can.

The premise I am working on is that humans get away with not consciously knowing the precise meaning of every word they use or the exact steps involved in coming to a conclusion because we have a piece of "black box" technology that does that for us: the subconscious. The subconscious handles the details and then presents my conscious mind with the results, but not necessarily with the steps leading to those results.

Unfortunately, if I'm going to program a computer to think it's not enough that I have such a "black box" myself. I need to know exactly how it works so that I can design a software equivalent. Thus, I need to know exactly what the irreducible concepts are that my mind uses, exactly what each one means and exactly what rules govern their combination into more complex concepts. Kind of like Aristotle's categories, but taken to the next (and final) level.

To this end, I'm having to go even deeper than Rand did in identifying basic concepts. To give you an idea of the sort of thing I'm doing, I've been going through lists of words we use all the time but never really think about the meaning of - "I," "the," "and," "one," etc. - and trying to explicitly identify what I mean by each one and if I can completely define any of them in terms of others on the list (establishing that they're reducible concepts after all).

Right now I'm working on basic logic, and in addition to a couple of other rather interesting discoveries I finally managed to bridge the gap between logic and basic mathematics just recently. I've derived the concepts "one," "plus," "equality,"

"inequality," "greater than" and "lesser than" from basic logical operators. I'm still a long way from differential equations - I haven't even defined "zero" or "minus" yet - but I've definitely got a solid foundation laid down.

However, I'm going to need to know how to define "infinity" for various areas of my work. Without that, I'll be stuck before long. That's why I'm asking about it; I don't expect that any one definition out there will be what I want, but I'm hoping that by considering various definitions it might help me to abstract out the element that I'm looking for.

Is it clearer now?

[An Evening With Bryan Larsen. Were You There?]

Nice artwork. But I am visually confused: What is the exact degree of space between that locomotive and the steel structure (bridge) -- two inches or what!? Considering the Z-axis, isn't that train at risk of scratching its polish?

I wouldn't bet on that. I passed through Chicago this past summer, and to get from the airport to the train station I rode the "Blue Line," one of a series of train lines that ran through the city providing mass transportation. It went through several tunnels, and looking out the window it often seemed that the walls were barely a handspan (if even that) from the side of the train.

It was oddly exhilirating. On the one hand, it felt dangerous because contact with the wall could have been very bad (we were going fast). Yet at the same time there was also the realization that the train was staying perfectly on course and under control. I think that must have been a taste of how Dagny and Rearden felt during the first run of the John Galt line.

I'd lay money on two inches being enough, as long as it were done right.

[Linguistics: Minimal Rules For Language]

Entities and relations.

Entities, yes. They correspond to nouns. Also, actions (as they correspond to verbs).

But I'm not so sure on relations. If a complete thought can be formed with only concepts of entity and action (noun and verb), are concepts of relation impossible to do without? Granted, you'd have an incredibly crude and limited language, but you could still form a few valid thoughts ("I am hungry.").

How do you figure concepts of relation to be inescapable in forming a thought?

[Linguistics: Minimal Rules For Language]

A fundamental rule for the English language is that you can't have a complete thought without both a noun and a verb (even if one or the other is only implicit). My understanding is that this is a universal principle, that it's not possible to construct a complete thought in any language without these concepts.

Since that principle has played a key role in my own philosophic contemplations, I thought it would be a good idea to get confirmation and to explore the basics of language further. So for any objectivist linguists out there, I want to ask: what are the minimum rules and concepts that no language can be without and still deal with reality?

For the record, the only language I speak is English.

[Modern And Classical Physics Questions]

Maybe I have not made myself clear, so let me try another way. In relativity we are not really concerned much with light as photons, but rather with the geometrical optics approximation to light.

That helps a little, thanks.

Your view of this "oscillation" of photons (whatever that means and wherever you are getting that from) requires an integration of relativity with whatever theory you have in mind. 

Thanks, and I enjoy discussions like this.

I suppose I should spell out what I'm thinking. The image I have in my mind is a particle which moves back and forth (oscillates) along an axis perpindicular to its forward motion (tracing out a wave-like path).

I'm sure you can poke some holes in that.

[Mathematics: Reality And Infinity]

Mr. Speicher has temporarily overloaded my mental capacity in our conversation on physics, meaning: I've got some learning and thinking to do before I really get back into that conversation. But there are other issues that have been concerning me. So I'd like to turn to some of them now.

First off, the concept of infinity. I know that objectivism considers infinity to be a mathematical concept only (and not existing in physical reality), but what is the mathematical definition of infinity (or what are the definitions, if more than one)?

Second - and this question is directed primarily at you, Mr. Speicher, though others are welcome to chime in - what breaches exist between mathematics and physical reality? You said that you don't consider set theory to be the correct basis for mathematics... I'd like some more detail. Is it just because Russell's Paradox and other contradictions can be derived from it (not that that isn't enough), or is there something more?

[The O'ist view on "change" as contradictory?]

Quick question - are there any good sources out there which present the objectivist argument against change being an inherent contradiction (ie - the idea that after change we have a thing that is the same as before the change, but is not the same as before the change.  In other words, a thing has an identity of opposites and is thus contradictory).

OPAR, page 119. "Aristotle's law of contradiction states the above as a formal principle of thought: nothing can be A and non-A at the same time and in the same respect" (emphasis mine).

Or, as I describe it, a contradiction is "a claim that something is both A and non-A within a given context."

In either case, the answer to your problem is built right into the definition. The answer to the question "A or non-A" is only good within a certain context (whether specified or implied). You're not allowed to switch contexts in the middle of analysing a claim anymore than you're allowed to change the meaning of "A" partway through. This is simply a form of context-dropping (the context of the claim being checked for contradictions).

Does that help?

[O'ism: There is a finite number of axioms?]

Well, as to the difference:

Axioms are propositions, axiomatic concepts are... concepts.

And no - there is no reason to believe that Ayn Rand's list is exhaustive. In fact, I believe I know at least one other.

What would that be?

[The Atlasphere]

I don't see what real service your site offers.  Sure, it's easy to register, but why would anyone pay $25 just to see someone's profile? This forum offers that for free, and we can actually get to know each other by studying philosophy together rather than simply being "admirers."  Don't get me wrong, I think a "community-building web site" is a great idea -- that's why I started this one.  I just don't think yours offers nearly enough for the cost of membership.

You know, that might be a good idea for a new sub-forum or two... You could have one for "personal ads" (where people actually try to hook up) and a second for discussing dating technique, etc.

[Contradictions Accepted As Valid?]

Yes, but the fuller understanding will come just in time for you to start a new project! 

...Now turn the knife counter-clockwise and apply salt liberally.

[Modern And Classical Physics Questions]

There is a much longer history of applying quantum mechanics to chemistry than there is with relativity and chemistry. It is only really in the past few decades, since the 1970's, that the role of relativity in chemistry became appreciated, so I would not worry too much at this early stage in integrating the theories as much as first learning them independently.

Unless I'm getting more of those "little white lies" you mentioned, I'm thinking that the two are incompatible. The formula I'm getting from my chemistry textbook is (wavelength * frequency = c), and since wavelength is a straight-line measurement that means that oscillation is not taken into account. And it sounds like the same can be said of relativity's "light rays."

So unless the claim that observers will measure the same velocity for c refers only to a photon's motion along a single axis (which is not what I've been hearing), these two theories don't add up. If I measure a photon's motion along the x axis to be 1 lightsecond per second, but I also measure oscilation along a different axis, then I'm measuring the total path travelled per second to be greater than a lightsecond (and thus, a velocity greater than c).

Yes, the newer version has sharpened the terminology but I am sure the earlier work will suit you just fine. I once had an errata sheet for that edition; I'll look for it and pass it on if I locate it.

Have I mentioned how much I appreciate your help and patience with all of this? Because I really do.

I have not used it myself by Robert Stoll's Set Theory and Logic has been mentioned several times as a real gentle introduction to set theory.

I checked out both books yesterday. I've been through the first two parts of the first chapter of Stoll's book, and so far it seems good. There were a couple of parts where I had to go over the same paragraph or two several times to "get it," but I can already tell that it could have been much worse.

[Contradictions Accepted As Valid?]

Then you are probably not too far away from the Livingston facility.

Within driving distance, I believe, although I've never been there (yet).

Let's see ... McHugh or Whelan? ... I'm guessing ... Whelan. 

BZZZZT! Sorry, no. I'm Dr. McHugh's wage-slave. But tell him what the consolation prize is, Bob!

Out of curiosity, what made you guess that it was Dr. Whelan? Do you know them?

LIGO is a great project to be associated with. A real theoretical and technical marvel, yet it is a learning process.  The test bed for LIGO II that I saw was even more incredible. I think that the really significant results will be forthcoming when LIGO II comes on. Enjoy the work you are doing there.

I like it so far, although for some reason the computer I work on seems to have it in for me (I #$%ing HATE LINUX!). I would probably be able to appreciate what a "great project to be associated with" it is if I understood more of it, but I suppose that will come with time.

[Modern And Classical Physics Questions]

In special relativity we generally talk of rays of light, or a light beam. Relativity, per se, does not address the issue of what that light is composed of, nor does it ask what is the fundamental nature and structure of light.  So when you start to speak of the wave nature of light, or the particle nature of light, or whatever, you are then in the province of particle physics and quantum field theory, and then the answers are vey theory-dependent.

Hmm. I was trying to integrate some things from my modern physics textbook (the invarience of c and the claim that all of a photon's energy comes from momentum) with some things from my chemistry textbook (color being based on a photon's wavelength), but I'm starting to wonder which theories I'm supposed to integrate and which I'm supposed to treat as mutually exclusive.

As I understood you previously, I thought you were taking an introductory survey course in modern physics. If that is the case, these sort of courses just touch upon a variety of subjects and cannot give a grounding in any given area. Courses given in relativity, both the special and the general theories, have at least a half or full year of study devoted to each as an introduction, with follow-on courses to explore these areas in more depth.

Hmm... Off the top of my head I still need to take Thermodynamics, Electromag Theory, Classical Mechanics, Quantum Mechanics and Intro to Electronics.

On another note... Some questions about book recommendations.

1) In another thread you recommended a book called Spacetime Physics, and it turns out that I can get my hands on a copy from the library from one of my universities' libraries. The problem: they only have the 60's version, which you say doesn't define the concepts involved quite as precisely as the 90's version.

Is this a problem? Are there any errors I should be aware of before using the 60's version, or should I order and wait for the 90's version? Or can I just use the 60's version as is without worrying about it?

2) Elsewhere you've mentioned having issues with set theory, which I hear is currently used as the basis of all mathematics. Set theory is something I've been wanting to look into for a while. Can you recommend any book(s)? Something with a gentle learning curve is prefered, though not strictly necessary.

What are your problems with it?

3) This one is for anyone who cares to answer... I see that Peikoff has put out a taped lecture on his DIM Hypothesis and is working on the book. Does anyone know about when the book will be out? If it will be a while I may want to see if I can get one of the university libraries here to pick up the tape series, but I'm not sure how eagar they'll be to take requests that cost hundreds of dollars a pop...

[Contradictions Accepted As Valid?]

The ironic thing is that the project is older than you, but was stillborn until last April.

Heh. Better late than never, I suppose. Thanks.

I was referring, of course, to detection of gravitational waves. But, in what way is that your job? Do you work on the LIGO project?

Indirectly. Two of the physics professors here at Loyola are involved with LIGO, and I'm a student research assistant for one of them. I don't yet have the physics expertise to even understand the science involved, but I am quite good at programming. Hence my job is basically to take some of the raw numbers that some of LIGO's instruments spit out, sort them, crunch them and turn them into useful graphs.

I think that technically I just work for my professor, not for LIGO itself (even though I'm payed out of his LIGO grant money). I'm not 100% sure on that, though. I'd have to ask.

The really sweet part of the deal is that the time I spend studying science and mathematics related to the job counts as work hours. Now if I can just get a similar deal for computer science and engineering course to go along with that, I'll be in great shape.

[Contradictions Accepted As Valid?]

Almost no one in the field of gravitational physics expects Gravity Probe B to provide results that are not consistent with general relativity. Researchers in the field would love differing results (since that would indicate new physics), but few expect that.

What is this project? I haven't heard of it.

General relativity has withstood predictive verifications of light deflection,

Here's a question.

The formula for gravitational pull between two objects says it's the product of their masses and the gravitational constant divided by the square of the distance between them. But in the case of a photon, one of the masses (and therefor the final value) is zero. So according to my understanding of classical physics, photons should completely ignore gravity.

So why do planets, black holes, etc. have an effect?

As far as LIGO is concerned, I am quite familiar with the system. No one expects any significant results out of LIGO,

Gee, thanks. That's my job you're talking about, there.

[Contradictions Accepted As Valid?]

deleting and reposting... Something's very wrong with the way this thing's formatting, and it won't seem to fix.

[Modern And Classical Physics Questions]

Once there is relative motion between A and B their clocks are no longer synchronous.

Okay, I missed that point. Thanks.

But light speed is an invariant, not dependent on the motion of the source, nor dependent on the motion of the observer.

Question - does that include the oscillations due to wave-like motion? In other words, if a photon's overall motion is along the x axis but it's oscillating up and down in the direction of the y axis, is it only the motion in the x direction that equals c, or is it (x^2 + y^2)^1/2 that equals c?

There are no contradictions. Relativity is a completely consistent theory and if you think you have found a contradiction then you are either mis-using or misunderstanding relativity.

Probably a little of both, though neither intentionally.

Well, I hope you enjoy your studies. These survey courses usually cover a lot a ground, but they do so at the expense of any depth.  Do you intend to take a course in at least special relativity?

You mean this *isn't* such a course?

If I stay on this path, there's Quantum Mechanics in my future. Does that count?

[Modern And Classical Physics Questions]

No. That is a quite common misconception, even among some physicists. Special relativity can deal with accelerating and rotating frames just fine. They are handled differently than inertial frames, and at times can become somewhat complex, but nevertheless the framework of SR is sufficient. Many advanced texts on relativity have a section on this.

So what exactly is it that GR does that SR can't?

It is not that the conservation law itself breaks down, but rather that the concept of total energy on a global scale is ill-defined. The local energy density of matter is well-defined -- energy is conserved locally -- but it cannot lead to an unambiguous global conservation law.

So fields and energy conservation are both ill-defined... You're making it sound as though not just me but physics as a whole is in need of a linguistic overhaul. I'm not sure whether to be relieved or even more worried.

That is a bit of a strange way of putting it. ...  That we cannot Lorentz transform into the frame of a photon simply reflects the experimental and theoretical facts.

Okay, forget about frame transformations for a moment and let me try this another way. I'm going to describe a thought experiment, and maybe you can explain what happens and why.

Take two observers (A and B ), both using the same coordinate system (no transformations). A is standing at the point of origin (0, 0) and B is standing 10 meters away along the negative direction of the x axis (-10, 0). The experiment begins when (t = 0 seconds), with synchronicity ensured by means of a flashbulb halfway between them being set off (they each start when the light reaches them).

At t = 0, A generates a flash of light (which we'll designate as L) from his position in the positive direction of the x axis. A remains still. B begins moving backwards at a rate of 1 m/s.

Now, I have two conceptual problems here. First, according to Einstein L must be moving at velocity c with respect to both A and B, even though B is moving away from L in addition to L's own speed. Second, if A and B both try to compute L's position based on the amount of time that has elapsed using the same velocity of c, they should get differant positions for L (indicating that L is in two differant places at once). Both of these strike me as contradictions.

What gives?

He is referring to the constancy of the speed of light, which was demonstrated in the Michelson-Morley experiment in 1887. If light traveled at a speed with respect to something else, then one would expect results in the MM experiment that the speed with respect to the Earth would have been c - v in one direction, and c + v in the other. But the result was c.

Hang on. I'm somewhat familiar with that experiment, and my understanding was that the +/- v was supposed to come from the relative motion of Earth and the theoretical ether. If the measuring devices were not moving relative to the light source and mirrors, then once you discard the ether idea it makes perfect sense - even from a Galilean perspective - that you would measure the same speed for light in each direction. I see how that experiment discredits the ether theory, but not how it supports relativity.

Is engineering your field of study, or is it physics? Or, something else? It is nice to see a young student interested in thinking about these issues.

I'm older than you think, I just got a late start (for various unpleasant reasons I won't go into). I'm actually 27. I've been studying physics and computer science, and am just beginning to get into engineering-related courses.

[Modern And Classical Physics Questions]

Then of what are these entities, say, the gravitational field, composed?

Heh. This is where I'm supposed to say "energy," right? Maybe that's where my problem is coming from. Too many uses for the same word.

That said, though, I don't see the point of the question. I don't need to say that the Earth is composed of "matter" to classify it as an entity, I just need to know that it is something that acts and is acted upon, as opposed to being a process of action (or a relation). The same goes for the gravitational field the Earth generates. We can give it a name if you'd like, but where are you going with this?

That in itself is not necessarily bad. Definitions range from "the ability to do work," to "the generator of time-translation symmetry." In some aspects of quantum mechanics your view of energy makes sense as tracking the rate of change of the wavefunction. In special relativity when you project the time component of the 4-momentum onto a set of inertial coordinates, then you have energy. In general relativity the stress-energy-momentum tensor can specify the energy properties of matter, and local conservation of energy can be well-defined. But there is not, in general, anyway in GR to have global energy conservation. And in quantum chromodynamics, as well as in general relativity, your concern about potential energy is satisified because there really is no potential energy in these theories.

Oh yes, *definitely* too many meanings for the same word. Special relativity (SR) deals with frames moving at uniform velocity at not rotating with respect to one anthor, while general relativity (GR) deals with frames that can be accelerating and rotating relative to one another, correct?

Question. If the energy conservation law breaks down in GR, why is it still held to be a law? If GR and the conservation law contradict one another, why are both still around? My textbook jumped through some hoops to keep conservation of linear momentum and energy intact in SR...

It is a reasonable question to ask, but once you understand relativity then it becomes clear that it is meaningless to think about transforming into the rest frame of a photon.

Well, I'm not there yet. I still find the question very meaningful. Right now it makes more sense to me to say that something must be wrong with Maxwell's equations if they break down like that.

Long before relativity Einstein himself asked a similar question:

"How, then, could such a universal principle be found?  After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations."

Interesting. I haven't studied electrodynamics yet, so I can't really comment on Maxwell's equations. But what does he mean by "on the basis of experience?" There's no way Einstein was running around at relativistic speeds at 16, so what experimental data is he talking about?

It would be a good exercise to first calculate the length contraction for various fractions of the speed of light,

That part is easy enough. (L' = L/y), where L is the proper length (rocket's frame), L' is Earth's frame and y is gamma, correct?

and then, after determining a value that could be measurable,

Here's where I start having trouble. I don't know how precise the best of modern instrumentation can get, and I'd need that information before I could select values of L and v that would do the job.

determine the energy and thrust required to accelerate a spacecraft towards the Sun so as to reach the necessary speed before burning up in the Sun. As a bonus also calculate the size of the fuel tank to hold such a quantity, and the strength of the material to withstand the necessary acceleration.

I don't know how to calculate for fuel requirements and stress. Ask me again in two or three years when I have some engineering courses under my belt.

That said, keep in mind that to deal with stress you can always start from further out or just not bother using the sun (to give yourself more time to accelerate gradually).