Schrödinger's hat

Well if we have the blueprints we could tweak it a little. Or if it's on a computer we can watch what's happening in greater detail than we possible could in squishy-land. That way we could learn a lot more about it/ourselves. Of course when it comes to modifications there are ethical concerns to worry about.

Hmm, but if you were to keep moving the ball, the golfer would quickly get irate and stop you. On top of this, we know of systems that act in complicated but completely deterministic ways by a set of rigidly defined rules. Perhaps the turing test was too specific. What I had in mind when I said that was a more general version where one could interact with the entity in a variety of ways. If, after that interaction, you cannot distinguish between the entity you interacted with, and an entity that you consider intelligent. Then for the purposes of that type of interaction you would consider that entity intelligent. Hard to say. If the cherry tree were to suddenly make an entity that acted intelligently then I would call that entity an artificial intelligence. If it were to build a house, I'd call it an artificial shelter. I do not know where to draw the line, but the blossoms are more easily explainable through known laws and interactions than my ability to make a toy out of wood for my nephew. I don't consider my ability to grow hair or fingernails a skill. There is something difficult to define, but important about this distinction. Perhaps this definition for 'a skill' might work: An ability which can be absent in one entity/place, and then transmitted/induced from/by another place/entity without exchange of matter.

Hahah, missed a bit, my bad. Try this: In[1]:= F[0] = 1; F[n_] := n * F[n-1] /; n>0

Indeed. Intelligence also don't have to be artificial (made by man) to be this fake kind of intelligence. The behavior of some insects comes to mind. Primarily the digger wasp.

Set theory is about as fundamental as you can get. I can't think of anything you need to learn first, except maybe the language the set theory book of choice is written in I've even seen a children's/preschoolers' show teaching set theory, although it was in some kind of slavic language and so may not help you. Bear in mind that there will be a large amount of variation in the level at which a given textbook will be set. It may presume general mathematical skills you do not have. So if you start reading and find it confusing, browse further. Re: Basic knowledge. What 'basic' means depends heavily on who you're talking to. One good metric might be when you understand the proof that there is no universal set. Another would be understanding these terms and how to apply them in the context of set theory: compliment, intersection, union, power set, negation

That code is Haskell (i'm not that familiar with Haskell, it was just an example I'd seen recently that came to mind). In the mathematica syntax of your other example (bearing in mind that my total experience with mathematica is 5 minutes, so this may not be right) it would be: In[1]:= F[0] = 1; F[n_] := n * F[n] /; n>0 But bear in mind that recursion isn't what makes a functional language, just one of the things that is a functional style of thing to do. If you were more wondering how the Haskell code works. The way I like to think of it is that the language designers are wizards. On a more serious note, there'll be some way the VM/compiler assigns priority to the definition for factorial 0 =1 (whether it's that it was defined with a constant, or where it appears in the program, I'm not sure), but if it doesn't see the 0 it takes the general case of the factorial n definition.

Perhaps this: Was a little unclear. I was saying that the [math]\frac{GMm}{r^2}[/math] formula works if and only if you are outside an object which is spherically symmetric (it will be approximately correct for things that are far enough away that they are approximately spherical, but never exact). If you are inside a spherically symmetric thing the force goes to zero (if earth were hollow and you went anywhere inside you'd feel no force. If you dig down a bit you only feel the gravity from the mass that is at lower altitude than you). A torus is not spherically symmetric.You can rotate it one way and it's indistinguishable (you don't know whether or not it has been rotated, because it looks the same), but if you rotate it the other way you can tell the difference (a doughnut lying flat on the table is distinct from a doughnut on its edge). As a result the [math]\frac{GMm}{r^2}[/math] formula isn't going to work. Not only that, but any formula which just depends on r isn't going to work, you need two parameters to describe the field (because of circular symmetry, for something with no simplifying symmetry you need three parameters). That being said, your intuition about the 0.0001 + r^2 is pretty good. I can't be bothered working it out for a thick torus right now right now, but the formula you get in situations like that if you restrict your location to the axis of symmetry (the middle of the torus, which you could spin it around and it wouldn't look any different) then you get something a lot like what you said IIRC for a torus that is very thin compared to its radius (imagine a thin ring rather than a doughnut), it takes the form: [math]\frac{kr}{(r^2+R^2)^{\frac{3}{2}}}[/math] Where R is the radius of the torus. Which looks a lot like [math]\frac{k}{r^2}[/math] at long distances, but decreases as you get close to r=0. If you go off the symmetry axis it gets more complicated. For a thick torus it'll most likely look much the same, but probably have some logarithms in it. This is about as far as I can go without introducing some more advanced maths. Are you familiar with vectors and/or integration perchance?

(from wiktionary) Artificial: Etymology Via Old French (French: artificiel), from Latin artificialis from artificium "skill", from artifex, from ars "skill", and -fex, from facere "to make". When I read artificial intelligence I think intelligence constructed with skill, rather than fake intelligence. If we were to create something that is indistinguishable from intelligence (score on the turing test would be one metric for this, although probably not the only thing required), then I call it intelligent.

Well it's what's called a recursive function definition. You can do them in some/most imperative languages too, but they don't always handle them as well. What the haskell vm will do when it sees you ask for, say, factorial 4 is very loosely: factorial 4 -- I don't know what this is, but i have a definition that says factorial 4 is: 4*factorial 3 -- well factorial 3 is 3*factorial 2 so: 4*(3*factorial 2) 4*(3*(2*factorial 1)) 4*(3*(2*(1*factorial 0))) -- factorial 0 is defined as a number so 4*(3*(2*(1*(1)))) 24 This is a very functional-styled way of thinking about the problem of finding a factorial. I also don't quite know what compiling this (haskell does have a compiler) entails, Probably converting it to an equivalent, but more imperative, algorithm.

Another way you might be able to approach it: What do you know about about the eigenvalues of a positive-definite or semi-definite matrix? How do the eigenvalues relate to the trace? Perhaps writing an arbitrary vector as a sum of eigenvectors might help?

Just because I can look at a circle top down and see a circle, doesn't mean someone else can't see an ellipse by looking at it from a funny angle. We gave you your overview, but your response was 'no, prove it'. The reason for the disagreement lies in the minutae. Whether our reading of your stated assumptions is wrong, or they are logically inconsistent, the only way to reveal it is by getting into the nitty gritty. If you want animations rather than/as well as the graphs, I can add some more scenarios to this simulator* to outline the scenario. Other than that, the only way I know of to get a sufficiently precise description of the concepts is to use mathematics. On this we agree, and have always agreed. *please click on it now and go to a random scenario to confirm for me that it works on your browser, if it does not, tell me your browser and OS in a PM and I shall endeavor to fix it.

Couldn't quite figure out whether to put this in Physics, Calculus, Applied Mathematics, Computer Science, or Engineering :/ I'm trying to come up with a good scheme for integrating something similar to a thin beam equation: Something along the lines of: [math] A\frac{d^4y}{dx^4}+\text{Possibly other x derivatives}=q(x) + B\frac{d^2y}{dt^2}[/math] But unfortunately comp-phys is but a hazy memory. I can remember/find notes on enough to do similar things which are first order in time with finite difference methods. Would the obvious thing of adding degrees of freedom to make: [math]v = \frac{dy}{dt}[/math] [math]\frac{d}{dt} \left[\begin{array}{c} v\\y \end{array}\right] = \left[\begin{array}{c}\frac{1}{B}(A\frac{d^4y}{dx^4} - q(x))\\v\end{array}\right][/math] Then applying the same methods be an effective approach? Or would it be horribly unstable? Is there an out-of-the-box method somewhere that I'm completely missing?

Seeing as noone else is answering this, I'll try and provide something. It's been a while since I did anything C, and even then I was fairly ameturish -- so take this with a grain of salt, I may not even be explaining the right concept: Function prototypes are used to inform the compiler that you've defined the function elsewhere in your program. They allow you to get the full declaration of the function out of where you define it and put it somewhere more meaningful for a human user, so they're good for structuring the code and making it readable.

Don't think so, but this -- along with discussion on what constitutes a perception of now -- are interesting topics. I'd also like to explore that AI-that-can-only-transmit-information-east idea further. Start a new thread?

It does have the interesting feature that -- with a slight modification -- you can make the additional part both continuous, and non-zero for an arbitrarily small region.

Better than my solution, which I think is much more cumbersome, and a bit flaky as you have to assume positive square root. [math]x^2 + \frac{1}{2}\left(1- \frac{(x - 3)^2 - 0.5}{(( (x - 3)^2 - 0.5)^2)^{\frac{1}{2}}}\right)(\pi - 9)[/math] Also your rule of 'no trig' threw me waaay off of the trail of using (-1)^(f(x)) without prohibiting its use. Well done.

This looks a lot like a homework question. We generally don't provide complete answers to such things. Perhaps you could explain what you've done so far? People will be more inclined to help then.

This is an empty assertion. Show me an example of (or even logic that shows me that I could discover) a distance that has measured without a frame of reference and I'll happily run over to my nearest university and tell them that relativity is complete nonsense. NUHUH! YEHUH! NUHUH! YEHUH! Will get us nowhere. I don't get realism+presentism+constant speed of light+postulate of relativity because it doesn't make any sense. I do get realism+postulate of relativity+constant speed of light perfectly well. I also get realism+presentism+constant (measured) speed of light. I just think the resulting theory is too convoluted for it to be likely that it's true. Capn voiced my frustration at this very well. The showing involves diagrams and/or careful application of logic in small steps to make sure we're not leaving anything out. It is exactly what we've been trying to do for the entire thread, but you keep interrupting the process with 'NO SHOW ME HOW IT WORKS'. Just to recap. Respond to the jousters diagram/post I made. Can you read it okay? Explain anything you don't understand. Does it display the situation you were trying to explain? Note that it doesn't try to demonstrate anything about length contraction or simultaneity, it's just intended to be the situation you outlined (two things moving towards one another emitting a beam moving at twice their speed).

No worries. This way we can take credit for helping you out without actually having to do anything

Any time your objects are of significant size compared to the distance between them, you need to consider that the mass isn't all at a single point. Otherwise you will get an inaccurate result. There's a special case for spherically symmetric things where the maths works out the same as having a single point at the centre of mass. This will work as long as you are outside the spherical object, Inside a hollow spherical shell a [math]\frac{1}{r^2}[/math] force (like gravity) goes to zero, So for solid spherical objects you can consider the mass that is deeper inside the object than you as a single point in the middle.

From what I read, both styles have their uses, and you don't have to go all the way to LISP to take advantage of functional style. Here's someone saying it in more elegant words than I can: http://www.joelonsoftware.com/items/2006/08/01.html

For the umpteenth time, reality doesn't depend on frame of reference, but distance is not defined without one. If I give you two lines like so: And ask "What is the distance between these two lines?" The question is nonsense. It's undefined. If, however, I define a plane ('now' in some frame of reference) which intersects both these lines and ask: "What is the distance between the point at which these two lines intersect the plane?" You can answer. But if I change the angle of the plane (analogous to changing velocity), it changes. If I move the plane along its normal (analogous to allowing time to pass, and having some objects move), it also changes. You can also answer "What is the width of the blue line in the direction perpendicular to its length?". This would be the rest-width or proper width of the blue object. But you can't answer "What is the width of the blue line?". As this requires the direction we mean by 'width' to be defined. But no matter what plane we pick, it does not change the lines. The lines are perfectly real without the plane. You can say that the lines are not in fact lines, but points intersecting a single plane that moves (this would be the philosophy of presentism in this analogy), but then you have to define that plane. This is why we keep asking you 'what is the preferred frame?'. Your answer of 'at rest with whatever is measured' (in other words, no universal single preferred frame) is logically inconsistent with presentism. You can't have constant observed¹ speed of light in all frames, presentism, and lack of a universal preferred frame for all measurements. Constant observed speed of light is experimentally verified, so to debate this, you'd have to provide experimental results. No experiment we've done to detect a universal preferred frame of reference has worked. So either it's not there (things are lines through all time, not points at now), or it's undetectable (Lorentz Ether theory). Again, the logic behind this can't be summarised in a single post, and I need some small measure of cooperation to explain it. ¹I say observed, because in Ether theories, the moving person still measures light to be moving at c, but their measurements are wrong.

Uhmm, I'm not quite sure what you mean. The product rule is: [math] \frac{d}{dx} f(x)g(x) = \frac{d f(x)}{dx} g(x) + f(x)\frac{dg(x)}{dx}[/math] I can explain a bit about the intuition behind it if you like, or perhaps you could re-word your question?

Every time someone does discuss this (according to their model, which is consistent with SR) you respond with: NOPE I DON'T BELIEVE YOU LALALALALALALALA They then tell you that you're basing your arguments on assumptions that are inconsistent and offer to show you why, to which you respond with another post like this one -- telling everyone that they refuse do discuss it. Changed speed of observation along with constant observed speed of light, results in changed observation of simultaneity and distances. This is an irrefutable logical fact. You can't just say "no it doesn't". What these observations mean and whether they pertain to reality, or to a distorted view of reality is debatable -- even if doing so goes in the face of a century of science, this is philosophy after all -- but do do so you have to understand why to do so. In addition to this, claiming that such observations are incorrect has its own logical consequences. You should understand what these are before claiming presentism. My most recent 'manipulation of models' was intended to be a backdrop to show you the consequences of various assumptions, and the mechanism behind simultaneity/length contraction.

The key to getting good coverage from your analogies is to steam them properly first. Then apply a nice, even pressure. You'll find that you'll be able to stretch them much thinner that way.