Greg H.

It has nothing to do with coordinates, manifolds, or anything else but numbers. It works like this: Person A: Pick Two numbers and I will pick a number between them. Person B: 1 and 5 A: 2 B: 1 and 2 A: 1.5 B: 0 and 1 A .5 B: 1/2 and 1/10 A: 1/3 Basically, for any two numbers you can think of (m and n), there will ALWAYS be a number (p) that falls between them. One easy way to see this is to simply average the two numbers. For example: [math] Let\: m = 1 \:and\: n = 1.5,\: find\: p\: such\: that\: m < p < n[/math] One such value for p can be found by: [math] p = \frac{1 + 1.5}{2}[/math] [math] p = 1.25[/math] We can validate this by looking at the original inequality and seeing if our values hold true: [math] m < p < n = 1 < 1.25 < 1.5[/math] So what you see is that for every pair of numbers you can think of (m, n) there will always exist at least one number (p) between them. This is what we mean when we say that numbers are dense.

The easiest difference to spot between an analog line and a digital line is mostly in how the signal is shaped. In an analog line, the signal will be a continuous sine wave (see Sine Wave). A digital signal, on the other hand, is made up of discrete square signals that indicate discrete 1's and 0's (see Digital Signal). In an analog line, changes in frequency or voltage are used to indicate the digital 1's and 0's, and a modem is used to translate these analog waveforms into a digital waveform that the computer will understand. That is, in general sense, all a modem (MOdulator/DEModulator) does - converts one wave form into another. To answer your initial question, what the signals are made of depends on the transmission medium. In a standard phone line or network cable, they are low voltage electrical signals. You can also use microwave transmissions, infrared (the remote control for your tv, for example), and light (fiber optic) depending on the application needed.

Then forget the photosphere and show me the calculation that shows that Silicon can fuse into Iron at all under those conditions. Let me save you the trouble: It can't. It violates the laws of physics. So unless you have some damned amazing math to back up your claims, we're done here. On the other hand, if you do have such math available, I'd go ahead and pack for your trip to Oslo.

Please demonstrate, mathematically, how Si -> Fe fusion can occur at the low temperatures and pressures found in the Sun's photosphere given the following (at a standard optical depth of 1.0)1: Temperature = [math]6,533 K[/math] Pressure = [math]1.25 \times 10^5[/math] [math]dynes/cm^2[/math] Density = [math]3.00 \times 10^{-7}[/math] [math]g/cm^3[/math] Feel free to take your time, and keep in mind that your answer must also explain why we can't fuse hydrogen, a process that takes significantly less energy, at this temperature and pressure. Nieminen, T. A. (1995). Solar Line Asymmetries: Modelling the Effect of Granulation on the Solar Spectrum. Chap 2: p. 29. Retrieved on August 13, 2013 from http://www.physics.uq.edu.au/people/nieminen/papers/thesis/chapter2_photosphere.pdf based on Holweger, H. and Müller, E. A. “The Photospheric Barium Spectrum: Solar Abundance and Collision Broadening of Ba II Lines by Hydrogen”, Solar Physics 39, pg 19-30 (1974).

Fusion doesn't happen outside the core of the star. The temperature and pressures are too low to maintain the cycle. The same goes for fusing Iron inside our Sun. The pressures required simply do not exist in the Sun. In order for them to exist, the Sun would have to be considerably larger (or at least far more massive) than it is now.2 Additionally, if the sun were currently producing its own Iron through fusion, that would mean that we would expect to see fundamentally lower amounts of hydrogen than we currently observe, as fusing hydrogen is significantly easier. You have to keep in mind that nature is inherently lazy. It won't fire up a relatively expensive process until all of the less expensive ones have been exhausted. Proof of this is available in the math of the equations. The amount of energy required to power the fusion reaction you describe simply does not exist in the Sun - it's just too "light" a star to power such a reaction, photosphere or not. 1 - http://en.wikipedia.org/wiki/Sun#Core 2 - http://en.wikipedia.org/wiki/Silicon_burning_process

Wasn't there a movie where the basis of communications started with a simple representation of the hydrogen atom and worked up from there?

If we're going to speculate, then I don't see why a vertebrate with more than four limbs would be out of the realm of possibility. Obviously, we don't have any on Earth, but given the correct evolutionary motivations, I don't think it would be far-fetched. If you take a look at the "science" behind the movie Avatar, you'll find a lot of interesting thought went into designing what the movie's animal creatures would look like - a kind of evolutionary gedanken experiment. To your original question, I agree that you wouldn't get a human (or any other Earth vertebrate) with six limbs - the genetic code isn't there (so far as we know). We have not, to my knowledge, discovered any vertebrates in the fossil record with more than four limbs. There may be some much more distant common relative in the invertebrate family with more than four limbs, but evolution seems to have decided we don't really have any selective pressure to maintain more than four. That said, I don't think that puts it outside the realm of possibility that somewhere in the universe exists a vertebrate with more than four limbs. Proving it, of course, it a whole other matter.

The video in krash's link refers to it as Quantum Locking. Whatever you call it, it's interesting.

Briefly, yes. There's another thread here on these forums somewhere about that, and someone could give you a much more complete answer than mine, but it is possible that certain constants could change in conjunction and still result in a universe that behaves much like the one we currently live in. See: The Fine Tuning Argument Is Dead.

Which is really too bad, since you left before you arrived, and about three years before he was born. If only we had something to arrange all these random motions of particles.

To readdress the questions asked by the OP: "What is time? Does time exist?" 1. What is time? Time is the property of the overall space-time arrangement of the universe that prevents effect from preceding cause. Without time you could die from a gunshot wound before the bullet reached you - even before it was fired. There would be no sense to the motion of the universe because there would be way to order the events that describe that motion. (I'm not going down the path of SLoT here. It's not relevant to the topic at hand). In simplest terms time is the universal property that prevents the past from happening after the future. 2. Does time exist? Define "exist". We can certainly see the effects of previous causes, so in that respect yes time exists in that it provides an ordered arrangement of events that we can perceive. Without time, we would have no way of predicting anything, landing folks on the moon, probes on Mars, or even predicting the orbits of asteroids and planets. You cannot define a discrete event without using time. If I schedule a meeting with my boss (a discrete event), I have to define both the location of the meeting and the time that event should occur, or we might end up at the same place at different times, preventing us from meeting.

Speaking from a philosophical standpoint, the question of the OP is probably best interpreted as "What does it mean to say something exists?" or "What is existence?". If such a non-physical consciousness existed outside of space-time, I'm not sure we could even properly define their existence, given our still limited understanding of anything outside the physical universe. If they existed within space time, they would not be at odds with my previous statement.

The advantage of this approach is that no matter how good their hacking skills, a camera with a blocked lens is still useless.

So I'm biased and ignorant. You could have just said that. You'd have been wrong, but you would have sounded like less of a pompous ass. Except that, thus far, there's nothing confirming the FDW quantum gravity theory, so while it's nice idea (and frankly, I hope they're right - it would be nice to be able to answer one of the niggling little details of the universe), it's hardly proof of anything. Aside from that, a random google search on the FDW theory of quantum gravity shows that you, and the good Dr. are the only people really even discussing the theory in any kind of detail. Could it be that's because your ideas are predicated on the idea that it's correct? I think your bias may be showing.

No, we don't, so I wish you'd quit saying this. We have a couple (or more than a couple) of contenders, but they all have significant issues and none of them have (to my knowledge) been experimentally confirmed.

The problem with your word salad is that we don't currently have a functional mathematical model that unifies all of the four fundamental forces (aka A Working Theory of Everything). How do you make predictions (much less universal requirements) based on a model that does not exist?

Hi Where are you getting this reasoning from? There is no form of probablity that allows you to claim the chances of a firing squad intending to kill you and misses are 1. I never claimed they intended to kill me. Read the following two statements very carefully, because they are not the same. 1. What is the probability that I am alive after the firing failed to kill me? 2. What is the probability of the firing squad failing to kill me? If they fire, and I am still alive afterwards, the probability of me being alive after the shots were fired is 1. That statement makes no efforts to compute the probability of them all missing. It doesn't even say anything about missing. Maybe they hit me but I survived anyway. The point is, discussing the probability of a discrete event that occurred in the past is nonsense. It's like trying to multiply by infinity - it's useless to discuss. The probability that you were born is 100% because you were born. The probability that you logged into this forum and typed a post is 100% (otherwise I would have nothing to respond to). Probability is really only useful in describing future events. What is the probability that the sun won't be there tomorrow? Well, it's pretty low, but there is an infinitesimally small chance that it could just explode while I'm asleep tonight. Now, if you wanted to discuss the probability of another universe forming exactly like this one - that's actually a useful question. It's impossible to answer since we have No concrete idea (or mathematical model of) how this universe formed, and No other universes to compare it to even if we did. So it would be impossible to even begin to calculate the probability involved - we simply do not have the required information to even be able to formulate a WAG. . [citation needed]

Ironically, the atheist would be the one who wouldn't care about getting there.

We may be straying from the OP a bit here, and if so hopefully the moderators will set up straight, but... Mathematics, at least to me, seems to have a kind of meta-existence. It can be used to define things that exist (the universe for example), and it can be used to enumerate concepts that have no physical existence (someone please show me [math]i[/math] apples). I think it's this existence outside of what we think of as physical existence that makes it so powerful. The concepts of mathematics would exist regardless of physical form (though we might not have any reason to do them without it), but they are inextricably tied to the physical because without a physical universe to describe, math has no reason to be used. It both defines, and is defined by, physical existence, even though it has none on its own. It's not that math doesn't exist without the big bang (at least to my mind), it's that is has no purpose - there's nothing for it to describe. It some respects, it may not exist separate from space-time simply because of this. Without space-time, math has no reason for being.

Define "cool job" in an objective fashion and maybe we might know what you're looking for. I mean it takes no education at all to wash dogs all day long, but you might not find that "cool".

From what I can tell, there are a few basic leg/foot articulation types. What I'm really curious about is the difference in two of them: 1. The human bipedal one (basically straight leg, 90-degree angle at ankle to foot). 2. The general "chicken" shape (theropod, avian) The question I am trying to get a feel for is which leg shape is stronger at higher weights, and why. I don't know enough about engineering to be able to calculate the stresses on the bones with the varying bone angles. So here's the proposed question: Let us assume we have to identical cubes of lead A and B, each with a mass of 250 kilograms. Cube A is supported by two standard human legs, while Cube B is supported by a theropod leg arrangement. The question Which set of legs would require less structural mass to balance the mass at a standstill, and support it with a normal range of motion for the given leg type?

Rene Descartes spent a good deal of time ruminating on that very subject. In both Discourse on Method and Principles of First Philosophy, he arrives at the idea that if a something can doubt its own existence, then that something, of necessity, exists or else it could not doubt. And though Descartes wrote some 400 years ago, the question about what it means to exist is still with us. In fact, AJB put up a blog entry on the existence of mathematics, which asks the question does mathematics exist. I mean certainly the concept of mathematics exists. We use it everyday, in a wide variety of ways. But is the existence of a concept enough to say that some "thing" exists which defines (or is defined by) that concept?

Forget proving that God exists. If someone had managed to unify Gravity with all the other forces in the cosmos, the scientific community would be shouting about that from the rooftops of the world. Not only would it be front page news, but Nobel prizes would be showered upon them like rain drops in a monsoon. They'd probably have to invent a new one - Nobel Prize in Pure Awesome or something along those lines. Your paper is bunk. Your idea that God can be "proven to exist" is nonsense. After more than 2,000 years, out of all the millions of Christians that have puzzled over this very question, I think we'd have found some (scientific) evidence by now besides a book full of morality stories and parables.

Don't confuse faith for truth. They are not the same thing.

You are correct about what I meant. Copy pasta is the enemy. Thanks for the correction.