Strange

What do you mean by "too small"? Wavelength? That would not be changed by reflection. This is more of a biology question. "for animals ranging from bees to reindeer, ultraviolet lights up their vision" http://www.theatlantic.com/technology/archive/2011/08/6-animals-that-can-see-or-glow-in-ultraviolet-light/243634/ I think that needs a separate thread. http://www.explainthatstuff.com/projectiontv.html

Do they still say "there is no such thing as a stupid question" ?

But after (meaninglessly) converting time to a distance you then need another time axis if you want to define speed. So this is all nonsense. The Lorentz transform is fundamental. The trouble is that he has come up with what he presumably thinks is a catchy analogy. It is clearly highly misleading and uninformative. (As shown by the fact that you are confused by it.) You would be better off going and looking at the (pretty simple) mathematics of special relativity in order to understand the relationships between time and space.

Yeah, right. Good.

That is a strange definition of reflection. Why can't we see it?

So your only justification for "natural rights" is an argument from authority?

If you multiply time (seconds) by c (metres/second) you get metres, not speed. I guess he is alluding to the fact that you can regard the Lorentz transform as a rotation between the time and space axes. To say that this means that everything moves at c seems a little misleading.

It sounds like incoherent nonsense. For example: "the moon is travelling in the fourth dimension at about light speed" The "fourth dimension" is time. How can the moon be travelling through time at a speed measured in distance per unit time? It makes no sense.

Still no definition of "natural rights" nor any evidence that such things exist.

You are right (I was originally going to express it as a proportion). However, as noted, it is pretty much meaningless anyway. Except that it gives you an idea that space-time is pretty flat in the vicinity of the Earth.

Yes. Life is a series of complex chemical reactions. Everybody knows that already. Do you have anything new or intelligent to contribute?

Effectively, because matter was homogeneously distributed through all of space so, in a sense, there wasn't anything to stop it moving apart. If there is an even distribution of matter then there is no net force. And it requires a force to stop things being affected by expansion.

Science doesn't really work like that, though. It is not about what "feels right" but which theory best fits the evidence. Then maybe you should? I mean, kudos for imagination and interest, but I think it is always better to start from a position of knowledge about the idea you are going to criticise. This is a good intro: http://math.ucr.edu/home/baez/einstein/einstein.html It gets a little bit mathematical but I think it does a good job of getting the ideas across.

Thanks for that. I was having trouble putting my finger on why the concept of radius was not relevant. I think you mean extrinsic curvature here?

Are you unwilling or unable to explain what a "natural right" is, and how we determine if any particular right is natural or not?

Can you explain what is unsatisfactory with the current explanation? Stars and planets are formed from material that already exists and so do not make any difference to the mass of the universe.

It is not (just) space that is curved, but spacetime. IF it is possible to approximate this with a radius, then you would need four different values. This paper calculates that the difference in the radius of the Earth due to the curvature of space-time is about 4mm http://www.johnstonsarchive.net/relativity/stcurve.pdf So perhaps you could approximate the radius of curvature as 6x1010 x radius of the earth or about 100,000,000,000,000 kilometres. I really don't know if that answer makes sense or not.

It sounds like you want to encode the options as bits by making every option a value a power of 2 (A = 1, B = 2, C = 4, etc.) Then when you add the selected options together, it is equivalent to setting the appropriate bits. You can test any option with a boolean AND; for example: (choices & B) > 0 will be true if option B is in the choices. I don't know if this technique has a name or not ...

"Our curved spacetime need not be embedded in some higher-dimensional flat spacetime for us to understand its curvature, or the concept of tangent vector. The mathematics of tensor calculus is designed to let us handle these concepts `intrinsically' -- i.e., working solely within the 4-dimensional spacetime in which we find ourselves. This is one reason tensor calculus is so important in general relativity." http://math.ucr.edu/home/baez/einstein/node2.html

Actually, 4D spacetime. But the curvature is "intrinsic" so it doesn't require a higher dimesnional embedding.

The simplest description for a black hole is the Schwarzschild metric. This is only valid for a static mass in empty space: https://en.wikipedia.org/wiki/Schwarzschild_metric The expansion of the universe is described by the FLRW metric which assumes a homogeneous distribution of mass: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric More discussion here: http://astronomy.stackexchange.com/questions/7863/why-did-the-big-bang-not-just-produce-a-big-black-hole By an odd coincidence, the radius of the observable universe is roughly the Schwarzschild radius for the mass. Because Micheo Kaku, Hawking, and the other scientists always say that the [observable] universe was smaller than a proton at the moment of the big bang. I put "observable" in brackets because that is what they mean. They do not say the "entire" universe was smaller than a proton. Nobody has (seriously) suggested it (as far as I know). But it is still possible. Expansion is not a speed. There are now, and always have been, parts of the universe that are receding faster than the speed of light.

I don't think the curvature can be described by a single (radius) value (because it is the curvature of a four-dimensional surface). It is described by one of the tensors in the Einstein Field Equation (the Ricci curvature tensor, I think).

If self defence is a natural right then are firearms automatically a natural right as well? Perhaps the "natural" right is to defend yourself with no more than your attacker uses. On this basis you would have a right to use a gun if your attacker has one. But not if they only have a knife. Or words. On the other hand, there are many who hold that violence is always wrong, even in self defence. So perhaps it is not a natural right anyway. You haven't explained how you know it is a "natural right"; you have just asserted that it is.

How do you know which are a natural rights and which are not? Can you make this determination in a way that is not subjective; i.e. that everyone will agree on? For example, is freedom to marry who you wish a natural right? Is same-sex marriage a natural right (a lot of people don't seem to think it is). Is the right to marry an animal a natural right? If not why not?

Worth noting that in curved space-time it is possible to "swim" through empty space: http://dspace.mit.edu/handle/1721.1/6706