By the way, what you guys are talking about sounds like 2.5D graphics

Yeah, I guess that's what the hurricane I was describing is!
You could make a purely 2D hurricane sim by making it a many-state cellular atoma, making each point on the plane do what layers of them previously did. But since it's doing the same thing as the 2.5D sim, it's still simulating those layers just as much. And you could even reduce the sim down to 0D by just making it a static point with very complex properties, but you could do that with anything. If you wanted, you could decide that the universe is just a static point with very complex properties, but I prefer to think of the universe as 3D.

Thanks! I can't check anytime soon but I will eventually... probably when the next version comes out.

By the way, what you guys are talking about sounds like 2.5D graphics

Yeah, I guess that's what the hurricane I was describing is!
You could make a purely 2D hurricane sim by making it a many-state cellular atoma, making each point on the plane do what layers of them previously did. But since it's doing the same thing as the 2.5D sim, it's still simulating those layers just as much. And you could even reduce the sim down to 0D by just making it a static point with very complex properties, but you could do that with anything. If you wanted, you could decide that the universe is just a static point with very complex properties, but I prefer to think of the universe as 3D.

Great point!  Actually the Holographic Principle shows us that a 3D universe can be perfectly described as being a projection on the 2D surface of a black hole.  Also, at extremely high energies, cosmic rays seem to only have 2 degrees of freedom, which means it's possible the early universe was two dimensional (thus no gravity as an attractive force according to relativity.)

What if Uranus was as close as mars, with mars being a moon of Uranus?

What if Uranus was as close as mars, with mars being a moon of Uranus?

Having that big of a planet that close would probably mess with the orbits of the rest of the rocky bodies. Earth might get thrown out of the solar system or into the Sun, though it wouldn't happen for thousands of years or so. Also, you'd have to be careful where you put Mars, or you'll end up with rusty Uranus rings.

some question that came to my mind today is:
why some molecules have smell but some don't?
are all molecules have smell but humans can't smell them all?
and what is the origin of smell? i mean, why let's say: SO2 smell like it does? 

some question that came to my mind today is:
why some molecules have smell but some don't?
are all molecules have smell but humans can't smell them all?
and what is the origin of smell? i mean, why let's say: SO2 smell like it does?  :)

I'm surelly not an expert on this, but molecules don't smell intrinsically. I mean molecules have electric and magnetic fields around them, have intrinsic masses and intrinsic vibrational modes, but having smell is nothing but an experience that arises as an emergent property of millions of chemical reactions. You nose has reactive compunds that chemically react when they encounter certain ammounts of certain molecules. Natural selecction tunned our senses to have certain chemical reactions (that in the end stimulate the chemical inbalances of some neurons in our noses) so we could "detect" certain molecules. So smell is not something about the molecules but something about our interaction with them.

some question that came to my mind today is:
why some molecules have smell but some don't?
are all molecules have smell but humans can't smell them all?
and what is the origin of smell? i mean, why let's say: SO2 smell like it does?  :)

I'm surelly not an expert on this, but molecules don't smell intrinsically. I mean molecules have electric and magnetic fields around them, have intrinsic masses and intrinsic vibrational modes, but having smell is nothing but an experience that arises as an emergent property of millions of chemical reactions. You nose has reactive compunds that chemically react when they encounter certain ammounts of certain molecules. Natural selecction tunned our senses to have certain chemical reactions (that in the end stimulate the chemical inbalances of some neurons in our noses) so we could "detect" certain molecules. So smell is not something about the molecules but something about our interaction with them.

He's correct.
Like smell all other senses are just creations of our brain. The universe doesn't have colors, we see colors to recognize healty fruit/plants from toxic ones and so on, but it's just an invention of our brain (our and of all other animals), the same works for taste. You can read which molecules give you every kind of tastes right on Wikipedia.

FastFourierTransform, Salvo,
thank you for your information! 

So, apparently, time and space inside a black hole switch roles. Time can be traveled in either direction, while moving towards the singularity is inevitable. Could I, as a normal space-time geometry human being, meaningfully experience the inside of a black hole? Or would I not function like I do outside, since space-time behaves differently?

The short answer is, yes, you do meaningfully experience the interior of a black hole (and then inevitably meet the singularity at the center).  It is also true that one of the dimensions of space and the dimension of time switch roles inside, but there's some confusion as to what that means, which I'll describe in more detail.

Long answer:

What happens is that inside the horizon the inward direction starts acting like the future direction in regular flat space-time.  What this means for someone going through the horizon is that they are "forced" to move further inward, in much the same way as you right now are being "forced" to move toward tomorrow.  In other words, your future lies at the singularity -- once inside the horizon you cannot avoid it.  

To give some explanation for why this is the case, let's start with what we call the "space-time interval".  The space-time interval is a way to define distances in space-time, just like how the familiar Pythagorean theorem defines distances in 2D Euclidean space.  In 2D space we may write the squared distance as



Now, how to do apply this in space-time?  Isn't time totally different from space, even with the units?  The trick is to convert the time into a distance, and we can do that by multiplying by the speed of light.  (speed)x(time) = (distance).  Since the speed of light is the same in all reference frames, this conversion factor of c works the same for everybody.  Then, with time and space now having the same units, we define the distance in space-time as



It's basically the same thing as the Pythagorean theorem, except for the notable difference that there is a minus sign instead of a plus sign.  And it doesn't really matter if you say it is x^2 - (ct)^2,  or (ct)^2 - x^2.  All that matters is that you choose one of terms to have the opposite sign as the other, and then stay consistent with that choice.  Then what relativity says is that although different observers will disagree on what they measure for distances x and times t between events, everyone agrees on the space-time interval, s^2.  And this little equation basically contains everything about special relativity, including the effects of time dilation and length contraction.

Going back to that minus sign, this is what makes one of the directions of space-time act differently than the others.  Whichever direction has the opposite sign of the others is the "time-like" direction, while the other dimensions are "space-like".

What a gravitational field does is distort the shape of space-time, and inside a black hole the signs end up switching places.  Let's write the space-time interval for a black hole to see why.  Yes, this looks scary, but stay with me and don't panic.



The first term has t and represents the time coordinate.  The second term has r and represents the radial coordinate (toward or away from the singularity), and r_s is the specific radius of the event horizon.  Third is θ which is like latitude.  Finally, Φ is like longitude.

Outside the black hole, r is greater than r_s, so the first time has 1 minus a fraction less than 1, which is positive, and then a minus sign in front which makes the entire first term for the time coordinate negative.  The second term for the radial coordinate will be positive, and so will the third and fourth coordinate directions.  So the time coordinate is timelike and the three spatial coordinates are spacelike, just like in regular space-time.  But once we go within the horizon, r is smaller than r_s, and so the first term will become positive while the second term becomes negative.  That's why the behavior of these two directions switches, and the radial direction acts like time.  It doesn't mean we are free to move in time, but rather that we are forced to move inward.  Moving outward is as impossible as moving backward in time.

One last principle of relativity we can call on here is that physics in all inertial frames of reference works the same.  You cannot tell the difference between floating in a spaceship which is far from any gravitational field, or floating in a spaceship which is falling near the Earth.  And so too, with freefall into a black hole.  If you fell into a very large (supermassive) black hole inside a small box, then for the entire trip to and even inside the event horizon you would notice nothing unusual.  Just weightlessness the whole time.  

(There is a caveat in that close to the singularity, tidal forces become important, and eventually you will feel and be destroyed by them.  But for a very large black hole these forces are negligible at the horizon.)  

So in a real sense, the horizon of a black hole, and even most of its interior, is not a very strange place as far as physics and space-time are concerned, provided that your view is limited to only a small region which is falling into it along with you -- like the inside of the small box.  If you extend your view very far then the effects of the tidal forces start becoming noticible, just as you would notice things falling in different directions if you compare very distant locations on the Earth.  General relativity teaches that these tidal forces are the direct manifestation of curved space-time, and thus are the natural way to measure a gravitational field.

So a supermassive black hole would be a "peaceful" place.  How far down do you have to go before the laws of physics start breaking down?  I assume that only happens at the "singularity"- or whatever that actually turns out to be.

I'll take "Event Horizon" for $500 Alex

Nah, we can get very far below the event horizon before our knowledge of physics starts breaking. In terms of space-time curvature, things break at about 10^13 per centimeter, which is *very strong* and occurs extremely close to the singularity -- like within the radius of an atom!  For comparison, the space-time curvature at the surface of the Earth is about 10^-18 per centimeter, or a radius of curvature of about a light year.

A caveat to that however is that this assumes an idealized, non-rotating black hole.  In nature, black holes rotate, and that really messes things up in the deep interior, around the inner event horizon.  So for real black holes our knowledge of physics is still good within the outer event horizon, but breaks down farther out from the singularity than it does for a non-rotating black hole.

AAAAAAAAAAAAAAAAAAAAAAAAAA HELPHELPHELPHELP GINORMOUS EQUATION

Anyways, thanks. I guess, since space-time is "falling" into the black hole with you, you wouldn't notice any real change, so everything should still act normally. I mean, your entire 360° view of the universe would shrink to a tiny really blue dot and fry you, and you are also in the process of dying by transformation into spaghetti, but there are no weird new laws of physics.