Originally posted by wildespace
reply to post by yampa
How do you explain that dividing a number (for example, 5) by 0.00000000000000000000000000000000000000000000000000000000000000000000000000000001 results in a giganormous number? What happens if you keep adding decimal zeroes to the divisor? We're staring the infinity in the face, and that's what makes mathematicians throw their hands up in the air and declare the result undefined.
Originally posted by wildespace
@Moduli - does the gravitational collapse stop at some point, or does the collapsing body indeed diminish to a point of zero volume? With all the talk about equations and relativity, this question is fairly simple.
The source I cited earlier said it's thought if we had complete well-posed equations, there won't be a singularity. Are you saying there will be a singularity no matter what?
Originally posted by Moduli
In normal GR, this is okay, because once you hit the singularity you do not come out. It does indicate that the solution is not complete--the complete equations would be well-posed. But this is only an issue to worry about when you want to understand the quantum mechanics of black holes. Nothing to do with dividing by zero.
Originally posted by Arbitrageur
The source I cited earlier said it's thought if we had complete well-posed equations, there won't be a singularity. Are you saying there will be a singularity no matter what?
Originally posted by Moduli
In normal GR, this is okay, because once you hit the singularity you do not come out. It does indicate that the solution is not complete--the complete equations would be well-posed. But this is only an issue to worry about when you want to understand the quantum mechanics of black holes. Nothing to do with dividing by zero.
What about the density of the singularity? How can you say that has nothing to do with dividing by zero? If the volume of the singularity is zero, how do you calculate the density without dividing by zero?
You speak of real physics.
Originally posted by yampa
These people would have rather have you spend your life talking about infinitesimals, infinities and singularities than understand the real structure of the field of numbers and real physics.
Originally posted by Arbitrageur
You speak of real physics.
Originally posted by yampa
These people would have rather have you spend your life talking about infinitesimals, infinities and singularities than understand the real structure of the field of numbers and real physics.
Do we know the real physics of a black hole singularity without a theory of quantum gravity? Apparently not, and that's part of the problem, which gives us mass divided by a volume of zero in a density calculation for the singularity.
We do have lots of real physics with relativity and quantum mechanics, but since we haven't yet figured out the correct way to make those models compatible, there are gaps between those models, and the black hole singularity apparently falls in one of those gaps.
I'm usually the one arguing about the importance of observed data, so you have a point there.
Originally posted by yampa
Which still has absolutely nothing to do with the number line or observed data.
In some ways it seems like you're trying to change the topic of the thread from dividing by zero, to just zero. It's not exactly the same topic, though zero itself is also an interesting topic, as the Greeks didn't even have a symbol for zero, etc. But I think that could be a separate thread.
Originally posted by yampa
Zero makes a lot more sense when you put in the axes. The number line is positional, each space takes a unit, zero allows you to use all 10 positions from the decimal system etc. It allows you to use the same set of numbers for negative and positive on the same line.
Originally posted by wildespace
There are two things that show this (at least the two that I'm aware of):
1. Black holes. Density = mass / volume. The singularity at the centre of a black hole is an infinitely small point with infinite density. For a black hole, the formula is density = mass / 0 and the result is infinity.
2. Divide a number by a divisor that is 0, for example 0.5 ... Note the result. Then decrease the divisor by half (to 0.25) and note what happens to the result. Keep halving the divisor, and you'll see that as it approachers zero, the result approaches infinity.
For me, the two examples are quite enough to conclude that dividing by zero results in infinity.
Originally posted by yampa
I have no interest at all in listening to Michio Kaku. He is basically a propagandist.
Black holes are completely tenuous, totally abstract mathematical theories. They have nothing to say about the simple and natural division of the number line.
Originally posted by mbkennel
Originally posted by yampa
I have no interest at all in listening to Michio Kaku. He is basically a propagandist.
For whom?
Black holes are completely tenuous, totally abstract mathematical theories. They have nothing to say about the simple and natural division of the number line.
The reality is exactly the opposite. Black holes are physical real things.
The number line is a totally abstract mathematical construction.
And totally abstract human mathematicians have worked out the problems with infinities and their various types in the late 19th century.edit on 31-8-2013 by mbkennel because: (no reason given)