The second law of thermodynamic

[Bread_of_Life]

So JLW, do you or do you not admit that 1/inf /= 0?

If so, then you must admit that, given infinity is a concept, not a number, that 1/infinity cannot have a numerical answer (either finite or zero)?

Now, given you admit this, you then ask:

You will never have infintely many choices because infinity isn't a number!

The fact that infinity is a concept and not a number doesn't mean that you can't concieve of there being infinite possibilities. Actually, perhaps some examples might help:

1. Do you drive a car? I do. Here in the UK the speed limit is 30 miles per hour in built up areas. I live in a built up area, and I was going 30 miles per hour the other day, and then the traffic lights in front of me went red. So I applied the break, and decelerated to zero in time so as not to hit the car in front.

As I stood at the lights, I wondered, how many speeds did I decelerate through? Well, I went through 30, 29, 28, 27, 26... to 0. But hang on, I must also have passed through 29.5 also. And 29.51. And 29.511. In fact, thinking about it, I went through infinite speeds, I must have.

So I wonder, how long did I stay at each speed? Well, I cannot have stayed a finite time at each, because then I would never have stopped. So I must have stayed at each speed for an infinitessimal ammount of time (also a concept btw, I can't write down dt). How odd.

So then I wonder, what was the second speed I went through? I started at 30, and ended up at 0, I can define the two end points, but what was the second speed I was at? Hmmm. There must have been a second speed, but what was it? The answer is 30 - dv, dv also being a concept. So my second speed, whilst it did exist, is impossible to write down (it's not an number) and the ammount of time I stayed at this speed, dt, is also a concept, and therefore impossible to write down. But it did exist, and I did go through it. Instantaneously, at one point, I did go through this speed, and infinite others.

2. I'm sitting at the moment on a charming corner cream leather sofa, in my living room. My living room gives onto an open plan kitchen. Between writing this example and the last, I got up, and walked to the fridge to get a glass of water. Now I wonder. If I took my centre of gravity, and traced it's path to my kitchen, how many points will it have gone through? How many places will it have been? Indeed, if I take any arbitrary point on my body, how many points will it have passed through on the way to my kitchen?

Well, lets model it in one dimension, to keep things simple. It's about 4 metres to my fridge. So, my centre of gravity went through 1cm, 2cm, 3cm, 4cm ... 400cm, when I finally arrived at my fridge. But what about 1.5 cm? And 1.55 cm? I can't have avoided these can I? In fact, I must have passed through infinite points on the way to my fridge.

And now I wonder, how long did I remain at these points? Well, it can't be a finite time per point, so if I was constantly on the move, it must have been for a time dt (a concept, impossible to write down). Again I try to write down my second point. My first point was 0, my last point was 400cm, but what was my second? Hmmm. It must have been dx, another concept, impossible to actually write down. But I must have gone through it, there must have been a second point.

3. So now again I wonder, how many possible universes are there? Say I take a small subset of possible universes. Say, all the universes between 1.6x10^-19C and 1.7x10^-19C, in terms of the charge of the electron.

Well, in the first universe of this group, the electron has a charge of 1.6x10^-19C, and the last has an electronic charge of 1.7x10^-19C, then start points and the end points are definable. But how many are there in between this endpoint? What is the seperation between them? What was the second point?

Simple, there are infinite possible universes between these points, seperated by dC, and the second universe is 1.6x10^-19 + dC. Of course, I cannot write all of these down, I can never actually show you the number, but that doesn't mean they arn't all contingencies, just as all the speeds between 30 and 0 are all speeds.

4. A simpler example. There are infinite numbers between 0 and 1 in the number line. Of course, we can't write them all down, or show you them all, because they are impossible to ennumerate. But that doesn't mean they arn't there. It doesn't mean there arn't infinite numbers between 0 and 1. There are, they are seperated by a quantity dn, and the first one is dn. Weird, but true.

[JLW001]

The fact that infinity is a concept and not a number doesn't mean that you can't concieve of there being infinite possibilities. Actually, perhaps some examples might help:

What a contradiction I'm hearing here, SA. If infinity is not a number, then how can you have infinite possibilities?

Now, we both know that you can say that the number of decimal numbers between 0 and 1 approach infinity. Now, if you say that there are infinite decimal numbers between 0 and 1, then I wouldn't argue with you because I understand that infinity is a concept THAT CAN BE TREATED AS A NUMBER. However, you can only apply a select group of operations to this special type of number we call infinity.

SA, infinity is a concept that can be treated as a number in certain instances and must only be used in certain operations.

If you can conceive of infinite possibilities, then I'm proud of your understanding. If you tell me there are infinte possibilities , all with the same probability, then I say that is not possible because it defines the indeterminant form.

if you say,

Pi= 1/infinity

Then, if you integrate it you will not get back to unity. You will get,

Sum(Pi) = Area = infinity*1/infinity = inf/inf = indeterminant form.

This is what I was trying to show you a couple of pages back before you started saying 1/inf <>0

Remember, I said let's not evaluate the probability yet, let's see if it satisfies the probability distribution. Remember I said that the probability distribution is indeterminant for equal probabilities and infinite choices.

I'm really getting tired of explaining this to you. Show me your math that says you can have infinite choices of equal probability and get a determinant probability distribution.

Look, people can talk and have loads of words descibing the point that they are trying to make. But, if they can't describe to you their scientific point in mathematics, then their explanation holds no water. It's of no use.

All I've got to say, SA, is that I'm astounded that this hasn't sunk in yet. Is it because you hate the idea of God or a higher power existing? Its very clear from the universe itself that He exists. What is it about God that you spend so much time trying to prove to others or yourself that he doesn't exist?

What is it about God that makes you so uncomfortable, that you are ready to deny the mathematics? This logic that you so readily believe in is showing you something profound about the beginning of the universe, yet you seem to be resisting it tooth and nail.

[Bread_of_Life]

What's the point in me posting long posts if you only answer one single sentence, and even then, not the one that contained any evidence or content of my point? It's not like I didn't try to shape the conversation. I tried to give you several examples of real infinities, for example, but you didn't respond to one of them.

I even asked you a direct question, whether you now conceded that 1/inf /= 0. You didn't even answer that. Perhaps we should just end this thread, I'm getting tired of this pattern. Sorry mate.

[JLW001]

The answer is yes, 1/infinity does equal zero. However, for the sake of argument I have said, let's suppose that its not. Then we go on and integrate the probability distribution and low and behold we get the indeterminant form. So, it doesn't matter whether you concede that 1/infinity=0.

Show me some math! Either put up or don't, so to speak.

[JLW001]

Oh, I'm sorry. I didn't realize that the comment about decimal numbers between 0 and 1 didn't contain all of the succinct information. What other points did you make. You were talking about continuous verses digital, right?

[JLW001]

SA, I apologize if I hurt your feelings, but all your long posts were simply rehashing a single point over and over. I think with a mathematical mind and math is nothing, if its not concise.

Now you must realize that the mathforums site has made my point for me. If infinity is just a concept, then you can't use it to talk about numerically counted things and deduce numerical answers from it. However, because of the good Mr. Canton, we have seen that if we apply logic to infinity, then we can use it as a mathematical tool. I defy you to find any math, science, engineering, or astronomy book (real book, not a book for the layperson) that does not have within it integrals whose limits contain at least one infinite term.

I do hope you haven't abandoned the thread and taken your "toys" to play somewhere else. If you can't find an answer that supports your argument, its not time to leave reason and say the answers are wrong, but its time to think about your argument.

[JLW001]

WhySoBlind, that's an interesting way of looking at relativity. It looks as though you are saying that the object must orbit the earth in a circle and have a period of one day. Most of the objects we see do not have circular orbits relative to our frame of reference and do not complete an orbit in one day. The planets have little jogs or switchbacks in their orbit from our frame of reference. That's why when Copernicus looked at things from a sun centric model that everything lined up in near circles. He saw the simplicity and harmonics of the orbits as the music of the heavens.

The only other thing I would say is that you must bring time into the picture. We can only see things out to what I'll call the time horizon. That means that when the universe was created at time t=0, then we can only see objects that are as many light years away as the age of the universe.

So, if a group of stars emitted light toward earth at t=0 and they were 4 billion light years away, that light wouldn't reach the earth until the universe was four billion years old. So there is indeed a time horizon in the universe. It also means that the universe could indeed be infinite, but we will never know (physically) because the light from some galaxies and supernova would never reach earth. This is all an artifact caused by the finite speed of light.

This all depends upon the speed of light remaining constant from the beginning of the universe. If it changed in any way in the past, then all of this and a bunch of other stuff goes out the window.

However, suppose there was a large galaxy 2 million light years from earth. Then an observer on earth would not see light from the galaxy until the earth was 2 million years old (if the earth and galaxy were created simultaneously). However, the earth would have been feeling the gravitational force of the galaxy for all those 2 million years. How about that!

But what about gravity? Einstein treated the propagation rate of gravity as the same as the speed of light in his equations. He intentionally did not open up the can of worms that is gravity. Now, if gravity propagates at a speed faster than the speed of light (which it does), then it does not change relativity very much because of the force of gravity becomes small very quickly as you move away from an object. As a matter of fact it is an inverse cubic relationship, 1/R^3. So, the propagation of gravity is important, but only affects relativity when you have relatively (no pun intended) small distances between massive objects. Like two galaxies in (relatively) close proximity.

However, gravity waves are another thing entirely. If the propagation rate of gravity turns out to be finite, then gravity waves could be an incredibly fast way of transmitting information. It could be 100s or 1000s of orders of magnitude faster than the speed of light. Talk about fast computers! But, you have to have incredibly sensitive setups to measure gravity waves and they would have to be deconvolved to find the specific source that you were interested in.

As far as I'm concerned, I believe that gravity has an infinite rate of propagation and this would limit the usefulness for transmitting information. However, it does paint a very different picture of our universe than what scientists currently have.

So, gravity, this thing that we depend upon and the thing that we feel every day is a mystery to us. It doesn't fit into our pegs of quanta. It might be an effect of some continuum, but we have not yet measured or created an idea as to what that continuum might be.

[Shane]

SA

Just curious, what is the point of you being on this board, ie. what is your purpose, goal, agenda?

I dont mean this disrespectfully but if you dont believe in a creator what is all this about?

[Gerioke]

remember when getting the caramel inside the caramilk bar was all the rage?

[Gerioke]

WhySoBlind,Mar 21 2005, 11:06 AM

That is painfully obvious. Satan uses this pawn to destroy the faith of the little lambs that wander into this forum.

WSB -

I respectfully disagree with your reasoning. Lambs will come into contact with godless ideas everywhere. Our atheist friends on this board present nothing new that one will not be subjected to elsewhere. Maybe it is better for these lambs to observe a balanced discussion where both sides are represented.

It is my understanding that we are all on this board because we are drawn by God. None are here by some random action. You may feel that our friends are here for sinister reasons. Our friends might think they are here to somehow shipwreck God's elect. But the truth is God has drawn SA here because God loves him just as he loves you. God can certainly protect his elect from those who wish them harm.