Some Retorts, Rendundancies, E=MC^2 and Talk on Dimensions
Looking back at some of my former essays, I found them quite brash and rather crude when I come to think of them. Some logic I find is still correct, while others are wrong, but not quite evident. For instance, my title, Why Infinity minus Two does not equal Infinity, isn't completely correct. Infinity minus two sometimes does equal infinity, especially in set theory.
{1, 2, 3...} Set of Infinite Elements
{1.5, 1.6} Set of Finite Elemnts (2 Elements, to be exact)
Add them together, and poof!
{1, 1.5, 1.6, 2, 3...} Set of Infinite Elements plus Set of Two Elements!
Of course, one argues that the first infinity is not the same as the second infinity, so obviously infinity can equal infinity, or it doesn't equal infinity. Which makes it all strange, because this means that infinity covers a wide range of infinities, so one label couldn't possibly cover them all. I think there was some famous mathematician who came up with this stunning revelation before, so I guess that this isn't all so suprising.
So, when I compared trying to add an abstract property to a physical property and infinity with a number, it works sometimes, and it doesn't work other times. What about this?
{1, 2, 3...} Set of infinite elements
{1.5} A set that has an element that isn't included in that infinite element set???
So of course, we have more mind boggling aspects. Now, time for some vocabulary.
Infinity can be defined several ways, such as the largest number that can be processed by machine or human, so infinity for a machine would be when its memory cache has been totally filled up. It can also mean the integer of greatest magnitude, which is impossible from our current point of understanding. When we discuss infinity, we have to remember that we aren't really talking about infinity. A computer that creates an endless loop, which theoretically is infinity, would be terminated when the system runs out of hard drive space. A person who thinks about infinity terminates the idea when he stops thinking of higher numbers.
But, when you say infinite, you could simply be meaning too great to be counted. In that case, the number of bytes stored across all computers in this world is infinite because there are too many to be counted. More abuse for the word infinity is with semi-infinite, which means half infinite, which obviously is correct and incorrect, since semi-infinite means very big.
In the next chapter, I propose that the 4th dimension is time, just like many famous science-fiction writers did in their day. I have now come to the conclusion that this is incorrect. Time is seperate from space because it goes in one direction, a ray, geometrically speaking.
---------------------------------------------------------------------
It does not exhibit the properties of a line, or a plane, or a cube. It always has to go in one direction, because that is the nature of cause and effect. Because our world is how we percieve things, and our human minds percieve time as traveling in one continuous direction, it would seem evident that according to repeated observation, time travels in one direction. Who can object to that?
Of course, since light, the way we percieve almost everything, does not travel at an infinite speed, events that happen away from else will reach us at different times then they actually happened. This overlaps into time, and thus people can argue what time an event happened, and they would be right. Both of them. So, technically, our line of time may not line up with the worlds. And this leads to the perception that we might go backwards against the worlds time line. BUT THE FACT STILL REMAINS: Your time line cannot be set back, but you can go back to the time before the time you were living in... However, this time acts as a static image, and doesn't affect you, cause your timeline cannot be traversed.
If this indeed is true, then time travel is a possibility, and we would not have to worry about you going back in time and killing your grandfather, because in your time, your grandparents gave birth to your parents, and that is etched in history and unchangeable.
This also suggests that the Many-Worlds theory is correct, because the world time line then would be able to deviate from the course that you came from, even though your time line doesn't change. It works like this:
YOUR BORN -- YOU LIVE -- YOU GO BACK IN TIME -- YOU KILL YOUR PARENT
Even though you killed your parent, you being born in your conciousness is still there, you did not go back and erase that, and your time line still goes in a straight line. You cannot undo the past, but you can change the past. Strange, but that's probably the way the world works.
Then, seperate from time is space, and that's the three dimensions. We live in a 3-D world, and in order to theorize 2-D and 1-D images we have to stretch our imagination. But there is one thing that really riles me, the statement:
"A line is infinitely thin"
Now, you look at that statement, and say to yourself, "Is that right?" If you said, "Yes! It is right?" Then you are wrong. Let me explain.
In an earlier chapter, I prove that .999 = 1. This means that infinitely close to a number is that number. What are the implications of this? Well, let's reword the earlier statement into:
"A line's thinness is infinitely close to 0"
Which means:
"A line's thinness is 0"
Which means:
"The line does not exist"
Wha! How did that happen? Of course lines exist! So, the correct definition is:
"A line's width is null"
Notice the "Null" instead of "Zero". Any math teacher will tell you, especially when you're dealing with answer sets, that saying x={0} and x=NULL are two completely different things. x equals the solution set of 0, which is one element large. x = null means that the solution set has zero elements, and thus is an empty set. What are other common misuses of infinity?
THE BIG BANG THEORY
"The entire universe was condensed in an infinitely small point of infinite density at the very beginning."
WHOA! By saying that the point was infinitely small, you are saying this point doesn't exist. Next, since it has an infinite density, then either the point is nonexistant, which is not true, or there is infinite matter in the universe, which also isn't true if the universe is finite. In addition, if space truly is a property of this universe, then the universe couldn't be small in any sort of sense.
PLANE
"A plane in mathematics is infinitely thin."
Next!
BLACK HOLE
"At the event horizon the black hole becomes infinitely dense."
Oh! Is that so? Then either this black hole has a volume of zero, or infinite mass. Is that so? I don't think so!
There you have it. Common misconceptions about the word infinity. Next time, we will be talking about whether or not infinity exists in the real world.
C'est moi! Au revoir!
DISCLAIMER: The quotes presented here do not necessarily represent the views of competent/professional scientists but are renditions of commonly quoted "false" facts.
Looking back at some of my former essays, I found them quite brash and rather crude when I come to think of them. Some logic I find is still correct, while others are wrong, but not quite evident. For instance, my title, Why Infinity minus Two does not equal Infinity, isn't completely correct. Infinity minus two sometimes does equal infinity, especially in set theory.
{1, 2, 3...} Set of Infinite Elements
{1.5, 1.6} Set of Finite Elemnts (2 Elements, to be exact)
Add them together, and poof!
{1, 1.5, 1.6, 2, 3...} Set of Infinite Elements plus Set of Two Elements!
Of course, one argues that the first infinity is not the same as the second infinity, so obviously infinity can equal infinity, or it doesn't equal infinity. Which makes it all strange, because this means that infinity covers a wide range of infinities, so one label couldn't possibly cover them all. I think there was some famous mathematician who came up with this stunning revelation before, so I guess that this isn't all so suprising.
So, when I compared trying to add an abstract property to a physical property and infinity with a number, it works sometimes, and it doesn't work other times. What about this?
{1, 2, 3...} Set of infinite elements
{1.5} A set that has an element that isn't included in that infinite element set???
So of course, we have more mind boggling aspects. Now, time for some vocabulary.
Infinity can be defined several ways, such as the largest number that can be processed by machine or human, so infinity for a machine would be when its memory cache has been totally filled up. It can also mean the integer of greatest magnitude, which is impossible from our current point of understanding. When we discuss infinity, we have to remember that we aren't really talking about infinity. A computer that creates an endless loop, which theoretically is infinity, would be terminated when the system runs out of hard drive space. A person who thinks about infinity terminates the idea when he stops thinking of higher numbers.
But, when you say infinite, you could simply be meaning too great to be counted. In that case, the number of bytes stored across all computers in this world is infinite because there are too many to be counted. More abuse for the word infinity is with semi-infinite, which means half infinite, which obviously is correct and incorrect, since semi-infinite means very big.
In the next chapter, I propose that the 4th dimension is time, just like many famous science-fiction writers did in their day. I have now come to the conclusion that this is incorrect. Time is seperate from space because it goes in one direction, a ray, geometrically speaking.
---------------------------------------------------------------------
It does not exhibit the properties of a line, or a plane, or a cube. It always has to go in one direction, because that is the nature of cause and effect. Because our world is how we percieve things, and our human minds percieve time as traveling in one continuous direction, it would seem evident that according to repeated observation, time travels in one direction. Who can object to that?
Of course, since light, the way we percieve almost everything, does not travel at an infinite speed, events that happen away from else will reach us at different times then they actually happened. This overlaps into time, and thus people can argue what time an event happened, and they would be right. Both of them. So, technically, our line of time may not line up with the worlds. And this leads to the perception that we might go backwards against the worlds time line. BUT THE FACT STILL REMAINS: Your time line cannot be set back, but you can go back to the time before the time you were living in... However, this time acts as a static image, and doesn't affect you, cause your timeline cannot be traversed.
If this indeed is true, then time travel is a possibility, and we would not have to worry about you going back in time and killing your grandfather, because in your time, your grandparents gave birth to your parents, and that is etched in history and unchangeable.
This also suggests that the Many-Worlds theory is correct, because the world time line then would be able to deviate from the course that you came from, even though your time line doesn't change. It works like this:
YOUR BORN -- YOU LIVE -- YOU GO BACK IN TIME -- YOU KILL YOUR PARENT
Even though you killed your parent, you being born in your conciousness is still there, you did not go back and erase that, and your time line still goes in a straight line. You cannot undo the past, but you can change the past. Strange, but that's probably the way the world works.
Then, seperate from time is space, and that's the three dimensions. We live in a 3-D world, and in order to theorize 2-D and 1-D images we have to stretch our imagination. But there is one thing that really riles me, the statement:
"A line is infinitely thin"
Now, you look at that statement, and say to yourself, "Is that right?" If you said, "Yes! It is right?" Then you are wrong. Let me explain.
In an earlier chapter, I prove that .999 = 1. This means that infinitely close to a number is that number. What are the implications of this? Well, let's reword the earlier statement into:
"A line's thinness is infinitely close to 0"
Which means:
"A line's thinness is 0"
Which means:
"The line does not exist"
Wha! How did that happen? Of course lines exist! So, the correct definition is:
"A line's width is null"
Notice the "Null" instead of "Zero". Any math teacher will tell you, especially when you're dealing with answer sets, that saying x={0} and x=NULL are two completely different things. x equals the solution set of 0, which is one element large. x = null means that the solution set has zero elements, and thus is an empty set. What are other common misuses of infinity?
THE BIG BANG THEORY
"The entire universe was condensed in an infinitely small point of infinite density at the very beginning."
WHOA! By saying that the point was infinitely small, you are saying this point doesn't exist. Next, since it has an infinite density, then either the point is nonexistant, which is not true, or there is infinite matter in the universe, which also isn't true if the universe is finite. In addition, if space truly is a property of this universe, then the universe couldn't be small in any sort of sense.
PLANE
"A plane in mathematics is infinitely thin."
Next!
BLACK HOLE
"At the event horizon the black hole becomes infinitely dense."
Oh! Is that so? Then either this black hole has a volume of zero, or infinite mass. Is that so? I don't think so!
There you have it. Common misconceptions about the word infinity. Next time, we will be talking about whether or not infinity exists in the real world.
C'est moi! Au revoir!
DISCLAIMER: The quotes presented here do not necessarily represent the views of competent/professional scientists but are renditions of commonly quoted "false" facts.