Next he showed an example of what he called a non countable infinity. His example was the set of real numbers from 0 out to infinity, which includes all of the irrational numbers, things like fractions, and decimals. He asserted that this was a non countable infinity simply because there was an infinite possible amount of irrational numbers between each whole number. If you started at zero, no matter how long you counted for, you would never ever even make it to the number one.
Actually, I agreed with him about this one. This was an example of it being impossible to count to infinity. But, my original assertion was that it was not possible to count to infinity at all. And he never did anything to prove or disprove that. He totally ignored it and just said that the "normal" infinity had been redefined by mathematicians as countable.
As far as grammar and word usage actually goes, his first example basically defined countable infinity by saying it was simply infinity. He might as well have defined a chair by saying that a chair is a thing that you use for a chair. Then he went on, for his second example, to say because this infinity has an infinite amount of infinities within it, it cannot be counted.
I pretty much told him so and at this point he began to get frustrated. He then proceeded to make several disparaging remarks about how I was not a mathematician and as such was more or less not equipped to understand. The sad fact is, I did understand. I just completely disagreed.
Regardless of whether or not one mathematician or a million tells me that there is an infinity that can be counted to, it does not change the fact that the very definition of the word infinity proves their assertion to be false. All infinities are limitless. None of them can ever be counted, whether there are an infinite amount of infinities nested within them or not.
The only difference between the first and the second example he provided to me is that on one of them you would be making progress in whole numbers and on the other you would never reach the next whole number. With both you would die thousands of years before even making a small dent in the work of reaching towards the far end of the endless stream of numbers. I did not disagree with him that they were different. I just disagreed that either one could be counted.
My primary beef with the conversation wasn't his fault at all. Well it sort of was but not really. The problem I had with what he was saying was the nomenclature being used. Now he did not come up with the jargon that he was using. But he did choose to use it around people that were not mathematicians. And even though the jargon chosen for this particular thing was actually completely ridiculous to the lay person, he did nothing to fight against it or to attempt to change it.
I can sort of understand him not wanting to argue semantics with the people teaching him, sort of. But when speaking to people that know nothing of math, using mathematical terms that directly disagree with common grammatical practices without precluding his statements with something to the effect that he realizes that the choice of jargon flies in the face of what the individual words actually mean was stupid. And it made him look like an idiot to every other person in the room. He isn't though. He is one of the smartest people I know.
This whole argument/debate could have been completely avoided. He could have said there is the normal infinity that everyone knows about including all the whole numbers from 0 to infinity. Next he could have talked about the infinity that includes both sides of the number line, positive and negative whole numbers from 0 to infinity. He could have described this as the integer infinity. He could have applied the adjective rational to both of these to show that they included only whole numbers. And finally he could have said that if either of them included fractions or decimals that the the adjective irrational would be applied instead of rational.
I am not a mathematician. I am a philosopher. Words are my tools and my weapons. There may be and probably are more infinities but simply mentioning these in this fashion would not have caused an argument. Mathematicians are very often brilliant people. Many of the things they have done have massively improved life for the rest of us. But when it comes to naming conventions for the new things that they discover, they are either idiots or so blinded be their current discovery that they just latch on to whatever seems appropriate at the time and stick with it as the "new" name for a thing and logic be damned.
He was arguing math. I was debating logic. Who was crazy? Who was right? Who is to say?
Showing posts with label numbers. Show all posts
Showing posts with label numbers. Show all posts
Saturday, May 31, 2014
Counting to infinity pt1
Time is not a real object. It is simply a concept that we made up to differentiate the passing of days. Events in our lives happen sequentially. They do not happen to us all at once. Time and the different markers that we have chosen for it such as hours, decades and seconds are not real. They are just ways of making it possible to describe what came before, what came after and how to decide where to place things when describing the story of our lives.
Numbers are the same way. Although we can make physical objects that represent the different numbers, numbers themselves are concepts. A tree would still be a tree regardless of what we chose to call it. As would a fish a fish and a bird a bird. These things are real and tangible.
We, as a society, place definitions on things that describe exactly what they are. We define them so that we do not need to completely explain every detail about each thing to each person that we encounter every time we want to talk about that thing.
But, life is seldom black and white. There are so many grey areas. Those that fight against the establishment often think of themselves as revolutionaries fighting to make the world a better place. The people that they fight against often call them terrorists or murderers. History, or in other words, the story that is told, is decided by the winning side. Who is right and who is wrong? Well technically, both are both.
People that disagree with what society chooses to call a thing are generally thought to be having a psychotic break with reality. By definition when society does things one way and a person chooses to do things another way that other person is either labeled wrong or insane. I mean think about it. If I call a tree what everybody else calls broccoli, I'd be insane right? Or how about if I called daylight a bunch of bananas? And does it really matter if it was one person or a whole group of people that thought this way? How does it work when these people call their terminology for the redefined things lingo or jargon? Are they still insane?
This brings me to a story that happened recently. We had a guest over for a couple of days. He is someone who is a good friend of ours whom I have known for over fifteen years. We don't always see eye to eye though.
He is a math major who actually intends to spend most of his life studying and teaching advanced mathematics. My interests are more along the lines of English and philosophy. Knowing these two things the disagreement we got into should be a surprise to nobody. I say disagreement because, to him I am sure, we were arguing. To me we were debating.
Somehow, the subject of infinity came up. He was saying that there were multiple different types of infinity. We all just nodded and smiled. The lay person knows that there is only one infinity and that it is infinite. And that is all we need to know. Mathematicians however know that the rest of us are wrong. And he proceeded to tell me so in so many words.
Mistake number one. Never ever tell another person to their face that they are wrong, especially in public, unless you are actually grading work that they have done. Even then it should only be done with extreme diplomacy and tact. Do not just smack other people in the face with what you know to be facts. If you do, even if what you are saying is as plain as the nose on your face, they will not agree with you. In many cases, you will make an enemy for life and all you will have gotten out of it is the satisfaction of showing your intellect to be superior to that of the other person. In other words, you may lose friends in exchange for a mild boost to your ego.
We are both kind of hardheaded and both actually may have violated this rule. He began by saying that there is the regular infinity that everyone is aware of and that mathematicians call it the countable infinity. I of course stopped him there by pointing out that the definition of infinity is a concept describing something that has no ending and therefore applying the adjective countable to it was a logical fallacy. He more or less ignored my statement and went on to state that there were then several types of infinity that were labeled as not countable.
He provided an example of a countable infinity as the set of whole numbers. You know like 0,1,2,3,4 and so on out to infinity. I challenged him to count to infinity. Even though I sat back and offered to wait while he did so, even though I offered him the opportunity to show me that it was countable, he declined.
Numbers are the same way. Although we can make physical objects that represent the different numbers, numbers themselves are concepts. A tree would still be a tree regardless of what we chose to call it. As would a fish a fish and a bird a bird. These things are real and tangible.
We, as a society, place definitions on things that describe exactly what they are. We define them so that we do not need to completely explain every detail about each thing to each person that we encounter every time we want to talk about that thing.
But, life is seldom black and white. There are so many grey areas. Those that fight against the establishment often think of themselves as revolutionaries fighting to make the world a better place. The people that they fight against often call them terrorists or murderers. History, or in other words, the story that is told, is decided by the winning side. Who is right and who is wrong? Well technically, both are both.
People that disagree with what society chooses to call a thing are generally thought to be having a psychotic break with reality. By definition when society does things one way and a person chooses to do things another way that other person is either labeled wrong or insane. I mean think about it. If I call a tree what everybody else calls broccoli, I'd be insane right? Or how about if I called daylight a bunch of bananas? And does it really matter if it was one person or a whole group of people that thought this way? How does it work when these people call their terminology for the redefined things lingo or jargon? Are they still insane?
This brings me to a story that happened recently. We had a guest over for a couple of days. He is someone who is a good friend of ours whom I have known for over fifteen years. We don't always see eye to eye though.
He is a math major who actually intends to spend most of his life studying and teaching advanced mathematics. My interests are more along the lines of English and philosophy. Knowing these two things the disagreement we got into should be a surprise to nobody. I say disagreement because, to him I am sure, we were arguing. To me we were debating.
Somehow, the subject of infinity came up. He was saying that there were multiple different types of infinity. We all just nodded and smiled. The lay person knows that there is only one infinity and that it is infinite. And that is all we need to know. Mathematicians however know that the rest of us are wrong. And he proceeded to tell me so in so many words.
Mistake number one. Never ever tell another person to their face that they are wrong, especially in public, unless you are actually grading work that they have done. Even then it should only be done with extreme diplomacy and tact. Do not just smack other people in the face with what you know to be facts. If you do, even if what you are saying is as plain as the nose on your face, they will not agree with you. In many cases, you will make an enemy for life and all you will have gotten out of it is the satisfaction of showing your intellect to be superior to that of the other person. In other words, you may lose friends in exchange for a mild boost to your ego.
We are both kind of hardheaded and both actually may have violated this rule. He began by saying that there is the regular infinity that everyone is aware of and that mathematicians call it the countable infinity. I of course stopped him there by pointing out that the definition of infinity is a concept describing something that has no ending and therefore applying the adjective countable to it was a logical fallacy. He more or less ignored my statement and went on to state that there were then several types of infinity that were labeled as not countable.
He provided an example of a countable infinity as the set of whole numbers. You know like 0,1,2,3,4 and so on out to infinity. I challenged him to count to infinity. Even though I sat back and offered to wait while he did so, even though I offered him the opportunity to show me that it was countable, he declined.
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