##### Infinity

Feb 24, 2008Infinity is a puzzling concept. Mathematicians say there are as many odd numbers as there are numbers altogether.

Infinity: A Dialogue

05 March 2010

Joe: I’m not sure I agree with you Blow in denying that nature contains the infinite. But to settle this, why don’t we start out by defining infinity.

Blow: That’s a piece of cake. The infinite is that which is not finite.

Joe: But wait a second – you've only told me what infinity is not. That doesn’t tell me anything positive and definite about it. Suppose I ask you to define the color green. And you said green is the color that is not red, and not blue, and not orange and so on for every other color you can think of. That would tell me a lot about what green is not. But it doesn’t tell me much about what green is. I don’t want to know what infinity is not. I want to know what it is. I want a concrete definition to help me recognize infinity when I come across it.

BLOW: I hate to tell you Joe, but you’re not very likely to come across infinity. Every number you’ve ever counted to has been finite. Every extent of space you’ve ever crossed has been finite. And every span of time you’ve ever experienced has been finite too.

JOE: Okay, what’s your point?

BLOW: Well, take your color analogy and apply it to the case of number. If we followed your lead, we would define infinity like this. Infinity is the number that is larger than any finite number you can think of. Infinity is not 1, not 2, not 87, not even a million. What is it? It’s precisely the number that is not any of the finite numbers and is larger than every one of them.

JOE: But that definition is even worse than my negative definition of green, isn’t it? There are only so many colors. So you could pick out all but one and say green is the missing one. And when you came across a color that wasn’t any of the ones you already know. You could say, “Ah, there it is! That’s the one that wasn’t on the original list. So that must be green.” But you can’t do that with infinity and the numbers, because you never run out of numbers. You never get to the next-to-last number.

BLOW: In spite of yourself, Joe, you’re starting to get it. You’re starting to understand the concept of infinity.

JOE: What do you mean? I’m more confused than ever.

BLOW: Well, ask yourself how many numbers there are.

JOE: Lots. There are lots and lots of numbers.

BLOW: There’s more than a lot of numbers. There is an infinite number of numbers. And what shows this is the very fact that you cannot exhaust them by running through them “one-by-one.” Just try. I’ll give you as much time as you want to do it.

JOE: That reminds me of a little story. A friend of mine had a son who was four at the time. And he asked his mommy, “Mommy how old are you?” And I say, “Tommy, think of the biggest number you can think of. That’s how old your mommy is.” And Tommy got a wide-eyed look in his eyes and said, “Mommy, are you 17?” And I said, “Tommy, is 17 really the biggest number you can think of? What if you added one to 17. Would you get a number bigger than 17?” And Tommy, said, “Oh! So Mommy, are you 100?” And I said, “Is that really the biggest number you can think of, Tommy? What if you added one to 100? What would you get?” By now Tommy seemed to realize that we could keep playing this game. So he said, really rapidly, ”Mommy, you must be a zillion trillion billion million, billion trillion.”

BLOW: Poor Tommy. That was kind of a mean trick to play on a 4 year old kid. But you almost got him to grasp the idea of infinity by getting him to see that he could not exhaust the numbers.

JOE: So are you equating infinity with sheer “inexhaustibility?” Is that your positive and definite definition of the infinite – something you can't run out of?

BLOW: No, I wouldn’t equate infinity with inexhaustibility. That’s just one of the properties of the infinite. But infinity has lots of other cool properties.

JOE: Like what?

BLOW: For example, if you take half of infinity, you get infinity again. If you double infinity you get – guess what?

JOE: Infinity again?

BLOW Right. So there’s something else positive and definite to say about infinity. Infinity is that amount which you can’t decrease through division and can’t increase through multiplication.

JOE: If you can’t increase infinity through multiplication, that means that infinity is that which there is nothing greater than, right?

BLOW: You can’t quite say that, because infinities actually come in different sizes – some larger, some smaller! And as far as we know, there is no “largest” infinity. Think of the rational numbers and the real numbers. There are an infinite number of rationals and an infinite number of reals. But you know what, there are a lot more real numbers than rational numbers.

JOE: Wait a minute! Wait a minute! Something's not right. You just said you can’t increase infinity by multiplying it and can’t decrease it by dividing it. So how can there be different sizes of infinity?

BLOW: I’m afraid I’m going to have to keep you hanging there, Joe, cause I gotta go run and catch Philosophy Talk. Why don’t you come along? Maybe you’ll learn something about the infinite.

## Comments (15)

## Guest

Friday, March 5, 2010 -- 4:00 PM

Mathematicians handle infinity by decreeing that iMathematicians handle infinity by decreeing that it's not a number, therefore it's invalid to try to do arithmetic with it. A copout? Perhaps so.

## Guest

Monday, March 8, 2010 -- 4:00 PM

Dan, Great conversation!!! Just like on the radioDan,

Great conversation!!! Just like on the radio! :)

Dawn

## Guest

Monday, March 8, 2010 -- 4:00 PM

Nature or the universe is infinitely boundless andNature or the universe is infinitely boundless and immeasurable, yet I find myself measuring it, and confined by it.

=

MJA

## Guest

Thursday, March 11, 2010 -- 4:00 PM

Dan said: "Mathematicians handle infinity by decreDan said:

"Mathematicians handle infinity by decreeing that it's not a number, therefore it's invalid to try to do arithmetic with it. A copout? Perhaps so."

I say: http://en.wikipedia.org/wiki/Cardinal_number#Cardinal_arithmetic

## Guest

Sunday, March 14, 2010 -- 5:00 PM

If space is infinite, isn't its center arbitrary?If space is infinite, isn't its center arbitrary?

## Guest

Friday, March 19, 2010 -- 5:00 PM

Science explains all things. Creationism is not foScience explains all things. Creationism is not for lazy thinkers.All things on Earth MUST be explained.

BLOW was trying to comfort Joe from his thoughts and likewise.

## Guest

Monday, March 22, 2010 -- 5:00 PM

If space is infinite, then why cannot the earth beIf space is infinite, then why cannot the earth be considered its center by us if we so choose?

## Guest

Monday, March 22, 2010 -- 5:00 PM

I've also pondered still ponders about it. I've coI've also pondered still ponders about it. I've come to conclusion that there are 3 dimensions (infinite, finite, subfinite) only if we consider we place our self in a decimal point in space just for initial placement purpose! Doing so.. we can say we're at the "finite" existence because we can make applications for substance within the realm of our 6 senses 1.touch, sight, smell, hear, taste, and think. True we can say probability there are other living conscious in this finite existence perhaps capable of more than 1000 senses but let's focus on humans. Consider infinity as endless area of space and humans are among one of the creatures living in it. Even though we are conscious and want to understand, we're no different from fishes swimming in the ocean. Human senses provides us our purpose to understand that which is understandable to us, this process is what we call philosophy to science to numbers or (finite calculations) although science and numbers are limited to forms, Philosophy doesn't limit out imagination, but still our imaginations is within the realm of a fish swimming in water.

## Guest

Sunday, April 11, 2010 -- 5:00 PM

Dang, what a bunch of silliness all over the placeDang, what a bunch of silliness all over the place.

Infinity, when directly experienced, is quite simple and the properties, values and qualities of it are staggeringly obvious in their magnificence. Take a few moments to read about what one human has taken the time to elucidate about his experience of what I am alluding to.

http://actualfreedom.com.au/library/topics/infinitude.htm

http://actualfreedom.com.au/richard/selectedcorrespondence/sc-infinitude...

Below is a snippet from the above links.

Regards,

Trent

"The fundament characteristic, or nature, of the universe is its infinitude ? specifically having the properties of being spatially infinite and temporally eternal and materially perdurable ? or, to put that another way, its absoluteness ... as such it is a veritable perpetuus mobilis (as in being self-existent/ non-dependent and/or self-reliant/ non-contingent and/or self-sufficient/unconditional and/or self-generating/ unsupported).

Having no other/no opposite this infinitude and/or absoluteness has the property of being without compare/incomparable, as in peerless/matchless, and is thus perfect (complete-in-itself, consummate, ultimate).

And this is truly wonderful to behold.

Being perfect this infinitude and/or absoluteness has the qualities (qualia are intrinsic to properties) of being flawless/faultless, as in impeccable/immaculate, and is thus pure/ pristine.

And which is indubitably a marvellous state of affairs.

Inherent to such perfection, such purity, are the values (properties plus qualities equals values) of benignity ? ?of a thing: favourable, propitious, salutary? (Oxford Dictionary) ? and benevolence (as in being well-disposed, beneficent, bounteous, and so on) ... and which are values in the sense of ?the quality of a thing considered in respect of its ability to serve a specified purpose or cause an effect? (Oxford Dictionary)."

## Guest

Monday, May 17, 2010 -- 5:00 PM

Space is infinite. Time is infinite. God ( the tSpace is infinite.

Time is infinite.

God ( the thing that IS creation -- not a he or him )

is infinite.

What else ??

If and when the "big bang" occured which "big bang" was it and in what part of space did it occur? How many "big bangs" have there been? Was there an initial "big bang" ( how myopic is that )?

If you arrived at the end of space what was it that stopped you -- what was the thing that stopped you -- was it a wall -- if it was a wall ( awfully big wall ) what was the wall made of ( is this a stupid conversation or what? Of course space is infinite!!!

## Guest

Monday, May 17, 2010 -- 5:00 PM

Inifinite things. Ran out room in previous commInifinite things.

Ran out room in previous comment.

Who cares about infinity as it may relate to us ( mathematics ) ?

cb

## Guest

Tuesday, August 31, 2010 -- 5:00 PM

I felt my mind cave in last night as I looked at tI felt my mind cave in last night as I looked at the stars and tried to imagine the infinite universe. It's impossible

## Guest

Friday, October 15, 2010 -- 5:00 PM

Infinity is a word associated with time. Without tInfinity is a word associated with time. Without time there would be no need for the concept of infinity. If you believe that god created everything including time, then god is outside of time which is where we will finally understand. As of now we are like the old chinese proverb which says if you want to know what water is, don't ask the fish!!!

## Guest

Friday, October 15, 2010 -- 5:00 PM

After reading the Joe/Blow dialogue and the ensuinAfter reading the Joe/Blow dialogue and the ensuing list of comments, I have several OEOs (Opinions, Experiences and Observations) to offer. First of all, it appears that Joe and Blow have read and taken to heart Douglas Hofstadter, Daniel C. Dennett and some others. All well and good and laudible. But, as a subject of interest, dismay or distress, infinity just isn't all that compelling. True, it may give physicists and mathematicians much to ponder and ruminate and has probably assisted such mind-boggling research as superconductivity and nanotechnology. But for most of us, it is peripheral at best.

I liked the Truax comments, above most of the rest, and as stated, infinity is important in some circles of thought. Personally, however, I cannot get too worked up over it. Uncertainty has more impact upon most of us I think. Are infinity and uncertainty related to each other or are they simply coasting along, side-by-side? If there is a relationship, what would we do with that knowledge? Probably not much. Could be another discussion, though.

My advice is: don't lose sleep over any of this. Not unless you are a physicist---or mathematician. Working on anti-gravity or some such. If so, good luck with that.

## Harold G. Neuman

Friday, October 15, 2010 -- 5:00 PM

And then there is always Kurt Godel---(I don't knoAnd then there is always Kurt Godel---(I don't know how to do the two dots over the o thingy.) When I think of the concept of infinity, I am reminded of the mobius strip which we were shown in high school physics class. It was an interesting exercise, but I was lousy in physics and have not, to this day, found a practical use for a mobius strip.