Infinity: A Dialogue
中国伊朗亚洲杯比赛直播

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.

乔:但是等一下——你只是告诉我无限不是什么。这并没有告诉我任何关于它的积极和确定的事情。假设我让你定义绿色。你说绿色不是红色，不是蓝色，不是橙色，等等，你能想到的所有其他颜色。这能告诉我很多绿色不是什么。但它并不能告诉我什么是绿色。我不想知道无穷不是什么。我想知道那是什么。我想要一个具体的定义来帮助我在遇到无穷时识别它。

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:嗯，把你的颜色类比应用到数字上。如果我们听你的，我们会这样定义无穷。无限是比你能想到的任何有限数都大的数。无穷不是1，不是2，不是87，甚至不是一百万。它是什么?它不是有限数中的任何一个而且比它们中的任何一个都大。

乔:但是这个定义比我对绿色的负面定义更糟糕，不是吗?只有那么多颜色。所以你可以把剩下的都挑出来，然后说绿色的是缺失的。当你发现一种颜色不是你已经知道的颜色时。你可以说，“啊，在那儿!这是最初名单上没有的。所以必须是绿色的。”但对于无穷和数字，你不能这样做，因为你永远不会用完数字。你永远都打不到倒数第二个数字。

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:问问自己有多少个数字。

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?

乔:无穷?

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:你不能这么说，因为无穷实际上有不同的大小——有些大一些，有些小一些!据我们所知，没有“最大”的无穷大。想想有理数和实数。有无穷多个有理数和无穷多个实数。但你知道吗，实数比有理数多得多。

乔:等一下!等一下!东西是不正确的。你刚刚说过，你不能通过乘以∞来增加∞，也不能通过除以∞来减少∞。那么为什么会有不同大小的无限呢?

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's picture

Guest

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

Mathematicians handle infinity by decreeing that i

数学家处理无穷时，判定它不是一个数字，因此试图用它来做算术是无效的。?一个像警察搭档也许如此。

Guest's picture

Guest

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

丹,伟大的对话! !Just like on the radio

Dan,
Great conversation!!! Just like on the radio! :)
Dawn

Guest's picture

Guest

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

Nature or the universe is infinitely boundless and

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

Guest's picture

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's picture

Guest

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

Science explains all things. Creationism is not fo

Science 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's picture

Guest

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

If space is infinite, then why cannot the earth be

如果空间是无限的，那么为什么我们不能把地球当作它的中心呢?

Guest's picture

Guest

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

I've also pondered still ponders about it. I've co

I'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's picture

Guest

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

Dang, what a bunch of silliness all over the place

Dang, 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).
这种无限性和(或)绝对性由于没有别的对立面，就具有无比较/无可比拟的性质，如无双/无双，因而是完美的(完全自在、完美、终极)。
这真是太棒了。
作为完美，这种无限和/或绝对性具有无可挑剔的品质(品质是属性的内在属性)，如无可挑剔的/完美的，因此是纯粹的/原始的。
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's picture

Guest

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

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

Space 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's picture

Guest

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

Inifinite东西。Ran out room in previous comm

Inifinite东西。
在之前的评论中已经没有空间了。
Who cares about infinity as it may relate to us ( mathematics ) ?
cb

Guest's picture

Guest

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

I felt my mind cave in last night as I looked at t

昨晚，当我看着星星，试图想象无限的宇宙时，我感到自己的思想陷入了沉思。It's impossible

Guest's picture

Guest

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

无限这个词与时间有关。Without t

无限这个词与时间有关。没有时间，就不需要无限的概念。如果你相信上帝创造了包括时间在内的一切，那么上帝就在时间之外，这是我们最终会理解的。现在我们就像中国的一句谚语说的，如果你想知道水是什么，不要问鱼!

Guest's picture

Guest

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

After reading the Joe/Blow dialogue and the ensuin

在阅读了Joe/Blow的对话和随后的评论列表后，我有几个OEOs(意见，经验和观察)可以提供给你。首先，Joe和Blow似乎已经读过Douglas Hofstadter、Daniel C. Dennett和其他一些人的书，并将他们铭记于心。一切都很好，听不见。但是，作为一个有趣、沮丧或痛苦的主题，无限并不是那么引人注目。没错，它可能会给物理学家和数学家带来很多值得思考和反思的东西，而且可能会帮助超导和纳米技术等令人难以置信的研究。但对我们大多数人来说，这充其量只是次要的。
我喜欢Truax的评论，超过了大多数其他的评论，正如所说的，无限在某些思想圈子里是重要的。然而，就我个人而言，我对它不能太激动。我认为不确定性对我们大多数人的影响更大。无限和不确定性是相互关联的，还是仅仅是并肩前行的?如果存在关系，我们会用这些知识做什么?可能没有那么多。不过，这可能是另一个问题。
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's picture

Harold G. Neuman

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

And then there is always Kurt Godel---(I don't kno

And 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.