h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

http://www.bbc.co.uk/h2g2/guide/A536384

It's a sort of Q&A thing about infinity. I think infinity is quite an interesting subject, and hopefully it's not too boring to read. If you see anything that could improve this entry, please tell me.

w85

http://www.bbc.co.uk/h2g2/guide/A536384

Definitely an interesting read. It doesn't really explain infinity but it is quite a fun teaser for anyone with a little prior knowledge on the subject. There exist quite a few mathematical teasers on the subject, and they help explain what infinity means, although i understand your reluctance to touch that side of it. Definitely a fun subject to talk about. I also prefer the way you presented things, using fun questions rather than a long explanation of infinity...

Hello,

One thing I've noticed is that there seems to be an almost infinite selection of articles on infinity (well, if we count 1, 2, 3, infinity):

http://www.bbc.co.uk/h2g2/guide/A495371 (the one you ref)
http://www.bbc.co.uk/h2g2/guide/A294482
http://www.bbc.co.uk/h2g2/guide/A414523
http://www.bbc.co.uk/h2g2/guide/A488577

I guess it shows that people here think big, but I just feel like mentioning it, in case people want to read even more about infinity.

Yours,
Jake

This seems a little too vague and pseudosciency to me - most of the questions don't seem well defined, and the answers look to me like opinions. There is plenty that can be said about infinity in a mathematical sense, none of which makes your head explode, and doesn;t require piles of equations either. Its really a maths concept rather than a physics concept, and I think it needs to be dealt with in that way.

I did try to put in a couple of extra questions, but I found it was quite difficult. On this point I agree with you. I'm not sure I found the entry as vague as you did, though. Infinity is a pretty vague subject, and I'm sure the questions are meant to be more interesting, than informative.

Yes, the answers may be opinionated. However, most of them do seem pretty likely to be correct, no? As I mentioned in the entry, not everyone understands (or bothers to read) equations.
Finally, I only said that the sensation of understanding/experiencing infinity would be bad. In the Hitchhikers Guide to the Galaxy, on can be put in the "total perspective vortex". When inside the vortex, you see the infinity of the universe in comparison to yourself. That's sort of what I meant.

I'll make that point clearer. Thanks for your opinion, but please try to find at least something you like before you critisize an entry (e.g. Nice picture!)

w85

This is probably because I'm a mathmo - to me infinity isn't a vague concept at all, mathematicians use the concept of it all the time. Maybe we're talking about different things but calling both of them infinity. I'm thinking of infinite sequences of numbers and things like that, maybe you're talking about something else - travelling at infinite speeds etc, which to me is pretty much meaningless. It is meaningful to talk about going faster and faster, ignoring relativity, but thats not the same as going at infinite speed.

About the questions - a shape without borders is not a contradiction in terms. Here's a bad example: you could be standing on an infinte plane, at the shore of an infinite ocean covering 'half' of the plane. The ocean is infinite, but it still has an edge, and in a sense a shape also - its certainly a different shape from the whole infinite plane, which doesn't have an edge. Theres plenty of infinitely large things that don't have the same shape. The infinity sign (8 on side) is one way to write infinity, but there are others, in fact theres whole notations for dealing with different sizes of infinity.

"Is anything truly finite?" What does this mean? "Does it occupy a finite volume of space?"? Well most things do I guess. But from how you answer the question, I'm not sure thats the interpretation you mean.

"Can you wrap something around something thats infinite?" Again I don't really know what you mean. And your answer seems to contradict itself - first you say you can, then you say its impossible (and pointless).

"If you have infinite speed, how long will it take you to cross infinite space? " Well if you're talking Newtonian physics then theres not enough information, thats infinity/infinity which can be anything. With relativity the whole question doesn't work because you can't travel faster than light speed. Would you acheive time travel? No idea.

"Can an infinite amount of water fill a cup of infinite size?" If the cup is the universe, where is all the water coming from? It depends on how fast you're adding water to your cup. If you have an infinite amount of spouts all filling the cup at once (say one for each litre of space in the cup) then it wouldn't take forever.

"If something were infinitely small, would it really exist? " electrons (as far as we can tell, as far as I know) have no size and act like points (hmm, I don't know enough quantum mechanics to know how the quantum smudginess of things fits in here), and they exist.

You could claim that I (and other mathmos) aren't really 'understanding' or 'experiencing' infinity at all. You could be right, if the infinity you're talking about is a different one to the one I am. But I don't know what your infinity is. Maybe it needs more on what that infinity means, maybe a change of title, because its not going to be much use to someone looking up the mathematical sense of infinity.

I dunno about you, but I don't really believe that something like the total perspective vortex would really have the effect it does in the book. And entries are supposed to be factual, it needs some backup of the mindblowing aspects for infinity you're claiming beyond the book.

Sorry about not saying nice things, as it happens I do like the picture Hopefully I'm just missing what you're saying, and in getting it to the stage where I do get what you're saying, it'll make it a better entry.

I'm not going to come up with an unmathematical explanation for each question. But here is a comment to the first one:
The word 'shape' means "the external form, or contour of an object". In other words, something with a border. If infinity doesn't have borders, then infinity isn't a shape. The question started: "Infinity can have form (planets, stars, etc.)..." If there was a plane and an ocean, that would be the form.

I've tried to find some mathematical evidence for my questions, and some mathematical explanations for infinity. I can't find any! So, maybe you could show me some links?!

w85

Hello,

Infinity doesn't have a shape, because infinity indicates an uncountable quantity, and is totally unrelated to form and shape. If this doesn't seem to make sense, imagine asking if the finite has a shape, or more specifically if the abstract number 12 corresponds to a "shape".

You could instead ask if it's possible for an infinite volume to have a finite surface or vice versa. I don't think the first case is possible, but the second case is mathematically, thanks to our friends the fractals. But that's just my feeling.

I think a lot of people confuse infinity with a really big number, or a really big something else. It's more that something is uncountable, because even really big implies finitude.

Rambling Incoherently,
Jake

Yes, unless this is a different infinity from the mathematical one, it's a property of some sets of having a number of elements that isn't any finite number. Just to pick you up on a bit of terminology - infinite isn't the same as uncountable. Technically, the word uncountable has a meaning here - there are both countable and uncountable infinities (basically, its countable if you can put the elements in a list (of infinite length of course), and uncountable if you cannot).

HenryS,

True, my bad there. I know about countable and uncountable infinite sets (learned about Aleph and all that at school), but I said uncountable anyway. I guess a better way to describe infinity would be indeterminate?

Just an example of the sometimes poor mapping of mathematics to English.

Yours,
Jake

Cogito: "I guess a better way to describe infinity would be indeterminate?"

I'd say the best way to describe infinity is infinite... Seriously that's what it means. Not finite.

Hello,

Well, yeah. Never mind.

Yours,
Jake

The "infinite" that I refer to in the entry, is infinite space. Not infinite in a mathematical sense. It is entirely possible that the universe has an infinite area, so infinity is not entirey bound by mathematics. I think the best way of describing infinity as a phenomenon, is unthinkable. The best way of understanding infinity, is to say that it's infinite. Do you see the difference?

I have concidered re-writing the entry, so that the subject will be something like "Views of Infinity". That entry would be about peoples opinions about infinity.

w85

I'm afraid I'm going to have to niggle with some of your answers here...

Question: If you have infinite speed, how long will it take you to cross infinite space?

Suppose someone is going at X m/s, and is crossing X m. Then it will take them X/X = 1 second. Now let X tend to infinity - it will still take them one second.

The true answer is that it's indeterminate - the question, as stated, is unanswerable. The same goes for the quetions on filling a cup, and for wrapping a body.
--

I'm not clear on what you mean by saying that "infinity seems to be able to have form (i.e. planets, suns, black holes)" - In what way are planets or suns infinite? Even for black holes I'm uncertain about exactly what you mean, I'm afraid.

Maybe I'm just thick...

w85 --

Well *I* enjoyed it. I see the problems with your examples. I can offer a couple of possible directions to take this.

1) A totally different angle, upon which you brushed and then said no more, is, of course, religion.

Mathematical infinity is very simple and comprehensible to mathematicians, and rather counter-intuitive to most non-mathematicians.

On the other hand, humanity has been creating/believing in/learning about omnipresent, omniscient, infinitudes of Being since cave people times. This kind of infinitude is fairly comfy to even the very non-mathsy mind, and is not hostile to mathsy minds.

The terrific advantage of a religious angle over what you tried to do with a spatio-temporal angle is that the tolerance for paradox necessary to make infinitude possible is built in to most theology: Can God create something so heavy that God can't lift it? Yes.
Can God lift it anyway? If God wants to.
Does God want to? How should we know what an Infinite Being wants?

The terrific disadvantage of a religious angle is infinity just got much, much bigger than you had planned, and a paper on the infinitude of Deity would probably have to be pretty vast. I can't see a way to write anything meaningful in under 50 word-processed pages, and that would be on the frivolous level of the above paragraph.

I love infinity. Infinity is terrific. But I love paradox too, and that's the stuff that tangles up most human brains. How many dimensions do I see in? The usual five, why? (It took me until the age of 38 to understand about the three everyone talks about... I assumed they meant five, and just called them three for convenience.)

2) You could maybe do something short and entertaining, which I liked about your current paper, on infinitude and paradox.

To the mathsy ones: a question which has bothered me since I was 10, and some Teacher told me one can't divide by zero... why not? The answer is obviously both zero and infinity, which are not really that different! Duh .

Arpeggio, for LeKZ

Arpeggio:
"How many dimensions do I see in? The usual five, why? (It took me until the age of 38 to understand about the three everyone talks about... I assumed they meant five, and just called them three for convenience.)"

I'm really interested in this, but its not really relevant to this discussion so I'll take it up on your personal space

"To the mathsy ones: a question which has bothered me since I was 10, and some Teacher told me one can't divide by zero... why not? The answer is obviously both zero and infinity, which are not really that different! Duh."

Dividing by zero can get you into trouble, at least if you want to keep using useful ideas like if a*b = a*c then b = c,
which doesn't work for a=0. This is the basis of some of the maths 'paradoxes' that 'prove' that 1=2 (theres an example currently at http://www.bbc.co.uk/h2g2/guide/A542413). However, you *can* define things such that it does work: you take the real line R, and form a new set 'the extended real line' which is R with a new point, 'infinity' added. The rules are then that for any x in R:
x + infinity = infinity
x * infinity = infinity
x / infinity = 0
infinity / x = infinity
x / 0 = infinity (unless x is 0, 0/0 is still undefined I think)

...and it all works ok, just it doesn't follow all the nice manipulating rules that we know from arithmetic, so you have to be a bit careful when playing about with it.

"x / 0 = infinity (unless x is 0, 0/0 is still undefined I think)"

0/0 won't ever be defined, just look at Sin(x)/x for x=0, which reaches 1 although sin(0)=0 and would therefore fit into the 0/0 category.


Well, infinity seems too big a chunk for a single researcher (seeing that all attempts to describe it in an entry obviously failed )

W85 has unsubscribed from everything but a journal entry and left for lunch

Any Scout seconding yet another move to the Workshop?

Bossel (Scout)

well, I don't agree with Bossel that an entry on Infinity is impossible - but I do agree that a move to the workshop for this particular thread would be in order...

I tell you: there's a curse!

Editorial Note: This conversation has been moved from 'The Writing Workshop' to 'The Flea Market'.