Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Soul Surfer on 10/02/2010 20:25:39

Infinity is essentially a mathematical concept and its mathematical use leads to many problems of understanding when it is applied ad hoc to the physical world. Many awkward questions on these pages are caused by the rigorous application of mathematical concepts of infinity to physical situations.
There is a television programme on infinity in the BBC horizon series starting in a few minutes time that will probably illustrate these quite well.
When I deal with infinities in a physical sense I tend to use the term indefinite rather than infinite because the true situation is usually that something will bridge the gap even though we may not fully understand it at the moment.
What do you think about infinity?

What do you think of larger and lesser infinities.
Now, that's a strange subject :)

Many awkward questions on these pages are caused by the rigorous application of mathematical concepts of infinity to physical situations.
I know I've seen these before, but I can't recall one at the moment. Can you give an example?

What do you think of larger and lesser infinities.
Now, that's a strange subject :)
Haha, yes, different sized infinities has always been a bit of a nono for me. I mean, sure, there are a lot of things in physics that are neither simple nor intuitive just because they reflect a complex and abstract world...but seriously? This one just goes beyond not being intuitive for me.

Many awkward questions on these pages are caused by the rigorous application of mathematical concepts of infinity to physical situations.
I know I've seen these before, but I can't recall one at the moment. Can you give an example?
The most common that comes to mind is describing The Universe as 'infinite', when 'open' or 'unbounded' may be better descriptions.

Many awkward questions on these pages are caused by the rigorous application of mathematical concepts of infinity to physical situations.
I know I've seen these before, but I can't recall one at the moment. Can you give an example?
The most common that comes to mind is describing The Universe as 'infinite', when 'open' or 'unbounded' may be better descriptions.
"Unquantifiable" perhaps? (Doesn't exactly "trip off the tongue")
or "Defies quantification" if there is a way to make a single word out of it.

Ah. I think using the proper word in each context would be clearest, then. Of course, the word "unbounded" is less intuitive than infinite, which might be why people tend to substitute infinity for the concept. There's also the case of infinity appearing in singularities, which has a different physical meaning as well as infinity appearing in a lot of equations as an approximation to "something really big."

One a related topic, you will have noticed that the word "exponential" is increasingly abused in the media and by politicians, to mean anything that increases faster than linear.
On the smarter programmes (Radio 4) we're now beginning to hear the word "geometrical" in the context of growth or expansion  meaning exactly what exponential used to mean. [;)]

What do I think about infinity? There are no infinities in nature. It's a mathematical concept, that's all.

One a related topic, you will have noticed that the word "exponential" is increasingly abused in the media and by politicians, to mean anything that increases faster than linear.
On the smarter programmes (Radio 4) we're now beginning to hear the word "geometrical" in the context of growth or expansion  meaning exactly what exponential used to mean. [;)]
Quite right! We need to train them to use "nonlinear" instead.
I once worked for an outfit that had a rather temperamental CEO (Managing Director). The engineers were careful to point out that the CEO's response to unfavorable events was nonlinear. As in;
"Old wotsizname went freekin' nonlinear on hearing we would not be able to ship the product for at least 18 months."

I not a mathematician but in any maths at high school level I don't like it when people use phrases that make it sound like infinity is just a big number, such as 'to infinity' or the real killer, 'an infinite number'. To my ears that is an oxymoron.
In my head I always replace these words with something like 'going on forever' or 'without end'. It has always seemed to me that infinity plus one doesn't even make sense because it treats infinity as a number.

Many awkward questions on these pages are caused by the rigorous application of mathematical concepts of infinity to physical situations.
I know I've seen these before, but I can't recall one at the moment. Can you give an example?
The most common that comes to mind is describing The Universe as 'infinite', when 'open' or 'unbounded' may be better descriptions.
The problem is that something can be finite, but unbounded. The two terms have different meanings.
From our point of view the Earth's surface is unbounded  you can set off in any direction and keep going. You never hit a boundary. But the Earth is also finite.

Many awkward questions on these pages are caused by the rigorous application of mathematical concepts of infinity to physical situations.
I know I've seen these before, but I can't recall one at the moment. Can you give an example?
The most common that comes to mind is describing The Universe as 'infinite', when 'open' or 'unbounded' may be better descriptions.
The problem is that something can be finite, but unbounded. The two terms have different meanings.
From our point of view the Earth's surface is unbounded  you can set off in any direction and keep going. You never hit a boundary. But the Earth is also finite.
Yes, this it true, if you try to separate space from time. In spacetime though, the surface of the Earth would be both unbounded and infinite (as time hasn't stopped yet) and your spacetime coordinates require all four values to be identical to be able to come back to exactly the same place (in spacetime).

True, but the words still have different meanings so you can't use one in place of the other.

Ah, but the point about spacetime is that either is meaningless without the other [;)]

I think Geezer is on to something there.
"Defies quantification"
How about Defqua?
Or does that sound to military?
"Well Sir, we spotted this defqua trying to take over our limited resources, so we attacked with our larger Defqua. But, alas, it refused to surrender insisting that is was just as much a defqua as the one taking over."

I think Geezer is on to something there.
"Defies quantification"
How about Defqua?
Or does that sound to military?
"Well Sir, we spotted this defqua trying to take over our limited resources, so we attacked with our larger Defqua. But, alas, it refused to surrender insisting that is was just as much a defqua as the one taking over."
The military would likely abbreviate it to "DQ". Wait a minute  I think that's already taken! It's disqualified. (or even DairyQueen)