Do you remember the quote, "to infinity and beyond"? Well how can you go beyond
infinity and what's the opposite of infinity? I'm about to jump in an
elevator and find out.
I hear you're going to try and teach me some maths and
I'm not the best with numbers so I think you might have your work cut out for you.
Everyone's great with numbers. They just don't realize they're good with numbers
yet. Or no one's talked to them about numbers in a way that makes sense to
them. Don't disappoint me! Let's go. Okay so what is infinity?
Okay so infinity as you said is this concept that we use to describe
something that doesn't have a bound. Right so if we think of the natural
numbers which are just the counting numbers like 1, 2, 3, 4, 5, etc. It's
something bigger than that. Naturally. So it's not actually a number but it's
something that's a number can tend towards so nothing ever
reaches infinity it just can get closer to infinity.
So how is infinity useful to us?
So I mean for me, I work with lots of different systems that change with time.
So I like to look at what happens to something as time moves into the future.
Right. So if I have like a pond of fish and I wanna know like what is - is there
something that's gonna limit that population of fish? So maybe there's not
food, not enough space. So I want to look at what happens in the future. Like do I
pick five years in the future? Do I pick 10 years in the future? It's all kind of
arbitrary. If I look at what happens in that system as T tends to infinity. Yeah.
Then I'm gonna see maybe some kind of limiting behavior like the fish is going
to reach a population. It's gonna blow up whatever. So you use it to describe something.
Ok so it sets the point so far that it always allows you to find the limit? Yeah
exactly. Yeah. What's the opposite of infinity? So in...
it depends! So, if I'm talking about infinity as a concept of being unbounded, the
opposite would be something that's finite. If I'm talking about time into
the future, it will be time in the past. It depends on what it is you're using infinity.
Right yeah sure. And so you know be an infinite amount of time in the past but
then if I put something like infinitely big, it would be something
infinitesimally small. So think - Woah! Let me just stop you there because we're halfway
through and I have a lot of questions about infinitesimally small. Yeah it's
not a great word to say. No it's not and it's not a great concept to think about
if I'm being honest because how can something be infinitesimally small? Well okay
so actually in reality like it's quite hard for it to be but mathematically
it's very easy for it to be. So if I I've got like a radioactive substance and I'm
talking about its half-life so the amount of time it takes for the quantity
of radioactive substance to halve. Yep. Right so after one half-life it will
halve, after another one, it will halve and it will halve and it will halve and it will halve.
So it will never actually reached zero because I'm still halving something that's not zero.
It's just like so many decimal places. Yeah yeah but in reality like eventually
you're gonna get to that last like atom and it's gonna decay and there'll be
nothing there. Yeah. So that's when
mathematically something can be
infinitesimally small in reality, you sort of do hit zero. Would we ever go
that far? Or is it just so that we don't have a limit on things and we can kind
of find the limit? Yes so it's more it's the mathematical equations that give you
this behavior as time goes to infinity but in reality like there's the smallest
kind of subatomic particle we can't get smaller than that. So infinity's
kind of like a
tool to let us find the limits. It's a tool. It's exactly, that's exactly it.
It's a really big tool. Haha. Or a really really tiny tool. Or a tiny tool. Awesome I think I nailed.
Yeah. I reckon you did too. Thank you. No worries.
Yes!
When you think about it infinity's a term that gets used casually quite a lot
and that starts to kind of dilute what it means to us and we don't think about
it as deeply so it's really interesting to kind of deep dive into what infinity
actually means and to realise that as humans we're used to applying our
physical understanding of the world on to pretty much everything. So when you do
that and you say infinity is something that means that there is no bounds. It
kind of doesn't make sense. We don't understand how that can be because
there's always physical bounds. But when you reframe it as a mathematical concept
or a tool it makes a lot of sense. It's something that we can use to find those
physical limits that we're used to and I really like knowing that. It's cool to be
able to reframe and realise that I think of things in terms of human physicality
when that doesn't always need to apply. You know infinity is just kind of a way
of life.
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