(Science Week, day 4!)

I still hear about people disliking math, particularly as they're introduced in school. And I think the main reason is that it's not apparently connected to anything real, so it's possible not to understand what you're supposedly learning. Few internal connections, few intrinsic rewards. It's natural to dislike that.

But first, let's talk about falling down.

As humans, you and I so quickly ingrained such a sense for gravity on Earth that it might be considered a fascinating and prodigious talent by an alien from different conditions. If we stumble and trip, we compensate to catch ourselves. (If we don't, we learn instantly that something went wrong.) If we're tossing a ball with somebody, we compensate to catch the ball. If we're at the edge of an open drop to a story – or 50 stories – below, we feel something profoundly fearsome. It all happens without noticing that we're thinking or calculating anything.

So, when we start learning Newtonian physics and deal with the motion of a cannonball across a field, and we're told the number representing the vertical height of the ball increases, peaks, then decreases, we think "of course it does." Nothing's "not connected to anything real" about that. (Nor, the insightful student or skilled teacher will have noted, was the introductory math.)

Once we understand math is mappable to real things, we discover that playing with those numbers allows us to predict exactly how high the cannonball would go, or exactly where it would land, if its explosive force were exactly this much greater, or if it were tilted exactly this much higher – and even what would happen if the cannon were tilted just high enough, and fired just forcefully enough, that the ball would go so fast, so far, around and around the whole planet, again and again.

And at around that point of comprehension, math and the imagination clasp hands and transcend our ingrained intuition about everyday existence on Earth's surface.

You might know there's a term for that kind of projectile which Newton himself employed. But the article I want to share today, one step further from our ingrained intuition, is this column:

• Wikipedia on Lagrange points

I noticed this term around the launch of the James Webb telescope. I knew it would orbit the sun rather than the Earth as Hubble does, but this reading elucidates how it isn't just flung further into space than the hypothetical cannonball and left to drift there, but aimed and guided to one of these five special points.

It's easy enough to imagine our massive sun constantly pulling everything toward it. Anything that hopes to remain in the area without a fiery end must orbit it the sun at some particular speed and distance. The Earth is one of those things, and that feels a little like the whole gravitational story.

But the Earth and sun, this two-body arrangement, and the force of gravity acting between them, turns out to determine this slightly more uneven sheet of gravitational gradients, if you will. If you draw a line from the centre of the sun through the centre of the Earth, there are three points on the line where a smaller floating object won't just drift away, but can sort of nestle and stay put. The first of those points is between them. The second is further from the sun than Earth is. And the third is on the far side of the sun! (I'd thought the Webb telescope was situated on the inside of Earth's orbit, but it turns out it's at the second point, further from Earth.) When the Webb telescope and other probes are nestled there, they don't need much of their own power to stay accessible to us. The points are stable enough even to be orbited at near distances.

The final two points are symmetrically off that Earth-sun line, lying ahead and behind the Earth's position along its own orbit.

Wikipedia's article (thank you, volunteers!), introduces all this in plain language with a few visual aids, all to help everyone – particularly those who haven't developed this kind of intuition – start not only to understand it, but to feel it. What would it feel like not to have to think about tripping and catching ourselves if we lived in open space between the planets, or throwing a ball into a basket around one side of Lagrange point 4?

As with this week's introductory article on genetics, I read this short column quietly, favouring my mind's visuals before regarding the provided aids. By the time I reached mention of other planets' Lagrange points, I was astonished, but a little less surprised, to learn that Jupiter's sideward Lagrange points are thought to bear over a million asteroids, thousands of which are already catalogued. Never has anyone happened to mention that to me before, in school, on YouTube, or otherwise. But this stuff all happens in our proverbial backyard.

Those who decided they dislike math? I wonder whether some think math majors or physicists don't need the intuition or sense of connectedness. They "need" it, they might think, so they must be worse at it, while the experts are all number-minded, with personality types that revel in Matrix-like calculations, all in the abstract, connected to nothing.

I imagine the opposite: math lovers and physicists see and embrace real-world connections right away, and thus elevate their intuition early. It's the needing of those connections that should tell a learner they can excel.

That open path is there for all, and goodness – to find you have a human life to live, and not to try the occasional stroll down it?