What’s the highest a human could possibly pole vault?

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Hello lovely curious-minded people.

Welcome to the podcast of Inside Science, first broadcast on the 18th of September, 2025.

Today, we're finding out how our brains tick

as we navigate our way through the world.

More on that strange sounds later.

We're also exploring science that can only be done at the very ends of the earth.

And I am joined in the studio by Katie Steckels, mathematician, science enthusiast, broadcaster.

Hi, Katie, welcome.

Hello.

Lovely to have you here.

You've been digging through some of the maths that's shaping our understanding of our world this week.

What have you got for us?

Well, it turns out there's been a couple of really interesting maths developments fairly recently, like in the last couple of weeks.

So there's a new shape that's been discovered.

Oh, wow.

And a new result in the area of knot theory, which is to do with kind of knots and tying loops and things.

Oh, amazing.

Right.

Well, we look look forward to hearing more from you on that a little bit later.

But first, this week, pole vaulting has hit the headlines.

Swedish athlete Armand Mondo Duplantis broke the world pole vault record again for the 14th consecutive time in his final attempt at the World Athletics Championships in Tokyo.

He cleared a height of 6.3 meters.

That's essentially equivalent to vaulting over a two-story house.

And there's some fascinating physics and engineering at play here.

So we want to know: can science tell us how high a a pole vaulter could vault?

Is Mondo simply the greatest athlete in his event, or are physics and engineering key to his record-breaking feats?

And when we need an expert take on the science that's shaping world-class sport, we call on Steve Haik, Professor of Sports Engineering at Sheffield Hallam University, who joins me now.

Hello, Steve.

Hi, thank you for having me.

Oh, it's always a pleasure.

Thank you for being here.

Can I start by asking you about the man himself?

Let's talk about Diplantis.

Talk us through physically, athletically, how he's achieving this.

Is he doing something fundamentally different and new to other pole vaulters?

He is

a PR man's dream.

Physically, he's perfect for the pole vault.

He's fast, so he's got a good sprint on him.

And he's very muscular, which means he's able to do the gymnastic rotation where he turns upside down, turns back to front, and goes over feet first.

He seems to be pretty average in terms of weight.

He's about 80 kilograms, so I've read.

So he's pretty average, but I think that's the only average thing about him.

Right.

And correct me on my terminology here, if you will, but can we talk about the pole?

Or is it the pole vault?

What are these poles made of?

How do they work?

They must have come a long way since this sport started.

Yeah, so I suppose that pole vault is the event and the vaulting pole is the thing.

So the vaulting pole, yeah, it started out as dike jumping across the low countries.

You know, you're basically a very stiff, solid hickory or ash pole and it wouldn't bend at all.

So basically you'd run at it, you'd grab hold of the pole and you'd go over vertically, whatever the thing is.

So that turned in 1896 into the event at the first Olympic Games.

And basically you'd go over almost upright, lifting your legs up.

After a while, about 1904, we had the bamboo pole.

So people realized that running with a solid wooden pole was actually quite heavy.

So let's make it lighter.

Let's have a hollow pole.

And bamboo was the material of choice.

Now that started to bend a little bit, but still, you more or less had to go over, you know, with your head up and your feet down, lifting them up as high as you could.

And then it was only until you got to about the 50s.

early 60s that glass fiber, carbon fiber started to come along not long after.

And that's very, very flexible.

And what we're trying to do with that pole is you've got kinetic energy as the athlete runs down the track.

That's converted to spring energy in the pole.

And that springs them up

over the bar and converts that to potential energy.

And the design of the pole is key to eking out those last few joules to get you as high as possible.

You talked a little bit about the speed, the spring, the energy conversion.

Is there a sort of geometry, a model of the perfect pole vaults, the kind of maximum height that you could get to in this sport?

Well, yes, I mean, there's a you can take a very simple physics approach where you go kinetic energy, that's the movement energy, so that when he arrives at the box, plants the pole in the box, and then goes up over the air, turn that kinetic energy turns to spring energy.

And we can create mathematical models of a spring.

And then potential energy is very, very simple as a mathematical model.

And then all that energy that Duplantis puts into the pole isn't used.

So that, you know, anything that you bend is efficient to maybe 80% in terms of spring energy.

So in terms of engineering terms, we could do with getting that up a little bit higher.

If you can get that up a little bit higher, he'll have more energy to use in the jump.

Does that mean that if you work out the speed, the kind of bend and spring in this material, you can predict how high a pole volta, you know, the perfect pole volta could theoretically go?

Yeah, so one of the things you could do is you could go, well, how much energy is an athlete going to put in?

and in terms of the energy they put in that's directly related to their mass so you could make them a bit heavier but then they might go a bit slower the kinetic energy is proportional to the velocity squared so actually it's the speed it's the velocity you perhaps want to maximize there and what it seems is that the Duplantis when he gets to the plant box so he's going full pelt he slides the pole along the ground the last few centimeters until it hits that box and then it starts to bend And other athletes don't seem to do that.

So he's obviously worked out that somehow that's more energy efficient and it seems he's a little bit faster.

He's about maybe 5-10% faster than his colleagues.

Wow.

So technique, the technology of the pole, the right pole, the right stiffness, the speed, all of that goes into this feat.

So what else, you know, you talked about how Duplantis is doing something slightly different, how fast he is.

What else are scientists and other athletes learning from him?

So one of the things that Duplantis seems to do is when he's going for world record, he's got a special pair of shoes that he puts on.

And they are very stiff shoes, which allow him to transmit all the force from his running into the floor to make him go faster.

And they also have some special kind of, I don't know, crampon-type spikes.

And he says that he doesn't use them very often because when he takes off, sometimes he catches himself.

And so he says, if you know, if you see him bleeding as he comes down to hit that mat, that's probably because he's wearing these special shoes and he's caught his arm on the way up as he's swinging his feet upwards over the bar.

Wow.

This is whole vaulting looks dangerous, but I had no idea there was actual, you know, you were wearing dangerous footwear as well.

Well, I could ask you so much more about this, Steve.

It's fascinating.

But thank you.

That's all we have time for.

So thank you so much for joining us.

And do come back and talk more sporting achievements in future, please.

Thank you ever so much for having me.

And Katie Steckles is still here with me.

And Katie, you've actually been doing some number crunching on the speeds that are involved in pole vaulting for a book you've been working on.

Is that right?

Yeah, it's a complete coincidence.

And one of the things we talk about is how often in these kind of physical situations where you've got things moving around or flying around, it's surprising how little information you actually need.

So for example, if you want to calculate the speed that a pole vaulter is moving at when they hit the mat at the end of a jump, the only piece of information you need is the height that they've been at because they start with zero velocity and they accelerate because of gravity.

And I guess this is ignoring some of the slightly fiddly real-world things like air resistance and things like that.

But the effect of those will be small enough that you can roughly approximate it.

It'll be about 11 meters per second, which is about 25 miles an hour at the moment when they hit the crash mat, which is why the crash mat is very important in this sport.

But yeah, there's some, like, if you can make these modeling assumptions and kind of think of it as a physical system, there's some really nice stuff about pole vaulting.

So when they actually go over the bar, the centre of mass of the athlete and the pole never actually goes above the bar because by the time their feet are over the other side, it just sort of moves horizontally across underneath.

So they can actually get over a bar that's higher than where their centre of mass is.

Interesting.

Well, more maths later on with you, Katie.

Thank you very much for that.

Now though, have you ever been walking and the fog suddenly descends?

Your sense of direction, of where you are, where you're headed, disappears.

And when your landmarks are swallowed up by the mist, the sense of how far you're traveling can also just desert you.

Now, in a study just published today, neuroscientists from the University of St.

Andrews have managed to pinpoint the internal mileage clock inside the brain and worked out what's going on when it stops clocking the distance you've covered and you start to lose your way.

Here's Professor James Ainge.

We know that there's lots of ways in which you can navigate around the world.

You can make use of cues within your environments, sort of, you know, that might be a mountain in the distance, or it might be the layout of the furniture in your room.

But you can also make use of your ability to know how far you've traveled, to know what direction you're facing, those kinds of things.

And there's been work in the past that suggested that some of these cells in this sort of navigation memory area of the brain might be involved in this ability to keep track of distance.

So that's what we were really interested in trying to test.

Like, can we set up an experiment that allows us to test people and maybe animals' ability to judge distance and then see if these cells respond to that distance in some way.

So that's actually quite a complicated thing to do, isn't it?

Because you then have to have a distance judging task and see what these cells are doing.

That's right.

So definitely the first stage of this is to come up with a really simple task where we're asking rats to run a very specific distance, to stop, turn around and then come back to the start.

And that sounds very straightforward, but rats are really smart.

They'll try and come up with simpler ways of solving any task you give them.

It took us quite a long time to actually train them, a few weeks, where we set up a big rectangular environment.

We put a little treat about two-thirds of the way along.

And we teach them to run, get the treat and come back.

And then over a few weeks, as I say, we will gradually teach them that the treat won't be there, but if they run to the point where the treat used to be and then come back to the start box, they'll get an even bigger treat in the start box.

What's the treat?

Treat's a piece of chocolate cereal.

That's what all neuroscience runs on.

Neuroscience runs on chocolate cereal.

That is that's good to know.

So where do you bring in figuring out what's going on in their brain?

You then get them to do that once they've learned it you do that and you actually record from their brain.

Exactly.

Yeah that's right.

Yeah so we have the technologies that allow us to isolate the signals from individual cells within the brain.

And then the critical thing is we can keep track of where the rat is in the environment with a camera that's looking down on the box where they're running.

And so we can correlate the activity of these individual brain cells with the position in space of where the rat is.

So we can ask how do these cells respond to the distance that the rat has run.

Wow.

So how do they respond?

What's happening in those cells?

What's happening to those cells when the rat's getting this task right and estimating a distance?

So as the rat is running sort of out of the start box, every sort of 20 or 30 centimeters or so, you'll get this burst of action potentials or spikes.

So, these are the way that brain cells communicate with each other.

And when we looked at the positions of those bursts of activity, the fascinating thing is that they're very regular.

So, sort of like a ticking, like a myelometer in the brain, sort of ticking away every 30 centimetres the rats run.

Yeah, exactly.

Yeah, so that's one of the things that we're really interested in asking.

Is the regularity of that signal related to the rats' ability to remember where that piece of chocolate cereal was.

Wow.

I know this it's not something that you hear but you've put some sound to that the cells firing for us so we can hear that sort of regular ticking pattern, this brain sort of myelometer.

Let's just have a listen to that.

What are we hearing there, Jamie?

So as the rats run, they'll run pretty quickly once they know how to do this.

So a trial will only last sort of three or four seconds.

So what you're listening to is the output of a single neuron as that rat is running from the start box to the reward point.

And so, what you'll hear is a burst and then a gap and then another burst.

If you looked at a visual representation of how the cell is responding, you'd see this kind of peak of activity, then a complete flat line, then another peak, then another flat line.

And so, each one of those peaks is about 20 or 30 centimeters that the rat has travelled.

I understand you scaled this up then for humans.

You turned your rat-sized room into a human-sized room.

How have you done this experiment for people as well?

Yeah, it was great.

It was a, it was a logistically, it was a well, it was a total nightmare.

Um, we uh had to get the student union to allow us to use one of their big bar areas, so we had to do this in the summer.

And we emptied out everything in there, built this uh human-sized rectangular arena, and then we did exactly the same thing.

So, we had people start at one end of the arena, we'd have them walk to a specific point in the arena, and we'd do a bunch of training trials where that point was specified for them.

And then over time, we'd run trials where the specification points, the marker for where they should go, that that was removed.

And we'd ask, okay, first of all, can people estimate distance?

And it turns out that yes, they can, not very surprising.

But then, when we do the same manipulation that we did with the rats, so when we change the shape of the room, we see exactly the same pattern of behavior.

So it sounds familiar to me, it might be familiar to people in the sense of where people start to kind of lose a type of function in their brain.

So, it might be familiar to people who've had a loved one or a family member with Alzheimer's that people start losing their way before they start losing their memory.

I wonder if what you're investigating here, you know, it's telling us something fundamental about what is happening in our brain as we're moving around the world.

But is it telling us something that could inform how we could diagnose or even treat neurodegenerative diseases where we start to lose that ability?

Quite possibly, yes.

So we know that memory, spatial memory, is one of the sort of very first cognitive deficits that you see in people with Alzheimer's.

So that can be, you know, very early on.

That's really one of the interesting ways in which this research could be applied because we know that the specific brain cells we're recording from are in one of the very first areas that's affected in Alzheimer's.

Thank you, Professor James Ainge from the University of St.

Andrews.

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And you are listening to Inside Science with me, Victoria Gill.

And we are continuing to devour the best science books of the year, combing through the shortlist of the annual Royal Society Book Prize.

This week, we're heading to the Frozen Poles with paleontologist and explorer Neil Shubin.

Before we hear from Neil, though, here's a voice you might recognise from TV's Ted Lasso and from his stand-up alter ego, Mr.

Swallow.

He's also a science student and one of the judges who had the difficult task of selecting the shortlist.

My name is Nick Mohammed, and I'm, I guess, an actor and comedian, so the most underqualified person here, basically.

This is The Ends of the Earth by Neil Shubin.

It's absolutely thrilling.

Now, I would say that, so I studied geophysics, so this is kind of right in sort of the kind of area that I would be kind of already fascinated by.

But there's just something so thrilling the way he writes, it feels like an adventure story.

And you know, it's called The Ends of the Earth, and you quite literally get a sense of what it means to kind of go and study and do research science at the ends of the earth

it's about climate really whereas maybe some climate books even popular climate books might be accused of being maybe a bit preachy or a bit divisive or even political this feels that it does a really good job of educating the reader in terms of the severity of what's going on at the ice camps.

But it's a very, very powerful science book.

And I think again it takes a topic that you feel like you might know a little bit about.

And actually, it suddenly kind of blows the whole thing wide open, but still makes it really accessible without it getting too kind of bogged down and technical.

So I adored it.

And I, even though we were only encouraged to read a few chapters of each book at this stage, I just felt myself just reading on and on and on.

Picture yourself at the edge of a vast glacier.

Ice stretching to the horizon, winds fierce and unrelenting.

Or imagine coming face to face with a polar bear defending its kill in that forbidding landscape.

These scenes, once accessible to only a handful of explorers, now reveal profound truths about our world and ourselves.

The more we learn about polar regions, the more we see how their future and ours are inextricably linked.

Moving ice has transformed our world.

Human history unfolded during the rare era of polar ice caps, a time when immense glaciers set the shape of every coastline, island, even the depths of our oceans.

Polar regions, even from afar, have quietly shaped civilization through their effects on the oceans and climate.

We have always depended on them, and now we find those distant lands changing at a pace driven by our own activities.

Vast amounts of data from the ice, oceans, and fossils tell us that the environmental shifts at the ends of the Earth ripple outward.

The ways we live in lower latitudes influence the Arctic and Antarctic, and in turn, the transformations there shape the conditions of our own backyards.

It's easy to forget how deeply intertwined we are when ice and snow seem so far away.

Running successful expeditions in polar regions is as much about values as it is about survival or science.

Sometimes the greatest insights emerge from unexpected encounters with the terrain itself.

I recall nearly wearing out the soles of my boots at my first Greenland camp in 1988.

Guided by blurry aerial photos, we chose a campsite, but quickly found the fossils we sought lay miles away.

Hiking along through fields of eroded boulders, knee-deep mud under our boots in the early season snowmelt, my mind was filled more with thoughts of keeping upright than scientific discovery.

One day everything shifted.

Out of the rocks and wind emerged an injured plover on the tundra floor.

The bird, seemingly in distress, limped away, dragging a wing and crying out.

Instinctively, I approached hoping to help.

Each time I came close, the bird flew just a little further.

Only later, pouring over field guides in the kitchen tent, did I realize that this was no injured creature, but a masterful parent pulling me away from its nest.

The plovers evolved to feign injury, luring intruders from their eggs nestled, exposed, on bare Arctic earth.

Over several days I found their simple nest, a trio of gray eggs, fragile and alone in the elements, their only protection a careful parent and near-perfect camouflage among the rocks.

These plover eggs became a symbol to me, representing both the fragility and resilience of life at the poles.

For thousands of years, chicks have hatched here, surviving on the thinnest edge between endurance and vulnerability.

After decades in polar regions, the image of those little plover eggs stayed with me on ice and traverse.

Like the plover, humans live in a delicate balance with the planet, a fragility masked by our built environments.

The polar landscape is humbling.

A human body is a speck on a continent-sized ice.

Our time is a blink in billion-year cycles.

Yet, Rather than make us feel small and insignificant, polar regions enlarge us.

Here, discovery and survival depend on looking beyond ourselves to collaboration and adaptation.

As the planet warms, the poles are facing increasing pressure to exploit them for resource extraction, new shipping routes, or military advantage.

The choices we make now, reducing emissions and backing science-based policy, are not just acts of distant stewardship, but steps in safeguarding the systems that have shaped every chapter of human history.

The resilience of life such as the plovers at the poles must become our own so these critical regions can continue, as they always have, to sustain us all.

Thank you, and good luck to Neil Shubin.

And we will be completing the shortlisted author interview box set next week when we're speaking to Tim Minchell about his book, Your Life is Manufactured.

Now though, mathematician Katie Steckles is here with me.

Katie, you have been looking through some of the most exciting mathematical discoveries that might have gone under the radar.

So what do you have for us this week?

It's a busy time in the world of maths research.

That's good.

good for the programme.

There's two very, very purely mathematical kind of new ideas that have been found.

So one of these is a newly discovered shape.

You might be aware that if you have a cube, if you take another cube, you can just about fit the cube through the first cube.

And this is a property that is called sometimes the Rupert property, which is named after Prince Rupert of the Rhine, who was a kind of a royal who historically was very interested in maths and science.

And this was one of the questions that he asked: is it possible to do this with a shape?

Can you push a shape through another copy of the same shape?

There's a lot of shapes that we think have this property, but no one's managed to find the exact right orientation and angle to push it through at.

So we think it's true of all of the sort of very standard 3D shapes, the platonic solids, like the octahedron and the tetrahedron and things like this that are the kind of familiar shapes.

The conjecture, the sort of major thinking on this was that actually for any shape that is what we call a convex convex shape, so where all of the corners point outwards, basically, there's no kind of inward bits anywhere, that it should be possible.

And that no one has found anything that doesn't work until now.

Ah.

So people have just discovered a shape which it kind of looks like a golf ball covered in triangles, but with one side stretched out slightly and then the end cut off.

Right.

And that's the best description I can give.

But if you want to see what it looks like, they've called it the no pertedron.

No perthhedron.

Because it's not Rupert.

It's the first non-Rupert shape.

Oh, I I love the math schema in that.

It's a wonderful name.

And if you search for that, you can probably find a picture of it.

But it has been discovered that this shape definitely doesn't have that property.

So it's the first thing we've ever discovered that you can't push through another copy of itself, which doesn't sound like a particularly useful thing to know.

But it's the kind of thing that kind of tests our ability to understand shapes and geometry and how things work.

Thanks, Katie.

That's fascinating.

Now, you have some knot news for us as well.

There's a whole mathematical theory of knots, which is to do with kind of, if you imagine a closed loop of line in 3D space.

And the theory of knots is kind of really nicely well studied.

It's been a big area of research since about the 70s.

The way that people study knots is by looking at their properties and the way they behave.

So if you imagine you have like an open circle, just an unknotted loop, that's what we call the unknot.

And then everything else is kind of in terms of that.

So if you have like a standard overhand knot that you might tie, but with the ends joined together, so it's a closed loop.

One of the questions you ask is, how many of the kind of crossings in this knot would we have to undo in order to make it into the unknot?

How do you untangle your headphones when you well exactly, yeah.

So if you're allowed to say, okay, this this line goes over the top of this line, if I were to switch that so they're the other way around,

that's a sort of crossing change.

How many crossing switches do you need to get something to be the unknot?

And this is a property that tells you essentially how complicated the knot is.

And you can use it for things like studying DNA or protein molecules and the way that things tangle in actual 3D space.

But if you want to add together two knots, you essentially put them next to each other, you cut the string on both knots, and then you join it across.

The theory that people were working on up until now was that if you take two knots with whatever their unknotting numbers are, if you add them together in order to unknot that whole thing, the simplest way is just to unknot each of the two things separately, to do all the crossing switches on both knots.

And the number of switches you would need would always be at least as many as it would be to do each of them separately.

So the sum of the unknotting numbers.

What someone's actually found is a knot that if you add it to another knot gets simpler.

So it's a knot with, I think it's seven crossings in each knot.

And they normally take three switches to unknot them, but if you put them together and add them, it only takes five, which is less than six.

And this is the first time anyone's discovered an example of this, so it's very exciting.

Amazing.

And the kind of application of that in biology, if you can understand how these coils and these knots sort of twist and turn and kind of fold back on each other, you can understand what's happening in quite complex biology and how those, say, proteins are shaping themselves.

Yeah, and the operation of undoing a crossing in a knot is actually something that you can do with an enzyme on a protein, right?

You can...

disconnect it and reconnect it using chemical reactions, I guess, for things like protein chains and DNA and things like this.

Finally, you have a record-breaking animal for us.

This doesn't sound like maths news to me, but there's some maths in here.

This is the story that a jaguar has been found to have swum a further distance than any jaguar has ever been recorded swimming.

So the way they know this is because there was a kind of camera kind of monitoring the area where the jaguar lived, and they saw this animal on the side of the lake, and then they saw it again later on an island in the middle of the lake.

Okay.

And there's a kind of a fun limit on this.

So the distance from the bank to the island is actually 2.3 kilometers.

So there is a potential chance that this jaguar has swum 2.3 kilometers in one go, which would be way more than has ever been observed previously.

But there is a little island on the way there.

So it could have had a break.

It could have had a little break and stopped there, but no one knows why the jaguar went there.

It's just, you know, animals being animals.

There's no particular reason.

There's no food source or anything on the island.

that it might have been going for.

But the thing that jumped out about this for me was the fact that they were able to tell tell it was exactly the same Jaguar because the pattern of spots on the side of the Jaguar is unique to each animal.

I hate to drag everything back onto maths, but it's one of the really nice applications of maths in studying animals.

You can actually understand how the patterns on animal coats came to be using some differential equations, basically.

Well, I love that we've brought everything back to pure maths this week with you, Katie.

Thank you so much.

And we have record-breaking jaguars and record-breaking humans on this week's Inside Science.

Thanks for joining us.

And that is all we have time for this week.

You have been listening to BBC Inside Science with me, Victoria Gill.

The producers were Dan Welsh, Tim Dodd, and Claire Salisbury.

Technical production was by Gwynford Jones and Leanne Joyce, and the show was made in Cardiff by BBC, Wales, and West.

To discover more fascinating science content, head to bbc.co.uk, search for BBC Inside Science, and follow the links to the Open University.

Next week, we will be following the life story of a bird that ornithologists are calling the Miracle Eagle.

Until then, thanks for listening and bye-bye.

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There are no account fees or minimums.

And you also get free instant withdrawals to eligible accounts 24-7.

So you always have access to your money when you need it.

And when you're ready to invest, you can transfer your cash to one of WealthFront's expert-built portfolios in just minutes.

More than 1 million people already use Wealthfront to save and build long-term wealth with confidence.

Get started today at WealthFront.com.

Cash account offered by Wealthfront Brokerage LLC, member FINRA SIPC.

Wealthfront Brokerage is not a bank.

Annual percentage yield on deposits as of September 26, 2025 is representative, subject to change, and requires no minimum.

The cash account is not a bank account.

Funds are swept to program banks where they earn the variable APY.