Welcome back to another episode of Particle Word for Word, the podcast where we bring Particle WA's stories to life.

Today's story might be a touchy one.

A five letter word may never have brought on such an array of panic, stress, excitement or hunger.

More on that later.

This week's episode is all about maths.

The three particle stories in this episode were written by Owen Cummings and Cassandra Zaza and read by Katt Williams.

Maths might bring back memories of quadratic equations, Pythagoras theorem, or late night cramming for tests.

For others, maths is a thing of beauty, a language of patterns, puzzles and logic.

But beyond calculus and times tables, what actually is maths?

Maths is a tool we can use to understand the world around us.

It's a way of spotting patterns, describing relationships and making predictions.

Whether you're measuring how long it takes to cook pasta or or calculating the trajectory of a rocket, you're using maths.

It's not just about numbers.

It's about how those numbers behave, connect and help us make sense of everything from the tiniest atoms to the motion of galaxies.

Nature uses maths, too.

The spirals of a sunflower, the symmetry of a snowflake, the rhythm of your heartbeat.

Mathematical models map out ecosystems, help us to understand climate change and simulate infectious disease spread.

And it's not just science that uses maths.

It pops up in art and music, in rhythms, in ratios, in perspectives.

Of course, maths isn't always easy.

It isn't always as beautiful as a university maths lecturer might want us to believe.

What the heck is an imaginary number?

What's infinity?

Why isn't one a prime number?

What even is a number?

Maths, like the rest of the world, is still surrounded by mystery.

Mathematicians still argue over what is right and wrong.

There is one thing I'm sure all mathematicians agree on, though.

With just a few small maths rules, you can build an entire world of logic and possibility.

But before we understand what those worlds of logic and possibility might be, we need to understand something.

What the fuck is maths?

What the fuck is maths?

What is maths?

It's a question that eludes a straightforward answer.

But let's try to break it down.

It's a class you slept through.

It's the language of nature.

It's a source of crippling anxiety.

Mathematics is a lot of things to a lot of people, and it's everywhere.

Buying a coffee and working out the change from a 20, that's maths.

Observing how spiral patterns in sunflowers Follow the Fibonacci sequence.

That's maths.

Considering your own relativistic velocity on a spinning Earth, orbiting around the sun, hurtling through the unfashionable end of the galaxy in an infinite universe that is somehow still expanding, that might be an existential crisis, but it's also maths.

The above are examples of how we use maths, but they don't really answer the question, what is maths?

It's been called the poetry of logical ideas and the music of reason, but neither really answer the question.

Maybe it's like pornography, it can't be intelligibly described, but I know it when I see it.

We might not land on the exact answer right here, right now, but.

But at least let's try to break it down a bit.

So it goes like this.

At its heart, mathematics is a system for logically describing all the things that could ever exist, even imaginary things.

As the concept gets more complicated, logical structures are built up from existing ones to represent a higher level of understanding.

It's kind of like philosophy, where each logical thought builds from the one before.

Mathematics is the language of understanding, a a language that allows us to describe things that could never be put into words.

Unfortunately, like all languages, if you haven't learned what the characters and word means, it's just gibberish.

A very brief history of maths the maths we use today probably has its origins in ancient Mesopotamia.

Around 3000 BCE.

The Babylonians used algebra and geometry and were the first to invent the number 0.

From around 600 BCE to 400 CE, Greek mathematicians made significant contributions to algebra, trigonometry and calculus.

The Hindu Arabic numeral system became popular during the 9th century.

It had almost entirely replaced Roman numerals by 1300 CE and spread to Western Europe, where mathematics developed into the system we know today.

Mathematics is possibly the greatest of all mankind's accomplishments.

Yes, some of us have very traumatic memories related to math tests that may or may not have shaped our attitude towards it.

But as a whole, the language of maths allows humans to describe the most profound and beautiful knowledge in the universe.

And that's something worth appreciating.

It's true.

Maths is probably one of our greatest accomplishments as humans.

We need to recognize it for its incredible ability to help us make sense of the world around us.

This appreciation for maths is all well and good, but it doesn't get us any closer to working out just how it works.

One plus one equals two.

But how did the next layers get so complicated?

There are Only so many permutations and derivatives and coefficients and parabolas that one can do before the brain starts to twinge and the eyes glaze over.

So how the hell does maths actually work?

Particle 101.

How the hell does maths work?

We're back to demystify the world of mathematics.

In our last Maths Explainer article, we asked, what the fuck is maths?

And delved into its philosophy and history.

If that wasn't enough to you, if you yearn to be sitting in the maths classroom again awaiting some mathematical magic, you're in luck.

This time.

We ask, how does maths work?

How is it constructed?

And how did it get so freaking complicated from the ground up?

The bedrock of mathematical theory is arithmetic.

Addition, subtraction, multiplication, and division.

We've used it for thousands of years to calculate the number of things.

Money, sheep, rocks, Bitcoin, whatever.

Even some animals can do it.

Built from its arithmetic is algebra, where some sadists put the Alphabet into mathematics.

But it's really just a way to do arithmetic with unknown quantities, such as 12 mango trees.

Each grow X number of mangoes to give Y total number of mangoes.

So y mangoes equals 12 times X mangoes.

Algebra leads into calculus and derivatives, which is a bit trickier.

In school, that's when a lot of people decided they were more of the artistic type.

Essentially, it's how these unknown values from algebra change in relation to one another, such as acceleration being a change in velocity.

We are not, I repeat, not about to try to teach calculus.

But trigonometry, integrals, and geometry are all constructed in similar ways.

That makes some sense, right?

Right.

Prove it.

Okay, this may not help anyone actually do maths, but.

But it gives us a sense of how maths works.

At a fundamental level.

Maths is taking something that you know is true and building a new idea from it.

Algebra is built from arithmetic.

Calculus is built from algebra.

This process goes on indefinitely, creating more and more complicated maths.

The idea of proving something to be true is a big part of maths.

Arguably, it's the whole point.

So much so that in the early 1900s, a mathematics textbook took 360 pages to unequivocally prove that one plus one equals.

Yikes.

In maths, no assumption is beyond scrutiny, and each truth requires a proof.

Mathematics works by painstakingly proving the simplest truth, then endlessly conceiving more complicated and abstract ideas to prove it again.

In this way, mathematics uses reason to transform imagination into truth.

And as they say, truth can be an ugly thing.

It's not everyone's cup of tea.

Much like mathematics.

Now that we've got the two big questions out of the way, we can start to understand just how powerful and important maths is in our understanding of the world.

It makes our world make sense.

It also helps us to understand some of the more trivial things in life.

Like how many goals did Caleb Sarong kick on the weekend?

How many times can I listen to the full bratt album in 24 hours?

And just what is the correct pasta to source ratio?

No pastor shape was created by accident.

They're not random fusilli, rigatoni, penne, macaroni.

They were all created with purpose.

Every ridge, curve or hole was engineered with mathematical intent for optimal source delivery.

Maths can be beautiful and pretty damn.

Tasty A very scientific investigation of the Geometry of pasta Shapes One scientific inquiry looms over the entire culinary experience.

Which of the endless pasta shapes is best suited to which source and why?

I'm sorry to be the bearer of bad news, but it appears that tortellini pasta may be based on the shape of a belly button.

Even if it's not true now, it's impossible to ignore the resemblance.

You are doomed to feel a small disembodied belly button rolling about in your mouth whenever you eat one of those stuffed morsels.

But what is the function of this pasta shape beyond a horrifying likeness?

And hey, why are there so many shapes of pasta?

Don't they all taste the same?

Why the spirals, the ridged tubes, those little bow ties that you may assume are eaten exclusively by 2012 era hipsters?

Of course, there are rich cultural histories behind each strange shaping of this beloved carb.

But there is also science.

Specifically, one scientific inquiry looms over the entire culinary experiences.

Which of these endless pasta shapes is best suited to which source and why?

Let's explore the question why while enjoying several examples of how to get it absolutely wrong.

Hilly Cool spirals.

Your geometer dad trying to be relatable at dinner?

Delicious helicoid.

Why art thou so adept at capturing creamy sauces in your crevices?

And why is that such an uncomfortable sentence to read?

Spiral pasta's cultural roots are rich and different regions, even singular towns in Italy, use different recipes and methods to create their very own rotini, fusilli, andorinos or whatever spiral is their specialty.

But one truth is nearly universal about these spindly wonders.

The increased surface area of these pastas, which resemble a three dimensional curve winding around a central axis, enables saucers to pool and cling effectively this results in a more flavorful and satisfying dish if your sauce of choice is something heavy or clunky.

On the other hand, when it comes to lighter sauces such as olive oil based or delicate herb infused creations, spirals might not be your best bet.

Their intricate curves and crevices can sometimes overshadow the subtlety of these sources, leaving them lost in the labyrinth.

Literary Ridges alright, let's talk about the venerable penne, whose shape cannot be discussed without acknowledging the etymology.

The tubular form emulates the old metal penninu or pen, much like its stationary ancestor.

Penne picks up pasta sauce with the ease of a quill and an inkwell, aided by its large diameter and hollow center.

So sauce can be held inside and out and only strengthening the already formidable gripping power of this pasta is, of course, those ridges.

As your penne cooks, those ridges create friction against the sauce similar to how fingerprint ridges help you grip a little snack in your gritty little claw, providing ample opportunity for it to cling to every nook and cranny.

This means that even the most delicate of sauces, such as light tomato basil, find a sturdy anchor in the roof, rugged terrain of Penne Regatta.

Basic Bocchetti let's not overlook the classic spaghetti, the thin string like pasta, which features in so many of our collective childhood memories of Bolognese dinners.

But while it may seem like a straightforward choice, many believe that spaghetti's thinness and uniform cylindrical shape is not the ideal for chunky sauces.

Yes, that includes crumbled meat concoctions.

In fact, spaghetti is well suited for dishes with thinner sauces like aglio a oleo, where the oily sauce and pasta are involved.

Why, you ask?

Ever heard of ying and yang?

The objective is to savor the sauce's flavor without overwhelming the palate with excessive oiliness in each bite.

Spaghetti's long and smooth surface allows these lighter sauces to adhere evenly, aided by the ever important sticky starch, without creating pockets where oil accumulates.

Equally, the slender, delicate quality of the thin spaghetti means the pasta taste won't overwhelm the subtle flavor flavors in the sauce.

Instead, the pear pas de deux in perfect harmony upon your tongue.

Chef's Kiss now that's amore.

Pairing pasta shapes and sauce goes far beyond mere aesthetics.

Each shape has been meticulously crafted and changed by culinary enthusiasts throughout the centuries, whether by maximizing sauce adherence or providing the perfect vessel for flavor absorption.

So the next time you're faced with a plethora of pasta options, remember to consider not only the cultural history but also the empirical logistics behind each shape and source pairing.

After all, a well informed choice is a first step towards pasta perfection every time.

And don't mix pasta shapes.

Don't you freaking dare.

Maths is more than just numbers on a page.

It's more than equations and theorems.

It's about understanding and making sense of our world.

It's a language, a tool, a a practice, a thing of great beauty.

And most of all, it gave us pasta, of which we should all be quite grateful for.

Maybe it's better to ask ourselves isn't what is maths but what isn't?

You can read the full articles or more stories like them@particle.scitech.org AU.