You swear you tidied things up half an hour ago, but then you turned your back and somehow the mess and clutter returned.

It's a perennial problem, one made more acute by all the extra time we're spending at home at the moment.

But what if it wasn't only you (and the recalcitrant members of your family who refuse to put anything away) that was causing the problem?

What if it was the universe?

The reason our homes always become messy is due to the second law of thermodynamics, says chemist and science communicator Alice Motion of the University of Sydney.

You know, the one that says the chaos or disorder of our universe always tends to increase.

#### Blame it on the entropy

"All of the laws of thermodynamics are really important because they describe what drives our universe," Dr Motion says.

Basically, the laws neatly summarise the properties of energy, and the way it changes from one form to another.

Even the most organised amongst us might have noticed over the course of a day or a week that our desk or our rooms get more and more disordered, she says.

And this is quite logical when you think about it.

"There are so many more ways in which your bedroom, or whatever room in your house, could be messy and disordered, than there are ways that they can be ordered," Dr Motion says.

We can measure this mess using a property called entropy, which is basically a measure of the disorder of the system we're looking at.

"The higher the entropy, the more disorder we have," Dr Motion says. "So basically disorder in our universe is always increasing."

But what's the entire universe and everything in it got to do with the state of your home?

Well, picture an idyllic bedroom that's neat and tidy, Dr Motion says.

"We've got a bed in there, we have some books on a bookshelf, and we have a wardrobe and a chest of drawers that has some clothes in it," she says.

If we open up the sock drawer, all of the socks could be neatly folded, Marie Kondo-ed in a beautiful fashion, like they are in Dr Motion's drawer.

"It's my one true exception," she laughs. "The place of lowest entropy in my life is my sock drawer."

But in a less idyllic bedroom, those same socks could be all over the floor, they might not be in pairs, they might be mixed up, or in a complete jumble in a basket at the bottom of the bed.

"An excuse perhaps for a messy bedroom is that it's simply obeying the second law of thermodynamics," Dr Motion says.

#### The maths of making a mess

The problem is when we consider how many things we have in our homes and the number of ways we could arrange them, that number gets really big really quickly, says statistician Jonathan Tuke of the University of Adelaide.

This field of maths is called counting arguments or combinatorics.

It's used a lot in probability — for example, if you wanted to calculate the probability of getting three aces in five cards from a standard 52-card deck.

Or applying it to the bedroom example above, the probability of your socks being arranged in an orderly fashion versus contributing to the overall chaos of your surroundings.

Does this suggest there might be some maths behind Marie Kondo's exhortation that we only keep the things that "spark joy" for us?

For if we own fewer things, surely there are mathematically fewer ways to arrange them?

"Absolutely," Dr Tuke says.

Consider a simple example.

Let's assume in your house you just had 10 things and you'd arranged them in a straight line on a shelf.

If you were to add an 11th thing to that line, there would be 11 places you could put it, at either end of the line or between any two objects already in the line.

But add another item and the number of places you could put it on the shelf has gone up to 12.

And that's just arranging one shelf, Dr Tuke says, "never mind that your house is going to be all the shelves, all the rooms".

While in the example above adding an extra item didn't make much difference, in some situations adding an extra item can dramatically increase the number of possible arrangements.

If you consider Sudoku puzzles, the number of possible 1x1 Sudoku puzzles is 1.

But by the time you get to a 9x9 grid, the number of different ways you can arrange the numbers in the grid without breaking the rules of Sudoku is 5,472,730,538.

This is called a combinatorial explosion.

In this way we can see that reducing the number of things you own even by one, can have a much greater effect on reducing the number of ways you can arrange all the remaining items.

#### Should you throw out nearly everything or never tidy up again?

Well, maths might be able to give us a helping hand if we're trying to figure out how much stuff we should own, Dr Tuke says.

Let's say you're trying to declutter your wardrobe.

"You could do it probabilistically, or you could do the classic argument of how many changes of clothes do you need?" he says.

Let's say you only want to do laundry once a week. A back-of-the-envelope calculation says you'll need seven items in each clothing category: tops, bottoms, shoes etc.

But if you don't want to look exactly the same every Monday, Tuesday, Wednesday, and so on, then counting arguments can also help you figure out how many possible outfits you have.

Multiply the number of choices you have in each category together to get your answer.

So if you have seven tops, seven bottoms and seven different pairs of shoes, that means you have 343 possible outfits.

And if you wore each outfit it would be almost a year before anyone saw another match.

"The other thing to remember is that there's definitely psychological evidence that too much choice paralyses people," Dr Tuke says.

"I think it's about seven or less you cope quite happily … If you have a huge amount of choice, it really just knocks you over."

So reducing the number of choices you make can also be good for your psychological wellbeing.

However, once you've decluttered and hence reduced the number of ways you can arrange what remains, you will inevitably reach the point where you need to tidy up.

"All of us at some point, do tidy up our bedroom or tidy up our house," Dr Motion says.

But isn't that pitting little old us up against the might of the universe and its increasing chaos?

Well no, Dr Motion says, because even though we might have increased the order or reduced the entropy in that particular room, by tidying up we've still increased the disorder of the universe.

Confused? Us too. Dr Motion explains one way it could work.

"We can't do work on our room — which is another way of describing thermodynamics — unless we have energy. And the way that we get our energy as humans is by eating," she says.

While the food you eat may be fairly ordered, when you digest it, it becomes a lot more disordered.

"It breaks down into carbohydrates, it breaks down into lipids or fats, it breaks down into proteins," Dr Motion says, until it gives us energy in the form of other biochemical reactions.

"So essentially what's happened is your room has got more ordered, but in order for that to happen ... we probably had to use some energy."

And to produce that energy in the first place, we increased the disorder in the universe.

So overall the disorder in the universe is always increasing, that's just the way that these things work.

Universe 1. Tidy house 0.