I fear that even contemplating writing the tirade of geekery that’s about to ensue might forever concrete my reputation as a mad scientist. Although I don’t really have a reputation as a mad scientist. Yet. This started out as a slightly bizarre twitter conversation with @Stellar190 and @PenguinGalaxy. About marshmallows. And the Universe. It all got a bit silly and ended up in a rather bizarre piece of recreational mathematics… After all of that, someone had to write a blog entry about it — so here it is! (By the way, if you’re not impressed by geekery for geekery’s sake, you may want to stop reading now.)

Still reading? Ok. Good for you! It all started when I posed the question (for no particular reason):

*“If the observable universe is a sphere, 46.5 billion light years in radius, how many marshmallows could you fit into it?”*

Well… A few approximations are necessary to figure this out. For a start, marshmallows are basically cylinders, roughly 3cm in diameter and 3cm in depth. For the sake of ease, let’s assume them to be perfect cylinders with a diameter of 1 cm and a depth of 3.085cm. Why 3.085cm? Because that’s one attoparsec!*

Using the dimensions of one marshmallow in parsecs, you can calculate the volume to be 7.85×10^{-55} cubic parsecs. So, if the observable Universe has a radius of 14 gigaparsecs, then it would have a total volume of 1.149×10^{31} cubic parsecs. Assuming my calculations are correct, it would, therefore, take 1.465×10^{85} marshmallows to completely fill the observable Universe. That’s rather a lot of squishy gelatinous goodness.

I’m reminded, however, that 10^{85} is certainly not 0.85 googol. But it’s still *1 456 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000* marshmallows! **

At some point (perhaps inevitably), black holes were mentioned. Making a black hole from marshmallows can be accomplished in one of two ways. Seemingly, both of these are non-trivial tasks. Here’s why.

Firstly, you could conceivably make a black hole from a single marshmallow. Any mass has a schwartzchild radius — a smallest size, below which it would be impossible to prevent gravity from collapsing the object into a singularity. To work that out, you need to know the mass of a single marshmallow. A 175g bag contains about 28 marshmallows, giving them an average mass of 0.00625kg. This would give a marshmallow a schwartzchild radius of 9.28×10^{-30} metres. Oh dear.

9×10^{-30} is a small number. A very small number. So small, in fact, that there isn’t really a proper name for it. A bit under one hundred thousandth of a yoctometre (the smallest SI unit of length). This scale is comparable to the amusingly named “shed” — a unit of area so small that it’s only been used a handful of times while studying subatomic particles like neutrinos. The schwartzchild radius for our single marshmallow is, however, still larger than the Planck length (the smallest unit of length with any physical meaning in our Universe!), so it’s still theoretically possible to do this. Theoretically. But somehow, compressing a marshmallow to the size of a subatomic particle doesn’t really seem feasible.

The other option for our marshmallow black hole is to gather enough marshmallows to let gravity do the job for us. The thing is, this isn’t directly possible. A thing about marshmallows is that, excluding the helium, they have a composition not entirely dissimilar to your average red giant star. They’re mostly made of hydrogen, oxygen and carbon, with some traces of things like sodium. Being as they contain hydrogen, if you gather together enough marshmallows, you’d actually form a star. Yes, you read that correctly. A star made from marshmallows.

The minimum mass required for a star to initiate hydrogen fusion in its core (becoming a red dwarf star) isn’t precisely known, but it’s believed to be around 0.075 solar masses. Given that we know the weight of those marshmallows, we can calculate that they have a density of roughly 73 kilograms per metre cubed. This means that 0.075 solar masses of marshmallows would make a sphere with a radius about 1.13 times that of the Sun.*** This sphere would contain approximately 20 nonillion marshmallows.

To be honest, I could probably say more about this. But this is probably the silliest thing I’ve ever written. I think that’s more than enough gratuitous geekery for one evening!

**EDIT–So evidently I had a couple of my values wrong in this post. But I’ve fixed them now. I should remember to double check my calculations before posting, the next time I engage in random mathematical silliness, I suppose. Thanks to those who picked me up on my mistakes.**

***I knew I’d find some use for that unit of measurement someday…**

**Just imagine how many smores you could make!

***Stars are denser than marshmallows. One solar mass of marshmallows would make a sphere with 2.67 times the radius of the Sun. Admittedly though, this is assuming that gravity wouldn’t start to collapse the marshmallows once you gathered enough of them — which it would.

Image credit: “Yella Mella Macra” by flattop341

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A Universe of Marshmallows