# Trying to break AI with marshmallows

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I was recently browsing Reddit when the following discussion came up.

Calculating the exact number of marshmallows needed to fill St. Paul’s Cathedral would require precise measurements of the cathedral’s interior space, which I do not have access to. However, I can provide some estimates and calculations based on average sizes and volumes.

Assuming that St. Paul’s Cathedral has a volume of approximately 200,000 cubic meters, and an average marshmallow has a volume of around 3 cubic centimeters, we can estimate that it would take approximately 66,666,666 (200,000,000 / 3) marshmallows to fill the cathedral completely.

It’s important to note that this is a rough estimate and the actual number could vary depending on the exact dimensions of the cathedral and the size of the marshmallows used. Additionally, filling St. Paul’s Cathedral with marshmallows is not recommended, as it could cause damage to the historic building and is not a practical or safe use of resources.

The author is of course correct that it is (a) a rough estimate because the calculations are wrong as 1 million cm³ = 1m³, and (b) while filling a cathedral with marshmallows is tempting, it is impractical — even though we live in times of a Puffy Pope.

In the subsequent discussion thread, the calculations were discussed further.

-SaC
Is this taking into account the fact that the weight of marshmallows en masse will compress those beneath to a degree?

-happyjoypeace
You just outsmarted AI.

I was rather taken aback by the use of a simple question to illustrate the cognitive distance between humans and AI, even to the supposed levels of thought that AI is now capable of.

So, I had some fun of my own.

Time for some creative experimentation.

Of course, putting 1 marshmallow on top of another won’t reduce the surface area sufficiently to allow more marshmallows into a defined space. But, what weight will do that?

It turns out that the combined weight of two O’Reilly programming manuals — in this case Javascript: The Definitive Guide and Perl Cookbook — will squash a marshmallow by 50% at an aggregate weight of 2.3kg. I thought that might help me to understand the weight required to squish a sufficient number of marshmallows in a surface area in order to allow for more, but it was a red herring. Or, rather, a pink Chamallow.

To figure out how marshmallows could truly fill St. Paul’s Cathedral, I had to get its dimensions. The problem is that although the building is unquestionably beautiful, it’s difficult to get a true representation of its surface area. So, let’s go for another building.

In keeping things simple I chose The Cube, which is a mixed-use building in central Birmingham and literally cubic; all sides are exactly equal.

My calculations are:

The Cube = 53.1m at all sides = 149721.291m³
Marshmallow = 0.03m at all sides = 0.000027m³
Marshmallows in The Cube = (100/((0.000027/147291.291)*100))=5,545,233,000

5.5 billion marshmallows are required to fill The Cube.

Weight of 1 marshmallow = 6g
Weight of all marshmallows = ((5545233000*6)/1000000)=33271398000g = 33,271.398 mt

5.5 billion marshmallows would weigh just over 33,000 metric tonnes.

Right then. Let’s start squishing them down.

If you reduce the surface area of one side of the marshmallows, ie you reduce the height by 2, then:

Marshmallow = 0.03*.0.015*0.03 = 0.0000135m³

Only the height is important for the sake of simplicity. You can only attack the marshmallows filling up The Cube from the top rather than the sides because open windows will allow marshmallows to escape. So, by doubling the amount of possible marshmallows in the height of The Cube, you have the possibility of…

Half-height marshmallows in The Cube = (100/((0.000027/147291.291)*100))*2=11,090,466,000

…. 11 billion marshmallows in The Cube. But, that can’t be true unless all marshmallows are equally squashed, and as they get to the top, you’re going to need quite a few copies of Javascript: The Ultimate Guide and Perl Cookbook to pre-squash them prior to entry into the building. It doesn’t work.

So, let’s assume that because marshmallows are good at retaining their mass under pressure, that the building can average out at half the marshmallows being 50% squashed, and the other half being not squashed as gravity will squash the marshmallows towards the bottom — as per the observation on Reddit. It’s not really 50/50 squashed/unsquashed though — I could probably work the ratio of squashed against unsquashed by performing more complex weight/height/volume calculations, but let’s leave it at 50/50 for now.

Weight if all marshmallows in The Cube were compressed = 66,542.80 mt
Weight of half each (144,176.06/2 + 288352.12/2) = 49,907.10 mt

Number of marshmallows at 50% full-height + 50% half-height to fill surface area of The Cube = 8,317,849,500

Weirdly, ChatGPT got the first calculation wrong too. 149721.291/0.000027 is 5,545,233,000 and not 5,549,297,407. It has overestimated how many marshmallows can fit into The Cube by 4 million; interesting in itself because ChatGPT is either trying to perform a calculation in a human way (ie with a certain degree of error) or it’s making an assumption that you can indeed fit more marshmallows in, given that the load at the bottom would be flattened under the weight of the top, which is how I came to my 50% squished ratio.

When I asked ChatGPT to explain itself, it got it wrong again.

There’s definitely room here to explore trustworthy AI in further detail. I would have entrusted ChatGPT to come up with the right answer because, put simply, it’s a computer and would use logic gates to come up with a logical answer. The concept of caveat emptor is writ large here.

Although AI is clearly at a nexus point in terms of consumer-grade practicality, there’s a long way for it to go in terms of understanding the subtleties of life. It doesn’t “understand” that marshmallows can squish because it doesn’t necessarily understand what a marshmallow is, and what its physical properties are. If you apply that subtlety to other parts of life, you’ll see that value comes to nuance in all sorts of ways. A GP’s receptionist saying “Well, the patient at 2pm is usually only here for a few minutes, so we can probably squeeze you in then” is several dimensions of nuance beyond a GP’s schedule being blocked for an appointment for 30 minutes at 2pm.

Nuance and subtlety is how we understand the world. AI will get there, but it’s that level of abstraction that is, in itself, several layers of abstraction away from pure logic.

My thanks to OpenAI’s ChatGPT software, and Haribo GmbH in the making of this article.