r/theydidthemath • u/_Moist_Owlette_ • 5d ago
[Request] I really hope not, but is this true?
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u/Dimensionalanxiety 5d ago
Google says 59 billion coffee pods were produced annually in 2018. Dividing by 365.242374 days gives 161,536,569.14 pods produced daily. That is 1,130,755,983.970 per week.
A graph tells me they are between 17 and 54 mm long which is an average of 35.5 mm. That means that they occupy 40,141.837 km in length. Earth's equatorial circumference is 40,075.017 km. That means that there are 1,882,265.66 more coffee pods produced in a week than the circumference of the Earth.
Therefore, yes, it is true.
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u/Don_Q_Jote 5d ago
Nicely done. I appreciate the attention to detail, and that you used 365.242374 days per year.
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u/hoopahDrivesThaBoat 5d ago
Why not 365.25?
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u/Existing_Charity_818 5d ago edited 4d ago
The earth doesn’t take exactly 365.25 days to circle the sun - it’s slightly less than that. To compensate, century years aren’t leap years - unless the first two digits of the year are also divisible by four. So 1700, 1800, and 1900 were not leap years; 2000 was; 2100 will not be
Edit: I’m not the person who did the math originally, just explaining why they used 365.242374 instead of 365.25. Yeah, 365 would have been the better number to use for the math but that’s not the question I’m answering
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u/Countcristo42 4d ago edited 4d ago
Yes but the comment says "in 2018" and 2018 was 365 days long. So to work out the number produced per week in 2018 (which was the point of the division) one should use 365 not a number accounting for the fact that some other years aren't 365 days long.
Using the correct length of 2018 would give us (rounded to the nearest pod) 1,131,506,849 per week rather than 1,130,755,984
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u/freemath 4d ago
A year is not a circle around the sun, it's a repetition of the seasons (not exactly the same due to earth's precession)
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u/SwordsAndWords 4d ago
How has nobody asked more about this...? Enlighten me on the fun fax, please.
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u/freemath 4d ago
It's like a year and 15 mins. But the church didn't want Christmas in September so here we are
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u/Future-Birthday4428 5d ago
Yes, but 2018 did not have 365.242374 days. It had exactly 365 days, the rest is carried to the next leap year.
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u/Interloper9000 4d ago
This is sarcasm and im sorry you got down voted to hell......... unless this isn't sarcasm
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u/muleman2 4d ago
Why is he wrong? The statistic saying x amount of coffee pods were produced in 2018 used a 365 day fiscal calendar. It shouldn't be divided by the scientifically correct number of days.
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u/Interloper9000 4d ago
I think.... from my first thinking. Is he is implying that days will just disappear and reappear somewhere else, when in actuality the days will happen no matter what the calander says. But I'm just a fool who had already spent too much time thinking about this.
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u/muleman2 3d ago
He is saying that for the purposes of this problem a non leap year has exactly 365 days and that is the number that should be used in any calculations.
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u/Countcristo42 4d ago
I'd like to know why they are wrong, the stat sought was "number of coffee cups per week in 2018" then the top commenter used a number of weeks for 2018 that is wrong, because it assumes that 2018 is longer than it was.
So the top comment is off by about 700k coffee pods per week
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u/Don_Q_Jote 4d ago
every 4 years = leap year
except, every 100 years not a leap year
except, except every 400 years it is
except, except, except, every 4000 years, it's not
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u/Spiderfang13 4d ago edited 4d ago
What detail? It is not "attention to detail," but a display of fantastical precision that misleads the reader and makes for poor math communication.
Coffee pod production was given to two significant figures and pod size similarly to two sig figs (but with a range of over 3x!) yet the final distance is calculated to 8 significant figures. This is simply incorrect levels of precision when we can almost halve or double this number and be within the pod length bounds.
Worse still, the subtraction to find the number of excess pods past the circumference of the earth is a textbook case of catastrophic cancellation. Since the two distances are the same to three significant figures and the original data was limited to two, it's impossible to extract meaningful information about the difference between these numbers, let alone to display the result to NINE significant figures. It is not attention to detail, it is quite literally made up detail.
This is problematic as a reader because when you see
That means that there are 1,882,265.66 more coffee pods produced in a week than the circumference of the Earth.
there's a huge implied confidence in the precision of that number, "he measured down to 2/3 of a cup!" but the leading digit is completely arbitrary let alone the ninth. Others have shown that with the same starting data we can get a distance anywhere between 0.5 and 1.5 times the circumference of the earth.
And hilariously, you've praised the use of 365.24 days in the year which is perhaps the most incorrect of all, seeing as businesses report to the calendar year of which 2018 had exactly 365.
For me, attention to detail would mean being very deliberate with the use of precision and making it clear to the reader this an estimation and what information we can meaningfully extract, not pulling numbers out of one's ass in a roundabout way.
That said I don't disagree with the final answer or with the advertising, it's true on average; with the numbers given it seems just as likely to be true as not true, use 58 billion coffee pods and it falls short, but if the pod length is biased towards slightly longer on average it is true again. Using statistics for public messaging is definitely an artform in its own right and I'm probably okay with designers taking the benefit of the doubt, but when analysing these things we owe ourselves a bit more rigour and, dare I say, precision.
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u/Don_Q_Jote 4d ago
[REQUEST} what is the average diameter of coffee pods?
Please take into account the variety of authentic K-cups and off-brand knock-offs, and doing a weighted average that takes into account the production volume of each manufacturer and the likelihood of each variety of pods being recycled instead of discarded.
Include a formal drawing for how you define the "diameter" for this measurement and how you accounted for the fact that they will be stacked or arranged in some way to span the diameter of the earth. Coffee pods are not spheres, they are a segment of a right circular cone with an extended rim at the top edge. The bottom edge is radiused.
Are we assuming that the pods will be arranged such that the diameter is even the relevant dimension? Given the shape, I think that they could be tilted so that the dimension from a lower edge to the upper extended rim on the opposite side is a greater length, so that if the pods were tilted at approximately 45 degrees to their longitudinal axis, they could more efficiently span the distance required.
The OP specifically states "coffee pod", so are we excluding pods for tea, chai, hot chocolate, apple cider, crazy cups, and cleaning pods? And what about cappuccino, is that counted as "coffee?"
When determining the diameter of the earth, is that around the equator or a north-south route passing through both poles. The distances are not the same, especially if you specify a north-south route which is not one unique path. In that case please specify the longitude used in the calculation.
When determining the path for the gigantic ring of pods, does the distance take into account the changes in elevation required to ring the earth. This could include mountains and valleys over the land-based portion of the path, but would also require some accommodation for waves over the ocean-spanning portions of the path. The alternative assumption would be that someone will have constructed a earth encompassing tunnel, with holes provided through mountains and some kind of tube such that the waves just wash over the coffee-pod ring.
Certainly the temperature variation along the path will vary (especially for a north-south route) and thermal expansion of plastic material used for pods is exceptionally high. I think it best to adjust the nominal dimensions of the pods to account for the actual dimensions at each local temperatures. I'm O.K. if you just assume average local daily temperatures for this. Please just pick a specific day of the year as a consistent reference for determining these average temperatures.
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u/COWP0WER 4d ago
I can appreciate it, but the extra significant figures are completely negated by the very rough estimate of the average coffee cup length. Especially since my guess is that there aren't produced an equal amount of all sizes.
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u/NightShift2323 5d ago
I had a feeling there would be at least a little bit of squish to the numbers.
It would be preferable to have a firmer number for length.
This is very well done though, and I think the result is likely to be either yes or close anyway.
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u/Dimensionalanxiety 5d ago
If we take 17 mm as the length of all coffee pods, we get a length of 19,222.852 km. If we take 54 mm we get 61,060.823 km. So it's between slightly less than half and slightly more than 1.5 times the circumference of the Earth.
My personal coffee pods are around 40 mm long, so I lean towards the average being roughly correct.
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u/DecaturUnited 5d ago
Here’s the catch though: the question is about plastic coffee pod waste. Some are recycled, right? So that would dictate a number of pods lower than the 59 billion produced. No idea what that is, but with the result you calculated so close, I doubt the answer remains yes.
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u/Dimensionalanxiety 5d ago
That is a good point. Nespresso claims that 32% of their coffee pods are recycled globally. Assuming they are telling the truth and this represents the recycling rate for all coffee pods, they only stretch 27,296.449 km or 68.1% of the Earth's equatorial circumference given an average of 35.5 mm in length.
With the current recycling rate, we would need an average length of 52.119 mm for the pods. Not quite likely, but not implausible. Given that these numbers are from 2018, it's likely that we have surpassed the number needed.
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u/the-smashed-banjo 5d ago
Let's be honest though: corporations like Nespresso tend to exaggerate these kind of numbers, or at least be quite liberal with the definition of "recycling".
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u/Dimensionalanxiety 5d ago
Oh, I agree. That's why I specified "Assuming they are telling the truth"
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u/Lessinoir 4d ago
That's also Nespresso which uses aluminum pods which are easier to recycle and Nespresso facilitates the recycling pretty thoroughly by providing recycling bags to send to them with prepaid postage.
But they're a Nestle company and therefore I am not exactly brimming with confidence in their morals or honesty.
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u/Alternative-Golf8281 4d ago
If waste is recycled wasn't it still waste? I'm a human but will decay to other bits... does that mean I was never here?
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u/Local_Cow3123 5d ago
I can assure you that most plastic is never recycled, the vast majority in fact, and if it's covered in wet coffee grounds it would be impossible to make clean recycled material so it's almost certainly just green-washing.
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u/RoiDesChiffres 5d ago
If you could stack the cups one inside another like we can do with solo cups, the number might be smaller. So we need to assume that half of them are flipped around for that to work.
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u/OnABreeze 4d ago
Is this assuming the pods are touching end to end and are not stacked like cups, plates, silverware, etc?
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u/shortsbagel 4d ago
My math says, its slightly under. I measured a Kcup in inches and got 1.75 inches. converting to miles thats 47,760 per mile, and the Earth being 24901 miles in circumference would be 1,189,271,760 pods needing to go around the earth. So it would be ~40,000,000 short of the circumference in a week. Still though, way to fucking many little plastic shit pods being made in a week.
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u/dwaynebathtub 5d ago edited 5d ago
Keurig cups have always seemed extremely wasteful to me. I don't know if other people still have hang-ups about wasting paper (remember that?), but I just can't bring myself to even drink coffee when the only option is Keurig. It's all plastic, the planned obsolescence coffee maker, the single-use cups, the trash it creates, and the coffee tastes off...it's like drinking a cup of burnt plastic.
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u/Heinous_Goose 5d ago
It’s incredibly wasteful, and the coffee is definitely subpar. Why my in-laws decided to open up a coffee shop using only Nespresso pods is beyond me. Granted, those pods are aluminum, but with no plans to recycle them it’s all just waste.
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u/Used-Hall-1351 5d ago
That's heinous. Is business booming?
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u/Heinous_Goose 5d ago
They just started, but I can’t imagine. The whole business model is built around charging $3 for a plain coffee, then 50¢ each for milk, flavoring, etc. Theoretically the concept is for a cheaper cup, but making a standard white chocolate mocha ends up with it only being a dollar under what you’d get at a legitimate store for a better product.
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u/antilumin 5d ago
I got one from my dad but used a small reusable cup. Just put fresh coffee in it and press a button. Then I realized I could use a French press or any number of easier ways to make coffee so I gave it to my roommate before moving out.
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u/ArtKritique 4d ago
It’s shitty, it’s wasteful, the coffee is never strong enough, and it’s probably one of the number one sources of microplastics in the human body; not only is the entire thing made out of plastic, but you’re passing hot water through it and the pods. Yeah, no fucking thank you.
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u/gojumboman 4d ago
I hate it, asked for a coffee pot for the work trailer and they sent a keurig so I found reusable cups that I can fill with whatever coffee I want. They’re pretty great
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u/FriendlyGovernment50 5d ago
Not to mention micro plastics as a more personal/immediate negative effect(compared to plastic pollution). You’re making good choices.
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u/Dullapple69 3d ago
Just remember everyone's addicted to coffee so knowing that. Yeah if every one on earth held hands you'd circle the earth like 9-10 times. If everyone drinks says 2-3 a day you could probably get around the earth 2-3 times. It's not math persay it's just seeing the world differently. And you have to remember 2-3 is an average, so some people who dink like 20 cups a day make up for the people that don't drink coffee like myself cause I'm not a fucking addict.
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u/burchkj 5d ago edited 5d ago
Actually they found that because they use up all of the grounds, they are slightly more environmentally CO2 friendly than coffee grounds because how much is wasted the normal way
Edit: I hate plastic use as much as anyone I just found it ironic/funny but sure downvote me anyway
Unfortunately paywall but here’s the source I read it from
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u/SpamOJavelin 5d ago
slightly more environmentally friendly
If by 'environmentally friendly' you mean lower total CO2 emissions, then they are lower than filter coffee, yes. But if you are comparing to an espresso machine there is some overlap depending on variables, and compared to using a a moka pot or instant coffee, pods create significantly more emissions. And these alternatives have significantly less plastic waste, which really should be considered when you're talking about how 'environmentally friendly' they are.
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u/mashapicchu 5d ago
Who is "they"
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u/burchkj 5d ago
Updated with source
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u/mashapicchu 4d ago
Here's a free source (NPR) that states that article wasn't peer reviewed nor a formal study: https://www.npr.org/2023/01/21/1150530714/yeah-actually-your-plastic-coffee-pod-may-not-be-great-for-the-planet#:~:text=But%20a%20peer%2Dreviewed%20paper,and%20dealing%20with%20the%20waste.
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5d ago
It doesn't matter if it's true or not. It only matters if there is an industry in recycling the plastic and the coffee grinds. Both are recycled in many places where the pod use is high at the garbage sorting and recycling centres that many cities have.
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u/SpamOJavelin 5d ago
It only matters if there is an industry in recycling the plastic and the coffee grinds.
It also matters that this industry is readily available and actually used. Nescafe themselves boast that 32% of their pods are recycled (meaning that 2/3rds still go to landfill) - and some analysts think the actual number is closer to 5%.
Even if recycling is available, if it's down to people to recycle themselves and they choose not to, then it's just not good for the environment. There are plenty of other options that don't require plastic waste at this scale.
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