The Valerian bill: Lars' proposal

Dominik Bärlocher

25.7.2017

Translation: machine translated

Last week I calculated in an article how big Wikipedia will be in the year 2700. In the article, I asked you to do the maths better if you can. Reader Lars Pautsch has a suggestion as to how big Wikipedia will be in the time of Valerian.

Lars Pautsch is actually Head of E-Learning at the Centre for Education in Healthcare of the Canton of Zurich, but in his spare time he is a science fiction fan and repairs old bicycles. His email to me begins with the words "Your article on the Luc Besson film (which I unfortunately haven't seen yet) was so fascinating that I had to read it". In doing so, he came across the paragraph in my article in which I ask the number geeks to do my maths better.

My question: How big will Wikipedia be in the year 2700?

The reason I'm asking this is the film "Valerian and the City of a Thousand Planets", in which the database of the Alpha space station plays a central role. The database contains the collective knowledge of over 3300 planets. I have therefore calculated the average growth of Wikipedia, which is then calculated linearly up to the year 2700 and then multiplied by 3300. I already realised that the calculation was inaccurate when I did the maths.

Lars writes: "I thought you could just misappropriate the compound interest calculation for this and do the calculation for the exponential curve. I'm not quite sure if that really fits, but it was worth a try."

The 38-year-old designer also explained the calculation himself and attached it to the email in an Excel sheet.

He took the basic data from my article:

• A wiki article is on average 6.36 MB (exactly: 6.35985333174044 MB) in size. With pictures and all edits and everything.
• Wikipedia went live on 1 January 2002
• Valerian's adventure takes place in the 28th century. In our example, we take the year 2700.

Lars does the maths

His explanation: "I have used the compound interest formula to ensure that the number of items does not increase at the same rate but that the new items from the year are also added each year, resulting in an exponential increase in the number of items: Ke=Ka(1+p/100)^n"

"This multiplies the final capital (in this case our final article quantity or ultimately the final data quantity) by an amount according to the formula from the annual interest rate p (in this case this is the article growth by which the total article quantity increases each year) and this times the number of years of the term (here 2700-2002 = 698 years term)."

But first he calculated the interest rate. It works like this:

Articles per year / total number of articles * 100

or

302269.4444 / 5440850 *100 = 5.55555554739

From this he draws the following calculation:

Sought final article quantity in the year 2700 = total article quantity 2002 (here 5440850 articles) * (1+article growth as interest rate (here 5.55555554739)/100) raised to the number of years term (here 698)

or

x = 5440850 * (1+5.55555554739/100)^698

It's clear from the ship that this is going to be a crazy high number. The number of articles is still manageable, which according to Lars is 133 497 045 298 808 000 000 000. Unless your editor is mistaken, that's around 133 sextillion articles.

From here on, it's easier. Because an article is 6.36 MB in size. So Lars has simply multiplied the 133 sextillions by 6.36.

133497045298808000000000*6.35985333174044 = 8.49022E+23

Good, this is where it gets hairy. The result is even more incomprehensible than the 133 sextillions. But Lars has gone to the trouble of breaking it down.

"If you count the zeros: According to abacus-friedrich, 1x10²³ is 100 trillions.
Here the conversion is described: And if you then add 3 more zeros to the 18 zeros of exabyte you are at zettabyte with 21 zeros and we have 23. therefore 849 zettabyte... plus / minus."

Then multiply that by 3300.

8.49022E+23 * 3300 = 2.8017726e+27

or, a little more human-friendly

849 * 3300 = 2801700

That's 2,801,700 zettabytes. And this is where it gets really hairy. That's about 2801.7 yottabytes. Incidentally, contrary to rumours, the unit is not named after the character Yoda from Star Wars. Or even 2.8 xenotabytes.

Wikipedia has an interesting little fact about the yottabyte.

• In 2010, it was estimated that if one yottabyte were stored on 1TB disks, then the data centres of apartment block size would have the same area as the US states of Delaware (6447 km²) and Rhode Island (3144 km²) combined. This equates to an area of 9591 km², or the area of the cantons of St. Gallen, Graubünden, both Appenzell and Basel Stadt combined.
• By the end of 2016, storage media were so advanced that the SD cards on which the Yottabyte would be stored would only take up twice the volume of the Hindenburg. That is around 400,000 cubic metres.

Why are you doing this?

All calculations aside, the question is: Lars, why are you doing this? "I'm a fan of Luc Besson films. I think he makes the best films ever alongside Ridley Scott. My favourite film of his is "The Fifth Element" with Milla Jovovich," he writes.

That's enough for him to work out how many yottabytes or xenottabytes a database will have.

However, Lars admits that the calculation is probably not correct. "It's just a bit of fun maths," he says. He's not entirely sure whether the calculation works at all and whether the result is in any way realistic.

So you can do better? Work out how big Wikipedia is in the year 2700, curve and all, and send me an email. Because I think we can work it out. Since Lars won the cinema ticket, we would have run out of prizes. We would have. Because at Pathé Films, the film distributors responsible have searched through their cupboards and drawers and found another cup that changes colour. Whoever dares to pick up the bill, owns it.

Finally, this: Incidentally, the trailer for "Valerian and the City of a Thousand Planets" features a cover version of the song "Gangsta's Paradise" by Coolio. Wouldn't you believe it?

Here's the trailer:

and here's the song without sound effects and everything:

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Dominik Bärlocher

Senior Editor

dominik.baerlocher@digitecgalaxus.ch

Journalist. Author. Hacker. A storyteller searching for boundaries, secrets and taboos – putting the world to paper. Not because I can but because I can’t not.