Back in the early 1900s, before calculators lived in our pockets, crunching numbers was painstaking work. Adding machines existed, but they weren’t exactly convenient nor cheap. Enter Wilken Wilkenson and his Maximal Multi-Divi, a massive multiplication and division table that turned math into an industrialized process. Originally published in Sweden in the 1910’s, and refined over decades, his book was more than a reference. It was a modular calculating instrument, optimized for speed and efficiency. In this video, [Chris Staecker] tells all about this fascinating relic.
What makes the Multi-Divi special isn’t just its sheer size – handling up to 9995 × 995 multiplications – but its clever design. Wilkenson formatted the book like a machine, with modular sections that could be swapped out for different models. If you needed an expanded range, you could just swap in an extra 200 pages. To sell it internationally, just replace the insert – no translation needed. The book itself contains zero words, only numbers. Even the marketing pushed this as a serious calculating device, rather than just another dusty math bible.
While pinwheel machines and comptometers were available at the time, they required training and upkeep. The Multi-Divi, in contrast, required zero learning curve – just look up the numbers for instant result. And it wasn’t just multiplication: the book also handled division in reverse, plus compound interest, square roots, and even amortizations. Wilkenson effectively created a pre-digital computing tool, a kind of pocket calculator on steroids (if pockets were the size of briefcases).
Of course, no self-respecting hacker would take claims of ‘the greatest invention ever’ at face value. Wilkenson’s marketing, while grandiose, wasn’t entirely wrong – the Multi-Divi outpaced mechanical calculators in speed tests. And if you’re feeling adventurous, [Chris] has scanned the entire book, so you can try it yourself.
“Vilin Vinson”? It says “Wilken Wilkenson”, legibly, right there in the article’s header image.
In fact, the only search result for “Vilin Vinson” online is this specific article.
I could understand if it was an anglicization of a name that comes from a language which doesn’t use the Latin alphabet, but Wilkin’s name doesn’t even use ÅÄÖ. Come on, now.
He was Swedish, so you would expect the Ws to be a voiced V sound and the Ks would most likely be an unvoiced sound I cannot adequately render, something but csh-ish. You evidently expect the latin alphabet to be voiced the same your langauge, so maybe you thought Sven’s name was Goran rather than Yoehran. Each to their own.
Except you wouldn’t expect the Ks to be pronounced like that if you actually knew the first thing about the Swedish language.
The pronunciation of K is highly dependent on the grapheme and even the word. Unless you’re trying to tell me that the word for “cow” (ko) is somehow pronounced with something other than a hard ‘k’. Or the name Karl. Or the word “kung”. Or the word for “the queue”. Which is an interesting one, as whether the K is pronounced soft or hard in “kön” indicates whether it’s the definitive “the queue” or the indefinite “gender”. Oh, and the word for “shall” (ska).
And yeah, sure, I must have just had some dust in my ears when earlier this evening some colleagues and I were having some beers and toasting each other (“skål!”).
But you know what, we don’t even have to go that far. How is the K pronounced in the word for “which” – vilken – which is just one letter off from the author’s forename? I’ll give you a hint: Even the most heavily-accented backwoods old dude from Nörrland would still pronounce it with a hard K.
But what would I know? I just live here. Thanks for incorrecting me, guy.
It’s pronounced vil-ken vil-ken-son just like you would in English (with the K). I don’t think this is a Swedish name, it was probably taken on by him during his trip to the US. I’ve never heard of anyone with these names here, especially not in northern Sweden (around Falun, where he was born). Villumsen is the closest I know around those neighborhoods, but it’s a very rare. People in that part and at around that time would typically be named after kings or norse stuff, like Erik, Gustav, Karl, Henrik, Johan, Birger, Alexander, even Adolf…
BR,
Actual Swede
Oh, and if this was not clear, with the -son suffix for surname. Svensson, Johansson, Eriksson, Henriksson, Gustafsson, etc.
His given name was Hanses Vilken Andersson which he later changed to Wilken Wilkenson. It’s all documented in “Gamla Falukamrater” (loosely translated: Old friends of Falu), see https://gamlafalukamrater.com/onewebmedia/GFK%202010%20tryck.pdf page 4.
I have no good explanation where they got “Vilin Vinson” from though, perhaps they were using speech to text and it got mangled or autocorrect did its usual shenanigans?
There’s at least one write-up about him on Gamla Falukamrater even without the PDF, t.ex. here: https://gamlafalukamrater.com/traditioner%20mm/wilken%20wilkenson.html
That article also links to a URL – wilkenson.se – which, notably, is not “vinson [punkt] se” (separating it out just in case the URL links to something bad). The link is in the last section of the article, “Ytterligare information finns på familjen Wilkensons hemsida.” (“Additional information can be found on the Wilkenson family homepage.”)
Doing some digging via the Wayback Machine, the last valid crawl of the latter site was on 16 Juni 2021 (inkl. the rather clear opening line “Hemsida för ättlingar till Nin och Wilken Wilkenson från Röjeråsen i Dalarna.” – “Homepage for descendants of Nin and Wilken Wilkenson from Röjeråsen in Dalarna county”). By the next two crawls, 9 December and 25 December 2021, the content of the primary frame on the site is replaced by the phrase “This site has been temporarily disabled, please try again later.” God jul indeed.
From and since the next crawl of the site in 3 October 2023, all archives are simply of a landing page from some Swedish domain-squatting company called “Domain Brokers”, until now, where the domain does not even resolve via DNS. An ignominious end to a great man.
To avoid the URL being claimed by domain-reselling squatters in the future, I have paid the princely sum of 323,75kr in order to acquire it myself. In the unlikely event that any of his descendents are still alive and would like to maintain his legacy – a chance made much less likely if the HaD editors don’t fix the erroneous name in the third sentence of this article – they can hopefully get in contact with HaD for the e-mail address and I will be more than happy to assign it directly to Wilkenson’s family.
There’s at least one write-up about him on Gamla Falukamrater even without the PDF, t.ex. here: https://gamlafalukamrater.com/traditioner%20mm/wilken%20wilkenson.html
That article also links to a URL – wilkenson.se – which, notably, is not “vinson [punkt] se” (separating it out just in case the URL links to something bad). The link is in the last section of the article, “Ytterligare information finns på familjen Wilkensons hemsida.” (“Additional information can be found on the Wilkenson family homepage.”)
Doing some digging via the Wayback Machine, the last valid crawl of the latter site was on 16 Juni 2021 (inkl. the rather clear opening line “Hemsida för ättlingar till Nin och Wilken Wilkenson från Röjeråsen i Dalarna.” – “Homepage for descendants of Nin and Wilken Wilkenson from Röjeråsen in Dalarna county”). By the next two crawls, 9 December and 25 December 2021, the content of the primary frame on the site is replaced by the phrase “This site has been temporarily disabled, please try again later.” God jul indeed.
From and since the next crawl of the site in 3 October 2023, all archives are simply of a landing page from some Swedish domain-squatting company called “Domain Brokers”, until now, where the domain does not even resolve via DNS. An ignominious end to a great man.
In the unlikely event that any of his descendents are still alive and would like to maintain his legacy – a chance made much less likely if the HaD editors don’t fix the erroneous name in the third sentence of this article, which would affect SEO – I have paid the princely sum of 323,75kr to register the domain so that it doesn’t fall into the hands of domain-squatting companies again, and will gladly reassign it for no cost. The only issue would be getting in touch, as the HaD moderators have shadowbanned the IPs and names I usually use to comment, so I am having to do this from my mobile.
Sorry about the double-post, it looks like comments from my desktop just take a while to show up rather than being outright shadowbanned, while from my mobile they show up immediately.
Using an AI summarizer on the video gives “The Maximal Multi Divy, published in 1951 by Vilin Vinson”
I wonder how many errors there are in the tables of numbers!
Well if you listened to the above, the author was so confident, that he offered 1000 if a mistake was found. Also the presenter checked a few and found no errors.
Neat, quick lookup for the time period.
Sheesh, whatever engine is behind posting removed my 1000 “I’ll call it dollars” so it doesn’t get removed.
You’ve got to sanitize your inputs if you want to avoid a bobby tables type situation
https://xkcd.com/327/
Reminds me of the Handbook of Chemistry and Physics aka “the CRC” (As in “get me the CRC”). Table of everything.
I have my dad’s copy from the mid 50’s. I’ve used it within the last 2 years to look something up, when I can’t get the internet to understand what I’m looking for.
The tome weighs around 6.5 pounds (~3 kg) . As a teen I always liked the “laboratory arts and fomulae” section.
There is (was?) a CRC Math Handbook. Table of integrals, lots of good trig + tables to 5 places, I think some Bessel function tables and maybe another special case of the hypergeometric equation. But most related to this story, nice precise tables of log and ln, plus interpolation formula in case you need to find a value between two entries, and you can use these to multiply, the same as a slide rule but more precisely. And pretty quickly. Mechanical calculators like a Marchant, were used a lot for interpolation calculations.
I used to have a couple cut down engineer’s vest pocket handbooks similar to this and would like to replace them. Now I’ll have to look for the CRC handbook as well, thanks.
I have a CRC index amongst other handbooks. They are some of my favorite books. This book though… Woah. I want to understand how they even did it.
Mine is the ’79 edition, right next to my copy of Perry6 Chemical Engineer’s Handbook.
It bring back some nice memories, the natural long rules book, the large tables used in Thermodinamics to calculate air conditioning, the tables used to determine the properties of steel, like percentage of carbon an other elements, and don’t forget those nice graphs( I don’t remember the proper name) where there was 3 or 4 vertical scales, one for R , one for L, another for C and the last one for the frequency of resonance. so you had to use a ruler to aline each value to find the last one. Sigh, time flies when you are having fun.
A nomograph?
There you go!, I loved the time when the teacher used to write down on the chalkboard a very complicated problem to solve and we spend the next our looking our big fat tables :) great memories( including one when I got a sweet bite in my arm from a lovely girl! but that’s anotther story :)
Vilken means “which one” in Yiddish. So as usual the Torah scholars were teasing the truth well in advance of his arrival!
Same meaning in Swedish also, interesting!
well thanks for confirming what i was thinking about this morning with the Vs and Ws while watching Tibees earlier. i had an old friend who used to pronounce letters the same way… and even though my old aim screen name from childhood was greatestone4eva i’d never call my invention “the greatest ever.” — having ambition for one’s self is a bit different. anyways i’m grateful for the corroboration. thanks Heidi!
I wonder if AGI were to scan the book—might it find patterns..and become the next Ramanujin
That’s not even close to a real Swedish name though. Must be something else. Nice book though.
Makes me wonder when was the last time someone evaluated lookup strategies to speeding up lower bit count multiply adds in modern hardware. Could fp4 or fp8 calculations go faster or use less power as 128 or 64 parallel table lookups into an onboard ROM? We did some of that in the 70s and 80s to accomplish real time calculus on 8 bit processors. Maybe this is still done in the FPGA universe.
It definitely is for a number of high volume operations like broadcast streaming encoders and network hardware but I don’t know the details. A number of manufacturers just ate the cost of sticking FPGAs everywhere in production hardware so they could iterate faster and it paid off. You can see this even in some 20 year old Cisco switches, while HP equivalents I saw at the time seemed to avoid it.
Just to give you an other Swedish mathematical hole do dig in to, I give you the Scheutzian calculation engine: https://en.m.wikipedia.org/wiki/Difference_engine#Scheutzian_calculation_engine