Cold Case: Carl Friedrich Gauss and the 100 Integers

Cold Case: Carl Friedrich Gauss and the 100 Integers

Remember the story of that kid who was given a class assignment to add the first 100 integers together, and solved it almost immediately to the astonishment of his teacher? That was Carl Friedrich Gauss, famed 19th century mathematician. A lot of us have heard this story in school, but American Scientist editor Brian Hayes got to thinking about its inconsistencies: was the story really true or even that amazing? Hayes writes:

The story was familiar, but until I wrote it out in my own words, I had never thought carefully about the events in that long-ago classroom. Now doubts and questions began to nag at me. For example: How did the teacher verify that Gauss’s answer was correct? If the schoolmaster already knew the formula for summing an arithmetic series, that would somewhat diminish the drama of the moment. If the teacher didn’t know, wouldn’t he be spending his interlude of peace and quiet doing the same mindless exercise as his pupils?

This article has also clarified something to me: the essential aspect of academia is documention.

When I was in grad school, the vibe I got from academia was that the process was a sort of hazing ritual you undergo, before you’re allowed “in the club” and can get your degree. However, the academic process, once you subtract the research lab drama and interdepartmental politics, is critically useful when it comes to “debugging” long-held assumptions. Without that paper trail of insight, we’d be doomed to repeat our mistakes or re-discover concepts the hard way. A true scholar has a deep understanding of his chosen field, and thusly stands on the shoulders of those who came before. The result: we can reach a bit higher than before.

The issue I have with academia is similar to the one I have with organized religious organizations: dogmatic, organization-centric protectionist thinking. This is perhaps inevitable when the academics (rich with generations of carefully documented theory) meet the street implementors (rich with what actually is working). Both camps circle the wagons when they encounter each other:

  • The academics, stung by how years of research have caused them to lose touch with working reality on the street, cling to the tradition of scholastic rigor as their prime differentiating factor. “We’ve got the discipline and the minds” they assure themselves. “We don’t just make stuff up and hope it works. This is valuable, and this approach is the very foundation of our modern civillization. Even if these guys who are making more money than us think otherwise.”

  • The street implementors, practical nuts-and-bolts people who have apparently rediscovered the classics, are stung by the academic position that, yeah, it’s been done before, and we’ve got a jargon-rich citation trail to prove it…what is your degree in again? So the street implementors, vaguely threatened by these claims and yet unimpressed by them (they’ve been scammed by such claims before) , cling to the idea that “what works is what matters”. But secretly…they wonder if they just aren’t smart enough.


p>Although I started out on the academic path, I became disenchanted with its emphasis on credentials and lineage within the school…when human selfishness to “work the system” for personal gain obscured the “purer mission”. In other words, I let the bastards get to me, both in organized religion and in academia. This is a second, significant personal datapoint. How many babies have I tossed out with the bathwater?

My takeaway from the article (and this is just something that is occuring to me as I type) is at a very minimum, it was academic process and organization—the libraries, the use of citation, and old-fashioned research—that allowed Hayes to even start to answer his question. As he uncovered citations and references, the search became more than “what’s the literal truth”. He came upon the natural human tendency to tell stories and embellish events that unintentially cause deviations from the source; these are the dirty pawprints of undeclared agenda. These are the very forces that the acadmic process seeks to minimize; through documenting a line of reasoning and stated assumption, transparent to all who would take the time to follow it again, academia does keep ideas moving forward.

There’s a parallel idea in journalism: the reporting of fact, citation of sources, and documented first-hand accounts is very similar in that it keeps our understanding of our society moving forward. However, the mainstream media has shifted to news as content, as opposed to news as documented reality. Consuming “news as content” is the equivalent of imbibing nutritionally-empty calories, temporarily satisfying our sweet tooth but ultimately killing us in the end.

We are doomed to repeat our mistakes when we don’t have a sense of history. Even worse, it’s far too easy to insert fabrications into the continuity of events because no one is checking up on them. It takes too much effort for the average citizen to work through the news media channels to verify a story, so the news media catches a break due to its unresponsive Jabba-the-Hutt like mass. And this makes the news media subsceptable to manipulation…witness the role of P.R. agencies that can insert news into tired journalists newstreams. Or the power of lobbyists in Washington, knowing that if they can inject their issues directly into the sensorium of the politicians themselves, they have the jump on the rest of America. And the system is fragile: in shows like 24 and Prison Break, we can see this illustrated dramatically, as “evil government agents” casually corrupt the information stream by subverting the systems that allegedly record it. It’s only possible because these systems—the organized media, corporate accounting systems, and government agency—are not transparent in a way that is accessible to the individual. We instead must observe by proxy. And we’ve learned to distrust the old proxies, because we know they are at best incomplete. At worst, they are incompetent. If this seems preposterous to you, just think of a more local example: spreading a rumor based on a half-truth. While ideally we can have a system where there really is an emphasis on trust, pragmatically speaking you can’t have trust without a means of verification. Yeah, I know…”trust but verify”.

In this atmosphere, it’s not surprising that blogger-journalists are on the rise. Though the “real” reporters poo-poo the lack of professional standards, they miss the point: the real journalists have already lost credibility because their organizations can’t compete with the new medium’s ability to transparently provide meaningful continuity. The blogosphere is self-documenting and self-validating, thanks to the low threshold of entry and concentrated fact-checking power of the Internet. We have Google, pings, trackbacks, and services like Technorati, we do have the infrastructure to rebuild our foundation of trusted sources. We can even incorporate old media sources back into the validation chain through hyperlinking, digital imaging, and audio sampling. We can finally follow the trail again. I am starting to believe that while Content is sexy, it’s Continuity that reigns in the long run.


  1. Steven 18 years ago

    Wow, that was a great piece.


  2. James Neal 18 years ago

    David … you are so intelligent and so passionate … everytime I read your blog I get inspired … Are you familiar with; I think it’s a great site and points to your arguments about blogger-journalists.

  3. Dave Seah 18 years ago

    James: I’d heard of newsvine, but I didn’t connect the dots like you just did! Awesome! I’ll have to check it out with that in mind!

  4. Yelena 17 years ago

    It would be a grand world if there were more thinkers such as yourself. You have an astounding piece of nonfiction here. Your thoughts are expressed clearly and the writing in and of itself is eloquent. I truly loved it!