Posted by: holdenlee | April 3, 2013

The Connection Machine and Collective Intelligence

Today in 6.868 (Society of Mind)Daniel Hillis gave a guest lecture on the potential of parallel computing for artificial intelligence. Hillis created the Connection Machine, the first massively parallel supercomputer.

What fascinated me most was the following analogy that came up during discussion:

processor:parallel computer :: human:society

With a good architecture, a parallel computer can carry out certain tasks much more quickly than a single processor, and can be said to be more “intelligent.” In the same way a group of people can be said to be much more “intelligent” than a single person.

How intelligent is a group mind?

However, we must be careful. We don’t simply get intelligence from putting a lot of computers or people together. Someone talked about an experiment, on estimating the number of jelly beans in a jar.

  1. When a lot of people are polled separately, the average of the guesses is quite good.
  2. When the same number of people are asked to deliberate together and come up with an answer, it can be quite bad.

The reason is that often the people who are best at convincing (or the ones who speak first), rather than the people who have thought through the problem, sway over the rest of the group.

The architecture of parallel computer is important, in making sure that there is actually a speedup. Moreover, certain problems are more parallelizable than others. Willis said that a lot of people mistakenly thought parallel computing was impractical because of Amdahl’s Law, but parallel computing is very good at certain specific problems.

In the same way, based on how a group of people conduct themselves, a group of people can be worse than the “stupidest” person in the group, or more intelligent than the combined sum. We often gripe about the stupidity of committees–which is not surprising considering that committees are not at all like parallel machines; everyone may be stumbling over everyone else trying to do the same thing, and the game becomes trying to rally behind a leader, as in the jelly bean story.

As a whole, though, society can be said to be much more “intelligent” than one person. What is the architecture of society? Rather than everyone trying to know a little bit of everything, most people in a society specialize in a profession, so that a society can make advances in many different areas at the same time. And some people, the managers, seem to embody the connections between these different areas.

Collective intelligence

Technology has vastly increased the amount of synergy we can get from a group of people. For instance, it has enabled us to assemble vast networks of knowledge, such as Wikipedia. It matches up people who have questions with the few who have answers (Quora, stackoverflow, mathoverflow). Connectivist MOOCs have assembled pathways of communication between thousands of learners. I think this is just the beginning. A key question for the future is

Will we come up with an emergent way of thinking that is better than thinking individually?

Jacob Cole brought up the following: Socrates believed in memorization of a lot of knowledge. Why? Jacob argued that the value of learning a lot of facts isn’t to have it all in your brain at once, but rather because when you have a lot of facts in your head, you can cross-link the knowledge in ways that aren’t written down! (In a previous post I argued that knowledge is more in the connections between facts than the facts themselves.)

In the age of the Internet, does each person still need to memorize a broad knowledge base? After all, we can look almost up almost any fact instantaneously. But if we don’t hold these facts in our head anymore–and with the explosion of scientific research, etc., it is impossible for one person to know any significant portion of a subject–how can we make the connections between them, that aren’t necessarily on the web? How can we implement computer systems that help cross-link knowledge?

This sounds like a faraway goal, but in fact there are very simple things we can do that facilitate the organization of knowledge, such as introduce a new hashtag: # classifies while #<-> connects  (see here for example of use). Information is usually stored on a computer hierarchically, but knowledge is not a hieararchy, it’s a network. We should use explicit graph visualization to better see the structure of knowledge on the web. For instance, rather than having blog posts be organized by just categories and hashtags, they should be the vertices of a graph, and a blogger should be able to draw edges with short descriptions to other posts. A reader would be explicitly presented with such a graph, and hence easily find other posts of interest.

Relation to mathematical research

I’ll explain my own interest in collective intelligence.

Mathematics research has exploded in recent years, so that it is impossible for one person to know more than a sliver of the math knowledge that is out there. Big results such as classification of finite simple groups and Fermat’s Last Theorem draw on so many ideas that few if any mathematicians know the entire proof—rather the knowledge is distributed in many different people.

As mathematical knowledge has grown, a student has to take more and more time to learn material before getting to the forefront of research. (This is true to different extents in different areas, but it seems to be very true in classical number theory questions.) What if, in some very far future, it takes more time than a person’s lifespan? One important way to combat this is to “decrease the diameter of intellectual space” (see Trefethen’s Index Cards, p. 135; I intend to write my own post about this sometime). But more and more, we have to accept the fact that a lot of researchers are extremely specialized and put faith these pieces of knowledge can be somehow put together by the group, and it is increasingly important to have technologies that enable people to connect knowledge together.

I’ve worked for a while on an open-source number theory textbook, but a plain pdf textbook is rather old-fashioned. So I’ve been wondering: what kind of platform could one build, that would allow knowledge in an area such as number theory to be more connected, more easily traversible, that facilitates a better collective intelligence?


  1. […] of learning comes from talking to people. Because the stuff hasn’t been written down yet. Two posts ago I wrote about how distributed mathematical knowledge is now, so communication becomes all the more […]

  2. “As mathematical knowledge has grown, a student has to take more and more time to learn material before getting to the forefront of research”

    – or are the group of mathematicians just communicating with each other in an non productive language?

    Gauss had some of his major realizations at the age of 19 – pnt – first “proven” by mathematical standards 100 years later. Related problems still outstanding.

    What did Gauss do? And if you somehow could do the same as him – wouldn’t it mean that you could reach the frontier of math much quicker – and travel beyond?

    It might be as easy as 1+10=2+9=3+8…

  3. @jorgen: You’re right in that there is new math to be discovered without heavy machinery, especially if one questions what one learns all the time – though more and more of those gaps have been filled.

    A lot of the big research questions still require much of that machinery though, and there is no doubt that that machinery takes quite some time to learn – although with a better “road map” and guidance for students I believe it can be sped up to be faster that it is today.

    On communicating, I think mathematicians communicate well to each other, but maybe not broadly. The ability to communicate broadly is getting better with technology – as exemplified by polymath projects such as the recent “bounded gaps between primes” project. Blogs, open-source notes, etc. are getting more common.

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