GrandmastersAndTheNumber7 < Kitchen

09 Oct 2005 - 04:01

grandmasters and the number 7

I had a beer (okay, a margarita) last night with a few work buddies, including my brilliant hardware guy from a recent post, and it turned out someone in the group had read Kitchen Table Math recently and seen KdeRosa's Terminator Essay, and was confused by all the references in the essay to the number 7.

7, of course, plus or minus 2, is the subject of this classic essay on the limits of our ability to separately manage objects in working memory. We humans have various tricks for getting around this serious limitation on our "RAM" (I'm calling it that because of its resemblance to RAM in your computer, which is the space available for storing information that the CPU is working on).

However, if you want to really feel the number 7 in action in your brain, and get a sense for how we work around it, consider this: most people would find the act of having to memorize a random ten-digit number onerous on the face of it. Yet, most of us do it all the time; we memorize phone numbers, with their area codes. This is because we 'chunk' the data; we recode the area code as a single quantity, and possibly also the exchange (the first 3 numbersin the 7-digit local phone number).

Here's another trick to try. When you look at a small set of pennies on the floor, say 2,3, or 4 of them, you can instantly take in the quantity of them without having to count, just from looking at all of them as a whole. This is called 'subitizing'. Most people quit subitizing at right around 7 objects, and have to start counting.

OK, enough digression: I'm getting to my point, gradually.

Hardware Guy is an avid chess player, and of course he immediately began thinking about this limit on working memory as it pertains to chess. I said I figured there must be some neat trick for 'chunking' scenarios in the mind that allows chess players to get past those limitations; either that or they have miraculous, computer-like powers to analyze a game several steps into the future.

He told me that they've done brain scans on highly competent chess players versus grand masters. The frontal lobes of the competent chess players light up, obviously, when the game is hot; they're analyzing. But they found that, in the same situation, nearly every part of a grand master's mind lights up, because not only are they analyzing, they are also tasking their memories heavily.

A grand master, he said, who is playing a game and lands in a certain configuration, is pulling up memories of every game he's ever seen played that was like the current scenario at some point, and remembering what was done, and whether the strategy was successful. In fact, a big difference between the grand masters and that next level down is the vastness of the grand master's database. He claims that his own memory is highly specialized to pull out and store this information: "If I were to meet a guy I played a chess match with once, 5 years ago," he said, "I couldn't tell you his name and maybe not even recognize his face. But I could easily associate him with the chess match I played with him. I could tell you what we did, what the major offenses were, and who won."

Thus, even in chess -- which is, ironically, generally considered the domain of some of the world's purest and most analytical thinkers -- permanently retained domain knowledge is necessary in order to achieve mastery. I don't want to call this sort of knowledge 'rote', because that implies that it's information that is held without being understood; but it's not procedural knowledge, either. I would rather call it 'static knowledge', because it's valuable reference information that doesn't change, and I believe it's an important component of any form of expertise.

Update

E. D. Hirsch got there first and said it better in this Education Next article.

keywords: terminator magical number plus or minus 2

grandmasters and the magical number 7
KDeRosa's tour de force

Back to main page.

Comments

After entering a comment, users can login anonymously as KtmGuest (password: guest) when prompted.
Please consider registering as a regular user.
Look here for syntax help.

Speaking of the magic number 7, it is true that chess grand masters are better chunkers of past game data:

A famous experiment conducted by Dutch psychologist Adrian de Groot illustrated this universal bottleneck in human processing skills. He noticed that chess grand masters have a remarkable skill that we amateurs cannot emulate. They can glance for five seconds at a complex mid-game chess position of 25 pieces, perform an intervening task of some sort, and then reconstruct the entire chess position on a blank chessboard without making any mistakes. Performance on this task correlates almost perfectly with one’s chess ranking. Grand masters make no mistakes, masters a very few, and amateurs can get just five or six pieces right. (Remember the magical number seven, plus or minus two.)

On a brilliant hunch, de Groot then performed the same experiment with 25 chess pieces in positions that, instead of being taken from an actual chess game, were just placed at random on the board. Under these new conditions, the performance of the three different groups—grand masters, masters, and novices—was exactly the same, each group remembering just five or six pieces correctly.

Read more about chunking and the magic number 7 in E. D. Hirsch's Not So Grand a Strategy

-- KDeRosa - 09 Oct 2005

okay. i give up. where's the grand database
for all these (wildly cool) e.d. hirsch pieces
you keep pulling out of thin air all over the place?

-- VlorbikDotCom - 09 Oct 2005

That's interesting that subitizing stops at 7!

I didn't know that.

But of course it makes sense.

-- CatherineJohnson - 09 Oct 2005

I think the term is probably declarative knowledge.

-- CatherineJohnson - 09 Oct 2005

It's time for me to start seriously blogging Willingham's textbook.

I gather that a great deal of what we know--or assume to be true--of expertise is based on extensive studies of chess players.

They have vast domain knowledge.

Your friend's description of his own mental processes is exactly what they find.

Experts know stuff.

'Know,' as it's lodged in memory.

-- CatherineJohnson - 09 Oct 2005

Experts also have a cool way of filtering, I think I'd call it; they somehow know what to pay attention to and they filter out all the rest.

It's pretty amazing when you think about it, because any situation, if you looked at all of it, could be said to have infinitely much info....

-- CatherineJohnson - 09 Oct 2005

I think most husbands develop a similiar filtering technique for dealing with their wives.

-- KDeRosa - 09 Oct 2005

most of Hirsch's articles are indexed here:

http://www.coreknowledge.org/CK/about/articles/index.htm

His output seems to have tailed off a bit in recent years.

-- KDeRosa - 09 Oct 2005

I first became acquainted with the magical number seven and the chess player experiment when I read Hirsch's article on reading comprehension two years ago. http://www.aft.org/pubs-reports/american_educator/spring2003/AE_SPRNG.pdf

This article had a HUGE influence on my thinking. I keep rereading it every so often just for the sheer pleasure of being in touch with lucidity. (A little New Age touch here).

Thank you for bringing up the important topic of the limitation of working memory and chunking and other strategies.

-- CharlesH - 09 Oct 2005

I think most husbands develop a similiar filtering technique for dealing with their wives.

LOL

-- CatherineJohnson - 09 Oct 2005

KDR: ta. got it bookmarked. (hmm ... a "chunking" strategy.) much here i haven't seen till now. hirsch rocks.

-- VlorbikDotCom - 09 Oct 2005

KDR, just read Hirsch's Not so grand a strategy. That's a great article. In fact, I could replace my whole post above with the three-word phrase what he said.

Hirsch is my hero.

-- CarolynJohnston - 09 Oct 2005

Wait!

KDeRosa!

I take that back!

I shouldn't be encouraging you.

-- CatherineJohnson - 09 Oct 2005

I actually get accused of having my filter set so high that I filter out a lot of supposedly important data; but I haven't noticed that yet

-- KDeRosa - 09 Oct 2005

I actually get accused of having my filter set so high that I filter out a lot of supposedly important data; but I haven't noticed that yet

by definition.

-- CarolynJohnston - 09 Oct 2005

That's interesting that subitizing stops at 7!

Remember how Rain Main subitized a whole box of toothpicks that fell on the ground? And I heard the 'twins' (prime factoring savants) did it too. But fo r the rest of us, the limit is about 7.

And I don't know if 'big subitizing' is a common type of savant skill, or fairly rare.

-- CarolynJohnston - 09 Oct 2005

My husband's filter is in fine working order.

-- SusanS - 09 Oct 2005

My husband's filter is in fine working order.

Oh yeah

-- CatherineJohnson - 10 Oct 2005

big subitizing!

I love it!

-- CatherineJohnson - 10 Oct 2005

we've gotta post Allan Snyders integers & savants article pronto!

-- CatherineJohnson - 10 Oct 2005

I took notes on the Extended Problem with Christopher.

What a joke.

-- CatherineJohnson - 10 Oct 2005

FWT

-- CatherineJohnson - 10 Oct 2005

_I took notes on the Extended Problem with Christopher.

What a joke._

I think I understand now; these 'extended problems' are Irvington's version of Science Fair.

No child could ever hope to do them without a lot of parental help, and it's not clear what the kid is intended to get out of doing them.

What will really clinch it will be if all the Phase 4 parents are asking each other in the hall tomorrow, "Did you get it?"

-- CarolynJohnston - 10 Oct 2005

On subitizing:

I've found this to be a very interesting subject, and have thought about it for some time. I know that I "see" 1-5 objects as single constellations along with their numbers of items. That is, when I glance at five [whatever]s, I see them as five without counting.

With six objects, I see them as two groups of three, unless they are in a hexagonal configuration. I'm still not counting them, but there's an addition stage.

I've done less experimentation with larger numbers, but I know that at some point I start actively counting individual elements.

It strikes me that it would be very interesting to run an experiment to measure processing time and accuracy for these sorts of tasks. (The sample sizes would have to be pretty large, both in number of problems per person and number of people, and you'd have to correct for cognitive fatigue, too.) I'm pretty sure that my results would have three plateaus, and I'd be really interested to find out whether the same is true of others.

-- DougSundseth - 10 Oct 2005

Doug

It strikes me that it would be very interesting to run an experiment to measure processing time and accuracy for these sorts of tasks

There's all kinds of research using this exact technique (timing people's response time).

I'm going to blooki an article in Daniel Willingham's edited collection of classic studies on children's response times in math problems.

It's wonderful.

-- CatherineJohnson - 10 Oct 2005

Ed was wondering last night why exactly teachers do things like Science Fair & Extended Problems.

He wants to know exactly what their thoughts are, how they justify and explain these things to themselves.

-- CatherineJohnson - 10 Oct 2005

A couple of years ago, before we were in Phase 4, there was a problem so hard all the parents were grabbing each other at the soccer game, trying to find SOMEONE who could do it.

I think this was at the beginning of 5th grade.

-- CatherineJohnson - 10 Oct 2005

WebLogForm
Title:	grandmasters and the number 7
TopicType:	WebLog
SubjectArea:	CognitiveScience
LogDate:	200510082357

Navigate KTM

Kitchen Table Math

KTM User Pages

Service Groups

Parent Groups

Personal Pages

Blogs

Special lists

Help