# The Magical Number Seven Plus or Minus Two

The seminal 1956 George Miller paper The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information is a true classic. In it, Miller observed that the results of a number of 1950's era experiments in short-term memory had something in common: most people could only retain 5 to 9 items in their short-term memory.

This is a companion discussion topic for the original blog entry at: http://www.codinghorror.com/blog/2006/08/the-magical-number-seven-plus-or-minus-two.html

Actually… I remember doing an experiment in college for a class called “Human Factors” where we looked at this very phenomina. And what we found is that its a combination of both items.

7 digits is too hard to remember if not broken into groups. So groupings of 3 to 4 is the most efficient.

However, you can’t just string together many groups of 3 to 4 numbers have people then remember 15, 18, or 22 digits either.

So the result is that the most you can remember is 3 to 4 groups of 3 to 4 numbers.

Are human beings only capable of holding
between 5 and 9 pieces of information in their
heads at once? That’s only 2.5 bits of
information.
That’s not 2.5 bits of information.

The number of pieces can be represented in 2.5 bits of information. The pieces of information themselves can be as small as 1 bit each (still 7 bits of information), or as large as 20 bits each – let’s say, the numbers 1 million, 2 million… to 7 million – making 140 bits of information.

Though the numbers “(1-7) million” could probably also be remembered as one piece of information, leaving 140 bits of information right there with room to spare.

Not sure where I’m going with this but your statement there was not really saying anything.

It’s the same argument.

Which is easier to remember? My telephone number…

510-307-8234

… or my email address?

jatwood(at)codinghorror.com

Let’s not forget the teachings of Dale Carnegie…

In the memory lessons of the class, we’re taught that through relating mental imagery and the memorization of a few key concepts, we can actually store 42+ units of information (he claims infinite, but I’ve never seen more than 42)

The process is his “one-run, two-zoo” paired listing…

For each paired list, the person visualizes a scenario in their head involving the number/item they need to remember.

I can personally remember up to 21 groups of numbers (3-4 in size) for rapid recall… But I haven’t been practicing nearly long enough.

So which is it? Can people remember 7 digits at once? Or are they really remembering chunks of 3 digits, 3 digits, and 4 digits?

I remember in a cog sci class back in college the professor gave a great presentation. He started by saying a bunch of random of words and asked us to remember them (without writing them down). Then he asked us to recite back as a class as many words as we can. Almost everyone remembered the first few words and the last few words but hardly the words in the middle of the sequence. He then tried it again but with the words somewhat related and in groups of 3 with short pauses between the groups. The retention rate is much higher.

When we group information as chunks we remember more but we’re still constrained by the 7+/-2 number for the total number of chunks retained in short term memory. Whether 7 digits at once or a group of 3 digits, 3 digits, and 4 digits which is just three chunks we’re still below the magic seven number.

Likewise, the fanstastic game Brain Age on the DS has a great memory game. You’re presented with 40 words for 2 minutes to remember and then you write back as many of the words as you can remember after the 2 minutes. I started out horribly with the brain age of 65 and could only remember a few. Once I started making silly sentences with the words (basically chunking it) I remembered almost all the words and got the brain age of 20.

There are some great comments in this interview with Cliff Atkinson on short-term memory research and how it relates to typical PowerPoint style presentations:

http://www.sociablemedia.com/articles_cowan.htm

An interesting article about memory tricks and some of the best memorizers in the world: http://www.discover.com/issues/apr-06/features/world-memory-championship/

I guess it’s really only loosely related, but I found it fascinating.

I can remember 16+ digits, it all depends on how you group them and relate them to one another.

Besides, everyone can remember loads of tidbits, otherwise you wouldn’t be able to communicate. It’s all patterns, IMHO.

As previously alluded to, the 7±2 applies and fits quite well when you consider it works based on units of information.
When you chunk (as people tend to do with numbers) you can get to about 7±2 chunks. If you do it with ideas that are harder to chunk, say a list of objects, without the use of memory aids (i.e. stories to create chunking and ascociation) you still tend to get the 7±2.

I first ran into this when learning structured analysis. Yourdon uses this single study to claim 9 is the limit of processes on a DFD. But are we really that limited? Look at a county map (especially one from northern NJ). There’s a zillion things on it and it makes it easy to figure out how to get from point A to point B.

Alan Le, we did something like that in a Psych class I took. Except we did three groups of letters.

Round 1: random 3 letter combinations.
Round 2: random 3 letter words.
Round 3: 3 letter words that told a simple story.

You can guess which round of trials had the best retention rate.

“I believe that you guys are nerds.” That word grouping (sentence) contains 7 words (chunks). Those 7 words are so much easier to remember than the following 7 letters: g q w e z p n. IMO, groupings makes things so much easier to recall.

Hmmm… Never thought of it before, but I was memorizing my bank account number (for endorsing checks), and was having trouble getting it to stick.

I finally did it by memorizing chunks - 5 digits, 4 digits, and 3 digits.

Another interesting fact about this ‘seven’ factor - Seems like u can fold a piece of paper (of any size - small or big) maximum of seven times only.

Recently took a memory test as a part of a control group for some medical trial the details of which are irrelevant. However, part of this test involved remembering and recalling dictated numbers, forwards and then backwards. As you’d expect, the longer the number, the more difficult, especially backwards, but what I found the real killer was when I didn’t know the length of the number - I was already trying to stamp it into memory with a fixed pattern - when an extra digit appeared, boom - all gone.

Seems like u can fold a piece of paper (of any size - small or big) maximum of seven times only

Aha! Not so! Check this out:

http://blogs.vertigosoftware.com/jatwood/archive/2005/11/18/Meet_Miss_Foldy_McFolderson.aspx

I can give you a string of 38 characters which you can memorise easily after seeing it only once:

“Aliens ate my baby sister’s underwear.”

Don’t worry about numbers, worry about structure.

The mind as a relational database:
I would say we remember things the easist way possible.

Phone numbers are a particulairly good case of this. Most people will follow something along theses lines:
1)Who am I calling.
2)What context can be surmised (call their cell, their home whatever) for this example we will says we are calling susie at home.
3)Where is susie number. (usually you will have all but area code memorized.)
3a) You may be very familair with an area and know some common landline prefixes (second 3 digits) And relate the numbers that way.
4)You remember the area code by where susie lives. Ah she lives in Long Island so her first three must be…

As you can see we have this vast network of information going on in our heads. I would say we do not have a solid black and white limit on what we can remember. But as we go up in complexity and ambuguity it takes us longer to store something to memory. The precision for remember is not anywhere closely resembling a machines abilities. In this way we are very different from computers as its not the capacity that matters most but how hard it is to relate to what we alreay know.

joshua.r.thomas {at} gmail.com

I used to collect basketball cards when I was a kid, plus I was even nerdier and had some strange interest in what numbers were used by which players and such. So at this point, I can remember just about any string of numbers as long as I can convert it to a series of basketball players (baseball and football will do in a pinch). I still rememeber the combination to the toolbox on my college buddy’s truck. Shaq, Price, Madkins.