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Thursday, 23 February 2012

The Curse Of Seven

I’d like you to memorise a number for me. The number is 111011101001101010010. Easy, huh? Now, read on.

Shouting at the Plastic

We humans have many unusual traits. We’re the only mammal that can’t swim when it's born, the only mammal whose male can’t tell when its female is fertile, we have large brains which we habitually attack with fermented grains, we walk upright other than in ongoing fermented grain situations, and, perhaps most importantly, we use language to communicate (even when fermented grains are involved).

Now language, of course, is a curious thing. Given the huge amount of brain space and energy it consumes it was clearly very important to our survival as a species. So it’s odd that many of us then use this gift to shout inanely at mobile phones in public spaces. That’s what we call an “unintended consequence” and it helps lead to a big investing problem, the issue of information overload.

Chameleon v Grizzly

Language defines us as a social creature and it suggests that social interaction was crucial to human evolution. Really, how could it be otherwise? How other than through sophisticated group co-ordination and social support could a hairless ape with no in-built weaponry or stealth mechanisms survive to dominate the planet? Had things been otherwise heavily armoured chameleons and sentient grizzly bears would be duking it out for global supremacy.
All forms of communication, of which language is but one, are built around transferring information. The better the recipient is able to understand the originator’s message then the more efficient the communication is considered to be. We’re pretty good at communicating pretty complex ideas so we’re pretty darned efficient. However, we’re limited by the capacity of our brains, a limitation which would, under most circumstances, reduce our ability to communicate to monosyllables. Imagine a world full of teenage boys trying to co-ordinate an attack on a herd of bison. Tragic.

Language Talks

Our escape from this limitation, the fact that our brains have a limited ability to process information, was language. Language allows us to recode information, to make it easier to transmit and remember. A single word can embody a huge amount of information: which is why garrulous people who can’t say in a simple sentence what they can otherwise say in a monologue, usually confuse rather than illuminate us: they’re inefficient communicators.

The fact that the brain has a limited ability to handle information tends to be hidden by our remarkable ability to recode it, but as we know from the behavioral psychology we’ve extensively looked at, it’s a less than perfect system. Economists refer to this as “bounded rationality”, Herb Simon's big idea that we discussed in Behavioral Finance's Smoking Gun, that we’re not perfectly rational because of processing limitations in the brain. In essence the brain uses rules of thumb that we call heuristics, based on experience, to approximate to rational behaviour.

Seven +/- Two

In fact it appears that one of the most fundamental restrictions of the brain is in short-term working memory. This is critical, because if you can’t hold an idea in this area you can never process it in any useful way. It turns out that the important number for short term memory is seven, plus or minus two. This was uncovered by George Miller back in 1955, and reported in his entertaining paper “The Magical Number Seven, Plus or Minus Two; Some Limits On Our Capacity For Processing Information”.

What Miller also uncovered, however, was the critical unit that working memory operates on.  The technical term for it is a “chunk”. Which, however, you look at it, is a pretty imprecise unit of data.  Anyway, a chunk is whatever makes sense to the person using it. A native English speaker will easily hold a short English phrase of seven words but will almost certainly fail on a Chinese sentence of similar length: there we’d probably need to break it down into phonetic syllables, which would reduce the carrying length of the information being transferred: if we can on-ly re-mem-ber se-ven syll-a-bles then we'll retain less information than if we're parsing seven words.

The seven plus or minus two limit seems to be true across all sorts of information, from musical tones, to visual positions and beyond: and the more information we’re asked to remember beyond this limit then the greater our error rate. Words, it turns out, are an incredibly efficient way of squeezing lots of information into a single “chunk”.

Imperfect Rationality

Miller’s research was just about the first that identified the real processing limits of the brain: the first clue that the idea of perfect rationality envisaged by economists and psychologists was a magic bullet that didn’t exist. Magic’s not real, you see. 

This evidence helped to confirm Herb Simon's intuitions and from that it was a shortish step to the behavioral finance paradigm of limited rationality as introduced by Tversky and Kahneman: we can’t handle more information than our natural limits, otherwise we  suffer from information overload. Studies of information overload show that as we gradually introduce more information then our decision making improves for a while but eventually plateaus and then declines as we add more and more information. This is the "inverted-u curve" of information load as described in this paper by Martin Eppler and Jeanne Mengis.

Investing Overload

Information overload leads us into some quite nasty investing behaviours: we ignore parts of the data presented, we favour recent, vivid and easily available information over other types and gravitate towards well presented arguments, even if they’re spurious, as described here by Thomas Moellers. Basically, the idea that more information is better than less when it comes to stock analysis is wrong, unless you have a well-honed mental model and proper support tools. One of the simpler ways is to build a checklist of items that you need to cross-check: the valuation fundamentals that you’re interested in, the competitive position, the previous track record of the directors, or whatever.

However, checklists are limited: they don’t support more than the most rudimentary of thought processes and all too often they get used by rote rather than in support of analysis activities. Perhaps a better method is to develop a concept map, which allows investors to generate their own model of what’s important to them, and how it fits together. 

Concept Maps

Concept maps lend themselves to a more elaborated view of the investing universe, and to modifying your world view when you encounter something that changes it. In addition, they allow you to focus on what’s really important and what’s not while simultaneously overcoming the curse of seven. They allow us to communicate not just concepts but also the relationships between them, and to build memory structures to hold them.  This paper by Joseph Novak gives an outline of the approach, but individuals need to build their own, to suit their own needs.

Of course, the alternative is to take a simpler view of the world and decide that there are only a limited number of factors you’re interested in, and determinedly ignore the rest. This isn’t always a bad approach – many value investors do this by focussing on a few critical ratios – but it means you have to take a view on what works. And what works often stops working after a while.

Seven's (Probably) Not Evil

Once you start looking for it the number seven appears everywhere. However, as Miller himself puts it:
“And finally, what about the magical number seven? What about the seven wonders of the world, the seven seas, the seven deadly sins, the seven daughters of Atlas in the Pleiades, the seven ages of man, the seven levels of hell, the seven primary colors, the seven notes of the musical scale, and the seven days of the week? What about the seven-point rating scale, the seven categories for absolute judgment, the seven objects in the span of attention, and the seven digits in the span of immediate memory? For the present I propose to withhold judgment. Perhaps there is something deep and profound behind all these sevens, something just calling out for us to discover it. But I suspect that it is only a pernicious, Pythagorean coincidence.”
Perhaps ... go to the bottom of the page for the answer to the riddle at the start.

Related articles: Behavioral Finance's Smoking Gun, The Death of Homo economicus, Robert Cialdini and the Weapons of Influence, Financial Memory Syndrome


Remember the number at the start of the article. Without cheating, can you remember it? If you can, as Miller showed, you’d be remarkable unless, of course, you were smart enough to recode the binary into a seven digit chunk.

Step 1: The number was: 111011101001101010010
Step 2: Split into three digit blocks: 111 011 101 001 101 010 010
Step 3: Recode as a seven digit number: 7 3 5 1 5 2 2 .
Step 4: Memorise seven digit number.
Step 5: Decode to recreate the original.


Information Overload added to the Big List of Behavioral Biases.


  1. Thanks so much for the post. Great read!! Really looking forward to read more. Want more.

  2. 111 break 111 break 10011 break 10100 10
    easier than 7351522