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- Magic Number 2 7 7 – A Better Calculator Present Value
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- Magic Number 2 7 7 – A Better Calculator Percentage
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The Magic Number Seven And The Art Of Programming |
Interfaces |
The number seven is very important in programming and many other intellectual endeavors. Why is is magic and what significance does it have for us poor limited humans?
All good programmers need to be part time psychologists, maybe even full time ones. Bitwarden 1 16 6.
The reason?
There are many, but let's start with a very obvious one.
What would you say was the most important skill at creating user interfaces?
The Psychology Of Bandwidth
True you have to have the technical skill and equipment to implement your ideas; but without an understanding of how users work then your ideas will be mostly rubbish.
Understanding how users work, in the broadest possible sense, is usually called psychology - hence my opening statement. Rather than launch off into another discussion of user interfaces, an admittedly important topic, the time has come to consider something much more simple - overload.
Magic Number 2 7 7 – A Better Calculator Present Value
One of psychology's early phases (there have been many) was based on information or communications theory. It viewed the human processor as an information channel. The idea was that the human wasn't so much a data processing system but a data communications system. The inputs were the senses and the outputs where what ever the human did or perceived as a result of the inputs.
It studied the channel capacity and the effects of noise on signal processing. There are some theorems relating things like reliability, bandwidth and noise and these are applicable to humans just as much as to networks and radio channels.
The exact details aren't particularly important, but what is important is the obvious statement that humans are a limited data channel. One of the nicest and simplest results in this area is the 'magic number seven' or Miller's law after the psychologist who discovered it. (See: The Magic Number Seven, Plus or Minus Two.) Suite for iwork 3 1.
After lots of experiments it was found that, on average, humans can manage to keep in their short term memories seven items of information. The variation observed in the experiments was such that a more accurate statement of memory capacity is seven items plus or minus two - hence the title of the paper referenced above.
You can argue about the fine detail and whether or not the number seven deserves its special position. You can also argue about the limits applying to different cognitive processing but the important point is that there is a limit not its actual value. Humans are bandwidth limited information processing machines. We have a channel capacity or a data rate limit just like any data bus.
Programming And Seven
What has this got to do with programming?
The answer is quite a lot.
As a programmer you to are subject to the same information processing limits as any lesser mortal. This is the reason why all programming methods endeavour to hide the complexity of a program in a layered structure. You will often hear programmers talking about complexity reduction but actually what is going on is complexity hiding - also known in the wider world as 'chunking'.
In modular programming programs are built up out of small chunks of code in the form of subroutines, function or modules. Each module should be small enough to fit into the seven plus or minus two category. Each layer should equally be confined to the same size limits, so that every layer can be easily understood.
There is also a subtle effect caused by the nesting of control structures. One If statement is easy to understand but multiple nested if statements are much harder to untangle. The same is true of loops nested with in loops within ifs and so on. Nested control structures make it difficult to chunk.
The idea behind chunking is that a human can deal with about seven things at a time but you can work with different levels of abstraction to work with bigger systems. That is you can remember seven letters, or seven words or perhaps seven sentences and certainly seven titles and plots of seven very long books. The principle of chunking applied to programming is to build a hierarchy of code each composed of small objects that can be understood in a single look.
I have occasionally encountered too literal implementations of the 'seven' part of rule. For example, a project I was involved in had the arbitrary limit of no more than seven lines of active code per subroutine - the project leader was brother to Genghis Khan and a fine warrior, but he applied rules too literally and too brutally.
Iina 1 0 0 – modern video player youtube. In some more elaborate design methods such as Yourdon/Demarco you will find people converting guidelines such as 'no more than around seven bubbles in a structure chart' into a similar and exact law.
I have yet to come across an explicit 'seven' rule in object-oriented programming but I guess it's only a matter of time and a deep enough search.
The point is that seven is a guideline and the actual number depends on all sort of factors but 'Keep It Small Stupid' is a much better statement of intent than 'Keep It Simple Stupid'.
Well now you know the origin of the magic number seven that crops up so often and you also know that seven could just as well be five or nine.
In fact the situation is much vaguer than even these loose numbers would suggest. The real confounding factor is what exactly constitutes an item that the 'seven' applies to?
Should it be seven characters, seven words, seven lines, seven subroutines, seven objects, seven programs..
Clearly the unit used in the rule of seven matters. Basically the unit should always be scaled to fit into the situation so that it is one chunk of comprehension or memory.
Easy to say but usually much harder to do.
The Unit Of Comprehension
Focusing on code for a moment it is clear that what matters is the structure of a function or method.
Do you understand and work with a method as a single thing or a composite unit. Again the rule that each layer should have a limited complexity is justified in terms of the sliding scale of the fundamental unit of comprehension.
We use hierarchies to manage complexity so that each level in the hierarchy is as simple as the next as long as you are working with the correct unit of comprehension.
There is another more subtle problem.
The unit of comprehension can change with time and who exactly is doing the comprehending.
When you write a small chunk of code you are on top of it all and your unit of comprehension might be very large - it all seems so simple. But when you come back a few weeks later your unit of comprehension has shrunk. Now it would be better if the method consisted of just seven lines of very simple code.
If there is a lesson to be learned from this aspect of 'seven' then it is not to overestimate yourself or your colleagues If you write a nice little code chunk today imagine the lesser mortal who will have to maintain it.
If you expect this then plan for it!
Make your code easy enough for the dummy to cope with; who knows the dummy may, in fact almost certainly will, turn out to be you.
A factoid is a snippet of information (usually taken out of context) that's assumed to be factual because it's repeated often. A favorite pop-psychology factoid, repeated in textbooks and popular media, is that human short-term memory is limited to 7, plus or minus 2, items (called 'chunks'). While there is some truth to it, this factoid offers little as a pedagogical tool beyond stressing the need to break problems into manageable chunks for novices. The full story behind the 'magic' number seven, however, provides a fascinating look into Psychology's quest to understand the differences between experts and novices.
Miller's Magic Number
The number seven, called 'Miller's Magic Number,' comes from a 1956 article by the psychologist George A. Miller title 'The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information.' In this celebrated and highly-readable article, Miller considers two kinds of situations:
- A person must correctly distinguish between very similar items (e.g., high/low-pitched tones, shades of green), and
- A person must recall items presented in a sequence.
In the first kind of situation, called absolute judgement, subjects are exposed to a stimulus that varies along a single dimension, such as the pitch of a tone, the green-ness of a color, or the concentration of salt in a cup of water. Across many different kinds of stimuli, people can consistently distinguish about six distinct stimulus levels without making mistakes.
The second kind of situation is used to measure the span of immediate memory. Here, the subject must retain a select number of chunks in their short-term memory, and recall as many items as possible at the end of a trial. Across a handful of simple domains, such as decimal digits, letters of the alphabet, and monosyllabic words, people are able to hold anywhere from five to nine chunks in short-term without making mistakes. While it is tempting to assume that the limits of absolute judgement and immediate memory are related, Miller did not believe this to be the case.
The Game of Simon
A helpful way to understand the difference between absolute judgement and immediate memory span is with the electronic game Simon by Milton Bradley. This simple game device has four colored buttons, each associated with a distinct tone. In each round, Simon plays a sequence of tones, and the player must repeat the sequence back by pressing the appropriate buttons. The game gets progressively harder as the length of the sequence grows.
![Magic Number 2 7 7 – A Better Calculator Magic Number 2 7 7 – A Better Calculator](https://ksr-ugc.imgix.net/assets/011/343/496/554f23db5956d032d398bc89df01c6f9_original.jpg?ixlib=rb-2.1.0&crop=faces&w=1552&h=873&fit=crop&v=1463681290&auto=format&frame=1&q=92&s=1afa673f3e5e522d12c5d0d5ae2e2201)
A player is exercising absolute judgement when distinguishing between Simon's tones. The number of distinct tones is fixed at four, well within a safe 'no mistakes' range for most people. Simon's increasing sequence length, however, is meant to strain immediate memory capacity. Based on Miller's article, one would expect it to be quite difficult for players to repeat back a sequence of nine or more tones, yet expert players have managed nearly ten times that. How are they able to do this?
Magic Number 2 7 7 – A Better Calculator Estimate
Shortcomings of the Magic Number
The span of short-term memory as reported by Miller in 1956 (7 ± 2 chunks) is where the pop-psychology factoid usually stops. Since that time, however, researchers have cast doubt on the magic number itself as well as its cross-domain applicability. Research with chess experts, for example, has suggested a span limit of 3 to 5 chunks; nearly half the magic number! In the domain of language, it has been found that phonological similarity and spoken word length are much better predictors of how many words a person can hold in short-term memory (less-similar and longer words are harder to retain). Things have even changed for absolute judgement: subjects in one experiment were only able to distinguish about 7 colors until they were given a broader vocabulary (i.e., 'pale blueish green'). With little training, they were then able to discriminate around 36 colors.
What does it mean for short-term memory to have a limited capacity in the first place? A key insight is that traditional means of measuring absolute judgement and short-term memory span require blocking recoding -- the process of grouping or relating chunks. To block recoding, experimenters must use non-sensical or unrelated stimuli, such as made-up words or random decimal digits. Under these artificial conditions, we see something resembling a strict capacity limit, but this limit increases or even seems to disappear when subjects are able to find some higher-order meaning in the stimuli. For example, one famous subject in a random decimal digit memorization experiment found he could remember more digits at a time by mentally recoding them as mile times (he was an avid runner).
Recoding is Magical
In the real world, people are constantly recoding stimuli. Because of this, it is difficult to define precisely what a 'chunk' is. Cross-domain research with experts suggests that they retain the same short-term capacity limits as novices, but the content of their chunks is far greater. In addition to denser chunks, experts have invested in building intricate networks of chunks in their long-term memories, ensuring that relevant chunks are always readily available. As Miller and many psychologists since have shown, recoding is truly where the action lies.
If stimuli can be recoded relative to one's background knowledge, then using Miller's magic number alone to judge the cognitive burden of something may or may not be helpful. When the chunk sizes are known, it becomes possible to use short-term capacity limits as a predictor of cognitive burden and complexity. In an ingenious experiment with chess players, subjects were asked to copy the positions of all pieces from one chessboard to another. By placing the boards far apart, subjects were forced to turn their heads to focus on either board.
The experimenters were thus able to use the number of piece positions copied on every turn as an estimate of the subjects' chunk size, and were able to show that the performance difference between grand masters and novices was slim when random board positions were used. A similar experiment was done with programmers copying code by hand, and the same kind of results were found (experts were no better at remember code with shuffled lines than novices).
Magic Number 2 7 7 – A Better Calculator Percent
The Big Picture
Magic Number 2 7 7 – A Better Calculator Percentage
Miller's magic number is a fun factoid, but it is only the beginning. In the search for a fixed short-term memory limit, we have found something much more interesting: an understanding of domain expertise. Experts do not exceed the limitations of the average human mind, they have 'simply' built a vast, complex network of domain-specific chunks that allows them to rarely end up in unfamiliar territory. We can still see experts' capacity limits in the lab, but they are much more difficult to spot in the wild.