Suggestions for making knowledge simpler and more powerful

Extending the reach of Occam's razor



General principles

Maths should not be hard: the case for making academic knowledge more palatable (7000 word article published in the Higher Education Review in 2002.)


I'll make it simple (Short article in the Times Higher Education, 2002.)


Simplifying academic knowledge to make cognition more efficient: opportunities, benefits and barriers (5000 word article, 2016. Draws on and expands some of this webpage and linked documents.)


Ideas which are too simple - dumbing down (Two pages on the opposite problem.)


News from a couple of alternative futures (short blog post)



A fairly haphazard collection of the simple and the complicated, and potential simplifications.

Six sigma and the Higgs Boson: a convoluted way of expressing unlikeliness (Blog post on a strange, and completely unnecessary, way of complicating a simple concept.)


Statistics. A major source of confusion and incomprehension in urgent need of reform.


Qualitative research - often jargon-ridden but for no good reason. Peer regard for pot noodles is a blog post reviewing such an article.


Sustainable Energy without the hot air by David McKay. Analysis of UK energy options. Uses everyday units and Insists on numbers instead of oversimplified adjectives like "huge".


Using Excel notation for mathematical formulae and equations (has advantages over conventional notation).


Feynman diagrams are simple pictures to visualize the very complex mathematical expressions describing the behaviour of subatomic particles. They are said to have "revolutionized nearly every aspect of theoretical physics". (Unfortunately, I haven't got the necessary background to understand even this pictorial version of quantum mechanics.)


Research methods for social sciences, management, education, etc. Much of the standard fare is misleading, or the obvious translated into jargon.


Compound (or exponential) growth and decline. Compound interest and population growth are usually analyzed using calculus and natural logarithms - but the concepts can be simplified and presented directly.


The case for crunchy methods in practical mathematics. Article published online in 2001 on the virtues of crude, repetitive methods.


There are More examples below.

Implications for education, growth of knowledge, etc, etc

Cambridge University closed to undergraduates. My prediction about the future of traditional university courses (blog post).


The death of a university (Blog post)


Journals, repositories, peer review, non-peer review, and the future of scholarly communication. Article on on making the system for publishing research more flexible and effective.


The cult of the truth. Truth is a slippery concept which shouldn't be taken too seriously (blog post).


Computer packages as cognitive paradigms. Paper published in 1997 arguing that computer packages may be a partial substitute for education. Smartphone apps and simple spreadsheets like this one and this one may play a similar role.


Other links

The Sceptical Academic (blog)

My university web pages 1 and 2

Everything should be made as simple as possible, but not simpler (widely attributed to Einstein)

It may be better to simplify a process rather than train people to cope with complexity (E de Bono)

Many ideas are too complicated and could be simplified without sacrificing their power and usefulness. The number MMXVII is now written as 2017 which is far more convenient from many points of view, and the metric system means that children no longer have to learn about stones, pounds and ounces, and pounds, shillings and pence, and so on. At the other end of the scale, Newton, Einstein and Darwin came up with beautifully simple theories which help us make sense of the world.

This principle deserves to be spread far wider. Many complicated ideas could be replaced by simpler and better alternatives. Otherwise human progress will slow down or cease as our minds become clogged with unnecessary technicalities, and inevitable over-simplifications take control of our thoughts and actions.

Why simple knowledge?

I know lots of things. I know how to make my lunch, how to make my way to Emsworth, the village where I live, and also a few more complicated things like how Newton's laws of motion work and a little bit about how the economy works. Knowledge is important to all of us. Life as we know it could not continue without it.

Some of this knowledge is easy. I have no difficulty understanding how to make lunch, turn the TV on and so on. But some of it is not so easy: it is difficult to understand, absorb and make use of. I think I understand about Newton's laws, but a lot of more recent physics (like quantum mechanics) leave me largely baffled. And although I can switch the TV on, I have only the vaguest of ideas of how it works, and how it manages to home in on the channel I am watching and ignore the myriad other TV channels, mobile phone signals, and so on that pervade the space around us all. I don't trust myself to distinguish between the many harmless blemishes on my skin, and a dangerous melanoma. And so on.

This is a real problem. There is so much to know, and a lot of it is hard to get to grips with.

Obviously, I'm not very bright, rather lazy, and my knowledge is certainly very limited, but even the brightest and best informed person in the world will still come up against their limits. Even for the most intelligent, quantum mechanics is difficult and will take time to master. And this must place constraints on what can be achieved by one person. My guess is there are very few people, if any, who are experts in quantum mechanics, and skilled film directors, and expert cooks. Life is just too short to master all these fields. But it would still be nice to make as much progress as possible in as many areas as possible.

There are a number of obvious approaches to help cope with difficult knowledge - go on a course, consult an expert, get some computer software to help, spend lots of time studying, become cleverer, and so on. All undoubtedly potentially helpful.

However, the core idea I want to explore here is that of redesigning difficult knowledge to make it simpler, or more appropriate for the context. The aim is to make knowledge more user friendly.

I suspect some readers' hackles will be rising at this point - phrases like "dumbing down" perhaps coming into mind to dismiss the idea out of hand. If you are such a reader, please hold on a minute and consider two examples.

In Roman times, the lack of the modern notation system for numbers meant that simple arithmetic was not simple. It is far easier to do arithmetic with numerals like 1949 than with MCMIL, and the difference is even more pronounced with fractional numbers. We are better at arithmetic than the Romans simply because we have better concepts to cope with numbers. Very similar comments apply to the adoption of the metric system of measures in place of 16 ounces to a pound, 14 pounds to a stone, and so on. Difficult knowledge has been made easier to the benefit of all.

These days word processors are easy to use. When they were first invented, however, they were complicated beasts requiring considerable effort, and training, to master. The education problem has been solved by making the task easier, and along the way providing help with spelling, grammar, formatting documents, and so on. Again, things have been made easier, by changing, in this case, the technology.

Simplification doesn't just make things easier. The simpler version is usually better, or more powerful, in lots of ways. It's not just that the modern notation system for numbers makes arithmetic easier: it's also possible to do things that would be more or less impossible with Roman numerals. And to take a more technical example, the randomization, or shuffle test, in statistics is a computer simulation method, whose rationale is completely obvious, which does the job of lots different statistical tests each with its own complicated mathematical theory and recipe for using it. The user of the shuffle test has far more statistical power at their disposal than the conventional statistician with chi squared tables, t tables, F tables, etc.

The idea of making things simpler so that we can manage them more easily is better described as "dumbing up". I hope to convince you that this has real advantages from many points of view in many walks of life.

But, you may think, these are special cases and, besides, helping people with spelling is a bad precedent because it will encourage laziness. OK, the principle that simple is good does not always apply (but I would say it does apply to spelling), but it is a really useful possibility in many more scenarios that you may at first imagine - the links on the right and below give some examples.

Lets imagine that some difficult knowledge can be simplified by a factor of about a quarter. (I think in many cases this fraction could be nearer 50% or 75%.) This might mean that people spend 25% less time learning about some knowledge, or using it, or that the simplification means that they can master 25% more than they would otherwise have been able to, or that they make 25% fewer mistakes, or that 25% more people are able to master it. Over the whole spectrum of difficult knowledge this has the potential to make an enormous difference. Imagine that students over the world could spend 25% less time on their studies! The rest of the time could be spent taking their studies further, or doing something completely different.

This is all based on the assumption that such simplification is possible. The only way to make the case is to show how it would work in particular examples - which I have done in the links in the boxes above and below. However, in all these examples, the problem is the same. To see that the simple version really is simpler, and yet will do the same job as, the more complicated version, the reader needs to appreciate both the power and complexity of the original version, which is not going to make for a brief and simple exposition.

Simplifying complex ideas, as a general epistemological and educational tactic, does not seem to be on anybody's agenda, and this is probably for reasons similar to those outlined in the previous paragraph. You need a certain level of expertise to understand the complex version, and once you have this there is no motive to simplify, and simplifying may seem almost disrespectful to the "proper" version. Those without the expertise, who have the motive to simplify, obviously aren't in a position to simplify something they don't understand, and are likely to assume that a simplified version is a dumbed down, relatively useless, version for the masses - and to be fair, this is sometimes the case. Understandably, but unfortunately, there is as yet no established tradition of trying to simplify unnecessarily complicated knowledge.

This idea raises issues that spread a little wider than may be apparent at first sight. For example:

        If difficult knowledge is made simpler, do we need school and university courses to help us master it? (Rough answer: sometimes we do, often we don't.)

        Is the idea relevant to experts at the frontiers of their discipline? (Yes. The simpler the perspective, the faster the progress. In the long term knowledge can't progress without simplification. Simplification is an essential aspect of the growth of knowledge. This has long been recognised at the frontiers of science, but it also applies to more mundane levels of expertise.)

        Surely the truth is given and can't be simplified? (Not so. Almost all understanding is partial which should encourage us to consider which parts we need and what we can ignore. Besides knowledge is not just about truth, and truth itself is a very slippery concept - see this blog post.)

        The difficulty of difficult knowledge may sometimes mean that we don't notice it's not answering the important questions, so the redesign may need to be more radical than a simple simplification. The simplified version may provide a new, very different, perspective, in effect a paradigm shift. (Statistical significance and p values are good examples of such problematic concepts - there are dozens of blogs and articles critical of these concepts on the web: my suggested alternative is explained here. And the modern notation system for numbers, and modern word processors are both more than a simplification of their predecessors - they are far more powerful tools.)

        Simplicity is not a simple concept. Sometimes it's good, sometimes it's bad, and the simple assumption that simple is always good would be a disaster. And there are many different ways in which things can be simplified - e.g. by omitting unnecessary complications, or redesigning concepts or terminology. (Agreed, which is why we need to understand simplicity - in the simplest possible way. Over-simplification is also a big problem - see Ideas which are too simple - dumbing down.)

But there are the obvious objections:

        Isn't this just giving in to the lazy and the not so bright? (Yes, it will help the lazy and the not so bright. What's wrong with this?)

        Isn't simplifying things likely to lead to dumbing down - over-simplified answers to complex problems? (If the answer are over-simplified, then yes, by definition. But a sensible degree of simplification should leave us free to ponder other things.)

        Isn't this just popular science? (No, not really. Pop science generally aims to provide an overview but without going into the level of detail that would allow you understand how to use it in a new situation, how it's justified and the detail of how it works. It is this level of useful, flexible, detailed understanding that I intend the slogan simple knowledge to refer to.)

Nobody seems to be researching this issue, or even thinking about it. There are numerous research projects devising ways of cramming more into students' brains; there seem to be none whose goal is to reduce the amount that needs to be crammed in. This is very odd. Suppose that in few years we encounter super-intelligent aliens, or even super-intelligent computers we have built ourselves. These super-intelligences are likely to have ways of looking at things that we cannot make sense of, so the race will be on to translate, or package, or redesign, their wisdom for less advanced intelligences. But ... we are already at this point. The conclusions of many scientists and computer packages are already at a point where we need to consider very carefully how they can be made accessible to a wider audience. The search for simple ideas, or the reduction of cognitive strain, deserves serious research now. The links on the right and below are just some tentative first steps on this endeavour.

The case for simple knowledge depends on being able to create more appropriate alternatives. The examples in the panels above and below illustrate a few, just a very few, of the possibilities. These are mainly topics I happen to know something about because I have been teaching them in a university. In fact, all the areas I taught in my university job - statistics, research methods, decision analysis, and aspects of operational research - are represented here - which suggests that the principle that useful simplification is possible is a very general one. It is likely that the opportunities for productive simplification are just as great in other areas about which I know little.

Some of these examples might strike you as being rather trivial, but this is really the point - improving trivia means we will have more time for more important matters. But there are many non-trivial examples. Statistics is the area I have thought about most: the opportunities for simplification here are enormous, as are the problems caused by the conventional version. And statistics is a good illustration of the possibility that a decent simplification may answer subtly different, and more appropriate, questions.

These examples are unlikely to fully live up to the simple knowledge manifesto. They are largely untested. What people find simple and appropriate for their needs is ultimately an empirical question; most of what I am doing here is proposing some hypotheses about what might work. They need testing, and I am sure they can be improved.

More examples

Bike power calculator (Excel spreadsheet) using intuitive concepts like an acceleration of 2 miles per hour per second (instead of metres per second per second).


Why is SPSS so unhelpful? SPSS is the main statistical package for social scientists. But it is horribly and unnecessarily complicated (blog post).

User-friendly statistical concepts for process

monitoring and a second article on the theme of quality control, published in the Journal of the Operational Research Society in 1998 and 1999.

The Pros and Cons of Using Pros and Cons for Multi-Criteria Evaluation and Decision Making. Academic decision theory is complicated and rarely used: this article tries to make it closer to common sense.