Is making a mistake a mistake?

Mistake

When we make a mistake, we regret it and we try to correct it or, what often and maybe more often happens, we try to conceal it (which is as human as human is). That’s okay – I mean the regret, of course – and that you want to do it better is inherent in the meaning of the word. But are mistakes really so bad? Everybody knows the expression “We can learn from our mistakes” and so, mistakes have a positive side, too. However, there is more, for according to Stanford University psychologist Carol Deck – and I hope that he doesn’t blame me for the shortcut – people who make mistakes are more flexible than those who do not. Basically, so Deck, one can distinguish between people who have a fixed mindset and people with a growth mindset. In a fixed mindset, people believe that their basic qualities, like their intelligence or talent, are simply fixed traits. People with a growth mindset, on the other hand, believe that their most basic abilities can be developed through dedication and hard work. The first type of people tries to gather stuff that supports their ideas, while the second type tries to develop their insights. But just the later kind of people has to try new things and by doing so they have to take chances. And then, you guess it, they run the risk of making mistakes. But this type of people has also a better awareness of their mistakes and what to do with them. Therefore they advance more than those with fixed mindsets (who, alas, often just are the persons with the biggest talents). Thus, open your mind, don’t fear mistakes and in the end you’ll profit by it. A bit like “reculer pour mieux sauter”, as they say in French.

See http://www.psychologytoday.com/blog/your-brain-work and http://mindsetonline.com/whatisit/about/index.html .

Counting knowledge

In my last blog I characterized knowledge as methodically justified interpreted belief in order to make clear that it is impossible to say that there is a certain quantity of knowledge (be it measured in bytes or otherwise). I am not alone in characterizing knowledge that way. I want to mention here only Günter Abel, who has a related view (see his “Forms of Knowledge: Problems, Projects, Perspectives”, in Peter Meusberger, Michael Welker, Edgar Wunder (eds.), Clashes of Knowledge, Springer, 2008; pp. 10-33). However, that knowledge cannot be quantified is not only so because it is perspectival. Basically, the question “what is knowledge?” has no unequivocal answer, and what cannot be defined clearly cannot be measured. Take my own characterization of knowledge. Assuming that it is correct, even then it refers only to intellectual knowledge or “knowledge that”, as Ryle has called it, a type of knowledge that has to be distinguished from practical knowledge or “knowledge how” (see my blog dated June 9, 2008). Supposing that we could measure knowledge-that, we would measure only a part of what we know. Maybe all our knowledge-that, our theoretical knowledge, might be caught in books, articles and computer files (which I doubt), but how should we catch and measure all the things that we practically know how to do but that we cannot put into words? For how should we measure the knowledge how to skate or to drive a car, activities that can perhaps be theoretically explained but that we know to do only when we are successfully able to do it? Moreover, for everybody the knowledge how to do it is a bit different: my knowing how to skate is not exactly the same as your knowledge how to skate (for instance because our physical capacities are a bit different). Or what do you think of doing research? The main lines may be listed in handbooks, but many of the choices you have to make are simply a matter of your experience and intuition.

All this becomes even more complicated, when we look at other possible distinctions of knowledge. For besides the distinction between knowledge-that and knowledge how, other classifications can be made. Let me quote Abel just by way of illustration: We can “distinguish … between (a) everyday knowledge (knowing where the letterbox is), (b) theoretical knowledge (knowing that 2+2=4 or, within classical geometry, knowing that within a triangle the sum of the angles equals 180^o), (c) action knowledge (knowing how to open a window), and (d) moral or orientational knowledge (knowing what ought to be done in a given situation). Across these [types] of knowledge … the following important distinctions and pairs of concepts have to be taken into account: (a) explicit and implicit (tacit) knowledge, (b) verbal and nonverbal knowledge, (c) propositional knowledge (that which can be articulated in a linguistic proposition) and nonpropositional knowledge (that which is not articulable within a that-clause), (d) knowledge relating to matters of fact and knowledge based on skills and abilities.” (Abel, id: 13).

Should we measure all these different types of knowledge, add them, subtract what we counted more than once and then say: this is the amount of knowledge in the world? But how could we count or estimate everyday knowledge or implicit knowledge, for instance? And how could we say, which is a precondition for the counting task, that there is at least theoretically a fixed quantity of everyday knowledge or implicit knowledge in the world at a certain moment, for instance at 18.56h on November 14, 2011? I think that nobody would endorse the view that we can. But then the idea that there is a total amount knowledge is not realistic.

The attitude towards science

There is no fixed amount of knowledge, even not at a certain moment. I have asserted this in my last blog and I have explained it in previous blogs. But besides that, I think that the idea there is shows a wrong attitude towards knowledge. It’s a bit like: that’s what we have already. Although it is true that today we “know” a lot more than in the past and that there are good reasons to value it, I think that for a scientist it is the wrong attitude. This becomes clear when we consider what knowledge is: justified true belief, as a standard definition runs. But already this rough definition, which goes back to Plato and which since then has been the starting point for any discussion on what knowledge is (albeit often in the background), raises a lot of questions, such as: When is a belief justified? What is true? What is a belief? For whom does this belief exist? And for each answer, many new questions can be raised. It is not without reason that Karl R. Popper came to the conclusion that “we can never rationally justify a theory … but we can, if we are lucky, rationally justify a preference for one theory out of a set of competing theories, for the time being”. The presently accepted theory is nothing more than the best approximation to the truth we have. (Popper, Objective Knowledge, p. 82) In other words, the right attitude towards knowledge is not: that’s what we have but, as once a Dutch electronics company said, “Let’s make things better”. This can be reached only by not taking the “facts”, the knowledge we have gathered, as a starting point but by starting from the method to come to the facts: Popper’s method of conjectures and refutations, or rather any method that leads to a critical attitude towards the facts. It is the scientific skepticism of Descartes (and before him already Montaigne). That’s one pillar of knowledge. The other pillar or at least another pillar is, of course, man, the one who makes knowledge and for whom knowledge is made. But man as such does not exist; only individual men and women do, and this is the other reason that there is no knowledge as such but only knowledge for someone (or for a community of kindred spirits at most), as Karl-Otto Apel explained. Therefore a characterization of knowledge as methodically justified interpreted belief would better fit with what scientists actually do.

Finding our way in the field of knowledge

Lucca, Italy: 2000 years old Roman theatre, now in use as an apartment building

Once I discussed here Popper’s rejection of what he called the “commonsense theory of knowledge” or “bucket theory of mind” (see my blog dated April 5, 2010). According this theory, so Popper, there is a fixed quantity of knowledge that we can gather in some way. However, the theory is false for several reasons; in short one can say because knowledge is perspectival. Basically, knowledge is a special way of interpreting the world around us. Of course, it is changing through the ages and we get also new knowledge. But this changing and renewing of knowledge must be compared with the restoration and reconstruction of an old building, not with constructing new buildings instead. The building gets a new painting every odd years; stone walls are restored and get new bricks; wooden beams are maybe replaced by iron beams; new extensions are added and old parts are pulled down; also the interior may change a lot through the years; and after 500 years we have a completely different building with original and modern parts and another appearance; not three or four new buildings. Moreover, the building looks different, depending on whether we are in front of it or look at the rear side and on whether the sun is shining, or whether it is dark. So it is with knowledge, too.

Therefore I was a bit surprised to read in a lecture by Prof. Robert Dijkgraaf, president of the Royal Dutch Academy of Sciences – summarized in the Dutch daily De Volkskrant of the 29th ult. – an estimate of how much knowledge presently exists, namely one zeta byte, or 10²¹ bytes (I pass over here that in the lecture no difference was made between knowledge, information and data). It gives the suggestion that the existing knowledge is something fixed, albeit continuously growing. It is as if one could say: if we would distribute all knowledge there is among all the people in the world, each person would receive about 143.000.000.000 bytes of knowledge. The problem would be then how to coordinate them.

Actually, the lecture was not about how much knowledge there is but about how to find one’s way through it, which is a problem, indeed, whether one sees knowledge as perspectival or as quantitatively measurable. But I guess that just this distinction makes a big difference in the solution of the way finding problem. From  the point of view of the bucket theory, ideally one would try to learn as much knowledge as there is, but alas, this is impossible, so Dijkgraaf proposes a strategic approach: learn those pieces of knowledge (at school, at the university) that have a strategic position in the sense that they are central by having relevant connections with those parts of knowledge that we do not learn and that are also important to know for some reason. The learned pieces of knowledge must give as best an entrance to the not learned pieces as possible. I think it is a conservative approach. It takes the old idea of pumping knowledge into one’s head as a starting point for science and maybe also for being intellectual. On the background (not so much in Dijkgraaf’s lecture but generally in such approaches) often the fear is present that people will lose the old values of learning and in the end certain valued capacities of the brain: the capacities to store facts. The latter is not impossible, for learning values simply do change and brains adapt themselves genetically to new circumstances.

Now, I do not want to deny that knowing facts can be useful and can also be an enrichment of one’s life. But is learning strategic facts really the solution to the problem how to find one’s way in the field of knowledge? I think that from the perspectival view of knowledge a methodological approach is more obvious: learning methods how to find knowledge rather than learning strategic points from where to start. If knowledge is perspectival, and when the perspectives are continuously changing in addition, I think that it is more important to know the right questions to ask in order to find your way than knowing the right places to start. For the appearances of these places are continuously changing. In other words: learn how to find your way, not from where to find your way.

The strategic facts approach and the methodological approach do not completely exclude each other, of course. For one thing, the methodological approach is not possible without a basic knowledge of facts. For another, once one knows the strategic facts, one must know how to find one’s way to the not learned facts. However, the differences between both approaches are fundamental: they are based on a different view what knowledge is.

The methodological approach asks for another mental attitude and in view of what is known about the development of the brain, it is not unlikely that it will lead to a genetic change of the brain, if it will become the leading approach to the world of knowledge. But should that be regretted? I don’t think so. Genetic changes of the brain are normal. They have taken place as long as man exists and they have led to a better adaption to the world around us. This does not imply that this will also be the case in future, no more than that it implies that our present genetic constitution is the best one for a changing world. Maybe it is, maybe it isn’t, but we simply cannot deny what happens to be.