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Tyrone Lai



Four Caricatures of the Knowing Process



Martian Mo

A Martian named Mo is visiting Earth and notices that a car, as we Earthlings say, has a box and four wheels. So Mo builds a box and attaches four wheels to it. Mo notices that a car has windows, so he builds windows. He notices also that there is a steering wheel, so Mo builds a steering wheel. After all this is done, Mo goes into the car and he turns the steering wheel. He turns it to the left and he turns it to the right … but the car still would not move!

Martian Mo has not built a car. He has built the caricature of a car. He did not intend to build a caricature; he intended to build a real car; but a caricature turned up anyway. It is true that a car has a box and four wheels, but a car is not just a box and four wheels. It is true that a car has windows and a steering wheel, but adding these to the box still will not make Mo's creation into a car. If Mo wants to build a car he cannot just look at cars, see how they appear on the outside, and then imitate them. He has to look 'under the hood' and understand how a car is put together, and why it works.

Mo's caricature is not intentional. Mo is new to Earth. A car is a complicated machine. Even if Mo should succeed one day in building a car, a real motor-car, it is to be expected that he will meet with failures along the way. Mo should not be blamed for building his caricature. Indeed, he should be commended for his enterprise. Most people who see cars make no attempt to build one.

Mo's creation cannot move: it has no engine. To make it move Mo will have to learn about engines, which in themselves are not simple things either. But if Mo wants to build a real motor-car this is what he will have to do. An engine is an essential part of an automobile.

Sherlock Holmes and Scientists

Sherlock Holmes solves crimes. He does so not by asking the criminals. Sherlock Holmes does not go amongst the criminals and say unto them, 'Which of you has committed the crime? Come forward and let me know.' This is not how he works. If it were, Watson would never have written his memoirs and we would not have heard of Sherlock Holmes. It is true that in most of the cases that Sherlock Holmes has solved the criminals eventually confess, but this occurs after he has solved the crime, not before.

Criminals usually do not confess; why do they confess to Sherlock Holmes? If we go back to Watson's accounts we will find they have a good excuse: Sherlock Holmes knows so much already. If he can find out so much on his own, what point is there in keeping the rest from him?

Sherlock Holmes likes to know the rest. He cannot find out everything. As he says, he knows only 'in essentials'. Still it is remarkable that he can know so much.

Sherlock Holmes solves crimes; scientists find out how the world is put together. Scientists do not know everything either. Still, it is remarkable that they know so much. Sherlock Holmes does not ask the criminals; scientists do not ask God. There is no record for example that Einstein ever dial God's number and ask, is E = mc2? Scientists are prohibited from dialling God's number. Like Sherlock Holmes they find out on their own. Sherlock Holmes sometimes manages to elicit confessions. In the case of scientists they do not expect there ever will be a 'confession'. Are confessions absolutely necessary? No, as we have seen. Sherlock Holmes finds out before the confessions. Moreover, there are such things as false confessions. How do we know that a confession is not false? By playing Sherlock Holmes again.

… but Sherlock Holmes is fictitious!

That may be so, but his method is not.

Ah …, but is there a method?

Elsewhere I have shown there is a method, one used by Sherlock Holmes and scientists--and cryptanalysts (people who crack ciphers), a method in which, surprisingly or not so surprisingly, clues play the central role (see Lai, The Art of Detection). But that presentation is rather long. Instead of repeating it, in the next section I shall give a simple argument to show that there must be a method.


Sherlock Holmes follows clues. All detectives do. We all know that in crime detection if we cannot find any clues we will never reach a solution. But we cannot assume that whenever we follow clues we will do so correctly. Mo says he is building a motor-car. Is he really building a motor-car? We cannot take it for granted that he is. Similarly we cannot take for granted that whenever we say we are following clues, we are doing so correctly.

If a car is really just a box with four wheels any one can build a car. Is following clues as simple as putting a box on four wheels? Is it something any one can do unerringly? Clearly, it is not. It is difficult to follow clues. Most of the time most of us do not do it correctly, the reason why we admire Sherlock Holmes.

How should we follow clues? This question is not often asked. But once it is asked, we see there must be a method: a method for finding out things on our own. For how does Sherlock Holmes find out? How does he find out before the criminals confess? He can only find out by following a method. He finds out by doing things the way they ought to be done. What things are we talking about here? Clues, of course. Sherlock Holmes finds out by following clues the way they ought to be followed. When we follow clues the way they ought to be followed we find out things on our own, things we originally did not know. This is why we follow clues. This is the reason why it is so important that when we follow clues we should go about it in the right way. There is a reward for following a method correctly. When we follow a method correctly we reap the benefit the method promises. We have a method (an algorithm) for adding numbers on paper. If we follow this method correctly we get the right answers. This is what the method promises, the reason why we take care when doing sums. Now, here we have another method. This method promises knowledge even in the absence of confessions. So when we follow this method correctly, and we have to take care that we follow it correctly, we obtain knowledge even in the absence of confessions. Sherlock Holmes does not have to depend on confessions; neither do scientists. Why do they not absolutely need confessions? Because they have a method.

Even without spelling out in detail how we should follow clues we can see that there has to be a method, a method for finding out things on our own. Sherlock Holmes uses this method, so do scientists. It is by using this method that they find out things they originally did not know. (Some readers will want to deny that there is such a method. If they do, they will have to deny also that it is possible to crack ciphers.)


Theseus went into the Labyrinth to kill the Minotaur. To make sure he can come out again he unwound a ball of thread on his way in. Afterwards, when he had to extricate himself, all he had to do was follow this thread. Now following clues is often compared to following a thread, so I have coined a new word: theseology, to stand for the study of how we should follow clues. Since there is a method telling us how we should follow clues, I have called this method the theseological method.


Sherlock Holmes was planning on writing a textbook on the art of detection when he retired. Since in detection we have to follow clues, the art of detection, I suggest, is simply the art of finding and following clues (we have to find clues first before we can follow them), in other words, theseology. If Sherlock Holmes had written his textbook, he would have explained to us systematically how we should follow clues. But, as far as we can ascertain Sherlock Holmes never got around to writing his textbook. However, we do not have to have a textbook to tell us how we should follow clues. It is better if we have one, but it does not mean that in its absence we will know nothing about this subject. Because of the popularity of detective stories; because of actual experience we have had in finding out things on our own; most of us know something about clues and something about how to follow them. We may not have been able to get everything right; it is possible that here and there we will have misunderstandings; but most of us are likely to have known enough about clues to be able to raise some interesting questions, questions that we would expect a textbook on the art of detection to answer. Below I give some examples of this kind of questions.

· Clues cannot be just anything we can observe. But if they are not, what are they? Why is it that among the things we can observe some are clues and some not?

· Why is it that by following clues we can find out things on our own, without asking those who already know, be they criminals, or God, or whoever?

· How do we know we have found a clue? How do we know when we are still in the dark, when we do not know yet what we will find?

· In solving mysteries by following clues we need evidence. By this we mean of course relevant evidence. How do we determine what evidence is relevant, and what not, on our own, in the dark?

· Clues can often be interpreted in more than one way. Not all these interpretations will be right or Sherlock Holmes will never be able to find out anything. But how do we determine which interpretation is right? How do we determine when we are still in the dark?

· To interpret a clues it seems we have to know in advance of the interpretation what the clue means. But if this is the case, when we follow clues, do we ever find out anything we do not already know?

These questions, I think most people can see, are not easy to answer. That we can ask them; that we think it is important that we should ask them; shows us that the art of detection--the art of following clues, or theseology--is not a simple art. If the art of detection were simple we would not have questions like these. In any case, that the art of detection is a difficult art is well acknowledged. After all, there is only one Sherlock Holmes.

Caricature One

Sherlock Holmes knows without asking the criminals; scientists know without asking God. How do they do it? Now there have been many answers to this question. In this section we consider one of them.

Sometimes people say, scientists know by collecting facts and then inferring from them. It is as simple as that (they say). To know, we first have to collect a body of facts. The larger this body, the better. Then, by reasoning from these facts we arrive at knowledge we formerly did not have, knowledge that goes beyond the facts. For example, by observing various pieces of metal expanding when heated we arrive at the knowledge that all metals expand when heated.

This view on how knowledge is obtained, we now say, is a caricature. It is a caricature because in the description given there is not even mention of clues. It is a caricature in the same way that Mo's motor-car is a caricature. It is true that Sherlock Holmes reasons. It is true that he observes. It is true that Sherlock Holmes would welcome a large body of evidence. It is also true that Sherlock Holmes's knowledge will eventually extend beyond the facts available to him. But there is much more to the process by which Sherlock Holmes knows than just observing and reasoning. Sherlock Holmes depends on clues. Of necessity he has to follow a method in which clues play the central role (the theseological method). If Sherlock Holmes did not find any clues; if he were prevented from exercising the theseological method; or if he exercised it incorrectly; however much observation he made, and however much reasoning he did, he would not have been able to discover anything. Sherlock Holmes is a theseologiser. Theseology (the art of detection) is a complex art. We cannot replace this complex art by a simple injunction: observe and reason! We can no more do this than replacing a real automobile with Mo's creation.

Some will say, but following clues is a form of reasoning …

We say it cannot be. For if following clue is a form of reasoning theseology should be a branch of logic. But look at the questions we raised earlier, questions that we expect a textbook on theseology to answer. Are they the kind of questions that logic answers? One of the questions is, what are clues? Is this a question that logic can answer? Logic can no more tell us what clues are than it can tell us what a crankshaft is. Logic is not automotive mechanics; neither is it theseology.

Caricature Two

How do scientists know? Instead of the answer given in the last section (which answer is in fact a caricature), sometimes people say they know by marrying theory with observation. Scientist create theories, they point out. They, scientists, then look at the world through the theories they have created. By doing so the world appears ordered to them. Instead of a chaotic world they now see a structured world. But this structure that they see is not really present in the world; it is in fact imposed upon the world as a result of the theories scientists bring with them in experiencing this world. Scientific knowledge, these people say, is created by scientists when they impose their theories upon the world. Different people create different kinds of knowledge, they continue; it all depends on what theory one brings to one's experience of the world.

This view of the knowing process, we say, is also a caricature. To show that it is let us use Sherlock Holmes as example again. It is true that in solving crimes Sherlock Holmes has to form theories as to how the crime was committed. But Sherlock Holmes does not form just one theory and then impose it upon the evidence he has gathered. Sherlock Holmes follows clues. A clue often suggests more than one possible interpretation. This is to say, in response to a clue we often can form more than one theory. But no one, least of all Sherlock Holmes, would take all these theories to be true, or equally good. If Sherlock Holmes is to solve the crime he has to determine which of these theories, if any, is true. Sherlock Holmes cannot impose theory upon evidence. Instead, he has to follow the clues wherever they lead. Now there is this interesting point about clues, which most of us would know even without reading a textbook on the art of detection. When we have enough clues these clues together will point in one specific direction. If we have just one clue it may point to a number of possibilities. For example, the clue may suggest that the butler, or the maid, or the master of the house, or the vicar, did it. But if we have not just one clue, but more and more, eventually these clues together will narrow down the field. Let us say in this case the clues narrow down to the master of the house. Now obviously this is a nice stage to have reached. But we have to ask ourselves, who suggested the master of the house in the first place? Who put forward this theory?

Who … but Sherlock Holmes! This he has to do. It is the right thing to do when following clues that we should suggest theories in response to clues (we often say clues suggest, but this is only a figure of speech). Those who do not are not doing things the way they should be done. The theory that the master of the house did it does not come forward by itself. Now what does Sherlock Holmes do after he has determined that this theory is correct?

After Sherlock Holmes has determined that this theory is correct, he will explain all the relevant evidence in terms of this theory. He will say all the evidence points to the master of the house. But in doing so, we should notice, Sherlock Holmes is not forcing his theory upon the evidence. It is true that he will explain all the relevant evidence in terms of this theory but he does this because the clues available in the evidence tell him that this theory is correct. When following clues one uses the right theory to explain the evidence. This is the right thing to do. It will be absurd if, after finding the right theory, one uses a different theory to explain the evidence. Suppose according to Sherlock Holmes's theory, the master of the house used his own revolver to kill the victim. When Sherlock Holmes sees the revolver he will point to it and say, that is the murder weapon, that is the weapon the master of the house used to kill the victim. No one would expect him to set aside his own theory and say, that is the weapon the butler used to kill his victim. In solving a crime the evidence will eventually have to be explained. In doing so we will of course use one of the theories we have formed. But this does not mean we are imposing our theory upon the evidence.

When we have succeeded in finding knowledge, whether in science or in crime detection, we will use a theory human beings have formed to interpret the evidence. But this does not mean that this is all that we do in the knowing process. To say that it is, is a caricature. Caricatures leave out important elements. One important element left out by Caricature Two is, again, the role clues play in the knowing process. To uncover knowledge, whether in crime detection or in science, we follow clues. There can be no hope of understanding this process properly if we leave out completely the mention of clues.

Caricature Three

When scientists first tried to work out the structure of the benzene molecule they discovered something very surprising: there were too few hydrogen atoms! The benzene molecule has six carbon atoms. According to the science at the time, each of these carbon atoms should be accompanied by two or three hydrogen atoms. But there are only six hydrogen atoms in the whole molecule! There are not enough hydrogen atoms to go around. How is this possible?

This puzzling fact--that the benzene molecule has only six hydrogen atoms--led to the discovery that the six carbon atoms in the benzene molecule, instead of being strung up together in a chain (as it was originally thought) is in fact arranged in a ring. In this configuration only one hydrogen atom can be associated with each carbon atom. This is why there are only six hydrogen atoms altogether. Six is not too few. It is the only number the molecule can accommodate.

There are many instances of this kind in science, that is, instances in which puzzling facts lead to new discoveries. So there is this suggestion that some people have made: In science, they say, we look for puzzling facts and we find theories to explain them. If we have some puzzling facts and we have found a theory that can explain them we have made a discovery. This is how new knowledge is acquired. It is acquired by using our ingenuity in devising theories that can explain puzzling facts.

This, we say, is again a caricature. To make discoveries we follow clues. It is true that sometimes clues are surprising. For example, in one of his cases one of the clues that led Sherlock Holmes to a solution was 'the curious incident of the dog in the night-time':


'The dog did nothing in the night-time.'
'That was the curious incident,' remarked Sherlock Holmes.

-- Silver Blaze


Some one came in the middle of the night to steal a horse. But the dog did nothing! It did not even bark! Sherlock Holmes found this curious, and used it as a clue.

But while surprising facts can be clues, not all clues are surprising. Sherlock Holmes regularly collects cigarette ashes at crime scenes. There is nothing surprising or puzzling about cigarette ashes; yet they can furnish important clues.

Most of us know that in an investigation, if we are to succeed we need sufficient clues. When we have sufficient clues they can narrow down the field. When we have surprising clues they may make our task easier. Lots of people can leave behind the same kind of cigarette ashes, but very few people can come and go in the middle of the night and not disturb the dog. However, that surprising clues can make an investigation easier does not make all discoveries simply a matter of finding puzzling facts and devising some theory to explain them.

Interestingly enough, in one of his cases Sherlock Holmes himself fell victim to this very mistake, that is, the mistake of thinking that an investigation is nothing more than finding a theory to explain some puzzling facts. In The Yellow Face Sherlock Holmes was given a set of puzzling facts by a client. A wife, the wife of the client, has been loving and devoted and perfect in every way; she has been like this since marriage. But lately she started to behave in a fashion that was nothing less than bizarre. Still loving and devoted, she for example would ask her husband for a large sum of money but would not give any reason, only begging that the husband trust her. And she would disappear in the middle of the night to the house next door, a house newly rented out, without letting the husband know. Sherlock Holmes was intrigued by what he had heard from his client, and after some questions quickly came to a solution. He thinks the wife is being blackmailed. His theory, as he lays it out for Watson, explains everything that he has been told. As he says, it 'covers all the facts'.

But it was the wrong theory! No blackmail was involved, as he and Watson soon found out.
The Yellow Face was one of Sherlock Holmes's most dismal failures, and acknowledged by him to be such. The crucial events happened in a village called Norbury. Afterwards, Sherlock Holmes had this to say to Watson:


Watson,… if it should ever strike you that I am getting a little overconfident in my powers, or giving less pains to a case than it deserves, kindly whisper 'Norbury' in my ear, and I shall be infinitely obliged to you.

-- The Yellow Face


In The Yellow Face Sherlock Holmes was definitely giving less pains to the case than the case deserved. He took the facts from his client and then simply fashion a theory to 'explain' these facts. For once Sherlock Holmes forgot to ask if he had enough clues to pin down any theory, whether his or some other. In an investigation we have to follow clues. It is a mistake to come to a conclusion when we have followed too few clues. And, of course, it will be a even bigger mistake if we do not follow any clues at all.

We do not make discoveries in science or in crime detection simply by fashioning theories to explain puzzling facts. The process is more complex. To find out things on our own we have to follow clues and we have to have enough of them.

Caricature Four

That Sherlock Holmes and scientists can find out on their own, without asking the criminals in the one case and God in the other, some people find surprising. 'How can this be possible?' they often ask. Now if they should be interested in an answer they should be prepared for other surprises as well. For this process, the process by which we find out things on our own, has some rather remarkable characteristics. One of them is that, while engaged in this process, we can correct our own mistakes. Indeed, if the mistakes are minor correcting them is relatively easy (being not all that different from correcting typographical mistakes). But even when the mistakes are serious they can still be corrected (at least sometimes).

That we can correct our own mistakes while following clues is unexpected. For we follow clues because we don't yet know those things we want to find out. If we knew, there would have been no need to follow clues. But if we don't yet know, how do we know we have made a mistake? When we do not even know that we have made a mistake, how can we correct it? If I know I am going to the North Pole I know I have made a mistake if I am heading south. But if I do not even know that I am going to the North Pole, how would I know that south is the wrong direction? And if I do not even know that south is the wrong direction, why should I change course?

However, surprising as it may sound, in the theseological process we can correct mistakes on our own! We can do so in the dark, while still ignorant of what we will eventually find.

Why should this be? Why is it that we can correct mistakes when following clues?

Since correcting simple mistakes is relatively easy, I shall concentrate on serious mistakes in my answer below. This is to say, the question I want to answer now is, why is it that we can correct even serious mistakes when following clues?

To answer this question we have to draw attention to another interesting characteristic of the theseological process:

When following clues, if we make serious mistakes we will be bogged down, we cannot find out more.

In following clues, when things are going well we find out more and more. But when we make serious mistakes this will stop happening. Instead of finding out more and more, we will stop finding out anything. Clearly, this is not a nice situation to be in but it happens often in investigations. It happened even to Sherlock Holmes. In The Twisted Lip the problem Sherlock Holmes was faced with looked simple enough. A man had disappeared immediately after having been sighted by his wife in a part of London in which she did not expect to see him. As it were, the man simply disappeared into thin air. For despite all searches no trace of him could be found--except his clothing and a few drops of blood. Now ordinarily Sherlock Holmes was not easily stumped, but on this occasion not only was Scotland Yard at its wit's end, Sherlock Holmes was in the same company. As he tells Watson,


It seems absurdly simple, and yet, somehow I can get nothing to go upon. There's plenty of thread, no doubt, but I can't get the end of it into my hand. … [A]ll is dark to me.

-- The Man with the Twisted Lip


Why should this be? Why is everything dark even to Sherlock Holmes? Why couldn't Sherlock Holmes come up with some idea as to what had occurred?
There was a good reason. On this particular occasion everyone had made a mistake, including Sherlock Holmes. And it was a major mistake. Every one, including Sherlock Holmes, assumed that a murder had taken place. But none had occurred! When we make a mistake as serious as this we will not be able to find clues. Without clues we cannot find anything.
That we cannot find clues does not mean the clues are not there. In this case the clues are there, but they are not clues for a murder. But since we are not looking for these clues; since we are only looking for clues that point to a murder; we will not see the clues that are there (the purloined letter syndrome). And of course, since there has been no murder, however hard we look we will not find any murder clues. When we cannot find even a single clue, how can we make sense of the situation?

In following clues we can tell on our own that we have made serious mistakes. This is because when a serious mistake has been made, our movement forward will be blocked, or as the saying goes, we will hit a brick wall. How do we know if the mistake has been corrected? We know if we are able to make progress again. So this is what we do when we meet with blockage in an investigation. We replace some of the steps we have taken. If after these replacements we are able to make progress we have both located the mistakes and corrected them.

That we can correct mistakes on our own, without asking God or those who already know, is no mystery when we understand what we are doing when following clues. If we do not understand; if we do not even know that we are following clues; that we can correct mistakes on our own will indeed be a mystery.

Notice also that when following clues if we do not correct our own mistakes, we will be paying a heavy price. If we refuse to correct our own mistakes we will be bogged down for ever. In following clues we cannot talk ourselves out of a mistake; that is, we cannot deny we have made a mistake if we have.

Karl Popper has noticed that in science we can correct mistakes on our own (see Popper, Conjectures and Refutations). He finds it remarkable that scientists can propose theories in answer to problems and then later find out on their own, without asking God or some other infallible authority, that some of these theories are false. So he suggests that if we want our knowledge to grow we should look for worthwhile problems, propose theories in answer to them, and then test these theories until we succeed in refuting them, at which point we will have new problems requiring new theories, which new theories we can treat in the same fashion. This process of conjectures and refutations can continue indefinitely, Popper says, and it is good that it should.

As we have seen, there is some truth in what Popper says. Scientists follow clues. When following clues we can correct mistakes on our own, without asking God or some other infallible authority. And it is important that we should correct mistakes on our own; otherwise we will be bogged down for ever. But although there is some truth in what Popper says, ultimately Popper's theory of how knowledge grows is still, unintentionally, a caricature. It draws attention to one important characteristic of the knowing process, but says little about the rest. In particular, like Caricatures One, Two, and Three, it tells us nothing about clues. Clues are the engine of the knowing process. Without clues, without our detecting them, without our finding out what they mean, without enough of them, knowledge cannot increase. Mo's creation is not a motor-car, only an unintentional caricature of one. In his case the engine is missing also. (For an explanation of what clues are, and why they can lead to knowledge, see Lai, The Art of Detection.)


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