Is it a good idea to teach a class that is new like “Sustainability in Civil Structures” or the highly technical “Advanced Matrix Analysis” and replace classes that reinforce the basics? There are only so many hours in the current curriculum. Regardless of which class we may add (and consequently which class we remove), every class needs to foster enquiry. We need to resist cramming their heads with more and more knowledge (whether it is more mathematics, new theory based on a particular research agenda or trends in the marketplace). This may numb the minds of our future engineers. Teaching should be about assisting the student in discovery (a liberal education), not supplying the knowledge or listing the latest facts. Let’s turn to what liberal learning means from the master of inquiry, Socrates.
Socrates can best help us understand the importance of a liberal education. He is someone who literally lost his life in defense of the spirit of inquiry (read the Apology or Crito). I think his most telling debate on the importance of inquiry is in the dialog Meno. It is in the work written by Plato where we find Socrates asking fundamental questions about learning itself. I am going to borrow and edit heavily the entire dialog (even replace words for the heck of it) because I think this is exactly the type of dialog that should exist in all of our classrooms.
Meno. Can you tell me, Socrates, whether structural engineering is acquired by theory or by practice; or if neither, then whether it comes to man through testing nature, or in what other way?
Socrates. O Meno, I am certain that if you were to ask anyone this, he would laugh in your face, and say: “Stranger, you have far too good an opinion of me, if you think that I can answer your question. For I literally do not know what structural engineering is, and much less how it is acquired”. And I myself, Meno, I confess with shame that I know literally nothing about engineering.
Meno. And how will you enquire, Socrates, into that which you do not know? How do we learn something that we have no knowledge of?
Soc. I will tell you how: all enquiry and all learning is but recollection. We do not learn, we recollect.
Men. What do you mean by saying that we do not learn, and that what we call learning is only a process of recollection? Can you teach me how this is?
Soc. I told you, Meno, and now you ask whether I can teach you, when I am saying that there is no teaching, but only recollection; and thus you imagine that you will involve me in a contradiction!
Men. Indeed, Socrates, I protest that I had no such intention. I only asked the question from habit; but if you can prove to me that what you say is true, I wish that you would.
Soc. It will be no easy matter, but I will try to please you to the utmost of my power. Suppose that you call one of your numerous uneducated slaves, that I may demonstrate on him – the question of learning is recollection. We will have to get to what structural engineering is another day – and concentrate on how one knows things. I will however use the area of a column as an example – something I am sure is used by the structural engineer.
Men. Certainly. Come hither, boy.
Soc. Meno please attend now to the questions which I askthis boy, and observe whether he learns of me or only remembers.
Men. I will.
Soc. Tell me, boy, do you know that a figure like this section of a column. Is it not a square?
Boy. Yes, I do. It is a square.
Soc. And you know that a square figure has these four lines equal?
Boy. Certainly.
Soc. And these lines which I have drawn through the middle of the square are also equal?
Boy. Yes.
Soc. A square may be of any size? So a column may be of any size?
Boy. Certainly.
Soc. And if one side of the column be of two feet, and the other side be of two feet, how much are will the whole column be? Let me explain: if in one direction the column was of two feet, and in other direction of one foot, the whole would be of two feet taken once?
Boy. Yes. So two by two would be four square feet.
Soc. Good. And might there not be another square column with an area twice as large as this? And what is the area of that doubled column?
Boy. Eight square feet of course.
Soc. Correct. And now try and tell me what is the length each side if the area of the square column is eight?
Boy. Clearly, Socrates, it will be double the length of the side, so each side will be four.
Soc. Do you observe, Meno, that I am not teaching the boy anything, but only asking him questions; and now he fancies that he knows how long the side of the column is necessary in order to produce a column of eight square feet; does he not? And does he really know?
Men. Certainly not.
Soc. Observe him while he recalls the steps in regular order. (To the Boy.) Tell me, boy, do you assert that double the area comes from doubling the side? Remember that I am not speaking of an oblong, but of a figure equal every way, and I want to know whether you still say that a double square comes from double line?
Boy. Yes
Soc. But does not this line become doubled if we add another such line here?
Boy. Certainly.
Soc. And are there not these four divisions in the figure, each of which is equal to the figure of four feet?
Boy. True.
Soc. And four times is not double is it?
Boy. No, indeed. It is four times as much. Sixteen! Oh no – that column is huge!
Soc. So what side length would give you a space of eight square feet? Is not a space of eight, half the size of sixteen?
Boy. Certainly.
Soc. Then the line which forms the side of eight square feet ought to be more than this line of two feet, and less than the other of four feet?
Boy. It ought.
Soc. Try and see if you can tell me how much it will be.
Boy. Three feet.
Soc. And how much are three times three feet?
Boy. I am counting and I am close but nine is not eight. So I was wrong again!
Soc. But from what length of line would give you eight square feet? Tell me exactly; and if you would rather not reckon, try and show me the line.
Boy. Indeed, Socrates, I do not know.
Soc. Do you see, Meno, what advances he has made in his power of recollection? He did not know at first, and he does not know now, what is the side of a column of eight square feet: but then he thought that he knew, and answered confidently as if he knew, and had no difficulty; now he has a difficulty, and neither knows nor fancies that he knows.
Men. True.
Soc. Is he not better off in knowing his ignorance? If we have made him doubt, and given him the “torpedo’s shock,” have we done him any harm? We have certainly, as would seem, assisted him in some degree to the discovery of the truth; and now he will wish to remedy his ignorance, but then he would have been ready to tell all the world again and again that the double the area should have a double side. He would of lived his entire life with false knowledge – and this is just area stuff, I haven’t even discussed buckling!
Men. True.
Soc. But do you suppose that he would ever have enquired into or learned what he fancied that he knew, though he was really ignorant of it, until he had fallen into perplexity under the idea that he did not know, and had desired to know?
Men. I think not, Socrates.
Soc. Mark now the farther development. I shall only ask him, and not teach him, and he shall share the enquiry with me: and do you watch and see if you find me telling or explaining anything to him, instead of eliciting his opinion. Tell me, boy, is not this a square of four feet which I have drawn?
Boy. Yes.
Soc. And how many times larger is this space than this other?
Boy. Four times.
Soc. But it ought to have been twice only, as you will remember. And does not this line, reaching from corner to corner, bisect each of these spaces?
Boy. Yes.
Soc. And how many spaces are there in this section?
Boy. Two.
Soc. And four is how many times two?
Boy. Twice.
Soc. And this space is of how many feet?
Boy. Of eight feet.
Soc. And from what line do you get this figure?
Boy. From this.
Soc. That is, from the line which extends from corner to corner of the figure of four square feet?
Boy. Yes.
Soc. And that is the line which the learned call the diagonal. And if this is the proper name, then you, boy, are prepared to affirm that in order to double the area of the column, you would square the diagonal?
Boy. Certainly, Socrates.
Soc. What do you say of him, Meno? Were not all these answers given out of his own head?
Men. Yes, they were all his own.
Soc. And yet, as we were just now saying, he did not know?
Men. True.
Soc. But still he had in him those notions of his-had he not?
Men. Yes.
Soc. Then he who does not know may still have true notions of that which he does not know? Without any one teaching him he will recover his knowledge for himself, if he is only asked questions? And this spontaneous recovery of knowledge in him is recollection?
Men. True.
Soc. And this knowledge which he now has must he not either have acquired or always possessed?
Men. Yes.
Soc. But if he always possessed this knowledge he would always have known; or if he has acquired the knowledge he could not have acquired it in this life, unless he has been taught geometry; for he may be made to do the same with all geometry and every other branch of knowledge. Now, has any one ever taught him all this? You must know about him, if, as you say, he was born and bred in your house.
Men. And I am certain that no one ever did teach him.
Soc. And if there have been always true thoughts in him, both at the time when he was and was not a man, which only need to be awakened into knowledge by putting questions to him, his soul must have always possessed this knowledge, for he always either was or was not a man? .
Men. I feel, somehow, that I like what you are saying.
Soc. And, Meno, I like what I am saying. Then, as we are agreed that a man should enquire about that which he does not know; that is a theme upon which I am ready to fight, in word and deed, to the utmost of my power.
In other words, we should want our students to acquire the freedom that allows them to acknowledge the one certainty in life: “Indeed, Socrates, I do not know.” Recognition of that certainty, we are all ignorant, is the pathway to learning. Then learning things will belong to them, instead of just repeating things that belong to others (memorization of facts, test taking, etc). Future engineers need to process the tools resulting from a liberal education to help them to listen and to read attentively and deeply, to express themselves intelligibly and precisely, to measure and question the world, and to seek truth. This will help them become lifelong learners. Another useful result, it will make them better at understanding the highly technical and theoretical aspects of engineering too. We don’t want engineers who regurgitate what they have been taught and memorized. We want them to struggle and to engage the world and people in a meaningful ways. We want engineers with a spirit of inquiry and love of learning that will last a lifetime. So even if we add classes that submit to trends in the marketplace or wrongly decide our students need more mathematics, we better make sure that Socrates joins every class.
