There are three “dimensions” to every intellectual concept:
1) The length of a concept is the “lowering down” of the concept to make it accessible to the mind. In other words, this is the “descent” of the concept through the use of examples and analogies so that even a very lofty and abstract concept is expressed in terms that are tangible, even to the understanding of a child. This is analogous to the length of a river. Its source is in the mountain peaks from which it flows down until it reaches sea level. This may be compared to a great mathematician teaching arithmetic to a small child.
Numbers, in and of themselves, are abstract concepts, unrelated to physicality. Nonetheless, the mathematician lowers the concept by using physical examples to bring it within the scope of the child’s comprehension. For Instance, he asks the child, “If I give you one apple and your mommy gives you another apple, how many apples do you have?” “Two apples.” “If you find two more apples, now how many apples do you have?” “Four apples.” “Now, if you eat one of those apples, how many apples do you have left?” “Three apples.” In order to explain addition and subtraction, which themselves are abstract concepts unrelated to physical objects, he had to “lower” the concept and put it into tangible terms that the child’s intellect could accept. In the same way, whenever a person studies any deep subject, he must “lower” the concept to his own intellectual understanding by finding analogies and examples for himself, which will make the concept more accessible and “graspable” to him.
2) The width of a concept is the many different ways and angles in which it may be understood. In other words, a single concept may be explained or viewed from many different perspectives and approaches, rather that just single way. This is what gives “breadth” to the concept. This is analogous to the width of a river.
3) The depth of a concept is analogous to the depth of a river. The depth of the river is its undercurrent and its “strength”. In its depth, the river does not have much of a width. Nonetheless, it is from the power of this depth, the force of the undercurrent, from which the width and length overflow. Likewise, in a concept, the depth of the concept is what brings about its length and breadth. This is because the depth of the concept is its essential point even before it spreads to the length and breadth of explanation. This is called, Omek HaMoosag (The depth of that which is being grasped).
The game of “Tic-Tac-Toe” is not deep at all. Therefore, it has little breadth, in that it may be explained in only one way. Because it is not deep, it is also short. In order to be explained it need not be invested into examples and analogies. It may be explained simply, as is. In contrast, a subject, such as physics or medicine is much deeper. Therefore it is very broad. There are many fields of physics and medicine, and many particulars to each one. It also has great length. It takes many years of earnest study to become either a physicist or a medical doctor. This is to say that one must go through the length and breadth of the explanation of physics or medicine before he can grasp their depths and truly be called a physicist or a doctor.
