Why to know how to multiply numbers does not mean to know the result?

Question

What is the difference between these two situations?

1. A subject thinks she knows somebody's name. However, when asked she cannot recall it immediately. After some efforts, the name is coming and she reports it. Normally, regardless this apparent difficulty to reproduce the word, we say about this situation "the subject knows this name".
2. The subject has two numbers and is calculating their product (i.e. these are two sides of a rectangle and she is asked to find its area). In this situation, we do not say that the subject knows the product of two numbers until she has calculated it.

Why these situations differ? There is much similarity between them. First, the two numbers and the multiplication rule together are equivalent to the final product - in some sense they encapsulate it; therefore, it seems justifiable to say that the subject has it. In both situations, the process passes in the subject's head without any external help or additional information. The efforts are comparable. In both cases, there are periods when the subject is incapable to give an answer. Why 1 is "situation of knowledge" and 2 is not?

Answer 1

In the first situation she knows the name by remembering it. A person's name cannot be calculated, only memorized.

In the second situation she knows the result by calculating it. She has memorized (i.e. knows) how to multiply, how to calculate a result, but does not know what the result is until after doing the calculation.

The premise (that #1 is "know" and #2 is "not know") is true if "I know" is a synonym for "I have memorized" (but not a synonym for, "I am able to calculate").

Sometimes we can, colloquially, say that #2 is an example of "knowing the product of two numbers": we might say that the subject is "numerate" or "knows her numbers", or (more formally) "knows multiplication".

Answer 2

If the subject could not tell you the person's name from memory, but is sure that she can look it up in a photo album, would we then still say that she "knows" that person's name?

It doesn't seem much different from the multiplication case, in that both cases require a process other than recalling from memory to produce the information.

That there are periods where the subject cannot recall the name immediately can, in my opinion, be somewhat ignored. It's like how a computer program sometimes fails to load or locate a file, even if we ourselves are sure it's there.

Answer 3

Some of hour knowledge is hidden deeper in our brains than others. That doesn't mean it's not knowledge, as long as it still can be remembered, even with effort. So the name hidden deeply inside someone's brain is still knowledge.

While I have knowledge of many products (I know that 2 by 2 equals 4; I remember it, I don't calculate it), for larger numbers the result is not stored anywhere. It's not knowledge. And you are right, knowing how to produce the answer when you don't remember it isn't knowledge of the answer. Like knowing how to bake a cake, and even knowing it and having all the ingredients, plus time, plus an oven, is not the same as having a cake.

Answer 4

I would have an issue with your claim that "the efforts are comparable", but this has been mentioned by @ChrisW.

Thinking about your question, and in particular statement (1), one is confronted by an interesting aspect of our memory.

Before we can name the person, we must first identify the person in our mind. We may in our mind see and image of the person, hear their voice, and recall other personal details, all as part of readily identifying the person with ease. Yet we may still struggle to remember their name. This seems to imply that we do not store the name of the subject in a manner that connects it readily to the personal details we use to identify the subject in our mind. In other words, we do not necessarily identify the subject with the name. I'm sure this is hardly an original thought, but it is new to me and I have learned something from your question.