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I just watched this video on Ted.com entitled:

Joshua Foer: Feats of memory anyone can do

and it got me thinking about memory from a programmers perspective, and since programming and mathematics are so similar I figured I post here as well. There are so many abstract concepts and syntactic nuances that are constantly encountered, and yet we still manage to retain that information.

The memory palace may help in remembering someone's name, a sequence of numbers, or a random story, but are there any memorization techniques that can better aid those learning new math concepts?

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    Are you asking how to be able to recall theorems/axioms etc... faster? That's a different question.2012-10-13
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    I once heard an interview with a memorization champion on NPR. He was asked if his techniques for memorizing long lists of random numbers and names and such could help doctors, scientists, etc. His answer was simply "No". Memory tricks are just that...tricks. He went on to say that doctors and other experts can remember vast quantities of information because they understand the connections between facts and concepts. He went on to say that there really is no short-cut to true understanding. I agree.2012-10-13
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    Another example: I was discussing a topic with my PhD adviser and he recalled that there was a great paper by so-and-so which addressed the issue at hand. He went after a moments thought to recall the date of the paper (15+ years old) and picked it mysteriously out of a stack of stuff in his office. At the time I thought that he must have a most singularly amazing memory. Now years later as I study and read more and more, I find myself able to do the same (and trust me, my memory leaves much to be desired). Expertise and time builds these things.2012-10-13
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    One more thing...now that I think of it, the NPR interview was with Joshua Foer. I guess my memory is better than I thought. :)2012-10-13
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    It might come as more helpful if you mentioned specific concepts you feel important for you or others to learn.2012-10-13
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    @Doug, I would have to say it's just general logic for me. I did great in all of my math classes up to precalc, but once I got into discrete math I just couldn't follow the material. It barely made sense to me and I believe it may have had something to do with my lack of remembering the truth tables and various operators.2012-10-13
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    @Ein: can you be more specific? What kind of problems or concepts did you have trouble with?2012-10-13
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    @BillCook: Do you know (or remember) where this interview can be found?2012-10-13
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    It does help to know the names of the students. I used to draw up a diagram of their usual seats, and call on different students just to have occasion to associate their names with their faces. I did eventually learn their names. I'm not so sure what they learned.2012-10-13
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    @Will, Your students keep their sitting positions across classes? I am jealous! Jealous!2012-10-13
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    @MarianoSuárez-Alvarez, after a week or two they mostly did. Those that continued attending, that is.2012-10-13
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    Ah, I see. You managed to get rid of all except *one*! :-)2012-10-13

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You shouldn't try to learn mathematics through memorization at all. It will get you nowhere: anything that can be memorized can be looked up these days. What you should try to learn is the underlying concepts and the way they relate to each other. If you understand those well enough, you won't need to memorize anything.

Think of learning mathematics as being like learning, say, chess. Would you learn how to play chess by memorizing openings? Well, maybe that could work, but it's probably a better idea to learn how to play chess by, y'know, playing a lot of chess.

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    This doesn't the answer the question. It questions the validity of the question and basically moralizes towards the person who asked the question. Also, people DO learn how to play chess *better* in part by memorizing openings. So, by analogy the question has validity.2012-10-13
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    @Doug: I think that questioning the validity of a question is a valid answer to a question. If someone asks you "have you stopped beating your wife?" then I would prefer that "that question is predicated on a false assumption" be a valid answer.2012-10-13
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    You told me about what you *prefer* NOT what actually consists of a valid answer to such a question. Thus, you don't have an actual answer. Also, it does sometimes come as possible to answer a question while also questioning it's validity, "no, I haven't stopped beating my wife, because I never started beating my wife."2012-10-13
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    @Doug: then you should feel free to interpret my answer as "whether there are any such techniques or not is irrelevant because I don't think you should use them."2012-10-13
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    Such an interpretation consists of a judgement with respect to the appropriateness of the question. An answer to a question has (potentially or actual) factual content which responds to the content of the question. And this question is *not* implying anything by a rhetorical means like "have you stopped beating your wife?".2012-10-13
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    You can’t understand a poem fully until you have it in your memory. Consider the case of a first-year student trying to understand the definition of continuity. She can look it up again and again, but it will still be mysterious and unreproducible until she comes to understanding. If one memorizes the definition, even before understanding, one may turn it over and over in the mind until it becomes internalized. The ultimate aim is for the understanding to be deep enough that memory is no longer required.2012-10-13
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    @Lubin: I think it would be a better idea to do problems, with the definition handy for reference somewhere, until the student gains some experience and sees how the definition is used. It would be even better if the textbook the student is working off of says something about why the definition of continuity is a reasonable definition. Memorization should not be necessary for this process (and might actually hurt it; if you successfully memorize the definition you might fool yourself into thinking that you have thereby understood it). The definition should sink in naturally with experience.2012-10-13
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    @Lubin: I also don't think the analogy to poetry holds water. Understanding a poem and understanding a mathematical concept strike me as very different types of experiences although I can't really verbalize what I mean by that.2012-10-13
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    @QiaochuYuan, from my personal experience I was able to pick up math quickly simply because I memorized the multiplication table when I was a child. Now, something like that is almost expected but isn't much of the rest of math the same thing. Simply memorizing the properties of exponents or real numbers can have a similar benefit to that of remembering the multiplication table.2012-10-13
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    @Ein: I disagree. Understanding is longer-lasting and more beneficial than memorization. You don't need to memorize the properties of exponents if you understand them. (The multiplication table is different: it's too dependent on a particular representation of numbers to count as a concept.)2012-10-13
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    @QiaochuYuan, in an ideal world that may be true, however, almost all of the math books and training material out there takes a very left-brain approach and doesn't demonstrate how such rules are reached, most books only state the rule and assume that that is enough.2012-10-13
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    @Ein: yes, I agree, and this is a terrible state of affairs. That's what math.stackexchange is for!2012-10-13
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    [Related](http://math.stackexchange.com/questions/85681/is-memorization-a-good-skill-to-learn-or-master-mathematics)2012-10-13
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    @DougSpoonwood This is clearly the right answer to give in this situation. It is not "moralizing" to offer the best answer you have, even if it doesn't address the original question directly. Often students get on the wrong track and are asking the wrong questions and don't know it, and it's an educator's responsibility to prod them back towards reason. The chess analogy also is solid: improvement only happens after memorized lines are understood (just as in math.) A player with the world's best memory will be crushed by any average player that takes them out-of-book.2012-10-14
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    @rschiweb If it were clearly the right answer to give here, then *everyone* who can accurately read what Qiaochu wrote would agree on such as clearly the right answer. Again, Qiaochu Yuan did not give an answer. And I disagree that the person who asked the question strayed away from reason.2012-10-14
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    @QiaochuYuan: How a learner can be sure that he is truly understanding concepts instead of rote chugging it ? [ One test can be to derive the idea in entirely original self derived unique way, but except that]2016-04-10
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For math there is no better way to remember than to just understand. Though the time required to reach that point may be too difficult to forget.

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    This doesn't answer the question and basically just consists of criticism of the question similar to Qiaochu Yuan's "answer".2012-10-13
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    True, I just couldn't resist the quip, memorization techniques really are not the best help in mathematics...2012-10-13
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If you say that the techniques that exist to help memory are amazing, I would not disagree. Visualization, they say, is the best way to memorize. I have not seen or heard of the "memory palace" other than what you wrote here and maybe in passing on an infomercial one time or another (am I correct in understanding it as a visualization technique?) I can say that I believe in the power of any visualization that helps in understanding or even just remembering mathematical concepts. The difficulty is in finding the personal imagery that works. Only after much meditation have I ever found such imagery that works for me on any particular problem I am considering, but it would not be something I could translate in order to benefit the random person.

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    It is a visual technique, however, from what the speaker describes it's about creating the craziest association you mind gravitates to on a subject. For example, don't remember the name "Ed," instead think about the talking horse Mr. Ed after you enter your bedroom in your mind. Anyways, I think you might be on to something. I do remember that my computer networking class was easier when I visualized packets of information moving about. I'm curious, when you think about math concepts is any movement (animation) involved, or are they static visualizations?Could you please describe, if possible?2012-10-13
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    As I said, description might be difficult. And especially considering we live in a 3-D world, where math is of many dimensions. One simple visualization could be that of shadows (good one for Halloween maybe) when considering projections in vector spaces. But to your movement question, yes my visualizations are usually very animated in one way or another. Paths taken through a tree structure, rotations about an axis, and shifts and scalings of topological shapes are a few easy examples.2012-10-13
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For propositional logic operations, you can remember their truth tables as follows:

Let 0 stand for falsity and 1 for truth. For the conjunction operation use the mnemonic of the minimum of two numbers. For the disjunction operation, use the mnemonic of the maximum of two numbers. For the truth table for the material conditional (x->y), you can use max(1-x, y). For negation you can use 1-x.

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    What never made sense to me is logical implication. If p implies q, then how can p(False) and q(True) mean that p->q is True. If p has an affect on q then q being true shouldn't matter since p determines q. Also p(False) and q(False) means p->q is True. Is just doesn't make any sense.2012-10-13
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    @Ein: in mathematical logic, "$p$ implies $q$" doesn't mean "$p$ has an effect on $q$." (Ordinary propositional logic doesn't talk about effects at all.) It means nothing more and nothing less than "if $p$ is true, then $q$ is also true" (so the only way it can be false is if $p$ is true but $q$ is false). The notion you're looking for is called strict implication (http://en.wikipedia.org/wiki/Strict_conditional).2012-10-13
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    Wow, if the book or teacher had put it that way then I may have not done so badly. Thanks @Doug2012-10-13
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While some of the comments above have some validity, I can see you just needing to memorize some quick formulas. I do agree practice makes perfect. But what many of the memorizers AND Joshua Foer said is yes, they are tricks but they FORCE you to memorize things. And Foer goes on to say that they aren't even really tricks. They are actually harder to do that just doing it, because you're kind of setting up a safety net in your mind, and it often involved preparatory work.

Anthony Metivier is another memory "guru" who.. I guess.. throws out all forms of memorization stuff EXCEPT the "memory palace" (google it if need be). Though, while he focuses only on memory palaces, other systems like the Major Memory System, (where you associate the phonetic alphabet with numbers) make guest appearances.

http://www.magneticmemorymethod.com/mmmpodcast-episode-003-memorizing-mathematical-formulas/

https://litemind.com/major-system/

^^^^^More info here^^^^^ Major Memory Sytem

So, in Metivier's mind, if you have this..

Major Memory Sytem

notice vowels and w, h, y are ignored ..you can associate formulas with words like:

C2 = CaN (You keep the c, ignore the a, use the n)

'=' becomes an image of something meaningful to you, he chooses to use a FLAG

A2 = yawN (again, since you're ignoring the letters y, a, w, you can place them anywhere to make words)

'+' = this becomes another image of your choice- try using a cross, or hospital symbol

B2 = Maybe this is BuN, BaNe, etc.

Now, he went a slightly different (I believe more complicated) route. I simplified this for you if you're new.

You now have images. You throw them into a story. And he would say "USE A MEMORY PALACE TOO!"

The idea would be you would walk through.. say.. your house and in your mind, you're placing these items in your house, in order.

Anyone into memory techniques will say to use your own images, your own words, your own palaces. Do not expect to find any Website on memory palaces and have things mapped out for you. Things like the Major System and Peg System will suggest things for you but if they aren't "sticky" TOSS THEM OUT.

Read more on building memory palaces and rules for doing so.

Other sources:

The Bible of Memory folks- Google "The Memory Book" by Harry Lorayne

This one focuses on academics- Super Memory Super Student by Harry Lorayne