Saturday, January 17, 2009

The Long Division Poem

I would like to introduce the long division poem structure to this blog. The structure has been used for quite a few years primarily by Bob Grumman. It is similar to an orthogonal space poem with the exception that it uses a remainder. Because of its simplicity Betsy Franco and others including teachers have used it to help children play with mathematical ideas in the form of language. I think this is an excellent way to give children a fun way to play with poetic ideas and at the same time introduce them to the idea of applied mathematics. Here is a Christmas poem and one of my favorites by Bob Grumman:


C. Om said...

Hi Kaz,
The picture for this post reminded of a post I did in November. Please check it out and let me know what you think about it.

I appreciate your opinion. Thanks.

Kaz Maslanka said...

Hi C,
Thanks for dropping by. I read your link and found it more in line with the following poem

as opposed to Bob’s poem. Bob’s big ‘O’ is more of a metaphor by mixing the word “cold” and the visual idea of snow however, the snowflakes are little “o’s” that are falling to the ground. I am sure that Bob would have more to say about the big ‘O’ however I doubt that he would say that his poem is dividing by zero. Because the math says we are dividing by children not zero. That is not to say that the poem will not make you think about dividing by zero because it obviously did in your case.

Concerning your blog entry:
The following statements would probably make a math professor get fidgety.
• A positive or negative number when divided by zero is a fraction with the zero as denominator.
• Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator.
• Zero divided by zero is zero.

Technically speaking, dividing by zero is undefined and every math professor I have spoken with tells me to avoid it like the plague. The gray area here is when the topic of mathematical poetry comes up due to math poets liking to break rules it seems like someone is always trying to divide by zero. I personally have started to avoid it, because I believe if mathematical poetry doesn’t follow the rules of mathematics then it CAN NOT be considered mathematical poetry … yet it could be considered visual poetry. So the bottom line is that as far as mathematics is concerned the three statements of yours (above) are not true. There may be some argument that these statements could be true in some sort of philosophical dream world but you don’t seem to be presenting them this way.
Again Thanks for your comment,

C. Om said...

I agree with the answer to anything being divided by zero is an undefined value. Even this, however, supports the point I am making with zero.

An undefined value is not zero, but it is no other number either. An undefined value is like an infinite potential variable just as empty space is. Empty space can be filled with anything possible until it is filled. Then we are forced to "collapse the wave function" of possibilities to one specific value.

In either case (zero or the undefined value) the illustration I am making about zero and the nature of the nothingness that is always there and is a part of everything stands up.

I appreciate you taking a look though Kaz.

Kaz Maslanka said...

My Pleasure.
Thanks for dropping by.

Anonymous said...

I hadn't seen this poem of Bob's. I think it is one of the best he's done in that form -- i can relate all the images in the piece and how they fit the long division structure he has fit them into. It's also very nostalgic, so there's a real emotional, as well as cerebral content in it.

As far as the whole dividing by zero business, i will say that it really depends on what you mean by zero, and that, usually, it's a case where you are taking some sort of limit. lim(x->0) n/x will always blow up, but 0/0 in various forms is undefined: lim(x->0) x^2/x = 0, lim(x->0) x/x^2 blows up, and lim(x->0) kx/x = k. The specifics of the circumstance will tell you what you have when you are have a 0/0 situation, rather than it being some sort of quantum variable or whatever C.Om wants it to be. 0/0 doesn't "collapse" because you've observed it, but rather whatever situation you have that creates the 0/0 also creates the resolution of the conundrum.


word verification = "axidings", "coftyper"

Kaz Maslanka said...

Yes, Endwar that is exactly why I chose this poem of Bob's because it actually makes sense in all areas. (like you said)
Thanks for showing up and give further illumination to the dividing by zero topics. It’s always nice to have a physicist give input on these matters.

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