So-called "short multiplication" is a method, an algorithm, that can be relatively easily used to multiply a multi-digit number by a single-digit number, using pen and paper (or even in your head, with enough practice).
"Long multiplication" is a similar related algorithm that allows relatively easily to multiply two multi-digit numbers (no matter how many digits they may have), using pen and paper. It is, essentially, doing short multiplication of the multiplicand with each digit of the multiplier, and adding up the results.
Long multiplication is a relatively simple and straightforward method, and its genius is that it scales up to large numbers extremely well: No matter how large the numbers to be multiplied are, the task doesn't become significantly more difficult. It will take longer, but it's not more difficult.
If you need to multiply a 2-digit number by another 2-digit number, long multiplication is the easy way. If you need to multiply a 10-digit number by another 10-digit number, long multiplication is your tool of choice. If you need to multiply a 100-digit number by a 85-digit number, long multiplication is the way to do that relatively easily. It might take longer than with smaller numbers, but it isn't inherently more difficult.
It is safe to say that if you need to multiply two numbers using pen and paper, no matter how large the two numbers might be, long multiplication is the way to do it. It's simple, and it easily scales up to numbers no matter their size.
Given how useful, simple and scalable the long multiplication method is, it feels very strange how much hatred it has received especially during the last couple of decades.
In some countries, most prominently the United States, the method is so utterly hated by the schooling system that they have completely stopped teaching it in grade school! I'm not even kidding. It's not even that it's taught as an alternative to other methods: They have stopped teaching it completely (at least in most schools in most states)! Kids don't learn it at all! They grow up without knowing the method even exists.
To this day I have never, ever heard a reason for this, a reason for the hatred and for why it's not taught anymore, not even as an alternative method.
And the thing is, the methods that they are teaching are much, much worse. The multiplication methods that they are teaching are much more convoluted, much more complicated, take a lot longer and, most crucially, scale up extremely poorly to multiplying larger numbers. In fact, most of the methods being taught are reasonably usable only for multiplying 2-digit numbers and that's it. Anything larger than that, and they become unyielding, infeasible, or even don't support it at all.
The funny thing is that the good old short/long multiplication method allows doing 2-digit multiplication faster than those newer methods being taught. Those newer methods are genuinely worse in every single aspect. Yet, in some parts of the world, especially the United States, those worse methods are the only ones being taught to kids. Long multiplication is not mentioned even in passing.
I cannot even begin to comprehend why. Where's this hatred and aversion of the long multiplication method coming from?
And it's not restricted to the education system of some countries. If you search, you can find plenty of eg. YouTube videos that show "cool new efficient methods" for doing multiplication... which only turn out to be needlessly complex and completely non-scalable to larger numbers.
In one particularly egregious video the author commented on such a "cool new multiplication method" video, criticizing it, pointing out how needlessly complicated and non-scalable it was (the shown method required way too many needless steps, and only worked for very small 1-digit or 2-digit numbers), and then the author proceeded to demonstrate a "better" and "easier" way... which wasn't actually long multiplication but some other needlessly complicated way that didn't scale up to larger numbers at all either. He did not even mention long (or short) multiplication in the video at all (not by name or showing how it's done)!
I wrote a comment to that video about it, and the author actually responded to my comment. He was dismissive, defended his "better" method, and did not acknowledge at all the strengths of the long multiplication method. (In a response comment I asked him to demonstrate his "better" method on multiplying two 10-digit numbers, and how it was "better" than long multiplication. He did not respond.)
I cannot understand this irrational hatred of the long multiplication method. It's simple, it's beautiful, it easily scales up to numbers of any size. Where is the hatred coming from, and what causes it?
Comments
Post a Comment