Subjective Intent in Mathematics.
January 5th, 2013
Whether 6 ÷ 2(1 + 2) = 1 or 6 ÷ 2(1 + 2) = 9 depends on who
is asking and why. Ultimately, the
answer depends on the subjective intent of the person who wrote the
equation. Subjective intent in
mathematics is something we obviously don’t hear very often, especially when
speaking of mathematical equations and mathematical operators.
For the various arguments involved as to whether the answer
is nine (9) or one (1), the best place to look is Ask a Mathematician / Ask a
Physicist at http://www.askamathematician.com/2011/04/q-how-do-you-calculate-6212-or-48293-whats-the-deal-with-this-orders-of-operation-business/. Also,
Wikipedia has a good synopsis on the order of operations in mathematics which
seems to be correct, located at http://en.wikipedia.org/wiki/Order_of_operations. By any reader of this blog entry reviewing the
arguments at those other sites listed above saves me the trouble of having to
repeat it all here, by the way. :) Nevertheless, as we can see, this matter
appears as a heated debate among the internet mathematicians.
A. The ultimate
answer depends on who is asking, why they are asking, and who or what is
performing the mathematical operations.
Starting in reverse order:
1. The answer is
dependant on who or what is performing the mathematical operations represented
by the equation. As in the real world we
mostly have been taught to clear the parentheses first and then proceed on from
there - additionally, it is likely that a second set of parentheses is implied surrounding the two (2) multiplying the quantity of one plus two, ie: 6 ÷ (2 (1+2)). This would yield an answer of one
(1). But a computer program would likely
proceed from left to right and would divide six (6) by two (2) and then
multiply by three (3, or 2 + 1 as given in the equation) which would then yield
an answer of nine (9). :) But
then again, a computer program would likely need a mathematical operator to be
inserted between the two (2) and the parenthetical sum of two plus one (2 + 1). Also, the operation represented by the
division sign would likely be an issue for a computer program as well - as most programming languages use a slash for the division operator.
2. Then we have to
look at why someone is asking this question regarding the numerical answer of this
poorly written equation and in light of the confusing notation of this equation as well. Are they asking because they have a genuine
need to decipher the poorly constructed equation or are they asking because
it’s a trick? Most likely they are
asking because it is all a trick and therefore the answer they are seeking would
probably be nine (9). Because as I said
above, the typical answer in the real world to humans would probably be one
(1). So if one were being asked by a
jokester or trickster, the trickster would likely be looking for the answer of
nine (9).
3. Ultimately, the
answer is dependent on who is asking or who wrote this equation because it all
depends on the subjective intent of the individual who wrote or transcribed the
equation. What did they intend to be the
order of the operations when they wrote the equation? As I mentioned above, in the human world,
such notation probably intends an answer of one (1).
But this all begs the question that in math, there can only
be one right answer. Right? If math is done properly, shouldn’t we all
get the same answer? Well, maybe, but
maybe not – as displayed by this equation in this matter/blog.
So, in this blogger’s mathematical world, the answer could
be one (1) or nine (9). But most likely
to us humans the answer would normally be one (1). That is to say, if a human wrote this poorly
clarified equation, he/she probably was looking for an answer of one (1),
unless they are a trickster as explained in paragraph A.2. above. But if a computer displayed this equation,
regardless of the syntax errors for the typical computer program, the answer
could be nine (9) as contrasted in paragraph A.1. above.
The answer is particularly and ultimately dependent on the
subjective intent of the creator of the equation, as discussed in paragraph
A.3. above. So, to make an analogy for
those who were told there was no math involved in blog reading, it’s sort of
like the use of certain punctuation (and wording) in grammar. With such an analogy being, when is it proper
to use a comma, when is it not, and when is it up to the discretion of the
writer as to use of the comma (or colon, or question mark).
Therefore and as such, the answer is: It depends.
Start at the top of this blog and reiterate through the paragraphs
herein again, if this answer bothers you.
If so, it will probably only bother you more as you repeat any iterations of this blog. :)
AVT
6 ÷ 2(1 + 2)
6 / 2(1 + 2)
6 ÷ 2(1 + 2)
6 / 2(1 + 2)
