How Much is 2+2?
Musings on Math
How much is 2 + 2?
What a fascinating question!
What? You don't think this is fascinating? Sorry. You've been subjected to math education, and had the wonder drained out of you.
If your reaction is "2 + 2 is 4, what a stupid question!" ..... well....
Let's just see.
2+ 2 = 1
2 drops of water plus 2 drops of water = 1 drop of water
2 + 2 < 4
2 cups of water plus 2 cups of salt = much less than 4 cups of salt water
2 cups of water plus 2 cups of alcohol = a little less than 4 cups of 100 proof alcohol
hmmmm
.
2 + 2 = 2
Suppose you divide people into "men" and "women". Two types of people Then
2 types of people + 2 types of people = 2 types of people.
oh dear.
Now suppose I divide people into "men", "women" and children. Add a group of men and women to a group of men and children and ..... 2 + 2 = 3!
Of course, we could divide people into "men", "women", "boys" and "girls" in which case 2 + 2 could be 2 or 3 or 4!
I have a t-shirt that says "2 + 2 = 5, for extremely large values of 2".
Huh?
Well, there's rounding. Take 2.4. That rounds to 2. Add another 2.4. That rounds to 2. Add them. 2.4 + 2.4 = 4.8. Round that. 5. And this is serious! In computers, stuff like this can cause big problems, albeit at small decimal places. For example, in the computer language R I took the square root of each integer from 1 to 100, squared them, and then subtracted from the original number. For instance, I took the square root of 2, squared that, and then subtracted it from 2. Roughly half of the results were NOT 0! OK, they were all very very close..... but .... exact is exact!
What a fascinating question!
What? You don't think this is fascinating? Sorry. You've been subjected to math education, and had the wonder drained out of you.
If your reaction is "2 + 2 is 4, what a stupid question!" ..... well....
Let's just see.
2+ 2 = 1
2 drops of water plus 2 drops of water = 1 drop of water
2 + 2 < 4
2 cups of water plus 2 cups of salt = much less than 4 cups of salt water
2 cups of water plus 2 cups of alcohol = a little less than 4 cups of 100 proof alcohol
hmmmm
.
2 + 2 = 2
Suppose you divide people into "men" and "women". Two types of people Then
2 types of people + 2 types of people = 2 types of people.
oh dear.
Now suppose I divide people into "men", "women" and children. Add a group of men and women to a group of men and children and ..... 2 + 2 = 3!
Of course, we could divide people into "men", "women", "boys" and "girls" in which case 2 + 2 could be 2 or 3 or 4!
I have a t-shirt that says "2 + 2 = 5, for extremely large values of 2".
Huh?
Well, there's rounding. Take 2.4. That rounds to 2. Add another 2.4. That rounds to 2. Add them. 2.4 + 2.4 = 4.8. Round that. 5. And this is serious! In computers, stuff like this can cause big problems, albeit at small decimal places. For example, in the computer language R I took the square root of each integer from 1 to 100, squared them, and then subtracted from the original number. For instance, I took the square root of 2, squared that, and then subtracted it from 2. Roughly half of the results were NOT 0! OK, they were all very very close..... but .... exact is exact!
Published by Peter Flom
I am a statistician, working with a wide variety of clients, mostly researchers in psychology, education, medicine, social sciences and other fields. I also have given talks and written articles on learning... View profile
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13 Comments
Post a CommentGreat article. My head is still spinning...
"For example, in the computer language R I took the square root of each integer from 1 to 100, squared them, and then subtracted from the original number. For instance, I took the square root of 2, squared that, and then subtracted it from 2. Roughly half of the results were NOT 0! OK, they were all very very close..... but .... exact is exact! "
Why Peter that is exactly what I do on my spare evenings! LOL - had to give you SOME grief
Amazing article - I had fun reading it - I hope your kids realize what a geat dad they have to make them look at the world in new ways! Keep up the great work.
Very cool math facts. Well done!
You would make a great teacher! Fun article.
I've encountered 2+2 =1 during a couple relationships;)
LOL. 2 has always equaled one, in my book...lol. :-)
Nice work. I love this kind of stuff.
We often forget that our numbers and just symbolic representations of a concept -- and we get to decide what concept they represent. We all know that 1+1=1 in a good marriage.
well written - thank you