Math problems too big for our brains

Ottawa Citizen via The Windsor Star ^ | November 8 2005

[gondramB]

"
Really? I can prove that 2 + 2 = 11"

Yep, I questioned immediately whether that statement really came from a serious mathmetician. I am but a mere physicist and I know that the answer depends on what base you are using.

[Clock King]

Getting ready for the new P.C. Social Theory: Kids fail at math because humans weren't designed to understand math. It's not their fault if they bring home 'F'.

In other news, 8 Year enters...

[kidd]

My brain hurts!

[headsonpikes]

"Basically, mathematicians are not very good philosophers."

I don't want to start a flame war, but in my academic experience(chiefly in Logic seminars), this was generally true.

Of course, the converse is true, as well.

[MineralMan]

"Then that's redefining what the 11 is."

Nope. It's not. The article said that 2+2=4. It does, in several number bases. It does not equal 4 in base 3. Without defining the number system you are using, such statements are false.

As several people noticed, 2+2=11 ONLY in base 3, but the sum is correct as written. Since the number base was not defined in the first example, I have changed nothing about the definition. I simply used a different base and came up with a different answer.

The article said that 2+2=4 always. That is clearly not true.

Now, I do not know of a practical use for Base 3 math, although they may be one, if there is a physical system somewhere that has three states.

[LexBaird]

Russia touches at least 10 other countries. If you only used four colors, you would have to have the same color touching at least thrice.

Yes, but those 10 (may be more than that now...) don't all touch each other. Thus, Russia is color 1, and all the others touching it are 2, 3, or 4.

[DustyMoment]

Well, now we know where the French surrender to the Muslims has gone - it's in Ottawa surrendering to the EVIL genius of Dr. Computer Math!!!

I'll bet the ancient Greeks, Mayans and Aztecs would argue the premise that human brains can't handle math.

I'll also bet that medical science will dispute the argument that our brains have shrunk and can't handle today's math problems.

Finally, I'll bet that this idiot has become lazy and has grown too reliant on his computer and calculator to perform the tasks that manually solving math problems used to require.

[1L]

You didn't read it clearly: all that's required is that Russia be a different color than any color touching it, not that all countries touching it be a different color, unless they themselves touch. So, Mongolia and Finland can be the same color.

[DarkSavant]

Math has been the only sure form of knowledge since the ancient Greeks, 2,500 years ago.

Incorrect, it's not a sure form of knowledge because we can't even prove numbers have any external existence.

[megatherium]

A few still do it the old-fashioned way, he says: "By individuals sitting in their rooms for long periods, thinking.

A few? Most mathematics papers are still single-author. 75% or 80% if memory serves. A lot of highly significant results in mathematics are still created by lone wolf thinkers.

[ko_kyi]

There are 10 kinds of people in the world. Those that can count in binary and those that can't.

[Sofa King]

"Without defining the number system you are using, such statements are false."

If you don't define your number system, then you're talking about base 10. That 10 means 1x10^1 + 0x10^0 is defined in our language, and if you don't specifically state that you're redefining it to mean 1x3^1 + 1x3^0, then 2 + 2 = 11 is wrong. Math books, calculators, and most programming languages work that way.

[ILikeFriedman]

Assume a=b=1
then
(a+1)=(b+1), (a-1)=(b-1), and (a*a)-1=(b*b)-1
and ......

(a*a)-(b*b)=(a-b)
use this last equation and apply the difference of 2 squares
(a+b)*(a-b)=(a-b)
divide both sides of the equation by (a-b)
(a+b)=(a-b)/(a-b)=1
since a=b=1, and substituting for a and b
1+1=1 or
2=1

[MineralMan]

"If you don't define your number system, then you're talking about base 10. "

Not so. That is your assumption, and it is not accurate. If I am reading a book on programming, there will be a different assumption, depending on the type of computer being programmed.

The moment I write 2+2=11, everyone should know I'm in Base 3. If I write 2+2=10, then I'm in Base 4. In all bases from 5 up, 2+2=4.

[SlowBoat407]

iThink, therefore, iAm.

[Darksheare]

I thought it is always my fault, except when it isn't.
;-)

[mollynme]

Human computer ping ;o)

[SlowBoat407]

Base 8 is like base 10, really... if you're missing two fingers.
- Tom Lehrer

[Senator Bedfellow]

I can prove that 2 + 2 = 11

Ha. I can show that 5 + 4 = 4.

[aruanan]

"We are beginning to see the limits of our ability to understand things."

Welcome to the rest of life, baby!