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Math problems too big for our brains
Ottawa Citizen via The Windsor Star ^ | November 8 2005

Posted on 11/08/2005 8:48:52 AM PST by RightWingAtheist

Our brains have become too small to understand math, says a rebel mathematician from Britain. Or rather, math problems have grown too big to fit inside our heads. And that means mathematicians are finally losing the power to prove things with absolute certainty.

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

You can't prove the sun will rise tomorrow, but you can prove two plus two equals four, always and everywhere.

But suddenly, Brian Davies of King's College London is shaking the foundations of certainty.

He says our brains can't grasp today's complex, computer-generated math proofs.

"We are beginning to see the limits of our ability to understand things. We are animals, and our brains have a certain amount of capacity to understand things, and there are parts of mathematics where we are beginning to reach our limit.

"It is almost an inevitable consequence of the way mathematics has been done in the last century," he said in an interview.

Mathematicians work in huge groups, and with big computers.

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

"But there are other areas where the complexity of the problems is forcing people to work in groups or to use computers to solve large bits of work, ending up with the computer saying: 'Look, if you formulated the problem correctly, I've gone through all the 15 million cases and they all are OK, so your theorem's true'."

But the human brain can't grasp all this. And for Davies, knowing that a computer checked something isn't what matters most. It's understanding why the thing works that matters.

"What mathematicians are trying to get is insight and understanding. If God were to say, 'Look, here's your list of conjectures. This one's true, then false, false, true, true,' mathematicians would say: 'Look, I don't care what the answers are. I want to know why (and) understand it.' And a computer doesn't understand it.

"This idea that we can understand anything we believe is gradually disappearing over the horizon."

One example is the Four Colour Theorem.

Imagine a mapmaker wants to produce a colour map, where each country will be a different colour from any country touching it. In other words, France and Germany can't both be blue. That would be confusing.

So, what's the smallest number of colours that will work?

A kid can work out you need four colours. But can you prove it? Can anyone be certain, as with two-plus-two?

The answer turns out to be a hesitant Yes, but the proof depends on having a computer to work through page after page of stuff so complex that no single person can take it all in.

And it's getting worse, Davies writes in an article called "Whither Mathematics?" in today's edition of Notices of the American Mathematical Society, a math journal.

Math has tried to write a grand scheme for classifying "finite simple groups," a range of mathematical objects as basic to this discipline as the table of the elements is to chemistry -- but much bigger.

The full body of work runs to some 10,000 difficult pages. No human can ever understand all of it, either.

A year ago, Britain's Royal Society held a special symposium to tackle this question of certainty.

But many in the math community still shrug off the issue, Davies says. "Basically, mathematicians are not very good philosophers."


TOPICS: Miscellaneous; Philosophy
KEYWORDS: computers; epistemology; fuzzymath; mathamphetamine; mathematics; philosophy; science; thenewnewmath
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1 posted on 11/08/2005 8:48:52 AM PST by RightWingAtheist
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To: Fierce Allegiance

See, it wasn't my fault.


2 posted on 11/08/2005 8:50:30 AM PST by Jersey Republican Biker Chick (People too weak to follow their own dreams, will always find a way to discourage yours.)
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To: RightWingAtheist

This is a conspiratorial news release by the big computer companies to promote their new products. Pencil pusher mathmeticians, UNITE!!!


3 posted on 11/08/2005 8:50:50 AM PST by Tulsa Ramjet ("So far, so good. But this is only phase 1."--Captain America)
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To: RightWingAtheist

Too small to understand self responsibility, now math.


4 posted on 11/08/2005 8:52:32 AM PST by right right
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To: RightWingAtheist

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'.


5 posted on 11/08/2005 8:52:41 AM PST by theDentist (The Dems have put all their eggs in one basket-case: Howard "Belltower" Dean.)
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To: RightWingAtheist

Everything that can be invented has already been invented. Didn't someone say that over 100 years ago?


6 posted on 11/08/2005 8:55:41 AM PST by Moonman62 (Federal creed: If it moves tax it. If it keeps moving regulate it. If it stops moving subsidize it)
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To: RightWingAtheist

Nothing new here. I told my mother this as I handed her my report card in 1958.


7 posted on 11/08/2005 8:55:50 AM PST by Eagles Talon IV (Still waiting for the)
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To: RightWingAtheist

So easy a three year old can do it! Somebody run out and get me a three year old.


8 posted on 11/08/2005 8:56:11 AM PST by ghitma (Lifter)
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To: RightWingAtheist

Math not so hard, dumb dumb!

9 posted on 11/08/2005 8:57:33 AM PST by martin_fierro (< |:)~)
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To: Jersey Republican Biker Chick

I agree it's not your fault, but Bush?


10 posted on 11/08/2005 8:57:43 AM PST by Malesherbes
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To: RightWingAtheist

This is too funny. I'm a math teacher on a professional development day. I just took a break. and this is the top story!


11 posted on 11/08/2005 8:58:37 AM PST by Tanniker Smith (By defiintion, we cannot have Consensus until you agree with me.)
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To: RightWingAtheist

This is too funny. I'm a math teacher on a professional development day. I just took a break. and this is the top story!


12 posted on 11/08/2005 8:58:39 AM PST by Tanniker Smith (By defiintion, we cannot have Consensus until you agree with me.)
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To: Jersey Republican Biker Chick; Darksheare
See, it wasn't my fault.

Nope. It's Darks' fault...

13 posted on 11/08/2005 9:00:01 AM PST by null and void (People who say it cannot be done should not interrupt those who are doing it.)
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To: RightWingAtheist

What mathematicians are trying to get is insight and understanding. If God were to say, 'Look, here's your list of conjectures. This one's true, then false, false, true, true,' mathematicians would say: 'Look, I don't care what the answers are. I want to know why (and) understand it.' And a computer doesn't understand it.

Ummm, build better computers?

14 posted on 11/08/2005 9:00:21 AM PST by GOPJ (The French should ask immigrants "Do you want to be Frenchmen?"- Not "Will you work cheap?")
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To: RightWingAtheist

"You can't prove the sun will rise tomorrow, but you can prove two plus two equals four, always and everywhere. "




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


15 posted on 11/08/2005 9:00:33 AM PST by MineralMan (godless atheist)
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To: RightWingAtheist
cute little casher: that'll be $1.63
Doogle: (gives cute little casher two one dollar bills)
cute little casher: can you hold a sec? I don't have any quarters.
Doogle: ah yeah
cute little casher: (after banging roll of quarters on cash register draw and spraying draw with quarters) I'm sorry, here you go, (she handed me three dimes,a nickle,and two pennies)
Doogle: thanks


Doogle
16 posted on 11/08/2005 9:01:19 AM PST by Doogle (USAF...7thAF ..4077th TFW...408th MMS..Ubon Thailand.."69",,Night Line Delivery..AMMO)
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To: Malesherbes

I knew it all along.


17 posted on 11/08/2005 9:01:45 AM PST by Jersey Republican Biker Chick (People too weak to follow their own dreams, will always find a way to discourage yours.)
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To: MineralMan

Depending on what you pay me...I can make any amount add up to what you want.


18 posted on 11/08/2005 9:02:22 AM PST by wallcrawlr (http://www.bionicear.com)
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To: null and void; Darksheare
OK, Its Darks fault I was so wrong on the geometry question last Friday.
19 posted on 11/08/2005 9:02:47 AM PST by Jersey Republican Biker Chick (People too weak to follow their own dreams, will always find a way to discourage yours.)
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To: RightWingAtheist
Math has been the only sure form of knowledge since the ancient Greeks, 2,500 years ago.

Um, I beg to differ. My spouse and I know a different kind of knowledge. And it's not Greek.

20 posted on 11/08/2005 9:03:03 AM PST by LurkedLongEnough
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To: RightWingAtheist
Well then... let us bring forth the microchips and let the Borg(unization) of humanity begin. I'm just a little afraid that it will actually happen in some socialist parts of the world. Cloning and Cyborgs, ah the 21st century will be interesting indeed.
21 posted on 11/08/2005 9:03:29 AM PST by Camel Joe (Proud Uncle of a Fine Young Marine)
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To: RightWingAtheist

I wanted to impress my grandpa with my math skills so I told him the formula Pi-r-square.

He laughed at me and said "No, boy. Pie are round. Cornbread are square!"


22 posted on 11/08/2005 9:05:59 AM PST by CommandoFrank (Peer into the depths of hell and there you will find the face of Islam...)
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To: MineralMan

2+2 = 11? only if you redefine = or + or 2 or is...


23 posted on 11/08/2005 9:06:32 AM PST by slobie
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To: slobie

"2+2 = 11? only if you redefine = or + or 2 or is..."

Nope. Base 3.


24 posted on 11/08/2005 9:07:30 AM PST by MineralMan (godless atheist)
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To: LurkedLongEnough
This Kind ?


25 posted on 11/08/2005 9:08:30 AM PST by al baby (Father of the beeber)
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To: RightWingAtheist

How can the article say "Four Colors"?

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.

I suppose if you just limited the scope to "map of Europe", but even then, you'd have to leave out the Balkans to use just four colors.

If a computer can "prove" that only four colors are needed, then the computer is clearly in error.


26 posted on 11/08/2005 9:09:54 AM PST by Vicomte13 (Et alors?)
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To: slobie

redefine is ? The stainmaker tried to do that


27 posted on 11/08/2005 9:09:55 AM PST by al baby (Father of the beeber)
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To: slobie

Try it in a "Base-3" number system.


28 posted on 11/08/2005 9:10:18 AM PST by DuncanWaring (The Lord uses the good ones; the bad ones use the Lord.)
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To: MineralMan
Really? I can prove that 2 + 2 = 11.

Yes, in Base 3.

29 posted on 11/08/2005 9:11:07 AM PST by andy58-in-nh
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This writer and perhaps his subject need a course in logic. Deductive reasoning can prove truth statements - not only mathematics.

And much of what the articles gives as examples are inferences, inductive reasoning which are not considered proof.

His point about computers is ok, but the rest of this article..


30 posted on 11/08/2005 9:12:06 AM PST by D-fendr
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To: CommandoFrank
Pie are round. Cornbread are square!

That was my science teacher's favorite bad joke. Wonder if we're talking about the same guy....

31 posted on 11/08/2005 9:12:13 AM PST by r9etb
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To: andy58-in-nh

Yup. That always gets 'em. It also makes the statement in the article false.

And for those who think there's no point in using math in anything other than base 10, I give you the computer you're typing on right now.


32 posted on 11/08/2005 9:13:04 AM PST by MineralMan (godless atheist)
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To: MineralMan
Never forget:

There are 10 types of people: Those who understand binary math, and those who don't.

33 posted on 11/08/2005 9:13:12 AM PST by smokinleroy
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To: smokinleroy

Very good.


34 posted on 11/08/2005 9:14:02 AM PST by MineralMan (godless atheist)
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To: MineralMan

Then that's redefining what the 11 is.


35 posted on 11/08/2005 9:15:01 AM PST by Sofa King (A wise man uses compromise as an alternative to defeat. A fool uses it as an alternative to victory.)
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To: r9etb
That was my science teacher's favorite bad joke. Wonder if we're talking about the same guy....

I think we're giving away our age...

36 posted on 11/08/2005 9:15:07 AM PST by CommandoFrank (Peer into the depths of hell and there you will find the face of Islam...)
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To: MineralMan
And for those who think there's no point in using math in anything other than base 10, I give you the computer you're typing on right now.

Binary dittoes!

37 posted on 11/08/2005 9:15:12 AM PST by andy58-in-nh
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To: MineralMan

Remember when big fat Rosie O'Doughnut said that nobody needs to learn math any more - we have computers. What a retard.


38 posted on 11/08/2005 9:15:26 AM PST by smokinleroy
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To: RightWingAtheist

The computer has to be programmed, does it not?


39 posted on 11/08/2005 9:17:24 AM PST by 1L
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To: Vicomte13

Think again.

You could use the same color for Finland, Poland and China, as they don't border each other.


40 posted on 11/08/2005 9:18:18 AM PST by Our man in washington
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To: MineralMan

"
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.


41 posted on 11/08/2005 9:18:25 AM PST by gondramB
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To: theDentist
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...

42 posted on 11/08/2005 9:18:30 AM PST by Clock King ("How will it end?" - Emperor; "In Fire." - Kosh)
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To: RightWingAtheist

My brain hurts!

43 posted on 11/08/2005 9:18:35 AM PST by kidd
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To: RightWingAtheist
"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.

44 posted on 11/08/2005 9:19:07 AM PST by headsonpikes (The Liberal Party of Canada are not b*stards - b*stards have mothers!)
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To: Sofa King

"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.


45 posted on 11/08/2005 9:19:09 AM PST by MineralMan (godless atheist)
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To: Vicomte13
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.

46 posted on 11/08/2005 9:19:18 AM PST by LexBaird (tyrannosaurus Lex, unapologetic carnivore)
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To: RightWingAtheist

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.


47 posted on 11/08/2005 9:20:20 AM PST by DustyMoment (FloriDUH - proud inventors of pregnant/hanging chads and judicide!!)
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To: Vicomte13

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.


48 posted on 11/08/2005 9:22:27 AM PST by 1L
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To: RightWingAtheist
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.
49 posted on 11/08/2005 9:22:44 AM PST by DarkSavant (I touch myself at thoughts of flames)
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To: RightWingAtheist
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.

50 posted on 11/08/2005 9:28:11 AM PST by megatherium (Hecho in China)
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