The basic rules of arithmetic may be broken

[pokerfan]

Something doesn't add up
(Image: Steve Allen/Brand X Pictures/Getty)

16 August 2010 by Richard Elwes

Mathematicians are facing a stark choice – embrace monstrous infinite entities or admit the basic rules of arithmetic are broken

IF YOU were forced to learn long division at school, you might have had cause to curse whoever invented arithmetic. A wearisome whirl of divisors and dividends, of bringing the next digit down and multiplying by the number you first thought of, it almost always went wrong somewhere. And all the while you were plagued by that subversive thought- provided you were at school when such things existed- that any sensible person would just use a calculator.

Well, here's an even more subversive thought: are the rules of arithmetic, the basic logical premises underlying things like long division, unsound? Implausible, you might think. After all, human error aside, our number system delivers pretty reliable results. Yet the closer mathematicians peer beneath the hood of arithmetic, the more they are becoming convinced that something about numbers doesn't quite add up. The motor might be still running, but some essential parts seem to be missing- and we're not sure where to find the spares.

http://www.newscientist.com/article/mg20727731.300-to-infinity-and-beyond-the-struggle-to-save-arithmetic.html

[mysuzuki2]

1. You mean 2 plus 2 really could be 5?

wait until I tell my ex-wife!

[pokerfan]

3. Yes...

For large values of 2...

[Warpy]

2. I always found the world of basic numbers very comforting

because there were usually a limited number of right answers, even in slightly higher math like calculus.

Once we leave the Newtonian, "stack these rocks on top of each other" practical sort of world and get into theoretical areas, things start to get very messy, which is why I probably failed to pursue that line of study.

This article doesn't surprise me in the least.

[mike r]

4. They ought to stick to the empirical evidence

Infinities are invaluable as a calculational device, but once people start speculating on the exact properties of infinities, well, there is just no empirical evidence as to what they are...

Best quote: "Infinite sets are a paradise of fools. Infinite mathematics is meaningless because it is abstract nonsense."

[laconicsax]

5. After reading the article, I'm a bit disappointed.

I may have misunderstood, but it seems to simply say that the axioms of arithmetic cease to make sense when dealing with the concept of infinity. That either the concepts of infinity lead to counterintuitive conclusions, or the laws describing arithmetic simply need revision to adequately explain infinity.

Sounds like the problem of reconciling the vast with the small in physics.

[dimbear]

8. The number of folk who can both understand and write science is small.

Thankfully they are well remembered and honored when they do, rarely, appear.

IMHO, capable science writers are becoming even more rare as time goes by. As laconicsax points out to us, the cited author is not one of them.

We won't be seeing the discovery of any new integers between 6 and 7. Let peace reign over that family.

[Joe Chi Minh]

12. Do you really think infinity can be explained? The fact that the concept seems to

have had practical uses in mathematical calculations seems astonishing.

Is it not this development, rather, one of the more predicable instances of the deeper that scientific truths are penetrated, the more that paradoxes proliferate.

'Naive realists' who have a comically-exaggerated notion of the potential of science for explaining everything, seem unable to grasp the 'a priori' obstacle to human understanding, constituted by paradoxes.

One example relates to the Big Bang. It is a logical impossibility for us to conceive of the Big Bang event occurring outside of time, i.e prior to its creation. What was the medium in which the Big Bang occurred, if not time (or space-time)?

[laconicsax]

13. Did I ever say I did?

As for the big bang, it didn't occur prior to or outside of time, it was the beginning of time.

[Joe Chi Minh]

17. I'm not aware that I was having a shot at you. However, as regards

your explanation of the Big Bang as the beginning of time, you are totally missing the point: physical events in all of our experience, begin at a particular point in time.

What is the non-temporal nature/dimension, in which the Big Bang occurred? Since we can't ask what preceded the Big Bang, can we speak of a context in which time began? Obviously not. It certainly couldn't have been metaphorical, could it. It's physics we're talking about. Or is it? Maybe everything is a hologram, as some leading-edge, theoretical physicist posited the other day, and was referred to on this thread. God thinking his creation, as I believe Aldous Huxley put it. Maybe the hadron collider will throw some light on the question, if only revealng that there is no fundamental particle.

It's certainly what Christians and other religious believers would categorise as a mystery, isn't it, like much of quantum physics, paradoxical and thus intrinsically incomprehensible to human reason?

[laconicsax]

18. The subject line of your post was a direct question to that effect.

If you want to deny it, be my guest.

[Name removed]

20. Deleted message

Message removed by moderator. Click here to review the message board rules.

[laconicsax]

21. "Do you really think infinity can be explained?"

Looks like a question to me. The curvy line and dot immediately following "explained" is known as a "question mark" and is used to denote a question. The words "do you think..." is also a classic way to start a question. As you posed the question in response to a comment I made, the implication is that the question was directed toward me.

Here's an article about punctuation you may find helpful: http://en.wikipedia.org/wiki/Punctuation

What's more, this is a thread about mathematics in a science forum. If you want to discuss teleological arguments, may I suggest the Religion/Theology forum? You may find it a more appropriate forum to make to your arguments which beg the question.

[bananas]

19. No, it's much more interesting than that.

[Possumpoint]

6. I Am Very Happy With Basic Math

working in my life. I've seen upper math used to prove that the opposite side of the moon doesn't exist. Yet we've seen pictures of it. Did they lie?

[EmilyKent]

7. I could have told them that

by grade 3!

:rofl:

[supernova]

9. My Mother the Math Teacher

For many years, she taught 9th Grade Algebra in our school district. She was very much a "numbers" person. That's the way she understood the world and in another life would probably have gotten the Engineering degree denied her during the 1940s for the sexism then.

I, OTOH, am a language person. I love words and pay attention to how people use them.

We used to have great debates about "language" people vs "math" people.

My teenaged self would say, "but math doesn't make any sense to me! Words, at least I can figure out with the speaker/writer probably really meant to convey."

"All you have to remember," she would say is that "math works because we say it does."

IOW, the "rules" of mathematics are arbitrary and can be changed at any time.

:crazy:

[freebrew]

10. Ummm.....NO.

[supernova]

11. Did you even read

the article in the OP?

It doesn't sound like it.

[laconicsax]

14. "The rules of mathematics are arbitrary and can be changed at any time."

No, they're not. 2+2=4 whether you like it or not. If the rules were truly arbitrary (ie as with language) you could simply change them to make the sum of 2 and 2 equal 5 or any other number.

[dimbear]

15. I'm with your mom!

The rules of math can be changed at will, but the difficulty is that usually you will end up with a useless system, and end up being the only individual in the universe practicing it. Working more or less at random you are likely to choose contradictory 'rules' and face the result that everything you can say is both true and false, and hence pretty meaningless. Of course the best example of such a change which actually works is Boolean algebra.

The standard old chestnut about the problem with 2+2=4 is that when you go into an elevator and press 2 and then press 2 again, you don't go to floor 4. That's just to keep your courage up, I don't claim it's exactly addition.

[dimbear]

16. I'm with your mom!

The rules of math can be changed at will, but the difficulty is that usually you will end up with a useless system, and end up being the only individual in the universe practicing it. Working more or less at random you are likely to choose contradictory 'rules' and face the result that everything you can say is both true and false, and hence pretty meaningless. Of course the best example of such a change which actually works is Boolean algebra.

The standard old chestnut about the problem with 2+2=4 is that when you go into an elevator and press 2 and then press 2 again, you don't go to floor 4. That's just to keep your courage up, I don't claim it's exactly addition.