Is Math Flawless or Can it be Wrong?

[Chronos]

I was thinking about this while at McDonald's yesterday. If 1 + 1 = 0, would that change the constants of nature? I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

 

[ArmoSkater87]

I was thinking about this while at McDonald's yesterday. If 1 + 1 = 0, would that change the constants of nature? I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

LOL...sorry but that's funny. Well, you have a good question there. The thing about math is that it is created from logic. Changing math would mean changing the logic from which it came, which would mean that this new logic would apply to everything as did the logic before. So it seems to me that the constants wouldn't "change", but be in a different form (different units?). The constants are based on measurements which are based are a set unit. lol, if you were to be in medieval kingdoms, the constants would change every time there was a new king, because the meter was defined by the distance from the nose to the fingers of the king.

 

[Chronos]

That explains why my brain is wrinkled... it is puckering in fear of the unknown.

 

[russ_watters]

Math isn't wrong - it works. You can prove 1+1=2 through experimentation with countless physical processes.

 

[HallsofIvy]

I was thinking about this while at McDonald's yesterday. If 1 + 1 = 0, would that change the constants of nature? I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

Thus proving that even at McDonald's there are some reasonably intelligent people.

 

[jcsd]

Iwas thinking the other day that amounts of money are strictly limited to a subset of the rational numbers. Wouldn't it be better if we represnted money using complex matrices?

 

[pmb_phy]

I was thinking about this while at McDonald's yesterday. If 1 + 1 = 0, would that change the constants of nature? I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

1+1 cannot equal zero. We define the sum 1 + 1 to be the number 2. Whether this corresponds to something in nature is another story and which is true by observation.

However it'd be nice if math was wrong if it worked to my advantage. I could pay off a lot of debt that way!

Pete

 

[ZapperZ]

I suppose this is as good of a time as any to introduce this. For those of you haven't read it yet, I highly recommend Eugene Wigner's essay on "THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES". A reprint of this essay can be found here:

http://nedwww.ipac.caltech.edu/level5/March02/Wigner/Wigner.html

Zz.

 

[daveed]

what if... what if i could fly AND be invisible...? that would be the best

 

[daveed]

but no, as we've all learned, when you have an apple and take another apple, you have two apples.

so what its really no apples and our senses have failed us
*shrugs* it works as far as we can telll...

 

[n0n]

chronos, this might actually be a good consept. Everyone is alway trying to fine the right answers, but their must be an infinite amount of incorrectnesses to every right idea. now thies incorrectnesses, can determin limits to the idea, say yea 1+ 1 =2, but also, untrue is 1+ 1 = 1, and 1+ 1 = 0, ect. now if this didnt work we wouldn't have if/then statements in programing, and the such.

for a = 1 to 10
if a = 2 then print " correct"
next a

were " next a" adds one to a.

 

[Locrian]

I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

Hah.

On a different note, I was thinking of starting a postmodern bank. People would deposit money. All accounts would always read ? where their balance was. If people called saying they wanted their money back, I would just ask them how they know they deposited it in the first place.

 

[Nenad]

I suppose this is as good of a time as any to introduce this. For those of you haven't read it yet, I highly recommend Eugene Wigner's essay on "THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES". A reprint of this essay can be found here:

http://nedwww.ipac.caltech.edu/level5/March02/Wigner/Wigner.html

Zz.

The article Makes a lot of sence.

 

[mewmew]

Well, math got many men to the moon and back, if 1+1=0 I don't think things such as going to the moon would work so well...

 

[quasar987]

Nothing good can come out of eating at McDonald's.

 

[K.J.Healey]

maybe the number "1" represents one of some "thing", which when added to the exact same thing they cancel out. Its sort of like particle/antiparticle but perhaps the simple adding of some particle to the state of another one of these particles induces its properties to change to that of an antiparticle. Then it could work? 1+ 1 = 1 + (-1) = 0
This is too abstract of a discussion anyway.

 

[NateTG]

I was thinking about this while at McDonald's yesterday. If 1 + 1 = 0, would that change the constants of nature? I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

Actually, your question is a bit imprecise. If you're talking about "the constants of nature" you're not talking about math, but about physics, or some other science.

Regardless, science is specifically structured in such a way that it reflects the history of reality. If reality suddenly and fundementally changes then science will not longer be applicable.

Mathematics is more like a philosophy than a science. Asking what happens when 1+1=0 is a bit like asking how many angles can dance on the head of a pin. There is mathematics where 1+1=0, but, in practice it isn't applicable to money.

There are many different mathematical constructs, and, in order to apply them, people must select an appropriate one, or create a new one. Science is a process for selecting appropriate (typically mathematical) models of the real world.

Consequently, it's silly to suggest that changing mathematics changes the amount of change that you get at the cash register. You might as well ask congress to repeal the 'law' of gravity. The process of subtraction ultimately only serves to predict the amount of change you should get, rather than controlling it.

 

[khai06]

hmmm 1+1 = 0 it's possible for this mathematic equation to be true...that 1+1 might means 1( to the I direction ) + 1 ( to the J direction ) which = 0 since I and J are opposite of each others...i'm just guessing I = X and J = Y

 

[subluminous]

math is logic applied to a set of axioms, generally the axioms chosen model physical situations like counting apples: 1 apple + 1 apple = 2 apples.

We could however use different axioms, i.e. drops of water: 1 drop + 1 drop = 1 drop. This is a different kind of math, it has the same logic, but different assumptions, and is probably not all that useful.

Hence math cannot be wrong because the axoims are held to be truisms. The closest math can get to wrong is if poor assumptions are made; this is human error and not a flaw in the mathematics itself.

 

[MiGUi]

Zero is the neutral element of the sum, so by its definition x + 0 = x for all x.

Lets have an element 'x' of the integers ring 'Z' . As a ring, Z has a neutral element represented by zero, the inverse of 'x' is '-x', and so...

If x + x = 0, that would mean that x is a number whose inverse is itself, and there is no number at all which can verify that property except zero, so one plus one can not be zero.

No matter to do with this, physics are safe by the moment

 

[K.J.Healey]

Zero is the neutral element of the sum, so by its definition x + 0 = x for all x.

Lets have an element 'x' of the integers ring 'Z' . As a ring, Z has a neutral element represented by zero, the inverse of 'x' is '-x', and so...

If x + x = 0, that would mean that x is a number whose inverse is itself, and there is no number at all which can verify that property except zero, so one plus one can not be zero.

No matter to do with this, physics are safe by the moment

It always depends on the mathematics of it. What if you mean the expectation value of some operator "x" (non spacial). That when you operate on a wavefunction you get its eigenvalue, but changes the wavefunction to its "negative" or inverse about the 0. Then it could hold, while x could be anything. Its all about definitions. <O|xO> + <O|xO> = 0, i think. Its been a while since quantum. O is a function.

 

[The Binary Monster]

I was thinking about this while at McDonald's yesterday. If 1 + 1 = 0, would that change the constants of nature? I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

I think you just struck upon an important idea! ...never eat at McDonald's. Ever. Bad for the brain, I say!

:: Ben ::

 

[MiGUi]

We were talking about numbers, or not?

 

[kjones000]

Math where 1 + 1 = 0 is perfectly reasonable. There are even a few situations where some of the maths where 1 + 1 = 0, would be useful. It changes nothing.

The universe is not affected by math. We are affected by math. We choose a math based on its ability to predict events in the universe. When it fails us, we choose a new one. Perhaps in the future we will find that our use of real and complex numbers to describe a quantized universe has led us astray (or, more likely, blinded us to deeper realities).

You can say this for certain - the rules of the universe are internally consistent and there is no situation where the rules of the universe break down. If our math, our intuition, and our universe all seem to indicate that 1 + 1 = 2, that's gravy.

 

[Math Is Hard]

Oops!

I was thinking about this while at McDonald's yesterday. If 1 + 1 = 0, would that change the constants of nature? I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

Chronos, I forgot. I owe you $1.32. I never gave you your fries with that order. My bad.

 

[doubleteam9]

anyone here heard of modular arithmetic?

 

[radou]

I was thinking about this while at McDonald's yesterday. If 1 + 1 = 0, would that change the constants of nature? I asked the same question to the girl running the cash register, yet she stubbornly refused to return my money.

...and then you asked yourself: 'Is the food in here, or is it just me?'

It definitely must have been the food.

 

[AlphaNumeric]

^ That was my thought too (though I know plenty of people in this thread have). 1+1=0 in mod 2 systems, so when someone said 1+1 = 1+(-1) = 0, that can sometimes be true.

The person who said "1 in the i direction and 1 in the j direction gives 0" is wrong, i+j = ... i+j! Adding two orthogonal vectors together than NEVER give zero unless they are both zero themselves! You're thinking of the scalar product where i.j = 0.

 

[AlphaNumeric]

^ That was my thought too (though I know plenty of people in this thread have). 1+1=0 in mod 2 systems, so when someone said 1+1 = 1+(-1) = 0, that can sometimes be true.

The person who said "1 in the i direction and 1 in the j direction gives 0" is wrong, i+j = ... i+j! Adding two orthogonal vectors together than NEVER give zero unless they are both zero themselves! You're thinking of the scalar product where i.j = 0.

 

[Claude Bile]

Mathematics starts with a set of axioms, or assumed truths, from which all laws and theorems are derived. You could start other 'versions' (for want of a better term) of mathematics using different axioms (i.e. ones where 1+1=0), however the thing that differentiates 'our' system of mathematics from all the other possible systems that exist is that the axioms that form the basis of 'our' system are observed to be relevant w.r.t. the reality we observe.

For example, we observe that when you add nothing to something, nothing changes, i.e. a + 0 = a. We observe that no groups of anything is nothing, i.e. a.0 = 0. Henceforth, our version of mathematics is useful than say a version where a + 0 = 0 and a.0 = a, because our version is rooted in reality in some sense, therefore we can make predictions about our reality.

Claude.

 

[matt grime]

anyone here heard of modular arithmetic?

Yes, plenty of us. Though how many of the people in the thread that is over two years old still read these posts is another matter entirely. Or indeed so is how many of us who post now were around at the time... Nevermind those around at the time who couldn't be bothered with that thread since answering it would only create more pointless philosophical threads, and there might have been too many of those around...

In short, stop reviving the dead threads!

 

[daniel_i_l]

Math isn't wrong - it works. You can prove 1+1=2 through experimentation with countless physical processes.

The fact that if you put one apple together with another apple doesn't prove anything about math, there're lot's of places in physics where 1+1 doesn't equal 2, for example:
velocities (relativity)
liquid volumes (1L of water + 1L of oil doesn't equal 2L of water/oil)
thats all i can think of now but i know that there're more.