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Inconsistency between mathematics and our universe.

  1. Apr 25, 2012 #1
    For example, when a proton and an anti-proton collide, they cancel each other out. They become neutral. However when you multiply a positive and a negative number, you get a negative. You would need negative(electron) and a neutral(neutron) stay negative, but that would mean that our number system is missing an entire set of numbers.

    If our universe consists of Positives(protons) Negatives(electrons) and Neutrals(neutrons) then how can we expect to describe its behavior using a number system that only consists of Negatives and Neutrals?


    Should there be a third branch? Positive numbers, negatives, and neutral numbers? -1, 1, +1 all being different things?

    Can someone explain this to me?
     
  2. jcsd
  3. Apr 25, 2012 #2

    berkeman

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    Why would the operation of combining a positively charged particle and a negatively charged particle be multiplication? There is another mathematic operation that would seem to make more sense, and gives the right answers both in the physical and mathematical scenarios....
     
  4. Apr 25, 2012 #3

    I, for one, couldn't care less if our universe was inconsistent with mathematics: worse for it.

    Either the universe mends its ways or it'll remain inconsistent. Its call.

    DonAntonio
     
  5. Apr 25, 2012 #4
    I dont see the point of all the blue but ok.

    Also seeing it as addition is kind of a duhh way of looking at it. That makes a lot of sense. I dont see why i didnt look at it like that.

    The thing that bugs me the most is that - multiplied by + gives you -. I just cannot understand why it cannot be positive for the same reasoning that it comes out to negative.
     
  6. Apr 25, 2012 #5

    berkeman

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    Probably the easiest way to get comfortable with that is to think of the number line.

    Take the product x = -2 * 5 = -10.

    Think of this as pushing the -2 five times farther negative, away from the 0 on the number line.

    Does that help?
     
  7. Apr 25, 2012 #6

    HallsofIvy

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    Actually, the statement "Inconsistency between mathematics and our universe" doesn't even make sense. The consistency would have to be between a specific mathematical structure and some phase of "our universe". There are many mathematical structures that work very well at descriptibing specific parts of our universe- of course, no one expects them to be perfect because any information from our universe is the result of measurment and measurement itself cannot be perfect.
     
  8. Apr 25, 2012 #7
    but why not look at it the other way? Why wouldnt the 5 move the 2 five times more in the Positive direction? why the weighting on the negatives? Why are they more "influential" so to speak?
     
  9. Apr 25, 2012 #8
    I didn't join this forum to be criticized of my grammar and sentence structure. I admit I did word it awkwardly but I hoped the community here would be above that.

    I didn't provide a situation specifically because I intended for it to be in a very general sense. Just the way we count numbers compared to the way nature and our universe behaves does not match up.
     
  10. Apr 25, 2012 #9

    berkeman

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    Maybe a better way to think of it is in the sense of vectors. The +/- sign gives you a direction on the 1-dimensional number line. So in my example, it can be re-written as:

    x = (-1) * (2 * 5) = -10

    So the (-1) term gives you the final direction of the positive product.

    Halls wasn't objecting to any grammar or sentence structure, IMO. He was pointing out the problem with your problem statement in a logical sense.
     
  11. Apr 25, 2012 #10
    So basically you're saying that 10*-1=-10, at which point i argue the same thing as before. Why wouldnt the 10 make the -1 go into the positive direction instead. why is it the negative that take precedence?

    On account of halls, my point still stands. My question was clear enough to be understood, theres no sense in criticizing the way i worded it. I agree that it could have been said better but if you both know what i meant then its just nonsensical to point it out and use it as an argument.
     
  12. Apr 25, 2012 #11
    HallsofIvy was merely pointing out that this doesn't necessarily show any sort of inconsistency, because there is no reason why collision of particles and antiparticles should correspond to multiplication rather than some other mathematical operation.
     
  13. Apr 25, 2012 #12
    whatever lol my mistake for misunderstanding i guess
     
  14. Apr 25, 2012 #13

    micromass

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    It's simpy by definition. We have define 10*-1 as -10, and we notice that everything works fine.
    We could also have define 10*-1=10 and then we would obtain another number system which we can calculate with.

    So the question "Why is the result -10 instead of 10" is easily answered by noticing that we chose it to be this way.

    The question that you should be asking is "why did we choose it this way and not the other way".

    There are many answers to this. One answer is that otherwise the integers wouldn't be a ring, and being a ring is a very desirable property.
    That is, the following are true for natural numbers:

    a+(b+c)=(a+b)+c
    a+0=a=0+a
    a+b=b+a
    a*(b*c)=(a*b)*c
    a*1=a=1*a for nonzero a
    a*(b+c)=a*b+a*c
    a*b=b*a

    Now we adjoin for each element a, an element -a such that a+(-a)=0
    We want all the above properties to still hold because they are familiar for natural numbers.

    From this we get:

    0=10*0=10*(1+(-1))=10*1+10*(-1)=10+10*(-1)

    Adding -10 to both sides gives us

    -10=10*(-1)

    So IF the above identities are all true, then it immediately FORCES us to accept -10=10*(-1), we have no other choice.

    This is a pure mathematical way of looking at things, but there are other ways as well!!

    For example, one may motivate the existence of negative numbers with a bank account.
    In this case, if you have -10$ then this means that you owe the bank 10$. So you are in debt.
    What happens if your debt is twice as big?? Then we should look at 2*(-10$). It makes sense that this value should be -20$ rather than 20$. Because if 2*(-10$)=20$, then there is no easy way to describe your debt being doubled!! Things like 2*(-10$)=-20$ happen a lot in real life, things like 2*(-10$)=20$ are much less occuring and thus not interesting.
     
  15. Apr 25, 2012 #14

    Mark44

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    Going back to your previous question about 5 * -2 (because I don't have to write so much), we can look at this product as repeated addition. IOW, as
    (-2) + (-2) + (-2) +(-2) +(-2) = -10

    You wouldn't expect that adding 5 negative terms would give you something positive would you? Nor would multiplying a negative number by a positive number give you a positive result.
     
  16. Apr 25, 2012 #15

    Mark44

    Staff: Mentor

    As far as I can tell, HoI was not criticizing either your grammar or sentence structure, and in fact there is nothing in what he said that is concerned with either grammar or sentence structure. He was questioning the validity of your statement about inconsistency between mathematics and the universe.

    If you're going to complain (twice) about what someone said, at least take the time to try to understand exactly what was said.
     
  17. Apr 26, 2012 #16
    Of course the OP is wrong, but I would like to point out that 00Svo is excusable.

    Physicists are often lost for words, I smile when I read that particles have flavour, charm, etc. Isn't that poetical?
    Now, they say that there is anti-matter, that an electron and a positron annihilate themselves. Op is only quoting them:
    That is not true, not exact; simply false, or anyway misleading

    Trying to explain the basic linguistic/semantic/logic mistake with brilliant, clear explanations, masterly but 'mathematical' arguments...
    ...doesn't solve the problem, probably adds confusion, because you are certainly right, but also 00Svo is not completely wrong drawing the wrong palrallel:
    ... +1 and -1 do annihilate themselves, dissolve themselves into 0, nil, nihilum, the Nothingness.
    ... antiparticles do not, they complement each other, transform into a photon, more or less like Na and Cl 'cancel each other out' into kitchen salt.
     
    Last edited: Apr 26, 2012
  18. Apr 26, 2012 #17

    1) You weren't criticised because of your grammar. If at all, it was because of the title you decided to give your post

    2) The community here is mostly academics/students; it is expected people will be able to express themselves properly

    and within a certain level of correct grammar, putting aside people for which english is not their mother tongue.

    3) You were already given an explanation how to comprehend and understand products of positive and negative numbers.

    You may think still this is in contradiction or not in accordance with what you see in the universe, but so far it

    doesn't seem to be an example by you that shows this.

    DonAntonio

    Ps. The blue coloured fonts here are cute and provide a nice contrast, imo, with the black ones. That's their point.
     
  19. Apr 26, 2012 #18
    Hello 00Sv0 !

    You first mistake is to make a confusion between "physical modelling" and "computation".
    There is no inconsistency in mathematics used in the addition or in the multiplication of positive and negative numbers.
    But numbers and physical objects are not the same things.
    The inconsistency is in your way to model a proton and an anti-proton collision. Your false modelling involves a mathematical operation which is not the good one. Then, even if the operation is correctly carried out (without mistake in the mathematical process), it is not suprising that the result be false.
    So, you should not write "Inconsistency between mathematics and our universe", but:
    "Inconsistency between my own model of universe and our real universe".
     
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