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Maybe philosophical question

  1. Jul 29, 2008 #1
    hi all
    maybe my question seems funny.but it is challenging for me
    why multiplication of two or more physical quantity make a new one?
    for example F=Ma the third newton's low tells us that the multiplication of acceleration and mass produce force.i always question myself why?
    I will wait for your replies
    thanks in advance
     
  2. jcsd
  3. Jul 29, 2008 #2
    are you expecting Ma=Ma ?
    the whole purpose of the equation is to show the relation between things

    so in this situation the force of something can be calculated based on its mass and acceleration, and it just so happens that the interaction between mass and acceleration works out to be best suited by our laws for "multiply"

    its not that taking the mass of something and multiplying it by the acceleration of the same thing magically produces something else, its just that that number (which is obviously still Ma) just happens to be the same number as F. (by just happens I mean according to our current physical laws)

    or did I misunderstand your question?
     
    Last edited: Jul 29, 2008
  4. Jul 29, 2008 #3

    russ_watters

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    Staff: Mentor

    Yeah, it looks to me like you're just asking why math works the way it does. Math is logic.
     
  5. Jul 29, 2008 #4
    right, but even what we call logic has a rule set we defined to it. Does addition actually exist, or is it a convenient construct we use to keep track of things?

    but thats neither here nor there :)
    </hijack>
     
  6. Jul 29, 2008 #5
    Well since mathematics is the relationship of quantities I'd imagine those quantities would exist even if humans don't! The patterns in our life though can be derived from mathematics.
     
  7. Jul 29, 2008 #6
    this was always a fun question I've had with myself.

    would math exist without humans?

    sure the core concepts behind math would exist, but those concepts are made up by us. I dont think math would exist.

    I think we use it as a way of conveying, interpriting and modifying "quantities" we call numbers.

    like, sure putting two rocks together still works obviously, but would you have to call it two? it doesnt necessarily need to be called anything, I think that language and math are so interwoven into our society its hard for us to picture life without them.
     
  8. Jul 29, 2008 #7
    Well I think math would still exist but it wouldn't be utilized. 2+2=4, 3+3+6 the general relations and concepts would still be there. All the concepts should exist too. Actually I believe everything involving math has only been discovered. Say some object wanted to determine the roots of an x^4 equation, the object still could use synthetic division to determine the answers. See the mathematical relation would exist, its just not as direct as say (x-1)(x+1)(X-2)(X+2). One could also get 2+2=4 by -4+8=4. Its a simple example but it shows that our concepts are nothing more than different types of relationships.

    Language though does not really connect with math but rather its a communication medium. Two is just an identifier for, well 2, of an object. Two, dos etc its the same thing. However language is very important because it allows us to share ideas and such. Think about how the world would be if humans could not communicate. Knowledge couldn't be shared and we'd be stuck in the same spot until we learned another way to convey information to each other.
     
  9. Jul 29, 2008 #8
    You've scratched the surface of a very fundamental question in physics and math.

    Let's look at a basic math truth that has been established. Acceleration is a vector quantity. Mass has no direction and thus a scalar quantity. F = ma merely tells you that there is an indirect relationship between mass and it's acceleration. Physics and good ole newton tells us that this indirect relationship is called Force. And, Force has a direct relationship with mass and acceleration. Thus, the more mass an item has, the more force is required to create acceleration.
     
  10. Jul 30, 2008 #9
    im not sure how one goes about discovering math, you said "roots of an x^4" but that implys that x^4 is something that actually exists.

    there are much more complicated relations that exist in nature, that we just use more and more math to describe, why couldnt we have made one of those "truths" or "realations" an operator

    what in nature would let us discover addition, other than our desire to keep track of things so we invented a means to group things by simplifying them.
     
  11. Jul 30, 2008 #10
    I'll put it this way: the America's were discovered by the Vikings and Columbus but even if they weren't discovered they'd still exist right? Just as an X^4 can still exist even if we dont, its nothing but numbers. How we apply math though is strictly human.
     
  12. Jul 30, 2008 #11

    FredGarvin

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    Science Advisor

    My reply is that it is Newton's second law, not the third. Math is math. There's nothing existential about it.
     
  13. Jul 30, 2008 #12
    dear buddies
    I can underestand the relations you answered.for example i know that the more the mass (in newton's low) the more the force,but i cant underestand the dimensions.You guys know that we have to regard dimensions when we are trying to obtain an equation in physics.so it seems that multiplication really change dimensions.
    I would still wait for your replies
    Best regards
     
  14. Jul 30, 2008 #13
    Mathematics is simply a language persay of quantities via relationships. Mathematics as we know it didn't exist I think until the Greeks. They used to use language - one and one is two. Then some guy came along and said, hey, lets have a symbol for one AND one, and then we get +. Etc... for all the other basic operators.

    deep_tought, look at like this: You have a cup in your hands, and I give you another cup - you have a cup, and a cup. I give you another, and you have a cup, and a cup, and a cup. This can get complicated if you're running a cup store, and you need to keep track of your many cups. Eventually you learn that 1 cup + 1 cup + 1 cup = 3 cups. You're just assigning symbols to a quantity. It's a bit abstract, but stay with me. If you'd like to extend your store to say, cups and balloons, well you won't say "I have 3 cups, and a balloon and a balloon and a balloon." You'll eventually learn to say 1 balloon + 1 balloon + 1 balloon = 3 balloon. I hope you get what I'm saying. Eventually you decide you want to be a physicist and you need a way to measure objects to compare them. So you get a bar of iron, and you say that "this amount of mass is 1 kilogram" and you compare every thing you weigh to this bar of iron. You can say I weigh 3 iron bars. That just means you weigh that 1 iron bar + 1 iron bar + 1 iron bar = 3 iron bar. Or, 3 TIMES the iron bar.

    Acceleration is a magnitude of some distance in some direction over time*time. And you are taking that iron bar (or whatever we used to define the kg) and relating the weight to the distance over time (squared) with a direction. This is how you define things; relationships. We call this relationship force.

    Mathematics is just all about relationships. Physics is a bit more specific, as it applies math specifically to certain quantities, etc... You could break all of our definitions of time, weight, etc... down to some physical piece of matter or something with which we are comparing. Gotta start somewhere.

    And I don't get what you are saying about dimensions, how does multiplication "change" dimensions?

    Math doesn't actually DO anything, it is descriptive, i.e. it describes!
     
  15. Jul 30, 2008 #14
    Well, nice explanation. I agree.
     
  16. Jul 30, 2008 #15
    By dimensions do you mean the units? Like [force = kgm/s^2] since [kgm/s^2= mass*acceleration = a newton]. When you change units, you change what your solving for. Momentum is a good example of unit change: [P=mv=mass(velocity)=kg*m/s.= N/s] Notice how N --> N/s because seconds were no longer squared.

    Tell me if thats what you were looking for.
     
  17. Jul 30, 2008 #16
    where does x^4 exist? the americas exist sure, but x^4 is simply a correlation we made up.

    a pattern our pattern finding brains found. we like to find patterns even when there are none, its what we are built to do.

    what about 2 electrons make them 2
    being close to each other? referancing them together? being on the same atoms electron cloud at the same time?

    there is no real numbers out there, only interations that we have transcribed the best we could into language and math (math is a form of language im pretty sure)
     
  18. Jul 30, 2008 #17
    These are correlations that have always existed. Thats the beauty of math, its true everywhere. Numbers are just representations of quantities of an object so they must have always existed. How they are represented maybe different but the quantities will be presant.
     
  19. Jul 30, 2008 #18
    Im asking do quantities actually exist though? is there anything that denotes 2 electrons? or 3?

    there are plenty of correlations we dont have a nice little symbol for

    just because we picked correlations in life to denote functions doesnt mean that the correlations are special in any way does it?
     
  20. Jul 30, 2008 #19
    I dont see why they wouldnt exist. Without quantities wouldn't nothing exist?
     
  21. Jul 31, 2008 #20
    no, im saying quantities are not necessary.

    things exist whether they are labeled or not. stating how many, or how much is just as arbitrary as stating a name I think. We have rules for all of these things, but they are still made up.


    There is no need for 2 electrons sitting near each other to be in a state of 2. They simply are.

    If you dont call an apple, and apple its still there, but it doesnt HAVE to be an apple. There is nothing about it that universally is apple. Its just a word we assigned it based on our language and how we percieved it. Calling it an apple has a purpose, and logic behind it. But that does not mean it is still an apple universally. It simply IS.
     
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