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Thread: Novice math person tries to math.

  1. #11
    Senior Member
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    Dec 2013
    Quote Originally Posted by QuickTwist View Post
    You haven't demonstrated that you don't know what I am talking about. I am talking about this: Suppose you are solving for a completely unknown thing. If this thing can be a representation of infinity, then it is impossible to solve for it.
    'Solving': so you mean, an equation like 2x = x - 1? (Replace each side with what you want.)

    here's an equation:
    1/x = 0

    The solution is x = infinity - in a sense. (also x = -infinity)

    As you can see, what you're saying is not clear.

    Your response very clearly is "That's not the way this works. There are just some rules you have to follow."
    No. Not that you "just have to follow" as though it's arbitrary.

    Yes, there are rules in mathematics. And if you operate in that area of mathematics, you should follow them if you want to do something that makes sense in that particular area.
    Spoiler: ...

    1 + x = 2 so x = 1

    But, add 1 to the left hand side:
    2 + x = 2 so x = 0

    then in the first equation:
    1 + (0) = 2

    This doesn't make sense because I didn't follow the rules correctly, which allowed me to write something that makes no sense.

    If you are inventing a new type of maths, then you can break rules and redefine stuff, and see what happens there. If you are doing that, then you should be clear about it.

    You have yet to grasp what I said about the unknown variable in the first place which is that it could be a changing thing that never stays constant which would mean it has no predictability.
    Yes, I don't understand what this means. Can you explain it again?

    In particular, what do you mean by 'an unknown variable'? Is this in the context of an equation?

    Give an example or something. Like what are you actually referring to?

    This could even be a string of 0's and 1's. I mean, you even said it yourself that what I am saying is not what math is for. In short, you are focussed on the practical application of how math is useful to us rather than considering the merits of whether I am correct or not.
    So, you are trying to create a new system of maths and see what happens? I mean, I can get behind that. But from your original post, it didn't look like you're saying that. It seems like you're talking about a typical equation, and then stating some things that don't work. That 'normal maths' is all built upon practical things like the patronising cow/chicken thing I described, and so that's why it's useful to use to check if what you're doing actually makes sense.

    But if you're trying to create some new thing, by modifying some existing rules, then let's go with that.

    It also seems like you're trying to combine maths and physics. E.g. when you said this "then this means that time within the equation actually passes while manipulating the equation" and I don't understand this. The solution to an equation typically has no connection to the time taken to solve it - unless time is a variable within the equation.

    Perhaps that's what you mean? You want to have an equation that is both random and changes over time? f(x, t) or something.

  2. #12
    know nothing pensive_pilgrim's Avatar
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    Dec 2013
    it could be a changing thing that never stays constant which would mean it has no predictability
    You mean like the digits of pi?

    Most things that can't be predicted exactly can still be expressed as a probability. Like with the digits of pi, if we analyze enough digits we find that they all have an equal probability of appearing. We can observe the trend in the frequency domain even though it looks random in the time domain. However, for a totally non-periodic function we have to choose a range of inputs to analyze. We have to assume that there is never a point where, perhaps after the quadrillionth digit, all of the following digits are 9 repeating forever, or something like that. That would be weird but it's possible. We can say that it's extremely improbable, but we can't say that it's impossible.

    I am going off the assumption that you are solving for a completely unknown quantity rather than something that has a static value. What I want to know is why we assume when solving for an unknown variable that it has to be static.
    You used the position of an electron as an example. We don't know exactly where an electron is at any given moment (in fact the math seems to suggest it's everywhere it could be until we measure it) but we do have a probability function that tells us where it's likely to be. Here are examples of that type of function:

    I don't think it's true in that case that we're assuming that the value being measured is static. It changes with time and we can't predict exactly how, and our models account for that uncertainty. But maybe that's not what you meant, in which case I think another real-world example would be helpful.

  3. #13
    tsuj a notelpmis QuickTwist's Avatar
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    Oct 2016
    Yeah, I guess it's about probability. Like it depends if the unknown is completely random or if there is something about it that holds some sort of pattern. In this way, it's kinda like trying to predict where a flame lick will be at a given source of a fire. The problem comes when what you are trying to solve could be literally anything. Like it could be an equation in an equation, or something that doesn't even make sense like a pineapple or something outrageous like that.

    It is hard to come up with concrete examples of how this would work.

    I have in my notebook where I was working on this, is that what if you took a know part of infinity and cut it in half and cut it in half again? Well, the way I pictured this was by drawing a circle and separating it into 4 quadrants. That would be the first part and the known entity. Then I added another circle that I drew that was undefined that I just put a question mark in the circle representing that what is within the circle and how the circle is divided up, is completely unknown. so what would you get if you added these two circles together?
    But your individuality and your present need will be swept away by change,
    and what you now ardently desire will one day become the object of abhorrence.
    ~ Schiller - 'Psychological Types'

  4. #14
    tsuj a notelpmis QuickTwist's Avatar
    Join Date
    Oct 2016
    So I figured out (from some help) that what I was thinking is along the lines of continuous random variables. Dynamic integers came up as well.
    But your individuality and your present need will be swept away by change,
    and what you now ardently desire will one day become the object of abhorrence.
    ~ Schiller - 'Psychological Types'

  5. #15
    Join Date
    Sep 2017
    United Kingdom
    I think I can see where you're coming from with values changing over time. But I think it has to do with the very abstract and often inaccessible way that maths is often taught. When almost everybody starts to learn algebra, the first question they ask is, "what is X?" And the inevitable response is, "it's just an unknown number." That doesn't help, because that's trying to communicate the concept in a data only context, and data on its own is meaningless.

    To say X = Y / Z is completely meaningless. It doesn't do anything helpful to your understanding of the world around you.
    But if we typed Speed = Distance / Time, suddenly that equation makes perfect sense because that is now communicating useful information.
    So that means that as my mother's house is 10 miles away, and I get there in about 10 minutes, I'm averaging about 60mph across that journey.
    The relationship between those variables doesn't change no matter the distance or the time. Dividing distance by time will always obtain my average speed across any journey.

    So to say 3X = Y, whatever variable X is, then multiplying it by 3 will always be the same as whatever variable Y is in this equation. For example, it doesn't matter how many inches I want to measure, there will always be 2.56cm for every inch I measure. That is to say, X(256/100) = Y.

    So although the value of X (my speed) may be change over time, it's relationship to the distance travelled within a specified time will always be the same.

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