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  • Bedrock principles of mathematics?

    What do you consider the bedrock principle or principles of mathematics?

    I would say they are:

    1. The ability to differentiate two things

    2. The ability to rank two things (as to most value, shortest route, least danger, etc.)

    3. The ability to expand the above to more than two things (which essentially leads to the natural number system)

    Any thoughts?
    Last edited by lakechampainer; 23 May 10, 07:36.

  • #2
    Mathematics don`t have a “bedrock”; they are the “bedrock” of the Universe.
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    • #3
      Nice thread .

      Mathematics is logic given form .
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      • #4
        Originally posted by The Doctor View Post
        Mathematics don`t have a “bedrock”; they are the “bedrock” of the Universe.
        But math still must follow basic principles like any other discipline.

        As for the "bedrock of the universe" - I would think of physics first, which incorporates math, although I consider the whole affair to be randomly based on Chaos Theory rather than a rational creation based on math.

        Interestingly, religious creationism would seemingly have to exclude math, in order to allow a "devine being" to do whatever he wished regardless of rules.
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        • #5
          Originally posted by Mountain Man View Post
          But math still must follow basic principles like any other discipline.

          As for the "bedrock of the universe" - I would think of physics first, which incorporates math, although I consider the whole affair to be randomly based on Chaos Theory rather than a rational creation based on math.

          Interestingly, religious creationism would seemingly have to exclude math, in order to allow a "devine being" to do whatever he wished regardless of rules.
          Mathematics are the basic principles. The laws of physics are derived from mathematical relationships.
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          • #6
            Originally posted by The Doctor View Post
            Mathematics are the basic principles. The laws of physics are derived from mathematical relationships.
            Yes. The bedrock is the universe. Without maths there would not be physics or chemistry or, dare I say it, music.
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            • #7
              Originally posted by Mountain Man View Post

              Interestingly, religious creationism would seemingly have to exclude math, in order to allow a "devine being" to do whatever he wished regardless of rules.
              Ironically, math does what it wishes regardless of the rules. Look at imaginary numbers and calculus; one allows me to square root negative numbers while the other allows me to find something that can't be found.
              If you can't set a good example, be a glaring warning.

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              • #8
                Originally posted by Mountain Man View Post
                But math still must follow basic principles like any other discipline.

                As for the "bedrock of the universe" - I would think of physics first, which incorporates math, although I consider the whole affair to be randomly based on Chaos Theory rather than a rational creation based on math.

                Interestingly, religious creationism would seemingly have to exclude math, in order to allow a "devine being" to do whatever he wished regardless of rules.
                I wouldn't say that, certainly not for all. I'm not a creationist, but I do not need to dispense with mathematics to see the possibilites beyond your philosophy my dear Horatio. I see the universe like the Matrix, a rule based system that can be subverted by a being of sufficient power or skill. God comes to mind; he set up the rule system just so and he is diffentivly more powerful than his every creation. In practice though, I am skeptical of divine interference, but I won't immidiately rule it out either.
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                • #9
                  When I phrased the question, I guess what I really meant to ask was: What are the bedrock principles or cognitive abilities which allow one "to do" mathematics?

                  Some related questions I might ask:

                  Is an elephant matriarch who leads her group on the best route through a hundred square mile area doing mathematics? I would say, on a low level, yes.

                  Is a solar system doing mathematics when pieces of rubble combine to form planets due to what we mathematically characterize as "the laws of gravity"?

                  I would say, no, mathematics can only be done by "thinking" entities.
                  Last edited by lakechampainer; 23 May 10, 12:12.

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                  • #10
                    Originally posted by Freightshaker View Post
                    Ironically, math does what it wishes regardless of the rules. Look at imaginary numbers and calculus; one allows me to square root negative numbers while the other allows me to find something that can't be found.
                    But do mathematical rules dictate the random formations of the stars, planets, systems, galaxies, universe and cosmos, or does it merely explain it?

                    Before the creation of everything we know, there were no rules. We know this because the "rules", as well as the mathematics itself, are entirely our creation.

                    Math is not a living entity, merely a calculating system created by an intelligent lifeform to explain relationships which exist with or without an arbitrary external system.
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                    • #11
                      Originally posted by lakechampainer View Post
                      Is a solar system doing mathematics when pieces of rubble combine to form planets due to what we mathematically characterize as "the laws of gravity"?

                      I would say, no, mathematics can only be done by "thinking" entities.
                      Well, it conforms to mathematical rules. It is not calculating what it is doing but there is no way to prove one way or the other that the universe isn't. For all we know the universe is running a giant math checker on everything that is happening in every moment.

                      But I suppose that if we want to take it into the realms of philosophy then maybe the rubble does think. After all we are all made of the same material and just because we cannot understand a process does not mean it did not happen. If atoms grouped together can allow us to think then anything is possible.
                      Matthew 5:9 Blessed are the cheesemakers

                      That's right bitches. I'm blessed!

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                      • #12
                        Originally posted by Mountain Man View Post
                        But do mathematical rules dictate the random formations of the stars, planets, systems, galaxies, universe and cosmos, or does it merely explain it?

                        Before the creation of everything we know, there were no rules. We know this because the "rules", as well as the mathematics itself, are entirely our creation.

                        Math is not a living entity, merely a calculating system created by an intelligent lifeform to explain relationships which exist with or without an arbitrary external system.
                        The same could be said for the concept of time.

                        I believe math to be man's explanation for it all and a method of predicting the unknown, ie. statistics.
                        If you can't set a good example, be a glaring warning.

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                        • #13
                          Originally posted by lakechampainer View Post
                          When I phrased the question, I guess what I really meant to ask was: What are the bedrock principles or cognitive abilities which allow one "to do" mathematics?
                          After I thought about this for a while, I figured that was what you were asking.

                          It's easy to lose sight of the fact that mathematics and mathematical symbology are two different things.

                          Originally posted by lakechampainer
                          Some related questions I might ask:

                          Is an elephant matriarch who leads her group on the best route through a hundred square mile area doing mathematics? I would say, on a low level, yes.
                          I don't know if "doing mathematics" is the right way to phrase this. I doubt they have mathematical symbology like humans do. Human physiology constantly employs mathematical principles without actually "doing mathematics."

                          Originally posted by lakechampainer
                          Is a solar system doing mathematics when pieces of rubble combine to form planets due to what we mathematically characterize as "the laws of gravity"?

                          I would say, no, mathematics can only be done by "thinking" entities.
                          It's more like that mathematics are doing the solar system.

                          "Thinking entities" - like humans - develop symbologies and systematic descriptions of mathematics. The mathematics themselves pre-date humans... And probably pre-date the current Universe.
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                          • #14
                            Originally posted by Freightshaker View Post
                            The same could be said for the concept of time.

                            I believe math to be man's explanation for it all and a method of predicting the unknown, ie. statistics.
                            Our mathematical symbols and systematic descriptions of mathematical principles are our explanation for mathematics. The mathematical relationships themselves are part of the fabric of the Universe.

                            The mathematical relationships that comprise Kepler's Law were in place long before man figured out a way to describe them.
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                            • #15
                              I guess I'm not clear in my mind if the people 8,000 years ago who were figuring how much seed was needed to plant 10 acres for a grain field, or how much big a pile of food they needed to get through the winter, or how many cattle they had to kill to make winter clothes for their family, were doing mathematics (I would say yes). Or did the mathematics not come until there was a formal number system, a way for measuring area and volume, a form of land surveying, etc.?

                              At what point in Human development would you say something was on the verge of becoming mathematics?

                              Also, when I was referring to "thinking" beings, I was referring to beings such as ourselves, or maybe elephants or maybe computer programs, who have the self-awareness and memory to look back at their previous "decisions" and evaluate if there was potentially something that could have worked better, or would work better in the future.
                              Last edited by lakechampainer; 24 May 10, 08:23.

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