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  • #46
    Originally posted by dian View Post
    no, that cant be it.
    ?? did you get a different answer
    in Toronto Ontario - where are you?

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    • #47
      Originally posted by mklotz View Post

      One of the most intriguing questions mathematicians (and many physicists) proffer goes something like this...

      Is mathematics some sort of fundamental property of nature that we have been gradually discovering or is it the most incredible mental construct mankind has ever assembled?

      Think about it. Newton managed to bundle all of the phenomenon of gravity into a single, simple equation. Was this a discovery on his part or an incredible mental construct on his part? If the exponent on the 1/R^2 term is changed by even a slight amount from two, stable orbits are impossible. Did we just luck out with our creation of algebra so that the square of a number was the perfect fit for the description of gravity or are inverse square forces a natural feature that we happened to discover?

      I don't waste any time thinking about philosophical crap like this; it gets in the way of doing something useful.

      However, if you think you can inject theology into math, you should start by answering this question.
      This is a great question that has deeper implications for mathematics education than first meets the eye. The standard view in mathematics, both mathematical philosophy and mathematics as practiced is mathematical platonism. Put differently, it's the conjunction of the theses that

      (i) mathematical objects exist;
      (ii) mathematical objects are abstract; and
      (iii) mathematical objects exist independently of human minds.

      in the 1980s, a man by the name of Hartry Field attempted to ground math in fiction. The "fictionalist" approach said that mathematics was ultimately about nothing, but something tatken to be true because it was useful. His book "Science Without Numbers" attracted a lot of attention and scrutiny from philosophers of mathematics, and it was ultimately shown to be a failure. In science, particularly quantum mechanics, you can't dispense with mathematical objects or their relationships. Further attempts to salvage the fictionalist approach have all fallen up short.

      When you think about it, it's really hard to defend the idea that mathematics is something that just happens to be a useful construct. Everything in the world is made up of atoms which are made up of particles. The particles themselves are just excitations of a quantum field. Physicist Peter Woit refers to this level as the congruence between mathematical and physical objects.

      Just because we don't experience a perfect circle in our shops doesn't mean that such a circle or a relationship doesn't exist, it just doesn't exist when you factor in the time and space relations on the macro scale in our shops.

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      • #48
        Originally posted by dian View Post
        can somebody tell me if it can be proved that 1+1=2?
        Yes. The Peano axioms work just fine to establish a basis for arithmetic.

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        • #49
          Perhaps another way to say it would be, "It depends" on what scale you are referring to, and which scale is appropriate for the immediate problem. Chaos theory goes into this a bit.

          Of course, I like "It depends" instead of boxers or briefs. Or commando.
          25 miles north of Buffalo NY, USA

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          • #50
            Engineering IS a total act of continuous compromise.



            Originally posted by nickel-city-fab View Post
            Paul, you have a wonderful way with words. Very clarifying, thanks. I have always heard that one couldn't divide a circle by 7, but I would have to ask "Under what conditions?" The tools and techniques available to the HSM today, are so refined that error is either immeasurable, or negligible. I am a fan of George Thomas' writings about his "Versatile Dividing Head" and his system takes you down to one hundredth of a degree using extremely basic and simple techniques. Would I be able to measure a hundredth of a degree? probably not. But for my shop and what I do, it is an acceptable compromise. And isn't engineering just a collection of acceptable compromises?
            Paul A.
            SE Texas

            And if you look REAL close at an analog signal,
            You will find that it has discrete steps.

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            • #51
              Exactly!



              Originally posted by jim stewart View Post

              sure. But math isn't.

              -js
              Paul A.
              SE Texas

              And if you look REAL close at an analog signal,
              You will find that it has discrete steps.

              Comment


              • #52
                Basically, the simple and quick answer is NO.

                Why? Because 1 + 1 = 2 is the very definition of two. It is defined and therefore not something that is provable. There are fancy mathematical terms for that but this is what they amount to.



                Originally posted by dian View Post
                can somebody tell me if it can be proved that 1+1=2?
                Paul A.
                SE Texas

                And if you look REAL close at an analog signal,
                You will find that it has discrete steps.

                Comment


                • #53
                  As a bit of aside info, all the discussion about "old school" dividing procedures using real dividers... I have a nice old pair of Vierner calipers by Brown and Sharpe that have a feature I had not seen before. There are a pair of tiny punch marks that are used to set dividers to a predetermined measurement. Note the one "pit" and the corresponding on the sliding jaw.

                  Joe B Click image for larger version

Name:	caliper.JPG
Views:	81
Size:	520.0 KB
ID:	1929518

                  Comment


                  • #54
                    Originally posted by Paul Alciatore View Post
                    Basically, the simple and quick answer is NO.
                    Don't mean to be disagreeable but he answer is yes. The Peano axioms and Zermelo-Frankel set theory provide a solid foundation for basic arithmetic. Even if one objects to set theory as a basis for arithmetic foundations, the Peano axioms can also be understood and established by way of category theory.

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                    • #55
                      Originally posted by JoeCB View Post
                      As a bit of aside info, all the discussion about "old school" dividing procedures using real dividers... I have a nice old pair of Vierner calipers by Brown and Sharpe that have a feature I had not seen before. There are a pair of tiny punch marks that are used to set dividers to a predetermined measurement. Note the one "pit" and the corresponding on the sliding jaw.

                      Joe B Click image for larger version  Name:	caliper.JPG Views:	0 Size:	520.0 KB ID:	1929518
                      Those are nice calipers! How old are they?

                      Comment


                      • #56
                        Originally posted by mklotz View Post

                        Here you go...a page from Whitehead and Russel's Principia...

                        https://quod.lib.umich.edu/cgi/t/tex...aat3201.0001.0 01&frm=frameset&view=image&seq=401

                        but be advised, if you're not a professional mathematician and use math more as a tool, your time would be more profitably spent learning some practical math rather than farking about with abstruse, quasi-philosophical stuff like this.
                        sorry, link doesnt work.

                        the peano axioms cant prove anything, beause they are, well, axioms. i think paul is right.

                        explain to me how it can be excluded, that one day you put an apple into a basket, then put in another one and wind up with three apples (or none)? besides, apples (as stargazer explained) have nothing to do with mathemathics.

                        mathematics is a theory that cannot be validated, as actually nothing can be validated. as it cannot be excluded that one day you "drop" a stone and it takes off towards the sky (or e.g. disappears).

                        right?
                        Last edited by dian; 02-21-2021, 05:47 AM.

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                        • #57
                          Originally posted by dian View Post

                          sorry, link doesnt work.

                          the peano axioms cant prove anything, beause they are, well, axioms. i think paul is right.

                          explain to me how it can be excluded, that one day you put an apple into a basket, then put in another one and wind up with three apples (or none)? besides, apples (as stargazer explained) have nothing to do with mathemathics.

                          mathematics is a theory that cannot be validated, as actually nothing can be validated. as it cannot be excluded that one day you "drop" a stone and it takes off towards the sky (or e.g. disappears).

                          right?
                          Here's the link again...

                          https://quod.lib.umich.edu/cgi/t/tex...=image&seq=401



                          Regards, Marv

                          Home Shop Freeware - Tools for People Who Build Things
                          http://www.myvirtualnetwork.com/mklotz

                          Location: LA, CA, USA

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                          • #58
                            thanks, i guess i have to study the quran first.

                            Comment


                            • #59
                              Originally posted by Astronowanabe View Post
                              Sure arithmetic as drilled in school helps expressing ideas to others
                              and gives you a language/vehicle to learn what others have done.
                              But after that math is patterns, and patterns of patterns that just keep going
                              till they are completely divorced from our every day real world but
                              can still be brought back in a way that matters here.
                              Yes Sir, thats what I was trying to say. Math is self solving. If you made a number sequence that wont work you will find it with math. Just go backwards. (oh, then fix it) JR

                              My old yahoo group. Bridgeport Mill Group

                              https://groups.yahoo.com/neo/groups/...port_mill/info

                              Comment


                              • #60
                                Originally posted by dian View Post
                                mathematics is a theory that cannot be validated, as actually nothing can be validated. as it cannot be excluded that one day you "drop" a stone and it takes off towards the sky (or e.g. disappears).

                                right?
                                Well, different studies.

                                There is Theoretical Math and Real Math. Lol Thank god Einstein cant hear me now.

                                Most folks cant delve into the theory part of it. Most can get into the actual numbers of it though. JR
                                My old yahoo group. Bridgeport Mill Group

                                https://groups.yahoo.com/neo/groups/...port_mill/info

                                Comment

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