Originally posted by dian
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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.
(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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Engineering IS a total act of continuous compromise.
Originally posted by nickelcityfab View PostPaul, 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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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 Postcan 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.
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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
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Originally posted by Paul Alciatore View PostBasically, the simple and quick answer is NO.
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Originally posted by JoeCB View PostAs 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
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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, quasiphilosophical stuff like this.
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; 02212021, 05:47 AM.
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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?
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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Originally posted by Astronowanabe View PostSure 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.
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Originally posted by dian View Postmathematics 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?
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
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