 General History General History Forum  General history questions and discussions 
January 9th, 2017, 12:01 PM

#21  Historian
Joined: Jun 2015 From: Scotland Posts: 1,033  Quote:
Originally Posted by Jackdaw 1888 Pray tell?
WHY?  Because I was hoping for some insights into how human endevour in mathematics had changed and shaped our outlook and existence. Not reference to ancient beliefs of those who couldn't know better at the time. There are plenty threads under religion were the wildest beliefs can be touted to your hearts content.
 
 
January 9th, 2017, 12:03 PM

#22  Citizen
Joined: Dec 2011 From: PyrénéesOrientales, France Posts: 26 
Indeed ..... but in terms of the OP I think you know what I meant. (in response to Kotromanic).

Last edited by Meles meles; January 9th, 2017 at 12:29 PM.

 
January 9th, 2017, 12:05 PM

#23  Historian
Joined: Jun 2015 From: Scotland Posts: 1,033 
Mathematics is not an article of faith! It is a language we use to describe what we see in the Universe that surrounds us. The answers we glean from it can only be wrong, correct or incomplete but are subject to testing the same as any theory.
 
 
January 9th, 2017, 12:07 PM

#24  Historian
Joined: Aug 2013 From: Seattle Posts: 5,501   
 
January 9th, 2017, 12:22 PM

#25  Historian
Joined: Jul 2015 From: Netherlands Posts: 2,451 
Proof of god
I would add Pythagoras triangle formula, Fourier transformation, differential formula, wave equation, i=square of 1, matrices and anything from Euclid and Archimedes.
 
 
January 9th, 2017, 12:31 PM

#26  Historian
Joined: Oct 2012 Posts: 8,545  Quote:
Originally Posted by WITSEND Mathematics is not an article of faith! It is a language we use to describe what we see in the Universe that surrounds us. The answers we glean from it can only be wrong, correct or incomplete but are subject to testing the same as any theory.  Mathematics is not done with testing and experimentation, it's done with proofs. Proofs rely on the axioms and its the consistency of an axiomatic system that cannot be proven. It's interesting that you bring up completeness, because the incompleteness theorem teaches us that an axiomatic system cannot be both complete and consistent, so if we do find our axiomatic system to be complete, we can be confident that it's inconsistent.
And while our understanding of the universe may be dependent on our understanding of mathematics, our understanding of mathematics is not dependent on our understanding of the universe. Mathematics is, perhaps, the only field of human knowledge that if we were to wake up tomorrow and all the universe had ceased to exist, would still be just as valid as it was the day before.
'Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the actual world, but every possible world, must conform.'  Bertrand Russell
 
 
January 9th, 2017, 12:35 PM

#27  Historian
Joined: Oct 2012 Posts: 8,545  Quote:
Originally Posted by Willempie Proof of god
I would add Pythagoras triangle formula, Fourier transformation, differential formula, wave equation, i=square of 1, matrices and anything from Euclid and Archimedes.  If you want a proof of God, try Godel's Ontological Proof:
It relies on modal logic and the relationship between contingent truth and necessary truth. I can attest that it's a valid proof, but I will not speculate on the consistency of the axioms or the the implications. Nor will I pretend that I have fully got my head around modal logic.
 
 
January 9th, 2017, 12:38 PM

#28  Knighterrant
Joined: Oct 2011 From: Lago Maggiore, Italy Posts: 18,106  Quote:
Originally Posted by WITSEND Mathematics is not an article of faith! It is a language we use to describe what we see in the Universe that surrounds us. The answers we glean from it can only be wrong, correct or incomplete but are subject to testing the same as any theory.  Math is a system of rational abstractions ...
* these abstractions are rational for human mind
* the forms of these abstractions are conventions, not natural absolute laws.
For example:
9+1 = 10.
Great ... if you are an individual of a species with two hands and ten fingers with the habit to use a 10 base numeric system [also humans have used different bases, just to say 60, for their numeric systems, so you don't need to be an alien to do that].
The concepts of 10, 100, 1000 ... have got a certain meaning only if you use a 10 base numeric system.
10 ...
What's 10? A group of 10 units ...
Not always.
To be sure of the answer you need an other information: the base of the numerical system, in fact in HEX "10" is 16.
 
 
January 9th, 2017, 12:49 PM

#29  Historian
Joined: Jun 2015 From: Scotland Posts: 1,033  Quote:
Originally Posted by constantine Mathematics is not done with testing and experimentation, it's done with proofs. Proofs rely on the axioms and its the consistency of an axiomatic system that cannot be proven. It's interesting that you bring up completeness, because the incompleteness theorem teaches us that an axiomatic system cannot be both complete and consistent, so if we do find our axiomatic system to be complete, we can be confident that it's inconsistent.
And while our understanding of the universe may be dependent on our understanding of mathematics, our understanding of mathematics is not dependent on our understanding of the universe. Mathematics is, perhaps, the only field of human knowledge that if we were to wake up tomorrow and all the universe had ceased to exist, would still be just as valid as it was the day before.
'Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the actual world, but every possible world, must conform.'  Bertrand Russell  In some circles this is a bit old hat but we are always learning I suppose and my view may well be wrong or incomplete. You could look at it as pure mathematicians prove theorems and applied mathematicians construct theories. While I would suggest one is easy to reconsile with the world we see the other is no less routed in reality. It is our understanding of reality that is insufficient to place some theorems within it or recognise their significance.

Last edited by WITSEND; January 9th, 2017 at 12:52 PM.

 
January 9th, 2017, 12:52 PM

#30  Historian
Joined: Oct 2012 Posts: 8,545  Quote:
Originally Posted by AlpinLuke Math is a system of rational abstractions ...
* these abstractions are rational for human mind
* the forms of these abstractions are conventions, not natural absolute laws.
For example:
9+1 = 10.
Great ... if you are an individual of a species with two hands and ten fingers with the habit to use a 10 base numeric system [also humans have used different bases, just to say 60, for their numeric systems, so you don't need to be an alien to do that].
The concepts of 10, 100, 1000 ... have got a certain meaning only if you use a 10 base numeric system.
10 ...
What's 10? A group of 10 units ...
Not always.
To be sure of the answer you need an other information: the base of the numerical system, in fact in HEX "10" is 16.  Whether you say 9+1=10, 9+1=A, IX+I=X, θ+α=ι, S(9)=10, etc. is really just a matter of convention. The truly profound realization is, to borrow from Peano's axioms, that for any natural number n there exists a number S(n) (the successor of n), which is also a natural number and is distinct from n. And that says something fundamental about the set of the natural numbers.
 
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