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Author  Topic: Math: Eternal? If so Who Created It?  
Phat Member Posts: 13680 From: Denver,Colorado USA Joined: Member Rating: 1.1 
I just saw an interesting article from The Huffington Post in 2013.
Is Mathematics Invented or Discovered? by Derek Abbott, â€œThe reasonable ineffectiveness of mathematics,â€ Proceedings of the IEEE, Vol. 101, No. 10, pp. 21472153, 2013. quote: It always amuses me when critics claim that even God had to have an origin... yet these same critics won't say the same thing about math! Go figure... Edited by Phat, : No reason given. Chance as a real force is a myth. It has no basis in reality and no place in scientific inquiry. For science and philosophy to continue to advance in knowledge, chance must be demythologized once and for all. ~RC Sproul "A lie can travel half way around the world while the truth is putting on its shoes." ~Mark Twain " ~"If that's not sufficient for you go soak your head."~Faith You can "get answers" by watching the ducks. That doesn't mean the answers are coming from them.~Ringo Subjectivism may very well undermine Christianity.


PaulK Member Posts: 15916 Joined: Member Rating: 2.4

quote: But how often does that happen, really ? You quote quite a bit of discussion, Iâ€™m sure the subject has come up here  but I donâ€™t remember anyone explicitly refusing to say so without good reason. Donâ€™t you really mean that the subject is rarely discussed because it is of less interest ? (Although I will note that since mathematics is abstract while God is supposedly concrete there is a major difference which may be relevant in some philosophical systems.)


AZPaul3 Member Posts: 4814 From: Phoenix Joined: Member Rating: 4.8

My take.
First, math is both discovered and invented. The relationship between a circle and its circumference is a discovery. The invented part is the formula for determining what the circumference of a circle is; the symbolic language humans invented to manipulate and make use of the relationship we discovered. And then we go and confuse the invention of the language with the invention of the relationship. No we did not invent the circle and its circumference. That naturally occurring relationship has always been there well prior to any human having the capacity to even notice there was a relationship. Though the math we use to work the relationship is invented the math that is the relationship is discovered. Second, we should not be surprised at the power of math to model, even if imperfectly, the natural relationships we find in this universe since we inhabit a highly logical, if imperfect, universe. No outside influence was needed to say the circumference of a circle will be this. It is a natural relationship that is an intrinsic part of the structure. It just took a smart ape to discover the math in it and a smarter one to invent the math to manipulate and make use of it. Edited by AZPaul3, : No reason given. Edited by AZPaul3, : No reason given. Eschew obfuscation. Habituate elucidation.


Sarah Bellum Member Posts: 487 Joined:

Another interesting aspect of mathematics is the way it demonstrates how an extraordinary degree of complexity arises from extremely simple concepts.
Consider, for example, the mathematical concept of a "group", that is, a set with an operation (for example, addition) an identity element (for example, the zero) and a few simple rules (that every element has an inverse, a "negative" element such that if you combine the two you get the identity and other simple principles). Things that can be considered "groups" come in great variety, from the group with two elements {0,1} with the operations 0+0=1 0+1=1 and 1+1=0, to the set of all integers to the set of all permutations of the real numbers. etc. etc. etc. One of the most intriguing is the famous FischerGriess "Monster" group (https://math.berkeley.edu/...whatismonster/whatismonster.pdf http://www.math.s.chibau.ac.jp/~kitazume/monster3.jpg). Such an extraordinary degree of complexity from such simple principles... An important indication of how easy it would be for complex organisms to develop naturally, wouldn't you say?


RAZD Member Posts: 20539 From: the other end of the sidewalk Joined: Member Rating: 2.9 
Welcome to the fray, Sarah Bellum (love the moniker),
If you use [url=https://math.berkeley.edu/...whatismonster/whatismonster.pdf http://www.math.s.chibau.ac.jp/~kitazume/monster3.jpg] FischerGriess "Monster" group[/url] you get: FischerGriess "Monster" group or you can try [img]http://www.math.s.chibau.ac.jp/...monster3.jpg[/img]; to get Enjoy
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caffeine Member Posts: 1760 From: Prague, Czech Republic Joined: Member Rating: 3.5

But I think what the OP might be getting at is that the relationships we're looking at exist only because of how we define the terms. So, we define what a circle is, and can then disCover relationships between it's circumference and area. And we find that these relationships are good approximations to real world objects (only approximations, since a real world circlular object is onlt an approximation to a mathematical circle). But then what about much more esoteric maths? Are quaternions real? You may say their relationships to other mathematical objects are real; and something we discover; but then they only have those relationships because mathematicians defined them into existence by defining the properties of a quaternions. I guess the point is, that we can discover what the logical implications are if we define things to obey certain conditions. And we may find the objects we defined useful for modelling some aspect of the real world. But that does not necessarily mean the real world actually works in any way like the object we've defined  the similarity may break down under certain conditions.


Theodoric Member Posts: 7038 From: Northwest, WI, USA Joined: Member Rating: 2.5

Very nice to see a well though out, well presented first post.
Pull up a chair and hang out for a while. Find your niche but participate in any thread that interests you. There is nowhere on the internet where I have to work so hard to make sure I create a coherent, well thought out, well researched post, as here. The old timers will force you to think hard inside and outside of whatever box you bring to the table. It is all meant to make us all more intelligent, more informed and better people. Facts don't lie or have an agenda. Facts are just facts "God did it" is not an argument. It is an excuse for intellectual laziness. If your viewpoint has merits and facts to back it up why would you have to lie?


Sarah Bellum Member Posts: 487 Joined:

Thanks! I'm happy to find a discussion on mathematics in a creationism/evolution website. From what I've read the topics of evolutionary biology and the Bible have been gone over in great detail (though there's always room for one more!) but not much on math and its interesting philosophical implications (chaos theory, undecidability, nonEuclidean geometry, the Liar Paradox, etc.).


Sarah Bellum Member Posts: 487 Joined: 
Thanks!


Phat Member Posts: 13680 From: Denver,Colorado USA Joined: Member Rating: 1.1 
And I just reread it (that first post) and realized it was addressed to me! I think I must have initially ignored and/or overlooked replying because it went over my head. But I will think about it again. I agree with Theodoric. That was a well thought out post, Sarah.
Chance as a real force is a myth. It has no basis in reality and no place in scientific inquiry. For science and philosophy to continue to advance in knowledge, chance must be demythologized once and for all. ~RC Sproul "A lie can travel half way around the world while the truth is putting on its shoes." ~Mark Twain " ~"If that's not sufficient for you go soak your head."~Faith You can "get answers" by watching the ducks. That doesn't mean the answers are coming from them.~Ringo Subjectivism may very well undermine Christianity.


Son Goku Member Posts: 1153 From: Ireland Joined:

Over the years I've gone back and forth on this, but for a while now I've settled more on a combination of 2 and 3 mostly as a result of reading about Godel's theorem and Quantum Theory. The former tying into the whole area of model theory that shows the ambiguity in what any mathematical statement refers to "ontically" and the latter in recent years looking more and more like it points to a nonmathematically modellable layer of reality.


Sarah Bellum Member Posts: 487 Joined: 
Can you clarify what you mean when you write, "Godel's theorem ... the whole area of model theory that shows the ambiguity in what any mathematical statement refers to "ontically" "


Son Goku Member Posts: 1153 From: Ireland Joined:

Model Theory can basically show you that a single mathematical statement can have several models with completely different properties and a single formal statement can have multiple realisations.
So let's say the statement "The Reals are not countable". This is a provable statement in the ZFC formalisation of mathematics and basically refers to the fact that there isn't a bijection from the Natural numbers to the Reals. However there are several universes of sets that satisfy the ZFC axioms, these are models of the ZFC axioms. In some models of ZFC the statement "Reals are uncountable" is true because in that model the set that obeys the axioms of the Reals genuinely have a higher cardinality than the set that obeys the axioms of the Naturals. In other models the set filling the role of the Reals actually happens to be of the same cardinality as the set that is the Naturals but a bijection between them doesn't exist. So even a simple statement like "The Reals are uncountable", which seems to say something concrete about the Real numbers, is ambiguous because it's not totally fixed what "Reals" or "Uncountable" refer to. It's a purely formal/linguistic statement in ZFC. Edited by Son Goku, : Slight changes


Sarah Bellum Member Posts: 487 Joined: 
But doesn't the set of real numbers have the cardinality of the set of all subsets of the natural numbers, regardless of what model you're working in?


Son Goku Member Posts: 1153 From: Ireland Joined: 
It does. That doesn't change the fact that it might be countable though and thus have the same cardinality from the perspective of a more powerful model.
Basically there are models of the reals no larger than the standard model of the Naturals. So even when the Reals have the cardinality of the power set of the Naturals, it can be because they are genuinely larger than the Naturals or they're the same size but the construction of the Power Set is restricted in some way.



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