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AstroGeek
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20 Oct 2011, 2:05 pm

I tend to think that there were certain premises we used to set up math (a number system of some sort, definitions of the most basic operations etc.) and from that everything else follows logically. So we invented a system without really understanding it. Since then we've been trying to discover all of the details of what we created.

I think that if we ever come in contact with some sort of extraterrestrial intelligence that it would be fascinating to compare our math systems (I am assuming that if they have any form of technology beyond flint blades that it would require some math and that barring interstellar travel, the ones we'd talk to would all need some sort of high technology). What premises and notations would they have used. By premises I'm referring to a number system and basic operations again. What notations have they used. By using different ones have they been able to see things that are either difficult or impossible to discover using our math system? If so not, then that would imply that there are some universal aspects of mathematics.

As for the math/physics debate: true, physicists do need a qualitative understanding of what they're doing. But the basic job of physics is to represent physical phenomenon on mathematical form. The qualitative understanding that a physicist needs is, to a large extent, their ability to see the relationship between math and physical phenomenon.



LostUndergrad9090
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20 Oct 2011, 2:13 pm

hi



Last edited by LostUndergrad9090 on 24 Oct 2011, 1:18 am, edited 2 times in total.

ruveyn
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20 Oct 2011, 3:52 pm

AstroGeek wrote:

I think that if we ever come in contact with some sort of extraterrestrial intelligence that it would be fascinating to compare our math systems (I am assuming that if they have any form of technology beyond flint blades that it would require some math and that barring interstellar travel, the ones we'd talk to would all need some sort of high technology). What premises and notations would they have used. By premises I'm referring to a number system and basic operations again. What notations have they used. By using different ones have they been able to see things that are either difficult or impossible to discover using our math system? If so not, then that would imply that there are some universal aspects of mathematics.



I am sure the law of non-contradiction would be universal.

ruveyn



AstroGeek
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20 Oct 2011, 9:32 pm

ruveyn wrote:
AstroGeek wrote:

I think that if we ever come in contact with some sort of extraterrestrial intelligence that it would be fascinating to compare our math systems (I am assuming that if they have any form of technology beyond flint blades that it would require some math and that barring interstellar travel, the ones we'd talk to would all need some sort of high technology). What premises and notations would they have used. By premises I'm referring to a number system and basic operations again. What notations have they used. By using different ones have they been able to see things that are either difficult or impossible to discover using our math system? If so not, then that would imply that there are some universal aspects of mathematics.



I am sure the law of non-contradiction would be universal.

ruveyn

But isn't that a premise? An absolutely necessary one, if what you're doing is to make any sense at all, but a premise nonetheless?



Ancalagon
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22 Oct 2011, 1:35 am

AstroGeek wrote:
ruveyn wrote:
I am sure the law of non-contradiction would be universal.

ruveyn

But isn't that a premise? An absolutely necessary one, if what you're doing is to make any sense at all, but a premise nonetheless?

If you assume the law of non-contradiction is invalid, then the law of non-contradiction is valid. So no.


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ruveyn
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22 Oct 2011, 3:24 am

Ancalagon wrote:
AstroGeek wrote:
ruveyn wrote:
I am sure the law of non-contradiction would be universal.

ruveyn

But isn't that a premise? An absolutely necessary one, if what you're doing is to make any sense at all, but a premise nonetheless?

If you assume the law of non-contradiction is invalid, then the law of non-contradiction is valid. So no.


If the law of non-contradiction did not hold, then any formula you right down is true. Ex falsi quodlibet. From a contradiction anything follows. In that case mathematics would be useless because 1 + 1 would equal and not equal 2.

ruveyn



IDontGetIt
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22 Oct 2011, 3:39 am

Mathematics simply "is". It exists. It is not a human invention. Humans discovered that there was such a thing as maths, but did not invent it. Any advanced civilisations elsewhere in the universe (for the sake of this topic lets assume they exist, take any arguments to another thread please) would also have discovered maths. They would not call it maths of course, and they would use a different collection of symbols to represent it, but they would understand it.
Maths has clear distinctions between correct and incorrect. It is a bull**** free zone.



Burzum
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22 Oct 2011, 8:58 am

Would our understanding of math still make sense in another universe?



ruveyn
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22 Oct 2011, 9:07 am

Burzum wrote:
Would our understanding of math still make sense in another universe?


What does "make sense" mean. Does it mean the math corresponds to a reality external to our minds? Or does it mean the math has an internal structure and consistency that makes sense in and of itself?

ruveyn



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22 Oct 2011, 3:28 pm

I was watching a history channel special on math and they claimed the Mayans where the ones to first use math and that they did in fact invent math.



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22 Oct 2011, 8:07 pm

Math, like beer, is proof that God loves us and wants us to be happy.

Discoveries can be reduced to math proving something, yet math rarely leads to discoveries.

Math is how we check our thoughts for errors.

Thought verification process, where thought comes first.



ruveyn
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22 Oct 2011, 11:20 pm

Inventor wrote:
Math, like beer, is proof that God loves us and wants us to be happy.

Discoveries can be reduced to math proving something, yet math rarely leads to discoveries.

.


Rarely but importantly.

Dirac "discovered" anti-matter because he found solutions to his equation (called now the Dirac Equation). See http://en.wikipedia.org/wiki/Dirac_equation

Maxwell postulated the displacement current because of mathematical considerations. From his modification of Amperes equation we get waves propagating through space. Voila! Light and other electromagnetic radiation.

Einstein was led to the General Theory of Relativity by way of Reimannian Tensors.

And so it goes.

ruveyn



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23 Oct 2011, 1:45 am

ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


If mathematics is purely deductive, why does all of it depend on induction?
Counting is empirical, and physics was around long before mathematics.

Tadzio



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23 Oct 2011, 3:59 am

ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


It's the language of nature.



ruveyn
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23 Oct 2011, 6:59 am

cw10 wrote:
ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


It's the language of nature.


Nature is not sentient. Why should Nature have a language? Most of the Cosmos is devoid of consciousness.

ruveyn



AstroGeek
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23 Oct 2011, 10:11 am

ruveyn wrote:
cw10 wrote:
ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


It's the language of nature.


Nature is not sentient. Why should Nature have a language? Most of the Cosmos is devoid of consciousness.

ruveyn

1) This brings to mind Carl Sagan's idea that through us the universe has developed a way to understand itself. Quite a beautiful thought...
2) I think this is meant metaphorically. Mathematics is the language of nature insofar as it can be used to express what happens in nature.

Also, to reply to an earlier post, physics, as in the systematic study of the universe, really was not around before mathematics. The first real physicist in the modern sense was Galileo, but I suppose you could point to some of the ancients such as Ptolemy as trying to do theoretical physics. All used math.