|
BlueCoyote
Beyond


Registered: 05/07/04
Posts: 6,697
Loc: Between
Last seen: 3 years, 1 month
|
Re: Knowledge/ truth/ fact [Re: zouden]
#9827552 - 02/19/09 04:30 PM (15 years, 14 days ago) |
|
|
a constant which is not known in all its numbers, but only in its relations, is more an argument for nature's independence from math than for human minds which invented math IMO. 
If I want five apples from a specific tree or taste, would your five apples from different trees still make those five apples for me ? Or what if all these five apples had worms ?
|
Icelander
The Minstrel in the Gallery



Registered: 03/15/05
Posts: 95,368
Loc: underbelly
|
Re: Knowledge/ truth/ fact [Re: zouden]
#9827585 - 02/19/09 04:36 PM (15 years, 14 days ago) |
|
|
Quote:
zouden said: But some things are never false. If I have five apples, then I have five apples. That is undeniably true. Maths, I believe, is just an extension of that. It is undeniably true that the ratio of a circle's circumference to its diameter is π.
I would need to see a pic of the five apples. I'm certainly not going to take your word for it. This being the Shroomery and all.
-------------------- "Don't believe everything you think". -Anom. " All that lives was born to die"-Anom. With much wisdom comes much sorrow, The more knowledge, the more grief. Ecclesiastes circa 350 BC
|
lIllIIIllIlIIlIlIIllIllIIl
Stranger

Registered: 12/16/04
Posts: 11,123
Loc: Texas
|
Re: Knowledge/ truth/ fact [Re: zouden]
#9828352 - 02/19/09 06:15 PM (15 years, 14 days ago) |
|
|
Quote:
zouden said: But some things are never false. If I have five apples, then I have five apples. That is undeniably true. Maths, I believe, is just an extension of that. It is undeniably true that the ratio of a circle's circumference to its diameter is π.
That's not exactly true zouden... it depends on the rules you agree to beforehand. The idea of 5 apples is not mathematical necessarily, it is just an idea.
I think what you are saying is that if you calculate 1+1+1+1+1 the result is 5 no matter what. That is not the case.
All mathematical calculation hinges on certain, widely accepted, axioms, which can't be proven. These axioms are the assumptions that allow the addition of 5 individual units to equal the total of 5, but it only works out that way within the framework of that axiomatic system.
I have a feeling I've posted this before...
|
zouden
Neuroscientist



Registered: 11/12/07
Posts: 7,091
Loc: Australia
Last seen: 14 years, 4 months
|
|
What other axiomatic system is there where 1+1+1+1+1 doesn't equal 5?
Edit: wait, I see what you're getting at. But I'm pretty sure the Incompleteness Theorems don't apply to all cases, such as arithmetic - they are too trivial. But I'm by no means an expert on this sort of thing!
Edited by zouden (02/20/09 01:11 AM)
|
lIllIIIllIlIIlIlIIllIllIIl
Stranger

Registered: 12/16/04
Posts: 11,123
Loc: Texas
|
Re: Knowledge/ truth/ fact [Re: zouden]
#9831143 - 02/20/09 01:09 AM (15 years, 14 days ago) |
|
|
I dunno offhand, but they do exist.
I know for example there are some where 1+1=1-1 that is used for checksum calculations.
The trouble is I read most of this shit a few years ago and all my books are packed up, so it's hard for me to find specific info.
|
catboosh
©Ω§M¡K F€L1N∑



Registered: 09/26/06
Posts: 860
Loc: Humboldt, California
|
|
reality is for those who cannot handle imaginary numbers
--------------------
"Reality is a juxtaposition of beauty and bullshit, sometimes you gotta wade through the bullshit to see the beauty, and the other times the beauty you see is just full of shit."
|
catboosh
©Ω§M¡K F€L1N∑



Registered: 09/26/06
Posts: 860
Loc: Humboldt, California
|
Re: Knowledge/ truth/ fact [Re: catboosh]
#9831432 - 02/20/09 02:21 AM (15 years, 14 days ago) |
|
|
square root of -1!!!!
--------------------
"Reality is a juxtaposition of beauty and bullshit, sometimes you gotta wade through the bullshit to see the beauty, and the other times the beauty you see is just full of shit."
|
Ratci
Esper<3



Registered: 08/27/08
Posts: 1,039
Loc: Coumbia MD
Last seen: 11 years, 1 month
|
Re: Knowledge/ truth/ fact [Re: zouden]
#9836612 - 02/21/09 12:32 AM (15 years, 13 days ago) |
|
|
Quote:
zouden said: And yet, mathematics lets us predict the orbits of the planets and solar eclipses. So if it is just something that we made up, we did a pretty damn good job of it!
I maintain that an alien race would have still have mathematics identical to ours. There's really only one way to do it.
There could exist an alien race who were so different they didn't perceive apples as seperate entities from the rest of the world. XD
-------------------- People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion. --Albert Einstein
|
Noteworthy
Sophyphile


Registered: 10/05/08
Posts: 5,599
Last seen: 11 years, 1 month
|
Re: Knowledge/ truth/ fact [Re: zouden]
#9837859 - 02/21/09 10:24 AM (15 years, 12 days ago) |
|
|
Quote:
zouden said: And yet, mathematics lets us predict the orbits of the planets and solar eclipses. So if it is just something that we made up, we did a pretty damn good job of it!
Hell YEs!
Quote:
zouden said: But some things are never false. If I have five apples, then I have five apples. That is undeniably true. Maths, I believe, is just an extension of that. It is undeniably true that the ratio of a circle's circumference to its diameter is π.
Think about it this way - circles do not exist in reality
Even though it is undeniably true that a circles circumference to diameter is pi, this is because the notion of 'circle' (which cannot be found in reality, despite being a fundamental idea in our consciousness) implies a relation traced around a locus at a consistent distance, and it is this notion that leads to the certainty of C=2*pi*r
--------------------

|
Noteworthy
Sophyphile


Registered: 10/05/08
Posts: 5,599
Last seen: 11 years, 1 month
|
|
Quote:
adjust said:
Quote:
zouden said: But some things are never false. If I have five apples, then I have five apples. That is undeniably true. Maths, I believe, is just an extension of that. It is undeniably true that the ratio of a circle's circumference to its diameter is π.
That's not exactly true zouden... it depends on the rules you agree to beforehand. The idea of 5 apples is not mathematical necessarily, it is just an idea.
I think what you are saying is that if you calculate 1+1+1+1+1 the result is 5 no matter what. That is not the case.
All mathematical calculation hinges on certain, widely accepted, axioms, which can't be proven. These axioms are the assumptions that allow the addition of 5 individual units to equal the total of 5, but it only works out that way within the framework of that axiomatic system.
I have a feeling I've posted this before...
I honestly think that 1 + 1 + 1 + 1 + 1 will always = 5, unless you said that the symbols meant something else.
5 is defined as 1 + 1 + 1 + 1 + 1
2 is defined as 1 + 1
3 is defined as 1 + 1 + 1
3 + 2 would be defined as (1 + 1 + 1) + (1 + 1)
which is the same definition as 5
addition is definetely always true as we know it
the question is whether maths is incorporated in the universe or whether maths merely arises due to idiosyncracies of the human brain
--------------------

|
lIllIIIllIlIIlIlIIllIllIIl
Stranger

Registered: 12/16/04
Posts: 11,123
Loc: Texas
|
Re: Knowledge/ truth/ fact [Re: Noteworthy]
#9839565 - 02/21/09 03:16 PM (15 years, 12 days ago) |
|
|
It's not that different an idea as when mathematicians began to question euclidean geometry. It had always been assumed, for example, that the sum of the three interior angles of a triangle equals to 180 degrees. You can understand why people made this assumption because it seems self evident if you simply draw a triangle on a flat surface and measure the angles. So for a long time that was good enough and no rigorous proof was required.
There is nothing to stop you from assuming that the sum of the angles of a triangle does not equal 180 degrees. In fact you can make triangles where the sum of interior angles equals 185 degrees, but at the same time you are no longer in the realm of euclidean geometry. It is still geometry nonetheless.
Similarly there is nothing to stop you from assuming that addition is not commutative and then to create a set of numbers to satisfy that.
The main problem is in nature we see that "addition" is both associative and commutative. If you think of addition as if you are combining two sets (perhaps not even sets of numbers) you can see how adding them however you like you end up with the same result. If you have two pockets of coins and you combine them into one pocket, it does not matter if you did it all at once, you transfered one coin at a time or whatever method you used. You still end up with the same number of coins in one pocket.
That does not mean that the commutative and associative properties of addition always hold true. They hold true because they are self evident in our experience and so we created sets of numbers such as integers and real numbers to satisfy what we see in our day to day experience.
|
BlueCoyote
Beyond


Registered: 05/07/04
Posts: 6,697
Loc: Between
Last seen: 3 years, 1 month
|
|
They only hold true because we assume there are things which are 'equal'.
|
zouden
Neuroscientist



Registered: 11/12/07
Posts: 7,091
Loc: Australia
Last seen: 14 years, 4 months
|
|
Quote:
adjust said: It's not that different an idea as when mathematicians began to question euclidean geometry. It had always been assumed, for example, that the sum of the three interior angles of a triangle equals to 180 degrees. You can understand why people made this assumption because it seems self evident if you simply draw a triangle on a flat surface and measure the angles. So for a long time that was good enough and no rigorous proof was required.
Rigorous proof is still not required, because you can just specify if you're in Euclidean space or not. You can just add a clause to make things more clear, if you like: "The angle sum of a triangle in Euclidean space is 180 degrees" - still correct.
Aliens would also have a concept of Euclidean and non-Euclidean space. If it's drawn on a flat surface (or represented in 2D flat space) then it's Euclidean. That may not be the default way of thinking for an alien race, but they would still understand it.
What I'm saying is, the existence of different types of geometry space does not make mathematics any less certain.
-------------------- I know... that just the smallest part of the world belongs to me You know... I'm not a blind man but truth is the hardest thing to see
|
daytripper23
?


Registered: 06/22/05
Posts: 3,595
Loc:
|
Re: Knowledge/ truth/ fact [Re: zouden]
#9841073 - 02/21/09 08:13 PM (15 years, 12 days ago) |
|
|
I have a question while you guys are on the topic.
Take the basic example of non-euclidean geometry; the paper that is wrapped around, flipped once, and taped back together to create this matrix. Know what I am talking about?
Anyways, it seems to me that this is just a model in 3 ordinary, euclidean dimensions. I mean, thats how I think of it I guess.
So my question is, is there such thing as an intuitive version of non-euclidean geometry? That is, the brain doesn't have to process a model; where in a matter of speaking, the mind itself is the model?
Or would you say you have to process a model every time, no matter how used to it you get. Maybe thats even the case with euclidean geometry...
|
Noteworthy
Sophyphile


Registered: 10/05/08
Posts: 5,599
Last seen: 11 years, 1 month
|
|
good point, daytripper.
I dont know how any of you are gonna try and make a triangle with 185 degrees, without redefining triangle.
Even though the ancients knew triangles added up to 180 degrees before they proved it was true, the fact was that it IS true, and they later found this out. According to the definition of line and angle etc etc, all 'triangles' will always have 180 degrees all up (ie, the angle of a straight line to a vertex lying on that line).
Maths will always be true, to any observer capable of understanding maths.
Triangles will always have 180 degrees for any observer capable of conceptualising a triangle and thus perceiving it in the first place as something with angles that could somehow add up to eachother.
And as for euclidean space.. it is the way that our brain processes space. You cannot really escape it except with abstract notions that cant be properly visualised.
euclidean space is not just 2dimensional.. it is 2 dimensional, 3 dimensional.. any dimensional. though, only 3 are within our brains euclidean abilities.
if an alien race perceived space in ways otehr than euclidean... then they probably would not find euclidean geometry to hold true.
unfortunately, no person can imagine how they would be perceiving the world and so we cant really hypothesise how aliens would perceive the world and thus we cant test the above assersion.
--------------------

|
DieCommie

Registered: 12/11/03
Posts: 29,258
|
Re: Knowledge/ truth/ fact [Re: zouden]
#9842302 - 02/22/09 01:09 AM (15 years, 12 days ago) |
|
|
And yet, mathematics lets us predict the orbits of the planets and solar eclipses. So if it is just something that we made up, we did a pretty damn good job of it!
Yea, we did make it up and it does do a great job. Lots of things we made up do damn good jobs: levers, wheels, computers, spoken language.
I maintain that an alien race would have still have mathematics identical to ours. There's really only one way to do it.
I agree. An invention that is useful here would likely be useful elsewhere as well. That doesn't mean its not an invention. Im sure those aliens would also have levers, wheels, computers and maybe a spoken language.
Im not exactly sure what your asserting zouden, some type of inherent existence of math outside of an axiomatic construct? Sounds a bit metaphysical to me.. Math is just a model that can be formed in any way we wish. Yes, 1+1 could be other than 2 under different axioms (consider for simplicity that the number line is the axiom, as it is for most people - you could arrange the numbers in any pattern you like with operators that do a number of 'odd' things). But most of the possible set of axioms are not useful, and that is why they are not studied! For the same reason we dont invent a lever that requires more force, or a wheel that is harder to roll we also dont invent mathematics that poorly model nature. (Although, pure mathematicians do it for fun all the time - with out regard to nature at all.)
|
lIllIIIllIlIIlIlIIllIllIIl
Stranger

Registered: 12/16/04
Posts: 11,123
Loc: Texas
|
Re: Knowledge/ truth/ fact [Re: Noteworthy]
#9842341 - 02/22/09 01:32 AM (15 years, 12 days ago) |
|
|
Quote:
Noteworthy said: good point, daytripper.
I dont know how any of you are gonna try and make a triangle with 185 degrees, without redefining triangle.
If you don't know how to do it, you should learn how to instead of saying it is impossible.
|
Lakefingers

Registered: 08/26/05
Posts: 6,440
Loc: mumuland
|
|
how do you check to see if math is true? absolutely correct is more the ultimate value for mathematics true is for ontology, correct for metaphysics/epistemology
|
lIllIIIllIlIIlIlIIllIllIIl
Stranger

Registered: 12/16/04
Posts: 11,123
Loc: Texas
|
Re: Knowledge/ truth/ fact [Re: Lakefingers]
#9842419 - 02/22/09 02:35 AM (15 years, 12 days ago) |
|
|
You make it true by assuming a bunch of shit which is unprovable.
|
Lakefingers

Registered: 08/26/05
Posts: 6,440
Loc: mumuland
|
|
math is such a cool dictator
|
|