thpthial wrote:I think part of the problem is mixing pure maths and applied maths.
in an effort to get back on track, here is an example of what i mean.
so we have a right angled triangle (wait before you jump in with there is no triangle)
label the three sides a,b,c (c = the hypotenuse)
a = 1
b = 1
c = ?
can anyone tell me the exact decimal number? This is a problem with the decimal system, not a problem with the reality of the number.
now for the people who say there is no triangle, that maybe the case that i cannot draw one. however it is not the case that if i was to have a cube of quartz crystal that was 2cm / 2cm/ 2cm whilst this might not be a perfect cube, it will contain a number of _perfect_ 1cm/1cm/? triangles
i personally believe it does.
I am using 2d objects as the example because it is easier to visualise and realise. i understand the difference between what i am calling a triangle and a euclidean triangle, however this does not change the algebra and problem with the decimal system. there is a much more complex example i can give with spheres that shows this.
the problem is not the number cannot exits, just it cannot be represented in the decimal system. why it cannot be represented is the subject of much speculation.
word,
thp.
and yes a tree does make a noise if it falls in the woods if nobody is there to observe it
I think this example shows that maths isn't reality itself but merely a language to express reality. Any language has it's imperfections, there are always things that cannot be perfectly expressed in it.
Your comment about the tree is valid, but it doesn't aply to my statement that mathematic's is limited by physical boundaries it cannot know itself. The tree makes a noise, even if there's nobody to observe it, because it exists within the real world.
Maths depends on concepts instead of trees. If there cannot be something like a perfect circle or cube, any statement like "a perfect circle may not exist in the real world, but if it did, you would be able to say X about it" is invalid like a statement "if p then Q and Q equals R and not R and there is P", because you essentially say: " Something like X could by definition never realy exist, but if it would exist, then it would be like Y "
If pi doesn't depend on measuring real circles, then it isn't a formula for real circles but an aproximate formula of a circle or rather even a formula that represents the truth about circles without being the truth about circles itself.
Meaning that if you draw real circles based on pi, you'd have to violate pi at some point because you work with pixels instead of a fluid line, if you measure circumferences of circles you'll end up with a different answer each time (if you measure exact enough), and thus that the formula can never be accurately represented by any geometric object, not even by an imaginary geometric object.
But the decimal problem shows the same thing, because the amount of decimals of a number like pi is also limited by what theoretically could be calculated. Meaning that the decimal system in the end is like the western equal tempered tone-system, a compromis of wich it's value depends on margins.