19 Apr 10
2 edits
Originally posted by FreakyKBHDoes it?
Appearing out of man's imaginations necessarily equates with its non-existent status... and, yet, justice exists?
The laws of geometry were brilliantly set out by Euclid and to Kant they appeared to be the one and only way to do this. He pondered how come Euclid was able to discover and describe something that was clearly TRUE and the only possible truth. Was this comparable to Plato's Forms - maybe mathematical truths exist out there (somewhere). (Roger Penrose has given more recent examples to support this type of claim.)
The mad thing is that geometry does describe the world very well. The laws of gravity emerged from Newton's imagination but they describe very accurately when the next eclipse will fall. Still do today.
Yet after Kant, Non-Euclidean Geometry was described in the Nineteenth Century and was necessary to Einstein's Theory of Relativity which also describes very well the behaviour of the cosmos. So there are different grades of validity and different levels of explanatory power and it turns out that what we know is always fallible.
The idea of a God - or many different ideas about gods - emerged from our ancestors' imaginations many times in many forms and for a long time appeared capable of answering our most important questions. As Reason developed, the task of religion was to attempt to reconcile ideas about God with all sorts of other ideas and discoveries that were increasingly difficult to explain away - eventually religion failed. Not everyone seems to know this yet.
The idea of Justice has not always had the same status. In Greek democracy, it became a very important aspiration. Socrates disliked democracy and used rhetorical tricks to discredit this and other aspirations which were not compatible with tyranny. One was his facetious trick of questioning if Justice exists. There is no reason for this to matter, if you think about it, unless you want to discredit the idea. No it does not have existence in the sense that my computer monitor does. Yes it does, in the sense that it describes an aspiration and guides behaviour. Such as the behaviour that gave Socrates a public and fair trial. Well - more fair than Jesus got 500 years later for example.
20 Apr 10
You can't define Pi.
Yes I can - here it is to two decimal places.
Not enough.
Here it is to 20 places.
Still not definite enough.
Here it is to 100 places.
You are using your computer - that suggests you don't really know.
No it suggests the answer is not a neat whole number or fraction.
But if you can't define it, how can I know it exists?
What you can know is that it solves important questions like the radius of a circle and it keeps turning up when required. It's neat.
So it's just a matter of belief then? Why do I have to believe in something you cannot clearly define?
No it's not just a matter of belief. Without Pi you will not calculate correctly. It works.
Well I can't just take your word for it.
Of course not. You can go away and find an alternative and show that it works.
I have an alternative - it's a mystery.
AAAAAAA
20 Apr 10
Originally posted by finneganYou probably didn't realize it, but you unintentionally reinforced the point that you're arguing against.
You can't define Pi.
Yes I can - here it is to two decimal places.
Not enough.
Here it is to 20 places.
Still not definite enough.
Here it is to 100 places.
You are using your computer - that suggests you don't really know.
No it suggests the answer is not a neat whole number or fraction.
But if you can't define it, how can I know it exists?
...[text shortened]... alternative and show that it works.
I have an alternative - it's a mystery.
AAAAAAA
Pi relates to the physical world: things which can be measured. It doesn't 'turn up' when required, it occurs as a matter of fact, a mathematical constant. By equating pi with justice, you are at least inferring that justice shares some of the same attributes, specifically relating to the universality/transcendence of the same.
Pi is a rule, complete with its own formula description. How so justice, exactly?
20 Apr 10
6 edits
Originally posted by FreakyKBHpi does *NOT* relate to the physical world anymore than lim_{n->infinity}(1+1/n)^n relates to the real world. It is a mathematical constant for which it's definition relies *only* an idealised mathematical entity; that being a circle (as opposed to something which looks like a circle until you reach some critical level of magnification). pi is a measure of the ratio of said circles' circumfrence to its diameter.
You probably didn't realize it, but you unintentionally reinforced the point that you're arguing against.
Pi relates to the physical world: things which can be measured. It doesn't 'turn up' when required, it occurs as a matter of fact, a mathematical constant. By equating pi with justice, you are at least inferring that justice shares some of the sam ...[text shortened]... same.
Pi is a rule, complete with its own formula description. How so justice, exactly?
Perfect circles do not exist in nature. Moreover, with creativity or careless-ness, one can claim anything applies to the real world if your argument is valid.
Oh and...what are the rules of pi??? 😕
20 Apr 10
Originally posted by AgergThank you.
pi does *NOT* relate to the physical world anymore than lim_{n->infinity}(1+1/n)^n relates to the real world. It is a mathematical constant for which it's definition relies *only* an idealised mathematical entity; that being a circle (as opposed to something which looks like a circle until you reach some critical level of magnification). pi is a measure ...[text shortened]... he real world[/i] if your argument is valid.
Oh and...what are the rules of pi??? 😕
21 Apr 10
Originally posted by Agergpi does *NOT* relate to the physical world
pi does *NOT* relate to the physical world anymore than lim_{n->infinity}(1+1/n)^n relates to the real world. It is a mathematical constant for which it's definition relies *only* an idealised mathematical entity; that being a circle (as opposed to something which looks like a circle until you reach some critical level of magnification). pi is a measure ...[text shortened]... he real world[/i] if your argument is valid.
Oh and...what are the rules of pi??? 😕
Gee, that's quite an elaborate explanation you have going there. Just out of curiosity, in what realm do we find these circles? How are they measured, if not real--- or at minimum, represented as so?
Oh and...what are the rules of pi???
Here's one...
The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d.
21 Apr 10
2 edits
Originally posted by FreakyKBHpi does *NOT* relate to the physical world
[b]pi does *NOT* relate to the physical world
Gee, that's quite an elaborate explanation you have going there. Just out of curiosity, in what realm do we find these circles? How are they measured, if not real--- or at minimum, represented as so?
Oh and...what are the rules of pi???
Here's one...
The ratio C/d is constant, regar of another circle it will also have twice the circumference C, preserving the ratio C/d.[/b]
Gee, that's quite an elaborate explanation you have going there. Just out of curiosity, in what realm do we find these circles? How are they measured, if not real--- or at minimum, represented as so?
You may think of a circle as being the set of all points in some plane for which each point is equidistant from one point x_0 which we refer to as its centre. The distance between any point x_1 =/= x_0 is the shortest path between the two and (in the Euclidean geometry you're used to) is a straight line called the radius.
True mathematical circles lie in the idealised realm of mathematics. If for illustrative purposes you wish to draw one then you grab a pen and paper and do precisely that (and call it a circle safe in the knowledge that it isn't actually a 'true' circle).
Knowing the positions of 3 distinct points specifies precisely one circle. Also knowing the position of one point on a circle and knowing it's centre also specifies the entire circle (allowing us to 'measure' them).
To reinforce the point I made last, the notion of infinity is pretty ubiquitous in maths and that we can manipulate this entity (not a number) is the reason why you are surrounded by all the wonderful technology you take for granted.. But infinity does not relate to the physical world in any non-contrived sense; nor does pi.
Oh and...what are the rules of pi???
Here's one...
The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d.
A completely trivial rule then. No more a rule than heads are a rule; the rule being that they work best when attached to bodies.
21 Apr 10
Here's one:
The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d.
One more point I forgot to edit in earlier but this 'rule' doesn't even invoke pi in the first place (implicitly or explicitly).
21 Apr 10
Originally posted by AgergYou may think of a circle as being the set of all points in some plane for which each point is equidistant from one point x_0 which we refer to as its centre. The distance between any point x_1 =/= x_0 is the shortest path between the two and (in the Euclidean geometry you're used to) is a straight line called the radius.
pi does *NOT* relate to the physical world
[b]Gee, that's quite an elaborate explanation you have going there. Just out of curiosity, in what realm do we find these circles? How are they measured, if not real--- or at minimum, represented as so?
You may think of a circle as being the set of all points in some plane for which each point is equidi ...[text shortened]... ule than heads are a rule; the rule being that they work best when attached to bodies.[/b]
Um, no. I just think of circles as those round thingies.
True mathematical circles lie in the idealised realm of mathematics. If for illustrative purposes you wish to draw one then you grab a pen and paper and do precisely that (and call it a circle safe in the knowledge that it isn't actually a 'true' circle).
At the core of pi is the idea that no circle found within the universe is perfect. Emphasis on 'within the universe,' because that's where we find all of them. So, we have an idea of a perfect circle, but are ineffectual in our efforts to make one... similar to our shortcomings in the area of justice.
21 Apr 10
Originally posted by AgergOf course it doesn't invoke pi: it's simply stating that the circle's circumference ratio to its diameter is equated with pi, regardless of size. No invoking there.
[b]Here's one:
The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d.
One more point I forgot to edit in earlier but this 'rule' doesn't even invoke pi in the first place (implicitly or explicitly).[/b]
21 Apr 10
1 edit
Originally posted by FreakyKBHUm, no. I just think of circles as those round thingies.
[b]You may think of a circle as being the set of all points in some plane for which each point is equidistant from one point x_0 which we refer to as its centre. The distance between any point x_1 =/= x_0 is the shortest path between the two and (in the Euclidean geometry you're used to) is a straight line called the radius.
Um, no. I just think of ectual in our efforts to make one... similar to our shortcomings in the area of justice.[/b]
That does not surprise me...amusingly however you talk as though we're meant to believe you are in some way informed on these matters. (your 'big' numbers argument in a different thread recently was cringe-worthy!)
At the core of pi is the idea that no circle found within the universe is perfect. Emphasis on 'within the universe,' because that's where we find all of them. So, we have an idea of a perfect circle, but are ineffectual in our efforts to make one... similar to our shortcomings in the area of justice.
From which repository of ignorance are you dredging up this nonsense???
"At the core of pi is the idea that no circle found within the universe is perfect"?!
wtf are you on about? 😕