"The Sum of the Parts May Be Greater Than the Whole"

[the tree]

The whole being greater than the sum of its parts has meaning and application in pollitics, economics, philosophy, cuisine, theatre, sound design, card-pyramid-making, sporting and warfare tacktics, but not maths.

[matt grime]

Unless they mean something as trivial as

 

the integer part of 2.6 plus in the integer part of 2.6 is less than the integer part of (2.6 plus 2.6)

 

 

but the entire debate is pointless, meaningless and silly unless the OP deigns to tell us what he/she is talking about.

[bob000555]

Its usually just a saying used in business to justify a merger eg “the value of our company merged with theirs is grater then the sum of there individual values” only verry rarly is it ment literally.

[Sepiraph]

Although I'm not sure if this is what the OP had in mine, but I was wondering what mathematics has to say about emergence. To quote from wikipedia:

 

Although the above examples of emergence are often contentious, mathematics provides a rigorous basis for defining and demonstrating emergence. Alex Ryan shows that a Möbius strip has emergent properties (Ryan 2006). The Möbius strip is a one-sided, one-edged surface. Further, a Möbius strip can be constructed from a set of two-sided, three edged, triangular surfaces. Only the complete set of triangles is one-sided and one-edged: any subset does not share these properties. Therefore, the emergent property can be said to emerge precisely when the final piece of the Möbius strip is put in place. An emergent property is a spatially or temporally extended feature – it is coupled to a definite scope, and cannot be found in any component because the components are associated with a narrower scope.

 

Pithily, emergent properties are those that are global, topological: properties of the whole.

 

I wonder if the concept may also arise in area of computing like Complexity Theory, either way I'd really want to see if there is any mathematical paper on this subject.

[akmather]

I'm taking a Transformations & Geometries course right now, where the professor is exploring Euclidean geometry, and then is going to build towards hyperbolic geometry. He eludes frequently to a "point of infinity" in hyperbolic geometry where parallel lines intersect. Can this be thought of as giving something a value of infinity?

 

 

I think a better way of thinking of that (in the context of hyperbolic geometry) is to think of it as "putting a boundary on the universe" (or the plane) But any point on that boundary is a "point at infinity" and so what value are you assigning? There are still "infinitely" many of them!

[the tree]

Thread necromancy -- for when regular users aren't quite befuddled enough.

[grifter]

Is it just me or can we end all this by saying 2 + 2 = 5 for relatively high values of 2

 

e.g.

 

2.4 + 2.4 = 4.8

 

rounding all the above vales to the nearest whole integer gives us

 

2 + 2 = 5

 

everyone happy?

[the tree]

*sigh* 2+2= exactly 5 for extremely high values of two. That is 2*2.4999...=5.

 

Next person to post in this thread is a smelly-poo-head and doesn't deserve maths because they don't realise how boring and rubbish this thread is. Now everyone go away, or you'll all be smelly-poo-heads*.

* yes I'm fucking serious, go discuss something sensible.

[pcollins]

I never understood this concept. What proof backs this up?

 

All you have to do is show a set is not closed under an operation. That is, an operation on some subset T in S produces a set U that contains elements not in S. For example, the set of integers 1 through 10 under addition is not closed under binary addition, the generated set contains values from 2 to 20. Hence, the sum can be greater than the whole in two ways, the size of the generated set is larger and so is the maximum value therein.