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

[Kyrisch]

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

 

This argument is sometimes also presented as "2 + 2 = 5 for large values of two." This doesn't make sense to me whatsoever. Can someone please help?

[gib65]

In what application? In math, like the example of 2 + 2 = 5 that you gave above, I don't know how it could every be true. But take the example of a movie. All you need to make a movie is a collection of moving light bloches on a screen, but the movie is more than just the sum of these ligh bloches; it is a story as well.

[j_p]

2.4 + 2.4 = 4.8

 

Round to one digit.

[Mokele]

I'm not sure if it means something special in math, but in biology, it typically refers to systems with components that interact synergisticly to maximize the effects. The example I'm most familiar with is snake venom; any individual venom protien will have minor (or at least lesser) effects if injected into smeone, but when you combine them, they interact to heighten the lethality tremendously, far greater than you'd get from just injecting any random combination of toxins.

 

Mokele

[Kyrisch]

If I'm not mistaken, that's called emergent properties; I'm talking about math here. I found a forum where mathematicians were arguing whether or not two plus two can actually equal five. I was recently thinking how in the world could this be possible, but I can't find the site I looked at.

[BigMoosie]

I think it means:

 

[math]\lim_{n\to\infty}2n+2n = \lim_{n\to\infty}5n[/math]

[swansont]

What theorem is it? Feynman alludes to this in Surely You're Joking Mr. Feynman but doesn't give the proper name of it, only "So-and-so's theorem of immeasurable measure"

[Kyrisch]

I'm only in Algebra 2, so that stuff up there doesn't make much sense to me, sorry. I'm taking calculus next year.

 

Btw, what does your sig mean, Swansont?

[BobbyJoeCool]

Limits are as a function gets closer and closer to a certain number, the value of the function gets closer and closer to...

 

Most of the time, it's just the value of the function at that point...

 

but with both equations 2n+2n and 5n, as n approches infinity, both equations also aproach infinity. (as each function will get infinatly larger the larger the value on n, so when n finally reaches infinity, both funtions will equil infinity...)

 

so...

 

[math]\lim_{n \to \infty}2n+2n=\infty[/math]

 

[math]\lim_{n \to \infty}5n=\infty[/math]

 

[math]\lim_{n \to \infty}2n+2n=\lim_{n \to \infty}5n[/math]

 

But then again, this is also true as n goes to 0 (since both functions equal 0 at n=0)

[Kyrisch]

But that really proves nothing that has to do with the raw values of 2, 2, and 5.

[BobbyJoeCool]

exactly... but still...

[Kyrisch]

???

[BenSon]

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

 

I wasn't going to bring this up but seeing as someone brought up biology why not? How about the binding energy in the nucleus, the mass defect causes the sum of the individual nucleons to be greater then the nucleus when its bound together. Well thats what we get thaught in highschool anyway.

 

~Scott

[swansont]

Btw, what does your sig mean, Swansont?

 

A little song, a little dance, a little seltzer down your pants

[Kyrisch]

oh sorry, I posted it again on another thread, and then read this now... just kindly ignore the other request thanks.

[BigMoosie]

oh sorry, I posted it again on another thread, and then read this now... just kindly ignore the other request thanks.

 

That is the kind of thing you ask through PM, but never-mind.

 

But that really proves nothing that has to do with the raw values of 2, 2, and 5.

 

I do not know in what context this all is and I have never encoutered it myself, but that 2, 2 and 5 example looks just as that, an example. The original statement had no values in it: "The Sum of the Parts May Be Greater Than the Whole".

[Dave]

but with both equations 2n+2n and 5n, as n approches infinity, both equations also aproach infinity. (as each function will get infinatly larger the larger the value on n, so when n finally reaches infinity, both funtions will equil infinity...)

 

Except for the small point that there is no such thing as n "being" infinity, so neither function can ever attain that value.

[BigMoosie]

Except for the small point that there is no such thing as n "being" infinity, so neither function can ever attain that value[/b'].

 

are you saying infinity is a value not a concept?

[Dave]

I'm obviously not saying that at all.

[cosine]

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?

[Dave]

Yes, but projective 3-space is a lot different to the set of reals in which we're talking about. In that space, parallel lines are allowed to meet at points labelled infinity, and basically makes everything a lot nicer to work with. Or so I've heard at least - I've never really done all that much with hyperbolic geometry.

[Anjruu]

For cosine's question, I think that it is like limits. In theory, it is possible to reach that point, in the same way that certain functions in theory eventually reach their limit, however, it is more philosophical than literal. It is a necessary yet unreal extension of the mathematics in order to give correct results. At least, that's what I have been told by various teachers, but these have only been overviews of hyperbolic geometry, not in depth teachings.

[Tom Mattson]

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

 

Are you talking about the Banach-Tarski paradox?

[Anjruu]

Who, me? Ahehe, nope, I've never even heard of it before.

[matt grime]

Well, what are you talking about? If you can't at least explain what it is you're talking about then no one esle can even begin help. What forum are you referring to where this discussion takes place? Who are the particpants? In what vein is this discussion taking place?