[Europan Ocean (OP)]

Why did Elephants evolve such big brains? Their brains are bigger than human brains! They can be taught to paint pictures with their trunks. But don't know how to dip their own brush or make paint.

Example video.

In a wildlife conflict with Lions that I watched, the Elephants are not so clever, they lose the baby Elephant but injure the Lions afterwards. But without a history of needing art, they can easily learn it. The work is like child's play.

It made news a few years back, that an Elephant learned to speak a few words, in a South Korean Zoo.

Halfway down the page is a brain size comparison with humans.
http://www.animalcorner.co.uk/wildlife/elephants/elephant_anatomy.html

What does all that Elephant grey matter do? Why is it now they can paint, when in nature they never needed or learnt it?

[CliffordK]

Heck, here in Oregon  you can get your car washed by elephants too, although it is not guaranteed to come out cleaner than when you started.

As far as the painting, the question is how much training the elephant has had.  Are they taught to reproduce a specific shape, or is it their own design?  Of course, they can also do "abstract" art.

The elephant, of course, can wiggle its nose better than humans.  That has to take some extra brain matter.

Part of the answer is that with the larger body mass, there are more muscles, and more sensors. 

In the human, most of the muscles and sensors are mapped to a narrow section between the frontal and parietal cortices.  However, a much larger section of the brain would be required to process that primary sensory and motor information.

Perhaps that would be one of the inefficiencies in nature.  A mouse may choose to move its leg forward activating a certain number of muscle fibers.  An elephant would do the same action and require 1000  times as many muscle fibers and ultimately a nerve bundle that is 1000 times as large.  A robot, on the other hand might send the same command to flex a certain muscle independent of the size of the device. 

The question might be whether the mouse and elephant had an equivalent "control" section.  One could think of it as a tree where one just adds a couple of extra layers to get greater expansion of the command, but that may not be appropriate, and one may need a more widely parallel system, especially if one was to avoid additional neural synaptic delays.

Memory, of course, is helpful for adaptation in the wild including locating food and water. 

[evan_au]

A traditional interpretation was that body area (sensors) increases as the square of mass; body volume (muscles/actuators) increases as the cube of mass. So to compare a "constant intelligence" with size, brain mass would increase as the 0.67 power of body mass.

More recent studies have shown a power of around 0.75, although there are many confounding factors, like predators generally have bigger brains than their herbivore prey of the same size. The crows are very intelligent for their brain size, but a bird has extreme pressure to economise on weight, compared to a land animal or a sea animal.
See: http://en.wikipedia.org/wiki/Brain_size#Comparisons_among_animals

[CliffordK]

A traditional interpretation was that body area (sensors) increases as the square of mass; body volume (muscles/actuators) increases as the cube of mass. So to compare a "constant intelligence" with size, brain mass would increase as the 0.67 power of body mass.

Is that correct?  Mathematically speaking,
Surface area increase with the square of length of side.
Volume increases with the cube of the the length of side.
To a large extent, volume and mass should have close to a 1:1 relationship.

The surface area should increase slower than the mass.

[evan_au]

Sorry, my bad... I should have said Volume increases as the cube of the length (not mass).

[buawangji]

Points to do this, I provide full and do not have to worry about any errors that may be because you're doing great.