Why does the left hemisphere control the right and the right hemisphere control the left? I googled it but didn't find a good answer regarding this. Could someone explain? Does this adaptation help in the speed of transmission of nerve impulses?
Just to get the ball rolling here. This particular aspect of brain evolution is very old. The cross wiring of the hemispheres of the brain seems to be as old as the right and left hemispheres itself. It predates lizards - i.e. hundreds of millions of years ago. It possibly predates right/left dominance and the organ asymmetry which puts the heart on the left side of the body.
Digging back deeper, we can see that worms have bilateral brain structure, but as noted in the comments below, the nervous systems do not cross. I would guess that this means that the phenomenon appears sometime before lizards - putting the development having been done by the early Carboniferous period when the first animals came to the land and the first reptiles appears, which is the perhaps 350 million years ago.
Echinoderms (like starfish) are 'missing links' in bilateral symmetry as their larval stage has bilateral symmetry even though the adult has radial symmetry. Such wiring may be so embedded in the way most animal body plans develop that it hasn't changed in evolutionary history. If that is related to other animals trait, it could be a billion years ago. Some argue this is not the case.
One might guess that the cross over of neurons in brain control is good for integrating the signals from both sides of the organism. There are quite a few theories.
When I was in school it was discussed as an evolutionary survival advantage... If you are attacked from the right side, the left side of the brain is less likely to be damaged and can use the right sided limbs to fend off the attack as opposed to the right side being damaged and less responsive..
There's a good answer to this on https://www.quora.com/Why-does-our-left-hemisphere-of-brain-control-our-right-side-of-our-body-and-the-right-our-left.
In summary, a biopsychologist states that vertebrates and invertebrates have the digestive system and the nervous system in reverse locations. He also points out that the hearts are in the dorsal area for invertebrates and in the ventral area of an invertebrates. The evolutionary theory of these observations is that the body of an early vertebrate must have been turned upside down, and the easiest explanation is that a vertebrate ancestor swiveled its head 180°. In conclusion, it's believed that one vertebrate had its head turned around and that contralateral arrangement was conserved because it decreased chance of error in nervous system wiring (compared vs simpler same-sided wiring schemes).
Being a keen student of game theory and behavioural sciences one reason that comes to my mind is for the opposite wiring of brain hemispheres might be that
if right hemisphere controlled the right side and left hemisphere controlled the left side than cross hemisphere links and activity would be hard to achieve so the most efficient way of increasing cross hemisphere communication, links and activity with the least stress on physical resources is the opposite hemisphere wiring.
The second view that also compliments this cross arrangement might be the underlying law of increase in complexity and entropy (second law of thermodynamics), which is embedded in the universe from its births, dictates an increase in complexity hence cross wiring also achieves this underlying goal of increasing complexity because if you think about it straight wiring would have been too simple for such a complex structure as the brain.
It is simple. The brain through evolution split into two hemispheres when binocular vision was evolving. If you follow the neurons from the eye, the lateral neurons travel to the ipsilateral hemisphere. The medial neurons cross to the contralateral hemisphere. I would bet the protopathic pathways were around in evolutionary terms before binocular vision and the epicritic pathways developed after binary vision. Vision drove the hemispheres into two compartments. I could draw the diagram but unable to do so on this response
It's for control, coordination and balance. From a mathematical point of view, parallel lines won't intersect and thus line A won't affect line B unless they intersect and thus would hardly influence the other unless and an external force is applied to any of the lines.
This is also why corpus callosum connects the left and the right side of the brain.