The left brain is a dopamine-oriented world unto itself. Dopamine is a molecule that works in conjunction with the several types of dopamine receptor cells that respond to nearby emissions of what else---dopamine. The number of dopamine receptors in the left brain is higher than the right brain, and this imbalance is enhanced during puberty, particularly in males. Dopamine is a key neurotransmitter, and facilitates the functionality of fine motor skills, language, arithmetic, and monosemantic processing.
By monosemantic, we mean the "single-mindedness", or single meaning of a particular memory or stimulus. For example, let's take the word "God". In the left hemisphere, the concept of "God" is monosemantic, and is whatever the left brain has been conditioned to mean. To the left brain, "God" maybe Jesus Christ, Allah, Yahweh, or some other unambiguous concept. In contrast, the right hemisphere tends to be polysemantic or ambiguous, and tends to process many different meanings of "God" and searches for links between its meanings of "God" and hitherto unrelated stimuli. To the right hemisphere, "God" is much more ambiguous.
The monosemantic nature of the left brain is consistent with its syntactical and arithmetical functionality. Broca's area, or the language processing center of the brain, is a complex of nerve cells that structure a thought into a syntactically correct sentence. Broca's area is predominantly in the left hemisphere, even for left-handed people. The scattered and polysemantic thinking of the right brain is not very good at producing language or arithmetic. To the left brain, 2+2=4. To the right brain, maybe it is 4, maybe not. The right brain will eagerly search for scenarios in which 2+2 does not equal 4, and might be disappointed when it doesn't find any.
The right brain is a norepinephrine-oriented world, and as such, has certain advantages over its rigid next door neighbor. Norepinephrine is another neurotransmitter, not too unlike dopamine. Both act as stimulants to the nervous system. Norepinephrine receptors are very responsive to the external environment. The norepinephine receptors facilitate selective attention, and are very sensitive to unusual stimuli. In new environments, the right brain's norepinephrine system is running wild, making connections and analyzing multiple potential meanings in the flood of new stimuli. The left brain is in a bit of trouble here, as its structured dopamine-fueled approach can't perform as comprehensive analysis or relate information as well as the right brain can.
The left-brain seeks to avoid internal contradictions in its analysis of the environment. It tends to limit the analytical result to a set of predetermined outcomes that are consistent with its conditioning. This thinking approach works well in stable and non-threatening environments. The left-brain tends to bend reality to fit the way it wants to process it. There is a certain expectation that the left-brain has of reality, and pre-determinism in responding to the environmental clues is its natural operating mode. Time-orientation is a natural outcome of the left-brain's propensity for pre-determinism.
In contrast, the right brain has a lower propensity for pre-determinism, and is not as inclined to drive the information analysis to a particular outcome.
It also provides a varied neural network framework for connecting information together, and exhibits less linear information retrieval processing than the left brain. Its thinking approach promotes information connectivity and polysemantics. However, it can lead to more ambiguous and complex outcomes.