Final answer:
The assertion that second order neurons both cross and do not cross is false. Second order neurons from the dorsal column-medial lemniscal pathway and spinothalamic tract decussate at the medulla and spinal cord, respectively, and their fibers only ascend contralaterally after crossing.
Step-by-step explanation:
The statement that second order neurons ascend both crossed and uncrossed is false. In the somatosensory system, specifically looking at the dorsal column-medial lemniscal pathway and the spinothalamic tract, second order neurons exhibit distinct patterns of crossing over in the central nervous system.
The dorsal column-medial lemniscus pathway involves second order neurons located in the nucleus gracilis and nucleus cuneatus of the medulla, which receive input from the fasciculus gracilis and fasciculus cuneatus, respectively.
These neurons decussate, or cross over, at the level of the medulla and ascend in the brainstem as the medial lemniscus.
In contrast, the spinothalamic tract's second order neurons decussate at the level of the spinal cord before ascending to the brain.
Once decussated, they continue their ascent contralateral to their origin. Therefore, it’s important to note that while both pathways involve a crossing over, they do not maintain both crossed and uncrossed fibers; each second order neuron crosses over to the opposite side.