What is initial thought and discursive thought I am learning the 8 jhanas. And in the book im reading it states the five factors of possession are opposed of the 5 hindrance. What are initial thought and discursive thought? I can't find a definiton.
Ordinarily, when unrelated to jhana, the words 'vitakka' &amp; 'vicara' simply mean 'thought', 'thinking' &amp; 'thinking about'. For example, MN 19 is about 'two kinds of thinking'; MN 20 is about distracting thoughts &amp;, in MN 44, 'vitakka' &amp; 'vicara' are called the 'verbal conditioner' because they cause speech to occur, as follows: 


  Having first directed one's thoughts and made an evaluation, one then breaks out into speech. That's why directed thought &amp; evaluation are
  verbal fabricators. MN 44
  
  


In the context of jhana, the words 'vitakka' &amp; 'vicara' have a different &amp; special meaning. Here, they do not refer to ordinary verbal thinking but to non-verbal movements of mind that finalise the attainment of &amp; maintain the 1st jhana.

In respect to the attainment of the 1st jhana, 'vitakka &amp; vicara' refer to 'applied &amp; sustained thought', where the mind itself (rather than volitional intention) applies itself to bring to fruition the 1st first jhana. As said, these movements of mind are beyond the scope of ordinary volition.  

Once the 1st jhana comes to be, 'vitakka &amp; vicara' refer to 'directed thought &amp; pondering / exploring / moving about ', where part of the mind itself remains active in examining &amp; responding to its own response to the jhana factors (such as rapture), to ensure the jhana is maintained. 

As stated in SN 48.10, jhana is born from 'letting go' ('vossagga'). Thus, 'vitakka &amp; vicara' ('directed thought &amp; pondering') operate in the 1st jhana to ensure the letting go &amp; thus the jhana factors are maintained. Refer to Ajahn Brahm's explanation, here, about the "wobble".



There are many subtle different explanations of vitakka &amp; vicara in respect to the 1st jhana. For example, the monk Thanissaro has translated with the words 'directed thought &amp; evaluation'; and Buddhadasa had translated (from Thai) with the words 'noting' &amp; 'experiencing' (here) and 'looking at' &amp; 'knowing thoroughly' (here). 

I personally prefer Ajahn Brahm's explanation because the existence of vitakka &amp; vicara in the 1st jhana simply indicate the mind is not completely still, despite its attainment of 'one-pointedness'. 

I also like Jeffrey Brooks summation as "sustained application of a meditation technique" (namely, the now automatic technique of 'letting go' ) but I do not agree with Jeffrey's translation of 'sustained attention' because the mind has 'attention' in every jhana:    


  The correct translation of the Pali terms 'vitakka' and 'vicára,' with respect to the absorptions (jhanas), must be "applied and
  sustained attention" or "sustained application" of a meditation
  technique."
  
  Jeffrey Brooks
  
  


'One-pointedness' refers to the mind becoming unmovingly glued to a mental image ('nimitta'), which has arisen to replace the totally tranquilised breath as the object of meditation. This 'one-pointedness' can be compared to an axle upon which a wheel becomes fixed to. Although the wheel is fixed to the axle and cannot move off the axle, the wheel can still spin around the axle.

Similarly, although the mind is fixed or unmoving due to one-pointedness (which also results in ordinary volition ending), the mind itself can still actively move towards &amp; away from the other factors of jhana. These movements of mind that sustain the meditation are 'vitakka &amp; vicara'. 



In conclusion, understanding what 'vitakka &amp; vicara' are as factors of jhana will not assist in the attainment of jhana because these factors of jhana occur beyond the sphere of ordinary volition, as Ajahn Brahm has explained. 

For example, in the preliminary development leading to jhana, a more primitive 'vitakka &amp; vicara' refers to the volitional activity that keeps 'letting go'; that keeps wilfully non-attaching. But once jhana is reached, ordinary volition falls away and a new 'automatic volition' arises.