Backing for soul number that’s irrational and ridiculous (6)
I believe the answer is:
absurd
'ridiculous' is the definition.
(synonyms)
'backing for soul number that's irrational' is the wordplay.
'backing for' is a reversal indicator.
'soul number' becomes 'ba' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'that's irrational' becomes 'surd' (I've seen this before).
'ba' backwards is 'ab'.
'ab'+'surd'='ABSURD'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for absurd that I've seen before include "Really ridiculous, silly" , "'Derisory, cockeyed (6)'" , "word to describe Beckett's theatre!" , "Wildly illogical" , "Arousing derision" .)