He didn't have to be a scientist. I am talking about his influence on the culture. He encouraged the wholesale abandonment of any ideas, science, or anything else that didn't come from Islam. He set the tone and set the culture against open inquiry and scientific pursuit and against cross cultural exchanges of knowledge and inquiry. The resulting culture lasted a long long time, even arguably till this day.
His influence on the culture? What are you talking about

You do realise that Imam al Ghazali went walkabouts for ten years? In that time, he advanced his understanding of his place in the world and came away with knowledge that can only be reached via much contemplation. A spiritual insight into the inner workings of the human condition.
he did not promote his ideas publicly, as he ahad once done. Nope. Instead he wrote it all down in books. In these books, he clarifies that each person on the earth is given a gift, and they are responsible for nurturing it in the right way. For some people, that gift may be mathematics, others - science. So what you say makes no sense to me.
So when you say "he encouraged the wholesale abandonment of any ideas, science, or anything else that didn't come from Islam" I have to correct you with: in Islam, we are taught to be the viceregents of knowledge. To be trustees and keepers of knowledge, to be spokespersons for knowledge, to be those who take knowledge and turn it into wisdom - thru practice. No matter what that knowledge is... be it science, math, geology, history - whatever.
Al Ghazali never promoted that which you claim. I want to know how you came to this opinion. Care to explain please?
That was no dout also part of it. But why didn't it recover? I think that is where the cultural and religious forces came into play, with the economic and demographic having some influence too.
Since the year 1156 - right up to the 14th century - many battles were fought in the middle east between the crusader legions and the Muslims. This, no doubt, impacted the sponsorships of the arts and sciences in Muslim lands, because money had to be thrown into armaments so the Muslims could stay safe from Crusader attacks instead.
Let's not forget that many Muslim regions had to be repaired also, due to Timur the Lames excursions and burning of entire towns and villages, and a city or two aswell.
The Muslims had to salvage what they could. No doubt. So when you say "I think that is where the cultural and religious forces came into play, with the economic and demographic having some influence too." - I have to tell you, you are only partly right. Namely the economic and demographic part... the previous statement is entirely wrong. Cultural and religious forces did not come into play in order to ensure that which you think happened. The only force that had a major influence were the hoardes of Crusaders who basically threw a spanner in the works for Muslims in many more ways than they thought possible...
...But look around you today, and time is witness to what the western civilisation owes Islam. A debt of gratitude for advancing the western civilisation out of the "dark ages" into the revival of the Renaissance - for which, once again, we indebt ourselves to those Muslims who improved upon the works of the earlier Greeks and Romans, so much so, that their inventions became widely accepted due to the sheer craftsmanship and practicality of such inventions...
Scimi