Where does the bow and arrow come from?

I was wondering about the evolution of ideas and realised that there seems to be no intermediate stages for that simplest of weapons the bow and arrow.

If you have nothing similar to work from building a bow and arrow is quite a complex task.
Does anyone have any thoughts of what were the intermediate stages between man with sticks and string to man with projectile weapon system.

I still can't find a series of logical inventions that create a bow and arrow from other practicle weapons.

Its a simple step from short-spear / throwing arrows. Dutch arrows etc. Increase the power and range by using a bow.

The longbow (english Yew wood) was capable of penetrating plate armour at ~350m.

The bow seems to have been invented in the late Palaeolithic or early Mesolithic. The oldest indication for its use in Europe comes from the Stellmoor in the Ahrensburg valley north of Hamburg, Germany and date from the late Paleolithic Hamburgian culture (9000–8000 BC). The arrows were made of a pine and consisted of a mainshaft and a 15-20 centimetre (6-8 inches) long foreshaft with a flint point.

Mesolithic arrows have been found in England, Germany, Denmark and Sweden. They were often rather long (up to 120 cm [4 ft]) and made of hazel (Corylus avellana), wayfaring tree (Viburnum lantana) and chokecherry (Cornus alba). Some still have flint arrow-heads preserved; others have blunt wooden ends for hunting birds and small game. The ends show traces of fletching, which was fastened on with birch-tar.

Bows and arrows have been present in Egyptian culture since its predynastic origins. The nine bows symbolise the various peoples that had been ruled over by the pharaoh since Egypt was united.

Most Neolithic bows are made of yew. Ötzi the Iceman found in the Ötztaler Alps carried an unfinished yew longbow, with a bowstring of nettle or flax fibre.

In the Levant, arrow-shaft straighteners are known from the Natufian culture, ca. 12.800–10.300 BP) onwards. The Khiamian and PPN A shouldered Khiam-points are most certainly arrowheads.

Native Americans used longbows (especially on the east coast) and flatbows (especially on the west coast), often recurved, made from various hardwood species, such as hickory. Likewise, the Fenno-Ugrian nations in Eurasia have traditionally used ash, maple or elm flatbows. The bow was a late invention in the Americas.

So you are implying that somebody was successfully throwing short spears and one day decided to get some sinew and a bendy stick and put them together in a manner never seen before on the off chance that it would improve his throw by using a technique totally alien to him.

I still can't find a series of logical inventions that create a bow and arrow from other practicle weapons.

That was the only conclusion I could come up with (Post #5)

I am surprised that some think there must have been some in-between steps.

I am surprised that some think there must have been some in-between steps. Occasionally there are people who just invent something totally new. I have no reason to believe that people in the past were less creative than us.