Augustus
…
People have been playing around with stuff for thousands of years, with little progress -- and occasionally negative progress -- till true scientific understanding allowed is to abandon trial-and-error and focus our research on predictable results.
Sorry, but that's a complete myth. Trial and error/stochastic tinkering is as important as it ever was. Also, modern science developed at a similar time to the industrial revolution which was probably a more important factor in technological progress (and was driven by the trial and error of 'Gentleman inventors')
As an example of the way things often develop, the steam train is the kind of serendipitous, yet revolutionary invention that is typical of the process.
Trains were not invented by scientists to carry passengers, but by mining engineers to move coal. The first major railway was generally expected to move freight.
The first railway company didn't employ scientists to develop the train, but opened up a competition to the general public with a cash prize, and the winner was Rocket designed by Robert Stephenson.
People were so fascinated by the magnificent machine that won that they clamoured to be allowed to ride on the wagons of the first railway in Northern England. As it was so popular, people started to invest in railway companies which sprung up all over the Western world and its empires and revolutionised society, warfare, etc.
The jet engine wasn't invented by Physicists, but by engineers trying stuff out.
Much of the tech revolution was started by hobbyists and geeks in garages (Apple, Microsoft). The internet out of military comms network. Twitter was supposed to be for small groups of friends to send each other messages.
90% of medicines developed never reach the market, and the ones that do are often found to treat something they were never intended for (viagra is the best known example, but there are many more).
We aren't smart enough for an identify goal -> science -> winning process of invention most of the time.