We introduce an innovative technique that quantifies human expertise development in such a way that humans and artificial systems can be directly compared. Using this technique we are able to highlight certain fundamental difficulties associated with the learning of a complex task that humans are still exceptionally better at than their computer counterparts. We demonstrate that expertise goes through significant developmental transitions that have previously been predicted but never explicated. The first signals the onset of a steady increase in global awareness that begins surprisingly late in expertise acquisition. The second transition, reached by only a very few experts in the world, shows a major reorganisation of global contextual knowledge resulting in a relatively minor gain in skill. We are able to show that these empirical findings have consequences for our understanding of the way in which expertise acquisition may be modelled by learning in artificial intelligence systems. This point is emphasised with a novel theoretical result showing explicitly how our findings imply a non-trivial hurdle for learning for suitably complex tasks.