If it's such a "creationist mistake", please explain:
How can we, then, get inteliigence from a process that's absent of it? This is basically the crux of my inquiry, gentlemen.
1. The body structure of unicellular organisms involve chemical reactions instigated by various external stimuli.
2. As multicellular organisms evolve, some cells become specialized at converting external stimuli into chemical reactions. These eventually evolve into nerve cells.
3. Some multicellular organisms develop interconnections between nerve cells, as the improve coordination between body structures improves survival in their niche. This evolves into the nervous system.
4. Over time, new kinds of nerve cells evolve to detect more phenomena. Organizes combine various, specialized chemical sensors (taste, smell), photon sensors and eventually image-forming optics (sight), pressure/vibration sensors (touch, hearing), magnetic sensors (e.g., navigation in migratory birds, electro-sensitivity in sharks, duck billed platypuses, etc.). This increasingly complex nerve cell capabilities requires an increasingly complex nervous system. Control structures--ganglion--develop, themselves comprised of clumps of nerve cells, to better coordinate the nervous system.
5. Ganglion increase in complexity and size. Vast, hyper-connected networks form, meaning one stimulus triggering one nerve cell can result in an exponentially growing number of second-order nerve firings. This allows for evolution of complex causal relationships within the ganglion or--if they've passed some arbitrary rubicon--brains.
6. The complex neural network provides a toolkit for interesting capabilities to evolve. Stimuli--images, scents, tastes, etc.--can be saved (or rather, the nerve excitements they triggered can be saved) and reproduced by other stimuli.
7. Brains continue to evolve and their capabilities increase. Sensory recall begets learning and pattern matching, which begets strategy, learned mimicry, adaptive social behaviors, speech, tool use, etc. Throw enough of these capabilities together and we call it intelligence.