Something as simple as walking requires us to have made a profound number of calculations that we don’t even consciously think about. Imagine having to write out instructions to program a machine on how to walk. There are so many calculations that must be made. It’s far more complex than we realize when we stand up to walk.
Joints along with many muscles are engaged and to the proper degree. Legs are coordinated so the result is continuous smooth forward motion. How far is your foot from the ground and how far should the step be? Our eyes and other senses are constantly alert for any obstacles that would be a hazard and need to be avoided. This information is used in coordination with the rest of the calculations necessary to walk. Why did we decide to walk in the first place? To get somewhere our brain calculated we needed to be. On and on and on. So many calculations. Yet we don’t even have to give much thought to all of this as we walk. It’s mundane. In other words, there are profound calculations our brains make every day without us even noticing.
Perhaps that is what a gut feeling or instinct is, a series of profound calculations that our brains have made, but we didn’t even notice ourselves making. Yet we have a sense for something, the gut feeling, the instinct. This, of course, isn't to say that a gut feeling is always right; just as we may occasionally stub our toe while walking due to a miscalculation or distraction.