The Walking Dead

I have watched the first season of "The Walking Dead" and like it save for gaping holes in the head plot. The show is illogical. A single human being such as myself could fend off an entire world populated by zombies, even if I had no access to firearms, even if every bullet in existence were already spent. The simple fact is that, at least in season one, zombies are stupid. They are not even as cunning as animals. Therefore, all one has to do is secure a building, hilltop, or other point that is difficult to access, such as an island, and then cultivate a source of food via gardening or herding. Zombies could not storm a castle because they do not know how to construct ladders, ballista, catapults or any other device or tool. They know nothing of siege weapons or indeed of any weapons. Therefore the premise of the show, that zombies have overwhelmed all the world's armies, is laughable. Another problem is that zombies do not reproduce. Therefore, their numbers would quickly dwindle along with any reduction in the human population.