The second is the world of mental states, while the third world is that of ideas in an objective sense, which can be possible objects of thought. This indicates that the second world is that of subjective experience, while the third world is that of pure ideas, which show themselves in human culture. Each human being must then possess his or her own second world, which will be different from that of any other human. This means that there will not be one second world in this framework, but rather a very large number of second worlds. According to Popper, the first two worlds can directly interact with each other, while the last two can also do so in a similar way.
Popper states that the third world is a product of human activity.
If we try to understand present-day science in the framework of Popper's ideas, we might say that it is a science of the first world obeying the mathematical laws of the third world. This science then eliminates the second world. According to Penrose, the Platonic world gives rise to the physical world, because nature is describable in a mathematical way. The latter gives rise to the mental world, which in turn again gives rise to the Platonic world. His scheme is like that of a serpent chasing its own tail.