Hamming concluded that the four explanations he gave were unsatisfactory. They were:  1. "Humans see what they look for". The belief that science is experimentally grounded is only partially true. Rather, our intellectual apparatus is such that much of what we see comes from the glasses we put on. Eddington went so far as to claim that a sufficiently wise mind could deduce all of physics, illustrating his point with the following joke: "Some men went fishing in the sea with a net, and upon examining what they caught they concluded that there was a minimum size to the fish in the sea." Hamming gives four examples of nontrivial physical phenomena he believes arose from the mathematical tools employed and not from the intrinsic properties of physical reality. ):   2. "Humans create and select the mathematics that fit a situation". The mathematics at hand does not always work. For example, when mere scalars proved awkward for understanding forces, first vectors, then tensors, were invented. "Mathematics addresses only a part of human experience". Much of human experience does not fall under science or mathematics but under the philosophy of value, including ethics, aesthetics, and political philosophy. To assert that the world can be explained via mathematics amounts to an act of faith. "Evolution has primed humans to think mathematically". The earliest lifeforms must have contained the seeds of the human ability to create and follow long chains of close reasoning. A different response, advocated by physicist Max Tegmark, is that physics is so successfully described by mathematics because the physical world "is" completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. The same interpretation had been advanced some years previously by Peter Atkins. In this interpretation, the various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of certain aspects of more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics. Most of Tegmark's propositions are highly speculative, and some of them even far-out by strict scientific standards, and they raise one basic question: can one make precise sense of a notion of isomorphism (rather than hand-waving "correspondence") between the universe – the concrete world of "stuff" and events – on the one hand, and mathematical structures as they are understood by mathematicians, "within" mathematics? Unless – or optimistically, until – this is achieved, the often-heard proposition that ‘the world/universe is mathematical’ may be nothing but a category mistake.