- #1
FallenApple
- 566
- 61
Clearly math is a product of human thought. But is there a prior reason for this?
A possibility is that math is a byproduct of basic information that we obtain from nature, where that information come in the form of ideas in which we have to sort out into something more rigorous.
We absorb information from the environment, for example, from an image, we can see a primitive idea of the geometric relation between things, ideas that represent numbers, sets, and perhaps a very basic logical structure of the picture etc. So we take this very basic information obtained from the outside world, and then mix it together to synthesize new stuff with it. But is it really "new" stuff? I mean, when chemists make a non naturally occurring chemicals out of elements, they didn't invent anything new, because the compound must have always been allowed within the laws of nature; that is, it must have always been so. Hence, maybe, somehow, logic itself is absorbed from the outside world. Even if logic is inherent from birth, we could argue that it could be absorbed from the environment via DNA in the learning process of evolution. In that sense logic is, very roughly, like an element, or component if you will, of nature and hence when we create new mathematical structures with it, it has the possibility of being a actual physically valid structure and most certainly, a potential physically valid structure, using this picture. Although this may be stretching it too far, but we see that for geometry, this is the case.
Geometry relies on images of the outside world. We see huge successes between curved geometry and relativity theory even though curved geometry came prior. But this is because differential geometry is built from the basic ingredients obtained from nature in the first place; concepts such as logic, shapes, curved shapes, numbers etc. And we see how algebraic topology can be possibly used to model a mouse brain where it is clear that the mouse brain is just an emergent phenomena of the laws of nature. Algebraic topology may not obviously manifest itself in the basic laws of physics, but in the emergent physical structures that result because of these basic laws. Graph theory shows up in social networks, again another system in nature, and with the reductionist view, a product of physics. The list goes on.
Thoughts?
A possibility is that math is a byproduct of basic information that we obtain from nature, where that information come in the form of ideas in which we have to sort out into something more rigorous.
We absorb information from the environment, for example, from an image, we can see a primitive idea of the geometric relation between things, ideas that represent numbers, sets, and perhaps a very basic logical structure of the picture etc. So we take this very basic information obtained from the outside world, and then mix it together to synthesize new stuff with it. But is it really "new" stuff? I mean, when chemists make a non naturally occurring chemicals out of elements, they didn't invent anything new, because the compound must have always been allowed within the laws of nature; that is, it must have always been so. Hence, maybe, somehow, logic itself is absorbed from the outside world. Even if logic is inherent from birth, we could argue that it could be absorbed from the environment via DNA in the learning process of evolution. In that sense logic is, very roughly, like an element, or component if you will, of nature and hence when we create new mathematical structures with it, it has the possibility of being a actual physically valid structure and most certainly, a potential physically valid structure, using this picture. Although this may be stretching it too far, but we see that for geometry, this is the case.
Geometry relies on images of the outside world. We see huge successes between curved geometry and relativity theory even though curved geometry came prior. But this is because differential geometry is built from the basic ingredients obtained from nature in the first place; concepts such as logic, shapes, curved shapes, numbers etc. And we see how algebraic topology can be possibly used to model a mouse brain where it is clear that the mouse brain is just an emergent phenomena of the laws of nature. Algebraic topology may not obviously manifest itself in the basic laws of physics, but in the emergent physical structures that result because of these basic laws. Graph theory shows up in social networks, again another system in nature, and with the reductionist view, a product of physics. The list goes on.
Thoughts?