I recently posted some stuff about reality and the nature of mathematics and the physical world. My views have changed quite a bit and so I want to discuss the issue of reality in this post.
Before discussing things in the context of reality, one should realize that “reality” is just a construct of our minds. We are provided with inputs from the outside world through our senses and our brains construct reality in a way that satisfies all our input. For example I detect a pattern of excitement on my retinas as well as on my fingers and thus I perceive a keyboard in front of me. There is no “keyboard” on my retinas or fingertips, but I create the idea of a keyboard to make sense of my senses and be able to take action. The bottom-line is that all of reality is just an idea. This idea can get more sophisticated by introducing numbers and mathematical quantities. We have evolved to see things in terms of numbers and quantities and we have developed mathematics to describe, analyze, and predict the world around us. There is no sense in asking if these ideas exist in external reality – there is no answer to that question. All of these ideas (objects, quantities, etc.) are all ways to describe our input and make predictions. As long as these ideas make right predictions, they are considered “real” ideas.
On a separate note I also want to add that physics (or all science for that matter) is not about investigating the nature of these ideas, but rather expanding them. For example, time is a basic idea in “reality”. Physics does not try to tell us what time is. Maybe we can reduce the idea of time to a simpler and more general idea, but the problem stands because the nature of that idea is still questionable. Instead, physics develops the idea of time by measuring it and quantitatively relating it to other ideas to find things like the fact that time is relative. Thus we can only develop our ideas and make a more comprehensive, more accurate, and more predictive reality for ourselves.