Lians

Back in secondary school I used to struggle with the conceptual understanding of mathematics and how it fits in our world. I was good at applying what I was taught, but in the back of my mind I was never quite satisfied. Later, when I started participating in competitions I was confronted with a very dysfunctional world. The level of dissociation in those math circles was quite frightening (even though I didn't know anything about dissociation at that time). I often heard people suggesting that mathematics is a science, that it was, in fact, a conceptual interpretation of the world around us (everything is mathematics!). Some people even suggested that we should all communicate in mathematics because it's much more rigorous and logical. Where was all this coming from? Well, giving people definitions and teaching them how to reason is not in the interest of the public school system. Definitions and critical thinking make for incredibly poor propaganda tools, so most teachers prefer to completely bypass the subject. Sadly, a severe lack of conceptual understanding allows people to easily project all their unconscious thoughts on the subject matter. You can probably find a link between the introduction of the public school system and the rise of "mathematical science". Mathematics is a conceptual construct, and as such, it's built on a set of axioms. It's a language. Take your favourite fantasy novel as an example. It's probably inhabited by non-existing creatures living in a non-existing universe. However, the laws that govern their world are (ideally) internally consistent given a set of axioms that the author provides to the reader. That's what allows us to suspend our disbelief. We don't walk out the front door expecting to be assaulted by a wizard who's riding a dragon because the axioms in the context of which these entities exist don't apply to our universe. The predictive or descriptive value of a conceptual construct is proportional to the degree to which its governing axioms conform to the context of application. Any derivations of the axioms should, of course, be internally consistent. This is why the scientific method is so successful in advancing our knowledge of the universe. It requires that the value of a conceptual construct be measured against empirical evidence. Mathematics, similar to philosophy, can be a wonderful tool if handled properly. As with all great tools, its misuse can have terrible consequences. Unfortunately, over the last couple of decades we've seen the rise of what some call "mathematical physics". Here's a common trick: take a complicated-looking equation (or make one up), set one of the fundamental quantities in physics to zero (mass seems to be the favourite one) and derive a formula. Apply said formula to cases where the quantity isn't zero. If someone questions your methodology you can claim that examining the limit can give you important insight. Naturally, the preferred approach is much more convoluted, but I think you get the picture. Unprovable statements (no null hypothesis) and abuse of notation are now the tools of the trade. How are theories tested? You convince enough people (usually in government) that your research is important. You're quite happy that no one seems to demand a null hypothesis before investing millions of dollars in your experiment. Measurements don't support your theory? No worries, you can simply claim that you need more accuracy and therefore more money for research. It's quite beautiful in terms of profit. Few years ago I watched a National Geographic documentary about the origin of the universe and the context in which it exists (can't remember the name). They interviewed some of the world's "top" physicists that worked for an institute dedicated to this kind of research. Did they run any experiments? No. What did they do? They played around with equations. What's funny is that everyone had a completely different theory. The theories were derived through manipulation of existing laws of physics. Pick a set of physics laws, set a few of the constants or variables to zero, throw in a few extra dimensions and derive a theory explaining what you've done. Congratulations, you're a physicist with a six figure salary. Long story short, you've got every reason to be skeptical about modern-day physics. If anyone wants to pursue the subject academically, I suggest they go for an engineering degree. Physics and mathematics are wonderful fields of study, but as with most things in our current society, they've got way too much "government" in them. I think most of you know what I'm talking about.