Last night my eighteen-year old daughter and I engaged again in one my most favorite topics – reality. The funny part is that I have had these types of abstract academic chats with her since she was in Kindergarten. She’s always been more interested in the discourse than the actual conclusion – a fact that I think contributes to her not really having a lot of friends her own age. The last thing most college freshman want to do is argue the intersection of religious dogma and the scientific method – one of her favorite topics.
So three things collided last night for me and I felt compelled to share them as my day winds down. I feel like I will be long-winded so I’ll cover each in a separate post – here’s the first one:
Math is just another language
I read an article in Kifi last week about a panel discussion between a couple theoretical physicists – one Newtonian and one String Theorist – and a mathematical philosopher. I mean really – it doesn’t get any more abstract than that right? So anyway the philosopher was attacking the physicists on the point that they were using math as an absolute truth when in his view math is just another language.
I mean math is of course a language – most mathematicians describe it as the universal language. What the philosopher was saying is that since it is a language it intuitively has the same properties of other forms of communication, namely that is is descriptive but not definitive. The argument raged on for some time because the scientists claimed that by definition math is definitive. If you can express something mathematically and the observe that thing then it can be said that the math describes that thing. Therefore, if you can theorize something mathematically and you continue to build on that theory, observing along the way, then therefore math is a great predictor of reality. OK so in principal I’m fine with that but when it gets to the point where you start saying thinks like, “well because the math works out then it must be true” that’s where I start to have a problem. Take this example:
We all agree that based on our collective perception of reality that this is a Dachshund:
Furthermore we all collectively agree that we can express this quantity of Dachshund above numerically as 1. If we had more than one Dachshund it might look like this:
While they are visually different they are of the same class and in the practice of counting we would say that we have 1 Dachshund and we have 1 more Dachshund so by adding them together we have 2 Dachshunds.
This seems really obvious to us as non-mathematicians doesn’t it. Russell and Whitehead, two foundational figures in the math and philosophy world published the Principia Mathematica in 1910 – a three volume mathematical manifesto which included, among other things, a 360 page proof of the statement 1 + 1 = 2.
While this proof has stood the test of time it sheds some light on something that I’ve long believed – the simplest things are the hardest to explain. From this I would like to posit that even Russell and Whitehead’s proof of the statement 1 + 1 = 2 relies entirely on our collective interpretation or perception of the nature of 1 thing. What if 1 thing wasn’t really always 1 thing? What if sometimes it was nothing and other times it was more than 1 thing and still others it was just 1 thing?
Believing that math is the conclusive descriptor of the universe is comforting but if math is a language then it stands to reason that it has the same properties as all other languages. For example, it is syntactically and grammatically correct for me to describe the following in standard English:
“There exists a man that has and infinite number of heads where each head represents the result of every possible outcome of every chemical interaction within said man’s brain.”
Just because I describe it accurately using English doesn’t mean it valid, true or real – of course it also doesn’t mean that it’s not.
I’ll close with a question that my daughter asked me last night which has had me pondering the nature of reality all day.
Imagine two sets of people that have no interaction but are both said to exist in the same reality. Furthermore, imagine an observer who can only observe but not interact with both sets. Set A is placed in a room with double doors. Set A sees that the door on the left has a handle and therefore operates that handle to exit the room. Set B is then placed in the “same room”. Set B sees that the door on the right has a handle and therefore operates that handle to exit the room. Neither set of people knows of the existence of the other on any level. Consider the following:
- Does the observer “see” the double doors differently through the eyes of the set actively being observed?
- Does the observer “see” the handle consistently in both cases and observes both groups behaving the same while the groups themselves perceive their door to handle relationship differently?
- Does the observer, through the act of observing Set A and Set B link the two set’s realities forcing a convergence?
- Are you really reading this right now or are you doing something entirely different?