I just started reading Michael Shermer’s The Believing Brain: From Ghosts and Gods to Politics and Conspiracies – How We Construct Beliefs and Reinforce Them as Truths. Sounds awesome right? Totally up my alley. I’ve heard his premise before – that beliefs come first, and then we rationalize the belief after to make it true. Once we form a belief, the brain starts looking for and finding confirming evidence to support those beliefs, which adds an emotional boost (that whole dopamine thing that I talked about in previous posts), which accelerates the process neurologically, and round and round it goes in a feedback loop until the belief becomes a truth. Shermer calls this process “belief-dependent realism,” patterned after the philosophy of science developed by Stephen Hawking and Leonard Mlodinow called “model-dependent realism.” Model-dependent realism basically says that our brains interpret the input from our sensory organs by making a model of the world. When the model is successful at explaining things, we tend to say it’s “absolute truth.” Shermer pushes this thought one step further, arguing that “even the different models of physics and cosmology used by scientists to explain, say, light as a particle or light as a wave, are themselves beliefs, and when coupled to higher-order theories about physics, mathematics, and cosmology, form entire world-views of nature.” All models of the world, not just scientific models, are foundational to our beliefs, and belief-dependent realism means that we cannot escape this epistemological trap.
Disclaimer: I am still trying to understand my own beliefs, and understand that they are constantly changing based on new information. But writing about them and talking them out helps me process the information. If I can explain them in a concise way, then it means that I have a better understanding. I also recognize that since this whole feedback loop is hardwired into my brain, I’m only confirming previous beliefs I already held, but maybe couldn’t articulate as clearly. I’ve been on a neurological kick recently, so it makes sense that I would find the solution to reality in neuroscience. My brain gathered the evidence to confirm my own personal belief about the world.
I started thinking about our belief systems and Truth. We all hold a myriad of different beliefs about the world, based on our own experiences. I’ve often grappled with the concept of universal truth. Is there a universal truth, or is everything subjective, based on our own experiences? Am I merely putting my own subjective reality on a universal truth? One truth we all hold as an absolute or universal truth is mathematics. Mathematics is a priori. We didn’t create mathematics. The syntax of mathematics was invented, but the mathematical principles already existed. This seems to be an easily accepted Truth by some, but for some reason it doesn’t sit right with me.
In my previous post I wrote about how the structure of language is hardwired in the brain, but it is up to the individual to choose the specific words to use based on the context and individual expression. Mathematics though – there can be no interpretation. The variables and meaning of the numbers might change, but in this reality, 1+1=2. I started asking myself, why? Why is 1+1=2, and not 1+1=3?
I then found an article from 1998 in the New York Times called “Useful Invention or Absolute Truth: What is Math?” BINGO. Apparently a lot of people are as concerned with this as I am! (That was a joke – people have been debating the nature of Truth for as long as we’ve had rational thought). The article discusses how modern science and mathematics is based on Plato’s idea that numbers and mathematical law are ethereal ideas, existing outside of space and time. We base all our science – physics, chemistry, quantum mechanics – on this idea. However, there is a new school of thought that treats mathematics as a human construct, like language or religion. It appears that mathematics is hard-wired into the brain through evolution. Scientists have traced the basis of arithmetic by studying brain-damaged patients who have lost basic number skills. (It is important to study how things don’t work to figure out how they work). There is an area of the brain called the inferior parietal cortex, a poorly-understood part of the brain where visual, auditory, and tactile signals converge. This region apparently is also involved in language processing and distinguishing left from right, the article says. “Mathematics is, after all, a kind of language intimately involved with using numbers to order space.” As the article reveals,
Numbers are not Platonic ideals but neurological creations, artifacts of the way the brain parses the world. In that sense they are like colors. Red apples are not inherently red. They reflect light at wavelengths that the brain, as it was wired by evolution, interprets as red.
So when people are born with a rudimentary hard-wiring of mathematics in the brain, they are able to evolve their thinking of mathematics quickly. This is how the higher mathematics, from algebra to trigonometry, to fractal patterns, were created. The subsequent generations are able to build upon the thinking of the previous generations, based on the hard-wiring in the brain. The human mind was able to look at the body, and time and space, and create first simple math to explain this world. As the theory goes, primitive people developed numbers by playing with rocks and counting their toes. No wonder we like number systems based on 10: We have 10 fingers and 10 toes. Our world is three dimensions, plus time. We developed mathematics as a way to orient ourselves in this world. (Our mind is able to do things now like triangulate and orient ourselves spacially).
I am reminded of Lois Lowry’s novel The Giver, which had a great impact on me as a child. The novel is set in a utopian society where they have decided to eliminate pain and suffering by converting to “sameness.” The boy, Jonas, is selected to be the next Receiver of Memory, the person who stores all the collected memories of the time before Sameness, in case they are ever needed to aid in decisions that others lack the experience to make. There is one scene that particularly stood out to me. After Jonas has received his first memory, things start changing. A sled, a girl’s hair, an apple… they all had a same different quality. The Giver explains to him that Jonas is starting to see the color red. There used to be a time when everything in the world had color as well as shape and size. The Giver explains that in order for the society to gain control of some things, it had to let go of others. I remember how much this passage stood out to me, because I thought it would be horrible to eradicate beauty in the name of conformity and control.
As Shermer explains in The Believing Brain,
“Believe change comes from a combination of personal psychological readiness and a deeper social and cultural shift in the underlying zeitgeist, which is affected in part by education but is more the product of larger and harder-to-define political, economic, religious, and social changes.”
I believe we are on the brink of a great shift in the underlying thinking that has shaped our view of the world. As we scientifically explore this universe and our place in it, we are doing so with the idea that mathematics is the universal language. If we ever encountered life outside this planet, we would be able to communicate with our mathematics. As the New York Times article notes,
”If the alien species had evolved in an environment similar to ours — say, a world composed of distinct, movable objects — then most likely its brain would have incorporated, through natural selection, the same regularities about the external world as we have,” …”Thus, it would have a very similar arithmetic and geometry.
”But now, suppose that the alien species has evolved in a radically different environment, like a fluid world,” he continued. ”Then knowledge of movable objects would not be essential to its survival, while knowledge of fluid mechanics, vortices, etc. would be. I believe that this hypothetical species would have internalized in its brain regularities strikingly different from ours. Hence it would have radically different mathematics.”
The conundrum of course is that we are still approaching this within our model of the world. There are probably concepts that we haven’t even come close to imagining. But I suppose you have to start somewhere.
Steven Hawking does not believe time travel is possible. Yet. He has several reasons, including the fact that no one has ever come from the future. This opens up the possibility for multiple realities and different dimensions, and I won’t go into all that right now. But the problem though with Steven Hawkings’ theories is that he is still working within our model of reality that we have created. What would we be capable of if we hard-wired an understanding of different dimensions? Where would we look for life if we collectively understood that our mathematics, our universal truth, is just a by-product of evolution and living in 3D plus time? What would we be capable of then?
I find it very interesting that the memory of The Giver came up while I was writing this. I assume it was triggered by the image of the red apple, the symbol of the fruit of the Tree of Knowledge, in both the New York Times article, and in The Giver. It had such an impact on me as a child because of the emotional response to the beauty of the image and the feelings of what it would be like to lose that beauty. Part of me (the hard-wired part that draws connections) feels like it can’t be coincidence that I would stumble across an article with the same imagery of something that so deeply effected me and my beliefs as a child. But that’s the point – my brain is designed to make those connections and seek out the information that supports my beliefs. It just happens in funny and unexpected ways.