Our perspective is formed by our past experiences. Our memories, our friends, our environment, all play a role in constructing the world we see when we view our world. In this blog, I wanted to discuss some of the ways the world we see can fundamentally affect how we interact with the world. I do not mean that just because information affects how much we know about the world in that obvious way (reminds me of the weak Sapir-Whorf Hypothesis), but that there exists some nuances with the way we see the world that affects how we interact with it.
Firstly, the way we each see the world is different. I mean this literally! Our mind and body collect information about the world through our senses. The most well-known are the sense of sight, smell, touch, taste, hearing. However, we also have the vestibular sense (our sense of balance), proprioception (our body positioning), and temperature. However, what does it mean when our brain processes these senses? In actuality, all sensory information is converted into electrical signals that our brains can interpret. In this sense, the way we see the world is fundamentally separated by the way the world is. By the same logic, everyone perceives the world differently. To think of it another way, you may have seen famous images, lenses, or filters of how other animals, mosquitos, deer, dogs etc. see the world. Though we are all looking at the same thing, what we actually see and can process is completely different. In a similar vein, human perspectives are different despite all looking at the same thing.
What are some other ways you can get two measurements when looking at the same thing?
Fractals, Integration, and Coastline Paradox
The famous coastline paradox says that because coastlines are inherently jagged and irregular at every scale, the measurements you get will be different based on the size of your scale. If you try to measure the coastline with a meter stick and then do the same coastline with a ruler, your measurement using the ruler will be larger because you are able to better approximate the jaggedness of the coastline. Neither measurement are inherently wrong, as both perfectly satisfy their job of achieving a working, realistic approximation of the coastline. The same can be said for fractals because fractals are similarly irregular. The measurement of the perimeter of a fractal will differ based on how much detail you are willing to include.
Calculus and integration actually work in a similar way if you consider Riemann Sum approximations. In Riemann Sum approximations, you break down the shape or function into n shapes that approximate that section of the shape. Most importantly, just like with fractals and the Coastline paradox, the results change based on how exact you wish to be.
The human analogy
Interestingly, I think an analogy can be made to how humans interact with the world. In many cases in our daily lives we are required to make decisions about the world around us. For the sake of the analogy, imagine you are a member of the jury deciding the fate of someone who has just, let’s say, robbed a bank. I find it interesting that depending on how well personally we know that person or their situation, we may chose a more serious or merciful punishment. If we were simply told that he committed a crime, we would perhaps simply choose the punishment based on precedence, and the punishments for other past bank robbers. However, if we learned that they were driven to commit the deed out of desperation because, let’s just say, they needed to pay medical bills for a family member, we may choose to go a little lighter. If we have had a similar experience, we might advocate for an even lighter punishment. If we personally knew that person and we were certain of their character, maybe we would go even lighter.
However, in that thought experiment, we assumed that all additional information would make us more sympathetic. In actuality, the additional information may alienate the person on trial, causing us to go for a harsher punishment. Just like in the case of Riemann sums, the more information we have, the more accurate the decision.
Information in Probability
Having been forced to do countless probability problems in math, I’m often stuck wondering at the circumstances which causes John to be picking colored marbles out of his bag, ordering his bookshelf, or shuffling cards. However, I wonder how the degree of information we are privy to would affect our answer. A simple example would be as follows. What if in the bag of marbles, we know what the top marble in the bag is? Or what if in the case of the bookshelf, we find out that John has a favorite book that he likes to place in a specific spot, or that certain books are a series and must be placed in series? If we answered without any of this additional information, we would get a good, working approximation. However, if we got to know John’s situation more, we would be able to refine our calculations. In the case of card shuffling, it is even more interesting. Do we know the type of shuffle that they are using? Are they cutting the deck? How many times and in what positions? Are they using a riffle shuffle, in which case the cards are placed in an alternating pattern, not shuffled. In that case, the top and bottom cards can also be controlled easily, so with additional information, we could control for what they are and factor that into our calculations. While in abstract situations, the math is simple, in realistic situations, once again just like with the Coastline paradox, the answer depends on how much information we know. However, just as with the Coastline paradox, each answer is equally valid.
This is another way that information affects the world!
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