We most commonly use intuition when we need to come to a conclusion unconsciously, usually very quickly. This is usually the instant processing of information that we subconsciously do in day to day scenarios. This can be both reliable and unreliable. A time when it can be reliable was in the example we looked at in class where we tried to discern what emotion the people shown on the screen had when we were shown only their eyes. All of us assumed that we would get extremely low scores. However, all of us generally scored from 25-35/36, showing that in this case intuition is a reliable source of knowledge. However, there are certainly cases in which intuition isn’t reliable, like in the physics questions. In the physics questions, we were given questions that were designed to make you think a certain way upon first seeing the question. For example, in the question with the ship and the metal block, it is hard to intuitively say whether when the block is moved into the water whether the water will go up, down, or remain the same. Intuitively I initially thought that the amount of water displaced would stay the same when the block was moved. However, instead of this, the water actually becomes lower because of the block’s high density and the boat’s (comparatively) low density. Intuition is difficult because while it is certainly reliable for a significant amount of the time, it isn’t always reliable meaning that we will often act on impulse rather than on reasoning. I think that a large factor in whether we use intuition is time, because intuition is what we immediately subconsciously think upon receiving stimuli, like when we had to guess people’s emotions. This shows that while intuition can be reliable in many situations in the short term, it is based on our assumptions, meaning that it will not always be correct.

Our cognitive biases can interfere with our reasoning even when we perceive that we are only acting based on logic.

While we can rely on reasoning in areas of knowledge such as mathematics, when we apply it in the real world it is much more difficult to deal with. In mathematics, we are relying on axioms that do not need to be true in real life. However, in real life, an individual’s biases get in the way of reasoning that is completely logical. For example, as I mentioned in a previous post, if I were to read an article that presented data that showed vaccines as being harmful to people’s health, I would be instantly skeptical and try to challenge the article, because it directly contradicts my personal view. However, if I were to read an article that confirms my previous point of view, I would be unlikely to challenge the legitimacy of the data. This is just one example of how our biases can bar us from reason.

Reasoning has difficulty approaching truth because when we use reasoning, we are using logic that is based on assumptions.

When using reasoning, it is important to know what we are working towards. Truth is hard for reasoning to work towards because when we use reasoning, we are making decisions based on assumptions. What makes it particularly hard is that to reach true statement, we must go from one true statement to another. This makes it easier to use reasoning to approach certainty that something is true based on given information rather than an absolute truth.

A conclusion’s certainty is dependant on the validity of the reasoning involved and how true the statements it was based on were.

I touched upon this in my last CU, but I didn’t expand on it too much. I think that for something to be “certain” (not true) it needs to first be based in something that we assume to be true (or as close to true as we can get), and then use reasoning that is valid enough to reach a conclusion. Much of what we know today is based on these two things. For example, in the middle ages, the earth was assumed to be flat, because it was known that things fall towards the ground, and logically it made sense to assume that the earth was flat based on this. However, now, we have much more sophisticated equipment, as well as a better idea of how gravity works. So we base our conclusions on what we know about the earth, which is that gravity is generated by centers of mass, so flat earth wouldn’t make sense. We also have been able to see the earth from space, and have seen that it is spherical. This means that we used “truer” statements than what was used in the middle ages, so this conclusion, as a result, is truer than the old conclusion.

Confirmation bias

Out of the different cognitive biases we make, confirmation bias is one of the most common. Confirmation bias is when we are more likely to believe or favor an idea that confirms what we already know. For example, I inherently have the bias that vaccines are helpful towards human society. So, if I was to be presented with data or an article that has evidence that points towards vaccines being a health hazard, I would immediately be skeptical and try to challenge the article with things I believe to be correct about vaccines or doubt the reliability of the source. However, if I were to be given data from an experiment that shows that vaccines are helpful for everyone’s health, I would likely almost immediately accept the data as true. This is the issue with confirmation bias, as it makes us less skeptical of things because they share our viewpoint.

Anchoring bias

Anchoring bias is essentially when we are presented with information before making a decision, and while making that decision, we tend to cling to that initial information even when the decision at hand has nothing to do with that information. For example, if I was looking to buy a car, and I see a car that costs 30000 dollars and a car that costs 100000 dollars, I’ll think that 30000 dollars for a car is a reasonable price. However, if I were to be presented with a car that costs 5000 dollars and a car that costs 30000 dollars, I would think that the car that costs 30000 dollars sounds pricey and unreasonable. I only am really making this judgment because I am looking at the car’s cost in comparison to another car which really shouldn’t have a place in my decision. This is why anchoring bias can become a problem.

Narrative fallacy

Narrative fallacy is when we decide to lean towards one side based on the story behind it rather than logic because we find it easier to sympathize with due to the story. This can often be seen on shows like America’s Got Talent, in which contestants often bring a story with them to the show. If their story is compelling, people who watch the show are more likely to support that person. This means that your favorite contestant on the show may not be the most talented, which is why narrative fallacy obstructs logic.

Framing bias

Framing bias is very similar to narrative fallacy, as it also has to do with the way information is presented rather than what the information is actually saying. Framing bias is when we make a decision based on how information is presented to us making us more likely to believe it. Framing bias often comes into play when investing in things like stocks. For example, if investing in a stock presented a possibility of a 25% gain or a 100% loss, it immediately sounds like a bad decision. However, if I also give the information that the stock has been steadily improving for the last two years, it immediately sounds more attractive even though the possibility of failure is just as likely.

When we make a decision, we will always make assumptions about what we are doing. This isn’t necessarily bad, but some issues can arise when we make these decisions. For example, in the 9 dot game where we had to connect them all using 4 straight lines, we made several assumptions, but the main one we made was the assumption that we had to connect the dots together using the straight lines, and could not leave the box. However, with this assumption, there is no actual way to solve the puzzle. This assumption that wasn’t stated as part of the puzzle ended up restricting us from completing it. This means that when we make decisions based on subconscious assumptions, it is possible that we limit ourselves in trying to find a solution.

Why this is particularly problematic with logical decision making is that when we make a decision based on logic, we are attempting to arrive at truth based on deductive or inductive reasoning. However, in making the assumptions, we are already distancing ourselves from the truth, and this is unavoidable as we always make assumptions based on our perceived reality.

Since math is based in axioms, it cannot arrive in a real-life truth, but instead works towards certainty through the axioms.

In mathematics, everything is based on basic axioms rather than real life. With these axioms, there is no sense of them being true or false, they are all just assumed to be true. This means that when the axioms are used correctly, the resulting statement is assumed to be true as well. This gives us a level of certainty with what we are doing with the axioms. When a new theorem is presented that builds upon previous knowledge, it increases our level of certainty that what we have is true based on the axioms we based it on. We don’t need to arrive at a truth because what we are doing is not based on real life like science is. For example, in the video we watched about Andrew Wiles and Fermat’s last theorem, he had a good degree of certainty that his proof was correct, but was proven wrong. When he retraced his steps and eventually readjusted his proof, he gained a level of certainty that was greater than what he had before.

While math may initially seem to be a solitary area of knowledge that relies on personal knowledge, more progress can actually be made when personal knowledge is shared with others in order to build on each other’s ideas.

In this conceptual understanding, I am referencing the video we watched on Fermat’s last theorem last class. Andrew Wiles was able to “solve” the theorem the entire way without outside help. Throughout the process, Andrew Wiles kept his process extremely secret to prevent anyone from knowing his working. It was only after this that he decided to have his colleague look into his work. As a result, his colleague found an error in his working that threw off the entire proof for the theorem. I don’t think that Andrew Wiles would have come to find this error without someone else’s help. This led him to go on to look back at his proof and eventually fix it to be correct (as far as we know). This goes to show that even though it is perceived that mathematics is a solitary effort, more progress can actually be made when collaborating.

Although math’s nature is based on axioms (and therefore assumptions), it does have real-world applications, which ties together abstract concepts of math to the real world.

Although it is not always realized, mathematics is used all the time in our daily lives. In about every field that you could possibly want to go into, you will need to use mathematics, particularly in fields like business. This is because in our everyday lives, we use logic to make decisions, and although math is axiom based, it is also completely logical. Math is also our what we use to count, which makes it even more necessary especially when talking about money. This goes to show that even though math is assumption-based and abstract, it can still be useful to us in real life.

The arts allow artists to convey their personal knowledge and experiences to a larger audience, making it shared knowledge.

What I mean by this is that artists create art that has meaning to them, and in others viewing this art, allows them to share this meaning with them. The personal knowledge that the artist has is conveyed to an audience in a way that doesn’t even require language. However, what is interesting about art is that when someone tries to draw meaning from a piece of art, it is entirely possible that they will draw different meaning from the art. This still can be a positive thing, as even though the artist’s point is missed, it still is a thought-provoking piece of work allowing individuals to think about something on a deeper level.

While the arts can attempt to reach truth, they cannot arrive at a universal truth, as everyone’s interpretation of an art piece is never exactly the same due to individual bias and past experiences.

I already touched upon this idea in my first conceptual understanding, and even though artists may intend for some idea to be conveyed through their work, it is entirely possible people may miss that idea entirely. I would take this statement a step further and say that it is impossible to reach the same understanding and therefore truth from art. This is because every individual has different experiences and thus different opinions and views on different things. These different views mean that although the artist could attempt to convey their views through the medium of art, it will never reach a universal truth. The time period also can play a role in this personal bias. For example, in English class, we were discussing the #metoo movement, and the topic of art pieces depicting nudity throughout different time periods was being criticized for being sexually offensive. Everyone in the class thought that this idea was generally unfair. However, it goes to show that interpretations of art can never be the same for every person.

While math and science allow us to deepen a connection with our logical side and connect us to our surroundings, the arts allow us to contemplate interpretations of the world that math and science cannot.

I have talked about the differences in math and science in previous reflections, but haven’t talked too much about how they compare to the arts. While math allows us to connect with logic, and science allows us to understand nature, the arts represent people’s interpretations of the world and imagination using their creativity. What makes it even more different is that while math and science are portrayed to be extremely objective, the arts are the opposite. The arts are entirely based in subjectivity, which separates it from other areas of knowledge like math and science. This is because, in the creation of art, it is the artist’s interpretation and creativity of making an art piece. Not only is this subjective, but everyone who views the art piece will draw different meaning from it, making it’s meaning unique to every person who views it.

Axioms are the foundations of all mathematics, which makes it comparatively different to science. Science is largely based on our interpretations of our surroundings and basing rules off of them. While there are axioms in science, for example, that quarks are the smallest particles and they are able to do a specific set of things, these axioms are mostly found through experimentation with our environment, and also can be challenged if new data is found. In mathematics, it is completely different. The axioms in math are more difficult to challenge because rather than being based on nature, they are axioms mathematicians have developed on paper. Theorems are generally what is challenged in mathematics and in this way it is more similar to how science approaches theories. Theorems are merely logical deductions by mathematicians, which anyone can attempt to disprove, similar to science, where anyone can challenge laws with evidence. Another thing that is different about mathematics is that with the axioms of science, they are attempting to define truth in our reality, whereas in mathematics, it isn’t as much about finding a truth, but rather finding certainty in what we are trying to prove.

For me, a piece of art that has changed me is the Pantheon in Rome, Italy. I went to see it over the past summer with my family and it immediately became my favorite part of the trip. I found it amazing that it was built over 2000 years ago, and is still standing in excellent condition today. I also found it interesting that it stood as the largest man-made dome in the world for over a thousand years. Looking on the inside, all of the walls of the former temple are intricately detailed, but my personal favorite part was looking up to the ceiling of the dome, where there is a hole that opens up to the sky. The floors of the Pantheon are also designed to angle towards the entrance, so that water can leave through it. The reason that this changed me is that I previously had decided that I wanted to be an engineer, but hadn’t really decided what particular field of engineering to go into. This experience of visiting the Pantheon made me want to look more into architectural and civil engineering, because of how interesting I found this amazing piece of architecture that has been standing for over 2000 years.