I sometimes think of mathematics as a language. This notion of the right brain and left brain is a false dichotomy. Cognitive psychology sees processes in our mind as a series of systems that work together. We see this in math anxiety where panic impairs working memory. This is why mathematics is so difficult to perform under that condition. Mathematical ability is not impaired.
There are three things that I want to look into today. They are numbers with meaning, use of analogy, and some common sayings.
Numbers with Meaning
The first is a video from Numberphile featuring Dr. Sarah Wiseman. It is an interesting case of a man with aphasia. The patient lost the ability to say numbers. The only ones he could recognize were the numbers with personal meaning. Dr. Wiseman explains the 4 levels of cognition related to numbers.
Mathematics as an Analogy
I like using analogy to understand new concepts in mathematics. I have always felt the best way to learn something new is to compare it to something you already know.
One of my favorites involves the Twin Prime Conjecture. This was excellently explained in this Numberphile video. The professor talks about a world where prime numbers can only fall in love with other prime numbers. The gaps are smaller between lower numbers. We are talking about 5 and 7. When you go higher, like near a Googleplex, finding your twin prime is much harder. Yet with new research, it is becoming possible for numbers that high to find their partners. It is fascinating stuff if you are into number theory like me.
I am interested in how language has borrowed mathematical concepts.
The phrases that come to my mind in Engilsh are phrases with the word “count” in them. How many can you name?
Here are a few:
- We are often told by spiritual people to “count our blessings.” While the value here is not from an exchange, there is an important implication that the intangible is listable. Written down in some form.
- When people try to motivate us they tell us to “make it count!” This is a rallying cry to create something of value. Another way of saying to do your best
- When we can’t sleep at night we “count sheep.”
- The warning “not to count our chickens before they are hatched.” Lest we make an error of some sort and the thing we want doesn’t happen.
- “Count me in!” when we agree to do something.
In discrete mathematics, I learned that counting is called enumeration. Of course, it comes with all sorts of definitions about how and why we count things as we do. We are mostly counting all the elements of a set.
That’s why with only ten digits including zero,
You can count as high as you could ever go…
Forever, towards infinity,
No one ever gets there, but you could try.
Et cetera, et cetera, ad infinitum, ad astra, forever and ever,
With zero, my hero, how wonderful you are.
Strength Based Approaches to Learning New Subjects
I learned an important lesson when I realized that letters could be numbers. I used my strength in language to comprehend math. I have two go-to methods for dealing with challenges.
It is not surprising at all that Positive Psychology would study Strength-Based approaches. It gives a person a greater sense of agency of creating change in their lives.
“The strength-based approach allows for habitable conditions for a person to see themselves at their best, in order to see the value they bring, by just being them.”What is a Strength-Based Approach?
I highly encourage to look more into subjects studied by positive psychology. People sometimes misunderstand this as the psychology of happiness. it is not. Positive psychology is the study of flourishing. It covers subjects like hope, resilience, well-being, and flow.
There was a book recently published by Francis Su on the subject of “Mathematics for Human Flourishing.”. I haven’t read it yet but it is on my to-do list.
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