Entry Slip: Article on "Ancestral Genres of Mathematical Graphs"

Susan, the article you wrote is certainly interesting to read and analyze. I have also thought about why right and up indicate positivism, and left and down indicate negativism. I've encountered this especially in units on graphing and sketching equations, such as a linear equation, parabola, and many other shapes. I understand that it is common to think that right and up is associated with positive because of the points you touch on in your article. I also believe that our culture and norm definitely have something to do with the naming conventions. I mean, after all, they are supposed to be "arbitrary assignments" (15). And interestingly enough, because culture is different across the world, for instance, the North American (Western) culture may be different than South American culture, but the universality on the existence of culture leads to the same conclusion in the "genre" of mathematics. In Asia, specifically China, Chinese also associate any numbers left of 0 to be negative, and any numbers right of 0 to be positive. Again, this name convention is universal across culture.

One area that made me think more about this convention of this "hidden", "arbitrary" assignment is the CAST rule. I learned the CAST rule in high school in units on trigonometry. The CAST rule, which stands for Cosine, All, Sine, Tan, is a grid that is divided into four (4) quadrants where it tells us what trigonometric ratio (cosine, sin, tangent, or all) is always positive in a said quadrant. Counting using the CAST rule starts in a counter clock-wise fashion. First quadrant is positive in A, second quadrant is positive for S, third quadrant is positive for T, and the fourth is positive for C.

This is an image that was taken from Google to demonstrate the idea of the CAST rule. Applying the CAST rule to calculate the exact values (in fractions) of trigonometric ratios may not apply to the "right/up" positive and "left/down" negative convention, since trigonometry of a certain function follows a smooth, continuous curve that repeats itself depending on the degrees it has. The +/- sign of a trig function really depends on the angle or the degree that it is given. The angle and the exact position can be shown on a 360-degrees circle. So, I'm not really sure if the conventional naming of positive/negative still applies in this case because trigonometry deals with continuous functions, not something that is binary, which has front and back, up and down, or left and right.

While reading your article, I was also fascinated by the image included in your article of Albrecht's (1471-1528) portrayal of an artist is drawing a model through a frame using a grid system. This got me interested by the artist's sketch of human facial symmetry and the many patterns that exist in nature. I'm particularly interested in facial symmetry because body measurement, especially as seen on faces, influences judgement and qualities (e.g. positive and negative social cues) of an individual. The aesthetics behind facial symmetry in certain culture has a deeper meaning than just the appearance of the face. For instance, Chinese physiognomy used to be so popular that Chinese people assessed a person's character and personality just purely on their facial constructions. The connections between mathematics of symmetry in the human body with the culture aspect that is influenced by it is astounding and can be quite controversial. However, complex mathematics cases such as the trigonometry functions may show otherwise.