Puzzles to Unravel the Universe by Vafa Cumrun

Author:Vafa, Cumrun [Vafa, Cumrun]
Language: eng
Format: epub, azw3
Publisher: Cumrun Vafa
Published: 2020-07-21T16:00:00+00:00

FIGURE 57. The strings attached to three equal weights settles at a point which minimizes the total length of the strings on the table. It is easy to see that the angles should be 120°’s based on balancing three equal magnitude forces pulling the common point in three different directions.

Line of Best Fit

Imagine a graph of data points (x i , y i ). Suppose we want to find the line of best fit (for the purposes of linear regression), meaning that we want to minimize the sum of the squares of the vertical distance from the data points to the line. We can treat this as a physical situation by imagining that the points are nails on a table with the horizontal direction denoted as the x-axis and the vertical direction as the y-axis, as in Fig.58 . The nails, in turn, are attached to springs that are connected to rings on a straight rod. The springs are confined to vertical tubes that allow them to move only in a vertical direction. The distance squared between the nails to the rod thus represents the potential energy of the springs, so finding the best linear fit is exactly the same as finding the configuration of the rod that minimizes the springs’ potential energy.

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