Weekly Math (30/10 - 5/11)
Weekly Math (30/10 - 5/11)
Point
Reference
1. Point
Logarithms find the cause for an effect, i.e the input for some output
Logarithms put numbers on a human-friendly scale.
Our difficulties are often due to our approach, not the concept.
Developing a sense of scale helps us better understand the world and better convey that understanding.
In general, I see a few general use cases: (Modular Arithmetic)
Range reducer: take an input, mod N, and you have a number from 0 to N-1.
Group assigner: take an input, mod N, and you have it tagged as a group from 0 to N-1. This group can be agreed upon by any number of parties — for example, different servers that know N = 20 can agree what group ID=57 belongs to.
Property deducer: treat numbers according to properties (even, threeven, and so on) and work out principles derived at the property level
Square Numbers
Seemingly simple patterns (1, 4, 9, 16…) can be examined with several tools, to get new insights for each. I had completely forgotten that the ideas behind calculus (x going to x + dx) could help investigate discrete sequences.
It’s all too easy to sandbox a mathematical tool, like geometry, and think it can’t shed light into higher levels (the geometric pictures really help the algebra, especially the +1, pop). Even with calculus, we’re used to relegating it to tiny changes — why not let dx stay large?
Analogies work on multiple levels. It’s clear that the squares and the odds are intertwined — starting with one set, you can figure out the other. Calculus expands this relationship, letting us jump back and forth between the integral and derivative.