As we had explored in previous classes, division is subtraction again and again and again, multiplication is adding again and again. Exponentiation is multiply again and again and again— They are all inventions to simplify repeated computation.
So is the invention of logarithm: taking log is division again and again and again. They were invented by John Napier who was a Scottish mathematician, physicist, and astronomer in 1614 as a means to simplify calculations.
🙂 Today’s Python numpy class summary:
Log10 means how many times divide by 10 will return you to 1. log10(100) will give you 2 because 100 divide by 10 twice returns us to one.
One trillion divide by 10 twelve times returns it to 1.
>>> np.linspace(0.0, 3.0, num=4)
Out: array([0., 1., 2., 3.])
>>> np.logspace(0.0, 3.0, num=4)
Out: array([ 1., 10., 100., 1000.])
>>> np.linspace(0.0, 12.0, num=13)
Out: array([ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.])
>>> np.logspace(0.0, 12.0, num=13)
Out: array([1.e+00, 1.e+01, 1.e+02, 1.e+03, 1.e+04, 1.e+05, 1.e+06, 1.e+07, 1.e+08, 1.e+09, 1.e+10, 1.e+11, 1.e+12])
Bonus: Did you know that Engineers and scientists used to use a tool called “slide rule” (计算尺) to do logarithmic computations until 1970s when electronic computer and calculators came into use. You should go and check it out if any of your grandparents have one of these.