" For every complex question out there, there is an answer that is clear, simple and unimaginative. That is why we have to be really judicious about our use of the smartphones, we can't allow them to start thinking for us. We don't need to be a Physicist to figure out things by ourselves. "
1 of 8 :: Fermi estimates
Scientists often look for Fermi estimates of the answer to a problem before turning to more sophisticated methods to calculate a precise answer. This provides a useful check on the results: where the complexity of a precise calculation might obscure a large error, the simplicity of Fermi calculations makes them far less susceptible to such mistakes.
2 of 8 :: it's too easy to
neglect the power of our
For every complex question out there, there is an answer that is clear, simple and unimaginative!
We have to be really judicious about our use of the smartphones, we can't allow them to start thinking for us.
3 of 8 :: Estimating with slide
Before the graphing calculator, the slide rule was the archetypal instrument for engineering students. Do you know what a slide rule is or how to use it?
No Slide rule handy?Don't worry. To use a virtual slide rule Click here
4 of 8 :: M.I.T class of 2019 :
Do current students at M.I.T know what a slide rule is or how to use it? They're about to show us.
" Slide-rule is not digital, you don't get the exact answer. You get an approximate answer normally within two three significant figures which should usually be enough for the job that you are trying to do "
5 of 8 :: Approximations we
know from calculus:
Riemann sum that we learned in Calculus AB is really an approximation of the area under a mathematical curve between two X values. This area is approximated using rectangles that have a width of Delta X, which is chosen, and a height that is derived from the function f(X) given in the question Learn more..
6 of 8 :: Order of magnitude
How to carry out order of magnitude estimations based on very rough estimates for values
How does accurate estimation and scientific notation give powerful insight into questions ranging from the practical to the bizarre.
What is the length of toilet paper used annually in NZ?
How much land do we really need to house the population of the world?
8 of 8 :: The Method :
A clever way to estimate enormous numbers : Power of 10/order of magnitude
how to figure out things by ourselves
slide rules & their history
slide rules & class of 2019 M.I.T
approximations in calculus :: AP calculus
order of magnitude
how to solve a fermi problem: University of Canterbury
1. What are the assumptions or factors? 2. How big are the factors? Take the geometric mean of each under/over estimate pair Geometric mean = multiply numbers and take the Square root Example: Geometric Mean of 2 and 18 = √(2 × 18) = 6 3. Order of magnitude (rounding, scientific notation) 4. Interpret and compare with known quantities 5. Go back and question your assumptions
Which of those assumptions could I have changed?
Which of my answers might be a bit unreliable that influences my final answers)
My answer is different from someone else's: is it because we made different assumptions? or is it because we estimated those numbers differently?
These forces us to question our assumptions and check our values of things. 6. Refine each step (key thing in science in general is to question our assumptions and check our results and answers).