ESTIMATION
1. Introduction
2. Rough sizes of things/numbers
3. Fermi method
4. Getting in deeper/Applications
1.Intro
What's the difference between general knowledge, a guess, and an estimate?
(You might just know how many countries there are in the EU.
Or you might not have any idea, and take a wild guess.
Or you might know some related facts and work out an `informed' guess
from that.)
Often we might want an answer to a numerical question - how accurate to
we need to be? Sometimes we can look up the answer, but often questions
are less tangible, and have an unattainable exact answer. Whether it's
to win a jar of sweets, or to see through a dubious headline, it's
important to be able to estimate with reasonable accuracy and confidence.
(Example: suppose we won the contract to polish all the floors in the
university. How much floor polish should we get?
Nobody knows the exact area of all the floors! What would that even mean?!...)
Sometimes it is dangerous to trust calculators and computers for these
things. They are good at arithmetic, but don't _understand_.
You can use the greater sophistication of your brain to sanity check.
Discuss: What is the difference in the way a PC `thinks' to the way
you think?
2. Rough sizes of things/numbers
One good trick is to have in your imagination some examples of differently
numbered things. For example, can you think of something familiar that has
100 things? 1000 things? 10,000 things?
Rather than continuing to add zeros here, we might use "scientific notation",
which just displays the "number of zeros" in a quantity. This is especially
useful for huge numbers, like the number of atoms in a grain of sand. This
could be written 80 000 000 000 000 000 000, but is perhaps more readable
as 8x10^19, that is, 8 with 19 zeros after it. These zeros represent
"orders of magnitude".
(Exercise: Think of naturally occuring sets that have the sizes
1, 10, 100, 1000, 10000, ..., 10^6, ..., 10^100, ..., 10^(10^10), ...)
What about units? What are good units for measuring things in?
Some things formally make sense as whole numbers (or `real' numbers).
Some are measured in funny units (grams, megatons, Sieverts, dollars,...)
3. Fermi method
Enrico Fermi was an Italian nuclear physicist in the first half
of the twentieth century. He was well-known for being excellent
at scientific estimation, and gave his name to the "Fermi method".
The idea is to break an estimation problem up into a combination of
smaller sub-problems. We make an order of magnitude estimate for each,
and hope that any errors we make will roughly cancel each other out
when the estimates are combined to give an estimate for the original
problem. This method often produces surprisingly accurate estimates,
although may need some practice!
4. Getting in deeper
When we make an estimate it can be useful to think about what we are
going to us it for.
Discuss: What might an estimate be useful for?
5. Links
https://www.theguardian.com/environment/2017/feb/03/fukushima-daiichi-radiation-levels-highest-since-2011-meltdown