(a science fiction story)
Arithmetic coding is a way to represent a text using a single real number
Each symbol is represented using a fixed number of digits.
space↦00 and so on
We put all numbers together and form a large number
Then we write
0. in front of the number and we get a
Arithmetic coding encodes the entire message into a single number, a fraction q where 0.0 ≤ q < 1.0.
“Arithmetic coding” in WikiPedia
 "All Wikipedia"
Same, encoded as numbers:
 33 76 76 0 55 73 75 73 80 69 68 73 65
Finally, in the form of a decimal fraction
An alien visited Earth, collected all observations in a big file—let’s say, all Wikipedia
Then the alien encoded it using arithmetic code, resulting in a value q
Finally, the alien took a 1 meter bar, and made a mark at q meters
The bar is sent back to the alien country
What is the problem with this idea?
Our tools have limited “resolution”
We cannot “resolve” the difference between small variations
We need to know the margin of error of our measurement
That is, how well we know the values
This is also called “precision”
How big is the margin? How bad is the doubt?
We declare an interval: [xmin, xmax]
Most of the time we write x ± 𝚫x
Example: 20cm ± 1cm
Bertolt Brecht, in “Life of Galileo” (1939)
In 2016 a large stone ball was found in Podubravlje village near Zavidovici, Bosnia and Herzegovina.
We do not know how these stones were made
Similar stones have been found in Costa Rica
Nevertheless, people have made small round stones to sell as souvenirs
I was given a stone ball from Bosnia
We want to know its density
So we need to know mass and volume
Based on intuition we think that the mass is more than 100gr and less than 1Kg
Taking the geometric mean, we got 300gr
But it can be anything between 200gr and 400gr
We write 300gr ± 100gr
Comparing with a tea cup, we guess 80ml
But it can be anything between 70ml and 90ml
We write 80ml ± 10ml
How would you estimate the density?