When I was in middle school I first learned the basic idea of the fundamental theorem of arithmetic and my instantaneous first idea was that we should assign a unique prime number to each attribute that a biological entity can have, and then multiplying together the prime factors for all the characteristics would give the unique integer ID for that biological entity.
So if having a limb is “7” then some creature with three limbs gets 7^3 in its prime factorization, and so on.
Obviously it is an incredibly stupid idea, but 12-year-old me was quite impressed by the thought of it.
Lol, that's a great story; if only that sort of thing was practical, how much more fun life would be :-) I actually had the opportunity to do something similar not too long ago. I'm a beginner learning to program and I had a little puzzle that I got from my grandma ~15 years ago. You have a tower of blocks with symbols on them, and have to arrange the blocks so that all of the symbols on each side are distinct [1]. The problem was small enough that I could just model each symbol as a prime and check uniqueness by seeing of the product was equal to 2 * 3 * 5 * 7 * 11 * 13.
Whether or not it's incredibly stupid, you're in good company: it occurred to Leibniz, too. Search for 'prime' at https://pron.github.io/posts/computation-logic-algebra-pt1 (though for him the unique IDs were for concepts rather than individuals).
No it's not. It is likely too complicated to reduce to a formula that you can evaluate in reasonable time, or too complicated to measure with sufficient accuracy to even know what numbers to put into that formula, but life still follows the laws of physics and to the best of our knowledge they can be expressed in mathematical language.
> the error margin for the estimate [of number of trees on Earth] ranged between one trillion and ten trillion
A moment's googling gives primary forest being 1/3 of Earth land area and 40M km^2 ("world forest square km"), and primary forest tree density being 50k to 100k trees per km^2 ("trees per square km"). So there are at least 1T trees, as forests alone have more. And exceeding 10T would require non-forests to average at least half the tree density of forest, which seems unlikely. Suggesting bounds of 1T and 10T trees.
Just a reminder that rough quantitative reasoning and Fermi problem solving are powerful. Especially when approached as an exercise in order-of-magnitude bounding, rather than point estimate.
"How many trees are there in the world, is it more like 1, 10, 100, 1k, etc? Can anyone suggest a low bound?" "There's a tree outside the window. So one tree." "How confident are we? Should we consider that a hard or soft bound?" ... "Ok, a hard lower bound of 1 tree." "Can anyone suggest an upper bound?" "Ok, sigh, Jim?" "There can't be more trees on Earth than atoms in the visible Universe, because all Earth trees are part of the Universe, and each is made of lots of atoms! So a hard upper bound of 10^80 trees!" "Ok, is everyone ok with a hard upper bound of 10^80?" ... "Can anyone suggest some narrower bound?" ...
The phrase "I've no idea how many/much/etc" seems said far more often then it's true. You may not know it to some needed accuracy. But even young kids can be taught to estimate bounds. Which often turn out quite narrow enough to move on with.
If I recall correctly the main problem for evaluating the amount of trees on earth is in the tress density of forest which may vary by quite a lot more than we initially believed. And of course that numbers can easily vary by a factor on 100 if you vary the criterion you use for counting a plant as a tree.
So if having a limb is “7” then some creature with three limbs gets 7^3 in its prime factorization, and so on.
Obviously it is an incredibly stupid idea, but 12-year-old me was quite impressed by the thought of it.