Last thursday I posed the question of how often the water you drink has been pissed by a vertebrate already. If the number is very small, then those who baulk at drinking recycled water have more cause to complain than if the number is very high.

As some commentators to that post pointed out, in reality we are all drinking water that includes some recycled piss: every dam from which we drink has ducks, lizards, and all sorts of animals pissing and shitting in it, so it is already a bit of a myth to think one can drink water that has not been recently mixed with piss. Still, as another comment revealed, many think the idea of copying Singapore and drinking water that is officially recycled sewage is deemed ‘gross’. So the question how often water has been piss in the past still matters for the ‘yuk factor’.

The answer comes from a very simple formula, which requires a few guesstimates as inputs:

Piss ratio = (total water pissed)/(total water) = (total vertebrate biomass ever lived* piss rate)/ (total water) = (average biomass vertebrates * piss rate per year * years of vertebrates) / (total water)

This simple formula thus boils down to 4 inputs for which we can search for good guesstimates.

The amount of water on the planet (total water) is the easiest one because it is the sort of thing geologists and physicists are good at estimating. As this linked article computes, there is around 1.386 billion cubic kilometers of water on the planet. Whilst it is true that this water comes in various forms, that is not relevant for the calculation: since we are considering hundreds of millions of years, it doesn’t matter how much of that water is currently salt, fresh, stored in ice, or whatever: compared to such long time horizons it all circulates pretty fast so there is no problem in taking it all as one blob of water.

I can already say that my best guess for how much water we humans have pissed during our existence is around 800 cubic kilometers, meaning that only one 2-millionth of the atoms in the average water molecule will have been pissed out by a human. So we might be drinking reconstituted piss, but not much is reconstituted human piss.

Now, onto the other three inputs into our crucial equation. What is the average wet biomass of vertebrates? If we take the present as a reasonable guess for how much vertebrate biomass the earth continuously houses, then the answer we can gleam here is around 10% of total animal biomass (zoomass), or in the order of 5 billion tonnes of wet biomass (a lot more than dry biomass which you will often see reported). This includes up to 2 billion tonnes of dry-biomass fish, a little under half a billion tonnes of human, close to a billion tonne of things we might eat that walk on land (cattle and such), and 2 billion other wet biomass. In turn, this is in the order of one thousands of total biomass.

Admittedly, the estimate of 5 billion tonnes of wet vertebrate biomass may be out by a factor of 2 or so, but can easily be an under-estimate since I only found a dry biomass estimate for fish.

Then the next part of the equation: how much does a vertebrate piss per year? Again, this turns out to be a tricky question because only birds and mammals produce concentrated urine like we do. The rest pisses much weaker stuff, though things like fish still produce ammonia and the other normal elements of piss because the basic physiology is not that different between us and a fish. So the process and form of piss is not the same across species but the substances produced by our bodies and eventually excreted somehow are not that dissimilar.

So we need to slightly alter the definition of what we are looking for and think of piss as a ‘human-like’ substance. We can then again take a conservative approach and don’t count the watery piss that fish produce as ‘100% piss’ but rather as a much weaker variety of what we produce. We can then take ourselves as the measure of what a body produces and simply scale up, getting an easier question to start out with: how much do we humans piss in a year? The answer turns out to be that we piss around 1.5 liters per day, or 500 liters per year. Another way to put this is that we piss out 8 to 9 times our weight in wet biomass per year.

Then onto the last unknown, which is the number of years that vertebrates have been around in the abundant form of life we have now. Again, a tough one. The earth is now quite a bit cooler and probably less fertile than it was in the times of the dinosaurs, so the amount of biomass walking around now is probably quite a bit less than it was in the more productive phases of earth, but by the same token for much of the earth’s inhabited history the inhabitants were bacteria and not things with spines. If we concentrate on the period of the vertebrates, the best guess is that fish arose some 500 millions years ago, whilst land was conquered by vertebrates some 380 million years ago. Taking a conservative guess for the total period of time that the volume of vertebrates we have now has been present, this means that the wet vertebrate biomass we have now has occupied earth for around 350 million years.

We can now put the pieces together to compute our piss ratio: 350 million years of 5 billion tonnes of wet vertebrates pissing 8 times their body weight per year equals 14,000 million cubic kilometers of piss. This means the atoms in your average water molecule will have been concentrated piss some 10 times already. And that is a conservative estimate. In the more likely scenario, there would have been more like 10 billion tonnes of vertebrate biomass on average, pissing 10 times their own body weight, living 400 million years, equating to water having been piss around 25 times already.

Perhaps equally interesting I can give some idea how often the water has been piss from a particular group of vertebrates. Starting from the best guess estimate, water has been fish piss some 10 times, mammal piss around twice, and other forms of piss 13 times. Only a trickle has been monkey piss.

As per usual, champagne to all those who thought the answer was ‘often’ (which is all commentators game to give a guess). Unflavoured recycled filtered desalinated naturalised piss for the rest!