Cambyses was over the moon that such a golden opportunity had presented itself.
Usually, Alexander was very astute and methodical with his maths, but today it seemed he was having one of those days where nothing seems to go right for oneself.
Days where people have huge lapses in concentration, leading to mistakes that would normally never happen.
And this fortunate occurrence had happened by coincidence on her orientation day, presenting Cambyses with a silver bullet by which she could cement her mark on the council.
'Hahaha, the heavens have truly blessed me today,' Cambyses laughed out in her heart, ecstatic that she could increase her reputation and not least bother that she would have to do it by stepping a bit on Alexander's reputation and proving him wrong.
Noticing that all the men were expectantly looking at her for her explanation, she decided to longer keep them waiting.
Tapping her index finger on the table, Cambyses began," The first reason the twelve hundred square kilometers (1,200 sq km) answer is wrong is because it does not take into account the three crop rotation into account."
"From what I'm told, in this farming method, one-third (?) of the land is left fallow, meaning only two-thirds (?) of the total available land is used. So. we will actually need one thousand sixteen hundred square kilometers (1,600 sq. km) of land, and not twelve hundred square kilometers (1,200 sq km)."
Then without losing any steam, she placed her long finger on the table and continued, "Secondly, the lord's math assumes that the entirety of the obtained land will be good arable land. That is clearly wishful thinking, as only a tiny fraction of the total owned land is actually farmland. "
Cambyses then waved her palmed and said, "For instance, let's take the land surrounding Zanzan city itself. Yes. we might control one thousand square kilometers (1,000 sq. km) on the map, but the majority of it is the hilly, barren area in the Cisrian hills, full of rocky thin soil, totally unsuitable for cultivation."
"So we must find out how much of Zanzan's land is actually suitable for farming." Cambyses proposed.
Then she continued, "We know that even in good, fertile provinces, the amount of arable land would not exceed a third (33%) of the total land available. But for a barren place like the Zanzan province, even half that amount might be optimistic. A more likely figure will be one-tenth (10%). And that puts the required land at sixteen thousand square kilometers (16,000 sq. km)."
"But" Cambyses reminded, "Since we will be planting crops twice a year, this drops of eight square kilometers (8,000 sq. km)."
Cambyses here paused a bit to savor the faces of the men around her which ranged from pleasantly surprised to flabbergasted, and one particular one who was very flushed and embarrassed.
'Hmmm, Italy also only had a pre-industrial arable land of just 10%,' Alexander thought of a tidbit of information as he tried to distract himself from the huge embarrassment he was suffering at Cambyses's hands.
Cambyses, after a bit of basking in her own glory, then succinctly finished the third and ultimate point, "And last of all, in the first calculation, there is no consideration of slack. According to the previous calculation, we will only be able to produce the bare minimum, whereas, in reality, we must produce some excess to store for times of emergency."
"So the total required land area should be at least ten thousand square kilometers (10,000 sq km)."
As Cambyses finished showing her workings and sent a 'Praise me!' look at Alexander, the men around the table simply commented, 'Another monster'.
They were aware that Cambyses ran the medical camp before and all of them were very impressed by how she had managed to stymie the spread of the plague by following Alexander's orders.
But giving instructions to a few slaves and doctors was in no way comparable to making state-level decisions.
Thus they had assumed her to be just another pretty face that Alexander had bought here to bolster his own faction.
But it seems they were wrong in that assessment.
Very wrong.
The young girl seemed perfectly capable of holding her own against them and even Theocles, who was Cambyses's former boss was caught surprised by this display.
But instead of feeling down or even jealous, Theocles only piously thought, 'As expected of the lord's consort. How can we mortals compare to a vessel chosen by the gods?'
While these men were having their thoughts and musings, Alexander was himself thinking and evaluating the whole occurrence.
For many this instance might seem like a simple math calculation gone astray, after all, Alexander was actively engaging in a conversation while he multitasked the solution inside his head.
But still, it was not like it was just an innocent little misplacement of a zero or a decimal point or the error margin was small and within a rounding error.
That could have been forgiven.
Bu the numbers were orders of magnitudes off.
Almost by a factor of ten, a one thousand percent (1000%) discrepancy.
This was never going to be acceptable to Alexander or anyone else for the matter, and so he repeatedly chastised himself for not being careful enough which led to this huge error percentage.
He had missed not one, not two, but three crucial points.
'Slack! Oh god, I can't believe I forgot about slack!' Missing the third point particularly stung Alexander and he lampooned for making such a basic error.
Slack was the accommodation one made in the mathematical calculations to correct for any assumption error and usually, it involved multiplying the value with a factor greater than one.
For example, the most famous of slack would be the safety factor which was 2.5 times the calculated value, and every engineer who has ever made anything structural, i.e- designed to support weight, would use this value.
And thus this practice became pretty basic knowledge for every engineering major which made Alexander's lapse all the more egregious.
It was gross negligence on his part no doubt.
'I've been getting too cocky,' He self-reflected as he recalled that he had experienced the same feeling in Adhan with Pasha Farzah.
And so he repeatedly berated himself for making the same mistake twice.
On the other hand, Alexander did not doubt Cambyses's mathematical result.
In fact, he found them to be very accurate.
Though Cambyses had seemingly assumed and rounded off many things, the answer of ten thousand square kilometers (10,000 sq km) land for two hundred thousand (200,000) people was surprisingly spot on.
In fact, it was scarily spot.
And the reason was because the province of Zanzan's total land area was around three hundred thousand thirty to three hundred thousand fifty square kilometers (330,000 - 350.000 sq km).
And it was said that it had a population of around six and a half to seven million people (6,500,000 - 7,000,000).
This gave a population density of 20 per square kilometer (20 men per sq km), just like in Cambyses's calculation.
As a matter of fact, this could be extrapolated to all of Adhania, which had a total area of around four million square kilometers (4,000,000 sq km) and a population of around seventy to eighty million (70,000,000 - 80,000,000), which gave the same rough population density of 20 men per sq km.
And this was not even the most remarkable part.
The most astounding part was that this value of 20 men per sq km was even followed in Alexander's previous life, as evidenced by the Roman empire.
At its peak, the Roman empire was around four million square kilometers (4,000,000 sq km) in area and had a population of seventy to seventy-five million (70,000,000 - 75,000, 000), which, as you guessed, produced the magic population density of around 20 men per sq km.
So from this example, it could be seen that the average land really could only feed up to twenty people per square kilometer, or one man per five hectares.
Some places might have excess food, like the good arable farmlands around the banks of rivers and deltas, which can then grow into cities, as evidenced by most large, ancient cities situated by the banks of rivers and near the coasts.
And some places might have no agricultural value, like hills, mountains deserts, swamps, and marshes and the population around it would be mostly small and tribal.
But on average, one man per five hectares was the food-producing capacity of the land, even when 'advanced techniques' such as the three-crop rotation, horse collar, and natural manure were used.
And the only way to increase that capacity would be to industrialize and use heavy machinery to quickly cultivate vast swaths of land, while at the same time using copious amounts of various synthetic fertilizers, pesticides, and herbicides to boost the yield.
Or, if such high-tech solutions were not possible, the only low-tech option available would be to introduce potatoes.
These little buggers had insane yields, and historically, after they were introduced to Europe, the population density went from 20 men per square kilometer to 100 hundred per square kilometer and in some places to even 120 men per square kilometer.
And knowing this Alexander in the past years had searched high and low for these little globules of goodness, searching desperately for even the tiniest sniff of the thing.
But alas! It was to avail.
No traveler, no merchant, and certainly no one he knew that ever seen or heard of the famed potato.
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