The statement is more-or-less obvious if you think about it from a capitalistic economic system. If there was a cheaper way to fix nitrogen, then someone would be using it to undercut Haber-Bosch produced nitrogen and capture the market. So we can conclude that, given scientific knowledge acquired by this point in time, Haber-Bosch is the cheapest way to produce nitrogen. Given that the amount of food that can be produced is a function of the price of the inputs, we couldn't produce as much food if nitrogen was more expensive. If we couldn't produce as much food, then we couldn't support the current population. So, on the balance of probabilities, the statement is self-evident.
this is the original statement referred to: https://news.ycombinator.com/item?id=34577458
Haber-Bosch is offered as an example of something needing megacorp scaling to that original statement, obviously from reading the foregoing I never said anything about a replacement for Haber-Bosch.
My admittedly vague statement just meant that hey you need to at least come with a theory as to why whatever allowed us to get to 8 billion could not happen without megacorp scaling. I don't think a linke to Haber-Bosch is an argument for that - the process was developed without megacorp financing as I understood it and then sold to a large corporation (not really megacorp either I think, by normal understanding)
quote: "The process was purchased by the German chemical company BASF, which assigned Carl Bosch the task of scaling up Haber's tabletop machine to industrial-level production"
I suppose the idea is that megacorp needed to run or develop scaling to industrial-level production.
I'm not that averse to the idea, just it seemed in the original form (linked above) quite a bold statement that should at least have some theoretical backing.
Without megacorp scaling, we'd need to spend more money on the same amount of food. Is that possible? Or would a different equilibrium point have been reached? Say, 7 billion instead of 8?
Unless parts of a capitalist economic system undermines competition in the interest of maximising profits for individual corporations or sectors. Thus there is a fork in this chain of reasoning -- it is not necessarily the case that no alternative method can be found (whether fixing nitrogen specifically or producing food generally), it could also be that such methods aren't developed because they threaten the short-term return on capital. One way to think of capitalism is as an engine optimised to generate and preserve short-term returns on capital.
'Cheapest' is defined in part by the required short-term return on capital. Nothing could be cheaper, from an operational perspective, than letting fields lie fallow. It only becomes expensive when fixed capital absolutely must have its short-term return before any other considerations are taken into account.
If your reply to my "prove it" is also "prove it" then it would seem we are at an impasse.