Real World Math vs Fantasy Land Math
Posted: Wed Jan 29, 2025 4:44 am
Over and over in Holocaust debates we see disputes over calculations. Cremation, fuel, grave space, things related to gassing, and so on. I want to highlight a general point that is often lost in these arguments. This is intended to be a sort of meta-discussion. Some decades ago, Arthur Butz, a PhD electrical engineer, educated at MIT and Minnesota, offered the following very sensible comments regarding theoretical vs realistic calculations (from Supplement 3 of Hoax).
Muehlenkamp Math
The person who has really taken this to an artform is no doubt Roberto Muehlenkamp. In his calculations for wood requirements or mass grave capacity, Muehlenkamp does not even do the sort of super naive calculation Butz refers to. He goes beyond this, introducing great complexity in order to go even more extreme than what you can get with naive arithmetic.
Stacking Extreme Assumptions
If you are trying to estimate how much wood is required to cremate a human body, how do you come up with a silly value like 15 kg? The answer is that you break the problem down into a series of assumptions and for every individual assumption you pick the most extreme value you can think of in whichever direction is convenient for your argument. There is a compounding/multiplicative effect here and just by changing around assumptions you can get final answers that vary by orders of magnitude. If you assume a tiny body size AND big decomposition AND low fuel to mass ratio AND favorable weather AND ... you can end up with a much lower number. But you have to be right about ALL of those jumps.
The better way to do it is to consider the range of plausible assumptions and see how robust your conclusion is to changes in these assumptions. And, as Butz pointed out, you really need to sanity check your results with actual real world experience.
Possibility and Impossibility are Contextual
We must be precise here. Generally speaking, when we talk about what is possible or not possible, there is some implied framework, e.g., a particular technology, a particular context. Within a certain framework, X may not be feasible. If you change the framework, maybe it would be.
For instance, suppose you want to travel from NYC to LA by car. Google maps says this will take around 41 hours. This is an estimate based on realistic assumptions for traffic, average speed, etc., but it also assumes continuous driving (not realistic). Most people stop for food, sleep, gas, and these practical considerations would stretch the trip out to multiple days in most cases.
Now, we could ask, is it *possible* to drive from NYC to LA in, say, 40 hours? Sure. Is that practically possible on a family trip? No. That framework has a lot of practical constraints. Could we do it a lot faster if we dedicated ourselves to the task? Sure. People actually do this. It's called the Cannonball Run and the current record is 25 hrs and 39 mins.
https://en.wikipedia.org/wiki/Cannonball_Run_challenge
The record time works out to an average speed of 112 mph. To achieve such high speeds, they make all sorts of special preparations. They use a fast car obviously (preferably one that doesn't look flashy). They go when traffic will be light.
They have extra fuel tanks. They use various tricks to avoid getting pulled over by the cops.
But let's say you had a big budget to work with and had government cooperation. That changes the framework and changes what is possible. If instead of a car, we assume an SR-71, then you could say it takes something like an hour. Different framework!
What Actually Happened?
So often in these debates, it feels like revisionists are arguing that the stories are wildly implausible if not outright physically impossible while the other side seems to be arguing merely for possibility. And they seem to equate mere possibility with showing that it actually happened.
Butz is of course completely right about this. And subsequently we have seen the arguments go off in precisely the misguided direction he warned against.In considering cremation capacity, it is difficult to reach conclusions on a purely technical basis because of the distinction that must unavoidably be made between what is physically possible and what is practically attainable. For example, although I am told that my car can move at about 100 miles per hour, I know I cannot drive the 20 miles that separates my home in Evanston from the University of Chicago in twelve minutes; too many obstacles intervene. The technical data provides two numbers from which only an irrelevant conclusion can be drawn, whose only value is that the arithmetic is correct.
Muehlenkamp Math
The person who has really taken this to an artform is no doubt Roberto Muehlenkamp. In his calculations for wood requirements or mass grave capacity, Muehlenkamp does not even do the sort of super naive calculation Butz refers to. He goes beyond this, introducing great complexity in order to go even more extreme than what you can get with naive arithmetic.
Stacking Extreme Assumptions
If you are trying to estimate how much wood is required to cremate a human body, how do you come up with a silly value like 15 kg? The answer is that you break the problem down into a series of assumptions and for every individual assumption you pick the most extreme value you can think of in whichever direction is convenient for your argument. There is a compounding/multiplicative effect here and just by changing around assumptions you can get final answers that vary by orders of magnitude. If you assume a tiny body size AND big decomposition AND low fuel to mass ratio AND favorable weather AND ... you can end up with a much lower number. But you have to be right about ALL of those jumps.
The better way to do it is to consider the range of plausible assumptions and see how robust your conclusion is to changes in these assumptions. And, as Butz pointed out, you really need to sanity check your results with actual real world experience.
Possibility and Impossibility are Contextual
We must be precise here. Generally speaking, when we talk about what is possible or not possible, there is some implied framework, e.g., a particular technology, a particular context. Within a certain framework, X may not be feasible. If you change the framework, maybe it would be.
For instance, suppose you want to travel from NYC to LA by car. Google maps says this will take around 41 hours. This is an estimate based on realistic assumptions for traffic, average speed, etc., but it also assumes continuous driving (not realistic). Most people stop for food, sleep, gas, and these practical considerations would stretch the trip out to multiple days in most cases.
Now, we could ask, is it *possible* to drive from NYC to LA in, say, 40 hours? Sure. Is that practically possible on a family trip? No. That framework has a lot of practical constraints. Could we do it a lot faster if we dedicated ourselves to the task? Sure. People actually do this. It's called the Cannonball Run and the current record is 25 hrs and 39 mins.
https://en.wikipedia.org/wiki/Cannonball_Run_challenge
The record time works out to an average speed of 112 mph. To achieve such high speeds, they make all sorts of special preparations. They use a fast car obviously (preferably one that doesn't look flashy). They go when traffic will be light.
They have extra fuel tanks. They use various tricks to avoid getting pulled over by the cops.
But let's say you had a big budget to work with and had government cooperation. That changes the framework and changes what is possible. If instead of a car, we assume an SR-71, then you could say it takes something like an hour. Different framework!
What Actually Happened?
So often in these debates, it feels like revisionists are arguing that the stories are wildly implausible if not outright physically impossible while the other side seems to be arguing merely for possibility. And they seem to equate mere possibility with showing that it actually happened.