Numbers tell us about reality but numbers are always an estimate of reality

I am a numbers guy.  Intuition has its place and value but I always want to know what the numbers say.

The challenge being that there is the assumption that the numbers reflect the actual reality when in fact they are at best a proxy for reality.  Definitional precision is always an issue but so is the mere act of counting.  Numbers are indeed important but it is also important to always keep in mind how fragile they can be.  They are a representation, they are not real and the representation is more or less accurate.

For example, if I am a corporate safety person, I might want to know, "How many people work on this floor?"  Sounds straight forward and reasonable, but . . . 

Define people:  Employees based at this location or any employee who is using an office on this floor at this time?  What about visitors?  

Define work:  Are we including maintenance people, cleaners, equipment repair people, etc. who might be on the floor at any given time?

Define floor:  The entire footprint of the floor or only the portion we lease?  What about building common spaces such as stairwells and elevators?

Define workday:  9-5?  All 24 hours?  

What time of day?:  The number flexes 20% across normal business hours?  How do we treat people working after hours?

What day of the week?:  There are people here on weekends and holidays.  Are they included in the count?

What measure?"  Mean, median or modal?

Depending on the answers to each of these questions, the result might be anywhere between 10 (the minimum number of people on the floor at any given time) to 150 (the maximum number of people on the floor at any given time) or something in between (mean, median, mode.)  It is useful information but not especially precise nor as useful as it could be with better definitions and better counting.  

And that's for a straightforward question on a straight forward issue with a reasonable basis (I want to know how many people might need to be evacuated.)  

For numbers people there is an inclination to recognize all these challenges, but once we get our hands on a number we treat it as fact rather than the best estimate of fact that it is.  

Adam Zamoyski in his book, 1812:  Napoleon's Fatal March on Moscow, has a great example of this measurement challenge using Napoleon's invasion of Russia in 1812 as an example.  Over the years, I have seen numbers ranging from 400,000 to 700,000 in terms of the size of the Grande Armée.  Similarly, I have seen numbers ranging from 15,000 to 50,000 as to the number who survived and returned to France (the survivor numbers are especially shaky.)  

It is impossible to be precise about the numbers involved. On paper, the overall strength of the forces poised for invasion was 590,687 men and 157,878 horses, while the total number of French and allied troops in the whole theatre of operations, including Poland and Germany, was 678,000. But these figures beg many questions.

The strength of an army which has taken up positions, as the Russian had done over the months, can be established fairly accurately, as the units are concentrated in one place, and there is little reason or scope for anyone to absent themselves for more than the few hours it might take to report to headquarters or pick up some stores. But an army on the move is far more volatile.

Whatever the technical strength of any unit on campaign, it is never concentrated in a single place, or even area, at one time. It always leaves a skeleton force, sometimes a whole battalion, at its depot. It does not move, lock stock and barrel, from one place to another: its head races ahead, leaving its body and tail to catch up, which they occasionally do, only to be left behind once more, in the manner of a huge centipede. It is constantly leaving behind platoons or smaller clusters of men to hold, defend or police areas.  Numbers vary, almost always downwards, with every day.

[snip]

Numbers arrived at by means of adding up the paper strength of the units present in an army can therefore serve only as a rough guide to the situation on the ground. It is generally accepted that the strength of the Grande Armée as it invaded Russia was about 450,000, but this has been arrived at by computing theoretical data, and the reality was certainly very different.

On 14 June Napoleon issued a circular to the commanders of every corps insisting that they must provide honest figures on the numbers of the able-bodied, the sick and deserters, as well as the dead and  the wounded. ‘It has to be made clear to the individual corps that they must regard it as a duty towards the Emperor to provide him with the simple truth,’ ran the order.

This admonition was ignored. ‘He was led astray in the most outrageous way,’ wrote General Berthézène of the Young Guard. ‘From the marshal to the captain, it was as if everyone had come together to hide the truth from him, and, although it was tacit, this conspiracy really did exist; for it was bound together by self-interest.’ Napoleon was always angry when provided with dwindling figures, particularly if these could not be explained by battle casualties, so those responsible simply hid the losses from him. Berthézène went on to say that the Guard, which was usually written up as being nearly 50,000 strong, never exceeded 25,000 during the whole campaign; that the Bavarian contingent, given as 24,000, was never stronger than 11,000; and that the whole Grande Armée was no larger than 235,000 when it crossed the Niemen. One can quibble with his estimates, but not with his argument, which is supported by others.

Russian estimates of the French forces at this stage were much lower than the generally accepted figures (and intriguingly close to Berthézène’s), which has surprised historians and led them to believe that they must have had very poor intelligence. But it may simply be that while French figures were based on paper computations, the Russians based their estimates on reports from spies, and those reports may have been more accurate as to the numbers of troops actually present than the paper calculations.

It would be rash to try to be precise, but a sensible guess would be that no more than three-quarters and possibly as little as two-thirds of the 450,000 crossed the Niemen in the first wave, and that the remainder, if and when they caught up with the main body, were only plugging gaps left by men dropping away. 

James C. Scott in Seeing Like a State has a great discussion about legibility - the capacity of a state (or enterprise) to understand its world, environment and constraints.  Obviously, numbers come into play, but there are innumerable other issues which affect the quality of legibility.  Napoleon wanted accurate numbers but was angry with his subordinates who brought him accurate numbers he did not like.  His view of his Grande Armée was inflated because of their fear of him or their desire to tell him what they knew he wanted to hear.  They could count and the data existed, but it was not acceptable.