- Estimated numbers
- Measured numbers
- Exact numbers
Estimated numbers is the most useful form of numbers since they can be easy to obtain and are often accurate enough to make a decision. My belief is that most sound decisions in the world are and should be based on estimated numbers where the level of precision is known. Estimated numbers are frequently obtained by having an numerical model (of arbitrary simplicity or complexity), and create estimates by doing approximations/calculations or simulations within the boundaries of the model. Estimating extreme numbers (e.g. minimum and maximum) can also be useful for understanding.
Estimation techniques typically works within a range
An example an estimated number is to estimate distance by stretching your arm with your thumb up and use the thumb as a sight towards the point you want to estimate the distance to. Then the distance is roughly ten times the perceived distance you see when switching between closing left and right eye (e.g. if a mountain is 500 meter from you the perceived distance when switching eyes to aim with would be 50 meter). This estimation technique has its limits since it requires you need to be able to estimate the perceived distance by switching eye to aim with, and that probably doesn't scale up or down by orders of magnitude.
Measured numbers is the path (in retrospect when looking back)
Measuring something before it exists to my knowledge impossible (at least for all practical purposes), this means that measurement numbers only can be found in retrospect of an occurrence.
Measured numbers have limited accuracy
Heisenberg showed (roughly) that measurements of particles have a finite precision (or if the precision is overly high the measurement influences the particle being measured). I believe that in most cases of measurements there will be errors, but fortunately the error distribution can be estimated. When you hear someone talking about exact measurements they may be right, but usually they aren't, but the measurements could very well be exact enough for their purpose.
Exact numbers are rare
There are a few exact numbers, e.g pi and e (and even they rely on approximations when being used), but not overly many in the real world. Sometimes a number appears to be exact, but then it is usually a measured number or an approximation. Sometimes numbers appears as exact numbers but that is usually either a measurement or an estimate with what looks like high precision (but it could also be more or less educated guesswork), e.g. 0.00730100000000 looks impressively exact, or at least more accurate than 0.007 but that might not be the case.
value(estimates) > value(measurements) > value(exact numbers)