Measurements and Hypotheses

Let’s consider a scenario where you can measure the velocity over time of a pair of objects that are, presumably, subject to the same force.  Can you estimate their relative masses?  The short answer is yes, because we know that F = ma and a = dv/dt.  The relative masses of the objects would simply be m1/m2 = dv2/dt / dv1/dt.

Suppose we observe one of the same objects, say, the object 1, and another object, let’s dub it object 3, in another environment where they are, again, subject to the same force but not equal to the previous case.  Can the relative messes of object 2 and object 3 be compared?  Yes, in principle.  We know, theoretically, m1 = m2*dv2/dt/dv1/dt = m3*dv3/dt/dv1/dt.  So we can rearrange the terms and obtain m2/m3 = dv3/dt/dv2/dt.  Seemingly simple, isn’t it?

But have we actually “measured” the relative masses of objects 2 and 3, even indirectly? NO!  The relative masses that we have estimated is a conjecture, derived from a theoretical assumption, NOT a measurement.  We have measured the relative masses of objects 1 and 2, and again, objects 1 and 3.  We suppose that, in both instances, objects are subject to the same force and that the laws of motion that we have assumed to hold equally in both cases is valid.  In this sense, we extrapolate the assumptions to the observations and derive what “seems” to follow logically from what we believe to be true–i.e. the laws of motion. But this is not based on an actual observation and lacks the certitude of such.  It is a mistake to think that, just because the steps we have taken to derive this seem flawlessly logical, this is necessarily as true as the direct observation.  In other words, this is only a hypothesis and should be taken with a bit more caution until we can obtain a direct measurement.  This is, in other words, true as LONG AS THE ASSUMPTIONS WE MAKE REMAIN VALID.  This latter qualifier is frequently lacking in the way we use data, unfortunately, in all manner of settings.

Indeed, there are many potential reasons that the the relative masses might be off:  one possibility, for example, is that the objects are moving through a viscous medium in the first setting and vacuum in the other, and object 1 is far more aerodynamic than object 3.  The relative velocities in the respective settings cannot be compared using the basic laws of motion that fails to account for friction.  Ergo, the relative masses estimated on the assumption that f=ma is equally applicable in both settings are wrong.

In order to obtain the actual relative mass, there is no substitute for the direct comparison.  At minimum, some setting has to be created where the relative velocities of objects 2 and 3 can be compared against each other–an actual experiment.  The old estimate remains valid in this setting, though:  To quote Fermi, if the relative masses confirm what we estimated before, we have made a measurement, an actual one this time.  If not, we have a discovery to make–we might discover friction or something, if we keep at it.  The old numbers, wrong as they might be, were not a waste of time, but only if we remember how we got them in the first place–i.e. the assumption that the same laws of motion are applicable in both settings that we took the observations from.  The caveat is that until we have an actual measurement, we cannot presume that we have a measurement just because we have only semi-related measurements we can piece together through assumptions.

This raises an interesting question:  Supposing that the environments in which the objects move are indeed different, is the assertion that the relative masses of objects 2 and 3, which are never actually compared against each other, follow m2/m3 = dv3/dt/dv2/dt “fake”?  This information is, in light of actual “facts,” which are not yet available, “false” in the sense that they don’t jive with them.  However, it is “true” in context of information available to the observer and the seemingly logical, but, in full knowledge of the facts, misguided and incomplete, set of steps taken to derive the relative masses.  It just happens to be factually wrong, even if procedurally and conditionally true.  To condemn the information on the bases of being “wrong” and therefore “fake” would be misguided because, as it were, the estimates are wrong for the right reasons, so to speak. To reject the old numbers on the basis of being “wrong” would deprive us the opportunity for discovery, as to why the different sets of information are, well, different.  The important thing, then, is not so much whether a given piece of information is “fake” or “false,” but how that information was arrived at–the how, not the what.

The how, however, is often lacking in today’s informational environment.  How requires too much thinking and doesn’t even get us right answers:  we are too busy to bother with answers that aren’t “true.”  We merely trust or distrust the sources, and expect them to tell us the right answers so that we don’t have to think about the details.  So in this context, whether news is “fake” or “false” winds up taking an importance beyond it is worth.  This, in a sense, is the real problem posed by the “fake” news crisis:  we have so much information to deal with that we forgot how to think, and without thinking, it matters only if the information on hand is right or wrong, and having “wrong” information becomes far more damaging.


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