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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You Can’t Say That!

There is a lot to chew over in this essay and a much older essay that it links to.  I do wonder if the authors of these posts are themselves a bit trapped in their own (somewhat self-congratulatory, I’m afraid) bubbles of their own.

One book that went far to shape my thinking about the epistemology of science, even before I read Popper and Feyerand, was The Nemesis Affair, by David Raup.  Raup, who passed away in 2015, was a notable paleontologist who contributed to the idea that mass extinctions are cyclical and may have extraterrestrial origins–e.g. comets.  He began the book by going over theories like his that came before, almost invariably posed by great scientists with vast knowledge across multiple fields, including no small amount of expertise in paleontology and astronomy, but not professional astronomers or paleontologists–people like Harold Urey, the Nobel prize winning chemist.  Their arguments invariably made their way to top journals like Nature, journals that many scientists pay attention to, only to be met by total silence.  The reason, Raup suggested, was that the arguments of the sort that people like Urey were selling were just so far outside the conventions of the field that they were addressing that nobody knew how to respond, but, unlike some no namers who cannot be safely brushed aside  with the snide attribution that they say such things because they don’t know better, famous and accomplished  scientists cannot be so easily dismissed as cranks. So they get their hearing, the polite applause, and a publication in Nature, then everyone goes around around as if the whole thing never happened–because, for all practical purposes, it never did as their argument cannot be placed in context.

Could great scientists be the only ones who saw puzzling clues like what motivated his publication about comets causing extinctions?  It is doubtful:  far more likely, the younger, less accomplished scientists who thought up such crazy ideas were told that, if they press further, they will simply ruin their reputations and not get tenure.  Once they get tenure but settle down into being a routine scientist of middling sort, it is far easier to simply take conventional wisdom for what it is and live their lives.  It takes both a great scientist and a madman, someone who enjoys such prestige and influence that they cannot be brushed aside so easily, to obnoxiously push forward new ideas.  Of course, history reminds us that Galileo was such a person, forgotten though it is amidst all the mythmaking about his persecution–he was a friend of the Pope and half the cardinals who were presiding over his trial, was treated like an honored guest when he was being “tried,” and his sentence was to live outside the city limits at a luxurious mansion of his friend and supporter for a while.  Hardly “persecution.”  The rest of us have to conform to the conventions, if we value our lives, and quite frankly, “That’s something I should comment on. Nah, what’s the point? Too much downside” is the rule that all of us live by most of the time.

The trouble with this, of course, is that this creates an echo chamber of sorts–not necessarily one where everyone repeats the same thing and believes the same thing, but one where everyone knows what “the truth” is, repeats the same sanctimonious things, and keeps to themselves.  Societies like this are not uncommon:  USSR was like this:  everyone knew what the official Truth was–that’s literally what it says on the label on Pravda (the Truth, literally).  So everyone repeated it, acted like they took it seriously, and nobody believed a word of it, whether it was true or not.  Without means of evaluating the “truth” to satisfaction, everyone was essentially entitled to their private truths–whatever they believed was “really” going on in the world.  But this is not just true of an authoritarian society:  every society has certain myths that are “true” just because, that one cannot question.  To question these “truths,” indeed, is to expose oneself as an outside who cannot be trusted–say, a Korean who questions some of the national myths about horrors of Japanese rule, or an American who does not believe in Russians hacking the 2016 elections.  It is not so much that these official truths are false:  in fact, I’d imagine that, on average, vast majority of the content on Pravda was in fact very true factually throughout the entire Soviet era.  It is simply that overt questioning of the myths is not permitted.

The problem goes farther than that:  the truth is wrapped in layers of uncertainties, while the definitions that we use are poorly defined.  Can we even handle the truth when we see it?  As the saying might go, if we see God face to face, would we recognize even Him?  How people lie with statistics is at the margins, assumptions, and definitions:  the important thing, when dealing with data, is not whether something is or is not “true,” but whether the estimates are within an accepted set of margins of error given certain definitions about how things work.  What makes physicists, in particular, so much better at these than most other people is that they are very good at precisely crafting these definitions and assumptions and thinking through them logically.  But when the universe is itself murky, these clear definitions are self-deceiving:  as per my ever persistent rant about DW-Nominate:  yes, the numbers would indicate the “ideology” if the ideology were spatial and people acted both geometrically and asocially (i.e. based only on their own “preferences” without politics), but those would be some pretty damn stupid assumptions to make when you are dealing with politics.  If one is a physicist, the proper course of action as a scientist would be to conduct experiment in a setting where nuisances like air resistance or friction do not exist–or can be minimized, not pretend that universe everywhere is frictionless and pretend that the models that assume away friction provide usable guidance.  If one is an engineer, the theoretical models would be taken with a big grain of salt, consisting of a bunch of formulas and tables that account for frictions and such things for practical purposes.  By not being able to question sacred cows of assumptions that may not be challenged, we can do neither.  (I had the good fortune of just rereading this essay by Freeman Dyson about his experience crunching numbers for the RAF Bomber Command during World War II.  Basically, you can get people to trust you not just because your numbers are good–they wouldn’t know it even if they saw them:  they are NOT self evident, especially in a world where uncertainty is high–but because you are a famous scientist and, more importantly, decorated navy officer from World War I.  If you are neither, they trust you only so far as your “information” confirms their existing beliefs, rightly or wrongly.  Dyson has a wonderful description for this:  if the former, you are giving “advice”; if the latter, you can only give “information.”)

In a sense, this is the fundamental problem:  even if what you are saying is true–and, you yourself don’t always know this–there is no guarantee that your interlocutor will recognize it as true.  They have a certain set of ideas about what the “truth” should look like and if what you say does not look like it, you’d better give them reasons why your truth is bigger than their truth.  Not easy if they outrank you and tell you to “shut up.”  Feynman, in his famous Cargo Cult essay, had this to say about this:

“We have learned a lot from experience about how to handle some of the ways we fool ourselves. One example: Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right. It’s a little bit off because he had the incorrect value for the viscosity of air. It’s interesting to look at the history of measurements of the charge of an electron, after Millikan. If you plot them as a function of time, you find that one is a little bit bigger than Millikan’s, and the next one’s a little bit bigger than that, and the next one’s a little bit bigger than that, until finally they settle down to a number which is higher.

Why didn’t they discover the new number was higher right away? It’s a thing that scientists are ashamed of—this history—because it’s apparent that people did things like this: When they got a number that was too high above Millikan’s, they thought something must be wrong—and they would look for and find a reason why something might be wrong. When they got a number close to Millikan’s value they didn’t look so hard. And so they eliminated the numbers that were too far off, and did other things like that …”

Jessica Livingston is right:  when there is silence, we do lose in insights, as per the aftermath of the Millikan oil drop experiment.  But we also know that every new idea we have is potentially mad, and we have much to suffer if we are perceived to be mad.  Agreeing with the “right people” that their worldview is right, and only minimal changes are necessary, if any, is something we do all the time.  Of course, this pollutes the information provided:  some of the information says “I am your friend and I support you, whether you are right or wrong.”  Only a little bit says, “I think you are wrong.”  In a highly uncertain environment where the right and the wrong is not obvious, even on the mattes of facts, it’s better, easier, and safer, not to mention more rewarding in career, to be on the side of the conventional wisdom, or what the present important people have to say about the universe.  Since the presently important people are usually not stupid, they are probably right anyways and you probably did not make an important, earth-shaking discovery.  But, if they are wrong, they can be very wrong, and if everyone is trying to be friends of the powerful rather than tell the truth  Since we can only tell the truth secondarily, from the analyses by these people who crunch the numbers and NOT from our own analyses of the truth–remember, we can’t handle the truth, literally, at least not all of it, so we almost always have to learn about the universe secondarily–when everyone who crunches numbers is interested more in appeasing the powerful and important rather than raise questions, we don’t even know how big a mistake we are making.  (In retrospect especially, I think everyone knew that there was something fundamentally wrong with the Clinton candidacy, and there was so much wrong with it that everyone saw something different.  But everyone knew that she had to win because the alternative did not make any sense, so they all minimized their sense of how likely Clinton defeat was, until only the truly mad expected Trump victory.  I think that’s a worse outcome than just hedging bets–it helped validate the true nutjobs as if they are only sane people.)

If Livingston is only discovering it now, I think she has lived a charmed life that most of us don’t have the luxury of.

Trust, Christianity, and Economics.

There is one story, supposedly originating from Buddhism but, to me, forever associated with Christianity, as I had originally heard it in a homily when I was young:  Heaven and Hell are, in terms of physical configurations, exactly the same–people are dining using extra long chopsticks.  The difference is that, in Hell, everyone is trying to feed themselves to no avail because the chopsticks are too long, while, in Heaven, everyone is happy because everyone is feeding each other.

Indeed, to me, this is at the core of Christianity, or, indeed, any organized religion that works well.  Religion, if done right, provides a focal point for a society, a set of basis on which communal trust is built on.  Christianity is not, to me, fundamentally about God or Christ, but being able to trust one’s fellow humans.  God, in this sense of Christianity, is the God of Kierkegaard.  Trust in others IS irrational:  the outcome where everyone feeds each other even if they cannot feed themselves, under most configurations of payoff structure, is not an equilibrium–it is far easier to exploit others’ goodwill while contributing nothing for sake of others.  With no one contributing, what might have seemed heavenly to begin with descends rapidly to hell.  The necessary condition for the Heavenly equilibrium, then, is the willingness of those who would contribute to do so even at loss to themselves.  Not everyone needs to make that kind of sacrifice:  once there are enough of them to change the norm, the magnitude of “sacrifice” is reduced for all.  Even if you are making the endeavor to feed others at your expense, others will feed you to make good your losses.  But in order to keep the equilibrium going, to prevent it from sliding down the slippery slope, at least some people need to be of “true goodwill.”   This is the story of Bishop Myriel from Les Miserables, in a sense, but also the basic story of Christianity, perhaps:  the Christian message, as far as I see it, is not so much about faith in God as much as faith in other humans and their goodwill because God commands that faith–and hopefully, maybe, may even offer a reward not of this world for doing so even if others humans might not.

Is religion strictly a necessary condition for the existence of such people of true goodwill?  Perhaps not.  But some sense of “community,” the sense that there is something greater than one’s selfish well-being is, I think.  Religions that offer a reward not of this world can only help.  In a sense, offer of reward to those of goodwill–i.e. those who would willingly make the sacrifice for others–is a common feature of most religions that win over many sincere adherents.  Perhaps it is part  of human nature as social beings that fosters such religions after all, countering the evolutionary evils of the “selfish gene” at the individual level.

But faith is hard, precisely because it is so irrational.  Bishop Myriel offers Jean Valjean the other candlestick, after the latter stole the first one is caught red-handed, seemingly proving his faith in humanity wrong.  Bishop Myriel persists in his irrational faith, and turns around Jean Valjean instead:  Jean opts to steal because he feels that the only way to get by is to try to feed himself, because he resides in hell.  But in so doing, he met the Buddha in Hell. (actual Buddhist story:  Dizang Buddha refuses paradise so that he can help redeem souls trapped in Hell.)  Unfortunately, Bishop Myriel is a rarity, even among those who think they believe.  I can certainly attest to trying hard to believe, not in God, per se, but in basic goodness of the people–myself included–and always having trouble doing so.

The basic message of economics, at least of classical economic theory, with its emphasis on “selfish rationality” starts to deviate from that of Christianity (and of old “irrational” religions in general) from this point on.  Ultimately, the assumption is that people do what is good for themselves, for their own sake.  There is little or no room for “faith,” irrational as it is.  It is not so much that people who respect rationality cannot respect faith:  Tocqueville wrote admiringly of the people who believe and the power of religion in sustaining societies, as did Marx–who, after all, lived in an era that appreciated the good that opiates bring to the suffering.  But, in the end, they could not believe–and Tocqueville tried very hard to foster faith in himself–and, especially in case of Marx, bet their view of the future on a “rational” worldview.  Even in game theoretic terms, as long as there are enough people who would persist in behaving irrationally out of faith, a Heavenly equilibrium can be maintained, by at least not discouraging others from actively offering their now reduced sacrifice for the common good (even if not actively discouraging it).  The problem is that it offers no obvious reason as to why anybody should do so in the first place.

This is something that I was trying to explore in my novel-writing venture about Judas Iscariot–which, I suppose, has always been about myself and my own search for that faith.  Judas’ betrayal, as so many have pointed out, is an essential component of the Christian story of Redemption and not something for which he should be condemned for–and perhaps, his true sin was not that he betrayed Jesus, but he lacked faith.  And an extraordinary faith that would have taken–that, against all that is obvious, the act of betrayal is a good thing and that he should do so happily.  The story of Judas in the aftermath, in the Gospel of Matthew, is that he took it badly, that he threw away the 30 pieces of silver–the reward that he did not need or seek–and hanged himself out of shame and guilt, and perhaps it is this shame and guilt that was Judas’ central sin, much more than his betrayal.  In a sense, a New Testament version of the story of Job–God did not simply take away Judas’ possessions, health, and family, but He directly subverted the focus of his faith, and this challenge Judas could not overcome.  But how many mortals could keep their faith in face of such adversity?  Faith is irrational:  you believe in and put trust in things that make no sense, and perhaps, even things that you should not in good sense do so.

One person that I wonder who actually understood this contradiction is Frank Herbert, the author of the Dune series.  One scene, towards the end of God-Emperor of Dune, that always stuck to my mind, is how Leto, the near-immortal superhuman-Sandworm hybrid emperor who is the object of the cult, dies:  one of his own worshippers, confident in her faith that she is doing the right thing, obeys Leto’s command to destroy the bridge that causes him to fall into water–the only thing that could kill him.  In a sense, same action as Judas–an act of betrayal that leads to the death of the object of worship–and, in the storyline of the Dune series, leads to an analogous outcome, for Leto’s death leads to re-emergence of sandworms, in each of which resides “a pearl of his consciousness,” and, in the grand scheme of things, part of the same larger plan for the redemption of humanity (you need to follow the entire Dune series for this to make sense.)  But fundamentally different, at the same time, perhaps, because Judas, when confronted with his test of faith, obeyed at the cost of his faith–well, at least, that’s my novel and story.

In the end, the Heavenly equilibrium is where people do the “right thing,” without asking for reward–i.e. feed others with their extra long chopsticks–relying only on the faith that, in the end, God will provide.  When they ask “what is in it for me” and try to stipulate conditions, the path is set for a descent to the Hellish equilibrium when the arrangements start breaking down.  But without faith, or at least, enough people with strong enough–i.e. completely irrational–faith, Heavenly equilibrium cannot sustain itself.  Beneath this simple characterization is that what “the right thing” constitutes is hardly obvious:  is handing the other candlestick to Jean Valjean the right thing?  Is betraying Jesus Christ without questioning it the right thing?  Is creationism and other forms of religious extremism the right thing?  Is it simply doing your utmost as you see fit, or is it trying to find out what others want from you and trying to adjust everything to their sense of what they see fit?  Perhaps it is none and all of these things, and that the thing to do is to just place trust in the unknown and let things be while doing what you can, without trying to be too “rational”–that brings the point back to Kierkegaard’s original argument, that you “believe in” things that you do not understand, things that make no sense.  Perhaps Pangloss was right, after all–not because the world is objectively the best that it can be, but because cynicism subverts faith, and without faith, the world is set on a swift path to the Hellish equilibrium.