[Off-Topic] Math, Trolls, Haters, and Internet Discussions

In times of social networks and open discussions on timelines and forums, we’re already used to the fact that there’s never consensus on anything. And in times of Twitter, where 140 characters define what we’re going to say, throwing out something like “X works,” “Y doesn’t work,” “I agree with A,” or “I disagree with B” is a guarantee of a long, endless flame war.

I’m guilty too, addicted to arguing about serious subjects and irrelevant ones alike. It’s part of the entertainment, I guess, but I’ll admit that sometimes I just run out of patience. Anyone who watched my more recent talks will remember the part where I say this: people look for “validation” of their ideas and arguments. It seems that the more people agree, the more valid the idea supposedly is, the so-called “democratic” process where 50% + 1 guarantees victory.

There are several problems with this, and I already discussed part of the topic in Mea Culpa: Democratic Organizations Don’t Work. Although I’m not a formal, working mathematician, my foundation is mathematics. One of the good things I remember from my time at the Institute of Mathematics and Statistics at USP was precisely the heavy mathematical foundation I was put through. To this day I bring what I learned into my daily life.

Laws Are Laws

The first big thing I learned is this: given a set of axioms, and given that a certain theorem is proven, I can use that tool with the guarantee that it will always work within the stipulated premises.

So, given that natural numbers exist, given x belonging to the naturals and given the algebraic properties of the naturals, I know that y = x + x and that y will be in the naturals. With that, I can say with full certainty that 2 + 2 is 4 and will always be 4.

That matters because I don’t need a majority’s “validation” to know it. It doesn’t matter if someone proposes a vote and 1 million people say 2 + 2 is 5. Quantity of opinions doesn’t undo Algebra. Certain areas of scientific knowledge have been fully proven, and they don’t depend on the consensus of “opinions.”

Majority and authority mean nothing within that context.

This gives me several certainties. There’s an entire body of scientific knowledge across the most different areas, from mathematics to physics, biology, psychology, sociology, and medicine, that is trustworthy and at our disposal. And using it doesn’t depend on consensus, on voting, or on the “validation” of any group.

It also gives me the certainty that just because I don’t know something, that doesn’t mean someone else doesn’t already know it, and it raises my esteem for proper research into that body of knowledge. The error is being too lazy to do that research and assuming that because some majority said something, or because someone with apparent authority said something, it “must be true.”

To me, by definition, everything is wrong until it’s rigorously proven to be true, by the same methods that guaranteed that body of scientific knowledge.

First World Problems

In the self-help world there are thousands of “formulas,” or “recipes.” Recipes to lose weight, for success, to be happy, and so on. It’s an enormous industry that, at least by 2010, was moving around USD 11 billion. It won’t stop and should grow.

We move along Maslow’s pyramid. Our parents’ and grandparents’ generation still had to worry about the most basic survival: food, health. In this new generation, a huge portion of the population lives much better, and that base is no longer the biggest priority.

But human beings will always look for problems to worry about, the famous “first world problems”. Sometimes it seems we’re a species built to find problems even where they don’t exist.

That’s why the self-help market grows so much, and why problems that seemed not to exist a few centuries ago now seem so much bigger: depression, stress. Medications that were never so needed 2 or 3 centuries ago are now manufactured by the ton: Zoloft, Prozac, Paxil, Celexa.

For the record, I’m not belittling these problems. A huge portion is quite real, and thankfully modern medicine has the instruments to treat it. Still, it’s undeniable that a lot of people make bad use of that circumstance, since unlike a broken leg, there’s no physical evidence of this kind of problem.

I bring it up because it’s already part of our culture to assume this kind of pathology is a common thing. With each new generation, it seems everyone is made of crystal and any small disruption already breaks them. The impression is that if this generation were magically transported to the 17th century or earlier, no one would survive.

The Effect of Self-Help

All that said, here comes the part that bothers me most: the magic formulas, the silver bullets. Within the self-help market, I don’t mind that much. After all, what harm is there in someone reading “Who Moved My Cheese” to entertain themselves?

The problem is when pseudo-science gets taken as real science.

It’s what I call “because it worked for X it must work for Y,” or what plenty of people have heard me repeat ad nauseam: “correlation is not causation”.

All self-help is one or more formulas, duly wrapped in heavy marketing and sold as universal solutions.

“Just think positive.”

On their own, statements like that are harmless, but they quickly unfold into biblical proportions.

What’s the problem with formulas? Again I go back to my mathematical foundation. A mathematical formula, on its own, is useless: it’s undefined, incomplete. To be completely defined, it needs at least two more elements, a Domain and an Image. For example, look at the formula:

f(x) = 1/x

Immediately someone could say “but this formula is wrong, because if x is zero the calculation doesn’t work.” It’s a good observation, but it starts from a premise: that x can be any number that exists.

But if I define it correctly and say:

given x belonging to the domain of real numbers, and given x different from zero, f(x) = 1/x, will result in the image of real numbers

Now this formula, in the field of Algebra, is well defined and undisputable. Notice what I did with this simple example: I gave an incomplete formula and immediately generated a discussion about it. That’s exactly what happens in every social media discussion and every self-help topic.

To repeat: all self-help is one or more formulas that don’t define the domain or the image. Each person who reads that incomplete formula tries to complete it with their own domain, “for me it works” or “for me it doesn’t work,” and we’ve just found the simplest origin of every flame war, every hater, and every internet troll.

On the other hand, we also find the first way to distinguish an invalid formula from a “possibly” valid one. With the invalid one, you’ll have enormous difficulty defining the domain. We always start from the largest domain, the one that would work for everyone in every scenario. The formula breaks on the spot, so we start reducing that domain and, invariably, it shrinks until it reaches a single case that once worked.

Complex Systems, Biographies, and the Fallacy of “Evidence”

And normally the formulas really do reduce to a single individual. That’s the case with every biography: the sequence of events a certain individual went through, only they went through, and it doesn’t repeat.

I’ve been talking about complex systems for a long time, since at least 2009 the subject has caught my attention. I’ve fallen into the trap of deriving theories about the concept, but I’ll admit that so far I haven’t succeeded. In fact, the whole field of sociology and network studies is still in its infancy in this kind of knowledge, with little in the way of postulates and laws. So handle this kind of subject with far more care than usual.

Quantum physics has also been unduly exploited in the self-help world. Look at calamities like “What the Bleep Do We Know” to understand how to turn a serious subject into a joke (that plenty of people think is serious).

At the risk of being superficial, I’ll summarize the relevant part like this: in the real world, we’re all part of a complex adaptive system. An action I take can trigger several others, which in turn trigger several more, and many of them interact with each other, creating a network of incalculable nodes and connections.

It’s practically impossible to determine the end of a chain of events in a network with countless variables. I say “practically” because we still don’t know how to determine all the variables of the equation, and for all practical purposes that makes any prediction impossible.

Of course, given certain limits of space, time, and error margins, we can predict plenty, enough to send rockets to Jupiter with precision. On the other hand, there are many cases whose error margins are still hard to control, and meteorology itself is an example.

That’s where the idea comes from that a butterfly flaps its wings in China and a tsunami hits Rio de Janeiro. The butterfly didn’t cause the tsunami. It was only an initial condition of an intricate chain of events that happened to result in it.

Now, given a certain result, in many cases we can look backward and trace the chain of events back to the initial conditions. Anyone who watched CSI or some detective show knows we can collect evidence and use deduction to connect events back to a point of origin.

That’s how all “formulas” are created. The chain of events has already happened and won’t change anymore, because within our Universe the past is immutable and time only has one direction.

George Santayana once said “those who cannot remember the past are condemned to repeat it.” If we take what I’ve said so far literally, we’ll conclude that History rarely repeats itself. Just because the initial conditions and the result resemble those of another event, the chain in between is rarely the same. Reading it as “History repeating itself” is coincidence and a series of tricks our brain plays all the time, including confirmation bias.

I know this stretch can get complex, but the point is this: just because something happened once, that doesn’t mean the same chain will happen again.

The initial conditions and the chain of events are that restricted “domain” of the “formula” I mentioned above. And as Duncan Watts would say, everyone fools themselves all the time with the concept of “obvious.” Today it seems obvious to say Facebook is a success. But in 2002 no one could have predicted that in 2012 there would be this Facebook thing and that its IPO would open with a valuation of USD 104 billion. After the fact, we can try to trace the events backward and find the initial conditions and the chain that made it possible. Never before.

Empirically, out of everything I’ve seen offered as a silver bullet, the “best formula” looks very good, until you start to question it: “it looks like a Formula that leads to a good result (Image), but what are the necessary initial conditions? What is the Domain of this formula?”

And when you start to question that, the theory doesn’t hold up for 1 second. Take Lean Startup, the tech world’s fashion. Look at Eric Ries’ initial conditions: you’ll find examples of Groupon, Intuit, and HP, companies that are anything but “small startups,” but the book is evangelized to every small entrepreneur. There’s a clear contradiction of initial conditions, and the scientific method is very different from what the book suggests.

“But there are several good examples of small startups that followed Lean Startup and did well.” And here’s another lesson anyone who watched CSI knows how to spot: a contaminated crime scene is useless. In none of those cases can you say the “cause” of success was using Lean Startup. There may be a “correlation,” and a small one, because we’re talking about a complex adaptive system.

Did the butterfly “cause” the tsunami? The probability is very small. But then marketing comes in. As Joseph Goebbels, Nazi Germany’s propaganda minister, would say, “the bigger the lie, the more they’ll believe it,” or the derivative of that, “repeat a lie enough times and people will believe it’s true.”

As Carl Sagan would say, “extraordinary claims require extraordinary evidence.” And that depends on exhaustive work of testing to break the hypothesis. A medication, made seriously, takes years, sometimes decades, to reach pharmacies, but silver bullets go viral in a matter of hours or days. Depending on who speaks and how, it gains the status of “unquestionable truth” very fast. Any prosperity-gospel preacher can tell you that.

Just because it “seems” to have worked for 1, 2, 10 cases, that isn’t enough to make something true. Charles Darwin’s “Theory” of Evolution of species has tons of concrete, solid evidence, has been questioned, attacked, and meticulously torn apart for more than 150 years, and for all practical purposes is already close to an absolute truth. Even so, it still hasn’t earned the status of “Law.” If it hasn’t, why would something far less tested deserve it?

Conclusion

In practice, unless it’s part of the body of scientific knowledge already recognized and exhaustively documented, everything else is questionable, should be questioned, and should never earn the dogmatic status of “truth,” by definition.

Self-help is pseudo-science, by definition.

Formulas that guarantee a certain “result” (Image) without a Domain are incomplete and undefined, and that will necessarily split opinions, because each person has their own domain. And just because a group is bigger than whoever is questioning it, the formula doesn’t become true. The opposite would be following Goebbels’ doctrine.

And what actually is proven science needs no quorum, majority, or “validation.” 2 + 2 will always be 4, no matter who wants to argue otherwise.

A tip: for any subject that crosses your path, use Google. Put the term next to the word “debunked” or “skeptic,” “fake,” or “scam,” and you’ll find the answer. For example, search for “The Secret Debunked” and see how much has already been published taking down the so-called “Law of Attraction”. I do this all the time. Nothing is unquestionable, no matter who’s saying it.

Since childhood I’ve been a strong defender of destroying pseudo-science, because it causes more harm than almost anything else. Remember that coincidences happen, and they aren’t so rare.