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

In times of social networks and open discussions on timelines, forums, etc., 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.

And what can I do — I’m also guilty, addicted to arguing about both serious and irrelevant subjects (it’s part of the entertainment, I guess) — but I have to admit that sometimes I just lose patience. Anyone who watched my more recent talks will remember a part where I say: people look for “validation” of their ideas and arguments — it seems that the more people agree, the more the idea is valid. The so-called “democratic” process where 50% + 1 guarantees victory.

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

Laws Are Laws

The first big thing I learned is the following: given a set of axioms, 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, given the algebraic properties of the naturals, I know that y = x + x and that y will be in the naturals. Given all that, I can say with full certainty that 2 + 2 is 4 and will always be 4.

That’s important because I don’t need “validation” from a majority 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 — I don’t need consensus of “opinions.”

Majority, Authority, means nothing within that context.

This gives me various certainties: it means there’s an entire body of scientific knowledge in the most different areas — from mathematics to physics, biology, psychology, sociology, medicine, etc. — that is trustworthy and at our disposal to be used. And its use doesn’t depend on consensus, doesn’t depend on voting, doesn’t depend on “validation” from any group or set of people.

It also gives me the certainty that just because I don’t know something doesn’t mean someone else doesn’t already know it, and it increases my esteem for proper research of this body of knowledge. The error is being lazy about doing this 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, recipes for success, recipes 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, where this base is no longer the biggest priority. But no problem — human beings will always look for problems to worry about, the famous “first world problems” — sometimes it seems we’re a species made to find problems where they don’t even exist.

That’s why the self-help market grows so much — why problems that seem to simply not have existed a few centuries ago now seem so much bigger: depression, stress. And where medications that were never as 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 these instruments to treat it. But it’s undeniable that a large portion makes very bad use of that circumstance, since unlike a broken leg, there’s no physical evidence of this type of problem.

I mention this because it’s already part of our current culture to assume that this type 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 before, no one would survive.

The Effect of Self-Help

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

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

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

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

“Just think positive.”

By themselves, statements like that are harmless, but they quickly unfold into biblical proportions.

What’s the problem with formulas? Again I refer to my mathematical foundation. A mathematical formula, alone, 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 following formula:

f(x) = 1/x

Immediately someone could say “but this formula is wrong, because if x is zero the calculation doesn’t work.” And that’s a good observation, but it starts from a premise: that whoever said this is considering 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 self-help topics.

Repeating: all self-help is one or more formulas, that don’t define the domain or the image of that formula. Each person who reads this 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, 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 a huge difficulty defining the domain. We always start with the largest domain, which works for everyone in every scenario. Immediately the formula breaks — now we start to reduce that domain, and invariably, it will shrink until it reaches a single case that once worked.

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

And normally the formulas really reduce to a single individual — that’s the case of every Biography. The sequence of events that a certain individual went through, only they went through, and they don’t repeat.

I’ve been talking about complex systems for a long time — since at least 2009 this subject has caught my attention. I’ve fallen into the error of deriving theories about this concept, but I must admit that so far I haven’t been successful, and in fact the whole field of sociology and network studies is still in its infancy in this type of knowledge. Little is had in terms of postulates and laws. So interpret this type of subject with much more care than normal. Quantum physics has also been unduly explored in the self-help world — see horrendous calamities like “What the Bleep Do We Know” to see how to turn a serious subject into a joke (that many think is serious).

At the risk of being very superficial, I’ll summarize the relevant part this way: in the real world we are all part of a complex adaptive system. An action I take may trigger several other actions which, in turn, will each trigger several other actions, and many of these actions can 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 innumerable variables. I say “practically impossible” because we still don’t know how to determine all the variables of the equation, and for all practical purposes, this makes anything impossible to predict.

Of course, given some limits of space, time, and error margins, we can predict many things enough to send rockets to Jupiter with precision. On the other hand, there are many things whose error margins are still hard to control — meteorology itself being an example. It’s how the idea emerges that a butterfly flapping its wings in China causes a tsunami in Rio de Janeiro. That phrase doesn’t mean the butterfly caused the tsunami, but rather that it was an initial condition of an intricate chain of events that happened to result in the tsunami.

Now, given a certain result, in many cases we can look backward, into the past, and trace the chain of events back to the initial conditions. If you’ve already watched CSI or some detective show, you know we can collect evidence and use deduction to connect events until we reach a point of origin. That’s how all “formulas” are created. The chain of events has already happened — it won’t change anymore. Within our Universe, the past is immutable because time only has one direction.

George Santayana once said “those who don’t learn from History are doomed 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 of events in between is rarely the same. The fact that we interpret it as “History repeating itself” is mere coincidence and a series of deceptions our brain makes all the time, including Confirmation Bias.

I know this section can be complex, but the point I want to reach is the following: just because something happened once doesn’t mean the same chain will happen again.

The initial conditions and the chain of events are the restricted “domain” of the “formula” I mentioned above. And as Duncan Watts would say, everyone deceives themselves all the time with the concept of “obvious.” Today it seems obvious to say it’s obvious that Facebook is successful. 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 90 billion. After the fact, we can try to trace the events back and try to find the initial conditions and chain of events that made it possible — but never before.

Empirically, from everything I’ve seen offered out there as a silver bullet, the “best formula,” it really does seem very good — until you start to question: “it seems 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 sustain itself for 1 second. It’s like Lean Startup, the tech world’s fashion. Look at Eric Ries’ initial conditions: you’ll find examples of Groupon, Intuit, 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 distinguish: a contaminated crime scene is useless. In none of the cases is it possible to say the “cause” of success was having used Lean Startup — there may be a “correlation,” and small one, since we’re talking about a complex adaptive system. Did the butterfly “cause” the tsunami? The probability is very small. But then comes marketing, as Joseph Goebbels, the Nazi Germany 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 tests to break the hypothesis. A medication, made seriously, takes years, even decades, to reach pharmacies, but silver bullets become viral in a matter of hours or days. And depending on who speaks and how, it gains status of “unquestionable truth” very fast.

Because it “seems” to have worked for 1, 2, 10 cases isn’t enough to make something a truth. The “Theory” of Evolution of species by Charles Darwin, which has tons of concrete and solid evidence, that has been questioned, attacked, dissected meticulously for more than 150 years, and that for all practical purposes is already practically an absolute truth, still hasn’t gained the status of “Law” — so what else, less rigorously tested, could be different?

Conclusion

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

Self-help isn’t science, it’s pseudo-science, by definition.

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

And what is actually proven science doesn’t need a quorum, majority, or “validation.” 2 + 2 will always be 4, no matter who wants to contradict.

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

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