ON TRUTH, AND A COUPLE OF GRAPHS

Aristotle defines truth – The Parable of the woman who does not fart – Bernoulli, Uncle Bill and the Russians – Wahrheitsgehalt: There is truth to what you say

Friends, I couldn’t find a better way to start:

“To say of what is that it is, or of what is not that it is not, is true.” Aristotle (384–322 BCE).

aristotle
Figure 1 | Aristotle 384BC-322BC

Very few of us have a lot of things in common, and conversely, a lot of us have very few things in common. Here is a familiar one – the search for truth. It is what drives a glycobiologist to carry out brutal experiments overnight. To the point where he ask himself (deep in thought) during the weekly Sunday school service: Does Heparan Sulfate Controls Progenitor Expansion by regulating Sulfotransferases? (As the Pastor preaches from Leviticus 22).

Or on the other end of the spectrum, consider our dear friend blushing furiously at the incessant advances of a very young Scottish entrepreneur living in a mansion downtown. She ask herself every night before she sleeps: is he really the one?  (And tries to carry out her experiments, unlike our scientist, during the day).

The quest for truth, to say the least, is ubiquitous; and because truth is the aim of our beliefs, our quest should start by paying keen attention to our beliefs, our assumptions.

Capo and The Parable of the Lady who does not fart

Long, long ago, during the days where great (and sincere) intellectuals are easy to come by, a group of intellectual itinerants roaming around Šiauliai have occasional lectures on the hills of crosses. Usually lead by a frail, hoary man, whom for hierarchical purposes we can comfortably call The Capo. Capo has a slew of parables […] this particular parable is probably one of the most popular lessons among the Mindaugas, till this day it is taught to kids. It goes thus:

“There was a rich man who has a quite odd and unbelievable ‘ambition’ – to marry a woman who does not fart. His ambition was so entrenched that he extended his search to the Samogitians and Semigallians. After years and years of intense search, aging begin to set in, and he begin to lose all hope of getting married to a fartless woman.  Just before the door of hope was shut, a Semigallian woman came along, she claims not to fart. The man was gleeful and they started courting at the spot. His search for truth begins – he paid close attention. when they went for dinners, while taking a walk; carefully hoping not to be disappointed, and occasionally sniffing the air. After several years of courting (and of no fart) they decided to get married. On the first night after the marriage, the rich man told the wife he was going to get a friend who got sick into an inn, and the wife proceeded into the restroom to freshen up, but the rich man, almost halfway into the journey, forgot to pick his purse so he rushed back on his horse to get it. Just as he opened the door, he got an unbelievable putrefied smell enough to choke a new born to death. Before he could utter a word, the wife, unaware of his newly-wedded husband presence, engaged in another round of what we can call an endless bombastic fart session. Unfortunately, the next day they got divorced”

Capo ended his famous parable by saying “Verily, verily I say unto you the presence of an absence does not prove absence therefore to disconfirm is far better than any form of confirmation”

the-rich-man
Figure 2 | The Rich man, after his divorce: Haters will say it’s a photoshop

Before we quickly judge the rich man, we have to realize that he is not alone. On the contrary, a ton of us replicate this trait on a daily basis – and it is not restricted to individuals; corporations and institutions are not excluded. Let’s take a look at a popular example in social science research – this example will take us through a different (and intellectually stimulating) kind of fart.

Bernoulli, Uncle Bill and the Russians

The diminishing marginal utility of wealth dictates that the more money you earn the less the utility (desirability/happiness) you will derive from them. This leaves us with a familiar concave graph when we plot utility against wealth, there are so many things we can do with this idea but, first, let’s consider Uncle Bill’s story.

Bill isn’t exactly the type born with a silver spoon, and unfortunately things has gone even worse. At the age of 35, all he can really boast of was about $1200 in bank. Just before he clocked 36, Lady Fortuna smiled on him, and it was a big smile – he got lucky with this deal with the Russians (let’s ignore the type of deal for now), the end result is more important for us – a $4 million increase in his wealth.

He was extremely happy, painted his home town streets with the darkest form of red you can find in the market. His status swelled up. And you know the Russians loves Bill’s aura and charisma, it seems to be a perennial smile from Lady Fortuna. Not too long another deal ensued with the same end result – $4 million. The only thing that changes this time around is that he is not as happy as he was from the first deal even though he got the same increase in wealth each time.

This is the diminishing marginal utility of wealth. (An evidence I tender to folks who thinks getting more and more money will make them happier). The distance from $1200 to $4,001,200 is very different from that of $4,001,200 to $8,001,200 – It turns out that there is a BIG difference between the actual value of money and the psychological value of money. The German psychologist, Gustav Fechner, has a cool law for this called Fechner’s law – it concludes that utility is a logarithm function of wealth that is (U(W) = log (W), it is never linear), to put it more colloquially money cannot buy you happiness, if you manage to buy some, it wouldn’t last for too long (i.e the hedonic treadmill). We have enough information to start our own graph now.

Figure 3 | Bill after the smile from Lady Fortuna: The blue curve represents the diminishing marginal utility of wealth, that is the utility of wealth increases at a decreasing rate.
Figure 3 | Bill after the smile from Lady Fortuna: The blue curve represents the diminishing marginal utility of wealth, that is the utility of wealth increases at a decreasing rate.

Fechner was not the first to think about this problem, Daniel Bernoulli the Swiss Scientist has thought about this problem about a century earlier and came up with the expected utility theory (called moral expectation during in his time) – which explains how we make decisions riddled with uncertainties.

Back to Uncle Bill – Bill made a lot of friends in Russia particularly at the eastern side of St. Petersburg. Anytime he goes to Russia they do a lot of Vodka and Mors depending on their mood, and occasionally spend some more time gambling. Adrik, a billionaire, is the unauthorized leader of the Russian gang and he is notorious for his philanthropic gamble games under the influence of alcohol. In one of their numerous trips to bar, drenched in alcohol Adrik posed a gamble directly to Bill:  a) Toss the Russian ruble coin, if it lands with a head bills get $10 million with a tail he gets nothing or b) Take $5 million (and run).

Even in his stupefied state Bill obeyed the expected utility theory, he went for b) $5 million. Bill like most mortals is risk averse – you should note that, mathematically, 50% chance of winning $10 million also $5 million.

If we mark these points on our graph (Figure 4), we will note that the expected utility EU (which is, again, a measure of happiness or desirability) for the $10 million gamble, UW[10/0] (black line), is lower than the utility of the standard $5 million, UW[5] (blue line). That is, (UW(5) > UW(10/0)). This is the where Bernoulli made a great insight which is, the diminishing marginal utility of wealth explains our aversion for risk.

marginal_2
Figure 4 | Uncle Bill in the bar, gambling: UW(5) > UW(10/0). The black line represents a linear relationship between wealth and utility, that is for every ‘x’ amount of increase in wealth, there is a fixed value ‘y’ increase in utility.

The expected utility theory (EUT) makes so much sense, very brilliant theory and it was dully considered by Economists as the correct model for decision making under uncertainty for up to 300 years! Even though, as we will see very soon (in analogy to Capo’s parable) the theory is more or less like the rich man’s ex-wife who claims not to fart […]

On exactly Bill’s third deal with the Russians, EUT got dismantled. This time around, a newbie from America, Maxwell Smith, came around from Adrik’s external links. Max was this young Silicon Valley hungry rocket engineer. Bill at this point now worth $20 million and our hungry rocket engineer, just about $1 million dollars. This time around Lady Fortuna has just began to lose her patience with uncle Bill. He lost $15 million in the deal, on the other hand Max profited $4 million making the two men standing at par ($5 million).

As absurd as this might sound the expected utility theory predicts that both Max and Bill will be equally happy, that is, have the same utility; and that was the theory accepted as truth for years.

The missing information in the EUT is that it pays no reference to starting point of wealth of individuals – it predicts utility based only on the absolute value of wealth. The theory was only recently replaced by the prospect theory which considers this missing link, again after almost 300 years. This shows that folks in the field are completely blind or disregard evidence that negates their belief – an awful way to approach truth as Capo has showed us.

When you belong to any establishment, you are taught about theories (and beliefs) in the field, which are taken up by most as truths. As such, there is a bias at the onset to uphold the truth which leads to the intuitive scan for positive evidences. Daniel Kahneman calls this the theory-induced blindness and as he noted “once you have accepted theory, it is extraordinarily difficult to notice its flaws”

Another example: the discovery of the earth rotation by the observation and experiments carried out by Galileo – people has come to believe in the laws of earth motion as proposed by Aristotle for years. Galileo went on to pay a huge price for his quest.

Wahrheitsgehalt, there is truth to what you say.

Truth as an entity could bear some non-truths, kindly consider the following statements:

It rains every Friday

That’s probably true in your hometown, maybe, I don’t know. However, a way to test this assertion is not to look for positive evidence but rather, instances where it does not rain on Friday.

To restate Capo: The most reliable way to prove you are right is to show you are not wrong.

 

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