It’s easy to forget that modern society is a very new aspect of human evolution. Modern Homo Sapiens originated around 200,000 years ago, and the Genus Homo of Homo Sapiens is estimated to be around 2.5 million years old. Mammals themselves first appeared a distant 200 million years ago.
However, until about 10,000 years ago, humans generally lived as hunter-gatherers. The earliest known writing, cuneiform, is only 5,000 years old, and Copernicus didn’t even make the blasphemous proposition that the Earth actually orbited the Sun until a mere 500 years ago. Natural selection has barely even begun to account for the hustle and bustle of modern life, which has accelerated at an unprecedented pace. Simply put, humans are not designed for scrutinizing legal provisions, but for spearing fish and thieving secret squirrel stashes.
Naturally, these 200 million years of mammalian evolution, void of the chaos of modern civilization, have crafted stress as a means of triggering one of two physiological responses when in danger: fight or flight. If you see a lion when digging up plant roots, run! If an unarmed caveman who’s smaller than you wants to ransack your cave, fight! However, if a creditor sends out a collection notice, these options don’t suffice. If you drop your mail and run, someone will steal your identity. If you try to fight the creditor, you get to observe cement’s very slow rate of decay from your jail cell.
Stress is a primitive means of dealing with primitive danger. Its instinctive nature works great for avoiding traditional dangers such as rattlesnakes and vicious, blood-thirsty panda bears, but such dangers just don’t dominate modern life. Our evolution hasn’t caught up to instill instinctive fears of electricity, aspartame, or dice games in shady stairwells.
Stress now, however, is more often than not, a reaction to psychological upsets. This is the counterproductive nature of stress: unpleasant conundrums which require critical reasoning to solve are dealt with on a physiological fight or flight basis. Most of life’s lousy dilemmas require mental problem solving abilities, not fighting or escaping from enemies to protect the food hoard.
When experiencing inevitable stress, which is a part of life now more than ever, try to recognize it as a message that something is amiss. It takes a lot of discipline to suppress rash impulses, but try to figure out the heart of the problem. First try stating the problem, which is often half the answer, then try reasoning through it. Think of stress as a good thing, a message telling you that a predicament is at hand. Then counter the stress with relaxation and critical reasoning.
Whether by personality or experience, highly successful people usually aren’t motivated by stress. That’s not to say the danger of failure isn’t a motivator, but their reason for doing what they do usually isn’t stress itself. A life buried in stress often doesn’t get very far. Warren Buffett, for example, sees making a money as a strategy game. He doesn’t live a lavish lifestyle or bathe in Cristal (but then again, does anyone really know?), but yet he keeps on trying to make more money. But for what end? Perhaps his Bridge addiction is most telling. If evaluating price to earnings ratios made Buffett stressed out and miserable, he might be busy scrapbooking or baking instead.
Stress is old hat for modern society. It leads to shoddy judgment when sound judgment is needed most. The worst part is that stress and fear “occupies a person’s working memory,” draining the brain’s working capacity, which in turn leads to bad judgment when a cool head is needed most.1 The health consequences associated with stress also don’t go without warning: cardiovascular disease, brain shrinkage, and substance abuse. Unfortunately, our predisposed fight and flight reactions haven’t caught up to the pseudo-civilized nature of modern society. When stressed, it’s often probably best to take a step back and rationalize, and then respond in a well-reasoned way. Of course, well-reasoned might mean doing something radical like suggesting the theory of gravity.. just be smart about it!
1. http://www.reuters.com/article/idUSN1736444120070220
It’s simply human nature to attempt to justify our past mistakes. Psychology simply says we lie to ourselves to make ourselves feel better. This has benefit: we don’t dwell on mistakes and simply move on. It also keeps our brains from exerting too much energy for critical thinking by just bypassing a thorough analysis with a brief rationalization. As humans, we can blame this on our brains’ massive frontal lobes. This comes with downsides though, too. It makes reasoning through the true nature of our personal conundrums harder, which can be counterproductive if we repeatedly make the same mistakes. It also leads to many missed opportunities when trying to justify poor decisions by investing even more energy or money into those decisions.
Imagine a case where you’re the CEO of a major company and a year ago you hired a programming team build a massive software package tailored to a specific need. You’ve already dumped $1 million into this software team. They say $200,000 is all they need to finish the job. Then, another team happens to find you and makes a credible case that they can start from scratch and build the entire package for $100,000. Do you pay the first team $200,000 to finish their package, or a the second team $100,000 to start fresh with the package?
Painful as it is, the best decision is to write off the $1 million loss and simply move forward with the next team. It will save $100,000. Our rational minds know this, but it often happens in life and business that we try to justify our lost, sunk investments and go with the path that makes us feel better about our past mistakes. Of course, in corporate politics, you might have to finish with the first team so it doesn’t look to shareholders like you just vaporized $1 million of their money. Be aware, though, when it’s just your emotions at stake. If you feel like you do have to justify that misguided sunk cost, just chalk it up as a learning experience and move on.
Of course, this is a lot easier said than done. Many investors don’t cut their losses and sell stocks they’re convinced are going to go down. Instead they hold onto them, hoping to ride them all way out to eventually see them come back up just to feel better about their judgment. Many of these same investors sell a stock that goes up too quickly as well, just to get a winner’s endorphin rush and cash out. This kind of investing costs many a pretty penny, and while often your gut does provide a good heuristic rule of thumb, be careful not to let your ego get in front of your better judgment.
How many decisions are you trying to justify? Do you continue to rack up debt to make yourself feel better about the rest of your debt? Are you working a job which you go to every day to justify the day before? Are you in a relationship that’s not good for you or your partner, and your intuition knows it? Are you holding credit card debt you know you could pay off by selling an investment with a lower interest rate than your credit card’s APR?
In all of these cases, the answer is to cut your losses, let your ego take a brief beating, and move on. Live every day like it really is the first day of the rest of your life. Figure out what you have and want, and get rid of things holding you back, be it your house, a problematic car, or even the city you live in. What’s more important- numbing past decisions which didn’t work out by imprisoning yourself, or moving on to embrace, with open arms, the next opening doors of opportunity?
Every day presents less opportunities than the day before it. It’s the nature of fixed time and traversing towards the end of it. It doesn’t matter how many doors have closed though, because they simply don’t affect the doors that are open to you today. Think like an economist. Disregard your sunk costs in making future decisions. It’s hard, but your rational mind will thank you for it. Eventually, your frontal lobes will come around.
I love thought experiments and puzzles because I think they’re food for the brain. Working through them requires critical and logical reasoning, and can often provide tangible answers to elusive problems. Often times, thought experiments present themselves in the form of paradoxes, where a predicament leads to a contradiction or seems to oppose intuition.
One of the more fascinating puzzles I’ve come across in economics is known as the St. Petersburg paradox. In 1713, during the Age of Enlightenment, a time known for glorifying reason, mathematician Nicolas Bernoulli presented a lottery game with an infinite expected payoff. If something has an infinite expected payoff, one might think that a chance to play the game would be worth any finite price. However, to a rational person, a chance at this game is actually only worth a very small amount.
Anyway, onto the game:
The player pays a fixed fee to enter. Then a coin is tossed until a tail appears, which ends the game. The payoff starts at $1 and doubles every time a head appears. The event probability is calculated by multiplying the probability of a tail appearing for each flip, which is always 50%. So, the probably of a tail on the 4th toss (3 heads, then a tail) is .5 x .5 x .5 x .5, or .0625. (The payoff formula is 2n-1, and the probability formula is .5n)
Payoff analysis- Tail appears on:
1st toss: $1 50% probability
2nd toss: $2 25% probability
3rd toss: $4 12.5% probability
4th toss: $8 6.25% probability
Now, you might be thinking, why would anyone spend more than a few bucks to play this game? Well, watch what happens when taking the summation of the expected payoffs:
Despite the conclusion that most attempts at this lottery will likely pay little, the expected payoff is infinite! This means that if a casino has infinite money, a player should want to play repeatedly at any price, right? A good steward of reason probably won’t, though. Why?
Solutions:
(A solution to a paradox should reconcile the logical conclusions which appear to contradict.)
Nicolas’s cousin Daniel, another mathematician, attempted to solve the paradox by pointing out the obvious nature of diminishing returns. $8,000 does not actually provide 8 times the utility that $1,000 does. Likewise, $1,000 is of much more utility to a messenger than a rich man. Bernoulli depreciated the total utility of a payoff using the logarithmic function. However, in 1728, before Bernoulli presented his solution, Gabriel Cramer, another mathematician, depreciated money’s total utility using the square root function. Using the logarithmic versus square root function seems to be arbitrary, but the point is clear nevertheless. Although $1,000,000 equals 1,000 x $1,000, it is not worth 1,000 x $1,000 to a “man of good sense,” as stated by Cramer.
A diminishing utility limit actually suggests that a go at this game is probably worth no more than $10.
Some critics have argued, however, that there is still a paradox even when negating diminishing marginal returns. From that discussion follows:
THE SUPER ST. PETERSBURG PARADOX!
If we assume the payoff becomes increasingly greater for increasingly unlikely events, such as a player getting $2 million when he would have otherwise gotten $1 million, diminishing marginal returns are simply negated. Still, there are more solutions this paradox. Risk aversion is not a solution to this problem though either, since even larger payoffs can be given for rare events. Perhaps this should be called the super super paradox, but we won’t go there. If we assume that a casino will still offer a lottery with an expected infinite payoff, the only known way to solve such a super paradox is to assume that total utility has an upper bound. In other words, unlimited money cannot provide more than a certain limit of utility to begin with! It can infinitely grow towards that limit, but it still won’t surpass it.
Another solution to the paradox, according to Bernoulli, is that people disregard unlikely events, so they don’t account for them in the first place. However, empirical evidence suggests people greatly exaggerate chance events such as becoming a celebrity or winning the lottery.
One last thing to think about is that if a lottery has an infinite expected payoff to a player, it also has an infinite expected loss to the casino. No casino should then profit from providing it at any fee! Of course, chances are that they would profit from providing it, but it wouldn’t be legal to do so, because no financial institution can back an unbounded payoff under a casino’s worst case scenario. Of course, one can’t buy what isn’t sold, but the nature of utility seems to put a bounded, finite value on the game anyway.. if the mythical alien finance gurus ever offer it.
And that is how infinite money is really finite in worth 