## Why you should not be surprised when you meet two people who share the same birthday

joão pestana

This article is written with a coworker of mine in mind, given the disbelief shown when I presented what is know as the birthday problem or the birthday paradox — which is not a paradox, it just feels like it due to our weak probability intuition.

Let's start easy with the pigeonhole principle and a clear example of something everyone will surely agree with me — I hope. If we have 5 red balls and only 4 boxes to put them in (fig. 1), then surely one of the boxes must contain, at least, 2 balls. What does this have to do with people and their birthday? Well... Think of it this way. If we put 367 random people in the same room, then at least 2 of them must share their birthday. Like putting 367 red balls into 366 boxes, see?

Figure 1 — Visual representation of 5 red balls and 4 boxes.

Before you start to curse my name, because surely all those people can have their birthday occur at any day — including February, 29 — so why should they necessarily overlap? Try thinking about the problem the other way around. Imagine how you can make sure no one shares a birthday! Easy, right? Just have all the people celebrate their birthday in sequence. Let's say, Mark's birthday is January, 1, Lisa's is January, 2, Brian's January, 3, ..., Sarah's December, 31, and so on until every person is assigned to a non-overlaping birthday. Then... What about the 367th person? What about John? As soon as John enters the room, he must share a birthday with someone, because he must have been born in one of the different 366 days that make up a full year.

It still doesn't feel right, does it? Of course that happens, if I assign a day per person, but surely we can reason that some of the days might not even be celebrated! And that's were your reason it's tricking you. You are not thinking about people having birthdays, but rather you're thinking about you and your own experience. In your daily life, birthday's are a special and not frequent event and double birthdays are even scarcer! In light of this, you think about all the empty days in which you don't know a single person who's celebrating their birthday on. When you meet someone new, most likely he or she will have his or her birthday in some of those days that are empty to you. You assume that, because birthdays are a rare event to you, then they surely must always be a rare event — and that's just not true.

Just to complete the above idea, as soon as you start to create empty days, you must create shared birthdays. If you move Lisa's birthday from January, 2 to January, 1, then no one celebrates their birthday on January, 2, but Lisa is automatically sharing January, 1 with Mark. Hopefully, by now, you agree with me that when the number of people is 367, there is a 100% guarantee that, at least, 2 among the 367 must share their birthday. I can tell you now that you only need 70 people to reach the 99.9% guarantee and just 23 people will suffice for those fifty-fifty odds.

Do you not believe me? Here comes the fun part! Let's prove it... mathematically. First, let's forget about February, 29 and assume each day is equally probable. The problem is as follows. We want to find the probability that among N people, at least, 2 share a birthday. Since there are only two possible situations: 2 different persons share a birthday (A) and 2 different persons do not share a birthday (bar A), among N people, we can analyse it either way. If P(A) is the probability of 2 people sharing a birthday, then P(bar A)=1-P(A) is the probability of 2 people not sharing a birthday, among N people. I shall use this form, as it makes the process easier.

We shall think in sequence and analyse each person individually, comparing him/her to all the others we've analysed before. Starting with person 1, the probability of his/her birthday not being the same as the people before is 1, because we haven't analysed anyone yet. Let's write it as 365/365. Next, we analyse the second person and the probability that he/she doesn't share a birthday with person 1 is having been born in any possible day, except for person 1's birthday, so it becomes 364/365. Again, using the same reasoning, the probability that person 3 doesn't share a birthday with person 1 and 2 is having been born in any possible day, except for person 1 and 2's birthdays, so it becomes 363/365. Generally, we can say that P(X)=1-(X-1)/365 is the probability of person X not sharing a birthday with all the X persons before him/her.

Now, we are in a position to (almost) obtain the result we want! The probability that among N people no ones shares a birthday is thus P(bar A)=P(1)*P(2)*P(3)*...*P(N-1)*P(N) and we can write it as a formula:

P(bar A)=prod_(X=1)^N (1-(X-1)/365)=(365!)/(365^N(365-N)!)

You can test it yourself that for the values N=1 and N=366 we get the extreme results P(bar A)=1 and P(bar A)=0, respectively, meaning that the probability no one shares a birthday among a group of 1 single person is 100% and the probability of no one sharing a birthday among 366 people is 0%, as explained in the beginning. If we calculate the complement of P(bar A), then we get what we wanted all along: the probability of, among N people, at least 2 sharing a birthday P(A)=1-P(bar A). Input the values N=23 and N=70 and we get, as promised, P(A)=50.73% and P(A)=99.92%, respectively.

Meeting someone who shares a birthday with you is one thing, but among a group of N random people, 2 people sharing the same birthday is another thing. That's why your reason tricks you. You fail to distinguish the two situations even though the first is somehow rare and the second is clearly not.

Just in case you're wondering how to calculate the likelihood of finding someone with the same birthday as you among N people, it's not difficult. We can do a similar reasoning as before, but instead of comparing will all previously analysed people, we compare only with the first — you. And thus, it becomes the probability of person 1 not sharing his/her birthday with you times the probability of person 2 not sharing his/her birthday with you, and so on. That is, P(bar A)=364/365xx364/365xx364/365xx...=(364/365)^N and again P(A)=1-P(bar A) is the probability of finding someone with the same birthday as you. So how many people do we need for the fifty-fifty chance? N=253 will give you P(A)=50.05%.

## Sexuality explained through mathematics — a non-biased language approach

joão pestana

So you think you've got sexuality pretty much figured out, right? If you're born a male, you're attracted to women and the other way around. If you've ever had sex, it's not a big mystery and the mechanics are quite simple. Right? Think again. Biologists and psychologist are still working their way into figuring out how it all works out. What do I think I do better? Nothing at all, to be honest. I'll just try and use the language of mathematics not to explain how and why things are the way they are, but rather to give you a glimpse of how complex the whole subject is.

Maybe, just maybe, you're a somewhat open-minded person and you allow yourself to accept the concept of homosexuality. Great! Does it help? Well... Yes and no. It complicates things on my end, but it does take you a step closer to a fantastic member of modern society. But now that we can work with both heterosexual and homosexual men and women, we have much more ways we can arrange people. Both men and women can either be attracted to their own gender or the opposite one. This give us 4 different sets in which we can arrange people into (table 1).

 Man Woman Man Homosexual Heterosexual Woman Heterosexual Homosexual
Table 1 — Assigning men and women to each other in couples and grouping them into two different sets.

Now for the fun part — the mathematics, of course! Let m_i in M be some random male-born person and w_i in W be some random female-born person each belonging to the set of all Men and Women, respectively. We can thus arrange each m_i and w_i into couples (a tuple of length 2) such as (x_i,x_j) where x can either be m or w. We can define as homosexual any couple that is fully contained within just one of the larger sets M or W, that is (x_i,x_j) in W or M. An heterosexual couple can then be defined as any couple that is not fully contained within just one of the larger sets, but can only be contained by the union of both, that is (x_i,x_j) in M uu W.

What if some person is attracted to both genders? Should we allow for bisexuality? Of course, definitely! Let's do it. Let's fix the first member of the couple and keep the second one as undefined. Assuming that the order of the pair does not matter, we can define a bisexual man or woman as the first member of either (m_i,x_j) or (w_i,x_j) in M uu W. But isn't the constrain to a tuple of length 2 too strong? I guess we are mostly a monogamous species, but nonetheless, some people do find themselves as an element of a tuple with length larger than 2. Under such conditions, it is certain that whenever n > 2 two or more elements of the n-tuple has to be bisexual.

Let Q = (x_1,x_2,x_3,...,x_(n-1),x_n) be some n-tuple where n people are in a mutually consensual polygamous relationship such that x_i in M uu W. It should be obvious that at least two of the elements of the tuple must be bisexual. For example, we can have arrangements of 3 people in 2 different ways: (m,m,w) or (m,w,w), because the order doesn't matter and we have only two different possible elements to fill three positions. In the first situation, the men must be bisexual and in the second situation, the women must be bisexual. I'm excluding the all men and all women tuples deliberately, because they add no complexity to the analysis.

Of course, the subject of bisexuality is more complex then either homosexuality or heterosexuality. While some really have no preference over gender, there are some who do have a stronger inclination towards on. While sexual arousal is mostly set specific in men, with both heterosexual and homosexual men responding mainly to respectively female and male stimuli; women show no such preference which suggests a natural bisexual tendency as described by Chivers ML, Rieger G, Latty E, Bailey JM. A sex difference in the specificity of sexual arousal. Psychol Sci. 2004 Nov;15(11):736-44.

Maybe we can define a coefficient of bisexuality, say beta, and allow it to run all the way from 0 to 1, where 0 indicates heterosexuality, 0.5 perfect bisexuality and 1 homosexuality. The range where beta in (0,0.5) shall be called imperfect bisexuality with heterosexual inclination and the range beta in (0.5,1) shall be the imperfect bisexuality with homosexuality inclination. But how to calculate? Well... I don't believe it to be something that is easily measurable, so we must use some proxy. What about the relationship history of an individual? It might just work! Let's define the homosexuality counting function as:

pi_(x_i) (x_j) = {(1,if (x_i,x_j) in X),(0,text{otherwise}):}

Where pi_(x_i) counts in respect to person x_i and is 1 whenever x_i is paired with a x_j from the same larger set X which can either be M or W and 0 otherwise. Let's say we have H={x_1,x_2,x_3,...,x_(t-1),x_t} the ordered set of all people x_i has been in a relationship with (even if it was a one-time event) at time t and it can have any length N >= 0. Then, x_i's bisexuality coefficient is simply:

beta (x_i) = 1/N sum_(t=1)^N pi_(x_i) (x_t) and x_t in H

Or equivalently, it's simply the average of all x_t in X such that x_i in X. That is:

beta = text{all people of the same gender within the history} / text{all people within the history}

So what does all of this tell us? Absolutely nothing. Should we categorize people into distinct groups? Of course not! I just showed to you that bisexuality is a continuous function from 0 to 1 and thus cannot be split into finite groups unequivocally. Where along the line should you define the limits of each category? Why 0.32 and not 0.315?

Think we've got it all pretty much covered up? No. That's just half of it! What if you're a woman who is attracted to men? Are you heterosexual? Yes, you are. By our previously stated definition. But what if you were born with a male body? Does that make you homosexual? No, that's preposterous! In the same way that you as a person suffer zero change when you move from the inside of a Mercedes-Benz to a Tesla Motors vehicle, you suffer the same amount of change when you move from a male body into a female body and vice-versa: zero.

The body in which you are born, your sexual identity and your sexual orientation are completely different and independent things that have absolutely no influence over each other. Your body does not determine your sexual identity and even less influences your sexual preference. Your body is merely the vehicle that was assigned to you by default and sometimes mistakes do happen. Finally, I'd like to roughly quote John Oliver on this — "sexual identity is who you are, sexual orientation is whom you love."

Let's do some more mathematics! If we define theta = {XX,XY} as the property of your body, then it can assume only one of two values — even if you decide it should change at some point — XX for female and XY for male. Your sexual orientation can be determined by the bisexual coefficient beta. What about your sexual identity? Should we fall victims of Occam's Razor and define it can also — like your body — assume only one of two possible values? I'll do that only for mathematical simplicity, but explicitly state that it is seldom as simple as that. Let's just say that your sexual identity is omega={m,w}.

Using our previously defined variables, we are now ready to poorly classify a person using a 3-dimensional function P( theta , omega , beta ). This is a very strange and curious function, because two variables are discrete and one is continuous within the range from 0 to 1. Again, and only for the sake of the argument, let's say beta can be mapped into a discrete function in such a way that the limits 0 and 1 correspond to heterosexual preference and homosexual preference, respectively, leaving every other possible value to assume the value of no preference. Now, our P function can assume any of only 12 possible values. Because I believe a graph would be too confusing, I'll display these in table 2.

 Body (theta) Identity (omega) Preference (beta) P( theta , omega , beta ) XX w het heterosexual woman XX w hom homosexual woman XX w no bisexual woman XX m het heterosexual man XX m hom homosexual man XX m no bisexual man XY w het heterosexual woman XY w hom homosexual woman XY w no bisexual woman XY m het heterosexual man XY m hom homosexual man XY m no bisexual man
Table 2 — The possible values for P when mapped into a discrete domain.

The sole purpose of table 2 is to illustrate that no matter how you want to categorize people, in the end, the difference is negligible. I hope you are now capable of understand, by how ridiculous this article is, that you are only definable by your own identity and preferences. Your body has no influence whatsoever in the person that you are and is nothing but a mere shell for others to see and even that can now be changed. Sexuality is a complex issue and cannot and must not be expressed in a finite number of sets — that is, people are not categorizable. Every single person is unique and ever as interesting as the next one.

As a final note, for those of a more curious mind, you can search for terms like pansexuality, androphilia, gynephilia, ambiphilia and polysexuality. The way I see it is this: we'll create so many categories for people that, in the end, there is a category for every single one of us and then we abandon all categories, because we are already identifiable by other things — like our own name — that are singletons as well.

## The evil that bankers do — leveraging and the subprime mortgage crisis

joão pestana

I intend to continue on my previous article, but this time focus on the background gears that almost nobody noticed until it was too late. One might be tempted to ask such questions as why did people applied for loans they knew they couldn't repay? One might be equally tempted to blame the evil profit-seeking bankers for the whole crisis. Either way, only one thing is certain and that is the whole process involved millions of different individuals and possibly hundreds of different institutions.

We should start by understanding the concept of leveraging, which is a technique used to amplify gains — or losses, if things take a turn for the worst. Imagine that you have 100€ with you and while visiting your friend in another town you notice that the oranges there sell for just 0.5€ a piece while, back in your hometown, they sell for 1€. You seize the opportunity — a process called arbitrage — to buy all the oranges 100€ can get you — 200, if you're wondering. Back in your hometown, you go to the market and sell them for 200€ which, at the end of the day, represents a 100€ profit.

Having noticed what you have done, your friend also has 100€ with him and, since he's coming to visit you, he wants to make his trip profitable as well. Because he knows beforehand, he has time to go to the local bank and ask for a loan of 9 900€. Sum this up with the 100€ he already has and your friend has a total of 10 000€ to spend on oranges and he buys 20 000 units. He then arrives at your hometown and goes straight to the market where he sells the oranges for 20 000€. At the end of the day, he has paid back the 9 900€ to the bank plus interest — let's say 990€ at a 10% interest rate — and he's left with a total of 9 010€ profit — 100€ return from his own 100€ and 8 910€ return from the borrowed 9 900€.

As you can see, by using credit, your friend has amplified his gains compared to yours. This is the basic idea of leveraging and most institutions do this — including banks — in order to amplify their profits. Of course, this only works if what you get from the income exceeds the cost of borrowing the extra funds. In this example, you earn 2€ per every 1€ that you spend and, since each 1€ costs you 0.1€ to borrow, this translates into earnings of 0.9€ per 1€ borrowed.

Back to the main topic, the safest investment you can make is with the government. Believe it or not, it's even safer than banks' savings accounts due to the fact that even if the government lacks the funding needed to pay you back, it can just print more money and give it to you. Now, this doesn't hold true anymore for the individual governments of the euro-zone, but the European Central Bank will end up backing up those governments and it's true almost everywhere else in the world — including the U.S.A.

Because government bonds are a very low risk investment, it pays a very low rate of interest and it's not very attractive to serious investors that lust for riskier opportunities to earn more money in a shorter period of time. On the other hand, it's very attractive to banks and other credit institutions, because they can get money at a very low cost. That's precisely what banks did for two main reasons. The first reason is that it amplified their gains due to the leveraging effect. The second reason is that, with the extra funding, they could grant more loans. More loans translated into more cash flows from repayments and interest always amplified by the leverage.

Since everything is going so well and banks are enjoying large profits, other investors want to enter the deal as well — it has a greater and faster return on investment that government bons. This gave banks an opportunity to further increase their gains by letting these investors into the game and they did it with the mortgage loans — the ones you, your friend and many other people signed with the banks. Because you signed a contract with the bank promising to pay, for example, 10 000€ plus interest, that contract is worth at least 10 000€ to the bank. You can read more about how and why this works in my previous article what is money?

The investment banks started to buy the mortgages from the banks that granted the loans. The lenders received a good price for the mortgages and now the risk of default belongs to the investors. These investment banks applied for credit in order to increase their gains through leveraging and bought a huge amount of mortgages from the lenders. Every month, the investment banks would receive very large amounts of money in the form of payments from the homeowners. The cash flow was good, but what was not good was the associated risk of default. In order to dilute the risk, the investment banks created bundles of mortgages which they called collateralised debt obligations (CDOs).

Each of these CDOs had to be filled with payments from the homeowners. The investment banks split each CDO into three parts that would be filled in sequencial order. When the payments from the homeowners finished filling up the first part, the second would begin to fill and whatever remained would go into the third part. You can picture this as putting coins into three piggy banks and you could only start the next one if the previous was full. Investing on the first piggy bank is safer than the second and the second safer than the third one — which is the riskier and thus provides a higher return on investment.

If some homeowners default on their mortgage payments, only the third piggy bank gets affected. The last one to suffer from defaults is the first piggy bank and is considered to be the safest investment while still providing a better return than government bonds. To make this piggy band even safer, investment banks could include an insurance on the investment for a fee — called the credit default swap (CDS).

You may have heard about those swaps before and not know what those were and it's basically this. If there isn't enough money from the homeowners in the first piggy bank and you bought the CDS, the investment bank will compensate you. Because of all this, the rating agencies gave the first piggy bank the highest rating they could and it attracted many investors.

The investment banks are making large amounts of money in profits as well as the investors that bought the CDOs. These investors are so pleased that they want to invest in more and the investment banks try to buy even more mortgages. The problem is that there are no more mortgages, because the all the homeowners that were considered safe already have a house. This is the turning point, as you can imagine. Because houses have been increasing in value, even if the homeowners default, the bank sells the house and gets the money back and so banks that grant loans start to relax their requirements and everyone is entitled to credit.

By now, banks started to grant loans to people who possibly couldn't afford to repay them and they didn't care too much, because they would sell the mortgage to the investment banks and then the risk of default would be theirs. These guys were making so much money that they became reckless and eventually people did start defaulting on their payments. In time, more and more households defaulted and the investment banks ended up with a portfolio of houses that decreased in value with each additional house they received.

## Everyone wants houses until they don't — the subprime mortgage crisis

joão pestana

I'll start by assuming that if you opened this article then you want to know how the Great Recession that began in 2007 came to be. It has been classified as the worst economic event to affect the entire world since the World War II. It's closely related to both the financial crisis and the subprime mortgage crisis that struck the U.S.A. at the same time. Due to the open markets that exist nowadays, there is worldwide freedom to trade, so any individual or institution can make investments in any other country — not just domestic investments. That is the very basic idea of how an event that should be contained within a single country can propagate worldwide.

Why is this such a big deal? Mainly, because it affected everyone worldwide from investors — individuals, governments and institutions — to households (or the common folk). You probably felt it too, even if you are not an investor and didn't contract any kind of loan — not even for a mortgage. Banks are often also investors and when an investment goes wrong, they lose money. Let them lose enough money and they stop having enough money to give back to their costumers — that is, you go to an ATM and are not allowed to make a withdrawal!

What is the solution for a bank that ran out of money? The government steps in and bails the bank out so you, as a costumer, can have your money back. And where does that money ultimately comes from? Well... from you, as a tax-payer. In order to be able to do this, the government has to increase its revenues and it may do so by raising taxes or lowering wages. That's why even if you had nothing to do with the problem, you still suffer its from consequences.

How did it all start and how did investors and individuals get involved with each other? It all comes down to mortgage loans. If you want to buy a house, but can't afford to pay it, you can rent a house — but it's not your house. You go to a bank and realize that you can get a loan to buy a house and then pay a monthly fee to the bank close to what you pay for renting a house. You figure that a couple years from then you actually own the house, so it's a pretty good deal. It's also an investment, because the house has value in itself while renting a house is basically throwing money away. That's the reason why the house effectively belongs to the bank until you finish repaying the loan — it's a collateral, should you default on your payments.

So you contracted a loan for your house and told your friends about it and they think it's a good idea for them as well. The housing market is increasing in value — so it's a very good investment. They also go to the bank, contract a loan and buy a house of their own. Usually, the banks make sure you are able to repay your debt — they require a proof of income and perform other risk measures on you. No matter how thorough their risk assessment is, every now and then someone will default on their payments. There is no problem there, because banks know this and have money set aside as a buffer for these events. If someone repeatedly defaults, the bank sells the house to get their money back.

If all works so well, then what went wrong? Imagine that many people start going to the bank for loans to buy their own house. The demand for houses is on the rise, their price is increasing and the economy is doing great — jobs in construction are plenty, for instance. Overall confidence is high and there is no reason to assume the worst. Banks keep on granting loans and people buy more and more houses.

The problem starts when there are no more people with a good credit rating — those whom the bank assess can pay back their loans, called prime mortgages —, but there is still a very high demand for credit and houses. Because the overall confidence is high, unemployment is low and the economy is doing great, banks start to reduce their requirements to get a loan — no proof of income, no downpayment and so on — called subprime mortgages.

Of course, eventually, these people will not be able to pay back their obligations and start defaulting. The bank keeps their house and sells them to get back the money owed, but there are too many people defaulting and the bank ends up with a lot of houses. Because the bank wants to sell them as quickly as possible, there is a great increase in the supply of houses that exceeds the demand and the prices start to drop drastically. The bank also loses money with every house that is sold below the value of the original loan.

Up to this point, people that defaulted on their payments lost their house and banks are desperately selling houses to get some of their money back. The value of houses drops drastically and those other individuals that are still able to repay their debt also start to default, because now their house is worth a lot less that the loan they have to pay. Because of all this factors, some banks start to have problems with having sufficient enough capital to give back to their costumers when they demand it.

Usually, when a bank is lacking in funds, it can also get a loan from other banks or investors, but the other banks are having a similar problem and investors are now afraid that the bank will default or go bankrupt, so they refuse to lend money to the bank. This is what happened to many banks worldwide that had to be bailed out by governments in order to guarantee that their costumers didn't lose all their money.

By now, you should already have a not so bad idea of how the subprime mortgage crisis came to happen in the U.S.A. and the only things I didn't mention was why the investors refused to lend money to the banks and how did the banks become so careless with their loans. These two factors are related to each other and also with the desire for banks to increase their profits while reducing their exposure to risk. I'll explain that in a follow-up dedicated article.

## Carl Panzram's recipe for a sadistic serial killer

joão pestana

The reason I'm fascinated by deviant minds and individuals is because we learn very little — if anything at all — by observing what is the standard. Only by studying the unusual can one hope to understand what are the underlying mechanics. The story I bring can be true or a fiction of Panzram's constructed alter ego. Nonetheless, it offers an incredible insight into the construction of an individual.
In my life time I have murdered 21 human beings. I have committed thousands of burglaries, robberies, larcenies, arsons and last but not least I have committed sodomy on more than 1 000 male human beings. For all of these things I am not the least bit sorry. I have no conscience so that does not worry me. I don’t believe in Man, God nor devil. I hate the whole damed human race including myself.
Fear not, for those words were written by Carl Panzram, as in figure 1, while at the United States Penitentiary, Leavenworth in Kansas where he would end up killing Robert Warnke with an iron bar. For this crime, Panzram would finally receive the death penalty he wished — his own way of suicide. The sentence was carried in September, 1930.

Figure 1 — One of the papers where Carl Panzram wrote his autobiography and confession.

The story begins in 1891 when Carl Panzram (figure 2) is born to a couple of german immigrants in the state of Minnesota. His father abandoned the family when he was 8 years old and by the time he was 11, he was sent to a reform school for stealing from his neighbour. He graduated after two years and about that moment he had the following to say.
After serving about 2 years there I was pronounced by the parole board to be a nice, clean boy of good morals, as pure as lily (...) I had been taught by christians how to be a hypocrite and I had learned more about stealing, lying, hating, burning and killing. I had learned that a boy's penus could be use for something besides to urinate with and that a rectum could be use for other purposes than crepitating. (...) I made up my mind that I would rob, burn, destroy and kill every where I went and everybody I could as long as I lived. That’s the way I was reformed in the Minnesota State Training School.
He was young and poor and so he learned how to ride and sleep on freight trains. On one of his travels, he recalls being gang raped by a group of transients he had invited to share the box he found. He was again raped when he tried to beg for food near a group of stray people in some mid-west town, but they got him intoxicated on whiskey and he only found what had happened when regained consciousness. I'll try and let him tell most of the story, because for a man without proper education I do believe he writes remarkably well.
I cried, I begged and pleaded for mercy, pity, and sympathy, but nothing I could say or do could sway them from their purpose. I left that box a sadder, sicker, but wiser boy. (...) These two experiences taught me several lessons. Lesson that I have never forgotten. I did not want to learn these lessons but I found out that it isn’t what one wants in this world that one gets. (...) Another lesson I learned at that time was that there were a lot of very nice things in this world. Among them were Whisky and Sodomy. But it depended on who and how they were used. I have used plenty of both since then but I have received more pleasure off of them since than I did those first times.
From then on he proceeds to live his life according to his motto "rob 'em all, rape 'em all and kill 'em all." By 1910, he had already tried the army and failed — he got imprisoned in military facilities for insubordination. This is when he claimed that no more goodness remained within him. He succeeded in robbing the house of the then secretary of war and future president William Howard Taft that had previously approved his army sentence.

Figure 2 — A portrait of Carl Panzram.

From the spoils of the robbery, Panzram was able to purchase a yacht which marked the beginning of his killing spree. He started by hiring sailors as his crew which he intoxicated with alcohol in order to be able to sodomize, rob and kill them. He then proceeded to spread his legacy across different countries in Europe and Africa. While at the latter, he would target a very young boy around the age of 11.
He was looking for something. He found it too. I took him out to a gravel pit about one quarter miles away. I left him there, but first committed sodomy on him and then killed him. His brains were coming out of his ears when I left him, and he will never be any deader.
He finally returns to the United States where he spends most of his time incarcerated in different institutions. While at the Washington DC district jail, he befriended a young prison guard by the name of Henry Lesser — the only man in the world Panzram didn't want to kill — who insisted on him to write his life story and provided the writing materials.
You know that I spent several years in one of those places when I was a boy and the so called training that I received while there is mainly the cause of my being the degenerate beast that I am today. I have thought about that system of training young boys for all of my life and I know that the whole system is wrong. That system of beating goodness, religion and Jesus into boys in the 99 times out of 100 has the direct opposite effect of taking all of the goodness, kindness and love out of them and then replacing those with hate, envy, deceit, tyranny and every other kind of meanness there is.
Now that you know the story you may feel pity, anger, a mixture of both or even a whole panoply of feelings. You do have an opinion — at least, that's what I hope I induced upon you. We can analyse Panzram's life in different ways.

He may have been genetically predisposed to violent behaviour, had very high testosterone production or suffer from such a thing as the Klüver–Bucy syndrome. Some men are just pure evil psychopaths and nothing can be done to either alter or prevent their criminal tendencies. The question remains as what if not? What if we are really born blank canvas that can be painted anywhere from an ugly draft to a long admired masterpiece?
Yes, hurry it up, you Hoosier bastard. I could hang a dozen men while you're fooling around.
Those were the last words that Carl Panzram offered humanity before he hanged. It's not possible to account for the veracity of all the crimes he claims to have committed. Maybe he was only a scared little boy who realised how fragile he was and no one ever vowed for him so he constructed his own strong and unforgiving alter ego to take vengeance upon the society he visioned as an entity who wronged him. Maybe he admitted and exaggerated his crimes to increase the inspired fear on others. Either way, it remains an almost unbelievable story of this personification of nihilism.