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Creating Pretty Code Blocks in WordPress Sites

Getting Started

I use CodeMirror Blocks for WordPress by Vicky Agravat to create pretty little code blocks as opposed to the boring vanilla ones. To install it, simply go to plugins -> add new -> search -> “CodeMirror Blocks” and install the CodeMirror Blocks plugin.

Once it’s installed all you need to do is change the block type you’re working in to CodeMirror block.

Changing the CodeMirror Block Font Size

One thing I noticed is that the default font size of these code blocks was different from the default text size which created an aesthetic that I didn’t particularly like. To change this, you can simply go to appearance -> customize -> Additional CSS and insert the following CSS code snippet:

.code-block .CodeMirror {font-size: .8em;}

Where 8em corresponds to a font size of 8 points.

Now you can make blocks that look like this:

#include <iostream>

int main(int argc, char** argv) {
    std::cout << "Wow, this codeblock is so pretty!" << std::endl;
    return 0;
}

There you have it, the shortest guide ever to creating pretty formatted code blocks for your WordPress site.

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Autonomous Ground Vehicle Drifting

My knowledge of this topic mostly comes from interview prepping with an autonomous car research lab that I ultimately passed over, though I wish I was involved with the research itself.

I’ll start with the vehicle dynamics involved, phase portrait analysis of the nonlinear system, and then talk a little bit about control methodologies.

Vehicle Dynamics

The simplest vehicle model that is widely employed with autonomous vehicles is the well known bicycle model, as this captures the majority of the dynamics that are relevant to vehicles that do not exhibit large pitch and roll dynamics.

The traditional two state bicycle model consists of the dynamic equations for the sideslip angle, \beta, which is the ratio of the lateral to longitudinal velocities, and the yaw rate, r, with system inputs of longitudinal rear tire force, F_{xr} and steering angle, \delta.

Figure 1. Two State Bicycle Model

In order to relate the front tire lateral force, F_{yf} to the steering angle, \delta, we need to employ a tire model that establishes a mapping between these two quantities. In the literature from Chris Gerdes lab at Stanford, this model is typically a modified Fiala Tire Brush model.

\begin{aligned}   1) \displaystyle \qquad F_y = \begin{cases}   -C_{\alpha}z + \frac{C^2_{\alpha}}{3\xi \mu F_z} |z| z - \frac{C^3_{\alpha}}{27 \xi^2 \mu^2 F^2_z}z^3 & if |z| \leq \alpha_{sl} \\ -\xi \mu F_z sgn({\alpha})  & if |z| > \alpha_{sl}\\ \end{cases}   \end{aligned}

and

\begin{aligned}  2) \displaystyle \qquad z &= tan( \alpha ) \\ \alpha_{sl} &= arctan \left (3 \xi \mu     \frac{F_z}     {C_{\alpha}} \right ) \ \end{aligned}

By adding an additional state of lateral velocity, and augmenting the tire model to account for longitudinal force by using the well known friction circle relationship, we are able to derive the modified three state bicycle model that is used with autonomous drifting.

\begin{aligned}  3) \displaystyle \qquad \dot{\beta} &=    \frac{F_{yf} + F_{yr}}{m U_x}-r \\   \dot{r} &= \frac{a F_{yf} - b F_{yr}}{I_z} \\    \dot{U_x} &= \frac{F_{xr} - F_{yf} sin ( \delta    )}{m} + r U_x \beta   \end{aligned}
Figure 2. Three State Bicycle Model

Now, we come across a pretty enlightening thing when we look at two dimensional cross sections of this dynamical system as a phase portrait of r vs \beta .

Lets look at the nominal case of a 0 degree steering angle (\delta = 0) and a fixed velocity of 8 m/s.

Figure 3. Phase portrait of yaw rate vs sideslip angle for 0 degree steering angle

What the above phase portrait tells us is that we have a stable equilibrium point at the origin and two unstable equilibrium points at (-12.5, 0.6) and (12.5, -0.6). Intuitively, this makes sense, as the node at the origin is the case where we are driving in a straight line: the vehicle is not yawing and there is no sideslip. It is easily seen that the equilibrium point at the origin is a stable node due to all nearby trajectories being attracted to it. The two remaining equilibrium points are unstable saddle points corresponding to a left handed drift when the sideslip is negative and a right handed drift when the sideslip angle is positive. In both of these cases, the objective of control law design for a drifting autonomous ground vehicle is evident: it is to stabilize the unstable saddle points.

Let’s proceeding by sectioning the three state system at different steering angles: this time, let’s look at a steering angle of \delta = 5 deg.

Figure 4. Phase portrait of yaw rate vs sideslip for a steering angle of -5 degrees.

In figure 3, we see that as the steering angle is changed, so too is the position of the equilibrium points. The stable node is shifted downwards, as this coincides with a steady state right hand turn, while the two unstable saddle points shift to the left. This shifting of equilibrium points indicates that our region of attraction in the third quadrant is getting much smaller; this is due to the front tires getting closer and closer to the friction limit.

When we continue to increase our steering angle we see what is one thing that makes nonlinear systems so tricky: a bifurcation. At this steering angle, the stable node and the unstable saddle point collide and annihilate each other, leaving a sole unstable equilibrium point. This bifurcation effectively illustrates the case when the steering angle is increased until the front tires become friction limited and break lose, causing the vehicle to spin out.

Figure 5. Saddle Node Bifurcation

Controller Design

Now, as I stated above, I wasn’t involved in any of this research, and therefore have not implemented any of these controllers, but I can attest to the model derivations, as I’m intimately familiar with them.

Now then, let’s get down to business (to defeat, the huns!)

Voser, Hindiyeh and Gerdes used a cascaded longitudinal controller and steering controller architecture around a reference steering angle of -15 degrees.

The longitudinal control law is a simple SISO proportional controller:

\begin{aligned}  4) \displaystyle \qquad U_{mot} &= K_{vx} \Delta V_x \\ \Delta V_x &= v_x - v^{des}_x \end{aligned}

The steering control law is a two state, state space representation of the linearized bicycle model about the desired drift equilibrium (v^{eq}_y , r^{eq}). The choice of feeding back the longitudinal velocity is done in order to decouple the steering and longitudinal controllers, as selecting the sideslip angle, \beta would keep these dynamics coupled.

With this in mind the steering controller is designed as:

\begin{aligned}   5) \displaystyle \qquad \delta = \delta^{eq} + \Delta\delta = \delta^{eq} - K_{vy}\Delta v_y - K_r \Delta r  \end{aligned}

Putting this in state space form we obtain:

\begin{aligned}   6) \displaystyle \qquad \dot{x} = Ax + Bu  \end{aligned}

Where the state vector is x = \left [ \Delta v_y, \Delta r \right]^T and the control input scalar is u = \Delta\delta.

Upon defining the gain matrix K as K = \left [ K_{vy}, K_r \right ], it is easily shown that closed-loop stability of the system is achieved when the eigenvalues of A – BK have negative real part (remember back to your linear systems class where the closed loop state space representation is \dot{x} = (A-BK)x). With this in mind, the stable gain subspace is defined by equation 7, which will come in an upcoming update : ) .

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Tribe

Tribe: On Homecoming and Belonging by Sebastian Junger

Tribe is an interesting, relatively quick read about the phenomena of loneliness in modern society, a place where people, more or less, lack a tribe. Junger makes strong arguments about why we may feel better in tribal cultures, with more loyalty, sense of belonging, and meaning. He explains why many veterans, even if they have not seen the fields of battle, have increasing rates of PTSD after returning to civilian life.

This book was recommended to me after moving home to Minnesota and feeling like I had no community, no structure, that I didn’t really have anything that mattered all that much. While reading Tribe I found myself nodding my head along with the words and finding that a lot of what Junger had to say made a lot of sense to me and that I really related to it. It made me realize that a lot of what I felt, the sever loneliness and longing for something more, was likely due to the loss of community, and coming together to work towards a common goal, that I had at my former startup.

Favorite Quotes

“The sheer predictability of life in an American suburb left me hoping – somewhat irresponsibly – for a hurricane or a tornado or something that would require us to all band together to survive. Something that would make us a tribe.”

“This book is about why that sentiment is such a rare and precious thing in modern society, and how the lack of it has affected us all. It’s about what we can learn from tribal societies about loyalty and belonging and the eternal human quest for meaning. It’s about why – for many people – war feels better than peace and hardship can turn out to be a great blessing and disasters are somethings remembered more fondly than weddings or tropical vacations. Humans don’t mind hardship, in fact they thrive on it; what they mind is not feeling necessary. Modern society has perfected the art of making people not feel necessary.”

“It may say something about human nature that a surprising number of Americans – mostly men – wound up joining Indian society rather than staying in their own. They emulated Indians, married them, were adopted by them, and on some occasions even fought alongside them. And the opposite almost never happened: Indians almost never ran away to join white society. Emigration always seemed to go from the civilized to the tribal.”

“On the other hand, Franklin continued, white captives who were liberated from the Indians were almost impossible to keep at home: ‘Tho ransomed by their friends, and treated with all imaginable tenderness to prevail with them to stay among the English, yet in a short time they become disgusted with our manner of life… and take the first good opportunity of escaping again into the woods.'”

“For all the temptations of native life, one of the most compelling might have been its fundamental egalitarianism. Personal property was usually limited to whatever could be transported by horse or on foot, so gross inequalities of wealth were difficult to accumulate… Social status came through hunting and war, which all men had access to, and women had far more autonomy and sexual freedom – and bore fewer children – than women in white society. ‘Here I have no master,’ an anonymous colonial woman was quoted by the secretary of the French legation as saying about her life with the Indians. “I am the equal of all the women in the tribe, I do what I please without anyone’s saying anything about it, I work only for myself, I shall marry if I wish and be unmarried again when I wish. Is there a single woman as independent as I in your cities?”

“But as societies become more affluent they tend to require more, rather than less, time and commitment by the individual, and it’s impossible that many people feel that affluence and safety simply aren’t a good trade for freedom.”

“One study in the 1960s found that nomadic !Kung people of the Kalahari Desert needed to work as little as twelve hours a week to survive – roughly one-quarter the hours of the average urban executive at the time… The relatively relaxed pace of !Kung life – even during times of adversity – challenged long -standing ideas that modern society created a surplus of leisure time. It created exactly the opposite: a desperate cycle of work, financial obligation, and more work… Among anthropologists, the !Kung are thought to present a fairly accurate picture of how our hominid ancestors lived for more than a million years before the advent of agriculture… Early humans would most likely have lived in nomadic bands of around fifty people, much like the !Kung… And they would have done almost everything in the company of others. They would have almost never been alone.”

“…And as society modernized, people found themselves able to live independently from any communal group. A person living in a modern city or suburb can, for the first time in history, go through an entire day – or an entire life- mostly encountering complete strangers. They can be surrounded by others and yet feel deeply, dangerously alone… The evidence that this is hard on us is overwhelming. Although happiness is notoriously subjective and difficult to measure, mental illness is not. Numerous cross-cultural studies have shown that modern society- despite its nearly miraculous advances in medicine, science, and technology – is afflicted with some of the highest rates of depression, schizophrenia, poor health, anxiety, and chronic loneliness in human history. As affluence and urbanization rise in a society, rates of depression and suicide tend to go up rather than down. Rather than buffering people from clinical depression, increased wealth in a society seems to foster it.”

“…there is remarkably little evidence of depression-based suicide in tribal societies. Among the American Indians, for example, suicide was understood to apply in very narrow circumstances: in old age to avoid burdening the tribe, in a ritual paroxysms of grief following the death of a spouse, in a hopeless but heroic battle with an enemy, and in an attempt to avoid the agony of torture. “

“In the United States, white middle-aged men currently have the highest (suicide) rate at nearly 30 suicides per 100,000.”

“In 2015, the George Washington Law Review surveyed more than 6,000 lawyers and found that conventional success in the legal profession – such as high billable hours or making partner at a law firm – had zero correlation with levels of happiness and well-being reported by the lawyers themselves… The findings are in keeping with something called self-determination theory, which holds that human beings need three basic things in order to be content: they need to feel competent at what they do, they need to feel authentic in their lives, and they need to feel connected to others. These values are considered intrinsic to human happiness and far outweigh extrinsic values such as beauty, money, and status. Bluntly put, modern society seems to emphasize extrinsic values over intrinsic ones, and as a result, mental health issues refuse to decline with growing wealth.”

“The economic and marketing forces of modern society have engineered an environment that maximizes consumption at the long-term cost of well-being. In effect, humans have dragged a body with a long hominid history into an overfed, malnourished, sedentary, sunlight-deficient, sleep-deprived, competitive, inequitable, and socially-isolating environment with dire consequences.”

“…Clearly, touch and closeness are vital to the health of baby primates – including humans… Only in Northern European societies do children go through the well-known development stage of bonding with stuffed animals; elsewhere, children get their sense of safety from the adults sleeping near them.”

“Before the war, projections for psychiatric breakdown in England ran as high as four million people, but as the Blitz progressed, psychiatric hospitals around the country saw admissions go down. Emergency services in London reported an average of only two cases of bomb neuroses a week. Psychiatrists watched in puzzlement as long-standing patients saw their symptoms subside during the period of intense air raids. Voluntary admissions to psychiatric wards noticeably declined, and even epileptics reported having fewer seizures. ‘Chronic neurotics of peacetime now drive ambulances,’ one doctor remarked. Another ventured to suggest that some people actually did better during wartime.”

“The positive effects of war on mental health were first noticed by the great sociologist Emile Durkheim, who found that when European countries went to ware, suicide rates dropped. Psychiatric wards in Paris were strangely empty during both world wars, and that remained true even as the German army rolled into the city in 1940.”

“An Irish psychologist named H. A. Lyons found that suicide rates in Belfast dropped 50 percent during the riots of 1969 and 1970, and homicide and other violent crimes also went down. Depression rates for both men and women declined abruptly during that period, with men experiencing the most extreme drop in the most violent districts.”

“‘When people are actively engaged in a cause, their lives have more purpose… with a resulting improvement in mental health’, Lyons wrote in the Journal of Psychosomatic Research in 1979. ‘It would be irresponsible to suggest violence as a means of improving mental health, but the Belfast findings suggest that people will feel better psychologically if they have more involvement with their community.'”

“Fritz’s theory was that modern society has gravely disrupted the social bonds that have always characterized the human experience, and that disasters thrust people back into a more ancient, organic way of relating. Disasters, he proposed, create a community of sufferers that allows individuals to experience an immensely reassuring connection to others. As people come together to face an existential threat, Fritz found that class differences are temporarily erased, income disparities become irrelevant, race is overlooked, and individuals are assessed simply by what they are willing to do for the group.”

“The beauty and tragedy of the modern world is that it eliminates many situations that require people to demonstrate a commitment to the collective good. Protected by police and fire departments and relieved of most of the challenges of survival, an urban man might go through his entire life without having to come to the aid of someone in danger – or even give up his dinner.”

“What catastrophes seem to do – sometimes in the span of a few minutes – is turn back the clock on ten thousand years of social evolution. Self-interest gets subsumed into group interest because there is no survival outside group survival, and that creates a social bond that many people sorely miss.”

“For a former solider to miss the clarity and importance of his wartime duty is one thing, but for civilians to is quite another, ‘Whatever I say about ware, I still hate it’, one survivor made sure to tell me after I’d interviewed her about the nostalgia of her generation. ‘I do miss something from the war. But I also believe that the world we are living in – and the peace we have – is very fucked up if somebody is missing war. And many people do… Although she was safe in Italy, and finally healing form her wounds, the loneliness she felt was unbearable. She was worried that if the war never stopped, everyone would be killed and she would be left alone in the world.”

“‘I missed being that close to people, I missed being loved in that way’, she told me. ‘In Bosnia – as it is now – we don’t trust each other anymore; we became really bad people. We didn’t learn the lesson of the war, which is how important it is to share everything you have with human beings close to you. The best way to explain it is that the war makes you an animal. We were animals. It’s insane – but that’s the basic human instinct, to help another human being who is sitting or standing or lying close to you… We were the happiest then, and we laughed more.'”

“But in addition to all the destruction and loss of life, war also inspires ancient human virtues of courage, loyalty, and selflessness that can be utterly intoxicating to the people who experience them… The Iroquois Nation presumably understood the transformative power of war when they developed parallel systems of government that protected civilians from warriors and vice versa. Peacetime leaders, called sachems, were often chosen by women and had complete authority over the civil affairs of the tribe until war broke out. At that point war leaders took over, and their sole concern was the physical survival of the tribe… If the enemy tried to negotiate an end to hostilities, however, it was the sachems, not the war leaders, who made the final decision. If the offer was accepted, the war leaders stepped down so that the sachems could resume leadership of the tribe… The Iroquois system reflected the radically divergent priorities that a society must have during peacetime and during war. Because modern society often fights wars far away from the civilian population, soldiers wind up being the only people who have to switch back and forth.”

“Treating combat veterans is different from treating rape victims (PTSD), because rape victims don’t have this idea that some aspects of their experience are worth retaining.”

“Combat veterans are, statistically, no more likely to kill themselves than veterans who were never under fire. The much-discusses estimate of twenty-two vets a day committing suicide in the United States is deceptive: it was only in 2008 that – for the first time in decades – the suicide rate among veterans surpassed the civilian rate in America, and though each death is enormously tragic, the majority of those veterans were over the age of fifty… The discrepancy might be due to the fact that intensive training and danger create what is known as unit cohesion – strong emotional bonds within the company or the platoon – and high unit cohesion is correlated with lower rates of psychiatric breakdown.”

“35 years after finally acknowledging the problem, the US military now has the highest reported PTSD rate in its history – and probably in the world. American soldiers appear to suffer PTSD at around twice the rate of British soldiers who were in combat with them… Since only 10 percent of our armed forces experience actual combat, the majority of vets claiming to suffer from PTSD seem to have been affected by something other than direct exposure to danger. This is not a new phenomenon: decade after decade and war after war, American combat deaths have generally dropped while disability claims have risen… Soldiers in Vietnam suffered one-quarter the mortality rate of troops in WWII, for example, but filed for both physical and psychological disability compensation at a rate that was 50 percent higher… Today’s vets claim three times the number of disabilities that Vietnam vets did, despite a generally warm reception back home and a casualty rate, thank God, that is roughly one-third what it was in Vietnam.”

“The vast majority of traumatized vets are not faking their symptoms, however. They return from wars that are safer than those their fathers and grandfathers fought, and yet far greater numbers of them wind up alienated and depressed. This is true even for people who didn’t experience combat. In other words, the problem doesn’t seem to be trauma on the battlefield so much as reentry into society. And vets are not alone in this. It’s common knowledge in the Peace Corps that as stressful as life in a developing country can be, returning to a modern country can be far harder. One study found that one in four Peace Corps volunteers reported experiencing significant depression after their return home, and that figure more than doubled for people who had been evacuated from their host country during wartime or some other kind of emergency… It makes one wonder exactly what it is about modern society that is so mortally dispiriting to come home to.”

“What people miss (after re-entering civilian life) presumably isn’t danger or loss, but the unity that these things often engender. There are obvious stresses on a person in a group, but there may be even greater stresses on a person in isolation, so during disasters there is a net gain in well-being. Most primates, including humans, are intensely social, and there are very few instances of lone primates surviving in the wild. A modern soldier returning from combat – or a survivor of Sarajevo – goes form the kind of close-knit group that humans evolved for, back into a society where most people work outside the home, children are educated by strangers, families are isolated from wider communities, and personal gain almost completely eclipses collective good.”

“Our fundamental desire, as human beings, is to be close to others, and our society does not allow for that… In humans, lack of social support has been found to be twice as reliable at predicting PTSD as the severity of the trauma itself.”

“Israel is arguably the only modern country that retains a sufficient sense of community to mitigate the effects of combat on a mass scale… Those who come back from combat are reintegrated into a society where those experiences are very well understood. We did a study of seventeen-year-olds who had lost their father in the military, compared to those who had lost their fathers to accidents. The ones whose fathers died in combat did much better than those whose fathers hadn’t… The Israelis are benefiting from what the author and ethicist Austin Dacey describes as a ‘shared public meaning’ of the war. Shared public meaning gives soldiers a context for their losses and their sacrifice that is acknowledged by most of the society. That helps keep at bay the sense of futility and rage that can develop among soldiers during a war that doesn’t seem to end.”

“Such public meaning is probably not generated by the kinds of formulaic phrases, such as ‘thank you for your service’ that many Americans now feel compelled to offer soldiers and vets. Neither is it generated by honoring vets at sporting events, allowing them to board planes first, or giving them minor discounts at stores. If anything, these token acts only deepen the chasm between the military and civilian populations by highlighting the fact that some people serve their country, but the vast majority don’t.”

“Anthropologists like Kohrt, Hoffman and Abramowitz have identified three factors that seem to crucially affect a combatant’s transition back into civilian life. First, cohesive and egalitarian tribal societies do a very good job at mitigating the effects of trauma, but by their very nature, many modern societies are exactly the opposite: hierarchical and alienating… Secondly, ex-combatants shouldn’t be seen as victims… Third, and perhaps most important, veterans need to feel that they’re just as necessary and productive back in society as they were on the battlefield. Iroquois warriors who dominated just about every tribe within 500 miles of their home territory would return to a community that still needed them to hunt and fish and participate in the fabric of everyday life. There was no transition when they came home because – much like life in Israel – the battlefield was an extension of society, and vice versa.”

“There are many costs to modern society, starting with its toll on the global ecosystem and working one’s way down to its toll on the human psyche, but the most dangerous loss may be to community.”

“The earliest and most basic definition of community – of tribe – would be the group of people that yo would both help feed and help defend. A society that doesn’t offer its members the chance to act selflessly in these ways isn’t a society in any tribal sense of the word; it’s just a political entity that, lacking enemies, will probably fall apart on its own. Soldiers experience this tribal way of thinking at war, but when they come home they realize that the tribe they were actually fighting for wasn’t their country, it was their unit. It makes absolutely no sense to make sacrifices for a group that, itself, isn’t willing to make sacrifices for you. That is the position American soldiers have been in for the past decade and a half.”

“The public is often accused of being disconnected from its military, but frankly it’s disconnected from just about everything… This fundamental lack of connectedness allows people to act in trivial but incredibly selfish ways. Rachel Yehuda pointed to littering as the perfect example of an everyday symbol of disunity in society. ‘It’s a horrible thing to see because it sort of encapsulates this idea that you’re in it alone, that there isn’t a shared ethos of trying to protect something shared. It’s the embodiment of every man for himself. It’s the opposite of the military.’ When you throw trash on the ground, you apparently don’t see yourself as truly belonging to the world that you’re walking around in.”

“Gang shootings – as indiscriminate as they often are – still don’t have the nihilistic intent of rampages. Rather, they are rooted in an exceedingly strong sense of group loyalty and revenge, and bystanders sometimes get killed in the process.”

“Rampage killings dropped significantly during WWII, then rose again in the 1980s and have been rising ever since. It may be worth considering whether middle-class American life – for all its material good fortune – has lost some essential sense of unity that might otherwise discourage alienated men from turning apocalyptically violent.”

“New York’s suicide rate dropped around 20 percent in the six months following the attacks (on 9/11), the murder rate dropped by 40 percent, and pharmacists saw no increase in the number of first-time patients filling prescriptions for anti-anxiety and antidepressant medication. Furthermore, veterans who were being treated for PTSD at the VA experienced a significant drop in their symptoms in the months after the September 11th attack.”

“Today’s veterans often come home to find that, although they’re willing to die for their country, they’re not sure how to live for it. It’s hard to know how to live for a country that regularly tears itself apart along every possible ethnic and demographic boundary… To make matters worse, politicians occasionally (editors note: very often these days) accuse rivals of deliberately trying to harm their own country – a charge so destructive to group unity that most past societies would probably have punished it as a form of treason. It’s complete madness, and the veterans know this. In combat, soldiers all but ignore differences of race, religion, and politics within their platoon. It’s no wonder many of them get so depressed when they come home.”

“I know what coming back to America from a war zone is like because I’ve done it so many times. First there is a kind of shock at the level of comfort and affluence that we enjoy, but that is followed by the dismal realization that we live in a society that is basically at war with itself. People speak with incredible contempt about – depending on their views – the rich, the poor, the educated, the foreign-born, the president, or the entire US government. It’s a level of contempt that is usually reserved for enemies in wartime, except that now it’s applied to our fellow citizens. Unlike criticism, contempt is particularly toxic because it assumes a moral superiority in the speaker. Contempt is often directed at people who have been excluded from a group or declared unworthy of its benefits. Contempt is often used by governments to provide rhetorical cover for torture or abuse. Contempt is one of four behaviors that, statistically, can predict divorce in married couples. People who speak with contempt for one another will probably not remain united for long.”

“The most alarming rhetoric comes out of the dispute between liberals and conservatives, and it’s a dangerous waste of time because they’re both right. The perennial conservative concern about high taxes supporting a nonworking ‘underclass’ has entirely legitimate roots in our evolutionary past and shouldn’t be dismissed out of hand. Early hominids lived a precarious existence where freeloaders were a direct threat to survival, and so they developed an exceedingly acute sense of of whether they were being taken advantage of by members of their own group. But by the same token, one of the hallmarks of early human society was the emergence of a culture of compassion that cared for the ill, the elderly, the wounded, and the unlucky. In today’s terms, that is a common liberal concern that also has to be taken into account. Those two driving forces have coexisted for hundreds of thousands of years in human society and have been duly codified in this country as a two-party political system. The eternal argument over so-called entitlement programs- and, more broadly, over liberal and conservative thought- will never be resolved because each side represents an ancient and absolutely essential component of our evolutionary past.”

“If you want to make a society work, then you don’t keep underscoring the places where you’re different – you underscore your shared humanity.”

“The United States is so powerful that the only country capable of destroying her might be the United States herself, which means that the ultimate terrorist strategy would be to just leave the country alone. That way, America’s ugliest partisan tendencies could emerge unimpeded by the unifying effects of war. The ultimate betrayal of tribe isn’t acting competitively – that should be encouraged- but predicating your power on the excommunication of others from the group. That is exactly what politicians of both parties try to do when they spew venomous rhetoric about their rivals.” (*cough* Trump *cough*)

“In 2009, an American soldier named Bowe Bergdahl slipped through a gap in the concertina wire at his combat outpost in southern Afghanistan and walked off into the night. He was quickly captured by a Taliban patrol, and his absence triggered a massive search by the US military that put thousands of his fellow soldiers at risk. The level of betrayal felt by soldiers was so extreme that many called for Bergdahl to be tried for treason when he was repatriated five years later… The collective outrage at Sergeant Bergdahl was based on very limited knowledge but provides a perfect example of the kind of tribal ethos that every group – or country- deploys in order to remain unified and committed to itself… Bergdahl put a huge number of people at risk and may have caused the deaths of up to six soldiers. But in purely objective terms, he caused his country far less harm than the financial collapse of 2008, when bankers gambled trillions of dollars of taxpayer money on blatantly fraudulent mortgages… Almost 9 million people lost their jobs during the financial crisis, 5 million families lost their homes, and the unemployment rate doubled to around 10 percent… For nearly a century, the national suicide rate has almost exactly mirrored the unemployment rate, and after the financial collapse, America’s suicide rate increased by nearly 5 percent. In an article published in 2012 in The Lancet, epidemiologists who study suicid estimated that the recession cost almost 5,000 additional American lives during the first two years – disproportionately among middle-aged white men. That is close to the nation’s losses in the Iraq and Afghan wars combined. If Sergeant Bergdahl betrayed his country – and that’s not a hard case to make – surely the bankers and traders who caused the financial collapse did as well. And yet they didn’t provoke nearly the kind of outcry that Bergdahl did.”

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Allan Variance and Its Use in Characterizing Inertial Measurement Unit Errors

This is going to be a super quick and dirty writeup until I take the time to make it more presentable, but here we go!

For the time being this is mostly going to just be a link and short description of my allan variance github repo used to create synthetic IMU error models using a first order Gauss-Markov process: https://github.com/EVictorson/allan_variance

Also, I’m going to REALLY simplify the technical discussion here because this seems to be one of those areas where PhDs in control theory like to start waving their… boy parts… around to show who knows more about what, which is unnecessary.

Allan Variance Background

The Allan Variance (AVAR) is historically used as a measure of frequency stability in clocks, oscillators, and amplifiers. It is named after the one and only David W. Allan.

Mathematically the AVAR is is expressed as:
1) \displaystyle \qquad {\sigma_{y}}^2(\tau)

While the Allan Deviation is, as you may expect from basic statistics:
2) \displaystyle \qquad {\sigma_{y}}(\tau)

We often see the M-sample Allan variance, which is a measure of frequency stability using M samples, time T between measurements, and observation time tau. The M-sample Allan variance is expressed as:

3) \displaystyle \qquad {\sigma_{y}}^2(M,T,\tau)

To explain the AVAR as academically as you can in as few words as possible is to say that it is defined as one half of the time average of the squares of the differences between successive readings of the frequency deviation sampled over the sampling period. The Allan variance depends on the time period used between samples: therefore it is a function of the sample period, commonly denoted as tau, likewise the distribution being measured, and is displayed as a graph rather than a single number. (Editors note: TL;DR) A low Allan variance is characteristic of a clock with good stability over the measured period. [1]

The results of AVAR or ADEV are related to five basic noise terms appropriate for inertial sensor data, namely:

  • Quantization noise
  • Angle Random Walk
  • Bias Instability
  • Rate Random Walk
  • Rate Ramp

Now, you may ask, why the hell are we using something that was designed to measure the frequency stability of clocks in characterizing errors of an IMU? The answer is, to put it simply, we typically separate the errors of inertial measurement devices into two groups: deterministic errors like bias and nonlinearity, and stochastic processes like the ones mentioned above. Within the field of system dynamics, everything can be decomposed into frequency domain, and we are therefore concerned about the contribution to errors from different frequency sources.
As wikipedia succinctly puts it: “The Allan variance is intended to estimate stability due to noise processes and not that of systematic errors or imperfections such as frequency drift or temperature effects. The Allan variance and Allan deviation describe frequency stability.” Basically, the easiest way to think about this, if you’ve taken an undergraduate controls course, this will be a piece-meal Bode plot with different error frequencies. I’ll expand on this in a minute, but that’s basically what we are dealing with.

Again, the Allan variance / Allan deviation is nothing more than a Bode plot that analyzes the magnitude of different noise sources with differing frequency power. This will cause different contributing noise terms to appear with differing slopes on the Allan deviation plot; these differing slopes making it easy to see that each noise process differs by an integrator (1/s).

The following error terms are the ones most commonly used, and can be distinguished on the Allan Variance / Deviation plot with their corresponding slopes.

  • Quantization Noise: slope -1
    • Quantization noise is Gaussian and zero mean. It is strictly due to the digital nature of ring laser gyro outputs.
  • Angle Random Walk: slope = -1/2
    • ARW is high frequency noise that can be obvserved as a short-term variation in the sensor output. After integration, it causes random error in angle with distribution that is proportional to the square root of the elapsed time. It is often thought to be from randomized dither and the spontaneous emission of photons for a ring laser gyro.
  • Bias Instability: slope = 0
    • BI has an impact on long-term stability. It is a slowly fluctuating error so it appears in low frequencies as 1/f (pink, or flicker) noise. For a gyroscope, this measures how the bias of the sensor changes over a specified period of time at a constant temperature. For a ring laser gyro this noise originates in the discharge assembly, electronics, and other components susceptible to random flickering.
  • Rate Random Walk: slope = 1/2
    • RRW basically characterizes the time scale over which changes in the bias offset occur and can give an idea of when recalibration of sensors should occur. This random process is of uncertain origin, possibly a limiting case of an exponentially correlated noise with a very long correlation time. Mechanical as well as rate biased laser gyros exhibit this noise term.
  • Rate Ramp: slope = 1
    • Slow monotonic change of output over a long time period. This is more of a deterministic error rather than random noise. Its presence in the data may indicate a very slow monotonic change of the ring laser gyro intensity persisting over a very long period of time.

So, what do one of these bad boys look like you may ask? Well, to steal, er borrow, an image from Freescale’s application note AN5087 “Allan Variance: Noise analysis for gyroscopes” [2] we see something like this:

Allan Deviation Plot, courtesy Freescale AN5087

In the above plot, and with all AVAR / ADEV plots, the horizontal axis is the averaging time, an the vertical axis is either the AVAR or ADEV, ADEV in the case of the plot above.

Empirical Data Acquisition and Testing

For an in-depth tutorial on how best to collect data to perform AVAR, see Section B.4 of [4]. To summarize their recommendations, you can select the sample rate to be at least twice the sample bandwidth. The record length should be at least several times the required performance interval. The recommended approach is to limit the time/frequency domain dynamic range to about 3 orders of magnitude. In practice this is done by dividing the total range into overlapping intervals of geometrically increasing lengths. Thus, the high frequency data is acquired for a short period of time. Lower frequency data is filtered (integrated) and acquired for a longer period; e.g. 100 us data is collected for 0.1s, 0.01s data for 10s, 1s data for 1000s, and 100s data for 10^5 s. The appropriate sampling rates/ record lengths should be chosen to overap about one decade of frequency (time).

If we are considering a gyroscope, the Allan variance can be defined in terms of the output rate, {\Omega}(t), or the output angle as

4) \displaystyle \qquad {\theta}(t) = \int^{t}{\Omega}(t')dt'

The lower integration limit is not present in equation 4 because only angle differences are employed in all of the definitions.

The angle measurements that are fed into equation 4 are made at times t = k{\tau}_0, where k varies from 1 to N (the number of samples), and the sample period is \tau_0. For a discrete set of samples, a cumulative sum can be used to give N values of \theta. In this case the cumulative sum of the gyro output samples at each k\tau_0 is taken and each sum obtained is then multiplied by the sample period \tau_0 to give N values of \theta. [2]

A general heuristic to use is to set the averaging time to be \tau = m{\tau}_0, where m is the averaging factor. The averaging factor can be chosen arbitrarily as some value according the inequality m < (N - 1) /2. [2]

Cool, now that we’ve got our values of \theta calculated, we compute the Allan variance with the following equation:

5) \displaystyle \qquad {\sigma}^2(\tau) = {\frac {1}{2\tau^2}} < (\theta_{k+2m} - 2\theta_{k+m} + \theta_k)^2 >

Equation 5 represents Allan variance as a function of \tau and < > is the ensemble average. Upon expanding the ensemble average in equation 5 we obtain the following estimate of the Allan variance:

6) \displaystyle \qquad {\sigma}^2(\tau) = {\frac {1}{2\tau^2 (N - 2m)}} \sum_{k=1}^{N-2m} (\theta_{k+2m} - 2\theta_{k+m} + \theta_k)^2

For those who care, and if you want to swing your boy parts around in public, the Allan variance is related to the two-sided power spectral density, S_{\Omega}(f) by:

7) \displaystyle \qquad {\sigma}^2(\tau) = 4 \int_0^\infty S_{\Omega}(f) \frac{sin^{4}(\pi f \tau)}{(\pi f \tau)^2} df

Cool, so hopefully if you do this correctly you’ll have a plot that looks something like this:

Simulation and Validation

Alrighty, so we can get a plot from our time series data easily enough, what next? Well, if we presume to already know the noise coefficients we can simulate the Allan variance plot and compare the two, or we can try to characterize the noise coefficients from the Allan variance plot itself.

For simulation and modelling purposes, typically a first order Gauss-Markov process is used to model these kinds of errors, which is just an exponentially correlated, noise driven stochastic process characterized by the following differential equation:

8) \displaystyle \qquad \frac{dx}{dt} = \frac{-1}{\tau} x + N(\mu, \sigma)

Which is ultimately just an exponentially decaying autoregressive term with driven white noise. The discrete time version of this is:

9) \displaystyle \qquad x(n+1) = x(n) e^{\frac{-1}{\tau}dt} + N(\mu, \sigma) dt

The first order gauss-markov process may also be defined in terms of its autocorrelation function:

10) \displaystyle \qquad R_{xx}= \sigma^2 e^{-\beta \tau}

where \sigma is the entire process variation (NOT JUST THE DRIVEN NOISE VARIATION), \beta is the inverse of the correlation time, T=\frac{1}{\beta}, and \tau is the autocorrelation time lag.

For sufficiently long time series (much longer than the time constant), the autocorrelation plot of the first order Gauss-Markov process can verify the correlation time, which is the time lag at which R_{xx} = \frac{\sigma^2} {e}, and the entire time series variance will appear as the peak at time lag = 0. Note that the driven noise standard deviation cannot be validated via autocorrelation. Also note that matlab has two different autocorrelation functions that will produce slightly different results if your time scales are short (autocorr and xcorr), as well as an autocovariance function, xcov. Autocorr and xcov are normalized by the process mean such that a constant process will have a steady autocorrelation (autocorrelation is just autocovariance scaled by the inverse of the process variance). xcorr, however, does not do this, so a constant process will have a decaying autocorrelation as the time lag increases, which results in a shortening of the summation by 1 element each iteration.

For process lengths on the order of magnitude of the time constant or less the process will be dominated by the integrated white noise term, resulting in a random walk. For time scales much longer than the time constant the exponentially correlated term will begin to be apparent. This can be see on an Allan deviation plot, where for sampling intervals much shorter than the time constant the Gauss-Markov Allan variance reduces to that of a singly integrated white noise process (rate random walk), whose slope is +1/2, and the noise magnitude (standard deviation) may be picked off by finding the intersection of the +1/2 slope line and sampling_interval = 3.
This can also be verified by differentiating this time series to obtain Gaussian noise, whose Allan deviation has a slope of -1/2, and the noise magnitude is interpreted as the intersection of this line with sampling_interval = 1.

For process time scales large enough to see the decay time constant, and Allan deviations with sampling intervals ranging from much less than the time constant to sampling intervals much larger than the time constant, the slope will transition from +1/2 for sampling intervals much shorter than the time constant, to 0 as the sampling interval approaches the time constant at it’s maxima, to -1/2 as the interval becomes much larger than the time constant.

When multiple gauss markov processes are added together it will be nearly impossible to pick apart any of these parameters, but when run individually the driven noise magnitude (qc) and time constant (Tc) can be found on the allan deviation plot as follows:
Tc = argmax_sampling_interval / 1.89, where argmax_sampling_interval is the allan deviation sampling interval that maximizes the allan deviation. The driven noise magnitude may then be found with the following relationship:

11) \displaystyle \qquad q_c = \frac{\sigma_{max}} {0.437 * \sqrt{T_c}}

where \sigma_{max} is the Allan deviation maxima.

If the combined output of all of these Gauss-Markov processes are analyzed, the only easy thing to pick off will be the velocity random walk / angle random walk, which may be found by fitting a line to the segment with a slope of -1/2 and finding the intersection of this line with tau = 1.

Characterizing Error Sources

Angle Random Walk

Angle random walk appears on the AVAR plot as the following equation:

12) \displaystyle \qquad \sigma^2(\tau) = \frac{N^2}{\tau}

where N is the angle random walk coefficient. In a log-log plot of \sigma(\tau) vs \tau ARW has a slope of -1/2. The numerical value of N can be obtained by reading the -1/2 slope line at \tau = 1.

Bias Instability

Bias instability appears on the AVAR plot as the following cumbersome equation:

13) \displaystyle \qquad \sigma^2(\tau) = \frac{2B^2}{\pi}\left [ln 2 - \frac{sin^3(x)}{2x^2}\left (sin(x) + 4xcos(x)\right ) + Ci(2x) - Ci(4x) \right ]

Where x is \pi f_0 \tau,
B is the bias instability coefficient
f_0 is the cutoff frequency, and
Ci is the cosine-integral function.

As you can see it’s probably a bit easier to just pick off the part of the AVAR plot that has a slope of 0.

Rate Random Walk

Rate random walk appears on the AVAR plot with the following equation:

14) \displaystyle \qquad \sigma^2(\tau) = \frac{K^2 \tau}{3}

Where K is the rate random walk coefficient.

Because we are essentially dealing with Bode plots, the presence of \tau in the numerator indicates we will be searching for a slope of +1/2. The magnitude of this noise can be read off the +1/2 slope line at \tau = 3.

Rate Ramp

Rate ramp appears on the AVAR plot with the following equation:

15) \displaystyle \qquad \sigma^2(\tau) = \frac{R^2 \tau^2}{2}

Where R is the rate ramp coefficient.

With one more power of tau in the numerator we are therefore looking for a slope of +1. The magnitude of R can be obtained from the +1 slope line at \tau = \sqrt{2}.

Quantization Noise

Quantization noise appears on the AVAR plot with the following equation:

16) \displaystyle \qquad \sigma^2(\tau) = 3\frac{Q^2}{\tau^2}

Where Q is the quantization noise coefficient.

Quantization noise appears with a slope of -1 on the log-log plot and can be read off the intersection of the line with slope -1 and \tau = \sqrt{3}.

Exponentially Correlated (Markov) Noise

Markov noise appears on the AVAR plot as:

17) \displaystyle \qquad \sigma^2(\tau) = \frac{(q_c T_c)^2}{\tau}\left [1- \frac{T_c}{2\tau}\left (3-4e^{-\frac{\tau}{T_c}}+e^{-\frac{2\tau}{T_c}}\right )\right ]

Where qc is the noise amplitude, and Tc is the correlation time as noted above.

It is easier to view the behavior of the Markov noise at various limits of the equation. For cases with \tau >> T_c we obtain:

18) \displaystyle \qquad \sigma^2(\tau) = \frac{(q_c T_c)^2}{\tau}

Which is the Allan variance for angle random walk where N = qcTc is the angle random walk coefficient. For \tau << T_c we obtain:

19) \displaystyle \qquad \sigma^2(\tau) = \frac{q_c ^2}{3}\tau

Which is the Allan variance for rate random walk.

Sinusoidal Noise

Also, sinusoidal noise exists, but I won’t talk about it because it hasn’t concerned any of my work. Just know it exists.

Now, if we take and superimpose all of these noise sources on one plot we should see a piece-wise representation of the empirically derived plot like that shown in [8]:

References

  1. IA state AERE432 Lecture Notes, retrieved 8/10/2018 http://home.engineering.iastate.edu/~shermanp/AERE432/lectures/Rate%20Gyros/Allan%20variance.pdf
  2. Freescale appnote AN5087, retrieved 8/10/2018 http://cache.freescale.com/files/sensors/doc/app_note/AN5087.pdf
  3. IEEE Standard Specification Format Guide and Test Procedure for Single-Axis Interferometric Fiber Optic Gyros. IEEE std 952-1997 (R2008)
  4. IEEE Standard Specification Format Guide and Test Procedure for Single-Axis Laser Gyros. IEEE std 647-1995
  5. Kirkko-Jaakkola, M., Collin, J., & Takala, J. (2012). Bias Prediction for MEMS Gyroscopes. IEEE Sensors Journal, 12(6), 2157-2163. DOI: 10.1109/JSEN.2012.2185692
  6. Peng-Yu, C. (2015). Experimental Assessment of MEMS INS Stochastic Error Model. Graduate Thesis, The Ohio Sate University, Department of Civil Engineering.
  7. Martin, V. MEMS Gyroscope Performance Comparison Using Allan Variance Method, Brno University of Technology.
  8. ST Design Tip DT0064. Noise analysis and identification in MEMS sensors. Retreived 8/10/2018. https://www.st.com/content/ccc/resource/technical/document/design_tip/group0/bf/92/6b/31/e7/c1/4d/c8/DM00311184/files/DM00311184.pdf/jcr:content/translations/en.DM00311184.pdf
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How To Be Happy At Work

How To Be Happy At Work by Annie McKee

This is the book that started my deep dive into emotional intelligence… and I’ll give you one guess as to why I read it. One of the things that I loved about this book was that it did so much to validate some of the feelings I was having, as well as invalidate all the typical crap people of the older generation say like, “Well, they call it work for a reason.”

It managed to get me to evaluate some of my values, how they relate to my career, and gave me the opportunity to identify further reading material to help me start my journey of increasing my emotional intelligence… and let me tell you, engineers don’t usually have much of it.

I don’t really think this book needs much of a summary since the title does a pretty good job of explaining what it’s about, but it is one of those books that I have post it flags and highlighter marks all over. So without much summary, let’s just dive into the passages that resonated with me.

Favorite Quotes

OK, so this quotes section is going to be super long and is basically going to be my condensing of this book down to be able to continue to revisit in the future… Here we go.

“Life really is too short to be unhappy at work.”

“A lot of us give up and settle for less than fulfilling jobs. We tell ourselves that we’re not supposed to be happy at work; that’s for other parts of life. We try to cope by avoiding that bad manager or getting that stubborn, annoying person off the team. We shut down, give less, and fantasize about telling someone off. Sometimes we run away from the job, the company, even our careers. But running away isn’t going to make things better. To be happy, I’ve discovered, you’ve got to run toward something: meaningful work; a hopeful, inspiring vision of the future; and good relationships with the people you work with every day.“

“What leads to long-lasting fulfillment at work? What leads to happiness? And can we even expect to be happy at work? Does it really matter?
To answer these questions, I reviewed my work on emotional intelligence and resonant leadership and revisited the dozens of studies I’ve done in companies worldwide. What I found is both simple and profound: Happiness matters at work as much as it does in our personal lives. And when we are happy, we are more successful… My conclusion: to be happy at work, we need purpose, hope, and friendships.“

“We are wired to seek meaning in everything we do. It’s what makes us human. In some cases, it’s what keeps us alive. In his classic book, Man’s Search for Meaning, Austrian psychiatrist and holocaust survivor Victor Frankl shows that even in the worst of circumstances, purpose, hope and connection are what keep us going.“

“Hope, optimism, and a vision of a future that is better than today help us rise above trials and deal with setbacks… Unfortunately, we often assume that our organization’s vision is enough to keep us hopeful and focused on the future. I’ve rarely seen this to be the case. An organization’s vision, however inspiring, is for the organization – not you… To be truly happy at work, we need to see how our workplace responsibilities and opportunities fit with a personal vision of our future. This kind of vision is vitally tied to hope and optimism, which we can with focus and hard work, cultivate even in difficult jobs and toxic workplaces. When we see our jobs through a positive lens, and when a personal vision is front and center in our minds, we are more likely to learn from challenges and even failures, rather than be destroyed by them.”

“Resonant relationships are at the heart of collective success in our companies. That’s because strong, trusting, authentic relationships form the basis for great collaboration and collective success. But I’ve found, we need more than trust and authenticity to get us through good times and bad. We need to feel that people care about us and we want to care for them in return.”

“We’ve known for years that emotional intelligence (EI) is key to being effective at work. The more EI you have, the better you (likely) are at your job – no matter what kind of role you have or how senior you are… In practical terms, EI is a set of competencies that enables you to understand your own and others’ feelings, and then use this knowledge to act in ways that support your own and others’ effectiveness… Here’s a secret about EI: it’s a virtuous circle. The more you use it, the better you get.”

“Happiness at work is a choice. When you decide to look within yourself to connect with what’s most important to you, what makes you feel hopeful about the future, and what you long for in your relationships, you are taking that first, all-important step toward a work life that is deeply satisfying, challenging, and fun.“

“(When we are unhappy at work) Time away from our jobs (if there is such a thing) is affected, too, because we don’t leave our feelings at the office and unhappiness seeps into the rest of life. Our families and friends suffer when we are disengaged, dissatisfied, and unfulfilled. Worse, slow-burning stress, anger, and other negative emotions can literally kill us.
Destructive emotions like fear and constant frustration interfere with reasoning, adaptability, and resilience. We just can’t focus when we’re gripped by negativity or when we’re obsessing about how to protect ourselves (or get back at our boss).”

“She fostered a “we’re in this together” mindset that made people feel they belonged to an important group, one with a resonant microculture marked by excitement, enthusiasm, safety, and trust – the kind of environment where people can take big risks and have fun without the fear of losing their jobs.”

“But Candace had what Ari had lost: clarity about the value of her work, an inspiring vision of the future, and resonant relationships… With dedicated effort, Ari found his way, and he did not quit his job. The first step was accepting that he deserved to be happy at work (for some of us, this is a big step). Then, he focused on recapturing what was most important to him in life and learning how to bring it back to work.”

“I define happiness at work as a deep and abiding enjoyment of daily activities fueled by passion for a meaningful purpose, a hopeful view of the future, and true friendships... Happiness is not simply about feeling good in the moment. That is hedonism.”

“…What we’ve found is that positive emotions – like those we experience when we are happy – support individual and collective success… Most of us intuitively know that feelings and inner experiences like eagerness, enjoyment, optimism, belonging, and confidence fuel our energy and creativity.”

“The business case: happiness before success: A common myth tells us that once we achieve success, we’ll be happy. If this were true, all successful people would be happy. They are not… The belief that we will be happy once we become successful is backward. It all starts with happiness because happiness breeds resonance and resonance breeds success. Scholars agree, starting with the popular author and psychologist Shawn Achor, who says it in a straightforward, no-nonsense manner: “Happiness comes before success.” This statement is based on studies showing that when we are positive, we are 31 percent more productive and 40 percent more likely to receive a promotion, we have 23 percent fewer health-related effects from stress, and our creativity rates triple… “when we find and create happiness in our work, we show increased intelligence, creativity, and energy, improving nearly every single business and educational outcome”… So, if we sacrifice happiness, we sacrifice success.”

Happiness Traps

“I’ve always wondered why we don’t fight back – why we settle for so little happiness at work… First, we’ve bought into old myths about the meaning of work and what we can expect from it (or not). Namely, we believe that work isn’t supposed to be fun or fulfilling, and that we don’t have to like the people we work with. Instead, we’re there to follow orders and produce results. Our values, hopes, and dreams have a very small place in this picture.
Second, most of us have stumbled into happiness traps – mindsets and habitual ways of approaching work and career that keep us stuck on a hamster wheel and pursuing the wrong goals.
Third – and this is the good news – there’s something we can do to break free from these old myths and dangerous traps: develop and use our emotional intelligence.”

“Only one-third of US employees are engaged at work. The rest are either neutral or actively engaged.”

“Myth one: Work has to be grueling.
Myth two: How we feel at work doesn’t matter.
– By the middle of the last century, there was a vast body of knowledge showing that how we feel about our bosses, work, and workplaces affects our contributions and outcomes.
Myth three: we can’t ask for more of work.”

“But when we ask for more, well-meaning friends and family tell us to check our unrealistic expectations and pull out old sayings like, “that’s why they call it work.” Or, when we complain about not being trusted to make decisions or being asked to do things that are counter to our values, people say, “Stop making trouble. Be grateful you even have a job. Do what you’re told and you’ll be fine.”
In the end, far too many of us accept the notion that work is not where we can be fully human, not where we can realize our potential or our dreams. We pursue goals that don’t jive with our values or our own hopes for the future. We accept being treated as “doers”, not people.”

“But, organizations aren’t filled with mindless automatons that live for the privilege of serving the god of profit; they never were. And as the knowledge revolution takes the world by storm, more rand more of us think for a living, rather than make for a living, even in manufacturing. We need our brains to work at their best, and in order for that to happen we need physical, psychological, and spiritual well-being.
We need to replace outdated beliefs with new ways of understand what we can expect from work – and from each other. To start with, we need to create workplaces that honor our humanity and foster common decency, camaraderie, mutual respect, and sustainable success.”

“The overwork trap: We spend every waking moment doing something – checking our email, talking, dashing off a text. We’re always behind, running as fast as we can to catch up… We live in a world where overwork is overvalued… As Harvard Business Review’s Sarah Green Carmichael writes, “we log too many hours because of a mix of inner drivers, like ambition, machismo, greed, anxiety, guilt, enjoyment, pride, the pull of short-term rewards, a desire to prove we’re important, or an overdeveloped sense of duty.” Sometimes, too, work is an escape. When our jobs are less stressful than home, work becomes a “haven, a place to feel confident and in control.” Regardless of the reason, overwork has become so prevalent that “busy” is the most common answer I get when I ask people how they are doing… The first step out of the overwork trap is to try to figure out why you are working s much. Is it because you really have to? Or is t a habit? Or is something deeper going on, like trying to escape your home life or prove your importance?”

“The money trap: Money is great. Until our desire for it overshadows reason… How many of us have stayed in jobs that we hate because the money was good? Or taken a promotion that we didn’t want or weren’t suited for because it came with a raise?… There’s something deeper going on: the decision to choose money over happiness is fueled by insecurity, social comparison, and the need to display one’s power for all to see… Insecurity also comes from the belief that we aren’t good enough. We suffer from the imposter syndrome and are terrified that people will find out. Money, we think, will fool them into believing we are deserving of our success… When we feel we must have money and the power that goes with it, that we must display our wealth for others to see, then we’ve crossed into dangerous territory. At this point, we make decisions to choose emptiness over happiness at work – just to get more cash.”

“The ambition trap: This trap is linked to something we usually think of as good: ambition. But, when our ambition is coupled with an overdeveloped focus on competition and winning, we can find ourselves in trouble… some people put their own personal ambition above morals, ethics and reason. They’re blinded by their desire to win and will do just about anything to come out on top… But winning is downright destructive when other people get hurt, when it becomes the most important goal, when you’re willing to sacrifice anything to achieve your goal and to hell with the costs and consequences.
First, success isn’t really success when we define it as a win-lose, zero-sum game. Second, hyper-competitiveness in the workplace leaves us empty and unfulfilled, hurts our ability to lead effectively, and makes us no fun to be around.”

“The “should” trap: The next happiness trap is a big one, one all of us face at some point in our careers: doing something simply because we should, rather than because we truly want to… But, some of the cultural rules that guide us at work are outdated and destructive, especially those that limit or constrain our dreams…. Workplace “shoulds” are such powerful drivers of our beliefs and behaviors that we often go along with rules that make no sense. Social rules and “shoulds” are a fact of life. It’s not about getting rid of them; it’s about sorting through them and making conscious choices about which to follow – those that enable you to live your values, reach your potential, and be happy… This belief that we can make things happen is critical to happiness. Without it, you fall into the last trap: helplessness.”

“The helplessness trap: Some people truly believe that no matter how hard they try, they can’t influence the world around them, change things, or get what they want.”

Breaking free of the traps

“Why, we need to ask ourselves, do we work all the time? Why are we so seduced by money and power? Is our ambition and desire to win serving us or hurting us? Why are we so trapped by what we feel we should do rather than pursuing what we want to do? And why do we sometimes give up on being happy at all? To answer these questions, we need to return to emotional intelligence.”

“If we are to combat these outdated myths and happiness traps and take control of our own happiness… we need more than a modicum of emotional intelligence. Emotional intelligence is the capacity to understand one’s own and others’ emotions and deal with them in a way that leads to resonance in relationships as well as individual and collective success. There are twelve emotional intelligence competencies…”

“Emotional self-awareness: Avoiding the happiness traps starts with emotional self-awareness. You must tune in to those faint whispers in your mind, those almost imperceptible feelings of “something’s not right.””

“Self-management: Emotional self-control helps us stay tuned in to our feelings, even when we don’t like what we discover… Once you know what’s driving you, self-management helps you shift your attention. This subtle but powerful internal change supports willpower, focus, and courage – all of which you need to do the hard work of breaking free.”

“Social awareness and relationship management: When you focus on empathizing with people and understanding your organizational environment, you can see what is coming from inside you, and what’s coming from others or your company. With this knowledge, you are better equipped to make choices about what you will or will not accept at work.”

The power of purpose

“Purpose and work go hand in hand… When work is an expression of our values and we have positive impact on something we care about, we are motivated from within; we don’t need others to push us or beg us to do our jobs, and we can withstand challenge and turmoil. ”

“Today, our organizations are our tribes. Work is still where we express ourselves and make a difference… But work and life are no longer seen as vitally intertwined. Rather, we see our jobs as a means to an end, a way to earn money so we can have meaningful lives outside of work… The result, as management scholars Jeffrey Pfeffer and Robert Sutton tell us, is that “many companies do not worry that much about providing meaning and fulfillment to their people. Work is, after all, a four letter word.” But it’s impossible to pull life and work apart. We are meaning making creatures, no matter if we’re sitting in an office, giving tours of historical places, hiking Mount Kilimanjaro, or eating dinner with our family. We don’t give up the essential human need to do something worthwhile when we start our workday. We want to know that we’re doing something that matters.
Seeing our work as an expression of cherished values and as a way to make a contribution is the foundation of well-being, happiness, and our ongoing success. Passion for a cause fuels energy, intelligence, and creativity. And, when we see that the results of our labor will benefit ourselves and others, we want to “fight the good fight” together.”

Is your work a job, a career, or a calling?

“When we see our work as just a job, we’re focused on what we get for our labor – a paycheck and other tangible benefits like insurance… seeing work as just a job can be soul-destroying… We tell ourselves that the money’s worth it, but we feel empty.”

“We might, instead, see our work as a career. Our job is then linked to a bigger picture, often advancement in a profession or a company. We see our current role as an important step toward a destination. For example, we may see ourselves having significant impact on a field or rising in an organization we care about. This can be fun and exciting and can fulfill the need for a guiding purpose at work, presumably because our career is linked to our values. This can and often does make us happy. However, people who view work as a career are often largely motivated by things like prestige or upward mobility… but a singular focus on external recognition and rewards can make day to day work feel like a means to an end. We can find ourselves constantly seeking the next goal or prize, but each time we get that job, bonus, or raise, our ambition kicks in and we turn our attention to the next win.
When we view our work as a career, we should ask ourselves, “to what end?” If the answer is only to advance or progress, something vital is probably missing.”

“When we experience our work as a calling, our efforts are not simply the means to an end, and we’re not just jumping from one goal to the next. Instead, what we do every single day brings deep satisfaction. Even simple activities are seen as important, fulfilling, and meaningful. When work is a calling, our passion motivates us from the inside out… It’s becoming increasingly clear to me that if we are to experience our work as a calling we’ve got to understand which values matter to us and the act on these values to have positive impact.“

“In an attempt to keep up with continuous change, some leaders focus so intensely on business objectives that they bulldoze through people, crushing everything in their path… Josh was under pressure to move fast. But, rather than shifting into execution mode, he decided to invest time in understanding what people – wherever they sat in the organization – found fulfilling in their current ways of working and what got in their way… The more time I spent talking and listening to them about those elements rather than just about business issues, the more appreciation I had for their perspectives and the more ideas I had about how I could help. If you give people space, they’ll find the solutions themselves. They’ll understand how what they do every day has some purpose: to help the company, the customer, and society.”… His role was to create space for people to identify that purpose for themselves to help them feel heard, and to remove any obstacles that got in their way. This may sound like common sense, but frankly, in my experience, very few managers do this as well as they might. This is often because of a perceived lack of time or pressure from above to move fast.”

“Motivation that comes from inside us is a far more potent force than any carrot or stick used by our boss or the company… Studies show that people actually become less interested in tasks when they are externally rewarded… Real rewards, the kind that help us sustain commitment, engagement, and happiness, come from within us.”

Ok, at this point you may begin to realize that I’ve highlighted basically every other paragraph in this book, which I guess just goes to speak to how well I felt like I related to this book when I read it. Continuing on…

“To be happyat work, we need to make a difference. We need to be consciously attending to and enacting what we find to be inherently worthwhile – our values and beliefs… they’re often very private because they are derived from our upbringing and the culture of our families and communities… we are better off if we can find a way to incorporate what we care about into our day-to-day work.”

“Sometimes our values don’t align with our organization’s values, so we have to make a calculation about which values we can bring – and which we can’t… the reality is that sometimes, we and our values just don’t fit in certain workplaces. That’s where social awareness comes in.”

“If you want to bring more of your core self – your core values – to work, there are two things you can do. First, figure out what you care most about. One way to begin this process is to reflect on what you get excited about, what makes you proud. You can also spot values by examining what makes you uncomfortable or what makes you feel as if you are compromising in a way that does not feel good.”

“People want to feel that their work is linked to a larger, noble purpose… and that their company’s mission is meaningful. But often these missions don’t inspire people the way leaders hope they will. Sometimes they do the opposite. This is because a lofty, distant organizational mission can’t replace the need to live our values and have a personal impact on something that matters to us.”

Practical Ways to Find Purpose in Your Work

Human beings are inherently creative. We like to innovate, see new ways of doing things, and engage in activities that result in something that didn’t exist before.
For many years, we’ve known that we care more about the quality of our work when we see the fruits of our labor than when we’re told to move widgets from one part of a machine to another.
Doing meaningful work is rewarding in itself, and we are willing to do more work for less pay when we feel our work has some sort of purpose, no matter how small.”

Keep your eyes open for opportunities to join a group that is exploring a new idea or trying to solve a problem.
Find a way to track accomplishments .
Experiment with developing new processes to get work done.

“Don’t blame others for inefficient, broken work systems and processes. Don’t curse the proverbial “them” or wait for someone else to fix everything. They won’t. You can.”

Don’t be resigned to the way things have always been. Accept that most organizations are rife with old, worn out, and inefficient processes and pick some to fix.

Start small. You may not be able to fix an entire, convoluted budgeting process, but maybe you can change one report or form that will make your – and everyone else’s – life better.

“The very act of helping or supporting people can counteract the feeling that we’re toiling at a meaningless job. Because we’re so rarely working alone anymore, positively engaging with people may be the easiest way to express our values at work. Resonant relationships make us feel good and get more done because we are connected to and respectful of one another… People who give generously of themselves are actually more successful than those who sneak, connive, and take.”

Personal Reflection and Mindful Practice

  1. What is my definition of happiness? Where did my beliefs about happiness come from? What role do family, religion or spirituality, philosophy of life, and experience play in how I define happiness?
  2. Does my definition of happiness limit where, when and with whom I can experience joy, fun, and real fulfillment?
  3. Is my way of viewing happiness serving me well? Why, or why not?
  4. If I were to redefine what it takes to make me happy at work, what would my new definition be?

The Power of Hope

“Hope is the starting point for creating a future that is better than today. It encourages us to dig deep down inside ourselves to find our most unique talents and gifts and to use all of our resources to help us along the way. Whatever difficulties we face… the hope that tomorrow will be better is what helps us get up every morning.”

“Hope is at the heart of happiness at work.”

“when we’re angry or frightened, our thinking brain is essentially kidnapped and gagged by our limbic brain. In this state, we are guided by survival instincts. Our manager – or whoever is threatening us – begins to look suspiciously like a saber toothed tiger. We can to save ourselves and to hell with the consequences… Fortunately the exact opposite happens when we experience hope… When we are hopeful we are better able to access our knowledge and intellect, us our emotional intelligence, and rely on our intuition. We are more open and willing to consider new and different ways to reach our goals and have the emotional wherewithal to deal with challenges and problems.”

“… We can choose to view our memories through a positive lens or a negative lens… Obsessing about all the things that went wrong in the past and imagining it will all happen again today or tomorrow affects your ability to think, to process feelings, and to act in ways that will help rather than hurt you.”

Yes, You Do Need Friends at Work

“…We had our answer to the question: Sunglass Hut was doing well in part because of strong, warm relationships and a powerful sense of belonging in the company.”

“Having friends at work is critical. When we feel cared for – even loved, as one does in a friendship – and when we belong to a group that matters to us, we are generous with our time and talents because we’re committed to people, not just the job or the company.”

“… if employees suspect that someone doesn’t respect or care about them or their goals, they will likely become self-protective.”

“Love – the kind of love founded in companionship, caring and shared purpose – is the single most important factor influencing happiness in life… The love of family and friends is essential to our overall well-being. Similarly, caring relationships with colleagues at work enable us to thrive physically and psychologically. The positive emotions we feel in such relationships help us deal with stress, and we are even less likely to become depressed… Being in the company of friends helps us experience a deep and satisfying sense of belonging – another key element of happiness.”

Belonging: Our Tribe at Work

“From the time we lived in small, nomadic bands, we’ve needed one another to survive. We still do. There’s more to being part of a tribe, however, than finding food or protecting one another. We also have a deep human need to belong – to feel part of a group of people who share our values, hopes, and dreams… When we find ourselves in a team or organization that doesn’t want us or doesn’t accept us for who we are, we live in a constant state of physiological arousal: fears take over, we’re anxious, and we can even become depressed. Stress is constant and our physical and mental health suffer.”

“We thrive when we belong to groups where people care about, like, and respect us – and where we can give the same back in return. We want to feel that people we work with are our people, even if we come from different backgrounds and cultures.”

“Friendships don’t just form magically… to start, you can focus on trust, generosity, and fun… these help us to build warm, positive friendships in the workplace.”

“Make it a priority to get to know your colleagues. You can read about their cities, states, or countries.. or take time at the beginning of conferencealls to talk about nonwork topics.”

I Hate My Boss

“First, if your boss is indeed destructive, you need to defend yourself. You can start by creating psychological boundaries that protect you from emotional damage. If the situation is untenable, you should think about leaving.”

“Stop blaming and start creating a more positive relationship. When you respond with over the top negativity, you make the situation worse. People know when you don’t respect them and will often respond in kind.”

The Long March to Unhappiness

“Kala was caught in the boiling frog syndrome. When you’re in warm water and the heat’s turned up slowly, you don’t notice. You get used to it, whatever “it” is: being marginalized, unappreciated, treated unfairly, or taken for granted. The hot water feels normal, and we stay, even when it hurts… ‘I though I couldn’t do better. They devalued me, so I devalued myself.’… Kala’s problem is not unusual. It’s rarely one problem at work that leas us across the happiness line. More often, it’s a combination of many smaller challenges, seemingly logical compromises, and unending pressure. What kala did that’s less common, however, was to listen to her inner voice and bravely take a stand on what she wanted from her work experience.”

“overwork is a trap… it is not a good coping mechanism for stress. It makes things worse as we ignore our relationships, cut out fun, and eat and sleep poorly. “

Hearing the Wake Up Call

Physical wake up calls:

  • Eating too much or too little.
  • Difficulty sleeping, or sleeping too much.
  • Chronic Fatigue
  • Gastrointestinal issues
  • Headaches
  • Neck and back problems
  • Tightness in the chest
  • Too many colds and other seasonal illnesses
  • Onset or worsening of chronic health problems
  • Not smiling or laughing as much as you used to


Emotional wake up calls:

  • Seeing the glass half empty when you’re normally a half full kind of person
  • Seeing even small problems as insurmountable obstacles
  • Feeling sad more often than normal
  • Having difficulty snapping out of a bad mood
  • Feeling unappreciated or taken for granted
  • Feeling exhausted at the idea of doing something new and different
  • Believing that no matter what you do, it won’t be enough
  • Dreading your work
  • Getting frustrated easily or having a short fuse


Relational wake up calls:

  • Most conversations are terse and task-oriented
  • People say things like: “are you ok?” “Are you mad at me?” “you never listen to me anymore”
  • You are not interested in getting to know your coworkers
  • People in your life and at work are distancing themselves from you
  • People get quiet when you enter a room
  • You find yourself disagreeing and fighting with people about minor things
  • You are prone to criticize or blame others
  • You overreact when people disappoint you
  • You can’t remember when you last had a good time with coworkers – or anyone else.

Four Stages of the Journey from Despair and Resignation to Happiness

Stage One: Get Me the Hell Out of Here
Emotional self-awareness: Allow yourself to feel, really feel, those primal emotions.
Emotional self-control: Even if you think it might be time to leave, it’s a mistake to make decisions in amygdala hijack, when our limbic brain – not our rational brain – is calling the shots.
Positive outlook: When we choose optimism over pessimism, the parts of our nervous system that are involved in the stress response begin to lose power and we’re able to remain calm, energized, and focused

Stage Two: Figure Out What You Like and Hold Steady, Even When It’s Tough
“You’ve got to like what you do. You’ve got to find meaning in it and you have to feel that what you do will make a difference.”

Stage Three: Honestly Assess Your Work Situation
What’s really going on in your organization? Is the culture as powerful and toxic as you think it is? Are there any redeeming values that you can focus on? There usually are, and people have a hard time fighting you if you lead with something inspiring about the company, its noble purpose, and its values.

The Basic lesson here is that if we want to assess our work situation fairly, we have to let go of the habitual ways we view people and our work experience.

Stage Four: Run Toward the Future, Not Away From the Past
Sometimes running away is the right thing to do, but it’s better – much better – to run toward something… It’s important to understand that when you’ve heard a wake up call, you need to engage optimism and commit to a positive outlook about the future.

For intentional change to work, you also need to tap into confidence and self-efficacy. Trust yourself: if you’ve heard the call, and if you commit to moving toward a dream rather than running away, you are ready to craft a personal vision and a plan to get there.

Sharing Happiness at Work

“Cultivating happiness at work is a deliberate, conscious act. You now know what it takes: finding and living your purpose, focusing passionately on your future, and
building meaningful friendships.”

“…Create a resonant microculture on your team. A resonant microculture is marked by a powerful and positive emotional climate as well as shared purpose, hope, vision, and norms that support happiness and success. Everyone is supported to work hard and work smart, while also feeling good about themselves and their accomplishments… Take charge of the emotional climate of your team, commit to a shared purpose and vision, and create emotionally intelligent norms to support healthy ways of working together.”

“… Throughout his career, Roberto has worked to humanize his organizations, making it possible for people to learn, grow, and thrive… One of the ways Roberto has brought this to life has been to focus on culture, something he knows to be one of the most important drivers of individual and collective success… Unfortunately, too many of our organizations’ cultures do not help us to accomplish our goals, much less be happy. They are toxic: they stifle talent, hijack success, and make us miserable.”

Signs of Toxic Cultures:

  • Intense pressure to get short-term results
  • Taboos against speaking up to power
  • Us versus them mentality
  • Dysfunctional competition
  • Lots of talk about values but not enough action
  • Lack of clarity around a vision
  • Disrespect
  • Lack of appreciation
  • Pessimism
  • Incivility and hurtfulness tolerated or even encouraged
  • Inequity, absence of meritocracy, and injustice


Signs of Resonant Cultures:

  • A sense of unity around a noble purpose
  • Overt commitment to virtues and values like honesty, forgiveness, gratitude, wisdom, and love
  • A clear, inspiring, and shared vision of the future
  • Generosity of time, talent, and resources
  • Taboos against hurtful treatment of others, dishonesty, and cynicism
  • Respect for the individual’s right to grow and develop
  • Celebration of differences
  • Compassion and humane treatment of everyone in good times and bad
  • Fairness and justice
  • Integrity
  • Fun

“In Primal Leadership… ‘great leaders move us. They ignite our passion and inspire the best in us… Great leaders are awake, aware, and attuned to themselves, to others, and to the world around them. They commit to their beliefs, stand strong in their values, and live full, passionate lives.’.. Today each and every one of us must be a resonant leader.”

Create a resonant microculture, shape your team’s emotional reality, seek common purpose, nurture hope and your team’s shared vision.

Commit to Emotionally Intelligent Team Norms

  • Seek to understand each other’s viewpoints and feelings
  • Actively care for people
  • Respect and accept people for who they are
  • Connect with people around higher purpose and dreams
  • Engage in open, honest dialogue
  • Don’t shy away from conflict, but don’t harm people or relationships
  • Be reliable and consistent to build trust
  • Take the lead and also be a good follower
  • Celebrate success
  • Adopt norms that support a sense of belonging

TL;DR
Life is too short to be unhappy at work.
Free yourself from the happiness traps that keep you miserable.

  • Be authentically yourself and celebrate others for who they are
  • Live the virtues and values that support purpose, hope and friendships
  • attend to and honor your feelings
  • Celebrate and suffer together
  • Be calm
  • Be brave.
  • Fight Oppression
  • Break the rules about overwork; just don’t do it anymore
  • be compassionate with yourself and others
  • Love yourself and find something to love and honor in everyone
  • Have fun
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A Case Against Suicide by Exsanguination by Laceration of the Radial or Ulnar Arteries, aka How Long Does it Take To Die by Cutting Your Wrists?

Note: this is a working rough draft and has been unedited from the initial deluge of words, numbers and figures that first came to rest here.

If you’ve listened to the live version of “Waiting” by City and Colour on his album guide me back home, Dallas Green describes the song, whose content is about death, as being negative, but in a positive way. I’ve been told that is also a pretty simple way to paraphrase me, but also how I would describe this article.

Motivation

Suicide amounted to approximately 782 thousand deaths in 2008, or roughly 1.4% of total mortality, and 15% of mortality via injury. These numbers translate to 11.6 people per 100,000 inhabitants on a global scale. [1] Despite this relatively high occurrence rate, most people are initially, and persistently, exposed to suicide through the media, with internet playing a very important role in contemporary culture. [2] High-volume, prominent, repetitive coverage of suicide that romanticizes, glorifies, or otherwise resonates with individuals has been long since thought to increase the occurrence of suicide. [3][4][5]

This imitation of suicide is often termed the ‘Werther effect’, whose namesake is attributed to the protagonist in Goethe’s The Sorrows of Young Werther who killed himself and was then imitated by admirers of the book. [5] This may also be referred to as a copycat suicide, which in a community can cause social learning of suicide-related behaviors resulting in suicide clusters, that by definition, occur closer together in time and space than would normally be expected on the basis of statistical prediction. [6]

Some studies have reported that the presentation of suicide in entertainment media have an equivocal effect on suicide rates [7]. Despite the ambiguous affect in some studies, I argue, anecdotally, that entertainment media has a larger influence than news media. In support of this, one review concluded that newspapers, television, books, the internet, and mixed media all have a consistent association with influence on suicidal behavior. [8]

The dynamic list on wikipedia entitled “List of Suicides in Fiction” contains 535 entries as of 1/6/2019. [9] In fact, this article began by questioning the events of the film “John Wick: Chapter 2”, in which Gianna D’Antonio easily slits her wrists, lays back, and dies in a pool quickly. One PhD dissertation even goes as far as to discusses 350 popular films that depict suicide. [10]

Furthermore, music, and music related subcultures may tend to increase the prevalence of self harm and suicide. Self harm should never be confused with suicide, or even attempts at suicide, but for the sake of illustrating that individuals who do this are not alone in their actions, self harm with the intent to communicate distress or relieve tension has been found to occur with rates of 7-14% in young people in the UK. [11] Self-identification of belonging to the Goth subculture of the 90’s and 2000’s was found to be strongly associated with lifetime self harm and attempted suicide( n = 1258), with a prevalence of 53% and 47% respectively. [12] Lending to the influence of music, the wikipedia category “Songs About Suicide” contains a list of 196 pages of contemporary songs at the time of writing. [13]

Prominent Methods of Suicide

In order of decreasing lethality, firearms, suffocation and hanging, poisoning, fall from a great height, and cutting or piercing are typically recorded as the most prevalent paths of suicide. [14][15][16]. Unsurprisingly, because of gun laws in the United States, and the lethality of firearms, they account for the most completed suicides. One should note, that though this is the most common form of suicide in the united states, it does not follow that the suicide rate in the United States is high in comparison to other nations. In fact, 41 nations have a higher suicide rate than the United States, with Lithuania, South Korea, and Russia having nearly triple the rate per capita. [1]

Anatomy of the Anterior Forearm

In order to have an adequate discussion about this topic, we must first explore the anatomy of the anterior forearm.

Superficial musculature of the anterior forearm [17]

Let’s first make note of all of the critical structures related to the musculature of the anterior forearm, as shown in the figure above. At the palmar wrist there are 16 structures of note, including 12 tendons, two nerves, and two arteries. Notably the flexor carpi radialis (FCR) tendon, the palmaris longus tendon, and the flexor digitorum superficialis tendons are present here. In addition to prominent tendons we see the palmar carpal ligament.

Now, let’s we move beyond musculature to the nerves that innervate the hand as shown in the figure below.

Nerves of the anterior hand [17]

The three main nerves that pass through the distal anterior forearm and into the hand are the Ulnar, Radial, and Median nerves, so named because the ulnar and radial nerves parallel the ulnar and radial bones respectively, and the median nerve is in the middle of these. In this view we can also see that the radial and ulnar arteries are nearly co-located with the radial and ulnar nerves. This positional relationship is made a little more evident in the next figure.

Co-location of the arteries and nerves of the anterior forearm [17]

The radial nerve gives sensory supply to the dorsal aspect of the hand, as well as thumb, index finger, middle finger, and a portion of the ring finger. This supply to the dorsal portion of the hand is why it does not appear in the figure below. [18]

The ulnar nerve is sometimes colloquially known as the “musician’s nerve”, as it controls the fine movements of the fingers. [18] In addition to this role, it provides sensory innervation to the pinky, and portion of the ring fingers. Damage to this nerve can result in what is known as “claw hand.”[19]

The median nerve supplies innveration to two of the lumbrical muscles of the hand. This nerve also provides sensation in the lateral 3.5 digits. Damage to the median nerve at the wrist can result in “ape hand deformity”, resulting in an inability to abduct the thumb. Carpal tunnel syndrome is the result of compression of the median nerve as it travels through the wrist.[18]

Nerves of the anterior arm [17]

Ultimately, this brings us to the two main arteries that supply the hand with blood: the radial and ulnar arteries which are visible in the two previous figures. These are the arteries that individuals are typically concerned with when they imagine suicide by exsanguination, i.e. slitting one’s wrists. The radial artery is slightly larger than the ulnar, with mean diameters of 3.2mm and 2.5mm respectively.[20] Of note are also the large veins of the anterior forearm, which can be seen in the figure below.

Veins of the anterior arm [17]

From this primer we see that there are many critical structures associated with the forearm and hand, comprising tendons, nerves, and arteries. Due to their close proximity to one another, it is easy to see that the act of damaging any of these critical structures will likely result in damaging many others. If damage occurs to tendons, especially ones involving dexterous manipulation of objects such as the flexor digitorum superficialis, it is likely that dexterity will never be the same even with surgical repair. Furthermore, if nerves are damaged, it is even more likely that motor skills and sensation will never be the same.

In order for someone to attempt suicide by lacerating their wrists, and to obtain the requisite depth, they will necessarily damage other critical structures of the wrist that can lead to lifelong complications.



Anatomy of Blood

Blood, as you may already be aware, is a fluid that contains many enzymes and hormones, which carries out the important task of transporting oxygen and carbon dioxide between the lungs and cells of tissues. It may be separated into plasma and cells via centrifuge, with the plasma being roughly 90% water by weight, 7% plasma proteins, 1% inorganic substances, and 1% other organic substances. The cellular content of blood is almost entirely erythrocytes, or more commonly red blood cells, with leukocytes, or white blood cells, comprising less than 1/600th of the total cellular volume, and thrombocytes, or platelets, making up less than 1/800th of the total cellular volume. [21]

Erythrocytes, a) top view and b) side view forming rouleaux [17]
Various types of erythrocytes [17]
Thrombocytes [17]

Under normal circumstances, erythrocytes occupy approximately 50% of the blood volume, with a density of nearly 5 million per cubic mm. Comparatively, leukocytes and erythrocytes are much more rarified with densities of 5,000 to 8,000 per cubic mm, and 250,000 to 300,000 per cubic mm respectively. [21][18]


What would happen if someone cut their wrists?

So, let’s assume that someoneone manages to cut their anterior wrist to a depth that lacerates one of their arteries, let’s assume the radial, as that will be easier for people to damage using their other hand, what would happen? From the anatomy discussion above, the first thing that will be apparent is it will likely be very difficult to use that hand for much due to tendon and nerve damage. Second, obviously, and is the purpose of this act, a large amount of bleeding will occur, but how much?



Complicated Engineering Answer

If we want to model things precisely, the time varying velocity profile in arteries can be calculated by:

1) \qquad v_{f} (y,t) = \displaystyle \sum_{k=0}^\infty Re \left \{V_{k}e^{j(k \omega t - \phi_{k})} \left [ \frac{J_{0}(\tau_{k} ) - J_{0}(\tau_{k} y)}{J_{0}(\tau_k) -1} \right ] \right \}

Where Re is the real part of a complex variable, J_{0} is the zero order Bessel function of the first kind, y is the normalized radial coordinate, \omega is the angular frequency of the heart beat, t is time, \phi_{k} represents the phase of each harmonic, V_{k} is the centerline velocity of each harmonic, and \tau_{k} is :

2) \qquad \displaystyle \tau_{k} = a_{k} \cdot j^{3/2}

With a_{k} being the Womersley number for each harmonic.

3) \qquad \displaystyle a_{k} = d \sqrt{\frac{k \omega}{\mu}}

Where \mu is the coefficient of viscosity of the fluid, and d is the diameter. [22]

After calculating the time varying velocity profile, the flow rate can be calculated using:

4) \qquad Q(t) = 2 \pi \displaystyle \int_{0}^{d} v_{f}(y,t) y \;\partial{y}

Note, that blood as a whole is non-Newtonian because \mu varies as a function of strain rate. Interestingly, however, blood plasma alone has been shown to be Newtonion. This should not come as a surprise when one takes a moment to observe that blood is merely a suspension of cells in an aqueous solution of electrolytes and non-electrolytes. [21]

The amount that \mu varies is a function of the hematocrit, H, which is the volume fraction of red blood cells in whole blood. For normal blood with a low hematocrit, H = 8.25%, \mu can be assumed to be constant over the entire range of shear rate from 0.1 to 1000 s^{-1}. However, the hematocrit in a healthy individual typically averages 45% [18].

If we simplify our analysis to assume a Newtonian fluid, and assuming flow is laminar, we can use the well known formula:

5) \qquad \dot{Q} = \displaystyle - \frac{\pi a^4}{8 \mu} \frac{dp}{dx}

where a is the radial distance along the tube from centerline, p is pressure, and x is the axial distance along the tube. [21]

The above analysis results in volumetric flow rates that are 15 – 50% lower than those obtained using clinical ultrasound scanners, causing the authors to conclude that these scanners result in overestimation of flow rate and wall shear rate in radial and ulnar arteries. [22]

Simple Steady Flow Rate Answer

Let’s assume measurements are averaged over a time period much larger than time differential between heart beats, thereby allowing us to ignore differences between systolic and diastolic pressure. If we assume large timescales, we can simply look up empirical measurements of arterial flow rate. Studies have shown that an average flow rate through the radial artery is between 50 and 64 ml \;min^{-1}. [29][24] Due to the fact that smaller capillaries will be damaged, let’s assume a volume flow rate of \dot{Q} = 75 ml \; min^{-1}. With an average steady volume flow rate assumed, in order to calculate time, all we need to know is the volume of blood required.

It is generally accepted that blood loss resulting in death must be between 50% and 66% of total blood volume. This size of hemorrhage is classified as a class 4 hemorrhage, as it exceeds 40% of total blood volume. For a healthy, average sized, adult male weighing 70 kg, we can assume a blood volume of 5L. [18]

With this knowledge, we assume death will occur once 2500 ml of blood has been lost. This results in the simple equation:

6) \qquad 2500 ml = 75 \frac{ml}{min}\; \cdot \; x \;minutes

Note that dimensional consistency is easily validated in equation 6 by seeing that units of minutes in the denominator of the first factor cancels out units of minutes in the numerator of the second factor. Solving for our independent variable, x, we conclude that death will occur after 33.33 minutes.

Since there are 4 classes of hemorrhages, we can easily calculate the time to reach these class of hemorrhage.

Class 1 hemorrhages are all hemorrhages resulting in less than 15% of blood volume lost. At the early portions of this stage all that will really happen is vasoconstriction, or the dilation of blood pathways. By definition, we will have reached a class 1 hemorrhage as soon as our volume flow rate calculation begins.

Class 2 hemorrhages are classified as resulting in 15% – 30% blood volume lost. At this stage patients may become tachycardic, peripheral vasoconstriction continues, and skin may begin to look pale and be cool to the touch. 15% of our 5L assumption equates to 750 ml, or the volume of one bottle of wine. This stage will be reached in 10 minutes by our assumptions above.

Class 3 hemorrhages are classified as resulting in between 30% and 40% blood loss by volume. At this stage the patient’s blood pressure will begin to drop, heart rate increases, peripheral hypoperfusion (shock) with diminished capillary refill occurs, and mental status worsens. Blood transfusions will typically be necessary at this stage. Given the above assumptions, this equates to 1500 ml, or two bottles of wine, and will occur within 20 minutes.[23]


Analyzing Our Results

Now, you may be asking, what the hell, it will take more than 33 minutes, and you won’t really feel anything until after 10 minutes? They always show it to occur so quickly in the movies. The truth is that this is actually a very simplified calculation that will likely yield a time faster than in reality. The reason for this is simple, we managed to neglect hemostasis, the process by which the body stops bleeding. Additionally, it has been observed that direct trauma to an artery can cause a vasospasm[24], which may further disturb radial artery blood flow. One last contribution, is according the study mentioned in the “Complicated Engineering Answer” section, the measured arterial volumetric flow rate may be overestimated by as much as 50%.

Hemostasis may be decomposed into primary and secondary pathways, which converge to form a common pathway. Primary hemostasis constitutes the formation of a platelet plug, wherein platelets begin to stick together to form a temporary seal over the break in the blood vessel wall. Secondary hemostasis is the process by which blood begins to coagulate. Prior to these two efforts of the body to achieve hemostasis, vascular spasms will occur to constrict blood vessels so that less blood will be lost. Therefore, it is likely that our estimated flow rate above will be higher than in reality, and that flow rate will not be steady, but will decrease with time. [25]

We may then conclude that the time to obtain a class 4 hemorrhage with the aforementioned means will likely take closer to an hour, if it occurs it all.


Illustration by Case Studies

If we turn our attention to case studies of the outcome of suicide attempts from laceration we observe something that seems to confirm our above mathematical analysis: this method is usually unsuccessful. Indeed, only one observed case of suicide by laceration of the ulnar artery occurred in Britain in the year 2003, with the only case being the highly controversial death of David Kelly, who many believe was actually murdered. [26]

Furthermore, in 2001 it was observed that in the United States 63,275 individuals attempted suicide by means of cutting or piercing, with only 651 of these resulting in death. [14] That equates to 99% of people surviving their attempted suicides, many having life altering consequences as a result of their attempts.

So, what happened to these people?

Remember our discussion of critical structures above? Well, many of these individuals damaged more than just the artery they were hoping to, and almost all attempts did not result in death, as is shown in the movies; if they did, they were slow, and required a great amount of effort. A case study following 41 individuals who attempted suicide by wrist cutting was performed in 2015. This study illustrated that out of the 41 patients, 21 were unable to physically cut deep enough to reach any important anatomical structures. Furthermore, wrist flexor tendons were the most commonly injured anatomical structures, but specifically, the median nerve as the most frequently damaged individual structure. Of the individuals in this study, only 8 individuals were able to damage arteries. Of these 8 individuals, all had damaged the corresponding nerve, and all but one damaged large tendons. After surgical intervention of these structures, half of these individuals reported only poor to fair sensation or function. [27]

One reason these conclusions may be unexpected for some, is the fact that most suicide publications deal with single unusual cases, while retrospective studies are uncommon as suicide by this method has a low mortality rate. [27] Despite self cutting injuries having a low mortality rate, they often have special clinical significance due to the potential to lead to devastating disability and only increase one’s desire to commit suicide. [27]

Many have observed that the low mortality rate of this method is due to the amount of work required of the individual. Not only are they tasked with trying for some time to defeat their carnal sense of self-preservation, but the pain is great and they must physically lacerate themselves to a depth that is difficult for many to achieve without applying a very large amount of pressure.


So why write this?

Many publications indicate that wrist cutting patients cut themselves impulsively. [28] It is my hope that thinking critically about this will result in fewer people acting impulsively, and in a manner that only makes life more difficult for them. Additionally, this is often one of the first methods of suicide individuals become comfortable with, as the lethality of suicide attempts tend to increase as number of attempts and time increases.[2]

Final Thoughts

Everyone at one point or another considers suicide. Indeed, even Albert Camus in The Myth of Sisyphus states “There is but one truly serious philosophical problem, and that is suicide. Judging whether life is or is not worth living amounts to answering this fundamental question of philosophy. All the rest – whether or not the world has three dimensions, whether the mind has nine or twelve categories – comes afterwards.” I believe that many choose to shy away from topics that they cannot relate to well, or are afraid of, but these things should not be ignored. Many of us simply have been let down by the public schooling system and guidance of elders in learning about emotions and the myriad unobservable social stressors; we are taught to ignore these things, even be embarrassed by them. Enthralled by the grasp of suicidal ideations and immobilized by the weight of one’s own melancholia, reaching out is difficult, but I implore you to speak to others. We are all human, and implicit in that is the presence of emotions; we can all relate to and sympathize with the pangs of life. If you feel you are truly alone, and have no one to turn to, reach out to the National Suicide Prevention Lifeline in the United States. For an international list of suicide lifelines, please look here. If nothing else, and you want to reach out to some guy in his late 20’s that’s not associated with any of these entities, please, feel free to shoot me an email at Eric<at>Numerickly.com.

Resources

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  3. Bohann L, Wang X (2012). “Media guidelines for the responsible reporting of suicide: a review of effectiveness.” International Associate for Suicide Prevention 2012; 33(4):190-198.
  4. American Association of Suicidology, American Foundation for Suicide Prevention, et al. “Recommendations For Reporting On Suicide.” www.reportingonsuicide.org Retrieved 2019-01-06.
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