The Problem with Integrity

I think about Winston Churchill a lot. A successful writer, correspondent, painter, politician and businessman, he is known for his bold principled stand against Hitler. However, zoom in and a more complex narrative emerges.

After Neville Chamberlain negotiated the Munich Agreement in 1938, which sought to appease Nazi Germany by allowing them to take control of the Sudetenland region of Czechoslovakia, Winston Churchill famously said, “You were given the choice between war and dishonor. You chose dishonor, and you will have war.”

They look wise now, but his comments were unwelcome. Many people in Britain and other countries believed that the agreement would prevent war and that Churchill’s warnings were alarmist. He was even removed from his position as First Lord of the Admiralty in 1939 and was not given any major government positions until 1940 when he became Prime Minister as the war had already started.

He pushed through years of criticism and personally rallied a nation with his bold, counter-cultural, stand that led the allied powers to victory. If we stopped there, we have a tight schoolbook story of leader who did the right thing and was vindicated and honored.

Unfortunately for Sir Winston, shortly after the war, his government was defeated in the general election of July 1945. The British people were tired after six years of war and preferred the Labour Party’s program of social reforms. He found himself doubted, vindicated and then cast away.

Everyone and every organization wants integrity, but actually having it, keeping it and acting on it is a challenge. Nothing is simple when you find yourself at a different place than those around you. Holding a counter-cultural view means going against the dominant beliefs and values of the system you are working hard to support.

Yes, integrity can be dangerous. The word integrity doesn’t have meaning and power when everyone agrees. When integrity forces you to be different, it’s dangerous for you and others. You risk losing your friends, your job and your sleep.

Counter-cultural integrity threatens the status quo and big organizations need broad buy in to the status quo to get things done. The right thing may be good in the long run, but it can be disruptive now. Personal integrity requires standards that may not change with culture or a corporation’s strategy for risk mitigation. Anyone who holds to an independent set of standards will eventually find themselves a problem in a rigid and ever changing system.

Standing Alone

Worst of all, the road towards acting on integrity brings you into contact with the dark side. There is a temptation to be right and feel superior to the system you are in. You need the inspiration of the examples of Martin Luther King, Gandhi, Winston Churchill or Abraham Lincoln, but you can’t conflate your situation and your strength with theirs. You have to remain humble while not losing your convictions. You have to be continually open to being wrong. You have to push yourself to be flexible. You have to see and respect the other side.

The other temptation is to give in to self-pity and think that the world is against you. The professional world can be a dark, amoral, and heartless place. That is reality–true everywhere. No one is a unique and constant victim of unjustified persecution or mistreatment. There is no conspiracy, just people trying to make it all work and not lose their status, jobs or relationships.

The stress of finding yourself alone, against the crowd, is real. The only way to survive it is to have a trusted network of friends– not friends who just listen, affirm and agree, but friends who hold you accountable and clarify your thoughts. A good friend turns a dark and lonely road into conviction that can confirm your individuality and authenticity. Most important, sharing your story can lead to positive change. There is no tighter community than like-minded individuals who support, refine, and validate each other’s perspectives.

I’ve taken several counter-cultural stands in my life with a wide range of outcomes. All were painful. Every stand I’ve taken has resulted in some degree of lost friendships and increased pain. Some day I may be proud of these actions, but all of them resulted in a lost opportunity where I had to get off the boat and watch it sail on. If there is any pride in that, it’s drowned out by the sadness of it all.

I’ve learned that I’m not particularly brave or strong. However, I’m blessed with great community, a love of history and a deep care for others. Most of all, I feel convicted to protect others who trust and depend on me doing the right thing.

But this isn’t the movies. As I’ve post-processed tough stands, when I did the most good, I felt the worst inside. Taking a different road leaves you feeling alone and scared, self-conscious and unsure. Integrity put into practice in these scenarios makes part of you wish you didn’t have it. It’s not fun and it doesn’t feel courageous. When I’ve done the most right, the overwhelming emotion is sadness and insecurity.

Here I’m convicted and encouraged by two father son chats. The first is Polonius, who is giving advice in Hamlet to his son Laertes as he prepares to leave for France. Polonius urges his son to be honest with himself, to be true to his own values and beliefs, and to avoid the temptations and pitfalls of the world. He advises Laertes to “neither a borrower nor a lender be” and to “this above all: to thine own self be true, And it must follow, as the night the day, Thou canst not then be false to any man.” If Laertes is true to himself, he will not be able to deceive others; he will be true to himself and avoid compromise for the sake of others or for the sake of fitting in.

The second is from Cicero. He wrote to his son, Marcus, that an unjust act will never profit him.

Stop. Just let the gravity of this settle. This may be the most counter-cultural message ever written. A thief can at least enjoy his spoils a little bit, right? A boss who complies with pressure to promote a lesser qualified person at the expense of her/his better judgment may get a promotion that helps their career, right?

No, Cicero says it won’t help them. He believed in an absolute view of morality and integrity. He wrote that an unjust act is not only morally wrong, but it will also ultimately harm the person who commits it and the society that allows it. He believed that living a virtuous life and making the right choices, even if difficult, is the only true path to true happiness and fulfillment. In his letter Ad Familiares Cicero wrote: “There is nothing more virtuous, nothing more in accord with duty, than to take one’s stand for what is right.” He also wrote in this same letter:

“What is morally right is not always politically expedient; and what is politically expedient is not always morally right.”

Cicero believed that true success and happiness come from living a virtuous life, and that this requires standing up for what is right, even when it may be difficult or unpopular. Even when it looks like an easy compromise, it will never profit you. Never. Even if you are lucky and some good results from your actions, you have harmed your soul.

The wisdom of history, a deep personal faith and a tight network of friends all give me confidence to do the right thing, no matter the cost. This is true even with full knowledge of just how dangerous, costly and lonely the road of counter-cultural integrity is.

I’m jealous of those who can compromise, make things work and steer situations to a middle ground, but I have trouble here. This isn’t a brave or honorable as much as I see no other option. Without deep reflection on, and a commitment to hold to standards, I wouldn’t have individuality or authenticity.

Just as breathing is a necessary function for survival, holding to one’s standards and integrity is necessary for maintaining a sense of self and personal agency. Without it, one risks becoming a mere follower or conforming to the beliefs and values of others, losing their unique perspective and individuality. Holding to one’s standards and integrity can be challenging–it’s been the hardest thing I’ve had to do–but it is a fundamental aspect of being true to oneself.

It’s fitting to have just passed Martin Luther King day. MLK wrote:

“The ultimate measure of a man is not where he stands in moments of comfort and convenience, but where he stands at times of challenge and controversy.”

Character is revealed not in moments of ease, but in times of adversity, and when difficult choices and decisions are made. This quote reminds me that true strength and honor come from standing up for what is right, even when it is hard and uncomfortable, and that we should strive to be true to our principles and values, even in the face of opposition. All power is moral power and all strength requires the willingness to walk the hard road, even when it isn’t where you want to go.

Pairing Philosophers in 2023

Søren Kierkegaard and Friedrich Nietzsche are valued teachers and they generated many of the ideas bumping into each other in the culture today.

Søren Kierkegaard was a Danish philosopher, theologian, and social critic who is known for his contributions to the field of existentialism. He believed that the individual’s relationship to God was the most important aspect of human life, and that the search for meaning and purpose was an essential part of the human experience. Kierkegaard argued that the traditional institutions of society, such as the church and the state, were inadequate for helping individuals to find meaning and fulfillment in life, and he called for a return to a more personal and inward-looking approach to faith and spirituality.

Friedrich Nietzsche was a German philosopher who is known for his critiques of traditional values and his celebration of the individual. He argued that traditional morality, with its emphasis on self-denial and restraint, was destructive to the human spirit and hindered the development of truly great individuals. Nietzsche believed that people should embrace their own desires and passions, and strive to become what he called “overmen,” or individuals who had fully realized their own potential and lived life to the fullest.

These two philosophers define authentic to me. Neither of them would have been comfortable in my Church or in my society, but I can’t escape how much I would love to host a cup of coffee with these two thinkers.

Two Gents talking

Authenticity is really hard because we can’t escape our obsession with status no matter how hard we try. It’s better to not think about status too much because focusing on it can compromise authenticity. Kierkegaard and Nietzsche are good to match up because they both were independent thinkers who didn’t care about others’ opinions, yet were deeply wounded by the world’s rejection.

One stark difference: Kierkegaard embraced faith, while Nietzsche rejected the idea of a greater meaning in life.

Both Kierkegaard and Nietzsche were obsessed with finding the truth, wherever that quest went, and were both deeply troubled by what they found and by the process of finding it.

Desiring truth not consistency is probably the hardest intellectual challenge and it can be a lonely and troubling journey. Since I know that I’m not wiser than the weight of history or the leaders of my faith community, I tend to side on tradition when I don’t understand things. Yet I strive to overcome the temptation to prioritize consistency in my beliefs over seeking new information that may challenge them. Consistency is a good default, but it can prevent us from fully understanding the world around us and making informed decisions. An open and certain mind is a rare thing and both do and don’t have one.

Nietzsche and Kierkegaard inspire me on this point. They were concerned with the nature of human existence and the meaning of life, and they both sought to fundamentally re-think the traditional Western philosophical tradition. This makes them good foils to consider what they might think about three significant developments in the modern world: the rise of populism, the decrease in organized religion, and the rise of artificial intelligence.

The Rise of Populism

Nietzsche and Kierkegaard were both critical of the values of the Enlightenment and the modern world, and they both argued that the modern world had lost touch with the deeper meanings and values of life. In this sense, they might both view the rise of populism with a certain degree of skepticism. Populism is often associated with a rejection of traditional political and social elites and a focus on the needs and concerns of ordinary people. Both Nietzsche and Kierkegaard would likely argue that this focus on the needs and desires of the masses can lead to a superficial and shallow understanding of the world, and they would both caution against a reliance on the “tyranny of the majority” as a guiding principle for society.

At the same time, however, both Nietzsche and Kierkegaard placed a strong emphasis on the importance of individuality and the need for individuals to be true to themselves and their own values. In this sense, they might both see the rise of populism as an opportunity for individuals to reclaim their own autonomy and agency, and to resist the homogenizing forces of modernity.

Nietzsche the populist?

The Decrease in Organized Religion

Both Nietzsche and Kierkegaard were deeply concerned with the role of religion in human life, and they both grappled with the question of how individuals can find meaning and purpose in the absence of traditional religious beliefs. Nietzsche was highly critical of traditional Christianity and other monotheistic religions, and he is known for his arguments against the existence of God and his rejection of traditional moral values. He argued that individuals should create their own values and meaning rather than relying on traditional sources of authority.

Kierkegaard, on the other hand, was deeply religious and saw faith as a central aspect of human life. He argued that belief in God was not a matter of reason, but rather a matter of the heart, and he developed the concept of the “leap of faith” to describe the idea that individuals must make a leap of faith in order to truly believe in something.

In the modern world, we are seeing a decline in organized religion and a shift away from traditional religious beliefs. Nietzsche might view this trend as a positive development, as he rejected traditional religious beliefs and saw them as a source of oppression and illusion. Kierkegaard, on the other hand, might view the decline in organized religion with concern, as he saw faith as a central aspect of human life and argued that individuals need a sense of transcendence and meaning beyond the material world.

The Rise of Artificial Intelligence

In the 21st century, we are seeing a rapid development of artificial intelligence and the increasing integration of technology into all aspects of our lives. Nietzsche and Kierkegaard would likely have very different perspectives on the rise of artificial intelligence.

Kierkegaard and AI (picture generated by Dall-E 2)

Nietzsche might view the development of artificial intelligence with a certain degree of skepticism, as he placed a strong emphasis on the value of human creativity and individuality. He might argue that the increasing reliance on artificial intelligence could lead to a dehumanization of society and a loss of the unique qualities that make humans special. But! Nietzsche was interested in the potential of technology to enhance human life and enable individuals to overcome their limitations, and he might have seen the development of artificial intelligence as a potential way to achieve this.

Kierkegaard, on the other hand, might have been more skeptical of the role of technology in society and could have seen it as a threat to human dignity and autonomy. He might have argued that the increasing reliance on technology was a symptom of a deeper spiritual malaise in modern society and could lead to a loss of meaning and purpose in life. (Good grief, how much I love Kierkegaard.)

Who Else?

All this had me thinking, what other pair might be an interesting lens to view society? And I think five other pairings would be super fun to meet up with:

Jean-Jacques Rousseau and John Locke

Best friends?

These two philosophers had very different views on the nature of the state and the role of the individual in society. Rousseau argued for the primacy of the common good and the need for the state to exert control over the lives of individuals, while Locke argued for the importance of individual rights and the need for limited government. Comparing these two philosophers could provide a useful framework for thinking about issues related to the balance between individual freedom and the role of the state in modern society.

Karl Marx and Adam Smith

These two philosophers had very different views on the nature of economic systems and the role of the state in regulating them. Marx argued for the abolition of private property and the need for a socialist economic system, while Smith argued for the importance of free markets and the role of self-interest in driving economic growth. Comparing these two philosophers could provide a useful framework for thinking about issues related to economic policy and the role of the state in the economy.

Michel Foucault and John Rawls

Focualt and Rawls on the March

These two philosophers had very different views on the nature of justice and the foundations of moral and political theory. They pretty much define the camps in the American left today. Foucault argued that power relations are a fundamental aspect of society (#BLM, Woke!) and that justice is not an objective concept, while Rawls argued for the importance of a social contract based on fairness and equality (think Clinton/Blair). Comparing these two philosophers could provide a useful framework for thinking about issues related to social justice and the foundations of political theory.

Thomas Hobbes and John Locke

These two philosophers had very different views on the nature of the state and the role of the individual in society. Hobbes argued for the need for a strong, centralized state in order to maintain order and prevent anarchy, while Locke argued for the importance of individual rights and the need for limited government. Comparing these two philosophers could provide a useful framework for thinking about issues related to the balance between individual freedom and the role of the state in modern society.

Finally, Kant and Hegel!

Immanuel Kant, an 18th-century philosopher has had the same level of influence as Kierkegaard on me. I consider myself a Kantian. I love the idea that the moral worth of an action is determined by the motivation behind it, rather than the consequences that it produces. An action is considered morally right if it is done out of a sense of duty or respect for moral law, rather than as a means to achieve some other end or goal. Also, the moral law is universal and applies to all people, regardless of their individual circumstances or desires.

Kantian ethicists argue that we have a moral duty to treat others with respect and to always act in accordance with moral principles, even when it is difficult or inconvenient to do so. They believe that this is the only way to create a just and moral society, and that failure to live up to these standards can have serious consequences for individuals and for society as a whole.

Georg Wilhelm Friedrich Hegel, a 19th-century philosopher, would be a great contrast to Kant. Some specific areas of disagreement between the two philosophers include:

The nature of history and the role of reason: Kant argued that human reason was a universal and timeless principle, while Hegel argued that reason was an inherent part of the historical process and that the world was shaped by the interplay of opposing forces. Hegel used organic metaphors and language to describe the way in which history unfolds and develops over time. For example, he referred to the process of historical development as a “world-historical process” and described the different periods of history as “stages” in the development of human consciousness.

The nature of the state and the role of the individual: Kant argued for the importance of individual rights and the need for limited government, while Hegel argued for the primacy of the state and the idea that individuals should be subservient to the state.

The nature of knowledge and the foundations of moral and political theory: Kant argued for the importance of reason and the a priori principles that structure our experience, while Hegel argued that knowledge was a product of the historical process and that the ultimate goal of human development was the realization of the “Absolute.”

How fun it would be to pair all the philosophers mentioned above about up. They probably would find my company pretty boring, but it would be fun to tell them about the 1900s and answer their questions about what we believe today. Ah, well, I get to read their books, write this stuff up and, even better, talk to you about this stuff.

Review: From Strength to Strength

Devote the back half of your life to serving others with your wisdom. Get old sharing the things you believe are most important. Excellence is always its own reward, and this is how you can be most excellent as you age.

Arthur C. Brooks

How do you ensure you don’t get the most out of aging well: cultivate gratitude, practice compassion, build relationships, and create beauty. I love the simplicity and truth of that.

In “From Strength to Strength: Finding Success, Happiness, and Deep Purpose in the Second Half of Life,” Arthur Brooks addresses a common problem faced by many successful individuals (who he calls “strivers”) as they enter the second half of their lives.

Yes, but I’m 46, should I care about this? Well, yes, according to most research I’m past my professional prime. In the world of tech/science the most common age for producing a magnum opus is the late 30s. The likelihood of a major discovery increases steadily through one’s 20s and 30s and then declines through one’s 40s, 50s, and 60s. Research shows that the likelihood of producing a major innovation at age 70 is approximately what it was at age 20—almost nonexistent.

My brand is innovation and innovators typically have an abundance of fluid intelligence. It is highest relatively early in adulthood and diminishes starting in one’s 30s and 40s. This is why tech entrepreneurs, for instance, do so well so early, and why older people have a much harder time innovating.

Crystallized intelligence, in contrast, is the ability to use knowledge gained in the past. Think of it as possessing a vast library and understanding how to use it. It is the essence of wisdom. Because crystallized intelligence relies on an accumulating stock of knowledge, it tends to increase through one’s 40s, and does not diminish until very late in life.

Careers that rely primarily on fluid intelligence tend to peak early, while those that use more crystallized intelligence peak later. For example, Dean Keith Simonton has found that poets—highly fluid in their creativity—tend to have produced half their lifetime creative output by age 40 or so. Historians—who rely on a crystallized stock of knowledge—don’t reach this milestone until about 60.

No matter what mix of intelligence your field requires, you can always endeavor to weight your career away from innovation and toward the strengths that persist, or even increase, later in life.

This book underscores the tragedy of “peaking early” and failing to grow and adjust to life’s stages. But this is the lot of the striver. There will be a point where worldly accomplishment diminishes or even stops. What happens then when the most difficult task is the daily struggle with a sense of failure and despondency.

To address this issue, Brooks suggests that it is necessary for individuals to find a deep purpose in their second half of life. This can be achieved through the cultivation of gratitude, the practice of compassion, the building of relationships, and the creation of beauty. By focusing on these actions, individuals can find a sense of fulfillment and purpose that will carry them through the second half of life and enable them to finish well.

One of the most compelling aspects of Brooks’ book is his emphasis on the importance of gratitude. He argues that cultivating gratitude allows individuals to find joy and purpose in their lives, even in the midst of challenges and setbacks. By focusing on the things we are thankful for, we can find meaning and fulfillment that is not dependent on external circumstances or accomplishments.

But gratitude is empty without the practice of compassion. By seeking to understand and care for others, we can find a sense of purpose and meaning that goes beyond our own individual accomplishments. Brooks makes it clear that this can be especially meaningful in the second half of life, as it allows us to contribute to the greater good and make a positive impact on the world around us.

In addition to cultivating gratitude and practicing compassion, Brooks also emphasizes the importance of building relationships. He argues that strong relationships with others can provide us with a sense of belonging and purpose that is essential for a fulfilling life. By investing in these relationships and seeking to connect with others, we can find meaning and joy in the second half of our lives.

Finally, Brooks suggests that creating beauty is another key way in which individuals can find purpose and meaning in the second half of life. Whether through art, music, or other creative endeavors, the act of creating beauty or building beautiful things allows us to connect with something greater than ourselves and find a sense of fulfillment and joy.

Winston Churchill Painting as a Pastime

On a personal note, I have to contrast Brooks message with the story of the apostle Paul. Writing from prison, he emphasized the importance of pressing on towards the goal and finishing his course. However, this is not a problem unique to Paul, as many people struggle with a sense of failure and despondency in the second half of life. What would Paul think of the danger of peaking in one’s career between the ages of 30 and 50, and the potential for a sense of failure and despondency in the latter half of life.

Brooks suggests that in order to avoid this sense of failure, it is necessary for individuals to find a deep purpose in their second half of life. Paul would say it is also important for individuals to recognize that their identity should not be solely based on their accomplishments or successes. Instead, our identity should be rooted in our relationship with God and the gospel of Jesus Christ. This allows us to find a sense of purpose and meaning that is not dependent on our external circumstances or accomplishments.

I also found wisdom from a completely different angle: the varnasrama system of Hinduism which splits up our lives into four distinct stages, each happening every 20-25 years—with vanaprastha (वनप्रस्थ) being the all-important third stage.

After our youthful first stage (“figure out who I am”), in our early-20s we move to a second stage (“prove yourself”) that lasts until we are about 50 years of age. In the second stage, we are driven by the pursuit of pleasure, sex, money, and accomplishments. But by the third stage (“give back”), at around age 50, we begin to pull back from a focus on professional and social advancement. Instead, we become more interested in spirituality and faith.

The important transition is from stage 2 to 3, which typically occurs around age 50, can be difficult for many people, especially in Western societies, where there is often a strong emphasis on professional and social advancement. According to Arthur C. Brooks, this transition is important because it can lead to increased happiness and contentment, as well as better physical health. Additionally, as people age, they tend to become wiser, with greater ability to combine and express complex ideas, interpret the ideas of others, and use the knowledge they have gained throughout their lives. This “crystallized intelligence” can be put to good use by sharing wisdom with others and becoming more devoted to spiritual growth. It is important to let go of the things that once defined us in the eyes of the world and embrace this new stage of life in order to truly thrive in the latter half of adulthood. In summary, the older we get, the better we get at:

  • Combining and using complex ideas and expressing them to others
  • Interpreting the ideas others have (even if we didn’t create them ourselves)
  • Using the knowledge we have gained during our lives

As we approach the finish line of our journey, it is essential that we strive to finish well. This involves finding a deep purpose in the second half of life, cultivating gratitude, practicing compassion, building relationships, and creating beauty. By doing so, we can navigate the challenges and winds of life with a focus on the ultimate goal of glorifying God and finishing our course with joy and purpose.

“From Strength to Strength” is a thought-provoking and insightful book that offers valuable insights and strategies for finding success, happiness, and deep purpose in the second half of life. Whether you are just entering this phase of your journey or are well into the second half, this book offers valuable guidance and encouragement for navigating the challenges and winds of life with a focus on the ultimate goal of finishing well.

Shapeoko Troubles

I recently encountered an issue when generating a grid of holes for workbench. I had recently planed down an old workbench from our house in New Jersey. I was planning on 20 mm holes spaced in a grid with 96mm spacing to match the festool MFT table. I’m hoping to use the available array of cool attachments and eventually add the aluminum profile to the side. For example, an MFT table can be used as a bench with a variety of different attachments, such as clamping elements and stops.

Unfortunately, the holes didn’t create a proper grid and the spacing was off. I used a CNC machine to cut the holes, but I noticed that they were off. Just looking at it showed that each row had fairly consistent spacing, but the start of the rows varied in the X direction.

To accomplish a 96 mm grid, the g-code was programmed to start at the bottom of the workpiece and move across in a row. This process was then supposed to be repeated until the entire grid was cut. However, as I mentioned earlier, I encountered some issues with the spacing of the holes and had to troubleshoot the problem.

One theory I became aware of online (thanks gdon_2003, Julien, LiamN, SLCJedi and WillAdams) is that set screws are a part of Shapeoko drive system and a loose set screw can cause this type of behavior. That’s because the set screws transfer motion from the motor shafts to the pulleys, which rotate against the belts. They are intended to be pushed tightly against the flat spot on the motor shaft, causing the pulley to turn with the motor. If the set screw becomes loose, the pulley may turn independently of the motor before snapping into place, which can cause issues with the motion of the machine. This may show up as flat spots on circles or other imperfections in projects. You can see why a loose set screw is bad as captured in the screenshot below from this youtube video by See-N-C.

Screenshot that describes how set screws work

Doing some Math

In order to do some analysis on what happened, I needed to register the image and get the location of the points.

The drawpoint command in MATLAB is a function that allows you to draw a single point on an image or plot. You can specify the coordinates of the point on an image using the mouse to record position. Using drawpoint, I recorded the coordinates of the center point of each circle and put this information in a struct. I then wrote code to turn the struct into two arrays: one for the x coordinates and one for the y coordinates. This allowed me to easily analyze the variance in the x coordinates for each column and the variance in the y coordinates for each row.

I was also able to use the drawpoint command in MATLAB to mark points on the ruler captured in the image. This allowed me to easily record the coordinates of the points and then do the math and convert the distances between the points from pixels to millimeters.

I used the pdist2 function in Matlab to calculate the Euclidean distances between my two sampled points and then converted the distances to the desired units through a conversion factor of 610 mm/523.4087 px.

Since the job started at the upper right and progressed down and across, we could look at the variance throughout the job. The variance in the x direction seemed to increase in the last four columns:

x1.2610.36030.58540.76563.24253.963
Variance of X in each Column (in mm)

The variance in the y direction was much bigger across the rows and also increased as the job progressed. I used this MATLAB to generate this: makemm(var(y(:,:),0,2))

y24.753724.573630.623235.246736.3425
Variance of Y in each row (in mm)

To generate the ideal points based on a 96 mm grid, I wrote a function that takes in two inputs, iX and iY, which represent the starting x and y coordinates, respectively. The function first initializes two matrices, X and Y, to store the calculated x and y coordinates for each point. Then, it defines a conversion factor, cf, which is used to convert the units from millimeters to pixels.

Next, the function uses a nested for loop to iterate through each column and row of the matrices. For each iteration, the function calculates the x and y coordinates of the current point by adding the starting coordinates (iX and iY) to the appropriate offsets, which are determined by the loop variables and the conversion factor. The calculated x and y coordinates are then stored in the corresponding elements of the X and Y matrices.

To calculate the root mean squared (RMS) error, I subtracted the actual coordinates from the ideal coordinates to find the error in both the x and y directions and then took the square root of the mean of the squared errors in both directions.

123456
103.64134.867812.579612.847612.0532
21.29864.71474.923613.636513.884112.3934
31.6041.47845.26213.272213.526513.8716
42.61142.536214.100214.219514.898816.2787
56.15646.040717.367317.355818.812919.6045
RMS errors for each hole

You can see the error increasing as the job progresses, but the major error starts in column 4-6, supported by a big jump in column 3, row 4, which supports the idea that the screw isn’t seating well resulting in slippage.

Overall, doing this math allowed me to see what was really going on. By adjusting for the variance at 4,3:

Pattern in Holes