Similar to this post from a couple years ago, recently I used Gephi to create a network diagram of all the skills that an Algebra 2 student would gain over the course of the year. It didn't turn out as good as I hoped, but I still think it's cool to look at and digest.

• The size of the nodes (the skills, ex. Order of Operations) is based on the concept of betweenness centrality, a concept that Google's Generative Search summarizes as "Betweenness centrality quantifies how many times a particular node comes in the shortest chosen path between two other nodes" which to me means how vital or important it is. 
• The position or centrality (how central it is) of the node is also a measure of importance, based on Gephi's Force Atlas 2 algorithim, which Generative Search summarizes as, "Force Atlas 2 is a force-directed layout that simulates a physical system to spatialize a network. Nodes repulse each other like charged particles, while edges attract their nodes, like springs. These forces create a movement that converges to a balanced state", which again to me means that it algo-balances it and finds the best shape somehow.
• I honestly don't remember what the size of the edges (the connection between skills, that are in the same month) means.

The process I used was:

1. Asked GPT-4 what topics it thought were most important that a student would learn in Algebra 2
2. Asked it to break that list of topics into 8 different months worth of curriculum
3. Asked it for 10 problems per month that an exemplar student would be able to solve
4. Then asked it to list the skills needed to solve all of those problems, in order of how you'd learn them (earliest skill first, most recent last)
5. Within each month, I created an edge for each skill paired with each other skill in that month. This created 525 edges (or connections, or times both skills needed to be known to learn that month's content) between the 50 nodes (skills)
6. Used this tutorial again because I forgot what to do next

Here's the table of nodes (skills) a student should know by the end of Algebra 2:

*from the view of an old man (Millennial)

[The following was copied and pasted from GPT-4 after I fed it a transcript of a 3 minute ramble I had recorded while walking just now and asked it to turn it into a 1000 word blog in the style of Morgan Housel]

Title: The Unfiltered Lens: Observing the Authenticity of Gen Z

In my journey as an educator and observer of life, I've always aimed to see reality as it is - an objective observer. Over the past seven or eight years, my focus has been on teenagers, ranging from ages 13 to 18. Since I began working with this demographic in 2015, I've followed the transition of my oldest students, then 18 and now 24, and my youngest, then 14 and now 16. This wide spectrum of young minds, encompassing the entirety of Generation Z, has offered me a unique vantage point to observe and analyze.

Lately, society is intrigued by Gen Z, attempting to dissect their trends, their sense of humor, their style, their divergence from millennials and baby boomers. From the recurring cycle of fashion trends to the apparent openness of their personal lives, a lot is being discussed. However, amid this curiosity and analysis, I've noted a pervasive theme, a defining trait that encapsulates Gen Z in its entirety - Authenticity.

Let's begin by acknowledging that, indeed, Gen Z is significantly more open about their personal lives. They document everything, making their everyday lives an open book. For instance, I've observed that many have taken to the new Apple journal app on iOS 17, an AI-fueled reflective journal built right into their phones. This propensity to record their thoughts, to self-reflect, reflects a fundamental shift in their relationship with their inner selves. This generation isn't just capturing moments, they're capturing thoughts and emotions - a profound testimony to their authenticity.

But what about their trends, their styles? There's a common perception that Gen Z seems to be hopping on every new trend, mimicking dance routines, and appropriating fashion styles from past generations. Yet, there's more to this than meets the eye. What may appear as blind trend-following is, in essence, a form of personal expression. They're adding their unique twists to existing trends, amalgamating styles from various eras to create something truly their own. The apparent replication is, in reality, a form of reinvention, underscoring their authentic selves.

The authenticity of Gen Z extends into the realm of social media too. It's a widely accepted notion that social media tends to cultivate a culture of pretense. However, I believe that Gen Z is challenging this norm. Despite the inevitable tendency to project an idealized self-image, I've observed that Gen Z manages to maintain a level of genuineness in their online interactions. They're presenting more of their true selves in the digital world, reminiscent of Kevin Kelly's assertion that one should strive to become their true self.

I am not suggesting that Gen Z is immune to the lure of projection or pretense, but rather, they've begun their journey towards self-expression and authenticity from a higher starting point compared to previous generations. Their natural disposition towards authenticity, their desire to maintain a genuine self-image, reflects a significant cultural shift in our society.

So, where does this leave us, the observers, the educators, the parents, and the well-wishers of Gen Z? It's simple. We need to embrace authenticity. We don't have to imitate their trends or mirror their styles, but merely present our genuine selves. Gen Z, in my experience, values and respects authenticity more than anything else. Trying to 'fit in' with them is futile; what matters is being genuine, being ourselves. 

In a world where authenticity often takes a backseat to projection, Gen Z is defying norms, steering the narrative towards individuality and genuineness. Their pursuit of authenticity, their commitment to self-expression, offers us a profound lesson - to cherish our individuality and celebrate authenticity in all its forms. They remind us to remain true to ourselves, regardless of prevailing trends or societal pressures.

Take a step back from the intricacies of their trends, their humor, or their online persona, and one will notice a collective drive towards authenticity that defines Gen Z. They reject the homogenization of thought and expression, embracing individuality with open arms. This is apparent not only in their consumption of culture but also in the content they create - from TikTok videos to Instagram stories. Everything carries a touch of their authentic selves.

Authenticity, for Gen Z, isn't a strategic choice; it's an integral part of their identity. They're not afraid to express their authentic selves, be it through their digital footprint or their real-world interactions. Unlike previous generations who were often pressured into conforming to societal norms, Gen Z is more comfortable stepping outside the conformity box, laying their uniqueness bare for all to see. This is a generation that doesn't shy away from wearing their hearts on their sleeves.

Their inclination towards authenticity is also evident in their approach to problem-solving and decision-making. They reject superficial solutions and tend to look deeper, seeking authentic understanding over shallow knowledge. They don't just want to know 'what,' they want to understand 'why.' Their quest for authenticity extends beyond mere personal expression to the way they interact with the world around them.

To wrap up my observation of this compelling generation, it's worth noting that the authenticity they embody is not merely about 'being different.' Instead, it's about 'being oneself' - free from pretense, unapologetically original. This is the cornerstone of their identity, the foundation upon which they're building their futures.

As we watch, learn, and occasionally marvel at Gen Z, we would do well to remember that authenticity isn't just their characteristic; it's their clarion call. They're imploring us to embrace our authentic selves, to celebrate our unique identities, and above all, to cherish the unvarnished truth of who we are. In the end, our greatest homage to this intriguing generation might not be to understand them fully but to learn from their journey towards authenticity and walk our paths with the same unyielding commitment to being true to ourselves. As we do so, we'll undoubtedly find that authenticity isn't just a trend, but a timeless virtue that transcends generations and redefines society. 

So, the next time you find yourself perplexed by a Gen Z trend, remember that it's less about the trend itself and more about what it represents - a commitment to authenticity. They're not just 'Generation Z,' they're 'Generation Authenticity,' and that's a characteristic we can all aspire to emulate. After all, in the grand theater of life, it's authenticity that makes the performance memorable, genuine, and truly human.

[The following was copied and pasted from GPT-4 after I fed it a transcript of a 3 minute ramble I had recorded while walking just now and asked it to turn it into a 500 word blog in the style of Morgan Housel]

Title: Decoding Quality: The Consistency-Truth Paradox

To comprehend the essence of quality, a profound understanding of what constitutes 'truth' and 'equality' is required. Unraveling this relationship, I'm compelled to believe that one of the most compelling analogies to bring into play here is that 'consistency equals truth.' 

Visualize a simple pencil. You hold it up and let it go; gravity immediately pulls it down. This universal force is a truth, consistently proven by its unyielding manifestation, no matter the number of times the pencil is dropped. Instances that appear to defy this consistency - wind tunnels, zero-gravity flights, or spacewalks - can momentarily shake our belief system. Yet, these instances seem surreal precisely because they contradict our inherent understanding that consistency equals truth.

The same principle applies to emotions and human relationships. If you harbor genuine love for your partner, it manifests consistently. It endures through trials and triumphs, a daily testament of your feelings. An inconsistent demonstration of love often signals a lack of genuineness, offering a tangible realization that inconsistency is the inverse of consistency, just as untruths are the inverse of truth. 

The intriguing mathematics of it all dictate that if something is equal, its opposites must also be equal. Thus, if consistency equals truth, it follows that inconsistency must equate to untruths or lies.

This idea can offer invaluable insights within the professional domain. I recall a valuable lesson from a previous boss on this matter. Inconsistent performance can be far more disruptive than consistently poor performance. It's not necessarily the lack of ability that irks employers but the inconsistency, the unexpected variations in outcomes. 

It isn't the magnitude of the lie that generates reactions; it's the shattered consistency, the sudden dissonance in the harmony of belief and truth. An inconsistency, a deviation from the expected, is perceived as a lie, sparking a profound sense of betrayal. 

This extends to personal ambitions as well. If you're genuinely curious about the world, your pursuit of knowledge will remain steadfast. If you passionately aspire to be a doctor, you'll weather the storm of rigorous training and demanding qualifications. In short, if something rings true for you, your dedication towards it will endure, underscoring that consistency is a testament of truth.

It is hence crucial to recognize that consistency and truth are intertwined. If something matters to you genuinely, it will reflect in your actions persistently. If a belief, a value, or an aspiration holds true for you, your pursuit will echo that truth with unerring consistency. 

On the flip side, when inconsistencies mar this pursuit, they tend to signal a departure from the truth, leading to potential deceptions or lies. So, let the constancy of your actions, your persistent pursuit of what matters to you, be the barometer of your truth. 

Consistency is not merely a measure of dedication or persistence. It's a powerful compass guiding us towards our truths, helping us weave our narratives in the tapestry of life.

[The following was copied and pasted from GPT-4 after I fed it a transcript of a 3 minute ramble I had recorded while walking just now and asked it to turn it into a 500 word blog in the style of Morgan Housel]

Title: Unmasking Joy: The Equation of Reality, Expectations, and Happiness

The aphorism, "Comparison is the thief of joy," encapsulates a profound truth. We often find ourselves evaluating our happiness not solely based on our experiences but by juxtaposing them with others'. Paradoxically, this act of comparison can lead us astray, taking the joy we found in the simple act of existence and muddying it with unnecessary competition.

It's a convoluted equation, where happiness equals reality minus expectations. Take a splendid reality—abundant, joyful, and fulfilling. Yet, if your expectations are grander, inflated to the point of impossibility or improbability, unhappiness creeps in. If expectations outweigh reality, you're left in the deficit, the red zone of negative happiness.

But here's the rub. Setting expectations too low—expecting the worst—is also a fallacy. If we live our lives bracing for disaster, we confirm our worst fears, consciously seeking out negative outcomes. This leads to a pessimistic life view, curtailing our chances and stifling opportunities. The joy of risk, the fundamental human trait that has spurred evolution—our ancestors forging communities, taking chances—is lost in the morass of dread.

So, how do we navigate the labyrinth of expectations to uncover happiness? The answer lies in two concepts: embracing the 'base rate' and cultivating a 'zero expectations' outlook.

'Base rate' is a term borrowed from statistics, referring to the inherent probability of an event—the most likely occurrence, the center of the bell curve. Understanding the base rate is understanding the norm. It's accepting that if something regularly happens to others in your situation, you're not exempt—it's likely to happen to you too. This comprehension anchors our expectations to reality, taming the often wild imaginings of what could be.

On the other hand, harboring zero expectations can be equally liberating. This isn't about giving up hope or aspirations, but about viewing reality without the rose-tinted glasses of predetermined ideals. Without expectations, reality, whether brimming with positive instances or tinged with negatives, is seen in its true form. It's a raw, unfiltered perception of the world.

Consequently, to traverse the path to happiness, we must strike a balance between these two concepts. Accepting the base rate of outcomes tempers our expectations, aligning them more closely with probable outcomes. Simultaneously, encouraging a mindset of zero expectations allows us to experience life in its naked essence, undistorted by what we think it should be.

In conclusion, the dance between reality and expectations is a subtle art, a nuanced choreography that we must learn to perform in our pursuit of happiness. By acknowledging the base rate and adopting a zero-expectations attitude, we might just find that we have uncovered a new path to joy, undeterred by the unnecessary detour of comparison.

[The following was copied and pasted from GPT-4 after I fed it a transcript of a 3 minute ramble I had recorded while walking just now and asked it to turn it into a 500 word blog in the style of Morgan Housel]

Title: Transforming Life's Chaos into Order: The Power of Reminders

The hectic pace of life often feels like a chaotic swirl of events, responsibilities, thoughts, and ideas. As this whirlwind of activities plays out, it's easy to forget things, even those that matter. These forgotten fragments aren't a reflection of our character or a judgment on our capabilities. They're merely evidence that our minds are juggling a multitude of tasks, thoughts, and ideas.

Here's something to remember: you're not a bad person for forgetting. It's simply the reality of having a lot on your plate. But, as with many aspects of life, there are ways to make this manageable, to transform the chaos into order. How? The humble yet powerful tool of setting reminders and tasks.

Being adept at scheduling can be a game-changer. By organizing your day, week, or month, you ensure that important tasks don't fall by the wayside. The key here is not only to set these reminders but also to act on them when they buzz.

Say you suddenly remember you need to order something online. You're not currently at your computer, but you know you will be later in the evening. Instead of relying on your memory, set a reminder for 8:00 p.m. to "order X." It takes barely 30 seconds, but this simple act can relieve a surprising amount of stress. Research has shown that setting reminders can significantly alleviate anxiety about pending tasks, essentially offloading the mental burden.

The second part of this productivity equation, though, is equally crucial: acting on these reminders when they ping. If you're in the middle of your favorite TV show when your "order X" reminder buzzes, pause your show and place the order. Two minutes later, you're done, and you can return to your program.

However, life isn't always predictable. What if you're not lounging on the couch when that reminder sounds but instead are out to dinner with friends? No problem. The flexibility of reminders is part of their charm. Easily edit the reminder's time to when you expect to be home or to a quieter moment when you can handle the task, such as Sunday night.

Adopting this habit does more than ensure tasks get done; it also enhances your sense of agency. It empowers you to take control of your life and activities, leading to more productivity and less stress.

In our modern age, this strategy is all the more feasible because of technology. Your phone, computer, and the cloud serve as omnipresent assistants, ready to remind you of tasks wherever you are.

Remember: life can be chaotic, but you're not at its mercy. With the right tools and habits, you can transform life's tumult into manageable order, one reminder at a time.