Image prompt: Ice cool math teacher, in the style of batman cartoons

[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 2000 word blog in the style of Morgan Housel]

When you're young, "cool" is often synonymous with "popular" or "trendy". It's the kind of attractiveness that induces a sense of awe in others, the kind of charisma that turns heads, the kind of charm that makes you the center of attention. But as you grow older, your definition of "cool" evolves. For me, "cool" became about making a difference, about giving back, about helping others grow and learn. And in that sense, the coolest thing I've ever done, and continue to do, is teaching.

When I was a student, I always thought teachers were cool. Not because they were popular or trendy, but because they were molding young minds, preparing us for the future, sharing their knowledge and wisdom. They were doing it not for the fame or the money – because let's face it, teaching isn't the most glamorous or high-paying job – but because they believed in the value of their work. The enormity of their responsibility was awe-inspiring, and the humility with which they embraced it was truly cool.

Eight years into my teaching career, I still believe teaching is the coolest thing I've ever done. After three years, I took a break and contemplated shifting my career to become a data analyst or a college counselor. But the pull of teaching was too strong to resist. Like the old saying goes, "if you love something, set it free. If it comes back, it’s yours." That’s exactly how I felt about teaching. Despite the challenges, the sense of fulfillment and purpose it offered was unparalleled.

Now, teaching high school math, I find joy in taking something I understand and love, and breaking it down into comprehensible pieces for my students. Sure, math can be intimidating, and many students struggle with relating mathematical concepts to real life. But that's precisely the challenge and beauty of teaching it. When you can draw connections between abstract formulas and daily life, when you can ignite a spark of interest in a student who previously dreaded math, it feels like you're doing something truly cool.

Math is not merely about numbers and formulas; it's a mindset, a life skill. It encourages logical thinking and problem-solving, it cultivates precision and attention to detail. Math is about learning from mistakes, improving, and evolving – skills that are as valuable in life as they are in the classroom. 

One of my favorite equations is knowledge equals ideas times action. It's a simple equation, but it carries profound implications. If you have no ideas, no matter how much action you take, your knowledge will be zero because anything multiplied by zero is zero. On the other hand, if you have great ideas but take no action, your knowledge will still be zero. Only when you both have great ideas and take great actions can you multiply and gain substantial knowledge. I think this is a perfect illustration of the applicability of math in our daily lives and a testament to its coolness.

Teaching has allowed me to transform my passion for math into a means to inspire and motivate others. When I see my students understand a concept, when I see the spark of curiosity in their eyes, when I see them applying what they learned in real-life situations, I feel like I'm part of something bigger. That sense of contributing to the growth and development of others, the ability to positively impact their lives, is incredibly cool.

In the grand scheme of things, teaching may not be considered cool by conventional standards. But the satisfaction it brings, the changes it can spark, and the lives it can touch makes it one of the coolest things anyone can do. The version of me who sat in a classroom all those years ago could never have imagined the immense joy and fulfillment that teaching would bring. But now, as I stand at the front of the classroom, watching my students learn, grow, and succeed, I can confidently say that teaching math is the coolest thing I've ever done, and continue to do.

As we navigate life, our perspectives and priorities evolve. And along the way, our definitions of cool evolve too. For me, "cool" is about making a difference, about giving back, about helping others grow and learn. It's about using my passion for math to inspire others, to help them see the beauty and relevance of numbers and formulas in their daily lives. It's about being part of something bigger than myself. And for that, I wouldn't trade my job for anything else in the world.

Remember, the most rewarding paths often aren't the most glamorous. Sometimes, they're the ones that let you touch lives and make a difference. And in the end, isn't that the coolest thing of all?

[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 2000 word blog in the style of Morgan Housel]

At the heart of life, in the fabric of the universe, and in the workings of our daily lives, there's one constant: the ratio. It's a simple yet incredibly powerful concept. But first, let's clear the air about what a ratio is. In mathematics, a ratio is a comparison between two numbers, illustrating how many times one value is contained within another. Essentially, it's the slope of a line - a change measured in terms of division. Consider a slope of five: it means for every step we move to the right, we take five steps upwards. The fascinating thing about ratios is that they can represent two different things: a slope of five upwards and one to the right is essentially the same as a slope of five downwards and one to the left - positive over positive, negative over negative, they're the same thing.

But ratios aren't just about mathematical comparisons; they're about balance and proportion. The golden ratio, known by the Greek letter 'phi' and approximated as 1.618, is a perfect example. It pops up in numerous aspects of the natural world - in the patterns of a pine cone, the spiral of a galaxy, and even in the proportions of the human body. Often, what we perceive as 'beauty' aligns with the golden ratio - but why? The magic of this number doesn't lie in its value, but in the equation from which it originates: x^2 equals x + 1. From this equation, we derive the golden ratio via the quadratic formula, illustrating that ratios underpin not just numbers, but also harmony and aesthetics.

The concept of ratios extends to our everyday lives, too, shaping our behavior, goals, and relationships. It's the ratio of work to play, for instance. Some people might favor a ratio of five-to-one, where work far outstrips leisure. They might be ambitious individuals aiming for that corner office, relentless in their pursuit of career success. But others might prefer the inverse - a one-to-ten ratio, where relaxation reigns supreme. Or even, the 'negative ten', a tongue-in-cheek reference to those who are most content when work is a last resort, not a priority.

In every case, these ratios are a reflection of our personal values and aspirations. They inform how we allocate the most precious resource we have: our time.

You might wonder, aren't ratios just about division or multiplication? Well, yes and no. While they're essentially a mathematical tool, ratios go beyond numbers. They capture the essence of life's ebb and flow - they reflect our choices and priorities.

Consider the ratio of your attention. Where you dedicate your attention determines what becomes important in your life. We attach meaning to what we focus on - so the ratio of attention between different aspects of our lives is instrumental in shaping our experiences and our identity.

Ratios are even key to our relationships. Take, for example, the ratio of arguments to peaceful interactions. It's a simple number that can have profound implications for the health and longevity of a relationship.

In a world that often favors complexity, it's easy to overlook the simple power of ratios. But as we've seen, they are fundamental to so much of what defines our universe and our lives - from the spirals of galaxies to the rhythm of our daily routine.

Ratios reveal the beauty in balance and proportion. They guide us in our allocation of time and attention. They measure the health of our relationships. Even our bodies adhere to certain ratios considered aesthetically pleasing.

In essence, the humble ratio is a universal language, whispering the secrets of beauty, balance, and harmony. They have opposites, inverses, and negatives. They are simple, yet they hold the answers to complex questions. They are static, yet they encapsulate the dynamic ebb and flow of life. They are mathematical, yet they are intrinsically tied to our emotions, our decisions, our very existence.

So, the next time you're making a decision, consider the ratio. Whether it's how you spend your time, where you direct your attention, or how you balance work and play - remember that it's all about the ratios. The secret to balance, harmony, and even beauty lies in these simple proportions.

In conclusion, ratios may just be numbers, but their value is immeasurable. They offer insight, bring clarity, and provide a framework to understand the world around us and the lives we lead. Ratios, in their elegant simplicity, are a testament to the intricate complexity of life.

Image prompt: Centaur, but part human part AI

[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]

(Untitled)

The arrival of AI and advanced technologies such as GPT-4 often stirs up a wave of debate, as people grapple with the question: How will this new, potentially disruptive technology affect our lives, our professions, and indeed, our very existence? We, as humans, tend to grapple with uncertainty by seeking examples from the past to inform our understanding of the present and future. A time-tested approach, indeed. 

So, to understand our relationship with AI, let's revisit a pivotal moment in history: the moment when a computer first beat a human in chess.

In 1997, chess grandmaster Garry Kasparov famously lost a match to IBM's Deep Blue, marking the first time a reigning world chess champion had been defeated by a machine. This event signaled the dawn of a new era, where AI had demonstrated its capacity to outmaneuver human intelligence in a highly strategic game.

A similar scenario played out a couple of decades later when AlphaGo, an AI developed by DeepMind, managed to beat a human champion at Go, a board game considered even more complex than chess.

In these instances, AI showed us its potential - its ability to simulate, even surpass, human intellect in specific contexts. However, it's what happened next that's truly fascinating.

After their initial defeats, chess players didn't throw in the towel. Instead, they began to learn from AI, using it as a tool to improve their strategies. I first encountered this idea in a book called "Game Plan" by Frank DuPont, who writes under the Twitter handle @fantasy_douche. DuPont's work delves into the intersection of technology and sports strategy, revealing how decision-making in football, for instance, could benefit from technological insights.

His book also sheds light on the evolution of chess players in the wake of AI. Players began using AI as a tutor, exploring different scenarios, learning from the moves the AI proposed. And guess what? The players improved. Their game became stronger, sharper, better. They began working *with* the AI, not against it. They embraced the technology and leveraged it to their advantage.

Think about it: the introduction of calculators did not end math. Instead, they transformed the way we approached calculations, aiding us in complex equations and improving our overall efficiency. Similarly, the advent of AI does not signal the end of human intelligence, but rather a new partnership.

Some refer to this hybrid of man and machine as "centaurs" - creatures from mythology that are half human, half beast. It is a powerful metaphor for our potential coexistence with AI. Just as a centaur combines the strength of a horse with the intellect of a human, the human-AI partnership can merge the raw processing power of machines with the creativity, empathy, and nuanced understanding of humans.

As we navigate the era of GPT-4, we stand at a similar crossroads. Will we fear AI, fight against it, or will we embrace it, learn from it, and use it to our advantage? 

History has shown us that working with AI, instead of resisting it, has the potential to significantly enhance our abilities. By becoming 'centaurs' in our modern world, we can harness the power of AI to not only augment our professional lives but also to create a harmonious future where technology and humanity coexist, each enhancing the other.

The AI revolution, in all its disruption and uncertainty, offers us an incredible opportunity - a chance to expand our horizons, elevate our capabilities, and navigate complex challenges. 

In essence, our task is not to outsmart AI, but to use it as a tool to better ourselves. As we stand on the brink of a new era, we have the chance to harness this powerful technology

I previously wrote about how I used (and am still using) GPT-4 to do a curriculum review. I did that review for my Algebra 2 course and I did the new curriculum plan on a new Statistics/Probability course. Unfortunately this means no more teaching Calculus :( but it was a good run. I love the subject, it's so interesting to me in how it describes real life, so it'll be missed but I might just put my lessons online. That way someone else could use them or learn from them, hmm...

In the meantime, I wanted to show you an example of how I would be reviewing and revising my Calculus presentation slides before teaching it again, if I were teaching it. Here's my first lesson of the year (after prerequisites) on introducing the concept of a limit:  https://docs.google.com/presentation/d/1XwtgxMmjtSYJ59Z1C4STCjXu5PL-k7u4JEpnM69W4Vk/edit?usp=sharing

For the following examples, my prompts to GPT-4 with plugins Wolfram Alpha and LinkReader are bolded and GPT's answers are not.

To reimagine the presentation with the help of GPT-4, I first did this prompt:

Let's go through the presentation linked below together.

First, start by summarizing the key points from the presentation. After that, proceed through the presentation and summarize the main learnings from it. Finally, provide an enticing overall summary, make it compelling for the reader, and suggest ways to improve the presentation.

Second, critique your own summary. Does it accurately reflect the main points of the presentation? Is it compelling enough to make someone want to read the presentation? What improvements can be made to the summary?

Third, imagine how experts in math pedagogy and teaching, like Jo Boaler and Sal Khan, would summarize and critique this linked presentation. What key points would they focus on? What aspects of the presentation might they suggest to improve for better understanding?

Finally, synthesize all of those points above into one coherent and beautiful answer. Then provide your 3 biggest improvements you would make to either the flow of information or to the presentation to improve the student's understanding of the topic and include 3 examples of each of the improvements.

The linked presentation is:

with the Google Slides link I shared before. The results of that prompt was:

**Summary of the Presentation**

The presentation titled "Limits: Intro to Limits" by Mr. Jarrell on September 2, 2022, is an introductory lesson on limits in calculus. The presentation begins with a review of a homework assignment, followed by an exploration of the concept of a limit, one-sided limits, and the Limit Theorem. The presentation is interactive, with several 'You Do' sections where students are encouraged to find the limit by plugging in values. The presentation concludes with a list of resources for further study, including Khan Academy videos and other links.

**Critique of the Summary**

The summary provides a clear overview of the presentation's content, highlighting the main topics covered and the interactive nature of the lesson. However, it could be more compelling by emphasizing the real-world applications of limits and how understanding this concept is crucial in fields such as physics and engineering. The summary could also mention the use of multimedia resources, like the YouTube video, to make the lesson more engaging.

**Jo Boaler and Sal Khan's Perspective**

Jo Boaler, a renowned math educator, might appreciate the interactive nature of the presentation, as it aligns with her belief in active learning. She might suggest incorporating more visual representations of the concept of limits to cater to visual learners. Sal Khan, the founder of Khan Academy, might focus on the use of online resources and self-paced learning. He might suggest adding more step-by-step explanations and practice problems to enhance understanding.

**Synthesis and Improvements**

The presentation provides a comprehensive introduction to the concept of limits in calculus. It effectively uses interactive elements and online resources to facilitate understanding. However, to improve the flow of information and enhance student understanding, the following improvements could be made:

1. **Incorporate Real-World Examples**: To make the concept of limits more relatable and interesting, real-world examples where limits are used could be included. For instance, an example could be how limits are used in physics to calculate instantaneous velocity.

2. **Visual Representations**: Graphical illustrations of one-sided and two-sided limits could be included to cater to visual learners. This could involve showing how the limit changes as we approach from the left or right side.

3. **Step-by-Step Explanations**: More detailed, step-by-step explanations of how to calculate limits could be beneficial. This could involve breaking down the process into smaller, more manageable steps.

Overall, the presentation is a solid introduction to limits, but with these improvements, it could be even more effective in facilitating student understanding.

Then I wanted to see what improvements it would make. I then asked it this:

You are an AI program that is designed to create the world’s most fun, interesting, and informative math lessons for high schoolers. The lessons are not in the exact style of but are similar to Richard Feynman’s famous physics lectures. Above all, these lessons should be relatable to the students' lives so that the students care more about them. 

Give me at least 20 specific examples or math problems that would make that linked presentation you just looked at the world’s best math lesson

and it spit out this:

Absolutely, I'd be happy to help make this lesson on limits more engaging and relatable to high school students. Here are 20 examples and problems that could be incorporated:

1. **The Speeding Car**: Imagine you're driving a car that accelerates from 0 to 60 mph in 10 seconds. What's the instantaneous speed at the 5th second? This problem can introduce the concept of limits in the context of everyday life.

2. **The Shrinking Chocolate Bar**: You keep breaking a chocolate bar in half. What happens to the size of the chocolate bar as you keep doing this? This can illustrate the concept of a limit approaching zero.

3. **The Infinite Series**: If you add 1/2 + 1/4 + 1/8 + 1/16 + ..., what number do you get? This problem can show how limits are used to sum infinite series.

4. **The Leaning Tower of Pisa**: If the Leaning Tower of Pisa leans one more degree each year, will it ever lay flat on the ground? This can illustrate the concept of a limit not existing.

5. **The Bouncing Ball**: A ball bounces to half its previous height each time. How high will the ball bounce after an infinite number of bounces? This can illustrate the concept of a limit approaching a finite number.

6. **The Zeno's Paradox**: You want to walk to the end of a room, but first, you must walk half the distance, then half of the remaining distance, and so on. Will you ever reach the end of the room? This ancient paradox can be solved using limits.

7. **The Speeding Rocket**: A rocket's speed increases as it gets further from Earth due to decreasing gravitational pull. What would be its speed at an infinite distance from Earth? This can illustrate the concept of a limit at infinity.

8. **The Filling Glass**: You're pouring water into a glass at a decreasing rate. Will the glass ever be completely full? This can illustrate the concept of a limit in a practical context.

9. **The Growing Tree**: A tree grows half its current height each year. What will be its height after an infinite number of years? This can illustrate the concept of a limit approaching a finite number.

10. **The Half-Life of a Radioactive Element**: A radioactive element decays by half every year. How much of the element will be left after an infinite number of years? This can illustrate the concept of a limit approaching zero.

11. **The Cooling Coffee**: A cup of coffee cools down to half the difference between its current temperature and room temperature every minute. What will be its temperature after an infinite number of minutes? This can illustrate the concept of a limit in a practical context.

12. **The Fibonacci Sequence**: The ratio of consecutive Fibonacci numbers approaches a certain number as you go further in the sequence. What is this number? This can illustrate the concept of a limit in the context of famous mathematical sequences.

13. **The Harmonic Series**: The sum of the reciprocals of all natural numbers (1 + 1/2 + 1/3 + 1/4 + ...) does not have a finite limit. This can illustrate the concept of a limit diverging.

14. **The Squeezed Lemon**: You squeeze a lemon, and each squeeze gets out half the remaining juice. How much juice will you get after an infinite number of squeezes? This can illustrate the concept of a limit in a practical context.

15. **The Infinite Ladder**: You're climbing a ladder where each rung is half the height of the previous one. Will you ever reach the top? This can illustrate the concept of a limit in a practical context.

16. **The Music Fade-Out**: A song fades out by reducing its volume by half every second. When will the song be completely silent? This can illustrate the concept of a limit approaching zero.

17. **The Population Growth**: A bacteria population doubles every hour. What will be the population after an infinite number of hours? This can illustrate the concept of a limit at infinity.

18. **The Pizza Slices**: You keep slicing a pizza into smaller and smaller pieces. What happens to the size of a piece as you keep doing this? This can illustrate the concept of a limit approaching zero.

19. **The Traveling Light**: Light travels at a constant speed. If a beam of light travels half the remaining distance to a mirror every second, when will it hit the mirror? This can illustrate the concept of a limit in a practical context.

20. **The Stock Market**: A stock's price increases by half of the remaining difference to a certain price every day. What will be the stock's price after an infinite number of days? This can illustrate the concept of a limit in a real-world financial context.

These examples and problems can make the concept of limits more relatable and interesting to high school students, helping them see the relevance of this mathematical concept in their everyday lives.

To dive deeper into one of the examples, I can ask it this:

Let's dive deeper into one of the examples: "12. **The Fibonacci Sequence**: The ratio of consecutive Fibonacci numbers approaches a certain number as you go further in the sequence. What is this number? This can illustrate the concept of a limit in the context of famous mathematical sequences." Tell me everything you know about this topic in a way that I could explain it to a high school senior and they would intuitively understand it

and it will give me this:

Sure, let's explore this fascinating aspect of the Fibonacci sequence.

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

Now, let's look at the ratios of consecutive Fibonacci numbers:

1/1 = 1,

2/1 = 2,

3/2 = 1.5,

5/3 = 1.666...,

8/5 = 1.6,

13/8 = 1.625,

21/13 = 1.61538...

As you can see, these ratios are getting closer and closer to a certain value. This is where the concept of a limit comes in. In mathematics, a limit is the value that a function or sequence "approaches" as the input (or index) approaches some value.

In the case of the Fibonacci sequence, the ratio of consecutive numbers approaches a special number approximately equal to 1.61803, known as the golden ratio. This number is often denoted by the Greek letter phi (Φ).

The golden ratio is a mathematical constant that appears in many areas of mathematics and also in nature, art, and architecture. It's considered to be aesthetically pleasing, and shapes based on the golden ratio are often found to be more attractive.

So, when we talk about the limit of the ratio of consecutive Fibonacci numbers, we're saying that as we go further and further along the sequence, this ratio gets closer and closer to the golden ratio.

To make this concept more intuitive, you could think of it like a car driving towards a destination. The car is the ratio of consecutive Fibonacci numbers, and the destination is the golden ratio. As the car drives, it gets closer and closer to the destination, but it never quite arrives. That's what we mean when we say the limit of the ratio is the golden ratio.

I hope this explanation helps make the concept more understandable!

So, yeah, pretty cool and worthwhile to do. I don't know how this process and GPT-4 isn't extremely helpful and a value-add if used correctly.

Image Prompt: A democratic blue hand on the left shaking with a Republican red hand on the right, signaling bipartisan support

[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 700 word blog in the style of Morgan Housel]

(Untitled)

The Supreme Court's recent decision to veto President Biden's student loan forgiveness plan has sparked a wave of reactions. The plan was designed to erase up to $20,000 in student debt for some individuals, with a general forgiveness of $10,000 per eligible borrower. The court, however, deemed the act beyond presidential power by a 6-to-3 vote, underscoring the intricate dance between the executive branch and the law.

In the wake of this decision, the challenge Biden and his team face is how to navigate the deeply partisan views surrounding student loan forgiveness. Critics often label debt forgiveness as a form of welfare, a free handout, a viewpoint that draws a sharp ideological line between the Democratic and Republican parties. While the progressive wing of the Democratic Party advocates for complete student loan forgiveness, gaining bipartisan support for such a sweeping measure seems unlikely.

So, how can we move forward? A potential solution lies in redefining the issue as a 'win-win' for all parties involved. Rather than focusing solely on debt forgiveness, a more productive approach might involve bolstering and reforming the existing Public Service Loan Forgiveness (PSLF) program.

The PSLF program, as it currently stands, forgives the remaining student loan balance for borrowers who have made 120 qualifying payments while working full-time for a qualifying employer, typically a government or non-profit organization. However, the timeline is a hefty 10 years. 

What if we could adjust this to five years? This reduction would make the prospect of public service more appealing to more people. It could potentially encourage graduates to pursue careers in underserved sectors such as education, social work, and public health. The payoff? After five years of service, their student debt could be significantly reduced or completely wiped out.

Making the process simpler and more transparent could also be a major selling point. A clear, accessible program would alleviate some of the stress and confusion that often surround student loan forgiveness schemes.

To draw in Republican support, this revamp could be packaged with funding for school choice, a cause often championed by conservatives. This could take the form of a significant sum allocated towards innovative educational programs, effectively giving conservatives a stake in the game.

Consider a hypothetical scenario: a $400 billion bill proposed, with half of the funding going towards the revamped loan forgiveness program and the other half towards expanding school choice. Such a proposition would be a substantial gesture of compromise, signaling a willingness to meet halfway.

Turning down such a proposal would be a hard sell for any politician. It's one thing to vote against debt forgiveness alone, but rejecting a package that bolsters public service, eases the burden of student loans, and expands school choice would be a tougher pill to swallow.

The path to widespread student loan forgiveness is riddled with obstacles, but by framing it as a bipartisan win-win, we might just find a way forward. By merging public service, debt relief, and education innovation, we can craft a solution that benefits everyone: the students, the public, and the lawmakers on both sides of the aisle.