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.

[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)

In a world brimming with possibilities, we often hear the inspirational refrain - "You can do anything!" We're told that we're unique, and if we truly commit ourselves, we can achieve anything. It's a wonderful sentiment, grounded in truth, and it fuels our ambition to strive for greatness. Yet, in our quest for personal growth, it's equally crucial to have a keen understanding of reality, particularly regarding our situational contexts. 

There is a concept in statistics called the 'base rate.' Simply put, it refers to the likelihood of an event occurring in a given population. For example, if we're looking at the success rate of start-ups, the base rate might tell us that a certain percentage of new businesses will still be operational after five years. This rate offers an 'average' or 'median' outcome, offering a glimpse into what tends to happen under usual circumstances.

Applying base rate thinking to our lives serves as a reality check. It reminds us that while we might feel special and capable of extraordinary things – and we very well could be – we are not immune to the statistical realities that apply to individuals in similar situations. 

Now, don't get me wrong. I'm not suggesting that we diminish our aspirations or see ourselves as just another number in a vast sea of statistics. On the contrary, understanding the base rate of a particular situation can guide us in our decision-making process and help us make informed choices.

Consider Bayes' theorem, a principle in probability theory and statistics, which suggests that we should adjust our expectations based on new information. In essence, it nudges us to change our mind when the situation changes. If we only think deterministically – believing in fixed outcomes – we are at odds with our inherently probabilistic world, where outcomes are not set in stone but rather influenced by a myriad of variables.

Many situations in life reflect the pattern of a bell curve, a normal distribution where most outcomes cluster around the average. But others, especially in realms like wealth or viral popularity, follow a power-law distribution where a small number of cases account for the majority of the effect. Knowing where we are on these distributions can aid in setting realistic expectations.

Understanding base rates and adjusting our assumptions based on changing circumstances enables us to navigate life with a more grounded perspective. It's about embracing the fact that while we are unique, we are also part of a larger statistical reality. We are special, yes, but so is everyone else, each in their own unique way. Recognizing this interplay between individual uniqueness and collective statistics is not a deterrent to our aspirations but a compass that guides our journey.

Ultimately, the key lies in striking a balance between our individual potential and the wisdom gained from the experiences of those who have walked paths similar to ours. It involves recognizing our potential, understanding the statistical realities of our situation, and being open to changing course when new information warrants it. 

This balance, this marriage of individual potential and statistical reality, can be our most reliable guide. It whispers to us that while we are indeed capable of anything, we must also remain grounded in the understanding that others have been in our shoes before, and there is much we can learn from their experiences. Remember, the world is vast, the possibilities are endless, but an understanding of base rates can be our trusty compass on this exciting journey called 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 700 word blog in the style of Morgan Housel]

(Untitled)

It's been a recurring observation on Twitter, one that captures my attention - a shared consensus that those drawn to electronic music are a unique breed. I've found myself fascinated by this notion, circling around it, and teasing out the threads that form this intriguing tapestry of personality and music.

Electronic music, by its nature, can be challenging to the uninitiated. It thrums with repetitive beats and vocals, looping over in a rhythmic hypnotism that often requires patience and an appreciation of subtlety to fully savor. Songs can take their sweet time, unfurling over several minutes, before the compelling crescendo hooks you.

What sets apart electronic music lovers is their willingness to embrace the journey. This musical genre is not about instant gratification or a quick hit of a catchy hook. It's about the slow build-up, the ebb and flow of music that ultimately pulls you in. It's a long-term commitment, a relationship with a song that only deepens with each listening.

These enthusiasts have a propensity to appreciate layers - both in music and life. An electronic music track is much like an intricate mosaic, every beat and rhythm representing a unique piece. Together, they weave an auditory landscape rich in depth and texture. The fans of this genre are adept at identifying these layers, delighting in their complexity, and savoring the way they blend seamlessly to create a cohesive whole. This appreciation extends beyond music and seeps into their daily lives, enabling them to perceive nuances and complexities where others see only the surface.

The allure of electronic music, I believe, has much to do with its rhythm – a resonant frequency that seems to connect with its audience on a primal level. Every beat, every note strikes a chord, producing a euphoric roller-coaster of emotions that resonates with its listeners. It's about finding the right 'vibe,' that unique blend of beats per minute and the melody that seems to strike a chord within the listener's soul.

Interestingly, there seems to be a high tolerance for dissonance among electronic music lovers. They are prepared to weather the occasional rough patch in a song, the 'bad parts,' with stoicism, almost as if the discord adds to the overall experience. It is as though they are aware that one needs to wade through the unremarkable to truly appreciate the extraordinary - a mindset that suggests a long-term vision and an acceptance of life's inevitable ups and downs.

It makes me think of the famed 'marshmallow test,' a psychological experiment gauging gratification delay. Given the choice between an immediate reward or a greater reward after a delay, those who prefer electronic music, I suspect, would be more inclined to hold out for the bigger prize. Their music preference, with its emphasis on the build-up and journey, suggests a temperament more inclined towards patience and a focus on long-term gratification.

In conclusion, a penchant for electronic music might indicate more than just a musical preference. It may be a reflection of a certain mindset, an inclination towards seeing the bigger picture, appreciating life's intricate layers, and a propensity for delayed gratification. They're the ones who relish the journey as much as, if not more than, the destination.

Could a love for electronic music denote a particular kind of thinker? Could it serve as a telltale marker of a long-term visionary who savors life's complexities? While we cannot generalize, the connection is indeed fascinating, offering a unique perspective on how music preferences can mirror life philosophies. So, the next time the pulsating beats of an electronic track fill the room, take a moment to appreciate the journey it represents, the layers it unveils, and the resilience it inspires.