And… here we are

This week what we have all been fearing has happened to me: GitHub Copilot generated code for me which seems to meet all the requirements but which I don’t understand very much at all.

To date GitHub Copilot for me has just been mostly a useful auto-complete tool and it hasn’t given me any code which I didn’t understand. But with this code (to control two different hardware timers/counters on my Arduino) I don’t really understand it at all. I have passing familiarity with some of the registers used because I saw them named in the datasheet (which I have only skimmed so far) but basically I don’t understand how this works.

It is tempting to ignore the fact that I don’t fully understand and move on, but there’s a part of me which wants to return to the datasheet so I can understand what every assignment GitHub Copilot offered actually does and what every value it calculated implies. Is that the best use of my time?

Can a Directed Acyclic Graph always be put into the plane?

ChatGPT 4


can a Directed Acyclic Graph always be put into the plane?


A Directed Acyclic Graph (DAG) can usually be drawn in the plane, but whether it can be drawn without any edges crossing (i.e., as a planar graph) depends on the specific structure of the DAG.

Planarity of a Graph:

A graph is considered planar if it can be embedded in the plane without any of its edges crossing each other. Not all graphs are planar. The planarity of a graph is generally tested using Kuratowski’s Theorem, which states that a finite graph is planar if and only if it does not contain a subgraph that is a subdivision of either the complete graph K5 (five vertices each connected to every other vertex) or the complete bipartite graph K3,3 (two sets of three vertices with every vertex of the first set connected to every vertex of the second set).

DAGs and Planarity:

  • Acyclicity: A DAG, by definition, does not contain any cycles. This property alone does not guarantee planarity, but it does simplify the analysis since any subgraph involving cycles can be ignored when considering potential K5 or K3,3 configurations.
  • Structure and Complexity: The more complex the connectivity of the DAG (especially in terms of vertex connectivity and the number of edges relative to the number of vertices), the higher the chance that it could contain a non-planar configuration. A simple DAG with a tree-like structure, where each node has a few successors, is likely planar. However, as the number of edges and vertices increases, and especially if the graph forms dense interconnections between nodes, it could potentially include subdivisions of K3,3, making it non-planar.

To determine whether a specific DAG is planar, one would typically either:

  1. Look for subdivisions of K5 or K3,3 directly,
  2. Use algorithmic tools that implement planarity testing algorithms (such as the ones based on path addition or cutting algorithms).

Therefore, while many DAGs can indeed be drawn in the plane without crossing edges, it’s not universally true for all DAGs; the specific structure and connectivity must be considered.

ChatGPT 4 on Indian cuisine

User: tell me about Palak Paneer

Palak Paneer is a popular vegetarian dish from the Indian subcontinent, particularly in North Indian cuisine. It’s a creamy and flavorful dish that combines palak (spinach) and paneer (a type of fresh cheese) in a richly spiced curry sauce. The dish is known for its vibrant green color, smooth texture, and delicious taste. Here’s a bit more about it:


  • Spinach (Palak): The base of the sauce, blanched and pureed to give the curry its characteristic green color and nutritional boost.
  • Paneer: Indian cottage cheese, which is cubed and either fried or added as is to the curry. Paneer adds a rich, creamy texture and protein to the dish.
  • Spices and Aromatics: Commonly used spices include cumin seeds, turmeric, coriander powder, garam masala, and fresh ginger and garlic. These spices provide depth and complexity to the flavor.
  • Cream or Yogurt: Used to add richness and smooth out the flavors. Some versions use tomato for a bit of acidity and color contrast.


The preparation of Palak Paneer involves several steps:

  1. Blanching the Spinach: Spinach is quickly boiled and then plunged into ice water to retain its vibrant green color.
  2. Making the Curry Base: Aromatics and spices are sautéed to release their flavors, followed by the addition of spinach puree.
  3. Adding Paneer: Paneer cubes are added to the spinach curry and simmered until they are soft and have absorbed the flavors of the curry.
  4. Finishing Touches: The dish is finished with cream or yogurt to add richness and sometimes adjusted for seasoning with salt and a sprinkle of garam masala.


Palak Paneer is traditionally served with flatbreads like naan or roti and can also be enjoyed with rice. It’s a staple in Indian restaurants worldwide and is appreciated for its comforting taste and nutritious profile, being rich in iron from the spinach and protein from the paneer.

Nutritional Value

Palak Paneer is considered a healthy option due to the high content of spinach, which is rich in iron, vitamins A and C, and fiber. Paneer adds protein to the dish, making it a balanced meal. However, the nutritional value can vary based on the amount of cream or oil used in preparation.

This dish is a beautiful example of Indian culinary tradition, blending rich flavors, textures, and colors into a delicious and visually appealing meal.

User: what do you mean “fresh cheese”?

“Fresh cheese” refers to cheeses that are not aged or matured as part of their production process. Unlike aged cheeses, which can develop complex flavors and textures over time, fresh cheeses are meant to be consumed shortly after they are made. They are characterized by their soft texture, mild flavor, and high moisture content. Here are some key features of fresh cheese:

  • Texture: Fresh cheeses tend to be soft and moist. Some are creamy and spreadable (like ricotta or cream cheese), while others can be firmer but still tender (like paneer or mozzarella).
  • Flavor: These cheeses typically have a mild, sometimes slightly tangy or sweet flavor. The taste is more about the freshness and quality of the milk used rather than the fermentation or aging process.
  • Aging: There is minimal to no aging process involved. Fresh cheeses are usually consumed within a few days to a couple of weeks after production.
  • Uses: Fresh cheeses are versatile and can be used in a wide range of dishes, from salads and sandwiches to pizzas and desserts. They are also often enjoyed on their own or with a simple accompaniment of fruits or bread.

Paneer, the cheese used in Palak Paneer, is a perfect example of fresh cheese. It is made by curdling milk with a food acid (like lemon juice or vinegar) and then pressing the curds to form a firm block. Paneer is cherished for its ability to absorb flavors while maintaining its shape and texture, making it an excellent addition to various dishes in Indian cuisine.

User: tell me about Lamb Saag

Lamb Saag is a rich and flavorful dish from the Indian subcontinent that combines tender pieces of lamb with saag, a term used in Indian cuisine to refer to leafy green vegetables such as spinach, mustard greens, or a mix of greens. This dish is a variation of the traditional Saag, which is often prepared with paneer (cheese) or potatoes for vegetarian versions. Lamb Saag brings the unique, deep flavors of lamb meat into the mix, offering a hearty and satisfying meal. Here’s a closer look at this delicious dish:


  • Lamb: Typically, boneless lamb is cut into bite-sized pieces. The lamb is marinated and then cooked until tender, making it the star of the dish.
  • Greens: Spinach is the most commonly used green in Lamb Saag, but mustard greens, collard greens, or a mix can also be used. The greens are usually blanched and then pureed to form the base of the curry.
  • Spices and Aromatics: Aromatic spices such as cumin, coriander, turmeric, garam masala, and fresh ingredients like garlic, ginger, and onions are used to build layers of flavor.
  • Yogurt or Cream: To add richness and balance the flavors, yogurt or cream is often stirred into the curry towards the end of cooking.


  1. Marinating the Lamb: The lamb pieces are marinated in a mixture of yogurt and spices to tenderize and infuse them with flavor.
  2. Cooking the Lamb: The marinated lamb is then cooked with onions, garlic, and ginger, along with additional spices until it’s browned and tender.
  3. Preparing the Greens: The greens are blanched, pureed, and then cooked with the lamb, allowing the flavors to meld together.
  4. Final Touches: Additional seasoning adjustments are made, and yogurt or cream is added to create a rich, creamy sauce.


Lamb Saag is traditionally served with flatbreads like naan or roti, as well as with rice. The dish is garnished with fresh herbs or a dollop of cream to enhance its appeal.

Nutritional Profile

Lamb is a good source of protein, iron, and other essential nutrients, making Lamb Saag a nutritious option. The greens add fiber, vitamins, and minerals to the dish. However, the nutritional value can vary depending on the amount of oil, cream, or yogurt used in the recipe.

Lamb Saag is appreciated for its combination of tender meat, nutritious greens, and the depth of flavor from the spices. It’s a testament to the versatility of Indian cuisine, where a single ingredient can inspire a myriad of delicious variations.




ChatGPT 4:

When discussing programming and interfacing with microcontrollers, “ISP” and “ICSP” are two terms that often come up. Here’s a breakdown of what each means and how they compare:

ISP (In-System Programming)

  • Definition: ISP refers to the ability to program a microcontroller while it is placed within the actual system or circuit where it will operate. This method doesn’t require the microcontroller to be removed from its application circuit for programming. It’s a very convenient way to update firmware or make changes to the program running on the microcontroller without needing to disassemble the system.
  • Advantages: It enables easy updates and debugging since the microcontroller does not need to be removed. This can significantly speed up development cycles and make maintenance simpler.
  • Usage: Common in many microcontrollers, including AVR, ARM, and others. It typically requires a few specific pins to be accessible for the programming interface.

ICSP (In-Circuit Serial Programming)

  • Definition: ICSP is a form of ISP specifically using a serial interface to program the microcontrollers while they are installed in a circuit. It’s a subset of ISP with a focus on the serial communication aspect. This method is often associated with Microchip microcontrollers but is not exclusive to them.
  • Advantages: The serial nature of ICSP means it usually requires fewer pins and can sometimes support lower voltage programming, making it suitable for a wide range of devices and situations. It’s particularly useful for devices where space and pin count are at a premium.
  • Usage: Predominantly seen with Microchip’s PIC microcontrollers, though the concept applies broadly. Like ISP, it necessitates access to specific programming pins but often fewer than other methods.


  • Scope: ISP is a broader term encompassing any in-system programming technique, including serial, parallel, or any other method. ICSP is specifically about serial programming.
  • Interface and Protocol: ICSP typically involves specific protocols and hardware interfaces tailored for serial communication. In contrast, ISP can use various protocols and interfaces depending on the microcontroller and the system’s requirements.
  • Microcontroller Support: While many microcontroller families support ISP, ICSP is more commonly associated with certain brands or families, like Microchip’s PIC series.

In summary, ICSP is a specific form of ISP. The choice between ISP and ICSP often comes down to the specific requirements of the project, including the microcontroller being used, the available pins for programming, and the preferred programming method. Both aim to provide flexibility and ease of use for developers and engineers when programming microcontrollers within their final application environment.

The Brain User’s Handbook: A Neuroscience-inspired Guide to Peace of Mind

I am reading The Brain User’s Handbook: A Neuroscience-inspired Guide to Peace of Mind which has this awesome image I want to share:

An imagined interaction between a human baby and a young LLM in training. They are sharing impressions about the endeavor of modeling the world from scratch. Image generated with DALLE-3 via ChatGPT

ChatGPT teaches me about Amplitude Modulation

I wanted to record this conversation in which ChatGPT managed to convey to me an understanding of how an AM radio wave is demodulated.


in a crystal radio why have a diode and not just send the full signal to the output?


In a crystal radio, the diode plays a crucial role by acting as a detector for the radio signal. Here’s why it’s necessary instead of just sending the full signal to the output:

  1. Demodulation of the Signal: A typical radio signal is a form of amplitude-modulated (AM) wave, where the information (voice, music, etc.) is carried in the amplitude variations of a high-frequency carrier wave. The diode in a crystal radio serves to demodulate this signal. It does so by allowing current to flow in only one direction, effectively removing one half of the alternating current (AC) waveform. This rectifies the signal, leaving behind a waveform that varies in amplitude in a way that directly represents the original audio content.
  2. Detection: The process described above is also known as detection. The diode detects the audio-modulated envelope of the AM radio signal. Without the diode, the radio would be incapable of converting the high-frequency modulated signal back into audio frequencies that can be heard through the earpiece or speaker.
  3. Simplicity and Efficiency: Crystal radios are prized for their simplicity and ability to operate without an external power source. The diode, being a passive component, does not require power to operate. It efficiently performs the detection of the signal without the need for active components or power supplies.
  4. Directivity: The diode’s unidirectional current flow property also helps in filtering out noise and improving the selectivity of the receiver to some extent, though crystal radios are generally known for having broad selectivity due to the lack of an amplification stage.

The most common type of diode used in crystal radios is a germanium diode. Germanium diodes have a lower forward voltage drop compared to silicon diodes, which makes them more suitable for the weak signals typically received by crystal radios. This allows for more efficient demodulation of the signal with minimal loss, making it possible to hear the broadcast with just the energy captured from the radio waves themselves.


if the diode wasn’t there you would hear the carrier frequency?


If the diode wasn’t present in a crystal radio, you would not be able to hear the carrier frequency directly, but rather, you wouldn’t hear anything intelligible through the earpiece at all. Here’s why:

  1. Frequency of Carrier Waves: The carrier frequencies used in AM radio broadcasting are typically in the range of hundreds of kilohertz to several megahertz. Human hearing, however, is limited to frequencies approximately between 20 Hz and 20 kHz. The carrier frequency itself is far beyond what the human ear can perceive.
  2. Nature of the Signal: Without the diode to demodulate the signal, the radio would attempt to pass both the carrier frequency and the audio information as a combined signal. Since the earpiece or speaker in a crystal radio is designed to reproduce audio frequencies (the modulated information), it cannot reproduce the high-frequency carrier wave itself.
  3. Role of Demodulation: The process of demodulation (achieved by the diode) strips away the carrier, leaving behind the audio frequency variations that were impressed upon the carrier wave. These variations are within the human audible range and are what you actually hear as sound from the radio. Without the diode, the modulation on the carrier wave would not be converted into an audio signal.
  4. Energy Conversion: Even if somehow the carrier frequency could be directly converted to sound, the energy of the received signal in a crystal radio is typically too low to move the speaker diaphragm enough to produce an audible sound without the signal being demodulated and amplified in some way. The diode, by rectifying the signal, effectively extracts the modulated audio signal, which can then cause the diaphragm in the earpiece to vibrate and produce sound.

In summary, without the diode to demodulate the signal, the crystal radio would fail to convert the high-frequency AM radio signal into an audio signal that can be heard. The diode is essential for extracting the audio content from the modulated carrier frequency, enabling the crystal radio to produce sound.

ChatGPT for the day

ChatGPT 4:

User: explain profundity


Profundity refers to a state of being deep in thought or insight. It’s often associated with ideas, thoughts, or expressions that have significant depth of meaning, understanding, or insight. Profundity can apply to various contexts, including intellectual discussions, philosophical concepts, artistic works, and emotional experiences. When something is described as profound, it usually means it has a deep impact, is very thoughtful, or offers substantial wisdom or insight. Profundity involves layers of meaning that may not be immediately apparent and often requires contemplation or reflection to fully appreciate.