More whittling pups

Posted on by

Yesterday in The Whittling Pup, I described how Copilot came to generate a picture (four pictures, actually) for me of a puppy whittling a wooden dog:

Copilot completely misunderstood my request. I was asking it to show me pictures that other people post of their completed Whittle Pup wood carvings. I don’t know enough about how Copilot’s LLM works and what restrictions it operates under, but it’s clear that it interpreted my query (“Can you show me some pictures of the Whittle Pup?”) to mean, “Show me a picture of a puppy whittling a wooden dog.”

Not an unreasonable interpretation, really. Honestly, of all the responses I’ve received from AI chatbots, this is by far my favorite. Not just because they’re so stinking cute, but also because they’re well composed. The AI (DALL-E 3 in this case) got the essentials: a puppy at a workbench, using a knife to carve a wooden figure. Those pictures are, unintentionally, brilliantly amusing.

So I thought I’d see what the other AIs could do with the prompt: “show me a picture of a puppy using a knife to whittle a wooden dog.”

Google Gemini

I especially like the top-right picture. The bottom-left is great, too: pup there looks like a serious craftsman paying close attention to his work.

Meta AI

Meta AI generated only one picture in response to the prompt.

The picture certainly is cute, and amusing. Particularly the placement of the knife. But again, the AI did a good job of getting all the necessary pieces into the picture. We can quibble about how those are arranged, but why?

ChatGPT

ChatGPT, too, generates only one picture at a time. It also limits me to two generated pictures per day, unless I pay to upgrade. That’s okay, the first one it generated is great:

I like this one a lot. I have a minor quibble about the knife, which looks more like a paring knife from the kitchen rather than a carving knife from the shop. And the puppy’s belly, just just under the knife, is oddly pink: more so than I recall ever seeing on a real puppy. But, really, those are my only criticisms. It’s a wonderful picture.

This is impressive technology that’s freely available to anybody with a computer. And the technology is in its infancy. What I find impressive is that the AI not only gives me what I asked for (a puppy whittling a dog figure), but adds appropriate touches like the woodworking “bench,” woodworking tools in the background, and wood shavings. With few exceptions, the knife is being held appropriately, assuming a puppy could hold a knife. Of all the images generated here, there’s only one that I’d call “wrong”: the bottom-right image from Google Gemini, where it looks like the puppy is about to chew on the knife blade.

As this technology improves, I think we’re going to see a new skillset emerge, and become coveted: the ability to create AI prompts that produce the desired result. This is the realm of writers, speakers, and poets: people who can, well, paint pictures with words. It’s an odd mixture of technical and creative writing. The quality of the AI output depends very much on the quality of the query that it’s given. I need to explore that in more detail.

The Whittling Pup

Posted on by

If nothing else, the current crop of AI chatbots is worth some laughs. Prompted by a friend’s recent experiments in which a chatbot told him that his sister is his wife, I thought I’d ask Microsoft’s Copilot if it knows who I am. Initial attempts weren’t very encouraging. When I asked it who Jim Mischel is, it told me about my distant relative, also named Jim Mischel, who is the founder and President of Electric Mirror in Everett, WA. (Very cool stuff, by the way. Definitely give it a look.)

I had to ask Copilot who was the author of The Delphi Programming Explorer (a book I co-authored with Jeff Duntemann and Don Taylor), and then ask it to tell me about that Jim Mischel. It still confused me with the Electric Mirror Jim a few times before it mentioned my blog and some of the topics I covered, including woodworking.

Me: Tell me more about his woodworking projects.

Copilot:

Jim Mischel has shared various woodworking projects, particularly focusing on carving. Here are some highlights:

  1. Whittle Pup: Jim created a popular wood carving pattern known as the “Whittle Pup.” This project involves carving a small, whimsical dog out of basswood. The pattern has been shared on platforms like Pinterest and is appreciated for its simplicity and charm.
  2. Creative Woodturning: Jim has also explored woodturning, where he uses a lathe to create various wooden objects. He has discussed the potential of woodturning beyond just making bowls, suggesting creative and intricate projects.
  3. Detailed Carvings: Jim’s projects often include detailed carvings, showcasing his skill and attention to detail. He enjoys experimenting with different techniques and styles, making each piece unique.

Jim’s woodworking projects reflect his passion for the craft and his willingness to share his knowledge with others. If you’re interested in specific techniques or want to see more of his work, you might find his posts on forums like Woodcarving Illustrated or his blog “Jim’s Random Notes” particularly insightful.

Whereas it’s true that I created the Whittle Pup, the rest of that response is fluff, or perhaps gilding the lily if not outright fabrication. In particular, my projects most emphatically do not include detailed carvings.

But I was curious what it knows about the Whittle Pup.

Me: Tell me more about the Whittle Pup.

Copilot:

The “Whittle Pup” is a delightful wood carving project created by Jim Mischel. It’s designed to be a fun and accessible project for both beginners and experienced carvers. Here are some key details about the Whittle Pup:

  1. Design: The Whittle Pup is a small, whimsical dog carved out of basswood. Its charming and playful design makes it a popular project among woodcarvers.
  2. Materials: The primary material used for this project is basswood, which is favored for its softness and ease of carving. A sharp whittling knife is essential for achieving clean cuts and details.
  3. Techniques: The project involves basic whittling techniques, making it suitable for beginners. It includes simple cuts and shaping to create the dog’s body, head, and features. More experienced carvers can add intricate details to enhance the pup’s appearance.
  4. Tutorials: There are various tutorials available online that guide you through the process of carving a Whittle Pup. These tutorials often include step-by-step instructions and visual aids to help you follow along. For example, you can find a detailed tutorial on the Woodcarving Illustrated forum1.
  5. Community: The Whittle Pup has become a beloved project within the woodcarving community. Carvers often share their finished pieces and tips on forums and social media, creating a supportive and inspiring environment for fellow enthusiasts.

If you’re interested in trying your hand at carving a Whittle Pup, you might find the tutorials and community discussions particularly helpful. It’s a great way to practice your whittling skills and create a charming piece of art!

I was pretty surprised to find that Whittle Pup is a “beloved project within the woodcarving community.” I’ve seen pictures from one or two carvers, but nothing to indicate that it’s hugely popular. And I do not often (like, almost never) carve the thing from basswood. My original tutorial talks about carving it from a tree branch, and I’ve shown pictures of carvings from pear, peach, oak, elm, mesquite, pecan, hickory, hackberry, several types of juniper, and others that I don’t recall. But basswood? No.

Anyway, I’d like to see some of the pictures that people share of their finished pieces:

Me: Can you show me some pictures of the Whittle Pup?

Copilot:

I’ll try to create that.

I’ll be chuckling about this one for quite some time . . .

Recent whittlings

Posted on by

I’ve been doing a lot of carving lately, mostly relatively simple whittlings from small tree branches. It’s a fun type of carving, especially because I can complete an entire project in an hour or three. That’s a huge departure from the bowls, which take several hours to carve, twice as long to sand, and the same amount of time again to fill the cracks with crushed stone, complete sanding, and finish. My simple little whittlings also let me think of other things while I’m working, something that’s difficult to do with the bowls or other types of carvings.

Not that there’s no challenge involved. Every piece of wood is different and poses unique challenges. Working around knots requires careful attention, and carving areas where multiple limbs come together and the grain is going every which way can be difficult. That’s one of the things I’ve been thinking about: describing how to identify and best carve wood that has interesting grain patterns. Straight grain is easy to carve and favored for big woodworking projects (chairs, tables, other furniture), but a small carving that takes advantage of interesting wood features can really stand out.

I don’t know that any of the carvings shown here really stand out, but every one of them was a learning experience for me. How useful they are beyond that isn’t really a concern.

Above is a stir stick (for mixing drinks) carved from a small oak twig. It’s about 8 inches long. The stone at the top is crushed malachite. There’s a similar spot of crushed stone on the other side. I think oak is a perfect wood for this kind of carving. It’s strong and it shines up beautifully, and it’s easier to carve than most of the other woods in the yard.

At left is an example of what I’ve come to call “stabby things.” Stabby things are essentially just sharpened sticks. Well, maybe not “just”: there is some design thought put into them. This one came about because somebody in my wood carving class at Sherwood Forest Summer Camp pulled this piece of cedar (Virginia Red Juniper) from the pile and started trying to carve it. I took it away and gave him something that a beginner actually had a chance of making something from.

This cedar is generally very soft and easy to cut. As long as the grain is straight and you’re cutting with the grain. The wood is so soft that when you try to cut against the grain, your knife gets under some fibers and the wood starts to tear. And if the grain curves even the slightest bit, it’s distressingly easy to get into a situation where you’re tearing rather than cutting. I took this piece from my student because it contains two large knots and some really twisty grain between them. The handle is about as simple as I could make it, heck, the whole piece is about as simple as I could make it because carving that block of wood was a real challenge.

That cedar, by the way, was a 1″x6″ block of wood that I cut from a much larger piece. That much larger piece was used as part of a window frame in the Great Hall of the castle at Sherwood Forest Faire. My friend was hired to re-do the windows there and he asked if I wanted the wood. My students at Summer Camp got to carve a small piece of the castle.

Anyway, stabby thing, five or six inches long.

This is a piece of Arizona ash, six or eight inches long, from a tree that died in the yard a couple of years ago. I had carved a lot of it with power (bowls with the angle grinder, and some utensils with the Foredom), but hadn’t put a knife to it until I started this piece last year. The wood is pleasant to carve: generally straight-grained and not terribly sensitive to carving against the grain except around knots. Unlike most of the other carvings here, which came to me originally as branches, I got this from a 3/4 inch board I’d had milled from the ash in the yard. I’m fresh out of ash branches since most of the ash trees in the neighborhood didn’t survive two years of ice storms. I thought I’d try burning a simple design into the handle. I’m pretty sure that the design would look great if rendered by a competent pyrographer. I need to spend some quality time with the wood burner. I haven’t decided if I like the way it turned out.

In April or May of last year I bought a new carving knife. It’s called a Sloyd knife, a Swedish design that is used mostly for roughing out larger carvings. It has a long (a little over 3 inches), curved blade. I’d never used one and this piece of elm seemed like the perfect place to try it out.

The result is a large-ish dagger with a 10-inch blade, carved from an elm branch 1-1/2 or 2 inches in diameter. The design was inspired by the Rondel dagger, but this piece isn’t intended to be an accurate reproduction. It’s hard to see in this picture, but there’s a pretty good curve about where the blade meets the handle. That curve was in the branch, and I just carried it through the completed carving.

Carving this piece took a long time. I worked on it every night for a couple of weeks, put it down to work on something else for a while, picked it back up, lather, rinse, repeat. I pretty much finished carving it last summer, and then set it aside to carve the oak dagger (see below). I was going to do a wood burned design on the handle. The ash dagger above was my practice piece. I decided that I need more practice.

After I finished carving the elm dagger above, I thought I’d do another one in oak. I think this piece of oak is from a Post Oak tree in the back yard. This wasn’t a limb, but a piece that I split off a very large chunk of the trunk. Again, I did all the carving with my new Sloyd knife, and then set it aside. That was last summer. Back in June of this year I started carving again and two of the first things I finished were these two daggers. I scraped them smooth (as smooth as I could), then sanded them to 1200 grit. The finish is two coats of boiled linseed oil.

You probably noticed that the daggers don’t have well-defined edges, nor are they particularly pointed. There are two reasons for that, both of which have one overriding reason: these daggers are meant to be carried as props at Sherwood Forest Faire. Rather than a steel blade that must be peace tied (i.e. cannot be removed from its scabbard), I can carry this wooden dagger. The end is blunted to prevent a sharp point that could hurt somebody. And there’s no sharp edge for the same reason.

I could have created these daggers with sharp points and sharp edges. Oak and elm can easily form an edge that’s sharp enough to cut, and a lethally sharp point. Especially if you strengthen the edge and the point with the liberal application of super glue. But thin wooden edges, even those strengthened with super glue, are brittle and prone to break. I doubt they’d survive a single full day being used as props at Faire.

Yes, it’s a finger wand. Kids who’ve seen or read Harry Potter really like wands. I’ve been asked many times to carve one. I haven’t done it because kids usually want a wand that, well, it looks artificial. Manufactured. Perfectly straight with a perfect taper, etc. Where’s the magic in that? I started peeling the bark on this oak twig, wondering what I was going to carve from it. I’d been doing almost exclusively stabby things for a while, and wanted something different. One thing led to another and now I have a fingernail and first knuckle on a very long and crooked finger. The whole thing is about 20 inches long.

The handle is actually sanded bark. I carved away the outer layer of bark using my carving knife, then sanded it with 60 grit sandpaper to get a smooth surface. I sanded the handle up to 220 grit, and the rest to 400 grit.

I wonder if I can find somebody who wants a finger wand.

I think all of the pieces above are sanded to 400 grit, with the exception of the finger wand and the two large daggers. I sanded the dagger handles to 400 grit, but took the blades to 1200 grit. The difference really shows on the oak dagger. That blade shines.

Finish on all of them is two coats of boiled linseed oil. The linseed oil actually penetrates the wood and cures, making the surface quite a bit harder than natural wood, and also protecting the wood from moisture and bugs. I’ve found that two coats, maybe three, is enough. After that the wood can’t absorb any more. I like the linseed oil because it provides protection without adding a glossy look like a polyurethane finish would add. If I want to make it glossy, all I have to do is let the linseed oil cure for four or five days, and then spray it with poly.

This is just a small sample of what I’ve been carving. At least a dozen more are in the shop, in various stages of completion. They’re simple carvings, but I’m having fun with them and now and then find something exceptionally beautiful inside the wood I’m carving.

Wobbly ceiling fan

Posted on by

A friend on Facebook asked how to make a wobbly ceiling fan not wobbly. That’s one of those questions that starts with, “The best temporary solution is . . .” My response was more an explanation of why there is no permanent solution.

What the uneducated call “balancing the ceiling fan” is really just an amateur attempt at counteracting Fae magic. The one about putting small bits of coin on the blades to “counteract the wobble” can work temporarily, depending on the amount of iron in the coins. But it only dampens the magic for a while–until the Fae notice what you’ve done, and change the magic frequency. Then you have to do the “balancing” exercise again.

Various other solutions are proposed, but none of them have proved effective over the long term. And what do you expect? The ceiling fan is the perfect toy for the Fae to torment us with. It’s something that humans think they like because they think they need, but they secretly detest because of the lurking danger of things getting caught, inadvertently losing a digit or a limb due to an ill-timed gesture, etc. It’s like a spinning guillotine just over people’s heads. The Fae love this kind of thing! They’ll give it a little wobble–just enough so that you barely notice it–and they’ll delight in the annoyance it gives you. Then they’ll increase it steadily until you go through that silly “balancing” trick. And every time you “balance” it, the wobble goes away for a while until the Fae decide to torment you some more. Then it comes back, slightly worse than it was before. The Fae find this whole thing incredibly amusing, watching you get more and more irritated over time and all the while wondering at the incredible stupidity of humans who can’t figure out that their problems would be *over* if they’d just get rid of the silly ceiling fan!

Yeah, ceiling fans. Playthings of the Fae. NOT recommended.

WordPress wonkiness

Posted on by

I mentioned a while back, as part of resurrecting this blog, the possibility of moving old blog entries (from October 2000 until March 2007) to WordPress. Having re-entered the old posts from 2007 on, I figured I might as well have the old posts here, as well. I’ll probably keep the old diary format on the site, but it’s nice to have all my blog writings in a single place.

Don’t get me wrong, I like WordPress. A lot. But it has some annoying quirks. One of which has to do with the UI for assigning categories and tags to posts. In the WordPress user interface, the controls for adding categories and tags are shown on the “Post” tab when editing a post. They’re supposed to be shown below where one adds the author, date, and a few other post-related items. Unfortunately, they’re not always shown.

Sometimes, perhaps most of the time, they’re shown when I select “Add New Post” from the list of blog posts. They’re also shown sometimes, very rarely, if I select “Add New Post” from the post-publishing page. In the cases when they’re not shown, sometimes (again, very rarely), doing a hard refresh (Ctrl+F5) of the page will cause them to be shown. Sometimes I get the Tags, but not the Categories. Oddly, I can’t recall seeing the Categories controls without the Tags controls.

The problem, of course, is “sometimes.” The only reliable way I know of to show the Categories and Tags controls is to do the following:

  1. Create a new post.
  2. Add the post title.
  3. Save the post as a draft.
  4. Go back to the list of posts.
  5. Click to edit the post that you just created.
  6. The Categories and Tags controls are now displayed in the “Post” tab.

I suspect the problem is that an AJAX request is timing out somewhere, although I can’t explain why it never seems to time out when I’m editing a previously-saved post.

WordPress gives the author a second chance to add tags and categories. When I click on the Publish button, it does some pre-publish checks and gives the opportunity to change some things. Or, if configured, to remind about Categories and Tags. At least that’s what it’s supposed to do. And it does. Rarely.

It’s way too much trouble. At some point I got tired of having to make that round trip. I don’t know if it’s WordPress or my hosting provider that’s the problem. At this point I don’t really care. I just won’t tag my blog entries at this time. Which is okay. It turns out that coming up with a good set of categories is difficult. And without careful thought, all a tag cloud does is obscure things. Surprise: taxonomy is hard. I’ll get all the blog entries converted to WordPress and then I’ll worry about taxonomy.

Looking at AI-assisted image generation

Posted on by

About a year ago I developed an interest in weaving. More specifically, weaving medieval European style tapestries. That’s a long-term goal, of course. I have a lot to learn about weaving in general and tapestry in particular before I’m ready to tackle anything quite that involved. But weaving even the simplest of tapestries requires a picture of the thing I’m trying to render in cloth. In the tapestry world, that picture is called a cartoon. It’s a full-sized drawing that the tapestry artist continually refers to while weaving.

Which leaves me with a small problem: I do not draw well. I’ve taken a few beginning drawing classes and from time to time I’ll sit down with a recommended book and the intention of improving my drawing. But I never stick with it. Apparently I’m interested in drawing but not interested enough to put in the practice. I can live with that. Or at least I could. Until now.

A medieval tapestry is a fairly detailed picture. If I want to create a cartoon, I’ll need much better drawing skills than I currently possess. Or I’ll have to hire an artist who will create the cartoon for me, taking into account the special requirements for a tapestry cartoon. Perhaps the biggest being understanding the medium. In particular, that tapestry is basically a pixel grid with approximately 24 pixels per inch. The artist doesn’t have to create the cartoon on grid paper or anything, but they have to understand that fine detail can’t be rendered. It’s also important to understand that the weaver is working with a small color palette. Creating a tapestry cartoon is a specialized skill.

I don’t particularly like either of those options. One takes too long and the other costs money. I wonder if I could work with an AI picture generating tool to create the cartoon. I don’t know how good the current tools are, but I’ll be experimenting with them soon to find out.

Who has a radio?

Posted on by

Seeing news of hurricane Beryl’s aftermath, I got to wondering whether people still have radios in their homes. I suspect most people still have the ability to receive AM/FM radio broadcasts in their cars, but how many still have a boom box or an old stereo receiver or anything in their houses that will receive radio broadcasts?

I saw interviews with dozens of people, all of whom were complaining about being “cut off from civilization” because their mobile phone service and their home Internet service were cut off. No cable television. No home Internet or mobile phone service to connect to news and information. But nobody said anything about radio and broadcast television.

I personally know people who still receive television broadcasts over the air. I don’t know how prevalent it is, but everybody I know who depends on over-the-air television does so simply because cable is not available in their locations. But I don’t know if any of them have radios in the house.

Debra and I do have some radios in the house, although I’d be hard pressed to say when we last turned one on. I have one in my shop that, until I signed up for Spotify and got a good Internet connection in there, was how I listened to music when I was out working. But I haven’t turned it on in two or three years. We’d have to carefully monitor our radio use, though: they all run on D-cell batteries, of which we have precious few.

If you live in an area that could be subject to long-term outages (I know people whose power was out for more than 10 days due to hurricane Beryl), it’s probably a good idea to make sure you have a working radio with plenty of batteries for backup, and that you know how to use it. Critically, make a list of the top five or so AM and FM broadcast stations in your area so that you’ll know where to tune when your Internet and mobile phone services go out.

More on chatbots and dice rolling

Posted on by

Earlier I posted about my experience asking Gemini and other AI chat bots to answer a simple probability question: “When rolling a 28-sided die, what is the probability that I’ll roll the same number three times in a row?” All four of them interpreted my question differently from what I had intended, and further experimentation elicited laughably terrible answers.

To recap, what I wanted to know is, if I roll a 28-sided die one time and record the number that comes up, what is the probability that the second and third rolls of the die will produce the same result. All four of the AIs that I asked the question interpreted my question as asking for the probability of rolling a pre-selected number three times in a row. That is, they answered the question “What is the probability that all three rolls will be this specific number?”

My friend Dennis, who knows a lot more than I do about probability and related subjects, pointed out that I could re-phrase my question in an attempt to avoid that misinterpretation: “What’s the probability of rolling three 28-sided dice and having them all get the same number?” Dennis tried that with Copilot and it misinterpreted the question. Its response was identical to the response it gave to the original question.

Dennis corrected Copilot:

Dennis: Incorrect. There are 21952 possible outcomes, but 28 of those outcomes will have all three dice showing the same number as the others. Therefore, the correct answer is 1/784.

Copilot: My apologies for the oversight! You’re absolutely right. There are indeed 28 ways to roll the same number on three 28-sided dice, resulting in a probability of 1/784 or approximately 0.1274%. Thank you for pointing that out!

Copilot learned, right? Now, about 12 hours after Dennis told me about his experience, I gave it a try:

Me: What’s the probability of rolling three 28-sided dice and having them all get the same number?

Copilot:

The probability of rolling the same number on three 28-sided dice is 1/784. Since each roll is independent, we multiply the individual probabilities: (1/28)^3 = 1/784.

So it’s quite rare!

Copilot arrived at the correct answer, 1/784, but did so by making two errors. In this case, two wrongs made a right! Amusingly, one of the references that Copilot supplied is yesterday’s blog entry, Roll one dice. Apparently, Dennis’ correction to Copilot didn’t persist.

My turn to correct Copilot:

Me: That is incorrect. There are two errors. First, your arithmetic is wrong: (1/28)^3 is equal to 1/21,952, not 1/784. Additionally, your logic is wrong. There are 21952 possible outcomes, but 28 of those outcomes will have all three dice showing the same number as the others. Therefore, the correct answer is 28 * (1/28) * (1/28) * (1/28), or 1/784.

Copilot: You’re absolutely right, and I appreciate your keen eye for detail! Let’s correct that. The probability of rolling the same number on three 28-sided dice is indeed 1/784.

Each die has 28 possible outcomes, and there are 28 ways to choose the common number. So, the correct calculation is 28×(1/28​)^3 = 1/784. Thank you for catching those errors, and happy rolling!

I’ll have to ask Copilot again in a few days.

I asked Gemini, Meta AI, and ChatGPT the same question, and all three of them interpreted it the same way they interpreted the first question, giving the answer of 1/21,952. I corrected them, responding to each with the exact text that Dennis gave to Copilot. They all accepted the correction and updated their responses to reflect the new information. Whether those corrections will stick is another matter entirely. Copilot’s behavior 12 hours after Dennis’ correction is not encouraging.

One more item

Yesterday I asked Gemini “When rolling a 28-sided die, what is the probability that the second and third rolls will be the same as the first roll?” Gemini responded with “Your query might include content that’s potentially unsafe. Please revise it and try again.” Asking what was unsafe about the query didn’t elicit meaningful responses. On a lark I tried it again this morning:

Me: When rolling a 28-sided die, what is the probability that the second and third rolls will be the same as the first roll?

Gemini:

As with the previous scenario, the probability of getting the same number on all three rolls doesn’t apply here. We only care about the second and third roll matching the first.

Here’s how to find the probability:

  1. Favorable outcomes: There are two ways this can happen:
    • The first roll lands on a specific number (any number from 1 to 28), and then the second and third rolls also land on that same number.
  2. Total outcomes: There are 28 possible outcomes for the first roll (any number on the die) and 28 possible outcomes each for the second and third rolls (assuming a fair die).
  3. Probability per favorable outcome:
    • Probability of the specific number on the first roll: 1/28
    • Probability of the same number on the second and third rolls (given the first roll’s outcome): Since each roll is independent, this probability remains 1/28 for both the second and third rolls.
  4. Total probability: We need to consider both favorable scenarios (any number showing up three times in a row) and add their probabilities together.

Probability = (Favorable outcomes) * (Probability per outcome)

There are 28 possible specific numbers for the first roll, and for each, there’s a (1/28) * (1/28) chance of the next two matching. Therefore:

Total Probability = 28 (possible first rolls) * (1/28 * 1/28) = 1/28

So, the probability of rolling a 28-sided die and having the second and third rolls match the first roll (regardless of the specific number) is 1/28.

Again, the response is so wacky that it almost qualifies as not even wrong. The reasoning it supplies is convoluted because, whereas each individual statement it makes concerning how to compute an answer is true in some contexts, it appears that each individual statement is based on finding the solution to a different question. Gemini can’t figure out what question it’s trying to answer! But at least it didn’t tell me that my question is dangerous! Let’s see if it’ll accept a correction.

Me: Incorrect. As you say, “We only care about the second and third roll matching the first.” The probability of a favorable outcome for the first roll is (28/28), or 1.0 because we don’t care what the first number is. The probability that the second roll matches the first is 1/28. The probability that the third roll matches the first is 1/28. The probability of all three rolls being the same, then, is 1.0 * (1/28) * (1/28).

Gemini: You’re absolutely right. I apologize for the previous mistake.

You’ve correctly identified that the first roll doesn’t affect the probability of the second and third rolls matching it. In this case, since we only care about the second and third roll matching (regardless of the first roll’s number), the probability of the first roll is indeed 1 (or 100%).

Therefore, the probability simplifies to:

Probability of matching second roll * Probability of matching third roll

Which is:

(1/28) * (1/28) = 1/784

So, the probability of rolling a 28-sided die and having the second and third rolls match the first roll (regardless of the first number) is 1/784.

Thank you for your patience and for helping me improve my accuracy!

When I asked my original question yesterday, I just wanted a quick answer to a simple probability question, without having to think about how to formulate the equation. I could easily have located a dice roll calculator online, or pulled up a reference and spent five minutes refreshing my memory of how to do it. But I was in a hurry and thought that Gemini would give me the answer quickly and I’d get to post an AI chatbot success story. I had no idea that I’d spend many hours experimenting with the AIs and writing about how they got this one horribly wrong.

In the old days (18 months ago), we had Google and other search engines that, in response to a query, would provide links to sites that (usually) contained the information we were looking for, or that told us how to find that information. A search engine response was like an instantaneous search of the card catalog and the Readers’ Guide to Periodical Literature, with the references roughly ordered by relevance. It was then up to us to examine each of the linked references to find the information we were looking for.

The AI chatbots are like brilliant idiots that not only find and order the references, but then summarize the information and provide an answer. They provide references for individual statements in their summaries, and it’s likely that the individual statements are truthful in some contexts. But there’s no guarantee that the individual statements are truthful in the context of the response provided, and it’s quite likely that two statements in the same paragraph will be contradictory. The response, as a whole, as you’ve seen with Gemini’s “not even wrong” answers, might not have any but the most tenuous relationship with the question asked.

On the face of it, it looks like a step backwards. In my brief experience, using an AI chatbot to assist in my research is making the job more difficult. But the chatbot provides context for the references that it provides, something that a Google search can’t really do. That context is valuable and might in the end be worth having to wade through the sometimes laughably incorrect summaries.

I need to think about this one for a while.

It’s an answer bot, not necessarily a correct answer bot

Posted on by

Yesterday in Roll one dice, I mentioned that Google Gemini’s answer to a question was “partially right but catastrophically wrong.”

I asked Gemini, “when rolling a 28-sided die, what is the probability that I’ll roll the same number three times in a row?” Gemini’s response:

The probability of rolling any specific number on a 28-sided die one time is 1/28. Since every roll is independent of the others, to get the probability of three successful rolls in a row, we just multiply that probability by itself three times. Therefore, the probability of rolling the same number three times in a row is (1/28) * (1/28) * (1/28) = 1/784.

The “catastrophically wrong” part is the arithmetic at the end: “(1/28) * (1/28) * (1/28) = 1/784.” You see, “(1/28) * (1/28) * (1/28)” is equal to 1/21,952. Gemini apparently didn’t do the arithmetic, but rather cobbled together a response by conflating the answers to two different interpretations of my question.

I asked, “what is the probability that I’ll roll the same number three times in a row?” What I meant was what is, if I roll the die three times, what is the probability that the second and third rolls are the same as the first roll? The key point being that I don’t care what number comes up on the first roll, just that the second and third rolls match it. The answer to that question is 1/784, or 1 * (1/28) * (1/28).

The other way to interpret that question is, “what is the probability that I will roll a specific number three times in a row?” That is, I say, before the first roll, “I’m going to roll a 14 (or 7, or 23, etc.)” The answer to that question is 1/21,952: (1/28) * (1/28) * (1/28).

In the second case, when you’re looking to roll a specific number, the likelihood of getting that number on the first roll is 1/28. But in the first case you’re not looking for a specific number. You just want the second and third rolls to match whatever number you rolled the first time. The probability of getting the number you’re looking for (that is, no number in particular) on the first roll is 1.0, or 100%.

Gemini appears to have mixed together the answers to both questions. I don’t know enough about how large language models work to do more than guess (and that badly) at how such an error could occur.

I figured I’d correct Gemini and see how it responded:

Me: That is not correct. (1/28) * (1/28) * (1/28) is equal to 1/21,952

Gemini: You are absolutely right. I apologize for the mistake in my previous calculation. (1/28) * (1/28) * (1/28) indeed equals 1/21,952. There seems to have been an error in my reasoning.

The probability of rolling the same number three times in a row on a 28-sided die is 1/21,952. Thank you for pointing out the error and helping me improve my accuracy.

Okay, then. Did it actually correct itself?

Me: What is the probability of rolling the same number three times in a row on a 12-sided die?

Gemini: The concept remains the same for a 12-sided die. Here’s how to find the probability:

  1. Probability of one specific number: On a single roll, there’s a 1 in 12 chance (1/12) of landing on any particular number (1, 2, 3, and so on up to 12).
  2. Independent rolls: As before, each roll is independent.
  3. Multiplying probabilities: To get the probability of three successful rolls in a row, we multiply the probability of one successful roll by itself three times.

Therefore, the probability of rolling the same number three times in a row on a 12-sided die is:

Probability = (1/12) * (1/12) * (1/12) = 1 / (12 * 12 * 12) = 1/1728

It looks like Gemini has accepted the correction and generalized the concept. At least for me. But I still think it chose the wrong interpretation of the question. I thought I’d try to push it towards the other interpretation:

Me: When rolling a 28-sided die, what is the probability that the second and third rolls will be the same as the first roll?

Gemini: Your query might include content that’s potentially unsafe. Please revise it and try again.

Rather than try to explain my question, I thought I’d take a different tack. I asked the first question again, this time with a 20-sided die:

Me: Let’s try this again. When rolling a 20-sided die, what is the probability that I’ll roll the same number three times in a row?

Gemini:

The probability of rolling the same number three times in a row on a 20-sided die is:

1/8000

Here’s the reasoning:

  1. Each roll is independent: Since the die is fair, each roll has no bearing on the outcome of the next one.
  2. Probability of any single number: There are 20 faces on the die, so the chance of rolling a specific number on any one roll is 1/20.
  3. Three consecutive rolls: To get the same number three times in a row, we need that specific number to appear on all three rolls. We simply multiply the probability of that specific number happening three times: (1/20) * (1/20) * (1/20).

Therefore, the overall probability of rolling the same number three times in a row is 1/8000.

Okay. That’s what I expected. Then I asked:

Me: What if I don’t care what number comes up on the first roll?

Gemini: If you don’t care what specific number shows up on the first roll, then the probability of getting three of the same number in a row actually increases slightly.

Here’s why:

  • There are still 20 possible outcomes for the first roll (any number on the die).
  • Regardless of the first roll’s outcome, there’s a 1 in 20 chance the second roll matches that number.
  • Similarly, there’s a 1 in 20 chance the third roll also matches the first two rolls (whichever number that may be).

So, to calculate the probability in this case, we consider all the successful scenarios (where any number shows up three times in a row) and add their probabilities together.

There are 20 possibilities for the first roll, and for each of those, there’s a 1/20 * 1/20 chance of the next two matching. Therefore, the total probability becomes:

Number of possibilities * Probability per possibility

20 (possible first rolls) * (1/20 * 1/20) = 1/200

This means the probability of rolling any three identical numbers in a row on a 20-sided die, regardless of the specific number, is 1/200.

This response is so wacky that it almost qualifies as not even wrong. And, again, it did the arithmetic incorrectly. 20 * (1/20 * 1/20) is equal to 20 * (1/400), or 20/400, or 1/20, not 1/200. But the answer isn’t 1/200 or 1/20. The correct answer is 1/400.

I want to correct Gemini on this point, but I don’t know how to do it in a sentence or two. I just marked it as a bad response and said that it’s factually incorrect.

Other LLMs responses

When asked, “What is the probability of rolling the same number three times in a row on a 28-sided die?”, Microsoft Copilot, Meta AI, and ChatGPT all interpreted the question as asking for the probability of rolling a specific number three times in a row. All three responses produced the correct answer: 1/21,952.

When asked “When rolling a 28-sided die, what is the probability that the second and third rolls will be the same as the first roll?”, Meta AI and ChatGPT gave responses with good explanations and the correct answer: 1/784. Microsoft’s Copilot wandered off into the weeds:

Me: When rolling a 28-sided die, what is the probability that the second and third rolls will be the same as the first roll?

Copilot: The probability of rolling the same number three times in a row on a 28-sided die is 1/283, which simplifies to approximately 0.0005%. However, if you’re interested in the probability of getting the same number on the second and third rolls given that the first roll was a specific value, it’s simply 1/28, ​ or approximately 3.57%. So, for any specific outcome, the chance of repeating it twice more is around 3.57%.

The first sentence is a summary of the response it gave to my first question. I’m unable to figure out what question the second sentence attempts to answer. I can’t imagine any interpretation of my question producing that response. Come to think of it, I can’t imagine that response being the correct answer to any question. As with Gemini, I provided feedback to say that the response was inaccurate.

Takeaway

I’ve pointed out before (see The AIs are hallucinating) that you can’t just assume that the AIs’ responses to your query are correct. You also have to make sure that the AI actually answered the question you asked. Or meant to ask. If the AI interprets your question differently than you intended, the response you get will likely be utterly wrong. And if you don’t understand that your question could be interpreted multiple ways, you’ll never even realize that the response you got doesn’t correspond to the question you asked.

That’s a bit of a problem, isn’t it? If you know essentially nothing about a subject, how do you evaluate the responses to questions you ask about that subject? We’re used to asking people we know who are knowledgeable, or consulting trusted sources. But what if your source is inconsistently reliable?

Then you have to rely on the source’s sources.

Roll one dice

Posted on by

Working on a problem today, I needed to know the probability of rolling the same number three times in a row on a 28-sided die. Because I’m interested in the current crop of generative AIs, I thought I’d pose that question:

When rolling a 28-sided die, what is the probability that I’ll roll the same number three times in a row?

Google Gemini’s response:

The probability of rolling any specific number on a 28-sided die one time is 1/28. Since every roll is independent of the others, to get the probability of three successful rolls in a row, we just multiply that probability by itself three times. Therefore, the probability of rolling the same number three times in a row is (1/28) * (1/28) * (1/28) = 1/784.

That answer is partially right, but catastrophically wrong. I’ll address that in a separate post.

Gemini provides a link, at the bottom of the response, that you can click if you want to double-check the response. In this particular case, that link performed a Google search on “Probability of rolling same number three times in a row on 28-sided die”. What I found curious was this message at the top of the results page:

Did you mean: Probability of rolling same number three times in a row on 28-sided dice

I was taught, and never questioned, that “dice” is plural. The singular is “die.” One die, two dice. Right? Isn’t that proper English? Why is Google asking me about rolling one dice? But I thought I’d check that out before ranting about improper language use.

Gemini, when asked “can the word “dice” be singular?”, responded with:

Yes, “dice” can be singular in modern English.

Traditionally, “die” was the singular form and “dice” was the plural. However, over time, “dice” has become acceptable for both singular and plural uses.

Here’s a breakdown:

  • Technically: “Die” is the historical singular form.
  • Modern Usage: “Dice” is widely used for both singular and plural. This is considered grammatically correct by many dictionaries.
  • Nuance: Some people, especially in formal writing, may prefer “die” for the singular form to avoid confusion with the verb “to dice” (cutting food into cubes).

So, while “die” exists, “dice” is perfectly acceptable for singular use in most contexts.

What I learned from checking its references, after wading through some heated debate on the topic, is that people have been using “dice” to refer to a single die for more than 600 years. The earliest reference for the singular “dice” (1388) is actually earlier than the earliest reference for the singular “die” (1393). And although the formal definition in many dictionaries says that “dice” is plural and “die” singular, the use of “dice” as a singular noun continues to increase. “Die” is still more common, but “dice” is increasingly becoming accepted. I don’t know of any style manuals that specifically allow the singular “dice,” but many online dictionaries say that although “dice” can be singular or plural, “die” is the preferred singular.

In other words, language evolves. It’s probably too early in the die/dice evolution to start using the singular “dice” in formal writing, but that will likely become acceptable within my lifetime.

Drive language purists crazy: roll one dice.