The training with Venus has exhausted quite much of my physical energy for today, but after all, it was rewarding, as I have begun to learn a new skill that I could use to defend myself, and to train the coordination between my mind and the surroundings.

Shortly after the exercise has ended, Venus and I took a refreshing bath at the sixth floor of the Sailor Guardians' Tower, and after that, Venus returned to her room, while I sat down on the coach in the common room to take some more rest.

After having recharged by a bit, I got up, and made my steps towards Mercury's room, marked with the symbol of planet Mercury above the glowing azure blue doors, adorned with patterns of stars and bubbles in lighter shades of blue. Knocking on the door of her room, I called out her name, "Princess Mercury."

The doors then opened, revealing the figure of the studious and highly intelligent princess in her azure gown, reminiscent of the color of a clear sky at noon. She wears pearl earpins with a blue tint, and I could also notice her necklace, with both horns of the blue, metallic symbol of Mercury being tied together by chains of gold. With a blush, she greeted me in excitement, "Oh, Aurora!"

I noticed her shining blue eyes, concentrating her attention on my new gown and regarding in what is perhaps newfound curiosity. "Is that a gown Venus gave you?"

I looked a bit down to my new viridescent gown, and tilted my head back up at her, asking in return, "You noticed?"

She then looked back at me, telling me about how fabulous her sister's wardrobe is. "Venus always has fashionable outfits in her wardrobe. I think it suits you quite well!"

This is the second time, that I've been complimented by a princess of the Moon Kingdom, that I look beautiful in this dress. In particular, the way Mercury delivered her remark, carried a plainly cute aura!

With a playful smile on my face, I thanked her. "Why, thank you, Mercury!"

I then took a look around her room.

Her room has a massive bookshelf from the ground to the ceiling, and a giant blue holographic interface! Her bookshelf is full of books of various lengths and cover colors, and about various topics. Her books are well-organized, with a numbering system that categorizes her books into various disciplines, such as mechanical physics, electrical engineering and Lunarian linguistics.

This is a living space, that I could only dream of, when compared to the large, but relatively small bookshelf that I have in my wooden house. I couldn't imagine how many books Mercury has in her personal library, and how broad and deep the combined scope of her books are.

Being curious, I asked, "Tell me, Mercury, what kind of books do you read?"

Mercury responded, in her graceful and calm voice. "I like reading all kinds of books. As a princess of the Moon Kingdom, I aim to be well-educated and proficient in various disciplines, ranging from science, engineering, mathematics, to literature and politics."

The disciplines of books that she mentioned somehow rang bells for me, as I also read books in the related areas. I told Mercury, "Your taste in books sound similar to mine. On Earth, I often read books about astronomy, geography, sciences, mathematics and politics."

As I spoke, I realized one particular discipline that fascinates me the most.

Artificial intelligence.

The name of the discipline carries a magical charm to it, as if we could make a machine achieve sentience. As a princess from Earth, I would naturally be curious about this art. I asked, "It seems to me, however, that you and Serenity seemed to favor books that cover the field of artificial intelligence?"

Mercury affirmed, "Uh... You're correct, Aurora. Artificial Intelligence is an important component of life in the Moon Kingdom."

She then began to describe her fondness for the field. "We like to read books about the use of probabilistic models in robotic algorithms, about machine learning with neural networks, and about how can artificial intelligence be applied to enhance the quality of life of Lunarians. To make it simple, we utilize the power of probability and linear algebra, and write algorithms to make machines intelligent!"

Being curious, I asked, "What kind of probabilistic models do you make use of, Mercury?"

Mercury began to explain, "there is a rule of probability that is known by every Lunarian girl and boy alike." Typing on her virtual holographic keyboard, her holographic interface started to show a window, with text being entered.

"The probability of Event A given Event B, multiplied by the probability of Event B, then divided by the probability of Event A," she spoke, as an equation forms on the holographic screen, "returns the probability of Event B, given Event A."

She then clicked on a button on the holographic interface, starting a simulation of the rule.

"Suppose, the probability of you wearing your green gown, given that you are on the Moon, is 80%, the probability of you being on the Moon is 80%, and the probability of you wearing your green gown at any time is 64%."

The holographic interface showed a cute representation of me, Princess Aurora, in two different images. In the first one, my face was seen on the backdrop of the Lunarian horizon; in the second one, I was wearing a green dress on a transparent background. The corresponding probabilities also appeared on the interface, though in decimals, such as 0.8 and 0.64.

Mercury then explained, "Then, the joint probability of you wearing your green gown on the Moon is 80% squared, which is 64%." An image depicting me wearing my green gown and standing on the surface of the Moon then appeared on the interface, along with the number 0.64 at its right.

She then continued, "64% divided by 64% is 100%. That means, the probability of you being on the Moon, given that you are wearing your green gown, is 100%!" In a smooth transition, the interface showed 0.64 on top of a division line, and another 0.64 under the line, and then, with a special 'puff' effect, the equal sign and the result, which equals to 1, appeared. "In other words, if you wear your green gown, you must be on the Moon!"

Hearing her funny explanation of the rule, I was exhilarated and broke into laughter. "That's a funny way to explain the rule, Mercury. Your sense of humor is just as good as your brother and your sister!"

I then glanced briefly at my dress, before continuing, "I do plan to wear my dress on Earth, though."

Mercury said, "I think you will, Aurora!"

She then went back to the topic. "We make use of this rule very often in Robotics and in Machine Learning."

With a swipe of her finger, she explained. "There are mainly two types of models for machine learning: one is generative, which means we make use of old data to generate something new; the other is discriminative, which means we analyze new data by making use of old data."

Two "models", which are actually equations, appeared on the interface. There are labels matching descriptions to mathematical expressions, showing how a new probability could be yielded from given probabilities. The generative model works through generating new examples from each class, or, mathematically, calculating the joint probabilities of examples and classes through multiplying the probability distribution of classes, and the probability distribution of examples, given the relevant class. Conversely, the discriminative model works through calculating the probability distribution of classes, given the examples, which makes it handy for categorizing existing samples.

Princess Mercury then said, "I have a generative model here." She then opened a window on her holographic interface, and extended her hand to point around all the books of her tall book shelves. "I trained the model on the millions of physical books that stand in my room..."

Then she also made a swipe, showing all the virtual book files she has in her computer, "and on trillions of digital books that are stored in my computer as well."

Being fascinated, she expressed, "The model has quintillion parameters. On the Moon, we use the long scale like you do on Earth, so this big number has thirty zeros!"

I asked curiously. "Can this model generate something impressive?"

She affirmed, "Sure!"

She then typed a prompt on her keyboard as she said, "generate art of Prince Serenity in ten art styles!"

With just a second of processing time, the generative model returned drawings of her brother in ten very distinctive art styles - oil painting, watercolor, pencil sketch, and so on... I was impressed by how expressive the art styles are, and some of the art styles can even look as realistic as I could never imagine!

Afterwards, she typed another prompt, saying gladly, "generate... a poem of four lines!"

And swiftly, the generated results were presented on the screen.

"Standing in solitude by the lakeside,
She watches the motion of the tide.
With a gown viridescent like a Northern Light,
She gazes upon the starry sky of the night."

The rhymes, the scenery... Is that poem about me? I try to picture the scene, when I gazed upon the Northern Lights back on Earth, only that I am wearing my green dress now...

Mercury then showcased me the discriminative model.

She then presented me a gallery of thousands of photos in her microcomputer. "Here, I would simply type keywords in the search field, and..."

As she typed keywords into the microcomputer, the collage of photographs on the screen becomes more and more related to each other. As she finished typing, the photographs that were shown are all about Earth, when viewed from the Moon!

She said, "a discriminative model trained on a vast library of image data helps me sort out all kinds of photographs, from palace interiors, to photographs of planet Earth, to different kinds of flowers..."

She then replaced the keyword with another one, and with the blink of an eye, the screen showed photographs of boats instead!

Being amazed by all the practical uses of artificial intelligence that Mercury had demonstrated to me, I told her, "Mercury, you know..."

With a blush, she seemed to think that I would be on track to say something flattering to her. "Aurora?"

"I am impressed and totally charmed by all of that you've showed me!"

Mercury then said, "well... it indeed is impressive and charming, that machines could learn like we humans do..."

I then decided to take a slight turn in the conversation topic, and have an extensive discussion about the uses of artificial intelligence in various fields.

I asked, "How do Lunarians make use of artificial intelligence in their daily life?"

Mercury spoke profoundly, "Artificial intelligence and its applications help us in many fields, such as space navigation, ground transportation, cleaning, and even medical diagnosis. Like, our spaceship's autopilot systems have been trained to precisely calculate the orbit of planets and the positions of obstacles, such as asteroids, so that a smart trajectory could be calculated, avoiding all the obstacles while reaching the destination in a route taking the least viable time."

With a sense of realization in my mind, I said, "So that's how Serenity's ship flew me to the Moon swiftly..."

Mercury affirmed, "Exactly!"

She then continued to explain, in a scientific manner. "The ship has to take many factors into consideration, like the gravitational forces of the Earth and the Moon, and the position of the Moon in its orbit, which steadily changes while the spaceship is in flight. It is with these parameters that form the state space, and the navigation system of the spaceship take past state and action into consideration, when calculating the trajectory of the next instant."

"I see..."

Mercury then further explained. "Lunarian scholars have developed an assumption, where the next state is assumed to depend only on the current state and the imminent action. Some scholars of a later period found the assumption to be too strong in some cases, and so, they extended the assumption, to cover cases where a state depends on a fixed number of previous states. The spaceship's navigation algorithm is based on countless improvements of this assumption."

Being impressed by mentions of Lunarian scholars from long ago, I expressed, "It seems that science, technology, engineering and mathematics are highly valued and emphasized in the Lunarian civilization."

As we continued to engage in the discussion, we became oblivious to the swift passing of time.

It was then, when we were still discussing enthusiastically with occasional laughs, someone rang the bell on Mercury's door.

The discussion turned into a temporary silence.

On the other side of the door, a voice could be heard. "Mercury, it's time for dinner!"

Mercury pushed on the door button, prompting the glowing azure doors to slide seamlessly. I recognized the girl who stood outside Mercury's room - the girl with brown hair, tied in a ponytail.

Princess Jupiter has come to invite her brother and her sisters for the dinner of the day!

Mercury responded, "We're coming, Jupiter!"

We gathered around the dining table in the center of the common room. The cutlery were laid out in an organized and elegant pattern, and on the plates, there are visually scrumptious meals, cooked by the strongest princess of the Moon Kingdom.

On the inward-facing edge of the table, Serenity sat in the center seat, while I sat at his right and Venus at his left. Opposite to me is Mercury, while Mars took the seat opposite to Venus and Jupiter was seated opposite to Serenity.

As always, Jupiter was the first to raise her utensils and start savoring the meal she has made for herself and her siblings. We seem not to need to speak to agree, that Jupiter is the one who enjoys food the most!

Having finished one of her morsels, she asked me, "Aurora, did you have fun at the Moon Palace today?"

I nodded and responded. "Yes, Jupiter. I learnt sword skills with Venus in the morning, then after a nice bath, I went to Mercury's room and discussed quite much about Artificial Intelligence and its applications in the Moon Kingdom."

Jupiter said, "That's great, Aurora!"

We all continued to feast on the dinner, being satisfied by how good and how fresh it tasted.

Jupiter then turned slightly towards Mercury, asking her, "how did you discuss artificial intelligence with Aurora?"

Mercury replied, "I make use of visualizations. The funniest example is when I calculated the probability of Aurora wearing her green gown on the Moon, as an example!"

And it's indeed funny!

After breaking into laughter upon Mercury's mention of that example, I said, "Artificial Intelligence is indeed a fun field. You get to know its different aspects, such as probabilistic Machine Learning, as well as Robotics."

Jupiter responded, "That's quite interesting! You know, Aurora, we the other sisters don't really understand much about the deep theories of artificial intelligence. Sometimes, we'd say that what Mercury is studying is like the language of gods, and we admire that Serenity is bold enough to study these highly advanced topics with his blue-haired sister."

Upon hearing Jupiter's hilarious remarks, Serenity could not help laughing. Mercury seemed also to find her sister's remarks amusing, and chuckled along.

Jupiter then asked, "But by the way, what did you do with Venus today?"

This question reminded me of the scene, where I sparred with Venus in the hall under the rays of morning light. I said, "I practised some sword skills with her."

With a curious raise of her eyebrows, Jupiter asked, "Really?"

I confirmed, "Yes, it's true. I was taught some basic defensive stances to parry attacks and to protect myself."

Jupiter then exclaimed, "That's unbelievable! It seems you've experienced quite much ever since you arrived on the Moon. You're going to be an all-rounded princess who would go on to outshine all of us."

With a humble tone, I responded, "It might be true that I'd eventually outperform you in some areas. However, I seem to think that the value of competition between you sisters is to encourage one another to keep improving, so that when you come together, your combined strength would also be greater."

Mercury nodded in agreement, saying, "Your words are wise, Aurora. We will remember it in our hearts."

Soon, we would have finished our scrumptious dinner, and each of us went back to our rooms for a while. I gazed upon the stars from the Moon, trying to identify the constellations and the stars as I regard upwards, to the sky, while I ponder, which princess should I meet tomorrow?

Not long after that idea came into my mind, I already have an answer.