Alice was excited! Mom, Scott, and Charlotte were all here! However, Mom got a little concerned when she watched Charlotte play horsie for Alice, shouting out things like. "Hold on tight!" and then at Charlotte, "Don't you dare drop my baby girl, you hear!"

Of course, Charlotte didn't let anything happen to Alice. She never would. Scott had been scared of her, too, at first. But Charlotte was a good spider lady. She always took good care of her friends, and Alice was her best friend!

When Alice started to feel a little dizzy from screaming and laughing while Charlotte spun in circles, a new game Alice had taught her, Charlotte stopped and gently placed Alice on the ground. Of course, Alice then walked around intentionally twisting and spinning with the dizziness, laughing until she started hiccuping.

-

Charlotte watched in confusion as the tiny human spun around and eventually fell onto her rear while giggling. "How is this activity helpful to human development?"

Scott laughed. "Well, saying it's directly helpful might be a bit of a stretch, but a good amount of fun and entertainment are healthy. Though if we stay out here much longer, we might have to start giving Alice some lessons so she doesn't fall too far behind in her education."

Alice crossed her arms and protested. "Nooo! Lessons are boring! We're on vacation, and Charlotte is here! I don't want to do any lessons!"

Charlotte was familiar with all the words used, but how "lessons" was used indicated another meaning. "What are lessons in this context?"

Scott stopped and thought a moment. "Well, humans start out knowing very little. Some things we learn just by being around people, like walking and talking. However, there are other things we only learn through instruction and repetition, such as reading and math."

Alice made an exaggerated expression indicating distaste. "I hate math!"

Scott laughed as he looked down at his little sister. "We all do, munchkin, up until we need it. Trust me, you want to know math!"

Charlotte leaned forward, interested in learning more. "What's math?"

Lacy looked back and forth between Scott and Charlotte. "I thought Scott said you were more intelligent than humans. How can you not know what math is?"

Charlotte turned her attention to Alice's mom. "Humans took a very different evolutionary path, and not just physiologically, but also in your problem-solving. Where humans look for solutions to their problems from without, Shes tend to look within, growing what we need to overcome challenges. Scott has referred to our version of technology as 'bio-organic.'"

Lacy looked confused. "Shes..?"

Scott shook his head. "It's how Charlotte refers to her species. It's confusing, I know, but it is what it is. Like Charlotte said, her people tend to grow tools rather than create them. To her, combining a stick and a stone into an axe is mind-boggling because she could just grow a new 'appendage' to do whatever we might need an axe for. But at the same time, her understanding of bio-organic technology vastly outpaces our own, to the point she can manipulate her genetics to create things that rival even our most advanced technology. Why refine metal when you can just consume the minerals and use them to create a metallic bone structure comparable to even the toughest steel? Why build a computer when you can literally grow enough brains and link them together to create a bio-organic computer. And before you wonder just how far you can go with bio-organics, her people are apparently spacefaring. Charlotte is not native to this world."

Lacy looked back and forth between Charlotte and Scott again. "Wait, you mean she's an alien? From another world?"

Alice was now hopping up and down while holding onto Charlotte's hands. Charlotte lifted her hands in time with Alice's jumps to help the girl attain greater heights than her motor skills would typically allow.

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Scott shrugged. "Well, yes, but no more than us. It's just by luck that we found each other, though I'd say she's done a lot more to help us than the other way around."

While Scott was somewhat accurate, Charlotte felt the need to speak up. "That's not entirely correct. While the Shes have known of tool users in the past, they were usually primitive species who used stones and sticks to get food or defend their territory. As a result, we've vastly underestimated the potential of tools. How humans build tools from tools to create increasingly complicated and intricate tools mirrors our own progress in bio-engineering. I believe that the proper integration of the two thought processes creates a potential for a symbiotic combination of the two. While I may have done more to aid in your short-term survival, you've given me the tools to advance myself and my species in entirely new ways. I have hope that a long-term relationship between our two species may benefit both over time."

Lacy looked at her son. "Are you sure this is wise?"

Scott shrugged. "Well, we don't have much choice, and what's more, Charlotte has been more honest and upfront with me than most people I know. For now, at least, I trust her."

Lacy still seemed thoughtful, but Scott turned his attention back to Charlotte. "So anyway, back to what you originally asked, math is how we keep track of numbers. Alice, why don't you show Charlotte how to do seven plus three."

Alice grumbled at first, but when she realized she could do math by drawing in the dirt with a stick, she seemed happier about it. Charlotte watched as the human drew a symbolic representation of the numbers seven and three and how they 'added up' to ten.

Charlotte looked back at Scott. "Yes, this is true, but why do this as math? If you have seven and three of something, you just have ten. Why think of them as seven and three?"

Scott nodded. "Well, basic addition is kind of a starting point, but we can use it to expand to more complicated ideas. As well as addition, you have subtraction, which is kind of the opposite, then multiplication and division, both of which you still probably instinctively calculate. Still, from there, you have algebra, geometry, trigonometry, and calculus, many of which you must have some equivalent to, but our interpretations are probably less intuitive than the others. There are even disciplines more refined than that, but that's about as far as my education went so far."

Scott got a stick and started drawing out his own mathematical formula. "Here's a basic algebra theory. A squared, plus B squared, equals C squared."

Lacy shook her head. "That's already more advanced than my schooling got..."

Charlotte needed clarification. "I thought you said math is a way of keeping track of numbers? Those are not numbers."

Scott nodded. "Yes and no. In this case, the letters represent potential numbers. If we can figure out some of them, we can solve the rest. This particular equation lets us figure out how long the sides of a triangle are." He drew a triangle in the dirt, labeling the three sides A, B, and C, and continued drawing numbers and symbols as he spoke. "Now, if we know the length of A and B, let's say six and eight, we can square them, add them together, and take the square root of the total to get ten, so that's how long the last side must be. We could do something similar to determine any side we didn't know."

Charlotte was more confused than ever. It took a few questions to clarify the meaning of multiply, square, and square root, but eventually, it all made logical sense. However, it still left one question. "What is the purpose of this, math? How often do you need to find the length of one side of a triangle?"

Scott shook his head. "I remember saying that myself back in school. The truth is that this specific formula isn't helpful in the real world all that often. But again, just like addition led to something more complicated, so does this. Many of the things we use math for you probably do instinctively or simply by powering through with trial and error, but remember, each human life is precious to us. There are many things we have to get right on the first try, or at least close enough to right that it doesn't end disastrously. Take our first moon landing. We used math to calculate everything from the required amount of fuel to break free of our planet's gravity to how much air would need to be purified in the cabin. We even calculated how the moon's orbit would shift in the time our people spent exploring it. There were hundreds of people applying thousands of formulas for far more challenges than I described."

Charlotte looked at the complicated formula, which now seemed simple compared to what Scott described. She tried to picture how this little equation could lead to space travel. "I suspect this is a little too advanced for my understanding of human tools. I will require more instruction in this matter."

Scott laughed. "Well, I don't know if I have the expertise to get you all the way there, but I suppose we could get a little closer while also teaching Alice. For now, it's only important that you realize that math is the key to most of humanity's more advanced 'tools.'"

Looking around, Scott continued. "Besides, right now, a well is more important to us than the Pythagorean theorem. So, let's call that a teaser for what's to come, alright?"