"Tradition is not the worship of ashes, but the preservation of fire."
― Gustav Mahler

Stardate 2235.97

"What are these?" Spock asked, plucking one of the small, reddish brown sticks from the glass container.

His mother glanced up from her mixing bowl and smiled. "Cloves."

"What are cloves?"

"They're dried flower buds from a tree native to Earth. They're used as a spice to give the gingerbread its yummy taste."

Spock returned the unusual spice to its container and continued to observe her progress patiently. He stood on his toes for a better view and felt the stool wobble.

"Do you want to help me mix the flour and water?" she asked.

Spock nodded. It wasn't often anyone enlisted the assistance of an almost six year-old. She gave him the big cup of white powder and showed him how to slowly pour it into the bigger mixing bowl as she stirred with the unusual wire utensil. The dark brown liquid started to thicken and lighten in color as they worked in tandem and when they were done, his mother took the cup and said, "Thank you. That was most helpful."

"You are welcome," he replied proudly. "What do we do now?"

"Now we chill our dough and get everything else ready to decorate our gingerbread house."

She showed him how to mix a white paste she called icing and produced several canisters of brightly colored candies from the pantry. When she turned her back to check the temperature of the oven, Spock popped one of the round red treats into his mouth and was surprised by the overpowering taste of cinnamon.

"Are you pilfering my candy?"

Spock jumped, nearly falling backwards off the stool. His mother glared at him, hands on her hips. He wasn't entirely certain of the definition of the word "pilfer," but he sensed from her menacing pose that she was referring to stealing candy. "Yes, mother."

She laughed, took several steps forward, grabbed several of the purple gummies and tossed them in her mouth. "Good. That's the best part of making a gingerbread house."

She wiped down the counter and removed the dark brown mixture from the food preservation unit and started rolling it into a wide, flat sheet. He couldn't comprehend how she was going to build an entire house with the materials at hand.

Spock's sensitive ears detected the sound of the back door opening and footsteps approaching. "Father is home."

"He's early," his mother mused. She grinned and continued to stretch the dough with the wide, cylindrical instrument.

Several moments later his father appeared in the doorway of the kitchen and surveyed the scene. "Another gingerbread house?"

"You seem surprised," she sighed. "I make one every year. Spock offered to help this time."

His father took several steps forward and analyzed their progress. "Might I make a suggestion?"

She leaned back and shot him a look of surprise. "You've never been interested in helping before."

"You have never asked for my assistance and I know it often agitates you to receive unsolicited advice."

She set the heavy rolling pin on the counter and crossed her arms. "You're always welcome to participate in my illogical traditions. Tell me, what do you suggest?"

"Every year you underutilize your resources and fail to optimize your structure's dimensions. A few simple calculations would allow you to create a more efficient construction."

"How, father?" Spock asked.

His father glanced at him, raised an eyebrow, and took a step forward. "May I?"

"Please," she answered, stepping back to give him space. "Let's see your skills in confectionary engineering."

His father shot her a pointed look, rolled his sleeves at the cuffs, picked up the rolling pin, and spread the dough.

"Not too thin," she insisted, making a face as she looked over his shoulder.

"Spock, what is the fewest number of flat faces a three-dimensional object may possess?"

Spock furrowed his brow and considered the question. He wouldn't begin formal schooling until his sixth year, but he spent four hours every day learning with his tutor. His father would sometimes look in on his studies, but he never commented on Spock's progress.

"Four."

"Explain."

Spock tucked his chin to his chest and glanced at the towering figure of his father. "Four triangles."

"Which forms what?"

Spock didn't know. His studies in elementary geometry hadn't covered objects with three dimensions.

"Sarek, leave him alone," his mother urged, her face growing dark. "This was supposed to be fun, not another excuse to drill endless facts into his head."

Spock sensed another argument coming. They often fought over his education. His father said he only wanted Spock to have the best foundation possible before entering school, but his mother claimed he was being pushed too hard. He'd once overheard his father remind her that Vulcan children developed faster than their human peers, but his mother had reminded him that Spock was half-human, to which his father had replied, "And I am attempting to help him overcome that disadvantage." That had been a year ago, the day before Spock met his tutor for the first time.

"Allow him the opportunity to consider the question, Amanda."

Spock wanted to prove he was capable, but he didn't know the answer to the question his father had asked. Perhaps it had something to do with his disadvantage – whatever that was.

"I do not know, father," Spock replied, hanging his head.

"Have you studied elementary geometry with your tutor?"

"Yes, but only in two dimensions," Spock admitted, his voice barely rising above a whisper.

"He hasn't even turned six – you can't expect him to know everything," his mother groaned.

His father ignored her and said, "Spock, there is nothing wrong in not knowing. Do you wish to know the answer to my question?"

"Yes," Spock replied, finally gazing up at the imposing man.

"You were correct – the simplest three-dimensional object with flat surfaces is a tetrahedron – keh-muk in Vuhlkansu. It has four triangular faces, six straight edges, and four vertex corners."

"A tetrahedron," Spock repeated slowly, committing the word to memory.

His father launched into a detailed explanation of various polyhedra and their properties and Spock listened with rapt attention. It was a novel experience; his father was rarely home and when he was, he didn't often engage Spock in dialogue. He noticed his mother from the corner of his eye, watching them with a peculiar expression on her face. She was smiling, but Spock could not identify the source of her amusement.

"So if the number of equilateral triangles is expanded to twenty," his father continued, "the resulting object is called an icosahedron. Describe it."

Spock thought for a moment, picturing the structure in his mind and recalling the definitions his father had explained. "Twenty faces, thirty edges, and ten- correction, twelve vertices."

"Correct," his father replied with a swift nod. Spock stood a little straighter. "Now, icosahedrons have a number of symmetrical properties, most notably that they-"

"Ahem," his mother coughed.

Spock and his father looked away from one another to observe his mother grinning widely with her arms crossed over her chest. "I hate to interrupt because this has been very educational, but I'm putting my foot down – we're not making a gingerbread icosahedron."

"Of course not," his father replied with a little sigh. "That would be inefficient and illogical."

"Well, I was promised an efficient gingerbread house, and that's what I intend to have," she grinned.

He raised his eyebrows and glanced back at Spock. "Very well."

His father began a lengthy explanation about how the volume of dough and the estimated thickness of the walls would affect the size of finished product. They considered secondary constraints such as the size of the cooking sheets and thermal unit, and then his father explained the process of optimizing volume given a finite surface area, describing things like derivatives and intervals.

Spock struggled to comprehend his father's abstract lecture, but he listened closely and did his best to follow along. He was just on the cusp of feeling utterly confused when his mother cleared her throat again. "Sarek?"

"Yes, my wife?"

"How old were you when you first started learning multivariate calculus?" she asked.

His father regarded her carefully. After several seconds, he nodded and turned to consider Spock. "Excuse me."

His father breezed out of the kitchen and Spock looked nervously at his mother. Had Spock disappointed him? He felt an unusual emotion rising into his chest and started to use the techniques his tutor showed him to repress it. It wasn't working.

"Oh, Spock," she sighed, sliding around the corner of the central island to stand next to him. "Your father- he- well, sometimes… he just wants the best for you. Let's get this finished so we can get started on dinner."

"Yes, mother."

She picked up a knife and was about to press it into the dough when his father reappeared in the doorway, brandishing a long measuring stick. His mother's hand froze in midair and she watched as he cleaned the ruler in the sonic sink. He came to stand on Spock's left side and gazed at his wife. "Will you allow us to continue this project?"

Her eyes narrowed but she handed him the knife and backed away. His father set the ruler down on the raw gingerbread. Soon Spock was proudly demonstrating his knowledge of two-dimensional geometry by helping his father calculate the area of the four walls and the roof. When they started cutting into the dough, his father showed him how to use the ruler as a straight edge for enhanced precision.

His mother chuckled a few times and burst into a fit of giggles once, but she watched without further interruption. Soon they had five rectangular shapes on the cooking sheets and his mother slid them in the thermal unit.

His father left to change out of his work attire and his mother began preparing their end meal. A sweet, spicy, slightly savory smell started to drift through the kitchen and fifteen minutes later, they pulled the gingerbread from the oven and set it on the counter to cool.

His father returned wearing his evening meditation robes and the three of them sat down to a hearty meal of bertakk soup. He listened as his parents discussed their day, observing how frequently they touched their fingers together. When end meal was completed, his mother started to clear away the table and Spock and his father returned to task of constructing the gingerbread house.

They used the icing to seal the edges together and Spock learned how to square the corners using the ruler and simple properties of right triangles. Eventually they had a rectangular gingerbread structure with a volume of 14,000 cubic centimeters and a surface area of 2,900 square centimeters.

"We have finished, mother," Spock announced.

She was washing their dishes in the sonic sink, but turned to see the final product. A slow smile spread across her face. "It's a gingerbread… hut."

"Do you approve, mother?" Spock asked.

"Of course I do," she replied, wiping her hands on her hips and joining them at the kitchen island. "It's perfect."

"Perhaps you could clarify your standards of perfection," his father said.

"Anything made for me by the two men in my life," she replied, extending her two forefingers to her husband. He returned the gesture and they stared at each other for several seconds before she broke away.

"Ok then," she announced, clapping her hands together. "Let's decorate it."

She picked up the bag of icing and enlisted Spock's assistance in adhering the candies in a random arrangement on the roof and walls.

"Why not attempt a uniform pattern, mother?" he asked.

"Because half the fun is making whatever your imagination tells you to," she explained, drawing a lopsided window on the flat roof.

He heard his father sigh behind him, join fingers with his mother in ozh'esta, and say, "Illogical."

Stardate 2270.97

Lyra sat at the small table and watched her forefather mix the dark-colored dough. Cooking was a fascinating process – the practical application of chemistry and thermodynamics, as her father would say. Lyra was used to food replicators, having lived her entire life in Starfleet housing in San Francisco.

They had journeyed to New Vulcan to visit Sarek, her forefather, before her parents received a new assignment. Her mother told her she'd met her forefather in her infancy, but she had no recollection of the encounter. She wasn't sure what to think of him: he was a tall, imposing man who rarely looked at her, let alone spoke to her.

She knew it was illogical to be afraid of the man, but when her parents left her in his charge for the afternoon to meet with Starfleet officials at the space dock in orbit, Lyra had pleaded with her mother to take her with them.

"We'll only be away a few hours," her mother had reassured her. "You should take the time to get to know your grandfather. It's the holidays and we won't get to see him again for at least a year when we leave on the Enterprise."

Once her mother and father were gone, her forefather had attempted to engage her in conversation. He asked if she celebrated the Terran holiday season and during the course of their awkward discussion, she mentioned she'd watched her bibi – her mother's mother – bake pies once for the New Year festival. He asked if her father had ever shown her how to assemble a gingerbread house, and when she told him they replicated one every year, his brow had furrowed and he asked if she would like to help construct one. She had agreed, thinking they would use the replicator, but now her fingers were caked with white flour and brown sugar and she found herself marveling at the appealing aromas of cinnamon, ginger, and cloves.

"Now we must chill the mixture to solidify the lipids," her forefather announced, placing the dough in a bowl and placing it in the refrigeration unit. The longer the lipids remain in solid form, the less the dough will spread during the baking process."

"Lipids?" Lyra asked.

"A class of organic compounds insoluble in water but soluble in organic solvents. Examples include oils, waxes, and fats."

He explained the chemical properties of each, using terms like hydrocarbons and functional groups, and though Lyra didn't completely understand – she wasn't yet six years old, after all – she was still fascinated. She always marveled at her father's endless supply of knowledge – her father seemed to know everything – but her forefather seemed to know more.

They worked together to make a thick icing from confectioner's sugar, water, and a waxy substance he called artificial butter, and he paused to explain the chemical makeup of each and how they mixed together to form the sweet icing. When they were done, he filled several bowls with little candies from the cupboard, and Lyra found the appeal of the bright sweets nearly irresistible.

"You may help yourself," her forefather said, turning his back to her to remove the dough from the refrigeration unit.

Lyra fought back a little smile and dipped her fingers into the bowl of red candies. Cinnamon. Delicious.

"What do you know of elementary geometry, Lyra?" he asked, setting the dough on the counter and extracting a wide cylindrical object from a drawer.

She had only started learning about circles, triangles, and squares in the faculty preschool at Starfleet Academy before they had left from Earth the previous week. She often found the content of the lessons simple and boring and worked with her parents in the evenings to dive into deeper depths on subjects like math and science. Lyra particularly loved math.

"I can calculate area and perimeter," she offered.

"Very well," he replied. He left his post at the counter and strolled from the kitchen, returning a few moments later with a short stool and a long measuring stick. He set the stool on the floor by the counter, washed the ruler in the sonic sink, and motioned for her to join him.

She ascended the stool and listened closely as he started to explain various properties of geometric shapes. Lyra was captivated by the relationships of triangles – a triangle that had equal sides always had an area of two times the height divided by the square root of three. Always! How had she never realized this before? It was so obvious.

She supposed it was because her father had only started teaching her about square roots earlier that week. She tried to commit the equations to memory to share with him later that evening when they practiced her studies. She was determined to understand these wondrous mathematical rules in better detail.

Her forefather laid the ruler down on the dark gingerbread dough and started to ask her how she would determine the surface area of a three dimensional object when she noticed her mother was standing in the threshold, arms crossed and an enormous smile on her face.

"Hello mother," she said. "Forefather and I are making a gingerbread house."

"Yes, I see," her mother replied, venturing into the kitchen and taking a seat at the breakfast table to watch.

"Nyota, have you seen-" Her father appeared in the doorway but paused when he observed their effort.

"Hello father," Lyra exclaimed. "Did you know the length of any side of a right triangle can be found by squaring the other two sides, adding them, and taking the square root of the sum?"

"I did," he responded, tucking his hands behind his back and taking several steps forward.

"And so Lyra, if the length of this edge is 35 centimeters and the height of this edge is 20 centimeters, what is the diagonal distance from this corner to that corner?" her forefather asked, pointing to the rectangle they'd just cut in the dough.

She closed her eyes and worked to manipulate the numbers into the correct answer. "40.3112887415 centimeters."

Both her father and forefather raised their eyebrows at her response and she started to second-guess herself. Had she miscalculated? She started to run the numbers in her head again but stopped when her forefather declared, "A precise answer. Commendable."

"She has acquired her mother's gift for mathematics," her father explained, addressing her forefather.

Lyra heard a soft snort of laughter from behind her and craned her neck to see her mother rising to her feet to join them. Her parents watched as her forefather showed her how to use the ruler as a straight edge to cut more precise shapes, and soon they had cut two squares measuring 20 centimeters by 20 centimeters and three rectangles with the dimensions of 20 centimeters by 35 centimeters. They placed the pieces on baking sheets and inserted them into the thermal unit while her forefather continued to drill her on increasingly complex arithmetic.

The timer sounded fifteen minutes later and it was time to extract the gingerbread building materials from the thermal unit. Her forefather supervised as she donned the heavy mitts and placed the baking sheets on the counter to cool. She listened as the adults talked among themselves for a while, discussing timelines for their departure from New Vulcan and their new yearlong mission aboard the Enterprise-B.

Lyra didn't know what life would be like on a starship. Her mother promised it would be an adventure and her father assured her she would attend school with several other children and get see her godfather, James Kirk, more often. It sounded both appealing and terrifying.

She was soon lost in her thoughts, caught between excitement and worry. She struggled to suppress both emotions, but found she lacked the experience to confront such powerful feelings. Her father had only begun teaching her to meditate and control her emotions several months earlier when she'd spied him in his meditation chamber and asked what he was doing.

"Are you ready, Lyra?" She snapped back to the present and saw her forefather holding a bag of icing with the tip cut away.

"Yes, forefather," she replied, hoping he hadn't noticed her inattention.

He glued one of the square and rectangular gingerbread pieces together with icing and taught her how to ensure the angle was precisely ninety degrees using the formulae he'd introduced earlier. He allowed Lyra to finish assembling the structure, and when she was finished, she looked to him for approval.

"Now all that remains is to ornament the end result," her forefather explained, offering her the bag of icing.

Lyra wasn't sure where to begin, so he showed her how to put a small amount of icing on the roof and embellish it with one of the candies. Lyra started to make a neat little row of purple gummies, but her forefather stopped her.

"What is wrong, forefather?" she asked. "Is this incorrect?"

"There is no correct way," he replied. "But a very knowing individual once informed me that one half of the fun of constructing a gingerbread house making whatever your imagination tells you to."

She furrowed her brow and stared at the gingerbread house. Her father picked up a red candy and placed it in the neat row of purple gummies, ruining its uniformity. Her mother laughed, and soon her forefather and her parents were helping her attach various candies to the exterior of the gingerbread house in an arbitrary fashion.

"You know, this doesn't seem very… logical," her mother mused, watching her forefather sketch a crooked window on the roof of the house with the icing.

Her father and forefather glanced at her mother and replied in unison, "It is not intended to be."