If an unusual flash of color in a stark November garden draws your eye, the attention grabber might be a common summer annual. Its skeletal, upright spires hold fast against the northern wind in frost-bitten mulch beds. Even in death it holds a shade of its former crimson glory — its Greek name amarantos means “unfading” — a nod to its resilient nature. But amaranth’s claim to fame isn’t its pigment; it is noteworthy for its fecundity.

Hyper-Efficient Reproductive Machine

Tucked inside the plant’s soft, feathery spikes is a prolific seed factory. Amaranth doesn’t wait for bees; the plants self-pollinate or let their seeds fly on a breeze. When the spike dries in autumn, the grains drop to the earth or hitch a ride with birds and rain. Some wild species snap at the base and become tumbleweeds, shaking loose their progeny with every bounce. In the soil, the seeds can lie dormant for decades until a passing foot or shovel stirs them into the sunlight.

Even though amaranth is an annual, its flower heads can crank out up to 500,000 microscopic grains. The seeds comfortably sleep through sub-zero Hudson Valley winters, unfazed by ice and snow. Come May, the multitudes wake up and sprout. Amaranth mimics a perennial through aggressive overproduction; once invited into your garden, it becomes a permanent tenant.

A Crop That Sustained Empires

As a dietary staple for millions, amaranth stretches across human history. In the Andes, the Incas integrated it into terrace systems alongside quinoa to secure crops that could thrive in poor soil with little water. Similarly, the Maya of Central America cultivated amaranth for millennia, consuming both its protein-dense seeds and vitamin-rich leaves.

Other communities developed specialized uses: The Hopi grew a deep-red species as a food and textile dye, while Mississippi River basin groups relied on amaranth as a seasonal nutritional failsafe. The ultimate integration of amaranth was in the Valley of Mexico with the Aztecs, who elevated it from a vital crop to a sacred symbol, even using the seeds as currency. During festivals, popped amaranth seeds were mixed with honey to sculpt statues of their deities, which the community consumed at the ceremony’s conclusion as an act of religious devotion.

Cortés Was Anti-Amaranth

When Spanish forces arrived in the Valley of Mexico in 1519, Hernán Cortés realized the plant’s nutritional value fueled Aztec resistance, while its spiritual significance threatened Spanish control. Consequently, Cortés banned the plant, burning fields and punishing growers.

Aztec civilization survived by integrating ancient traditions into an emerging Mexican culture, proving that the Spaniards could not defeat botany. Amaranth seeds simply waited out the occupation in mountain cracks and ditches. It soon hitched a ride on global trade routes, exploding across Africa as a leafy green and traveling to the Himalayas, where it is consumed in India and Nepal as both a vegetable and a grain.

It’s a Faker: It’s a Pseudo-cereal

True cereal grains once powered historic gristmills along local creeks, where Dutchess County farmers processed wheat, rye, and barley for regional families and downriver export. Those true grains rely upon gluten to give traditional dough its elastic, chewy texture. But pseudo-cereals — such as buckwheat, quinoa, and amaranth — are broadleaf plants, not grasses, and are inherently gluten-free.

Amaranth is a botanical “faker” because its tiny seeds mimic grains in the kitchen, yet it lacks the genetic code to produce gluten. This is an asset for a gluten-free diet, but for bread-baking, amaranth requires binders for lifted structure.

Though pseudo-cereals lack gluten, they provide a rare, plant-based source of complete protein. There are nine essential amino acids the body cannot produce on its own, and pseudo-cereals provide them in the ratios it needs, whereas grains do not. Gram for gram, these ancient seeds also provide dietary fibers and vital minerals like magnesium, iron, and zinc, delivering sustained energy with a low glycemic impact.

Turkey Table Buddy

Given those health benefits, you should add this global survivalist to your Thanksgiving table. The tiny pocket of moisture sealed inside its hard outer hull means it will pop like corn, making it a great snack. Those nutty puffs can be mixed into stuffing, soups, and stews for added texture. Cooked amaranth can be served as a side dish or in a fall salad, and amaranth flour can be combined with other flours in baked goods.

Glen White of Clinton uses it in soups and stews for a change of pace from pasta. “I also make it into a porridge with fruit and yogurt,” White says. “It has an earthy flavor profile. Adding sweetener and cinnamon makes it a comforting dish.”

Classroom- and Homeschool-Ready Activities and STEM Books
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Global Superweed Worthy of a Thanksgiving Invite was originally published in Classroom on Medium, where people are continuing the conversation by highlighting and responding to this story.

Imagine yourself training a dog to perform a new trick. You don’t hand it a guidebook on how to do that trick. When the dog performs a trick correctly, you reward it with a treat. Over time, the dog learns to associate the correct actions with rewards.

How can a robot learn without being told every movement?

A robot learns how to walk in the same way as a dog learns how to perform a trick. Instead of specifying every movement, the robot is given feedback about its behavior. Let’s take a look at Figure 2. The robot (the agent) “lives” in an environment. Its sensor generates a set of measurements from the environment, called the states. The robot evaluates the states to decide the action to take next. If the action is correct, the robot’s program gives a reward; otherwise, it is penalized. Over time, the robot learns to associate the correct actions with the reward. This method has a name: reinforcement learning.

Reinforcement learning is a subset of machine learning where an autonomous agent learns to make decisions by interacting with the environment. Rather than receiving the correct action for every situation, it receives a numerical reward and learns a policy that aims to maximize the reward accumulated over time. Let’s compare this with two other approaches in machine learning: supervised and unsupervised learning. In supervised learning, the human engineer applies correct labels to the training data. The machine then learns to classify the data based on the given labels. Meanwhile, unsupervised learning simply throws the data to the neural network, leaving the neural network to cluster the data on its own. In this case, the data still gets clustered according to the features, but the data clusters are unlabeled. Reinforcement learning does not fall within the category of supervised or unsupervised learning. Instead of labeling or clustering data, reinforcement learning rewards correct or good action and penalizes incorrect actions. The rewards reinforce the connection to the correct actions, and the agent eventually learns to make correct actions.

What are the policy, reward, and value function?

A reinforcement learning system has four main elements. The first is the policy, which defines the agent’s behavior by assigning an environmental state to a specific action. The second is the reward signal, which determines whether an action gets a reward or not. The third is the value function. This one works like the reward function, but instead of giving immediate feedback, it estimates how much reward the agent can expect to accumulate from the future states. The fourth is the model. This is optional. Its function is to allow agents to predict the environment’s behavior for possible actions.

Reinforcement learning vs classical control

Reinforcement learning emerged as an alternative to classical control algorithms. In classical control, the engineer must make a mathematical model before designing its controller. The robot computer then calculates the necessary action based on the constructed mathematical model. This approach relies heavily on the engineer’s knowledge. It is not uncommon that the mathematical model is so difficult that constructing the control law becomes a really difficult challenge.

In contrast, reinforcement learning can perform without an explicit mathematical model. The robot learns proper control commands from observing its experience. In this sense, the robot behaves like a baby that is learning how to walk. It learns which actions lead to a stable gait, and which ones do not.

There is a catch, though. Often, before RL is implemented on a real robot in a real environment, the learning process happens in a simulator. A simulator is used to speed up the training process and avoid damage that might occur if the training were conducted directly in a real environment. In this case, an explicit mathematical model of the robot is necessary because the simulator has to know what the robot will do given a specific command.

Deep Reinforcement Learning

After the rise of deep learning, the architecture of reinforcement learning can take the form of a massive multilayer neural network (Figure 3). Deep learning relies on a massive neural network to turn raw input into meaningful data representations. Deep reinforcement learning can handle large, high-dimensional inputs better than the traditional reinforcement learning. Traditional reinforcement learning lacks this capability, so combining deep learning and reinforcement learning makes deep reinforcement learning more powerful. This is not to say that all reinforcement learning involves deep learning though; a good portion of reinforcement learning still has the traditional architecture.

Example

Let’s consider an example in a Sim2Real (Simulation to Reality) workflow. The first step in training a robot in a simulated environment starts with building a simulation of the specific robot. The robot’s specific physical parameters, like its mass, joint axes, limits, and moments of inertia have to be passed on to the simulator. The goal of this stage is not to build a perfect humanoid, but to build an adequate representative model that matters for walking. After completion, we can move on to modifying the computer model with the actual values from the actual robot hardware. Even a carefully calibrated simulation differs from the real robot. In this stage, the simulation conditions can be varied so that the policy learns to tolerate a range of conditions instead of relying on an idealized setting.

We can proceed by defining what the policy observes and controls. The practical starting architecture is a policy that outputs joint-position targets. These set points are the input to a low-level proportional-derivative controller whose job is to execute the joints’ movement. The last step is to define the walking objective. The reward should encourage command tracking while discouraging undesirable motion, excessive effort, abrupt commands, and unwanted collisions.

After training in simulation is complete, it is time to validate the algorithm. At this stage, the controller is transferred to the robot, then it is made to run in a physical environment. Its data log must be recorded. In this stage, if it works, that means the training can be finished, and it can be deployed. However, if there is any mismatch between the desired behavior and its actual performance, the robot must undergo retraining to eliminate the mismatch. After training and testing are complete, the robot can be deployed in its intended environment.

Epilogue

Reinforcement learning removes the need to rely solely on mathematical models. It has transformed how a humanoid robot learns how to walk. This doesn’t mean that hard work is unnecessary though; there’s still a lot to do even with reinforcement learning at our disposal.

How Reinforcement Learning Helps Robots Learn to Walk was originally published in Classroom on Medium, where people are continuing the conversation by highlighting and responding to this story.

Several years ago, I was attending a class on robotics. Upon arriving on the chapter about humanoid robot, the lecturer told us that building a humanoid robot is so difficult. I was surprised to hear that. After all, walking in a room and picking up a fruit are ordinary human activities. So how could they be really complicated?

For decades, we have been dreaming about robots that look and function like a human, and we call such machines a humanoid robot. The name “humanoid” means “human-like”. We have been making much progress, but we are still far away from making a humanoid robot that perfectly perform tasks a human can do, such as keeping the body balanced, walking, planning its path, understanding its environment, and picking an object. A humanoid robot must turn familiar human actions into measurable, controllable processes, and make sure they work together.

Walking

Let’s begin from the easiest: keeping balance. Translating this to the language of physics means positioning the center of mass correctly. For a human body, the center of mass is located at approximately below the belly button (Figure 1). Its projection on the floor is supported by a polygon bounded by the contact points of the feet with the surface. The name of this polygon is the support polygon. To maintain stability, the projection of the center of mass should remain within this polygon. Now let’s see what happens if one foot is lifted away from the floor. Half of the polygon area disappears, and the center of mass does not stand above a sole of the foot. To maintain balance, you’ll find that the upper body will bend slightly to the direction of the foot that isn’t lifted.

We humans take the walking ability for granted. But for robots, it’s not the case. Building a bipedal robot that can walk means working with complex physics and mathematics. At this point, there is a serious problem: the shape of the robot body is too complex for a comprehensible mathematical model. To tackle this challenge, the robot can be modeled as an inverted pendulum (Figure 2). An inverted pendulum is the opposite of the ordinary pendulum. Ordinary pendulum can swing at any angle and the mass can return to its initial equilibrium. In contrast, if the mass of an inverted pendulum swings, without external intervention, the mass would not return to its initial equilibrium. This model is simple yet powerful. The pendulum’s lumped mass is located at a certain height above the floor, representing the center of mass that also lies at the same position. This simple analogy exposes the instability of the robot: give a strong enough kick to the robot and the robot will fall to the floor.

In the walking process, at first, two feet are in contact with the floor. The center of mass lies above the support polygon. Let’s say that the robot will step its left foot forward. Before that, the robot must shift its torso so that the center of mass lies above the right foot. Then it steps the left foot forward and swing the arms to balance the angular momentum of the left foot. After the left foot comes into contact again with the floor, it can swing its torso back to the center. This process is then repeated in the next step. Walking, which is so instinctive for humans, turns out to be a complex process.

How does a robot see?

Being able to walk does not necessarily mean that the problem related to moving from one point to another is completely solved. Humans understand the environment they’re in through their eyes and brain. The eyes see what objects lie ahead, and the brain understands the surrounding environment. In a similar way, a robot sees with cameras and its onboard computer creates an understanding of the environment.

Robot vision is a difficult problem. Humans possess its vision ability from evolution. For a robot to have similar capability, an engineer needs to program its computer so that it can interpret the images from its cameras. Similar to humans that have two eyes to create 3-dimensional perception, a robot needs two cameras. Each camera views the scene from different positions. The onboard program matches two corresponding images and uses their disparity to determine the distance of the objects (Figure 3). Using this technique, it can estimate its position relative to the objects and construct a 3D map of its surroundings.

Path Planning and Obstacle Avoidance

The robot uses the map of objects to plan its path and avoid collision with surrounding objects. As an example, take a look at the map that shows several objects in the way of a robot (Figure 4). The robot needs to move from point A to point B. If there were no objects standing in the way, the robot could have walked in a straight line. In this case, though, there are objects that stands around the space and between the midpoint and point B. So, the robot starts at point A, then walks to point P at the middle of the environment. There, it detects that there is an obstacle, so it scans its surroundings and finds that there is an available space to its left. Therefore, it decides to turn left and walked straight for a moment until it reaches point Q. Then it finds an obstacle in front of it and an available space to its right. At this point, it turns right and walks straight for a moment until it reaches point R. Then it finds another obstacle in front of it, an available space to its right, and the finish point B. For one last time, it turned right and walked straight for a moment until it arrived at the finish point B.

It might sound surprising that the simple path planning process can be so tedious. After all, as humans, we don’t seem to think when we move in an environment. We avoid obstacles instinctively. Well, we should remember this: no robot comes pre-programmed with built-in ability to plan its path, so it is up to the engineer to program that ability on the robot.

Grasping

Now that our robot can walk, map its surroundings, plan trajectories and avoid obstacle, we need to equip it with a grasping ability. Again, for humans, this task couldn’t be easier, but for robots, it requires a really careful calculation and programming. Let’s assume our robots would have five fingers. Suppose that there is a table, and on that table, there is an apple. The robot must take the apple and hold it in one of its hands. First, the robot takes pictures of the apple with its two cameras and estimate the distance and orientation. It represents the apple’s visible surface as a collection of points in three-dimensional space, called a point cloud. This representation helps the robot to plan where to grasp and how the pose of the hand will be. Then, it computes how to bring the hand to the chosen grasp pose and its configuration when it’s grasping the apple. After that, it moves the hand according to the plan and put the fingers around the apple. The force applied to the apple should not be too weak as the object might fall, but it should not be too high, lest it might damage the apple.

General Purpose vs Limited Purpose Robot

When it comes to humanoid robotics, the ultimate dream is to create a robot that functions like us: a general-purpose robot. This is actually very hard to do. Humans seamlessly combine mobility, manipulation, perception, and intelligence. Current humanoid robots usually excel in specific tasks, not general ones. For example, Tesla Optimus Gen 2 / V3 is designed for full factory shifts to lower the cost of mass production, and 1X NEO is built for home assistance, emphasizing safety, design, and unsupervised operation. We can use them for the purposes they have been designed for, but not otherwise. Tesla Optimus and 1X NEO will not function if someone uses them at both the factory and home environment. General purpose humanoid robots will also require the use of AGI (Artificial General Intelligence), which hasn’t currently been reached yet. There are still plenty of challenges for humanoid robots.

References

[1] Toshio Fukuda, Paolo Dario, and Guang-Zhong Yang. Humanoid robotics: History, current state of the art, and challenges. https://www.science.org/doi/10.1126/scirobotics.aar4043

[2] John Pavlus. The clumsy quest to perfect the walking robot. https://www.scientificamerican.com/article/the-clumsy-quest-to-perfect-the-walking-robot/

[3] Shilong Sun, Haodong Huang, Chiyao Li. Advancements in humanoid robot dynamics and learning-based locomotion control methods. https://www.oaepublish.com/articles/ir.2025.32

[4] Saeed Saeedvand, Masoumeh Jafari, Hadi S. Aghdasi, and Jacky Baltes. A comprehensive survey on humanoid robot development. https://www.cambridge.org/core/journals/knowledge-engineering-review/article/abs/comprehensive-survey-on-humanoid-robot-development/CC2428375A1F38DD94079125FD8A45B6

Why Building a Humanoid Robot Is So Difficult was originally published in Classroom on Medium, where people are continuing the conversation by highlighting and responding to this story.