Two Months of Soylent


Though Soylent is experimental, the results are reproducible. I am very optimistic about the future of this idea. After the 30 days experiment, I decided I got some good data and I was going to eat whatever I wanted. This past month 92% of my meals were soylent. I haven't given up food entirely, and I don't want to. I found if I wake up early I sometimes crave a nice breakfast, I've gone to lunch meetings, and on the weekends of course I love eating out with friends. Eating conventional food is a fun leisure activity, but come Monday I usually have a strong craving for a tall glass of Soylent. In fact, with the money I save, I have the freedom to eat well when I do go out. I didn't give up food, I just got rid of the bad food. Innovation to me is as much about removing that which is unnecessary as it is about adding new things that are useful. This idea has done both for me.

Soylent doesn't force you give up food any more than email forces you to give up talking. The point is having another option. Perhaps this does not constitute the ideal diet, but I am quite confident that it is healthier than any easy diet, and easier than any healthy diet. I'm touched so many people are concerned about my intake of possible unknown essential nutrients. No one seemed to worry about me when I lived on burritos and ramen and actually was deficient of many known essential nutrients. The body is pretty robust. If you can survive on what most Americans or Somalians eat, you can surely survive on Soylent. I'm no longer just surviving, though. I'm thriving.

Trials Update

The first trials are underway. I apologize if you were not chosen. A handful of locals of diverse builds have been testing it, but the feedback so far has been segregated. I think I have a good model of the male proportions. For the males, besides the obvious fat loss and muscle gain, scores have increased, testers report better sleep and increased focus, and some even improved emotional health. There are many second-order benefits to being healthy and well fed. The women are not as happy, reporting they still feel hungry. Clearly this still needs some tweaking.

I'm trying to find the amount of discipline this takes. I personally found I did not have enough discipline to be a vegetarian, but feel Soylent takes much less. Eliminating something entirely from a diet is difficult, and probably unnecessary unless one does so for moral reasons. Eating unhealthy foods only for enjoyment just a few times per week satisfies my psychological cravings, and drinking Soylent the rest of time makes me very healthy. Sustainability is about reduction, not elimination. I would like to test on someone that tends to make poor dietary choices, but most people I know in San Francisco are frustratingly disciplined and healthy.

Personal Data

As for myself, I came across some problems. My original mixture gave me 1550 kcal/day. I hypothesized that "caloric restriction" had health benefits and that the human body could survive on fewer "higher quality" calories. I now consider that a failed hypothesis. After 30 days I exhausted my reserves of fat and started to feel hungry, lose weight and muscle mass, and my gym performance regressed. I ran some numbers and decided to increase my intake to 2629 kcal/day. I quickly put the weight back on, my chest and arms filled out, and I felt much healthier. My mixture now has 409g of carbohydrates, 65g of fat, and 102g of protein. I also stopped running 7 miles, which is really unnecessary and potentially harmful to the heart and joints. I just do 3.14 mi, which is quite easy, and weights, making sure I maintain the ability to easily benchpress my weight. That's good enough. I'm an engineer, not an athlete, but I like having the option to bulk up if I wanted to.

Since the FDA recommends a lot of potassium I tried experimenting with the amount out of curiosity. At about 9g/day I induced an overdose and my blood pressure and heart rate rose, along with experiencing muscle weakness and fatigue. Not that bad. Much easier than Magnesium poisoning. Low potassium affected my circulatory system and focus, but was not nearly as noticeable. I finally settled on 4.5g/day, which is a lot to try to get "naturally". I changed some of the chemicals, swapping chelated iron for ferrous gluconate and magnesium citrate for magnesium gluconate. It seems the gluconic acids have the best balance of bioavailability and cost. Choline is now part of the daily mix, as is Lithium, iron is down to 9mg, I dropped calcium a bit based on my blood work (which is otherwise excellent)1 and I add an emulsifier to aid the mixing of the oils. I now take a probiotic too, just in case. Believe it or not the optimal amount of fiber I found is only 1.2g. I know the FDA recommends much more, but that's probably assuming a more conventional diet. Also my room doesn't have a window, so I throw in some extra Vitamin D.

If you didn't see the update to the original post, I've been keeping better books and found my original cost calculation was wrong. At the old macronutrient proportions it actually cost around $100/month. The raw materials to provide me with 2629 kcal / day purchased at personal scale costs $154.82 per month, plus shipping. The cost of protein is by far the biggest issue at the moment. I'm confident I can bring this down, but it's already cheaper than living on groceries or fast food. By comparison, a 150lb female would consume about $102 worth / month. Based on the quotes I've gotten from suppliers, I am assured production at scale is entirely possible and would lower the cost dramatically.

Some people tell me going "ketogenic", or reducing carbs is healthy. I am now skeptical of this claim as lowering carbs makes me feel hungry and tired, and the drink taste less sweet. Perhaps it would be possible after an unpleasant transition period, but I don't see the ultimate gain and I have not found sufficient evidence for the benefit of this diet outside the treatment of epilepsy. To be fair, there isn't a whole lot of evidence Soylent is healthy either, but I feel completely satisfied with my health and do not feel the need to improve it.

I've also experimented with adding nootropics, specifically combining Choline with Pramiracetam and L-Theanine. I think it worked. My scores jumped 30%. Subjectively, when coding it seemed like the lines would write themselves. Everything was 'smoother', reaction times lower, everyday phenomena more interesting. However, it was a little stressful that I wasn't able to turn it off. I definitely wouldn't want to feel this wired on the weekend, but it's great for knocking out a lot of work. Though the euphoria of the first couple of weeks has faded, I have reached a happy, healthy, productive steady state that I really enjoy.

Finally, since many have asked, yes I do drink alcohol. In fact I probably drink more than I should. Soylent is great for hangovers! And it mixes pretty well with vodka, though I wouldn't call it my favorite drink. Also this may harm the probiotics.

When Can I Get Some / Kickstarter

Several individuals experienced in chemistry have already figured out how to make it on their own. I'd like to keep it this way for now, as I trust them to measure the ingredients properly. I don't have nearly enough capacity to support the interest expressed so far, so I have decided to launch a Kickstarter campaign. If accepted and successful, this will fund a larger controlled study of the effects, allow me to scale up production, improve control, and, my ultimate goal, use technology to alleviate global hunger, malnutrition, and improve the total health of the human race, especially the poor. If you can help me make a video please contact me.

New Hypothesis

I appreciate the skepticism offered so far. Some was useful, such as encouraging me to add a probiotic or that my protein intake was too low. I definitely didn't get this right on the first try. Though I don't think caloric restriction was valid, perhaps the longevity benefits came not from restricting calories, but the food that contains them. Scars that I'd had for years are barely visible now. People who haven't seen me in months say I look younger. Am I going to live longer? I'm certainly living better, and it's all thanks to chemistry.

For updates join the email list at and/or follow me on twitter: @robrhinehart

update: discussion board up here:

Blood Work (pdf)

What’s In Soylent


(this is the follow up to "How I Stopped Eating Food")

Edit July 2013: This was a prototype. While similar in spirit, the final soylent recipe differs in several ways and has been subjected to rigorous testing and expert evaluation. Also it tastes better.

There is precious little good data in nutrition science. Every study I've seen shows poor statistical methods, conflicts with other studies, or does not show statistically significant results, usually all three. It's a difficult field because there are simply too many variables and the parameters are difficult to control precisely. This is why diets are fads. I decided to ditch nutrition and focus on biology. The proportions in Soylent are closely based off of the recommendations of the Institute of Medicine (IOM), though I added a couple extras and changed a few based on my testing. Here is what my body needs.

Carbohydrates (400g)Any molecule consisting only of Carbon, Hydrogen, and Oxygen. Flour, corn, bread, rice, pasta, your cells don't care. What you need is D-Glucose. The Citric Acid Cycle metabolizes glucose and generates ATP, the cellular 'currency' for energy. Carbs can chain together and come in the form of monosaccharides (like fructose), disaccharides (table sugar), oligosaccharides, or polysaccharides, which are very long chains. Short chains get metabolized very quickly, leading to a 'sugar rush', and long chains can be difficult to digest. I use only oligosaccharides, like Maltodextrin, for Carbohydrates. This mechanism can also metabolize protein and fat, but the brain can only use Glucose for energy. In fact, the brain uses 25% of the body's glucose, though it accounts for only 2% of its weight.

Protein (120g): Protein is a very general term. What your body needs are 9 'essential' (meaning the body cannot produce it itself), amino acids: Histidine, Isoleucine, Leucine, Lysine, Methionine, Phenylalanine, Threonine, Tryptophan, and Valine. Eukaryotes use 21 different amino acids for protein synthesis. The human genome contains approximately 20,000 protein coding genes. It's a complex system. Without these essentials there are some proteins you will not be able to produce.

Fat (65g): Fat has gotten a bad rap. Without it you wouldn't be able to absorb some essential vitamins, like A, D, E, and K. Fats are triglycerides, and can be saturated or unsaturated, depending on the bonds within the carbon chain. Fat maintains healthy skin and hair, and cushions the body's organs. Some fats, though, like trans-saturated fats, are difficult for the body to metabolize, and have been linked to heart disease and obesity. I get all the fat I need, in nearly perfect proportion of saturated and unsaturated, and no trans fats, from olive oil.

Cholesterol(X): Cholesterol is used in cell membranes and intracellular transport. However, the body is able to synthesize it on its own and regulates the rate of production. So, even though the IOM mentions it I feel it's more of a maximum than a recommendation. Soylent has no cholesterol whatsoever.

Sodium(2.4g): You'll notice a lot of the elements the body needs are ions. Cells communicate with action potentials, electrical voltage differences which accumulate due to the presence of positive or negative ions. Sodium ions are used to regulate blood volume, blood pressure, pH, and osmotic equilibrium. Sodium and Chloride are conveniently found in table salt.

Potassium(3.5g): Potassium is important in neurological functioning, which is one reason it bothers me practically no one gets a full 3.5g / day. Raw Potassium is extremely reactive, so I use potassium gluconate, C6H11KO7.

Chloride(3.4g): Chloride is a negative ion, formed when Chlorine gets an extra electron. It's used in metabolism and overall pH balance.

Fiber(40g): Fiber is not digested by the body. It helps maintain a healthy digestive system. My digestive system is quite healthy as the only thing that it has to get rid of is the fiber itself.

Calcium(1g): Strong bones and teeth! Also used in muscle operation and the electrical system of the heart. Very important. I consume Calcium Carbonate, CaCO3

Iron(18mg): Iron is used by Hemoglobin in the blood to efficiently transport oxygen. Iron deficiency is one of the most common nutritional deficiencies. If you are a vegetarian I recommend taking a supplement. I dissolve iron chellate in fat separately before adding it to the mixture. 

Phosphorous(1g): Part of the structural framework for DNA and RNA. I use monosodium phosphate.

Iodine(150ug): Constituent of Thyroid Hormones, which regulate basic metabolic rate through gene transcription.

Magnesium(400mg): Another ion, used by many enzymes to catalyze reactions. Be careful, magnesium overdose is very unpleasant.

Zinc(15mg): Used by enzymes in transcription factors, which control the expression of select genes.

Selenium(70ug): Used in some amino acids and the Thyroid gland. Careful, can be toxic in large doses.

Copper(2mg): Used in electron and oxygen transport.

Manganese(2mg): Similar to selenium, used as a cofactor in many enzymes.

Chromium(120ug): Occurs in trace amounts in many foods. Though no certain biological role has been found, there have been reports of chromium deficiency. Just being safe here, may be fine without it, though.

Molybdenum(75ug): Used in the active site of many enzymes. Interesting fact: a shortage of molybdenum held back eukaryote evolution for 2 billion years. Make sure you get your molybdenum, and continue evolving.

Vitamin A(5000IU): Used by the retina of the eye to produce a metabolite necessary for both low-light and color sensitivity.

Vitamin B6(2mg): Or, pyrodoxil phosphate, is a coenzyme for many reactions and macronutrient metabolism.

Vitamin B12(6ug): Key to the normal functioning of the brain and nervous system. Like iron, difficult to obtain from plants so a supplement is suggested for vegetarians.

Vitamin C(60mg): Or, ascorbate, is a reducing agent in many enzymatic and some non-enzymatic reactions. Don't want to get scurvy.

Vitamin D(400IU): Needed for the internal absorption of calcium and phosphate. Can be synthesized by the body from cholesterol given enough sunlight, but is essential in most people.

Vitamin E(30IU): Several functions including antioxidation, gene expression, and neurological function.

Vitamin K(80ug): Post-translational modification. Once a protein is transcribed, it folds (which is a very important problem we don't understand well) and modified by factors such as Vitamin K which affect its final utility.

Thiamin(1.5mg): Used in thyamine pyrophosphate, a coenyzme in the catabolism of sugars.

Riboflavin(1.7mg): Required by a class of proteins called 'flavoproteins'. It's used in the cofactors (non-protein substances that bind to proteins) FAD and FMN.

Niacin(20mg): Niacin binds to and stimulates a certain membrane receptor, GPR109A, which inhibits fat breakdown in adipose (stored fat) tissue. This decreases the amount of free fatty acids in your blood.

Folate(400ug): Folate itself is not used by the body, but its derivative tetrahydrofolate, and a few others, are used in DNA synthesis and repair.

Biotin(300ug): Another coenzyme, used in the synthesis of a few macronutrients.

Panthothenic Acid(10mg): Used to synthesize coenyzme-A (which itself is used in the synthesis and oxidization of fatty acids), as well as metabolism.

Extras not considered essential:

Lycopene(500ug): Essential in some plants for photosynthesis, it is abundant in red plants like tomatoes and carrots. Lycopene is an effective antioxidant and there is preliminary evidence it has an effect on cardiovascular health, diabetes, cancer, and others. Also, not very scientifc, but the males in my family have always loved tomatoes. I wonder if this is because lycopene has an unusually positive effect given our genetics. The only other nutrients in tomatoes are Vitamin A and C, which I get plenty of.

Omega-3 Fatty Acids(750mg): Humans cannot synthesize these fatty acids, and though links with cancer have been largely debunked, there is limited evidence consumption of these substances improve cardiovascular health and inhibit cognitive aging.

Ginseng(50ug): Used in old folk remedies, limited evidence suggest a link with sexual health and lower fatigue.

Gingko Biloba(100ug): Consumed since antiquity in China and Japan, has limited evidence of positive effect on working memory and focus.

Lutein(500ug): A rather small study found that Lutein improves visual function and can inhibit macular degeneration. There is stronger evidence Lutein is linked to the pigmentation of the eye.

Alpha Carotene(140ug): A single study linked this with lower risk of mortality from heart disease and cancer. Couldn't hurt.

Vanadium(100ug): Limited evidence has a beneficial affect on glucose control.

The body is a complex machine. There are a lot of substances and chemicals required for it's optimal operation. However, it is also extremely robust. Many people aren't getting the recommended amount of any of these substances, but the body is able to compensate via complex regulatory systems. This hurts in the long run, though. In fact, turning food in to energy is the primary process that ages the body. By giving it only what it needs, and nothing it doesn't, I am optimistic about the long term effects. The short term effects are already clear.

If you want to make Soylent for yourself, be very careful. We're not making pie here. It's a lot easier to overdose or underdose with the raw elemental form than it is with food. It took me a while to arrange sources for all of these substances, as well. You can get many micronutrients from a simple multivitamin, but their contents vary widely. For others such as K, P, Ca, Mg, check your local lab supply store or university, making sure they are regulated for human consumption. I actually got a lot of mileage out of brewing stores as well.

I am reticent to provide exact brand names and instructions because I am not fully convinced of the diet's safety for a physiology different than mine. What if I missed something that's essential for someone of a different race or age group? Also, the cost is low but some of the ingredients are hard to find and/or must be purchased in bulk which can be an investment, and some of my suppliers are quite small and would have their stock depleted if many people rushed to purchase the exact same item I did. I think it makes more sense to test this more thoroughly, and then produce it at scale.

So…I'll just ship you some of my batch. If you are willing to consume exclusively soylent, and get a CBC, chem panel, and lipid blood test before and after the week and share your results with me it's on the house. Bonus points for getting a psych evaluation before and after. The brain is an organ. I can ship it worldwide but it would be nice if you were in San Francisco so we can meet in person.

Update: No longer running trials. Order Soylent at or join the DIY community at

Update: Choline is included of course

How I Stopped Eating Food


Food is the fossil fuel of human energy. It is an enormous market full of waste, regulation, and biased allocation with serious geo-political implications. And we’re deeply dependent on it. In some countries people are dying of obesity, others starvation. In my own life I resented the time, money, and effort the purchase, preparation, consumption, and clean-up of food was consuming. I am pretty young, generally in good health, and remain physically and mentally active. I don’t want to lose weight. I want to maintain it and spend less energy getting energy.

I hypothesized that the body doesn’t need food itself, merely the chemicals and elements it contains. So, I resolved to embark on an experiment. What if I consumed only the raw ingredients the body uses for energy? Would I be healthier or do we need all the other stuff that’s in traditional food? If it does work, what would it feel like to have a perfectly balanced diet? I just want to be in good health and spend as little time and money on food as possible.

I haven’t eaten a bite of food in 30 days, and it’s changed my life.

The Experiment

There are no meats, fruits, vegetables, or breads here. Besides olive oil for fatty acids and table salt for sodium and chloride nothing is recognizable as food. I researched every substance the body needs to survive, plus a few extras shown to be beneficial, and purchased all of them in nearly raw chemical form from a variety of sources. The section on the ingredients ended up being quite long so I’ll save that for a future post. The first morning my kitchen looked more like a chemistry lab than a cookery, but I eventually ended up with an thick, odorless, beige liquid. I call it ‘Soylent’. At the time I didn’t know if it was going to kill me or give me superpowers. I held my nose and tepidly lifted it to my mouth, expecting an awful taste.


It was delicious! I felt like I’d just had the best breakfast of my life. It tasted like a sweet, succulent, hearty meal in a glass, which is what it is, I suppose. I immediately felt full, yet energized, and started my day. Several hours later I got hungry again. I quickly downed another glass and immediately felt relief. The next day I made another batch and felt even better. My energy level had skyrocketed at this point, I felt like a kid again. But on day 3 I noticed my heart was racing and my energy level was suddenly dropping. Hemoglobin! I think, my heart is having trouble getting enough oxygen to all my organs. I check my formula and realize iron is completely absent. I quickly purchase an iron supplement and add it to the mixture the next day. I have to be more careful not to leave anything out.

On day 4 I noticed how much healthier my skin was. It’s long been dry and rough, with splotches and red bumps but now it’s soft, smooth and clear. Before I rarely had enough energy to go to the gym, but this day I had plenty so I decided to put the diet to the test. I’d been running off and on for several months, never able to do more than a mile straight, but this day I ran 3.14 miles non-stop. This is an irrational improvement.

My cravings and tastes closely matched with my needs. One day I accidentally put in a tablespoon of salt, rather than a teaspoon. I immediately noticed the mixture tasted unpleasantly salty. When I was deficient of iron I felt a strong craving for red meat. As I started running longer distances I craved more carbohydrates. After a week advertisements for fast food looked repulsive. All I crave is Soylent.

Week 2 was rough since I started experimenting with the proportions, trying to find the optimum amount of everything. When I was off I paid for it dearly, but I soon found just the right mixture.

The rest of the month went smoothly. It quickly became part of my routine and I didn’t have to think or worry about it. I was fully expecting to crave traditional food, but I don’t as long as I’ve had my Soylent. Hunger comes from two chemicals triggered by a lack of nutrients, ghrelin and leptin, as well as mechano-sensors in the stomach. If there’s something in your stomach and all your nutritional needs are met you won’t feel hungry. I feel full after drinking a single glass of Soylent and while the smell of Mexican food from the street used to drive me crazy, now I am unaffected. It’s like finding a new partner you really care about. When all your needs are met, you don’t have a desire to stray.



I had my blood tested in two ways: complete blood count and chemical panel, and got a lipid panel near the end. This shows stuff like red/white blood cell counts, Na, K, P proportions, and more. The internist had to bill it as “testing for blood-borne diseases”. She said a lot of providers do not support preventative care, which I thought was strange. I also monitored my heart rate, and bought a glucose meter to track my blood sugar (I’m not diabetic). I am 6’3″ so my BMI was on the upper end of normal at the start. Remember I am not trying to lose weight here.

Week 0 Week 1 Week 2 Week 3 Week 4
Weight (lbs) 204 196 192 188 191
Blood Work report (pdf) report (pdf)
Max run <1mi 3.5mi 5mi 6mi 7mi
Notes low blood sugar,
is this why I always
elt tired?
one belt loop down feel great two belt loops down,
blood work excellent
started getting chilly,
added a few pounds

I wasn’t able to get a lipid test until week 3 but my triglycerides and cholesterol are certainly low now. I have a family history of heart disease, but my risk is now well below average.

I also got my genome sequenced. Genetically, my body’s response to exercise should be typical, along with my response to diet, though on average I should have a slightly higher BMI, consistent with my status before the experiment. My LDL cholesterol is subject to be slightly higher than average, while my HDL levels typical. Though this is only one case, it should be representative of most people since my diet and exercise genetics are typical. Some people can eat all they want and never gain weight, others can’t shed pounds no matter how hard they try. The trick is in the genome, though both extremes are uncommon. 23andme is awesome!


I feel like the six million dollar man. My physique has noticeably improved, my skin is clearer, my teeth whiter, my hair thicker and my dandruff gone. My resting heart rate is lower, I haven’t felt the least bit sickly, rare for me this time of year. I’ve had a common skin condition called Keratosis Pilaris since birth. That was gone by day 9. I used to run less than a mile at the gym, now I can run 7. I have more energy than I know what to do with. On day 4 I caught myself balancing on the curb and jumping on and off the sidewalk when crossing the street like I used to do when I was a kid. People gave me strange looks but I just smiled back. Even my scars look better.

My mental performance is also higher. My inbox and to-do list quickly emptied. I ‘get’ new concepts in my reading faster than before and can read my textbooks twice as long without mental fatigue. I read a book on Number Theory in one sitting, a Differential Geometry book in a weekend, filling up a notebook in the process. Mathematical notation that used to look obtuse is now beautiful. My working memory is noticeably better. I can grasp larger software projects and longer and more complex scientific papers more effectively. My awareness is higher. I find music more enjoyable. I notice beauty and art around me that I never did before. The people around me seem sluggish. There are fewer ‘ums’ and pauses in my spoken sentences. My reflexes are improved. I walk faster, feel lighter on my feet, spend less time analyzing and performing basic tasks and rely on my phone less for navigation. I sleep better, wake up more refreshed and alert and never feel drowsy during the day. I still drink coffee occasionally, but I no longer need it, which is nice.


I used to spend about 2 hours per day on food. Typically I would cook eggs for breakfast, eat out for lunch, and cook a quesadilla, pasta, or a burger for dinner. For every meal at home I would then have to clean and dry the dishes. This does not include trips to the grocery store. Now I spend about 5 minutes in the evening preparing for the next day, and every meal takes a few seconds. I love order of magnitude improvements, and I certainly don’t miss doing dishes. In fact I could get rid of the kitchen entirely, no fridge sucking down power, no constant cleaning or worrying about pests, and more living space. I just need a water source.


Monthly I was spending about $220 on groceries, and another $250 eating out for lunch and the occasional dinner. The average american spends $604/month on food, about half of which is groceries.1,2 As a percentage of income this is actually the lowest of any nation. Kenyans for example spend 45% of their income on food.3 I used to dream of one day being able to afford shopping at Whole Foods, but now it’s irrelevant to me. Consuming only Soylent costs me about $50/month, another order of magnitude improvement, and would be cheaper if I didn’t need the energy for running every day. At scale the cost would be even lower.

Edit: this was a miscalculation from a mistake in my spreadsheet, at personal scale it actually costs me exactly $154.82/month.

The Quantified Diet

It’s wonderful to have full visibility and control over what’s going in to my body. Besides making food allergies irrelevant, it’s trivial to increase or reduce consumption of a particular substance by a precise amount. I am hopeful diabetics could use this to control their blood sugar. I was able to control mine to within about 5mg/dL by varying carbohydrates and fiber. Starting a more intense workout routine? Increase protein and carbohydrates 20%. Want to lose some weight? Reduce fat consumption by 30% (don’t eliminate it entirely!). Blood work shows potassium deficiency? Increase it by the precise amount required. In fact, unless you work on a banana plantation you’re probably not getting the recommended amount of potassium (3500mg is 9 bananas), and never have. Ever wonder what it would feel like if you did?

Social Implications

As any Instagram user knows, food is a big part of life. Food can be art, comfort, science, celebration, romance, or a reason to meet with friends. Most of the time it’s just a hassle, though. Americans only eat out for 12% of meals. I think it would be nice to have a default, healthy no hassle meal. Similar to drinking water most of the time, but wine or beer when you’re socializing. If you saved money on food at home you would have the freedom to go out more often.

I for one would not miss the stereotype of the housewife in the kitchen. Providing diverse, palatable, and nutritious meals for an entire family every day must be exhausting. What if taking a night off didn’t mean unhealthy pizza or expensive take out? How wasteful society has been with its women! The endless hours spent cooking and cleaning in the kitchen could be replaced with socializing, study, or creative endeavors. And why beg children to eat vegetables? Soylent has every vitamin and mineral the body needs, and it’s delicious.

To me diet always seemed to be a trade-off. Time, money, health: pick two. You certainly have the capability to be healthy, but it will cost you. What about the single mom, the poor student, struggling entrepreneur or artist, the unemployed, or the elderly? These people desperately need energy, and its harder for them to be healthy than anyone else. Living on fast food and ramen is cheap and convenient, but unhealthy. Shopping at places like Whole Foods costs a fortune to many people and cooking healthy recipes takes practice and time. Cooking should be a hobby, like hunting. People used to hunt for survival, now they just do it for fun.

Global Implications

With Soylent you can be in peak mental and physical condition for less than $2/day. Soylent does not spoil for months, does not require refrigeration, is easy to transport, cheap and environmentally friendly to produce, contains no pesticides, hormones, or preservatives, is trivial to prepare, without even requiring a heat source (though you do need clean water), does no harm to animals, and drastically lowers sanitation requirements. I almost forgot to mention, when everything going in to your body is diffused in to the bloodstream, you don’t poop. I only have to remove a few grams of fiber from my system per week. I also noticed I was generating far less trash than before. The vast majority of personal refuse is food-related. Why else would the trash can always be in the kitchen?


This is one case and it’s only been a month, so it’s early, but I’m certainly not stopping now. Also, every body is different and there may be long term effects so more data is necessary. However, I am consuming no toxins or carcinogens and I get all the nutrition and energy I need with about 1/3 the calories the average American consumes so I hope in the long term my longevity will be improved (caloric restriction has been shown to reverse the effects of aging in rodents)4,5 while lowering my risk of cancer and disease. If you would like to try this experiment as well please contact me so we can pool our results. It’s fine to have a normal meal too, nutritional fundamentalists really irk me. The point is freedom, you don’t have to. I started consuming Soylent exclusively just to test the effects. I see nothing wrong with eating traditional food as well, I just don’t have much of a desire to. The only thing I missed was eating with friends. Now that 30 days are up I’m going to start doing that again. I only drink socially, and now I only eat socially.

I notice only now how much of this city is devoted to the stuff. Wherever you are I challenge you to find a search term for google maps that returns more results than “food”. Traveling back home to the American south I am still shocked to see how prevalent obesity is. How many people still spend their lives just surviving, living to eat, and it’s killing them? The food is eating us. I don’t know how to change peoples’ behavior, but now that I’ve discovered Soylent, I’m healthier than I’ve ever been, have more freedom with my time and money, and never have to worry about the stuff. Finally, I can have my cake and eat it too.

update: Getting way more responses than I can respond to individually. Please sign up at Follow up post w/ ingredients here:

update 2: discussion board up here:


Columbia Researcher Turns Gonad Cells into Neurons

Digital Art by Neutrix on Deviant Art

Have you ever wondered how all the different types of cells in your body come from a single zygote cell? Every cell in your body contains a complete copy of your genetic code. The DNA in your skin cells is identical to the DNA in your liver cells, and all your other cells. So, how do all the different cell types come about? The key is transcription factors, proteins that interact with certain regions of DNA and cause them to be expressed, or prevent their expression, based on a variety of factors. Depending on which DNA segments are expressed, the cell will develop certain traits, which in turn make it become a specific type of cells. For example, neuron cells generate dendrites and axons, which connect to other neurons, while skin cells are more concerned with being structurally rigid and moving to the body's exterior. What if this wasn't a one-way street? What if you could make cells change form, regenerate, or invent new types of cells entirely?

Oliver Hobert of Columbia University and his team studied the gene regulatory logic of neuronal diversification. To better understand this mechanism, neuroscientists frequently use a humble, yet important species of worm called C. Elegans. This is essentially the 'hello world' of neuroscience. The C. Elegans worm has a mere 302 neurons and ~5000 synapses (connections between neurons) which have been carefully mapped out. Humans, by comparison, have around 85,000,000,000 neurons, and more than 1014 synapses.

Hobert et al tracked a specific neuron in the worm, ASE, basically a taste receptor. There are two, ASE-R on the right, and ASE-L on the left. This is a great example of biologal symmetry, with functional asymmetry. The same is seen in the human brain, which is biologically very symmetric, yet functionality is all spread about. So, while ASE-R and ASE-L are similar in that they are taste receptors, one recognizes positive ions of sodium, and the other recognizes negative ions of chloride. Hobert wanted to track the formation of these neurons in the developing organism, and find when they became what they are.


The team found that symmetry develops very early. In fact, functional division was seen when the worm was only a 4-cell blastula. Importantly, they were also able to track the 'terminal selector genes', which are the transcription factors controlling the cell's development route. If you turn on, or express these genes, you can control what the cell becomes. To study gene expression researchers commonly attach a sequence called GFP, which does nothing but glow green, allowing one to visually see gene expression. The researchers increased the amount of CHE-1, the protein causing the ASE neuron information to be expressed, in an embryo and as a result many more neurons became taste receptors. It must have been a very picky eater.

Now modifying the worm's development is one thing, but what if it was possible for cells to change what they are in an adult? The team tried introducing more CHE-1 in an adult worm, but it had no effect. After the cells had developed, modifying the terminal selection factor did nothing. However, the team later found that if they repress a certain complex called lysine-27, and then added the terminal selection factor, the adult worm's cells would suddenly change form. They found they could change healthy tissue in to muscle, or neurons. The worm's gonads even began to turn in to neurons, growing axons and dendrites. This is fascinating stuff. I'd love to see the research extended to mammalian cells, in which the vast majority of genes are weakly expressed, or unexpressed entirely.


For more see Hobert's page here:
The paper is here:
Patel et al., Removal of Polycomb Repressive Complex 2 Makes C. elegans Germ Cells Susceptible to Direct Conversion into Specific Somatic Cell Types, Cell Reports (2012),

How we Communicate

        What you are about to read contains about 53,704 bits of information (encoded as UTF-8). Your computer probably downloaded it in less than a second, but it will take much longer for you to receive it. Even if you have a 10Mbps connection to my server, the real bottleneck here is the connection between your brain and mine. What is the bandwidth of that true last hop? Communications pioneer Claude Shannon calculated that the average amount of raw information (entropy) in an English word is about 11.82 bits. If you're reading 250 words per minute, you’re really only receiving 49.25bps. Seems wasteful.

Humans and Computers Communicate in Similar Ways

Communication is the transmission of information, and there are many ways to implement it. You may be surprised that digital and personal communications protocols are remarkably alike. But given that communications theory is a mathematical theory, as opposed to say a physical one, it makes perfect sense.

The OSI Model is a standard way of characterizing a communications system using layers of abstraction. Each layer should not care about the implementation of the lower ones, and there must be agreement on the configuration used at every level.


At the physical layer, the tongue and esophagus act as a sort of adjustable horn, which sends pressure waves of varying pitch by changing its shape. The receiver in the ear has sensitive hairs which resonate with the waves of pressure. Similarly, a wireless router sends high frequency bursts of specially encoded electromagnetic waves, which are received by a sensitive antenna in a laptop. The antenna is also constantly receiving thermal noise and spurious signals, but filters them out. Your ear does the same and can even quickly tune in to faint signals. If there’s a lot of ‘noise’, you either speak louder, or wait for your turn to talk. When two people try to talk at the same time, they’ll both stop and wait a random amount of time before trying again. In networking this is known as CSMA/CD. I often wonder how the brain decides on this random amount of time.

Data Link

Often the first thing to ask someone you don’t know is: “What’s your name?” Your name is your local address. If there are several people around, you can easily direct your message by mentioning the person by name. Your name was given to you by your parents and it generally doesn’t change. Similarly, your computer has a MAC address determined by the network adapter’s manufacturer, which allows packets from the router to find it, even in the presence of similar adapters. Even if everyone hears a message meant for you, only you act on it. Just as spoken statements are often predicated with the target person’s name, all MAC frames start with a header that contains their source and destination addresses.


The network layer defines how a packet flows through the network of switches and routers that make up the internet. This is where computers are beating us. We can do this to an extent: “If you see Sally tell her I’m sorry I ran over her cat.” (2 hops) but it quickly breaks down, as every hop loses information. Word of mouth is notoriously unreliable, since our brain does not store exact copies of information.

Meanwhile your computer can effortlessly send and receive through dozens of hops across the globe. Before the internet the closest incarnation of this we had was postal mail, with our home address analogous to IP address, and the path determination taken care of by the postal service. Routers take care of this with complex least-cost routing algorithms with the best paths constantly being updated and propagating throughout the network, updated based on congestion and failures. This would be very hard for a person to manage.

Can you keep a secret? Gossip was the original BGP. Information deemed valuable would only travel along select links to preserve its content and scarcity, though this was more for the sake of interest than efficiency. If news was valuable enough, it would soon spread naturally to everyone.


The transport layer allows for endpoint connection handling and reliable delivery.

“Hello, Hey!” -> TCP SYN, open a connection
Nodding, eye contact, “yeah” -> ACK, “got it”
“What? Hm? confused look” -> NACK, resend
“Ummmm” -> Buffering…
“Bye” -> FIN, close connection

Note that the protocols are optimized to reduce overhead. The bits of communication that are used simply to facilitate communication are kept to a minimum. “Hey, what, bye, thanks, yeah” are all very short, easy to say words. Also, it’s annoying to talk to someone that’s not looking at you since you don’t know if your information is getting through or not.

You’re probably also noticing how much more diverse the human counterparts are. Redundancy provides robustness at the cost of efficiency and simplicity. This is a key difference between biological and synthetic systems.

Session / Presentation / Application

I’m going to lump these together since they are usually all taken care of by the application layer protocol anyways. Up until this point you could have been communicating with someone who doesn’t even speak the same language as you. Only now do you extract the payload, the original meaning of the information that was encoded. There are many application layer protocols, and there many types of conversation. When talking to a teacher, a lover, or a friend, the purpose of the conversation is usually different, though the underlying protocols are the same, just as FTP, HTTP, and SSH all accomplish different tasks over a similar connection.

I’d say this layer also involves body language and emotion, which can annotate your words. A significant percentage of communication is non-verbal. Lots of bits are encoded in tone, gestures, and stature. Computers haven’t quite cracked this yet. Until Siri recognizes your tone, its usefulness will be limited.


Channel capacity is a function of bandwidth, power, and noise.

A disagreement is information asymmetry. If you’re not getting through to someone a common response is to increase your power level by shouting. Conversely, as you get to know someone better, channel capacity generally increases, and you can exchange more information and talk about complex topics. It feels pleasant when your data is getting through, and the receiver indicates a strong link by smiling. People that have similar brains and experiences are easy to talk to, like radios conforming to the same specification.

So long as a signal is sampled at twice its frequency, it can always be reconstructed exactly. However, there is no lossless method of inter-brain communication. Our conversations have come a long way from pointing and grunting, but they still have a long way to go. It’s easy to transmit a word, but how does one encode an idea, an emotion, or an experience? We have great respect for authors, poets, musicians, and artists who are unusually gifted at encoding that which is hard to communicate. It can be hard to “get” art because there’s often a lot to unpack. The more complex an idea the harder it is to encode, like compressing a large file. All conversions heretofore have been lossy, always holding us back from a true connection with another person.

        By its very nature every embodied spirit is doomed to suffer and enjoy in solitude. Sensations, feelings, insights, fancies – all these are private and, except through symbols and at second hand, incommunicable. We can pool information about experiences, but never the experiences themselves[…]The mind is its own place, and the places inhabited by the insane and the exceptionally gifted are so different from the places where ordinary men and women live, that there is little or no common ground of memory to serve as a basis for understanding or fellow feeling. Words are uttered, but fail to enlighten. The things and events to which the symbols refer belong to mutually exclusive realms of experience.
         –Aldous Huxley, from The Doors of Perception

I don’t think we will always exist in this realm of solitude. Imagine a world where we could directly network minds with the bandwidth that our electronics enjoy. I eagerly look forward to the day when we can finally transcend words, and writings such as this will look as primitive as the barking of a dog.

An Introduction to Graphviz via R. Kelly’s “Trapped in the Closet” Hip Hopera

As our world becomes more connected it has become of the utmost importance to clearly and easily visualize the structures that represent the modern digital age: the graph. Anyone involved in object oriented programming, artificial intelligence, networks, social media, or of course the fascinating field of graph theory makes heavy use of these structures. Graphs are a fertile topic that I plan to write more about, but for now we will focus on the immediately practical: the fantastic open source graph visualization toolkit Graphviz.

Let us explore some of the useful features of Graphviz and its associated description language “dot” by tracing the convoluted relationships of the characters in R. Kelly’s (currently) 23 part epic “Trapped in the Closet”.

Like every other web tutorial I will solipsistically assume you are using the same OS I am, Ubuntu. However, Graphviz should work just fine on Windows and even on your shiny Macbook. Begin by listening to “Trapped in the Closet” (many spoilers below), and installing Graphviz, if you haven’t already:

sudo apt-get install graphviz

At this point our hero, “Sylvester”, played by R. Kelly, is just now awaking from his slumber. To his great bewilderment, he finds he is in an unfamiliar bed, with an equally unfamiliar woman, Cathy (not Mary).  Let’s add them to the graph. Create a new file called “” and write our two nodes. Since they have “connected”, let us define their relationship as two directed edges, denoted like so: “->”

digraph Closet{
    Sylvester -> Cathy;
    Cathy -> Sylvester;

Now compile:

dot -Tjpg -o closet.jpg

Note this will output a .jpg image but many other output formats are possible. Now that we have our graph, let us add enhancements as we follow the odyssey of Sylvester. Our protagonist breathlessly remembers he is married, and has committed an act of infidelity. Yet with hardly enough time to assess the situation, a new character, Cathy’s husband “Rufus” arrives home (at 7:00am, mind you) and Sylvester hides in the closet. Rufus and Cathy begin to make love, but our hero’s presence is betrayed by the ringing of his cell phone. Rufus searches intently for the intruder and eventually finds Sylvester in the closet (trapped), holding a gun. As an argument breaks out the group is interrupted by another man at the door (at the count of four). Let’s update our graph.

As R. Kelly would doubtlessly inform you, relationships are complicated. Let’s use different styles of edges to signify different relationships, and different node styles to signify men and women.

digraph Closet{
    Sylvester -> Cathy [color = red];
    Cathy -> Sylvester [color = red];
    Sylvester [shape = box];
    Cathy -> Rufus;
    Rufus -> Cathy;
    Rufus [shape = box];
    Chuck [shape = box];               // who is this man??

Note red edges signify infidelity. It is now revealed that Rufus and Chuck are intimately involved. Sylvester calls home and is startled to hear a man answer. Filled with double standards, he speeds to his domicile, resulting in an encounter with a police officer, who gives him a ticket. Upon arrival home he learns the man is merely his wife’s brother, Twan, who just got out of jail. A relieved Sylvester proceeds to engage in intercourse with his wife, Gwendolyn, only to discover a prophylactic on the bed. When pressed, Gwendolyn begins to discuss her high school friends Tina and Roxanne, and Cathy, who introduced her to the police officer, James, who is her secret lover. After you recover from the shock of this revelation let us continue updating our graph.

digraph Closet{
    Sylvester -> Cathy [color = red];
    Cathy -> Sylvester [color = red];
    Sylvester [shape = box, style = filled, color = ".6 .6 .9"];
    Cathy -> Rufus;
    Rufus -> Cathy;
    Rufus [shape = box];
    Chuck [shape = box];
    Rufus -> Chuck [color = red, style = bold];
    Chuck -> Rufus;
    Sylvester -> Gwendolyn;
    Gwendolyn -> Sylvester;
    James -> Gwendolyn;
    James [shape = box, style = filled, color = ".6 .6 .9"];
    Gwendolyn -> James [color = red];
    Gwendolyn -> Twan [style = dashed];
    Twan -> Gwendolyn [style = dashed];
    Twan [shape = box]

Note dashed lines represent family, and Rufus’ involvement with Chuck is bold, as he is a pastor. Also, individuals with guns are colored blue. The saga continues with James driving to Sylvester’s house, worried about Gwendolyn. The couple is now laughing hysterically at the mutually philanderous situation, which James mistakes for violence, and bursts in pointing his gun at Sylvester, who subsequently draws his own. The two wrestle for James’ gun, which unintentionally discharges, shooting Twan in the shoulder. Suddenly there is a knock at the door, which when opened reveals Rosie, the nosy neighbor with a spatula in her hand. An exhausted James who clearly has a lot of paperwork to do is invited home by his loving wife, Bridget, and leaves the premises.

digraph Closet{
    Sylvester -> Cathy [color = red];
    Cathy -> Sylvester [color = red];
    Sylvester [shape = box, style = filled, color = ".6 .6 .9"];
    Cathy -> Rufus;
    Rufus -> Cathy;
    Rufus [shape = box];
    Chuck [shape = box];
    Rufus -> Chuck [color = red, style = bold];
    Chuck -> Rufus;
    Sylvester -> Gwendolyn;
    Gwendolyn -> Sylvester;
    James -> Gwendolyn [color = red];
    James [shape = box, style = filled, color = ".6 .6 .9"];
    Gwendolyn -> James [color = red];
    Gwendolyn -> Twan [style = dashed];
    Twan -> Gwendolyn [style = dashed];
    Twan [shape = box]
    James -> Twan [style = bold, color = green, label = "shot"];
    James -> Bridget;
    Rosie [label = "Rosie the n nosy neighbor"]

Green lines represent shootings. All is not well at James’ household. His southern wife, Bridget, seems jittery, thus despite being invited upstairs for pears, he ventures to the kitchen to enjoy some chicken. Here he notices a slice is missing from the cherry pie, while Bridget is allergic to cherries, a rather rare condition. After an exhaustive search, James discovers in his kitchen cabinet the secret lover of Bridget, a midget, named “Big Man”. James reacts violently to the discovery and Bridget, who somehow has Gwendolyn’s number, calls her and invites her to come break up the fight. Gwendolyn, Sylvester, and Twan, who is playing cards rather than seeking medical attention for his gunshot wound, travel to the abode. Upon arrival, Bridget, who now has a shotgun, reveals she is pregnant, and Big Man is the father. Furthermore, Gwendolyn telephones Cathy to tell her the events of the morning, only to realize that it was her that Sylvester had slept with the previous night. Here is the complete graph through chapter 12 of the saga, with friendships from previous chapters included.

digraph Closet{
    Sylvester -> Cathy [color = red];
    Cathy -> Sylvester [color = red];
    Sylvester [shape = box, style = filled, color = ".6 .6 .9"];
    Cathy -> Rufus;
    Rufus -> Cathy;
    Rufus [shape = box];
    Chuck [shape = box];
    Rufus -> Chuck [color = red, style = bold];
    Chuck -> Rufus;
    Sylvester -> Gwendolyn;
    Gwendolyn -> Sylvester;
    James -> Gwendolyn [color = red];
    James [shape = box, style = filled, color = ".6 .6 .9"];
    Gwendolyn -> James [color = red];
    Gwendolyn -> Twan [style = dashed];
    Twan -> Gwendolyn [style = dashed];
    Twan [shape = box]
    James -> Twan [style = bold, color = green, label = "shot"];
    James -> Bridget;
    Bridget [shape=polygon, sides=5, peripheries=3, color=purple, style=filled];
    Rosie [label = "Rosie the n nosy neighbor"]
    bman -> Bridget [label = "impregnated"];
    Bridget -> bman [color = red];
    bman [shape = invtriangle, label = "Big Man"];
    /* Friendships */
    Gwendolyn -> Cathy [style=dotted];
    Roxanne -> Tina [style = dotted];
    Tina -> Roxanne [style = dotted];
    Gwendolyn -> Roxanne [style = dotted];
    Roxanne -> Gwendolyn [style = dotted];
    Gwendolyn -> Tina [style = dotted];
    Tina -> Gwendolyn [style = dotted];
    Cathy -> Gwendolyn [style = dotted];

Note individuals that are both pregnant and holding a gun are purple pentagons. Midgets that are also strippers are inverted triangles, and friendships are represented by dotted lines. Though the story continues, we’ll stop here for now. I hope this has been an informative introduction to some of Graphviz’s basic features. For more information see the Documentaion, and please try to remain faithful to your significant others.

What’s In a Wave?

Waves are all around us. At this moment your body is encountering many different types of waves from a vast array of sources. Some bounce right off your surroundings in to your iris, being seen as light. Some transfer their energy to tiny hairs in your ears, registering as sound. Many pass right through you without you even noticing, but are noticed by devices which use them to communicate, like the cell phone in your pocket. Some even originated at stars in distant galaxies millions of years ago. The only thing as diverse as physical waves are the ways in which we’ve figured out how to use them. Given their importance in science, mathematics, and industry it behooves us to understand them better.

How do we represent a wave? Here’s something you’ve probably seen before: a sine wave, or [latex]F(x) = A*sin(theta + phi)[/latex]. Here amplitude is 1 and phase is 0 so we just have sin(x).

It may not look like much given the fanfare above, but it’s important to distinguish the idea of a wave from ‘real’ waves. This is merely one method of representing a wave, and a poor one at that. The sine wave extends to infinity in both directions. Unfortunately a width of infinity is not supported by your monitor (or brain). Also this is only a 2-dimensional plot, we live in 4 dimensions (3 spatial plus time), so you have a right to be disappointed. What’s a better way to represent a wave? How can we represent any wave without losing information about it or requiring an infinitely large monitor? Differential equations to the rescue!

[latex size=”4″]\nabla^2{\vec A} = \frac{1}{v^2}\frac{\partial^2 \vec A}{\partial t^2}[/latex]

Don’t fear the notation! This is the wave function and it says something quite simple. Let’s call our wave “A”, arbitrarily so. More specifically, “A” is a measure of how much our system varies from equilibrium. The wave is oscillating like a spring. In fact the wave equation can be derived from Hooke’s Law. We’re describing how much and how quickly it oscillates as well as how fast it travels. The left side is the ‘Laplacian’, or, a description of how our wave changes in whichever universe or coordinate system we choose, for example, cartesian (3D):

[latex size=”4″]\nabla^2{\vec A} = \frac{\partial^2A_x}{\partial x^2} + \frac{\partial^2 A_y}{\partial y^2} + \frac{\partial^2 A_z}{\partial z^2}[/latex]

The curved ‘d’ symbol is a partial derivative, or, the value of the derivative of a term assuming the other terms stay constant. If you need a refresher, a derivative is essentially a description of how quickly a value changes based on its input. The derivative of position is velocity. The derivative of velocity (or, second derivative of position) is acceleration. If position is changing rapidly, the velocity is high. Now, let’s deal with the right hand side. First, ‘v’ is just the speed at which the wave propagates, or travels. The last term is the second partial derivative of our wave “A” with respect to time. Notice both sides are second order. So, we are talking about how our wave changes in time, while the left side talks about how it changes in space. Simple, right?

Now that we’ve discussed the idea of a wave, let’s talk about some real ones. I’m going to pick Electromagnetic waves because we understand them quite well. Electromagnetism can largely be described by Maxwell’s equations. Electricity and magnetism often appear distinct (what’s interesting is this is entirely unique to a 4th dimensional treatment) but they are really the same force. Take two of Maxwell’s (there are only 4 total) equations:

[latex size=”4″]\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}[/latex]

[latex size=”4″]\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}[/latex]

Again, notation is not your friend, but these equations rather elegantly describe how electricity and magnetism are related. By convention, E always refers to the electric field, and B the magnetic field. The first, the Maxwell-Faraday equation, basically says a changing magnetic field produces electric current. This is why when you swipe your (magnetic) credit card through a Square card reader, the audio jack can decode it based on the amount of electric current received, without needing to be powered itself.

The second, the Ampere-Maxwell equation, just says the opposite. Electric current produces a magnetic field. It’s okay if you don’t fully understand these relationships, just remember they depend on the two values: [latex size=”1″]\mu_0[/latex], or ‘permeability’, a universal constant describing how strong a magnetic field is in free space,  and [latex size=”1″]\epsilon_0[/latex] or ‘permittivity’, describing the same for electric fields. Here’s where it gets interesting. Recognize the [latex size=”1″]\nabla \times[/latex] operator? It’s called the ‘curl’. It’s just a mathematical operator, so what happens when we apply it again to both sides of each equation? Remember applying the same operation to both sides of an equation doesn’t change what it says at all. Now, I’ll spare you the complex process, but they simplify like so:

[latex size=”4″]\nabla^2 \vec E = \mu_0\epsilon_0\frac{\partial^2 \vec E}{\partial t^2}[/latex]

[latex size=”4″]\nabla^2 \vec B = \mu_0\epsilon_0\frac{\partial^2 \vec B}{\partial t^2}[/latex]

Don’t those look a bit familiar? It’s the wave equation!! These are the differential equations describing electromagnetic waves. Something’s a bit off though. If you look back to the wave equation you’ll see the propagation velocity is different, or is it? What happens when we equate the two?

[latex size=”4″]\frac{1}{v^2} = \mu_0\epsilon_0[/latex]

or equivalently,

[latex size=”4″]v = \sqrt{\frac{1}{\mu_0\epsilon_0}}[/latex]

Remember [latex size=”1″]\mu_0[/latex] and [latex size=”1″]\epsilon_0[/latex] are constants, so we can calculate a value for ‘v’.

[latex size=”3″]v = \sqrt{\frac{1}{[4\pi \times 10^{-7} m kg/C^2][8.8541878 \times 10^{-12} C^2 s^2 /kg m^3]}}[/latex]

[latex size=”3″]v = \sqrt{8.987552 \times 10^{16} m^2 / s^2} = 2.9979 \times 10^8 m/s[/latex]

That’s 299,790 km / s. It’s the speed of light! Of course, electromagnetic waves travel at the speed of light. Light is an electromagnetic wave. This begs the question, though. Are permittivity and permeability emergent properties of the speed of light? Or, is the speed of light an emergent property of permittivity and permeability? Perhaps they’re both based off of a lower level property of physics?

There’s much, much more to waves than this. Did you know particles and matter can also be described as waves? Take a look at the famous Schrodinger equation and see if anything looks familiar.

[latex size=”4″]i\hbar\frac{\partial\psi}{\partial t} = \frac{\hbar^2}{2m}\nabla^2\psi + V(\mathbf{r})\psi[/latex]

Again, the notation hurts, but it’s a relationship of incredible simplicity and beauty once you understand it. Clearly waves are even more fundamental and important than we originally thought. Can you imagine if our eyes could detect more than such a tiny sliver of the electromagnetic spectrum? The universe is much more fantastic and beautiful through the unconstrained eyes of physics and mathematics. More to come…