# E=mc^2

Derived in ten minutes while I was on the toilet:

Edit: 11-16-16

There was a slight error in the set-up of the center of mass calculation. Light appears to move an effective mass from -L/2 to L/2-l, the starting and stopping points of light. Here’s the reformulation to capture that.

Time spent on this derivation: ten minutes on the toilet last night and ten minutes before breakfast writing the correction (yeah, that’s what I get for going really fast).

Don’t thank me, this is Einstein’s calculation.

Edit: 11-18-17

As I’m still thinking about this post, I figure it might be beneficial to flesh out the reason that it was written. This post was used as a response to a comment on another blog… if you want to back up a statement you made about something and somebody is accusing you of not providing evidence, most people provide citations, net links, references, etc. In this particular case, the argument was about a piece of math and I was being accused of lying about said piece of math by someone who clearly likes to believe he knows everything without actually knowing practically anything. Yes, skeptics are guilty of Dunning-Kruger, just like everyone else (This is an unfair statement and I apologize for it.) What better way to slam the textbook in someone’s face than to actually work the problem? If you want the final word on what Einstein said about something, quote Einstein’s work! And so, a piece of Einstein’s work is posted above.

The argument in question started with a fellow suggesting to me that mass-energy equivalence can be derived but not proven with classical physics. I beg to differ; energy is a classical concept, from Thermo, E&M and classical mechanics… all three! You don’t need relativity or quantum mechanics to justify statements about how energy works; measurements of kinematics and force are sufficient to show that energy as a concept works. Mass-energy equivalence arose from Einstein’s notion that the newly completed classical field of electromagnetism must be consistent with the older fields of classical mechanics. The equation E=pc is not relativistic: it came directly out of electromagnetism (and, believe me, I’ve been through that calculation too because I didn’t believe it at first.) Imposing that these two fields must be cross-consistent is the origin of mass-energy equivalence…. light carries momentum (by Poynting’s vector and well defined in the electromagnetic stress-energy tensor) and light interacts with mass, therefore conservation of momentum (and consequently conservation of center of mass in absence of external forces) requires that light carry an equivalent of mass in order for forces to add up in a situation where light interacts with matter but no forces interact externally on the system comprised by the light and the matter. Mass-energy equivalence is required by this, no ifs, ands, buts or “yeah, but you didn’t proves…”

Einstein’s thought experiment validating this set-up is an exceptionally elegant one. It’s called “Einstein’s Box.” Everybody loves Schrodinger’s cat-in-a-box… well, Einstein had a box too and this box is older than Schrodinger’s. Einstein’s box is a closed box sitting out in space where it feels no external forces. A flash of light is emitted inside the box from one wall and travels across the box to strike the opposite wall. E&M states that light must carry momentum. If the system has no external forces acting on it, the emission of the light inside the box requires that momentum of the system be conserved, which requires that the box recoils with a momentum equal to that carried by the light, causing the box to move at some velocity consistent with the momentum carried by the light (which turns out to be directly proportional to the energy carried by that light as stated by E=pc). Net momentum of the system must remain zero by conservation of momentum. When the light travels across the box and collides with the opposite wall, the momentum of the light cancels the momentum of the box and the box stops moving. Thing about this is that center of mass, as a consequence of momentum conservation, could not have moved. No forces on the outside of the box.

Center of mass is a damn well classical concept, well worked out in the 1700s and 1800s… and since the box moved, the box’s center of mass moved! But no forces acted on the outside of the system, so the overall center of mass of the system could not have moved. This requires the light to have carried with it a value of mass, taken from the location where the light was emitted and deposited again at the location where the light was absorbed. But light is known not to carry mass since it is a wave-like solution of immaterial fields in the form of Maxwell’s equations. If you set up this situation and work through the calculation, Newtonian mechanics and electromagnetism –nothing more–, this turns out the classical requirement that energy and mass have an equivalence in the form of E=mc^2. No quantization or probability relations from quantum mechanics, no frame of reference shifting from relativity, not even delineating that light is some package of photons… this is purely classical. Moreover, energy is a tabular result to begin with: it is not something that is by itself ever directly observed and it must always be carried by something else, a field, a heat, a potential, a motion or what have you. The statement that this tabular relationship extends to something else that is technically only indirectly observed, mass, is a proof. And yes, mass is indirect since you can only know mass from weight, which is a force!

If you have concepts of weight, momentum and light together in the same model as expressed by classical physics, mass-energy equivalence is required for self-consistency.

Granted, special relativity quite naturally produces this result as well, but special relativity is not required to produce mass-energy equivalence. Had Einstein not discovered it, someone else damned well would’ve and it would not have required relativity to do –at all!

Now, the thing that doubly made me angry about this conversation is that it was with a fellow who absolutely craved physicist street cred: he name dropped Arxiv and seemed to want to chase around details. Sadly, his whole argument ultimately amounted to insulting someone and not backing up his ability to absolutely know what he was claiming to know. Does it matter that you don’t believe my statement if you aren’t competent to evaluate the field in question? Not at all: such a person has no place at the table to start with. This is why it’s possible for a Nobel Laureate to descend in to crankery… just because you have a big prize doesn’t mean you are always equally competent at everything! I’m guessing the guy was a surgeon given the ego and the blog, but if he was a physicist, I’m very disappointed. A physicist who doesn’t know Einstein’s box is a travesty. I’m not the greatest physicist that ever lived, but I work at it and I know what I’m talking about… where I have gaps, I do my best to admit it.

edit: 11-18-17

(Statement redacted. It was an unfairly insulting comment)

edit: 11-20-17

As this is still nagging at me, one further thought. What I consider the last statement of the conversation before it simply became obvious trolling, the fellow accused me of not including “a variable speed for light” in my calculation. In Einstein’s calculation, the speed of light is given the constant “c.” This is a constant which comes with a caveat; “c” is the speed of light when it is not passing through anything material, the speed of light in a vacuum. This distinction is important because light can travel at lower speeds when it’s passing through a material. This situation is well-handled by E&M and is considered a “solved effect” by Relativity, whose postulates include the explicit notion that E&M simply be true everywhere. The constant “c” is the maximum possible speed that light can travel, but it will travel at lower speeds in a medium with an index of refraction greater than 1, where permittivity and permeability might have values other than their vacuum values, which has the wonderful result of making lenses possible in glasses and microscopes. In my lavatory derivation above, a little screw up on my part is that I didn’t clobber the reader over the head with the constancy of the value “c,” I said “a box in zero gravity” and I said light travels at “c,” but I didn’t say “this is definitely all in a vacuum” which I probably should have. If index of refraction is “n”… the velocity of light in a medium with that refractive index is v = c/n. There are other ways to encode refractive index which allow for more sophisticated optical behaviors, but everything in that line is completely out of the pail for the argument in question, and drawing attention to it is simply chaff intended to shift the focus of the argument.

Light can travel at speeds lower than “c,” but “c” itself is so far found to be invariant. Moreover, the fact that light can travel at speeds other than “c” does not change the Einstein’s box derivation, which is set in explicit conditions where light would travel at “c.” Somebody who doesn’t know this isn’t a physicist (11-20-17: I’ll moderate this it’s unfair and was too angry.)

Also, as an aside, I mention above that Special Relativity can produce E = mc^2. Thinking about it, but not running through the calculations, I think this is actually backward; E=mc^2 is sort of needed first before it shows up in Special Rel. Einstein made some amazing leaps.

Edit: 11-20-17

As an added extra, here is a derivation of E=pc from the stress-energy and electromagnetic power continuity equations. These were written a few years ago, but I had the good sense to scan them:

The E=pc derivation begins on the second page above. The first page is the end of the continuity equation derivation. I’ll neglect that. No relativity here, just pure E&M. There are a couple pieces in here that I don’t remember so well and I need to think about to decide if they’re correct. The first page is included to show clearly the relation between force and the stress-energy tensor divergence.

Edit: 11-21-17

First of all, we have to be really sure of what is meant by “p” on the left side of this equation. My first reading of it was as “momentum,” but I’m realizing that it isn’t, and this may be leading to some misunderstandings about what is meant by E=pc. The thing in the middle is average poynting vector divided by speed of light… Poynting vector has units of Watts/meter^2 and speed of light has units of meters/sec, which works out to Newtons/m^2, or force per area, which is pressure, not momentum. The thing on the right is actually in units of energy… permittivity times peak E-field^2 over 2, which is just a form of electromagnetic energy, in units of Joules. For a literal reading of the equation above, unit analysis put me at momentum = pressure = energy, which is not right (apple can’t equal orange can’t equal pear). If I take “p” as pressure rather than momentum, the left side makes sense, but the right side still doesn’t quite work.

It’s a nice try, all the elements are there. It has energy and momentum can be massaged out of it. I think the route being taken here is to try to use the form of a plane wave to figure out the momentum based on the pressure and specifically for a plane wave form of the poynting vector, or else the peak E-field intensity wouldn’t be needed.

The approach in the E=pc derivation I posted above is really different. My starting point is with a classical structure called the Electromagnetic stress-energy tensor and with a second structure which is conservation of power given energy flux. (Wikipedia actually kind of pissed me off about this: they want to masturbate over the four-dimensional relativistic version, but wouldn’t provide me a clean on-line citation for the classical version shown above; the form given here is the same as it appears in Jackson E&M) The first equation is a consequence of the Lorentz force law (F = qE+qvxB) where the system has electromagnetic waves, but is sealed so that there is no net force… the equation says that the change in Poynting vector per unit time is equal to the divergence of the electromagnetic stress-energy tensor, all of which is in units of force or change of momentum with time. The second equation is a consequence of Power=current*voltage, believe it or not, and just says that the change in energy density in the system is equal to the divergence of the Poynting vector, all in units of power. These structures make no real initial assumptions about the form that the electromagnetic fields are taking, they speak only of change of momentum per time and change of energy density given energy flux and are derived directly from application of Maxwell’s laws.

The first step is to take the stress-energy continuity relation and to hold it as change in Poynting vector with time is equal to change in momentum density with time by direct application of Newtonian force. You end up with an expression that says that Poynting vector is equal to momentum density times speed of light squared.

The second step is to throw this Poynting vector relation into the power equation so that you get a relation that says that the momentum flux out of a volume of space is equal to the change of energy density with time. This gives you a “momentum current vector” equation, which is analogous to the relationship between electrical current “I” and current vector “J.”

I next establish a momentum current, basically just a beam of light with no specific frequency or field configuration. You could write this as white light in a Fourier composition. A set of very simple manipulations gets you to a relation that directly says that energy density is equal to momentum density times speed of light. Integrate out the density and you get E=pc directly. Please note, this set-up is explicitly agnostic on the idea of photons since it depends on a mixture of frequencies to produce a constant envelope of plane waves with constant momentum density distributed everywhere and therefore does not require quantum mechanics to work. I can’t claim this work is Einstein’s because I didn’t follow anyone to make it… this is me using Jacksonian E&M technique to prove E=pc for myself, all using classical physics.

With E=pc in hand by these means, the classical derivation of E=mc^2 is pretty much a shoe-in. Again, I used no quantum and no relativity. If I could do this, the geniuses at the turn of the century got it faster;-)

Edit: 11-22-17

I must’ve done something wrong with the Latex, it doesn’t seem to want to render in the body of my post; I’m still looking into whether I need to get the plugin…

Further, I figured out what was wrong with the unit analysis I did above… the right side of that equation is energy density (J/m^3) rather than energy (J)… and since J =N*m, J/m^3 is N/m^2…. the equation above is all in units of light pressure. To get to E = pc in approximate form in the plane wave, you just need to sub in the relation for momentum density per Poynting vector S = pc^2, then cancel the density by integrating over volume.

One additional thing about the Einstein’s box derivation that is important; it works in a classical framework. What I’ve provided above, then, is E=mc^2 as a classical equation, which is really torturing the point that it was “proven.” I’ve been thinking about whether or not I was doing this right since the whole discussion started and the derivation is only consistent from the standpoint that there are no effects included taking into account the potential relativistic characteristics of the box as it moves. I’m sorry about that, Narad. The derivation above would be insufficient from a modern physics standpoint because the box would undergo length contractions and dilations as it moves. To be perfectly honest, this nagged at me a tiny bit as I wrote the derivation, but maybe not as much as it should have… I drew the box as strictly “before” and “after” so that I ended up looking at the system only when it is located in the inertial frame of reference. That would call into question the nature of the boost pushing it into motion. I was assuming that the completely undisclosed relativistics located between the end-points were sufficient to conspire that the end-points be right! And, that’s an open end since length contraction would place the wall of the box in a different location depending on the frame… throwing off the whole calculation.

(For the people at home, here is something very important about how I designed to write this blog. I leave my edits visible so that the progression of my thinking is clear… one of the hardest, most human aspects of working in sciences is facing the fact that nobody is always right about everything. I think that being a good scientist is not about being right all the time, but about changing your mind when it’s important to do so. And, it’s about admitting when someone else was right, sometimes very publicly! Are you smart if you’re unwilling to abandon a sinking ship? I think not. Smart is being able to turn the steering wheel and to grow when its necessary to do so –especially when it effects your pride. I think this is the difference between arguing loudly and arguing productively.)

Here is the derivation converting the light pressure equation Narad offered into E=pc…

Hopefully that ties up all the loose ends! (Don’t be surprised to see me back here playing with a relativistic E=mc^2 proof at some point.)

# Revoke Shaquille’s Doctorate in Education… he doesn’t deserve it.

We are in a world where truth doesn’t matter.

Read this and weep. These men are apparently the authorities of truth in our world.

Everywhere you look, truth itself is under assault. It doesn’t really matter whether you believe, it really doesn’t matter what you want it to say. Truth is not beholden to human whims. We can’t ultimately change it by manipulating it with cellphone apps. We can’t reinterpret it if we wanted to. One of these days, in however great of importance we hold ourselves, the truth will catch up. And we will deserve what happens to us after that point in time.

“It’s true. The Earth is flat. The Earth is flat. Yes, it is. Listen, there are three ways to manipulate the mind — what you read, what you see and what you hear. In school, first thing they teach us is, ‘Oh, Columbus discovered America,’ but when he got there, there were some fair-skinned people with the long hair smoking on the peace pipes. So, what does that tell you? Columbus didn’t discover America. So, listen, I drive from coast to coast, and this s*** is flat to me. I’m just saying. I drive from Florida to California all the time, and it’s flat to me. I do not go up and down at a 360-degree angle, and all that stuff about gravity, have you looked outside Atlanta lately and seen all these buildings? You mean to tell me that China is under us? China is under us? It’s not. The world is flat.”

This spoken by a man with a public platform and a Doctorate in Education. This is the paragon of teachers!

First, arguments about whether or not Columbus discovered America are a non-sequitur as to whether or not the Earth is round.

Second, driving coast to coast can tell you very little about the overall roundness of the Earth, especially if you aren’t paying attention to the things that do. The curvature of the earth is extremely small: only about 8 inches per mile. This means that on the scale of feet, the curvature is in thousandths of an inch, so that you can’t measure it to not be flat at the dimensions that a human being can meaningfully experience standing directly on the surface. Can you see the couple feet of curvature at a distance of fifty miles looking off a sky scraper in the middle of Atlanta, or distinguish the deviation from the same direction of ‘up’ of two sky scrapers separated by ten miles? You can’t resolve tens of feet with your eyes at a distance of miles. That said, you actually can see Pikes Peak emerge over the horizon as you come out of Kansas into Colorado, but I suppose you would explain that away by some sort of giant conspiracy theory elevator device. To actually start to directly see the curvature at a meaningful degree with your eyes, you need to be at an altitude of hundreds of thousands of feet above the surface… which you could actually do as somebody with ridiculous wealth.

Third, how would you know that China is not ‘under?’ How would you know where China isn’t when you wouldn’t be able to see that distance along a flat surface no matter which direction you look? Can you explain the phase factor that you pick up to your day that causes your damn jet lag every time your wealthy, ignorant ass travels to places like China? By your logic, you should be able to use your colossal wealth to travel to where the globe of the sun pops out of the plane of the Earth in the east every morning. Hasn’t it once occurred to you that if you’re truly right, you should test a hypothesis first before making an assertion that can be easily shown to be wrong?}

You made a mint of money on the backs of a lot of people who made it possible for you to be internationally known, all because of the truth that they determined for you! You do not respect them, you do not understand the depth of their efforts, you do not know how hard they worked. You do not deserve the soapbox they built for you.

For everyone who values the truth, take a moment to share a little about it. Read other things in my blog to see what else I have to say. I have very little I can say right this second; I’m aghast and I feel the need to cry. My hard work is rendered essentially meaningless by morons like Shaquille O’Neal… men of no particular intellect or real skill dictating what reality ‘actually is’ while having no particular capacity to judge it for themselves.

From a time before cellphone apps and computer graphics manipulation, I leave you with one of the greatest pinnacles of truth ever to be achieved by the human species:

Like it or not, that’s Earth.

If you care to, I ask you to go and hug the scientist or engineer in your life. Tell them that you care about what they do and that you value their hard work. The flame of enlightenment kindled in our world is precious and at dire risk of guttering out.

Edit:

An open letter to the Shaq:

Dear Shaquille O’Neal,

I’m incredibly dismayed by your use of your public personae to endorse an intellectually bankrupt idea like flat earth conspiracy theories particularly in light of your Doctorate Degree in Education. If you are truly educated, and value truth, you should know that holding this stance devalues the hard work of generations of physicists and engineers and jeopardizes the standing of actual scientific truth in the public arena. The purpose of an educator is to educate, not to misinform… the difference is in whether you spread the truth or not.

There is so much evidence of the round earth available in the world around us without appeal to digital media, the cycle of the seasons, scheduled passages of the moon and the planets, observations of Coriolis forces in the weather patterns and simple ballistics, the capacity to jump in an airplane heading west and continue to head west until you get back to where you started, the passage of satellites and spacecraft visible from the surface of the Earth over our heads, the very existence of GPS available on your goddamn smart phone, to the common shapes of objects like the moon and planets visible through telescopes in the night skies around us, that appeals to flat earth conspiracies show a breathtaking lack of capacity to understand how the world fits together. That it comes from a figure who is ostensibly a force of truth –an educator– is truly deeply hurtful to those of us who developed that truth… modern scientists and engineers.

Since you are so profoundly wealthy, you among all people are singularly in a position to prove to yourself the roundness of our world. I bet you 50 million dollars that I don’t even have and will spend my entire life trying to repay, that you can rent an airliner with an honest pilot of your choice and fly west along a route also of your choice, and come back to the airport you originally departed from without any significant eastward travel. Heck, you can do the same exercise heading north or south if you want. And, if that experiment isn’t enough, use your celebrity to talk to Elon Musk: I hear he’s selling tickets now to rich people for flights around the moon. I bet he would build you a specially-sized two-person-converted-to-one berth in his Dragon capsule to give you a ride high enough to take a look for yourself at the shape of the world, if your eyes are the only thing you’ll believe. If you lose, you pay a 49 million dollar endowment to the University of Colorado Department of Physics for the support of Physics Education –and a million to me for the heartache you caused making a mockery of my education and profession by use of your ill-gotten public soapbox and mindlessly open mouth. Moreover, if you lose, you relinquish your Doctorate and make a public apology for standing for exactly the opposite of what that degree means.

Sincerely,

Foolish Physicist
of Poetry in Physics

Edit 4-5-17:

So, Shaq walked back his comments.

O’Neal: “The first part of the theory is, I’m joking, you idiots. That’s the first part of the theory. The second part is, I said jokingly that when I’m in my bus and I drive from Florida to California, which I do every summer, it seems to be flat. When I’m in my plane, and we’re getting ready to land, and I open up the window, and I’m looking at all the land that we’re flying over, it seems to be flat.”

“This world we live in, people take things too seriously, but I’m going to give the people answers to my test,” he said. “Knowing that I’m a funny guy, if something seems controversial or boom, boom, boom, you’ve got to have my funny points on, right? So now, once you have my funny points on, that should eradicate and get rid of all your negative thoughts, right? That’s what you should do when you hear a Shaquille O’Neal statement, OK? You should know that he has funny points right over here, and what did he say? Boom, boom, boom, add the funny points. You either laugh or you don’t laugh, but don’t take me seriously. When I want you to take me seriously, you will know by the tone of my voice that I’m being serious.”

“No, I don’t think that,” O’Neal told Harbinger of a flat Earth. “It was a joke, OK? So know that when Shaquille O’Neal says something, 80 percent of the time I’m being humorous, and it is a joke. And 20 percent of the time, I’m being serious, but when I’m being serious, you’ll know. You want to see me, seriously? See me and Charles Barkley going back and forth on TNT. That’s when I’m mad and when I’m serious. Other than that, you’re not going to get that out of me, so I was just joking people. The Earth is not round, it’s flat. I mean, the Earth is not flat, it’s round.”

One thing that should be added to these statements is this: there are people who are actively spreading misinformation about the state of the world, for instance that the earth is flat. The internet, Youtube, blogs, you name it, has given these people a soapbox that they would not otherwise have. Given that there is a blatant antiscientific thread in the United States which is attacking accepted, settled science as a big cover-up designed to destroy the rights of the everyday man, it is the duty of scientists and educators to take the truth seriously. In a world where Theory of Evolution, Climatology and Vaccine science are all actively politicized, we have to stand up for the truth.

Where real scientists are about studying and doing our work, the antiscientific activists are solely about spreading their belief… they don’t study, they don’t question, they spend their time actively lobbying the government and appealing to legislators, running for and getting onto school boards where they have an opportunity to pick which books are presented to school districts and various places where they can actively undercut what students are told about the truth of the world. They aren’t spending their energy studying, they are spending their energy solely on tinkering with the social mechanisms which provide our society with the next generation of scientists. As such, their efforts are more directed at undercutting the mechanisms that preserve the truth rather than on evaluating the truth… as scientists do. These people can do huge damage to us all. Every screwball coming out of a diploma mill “Quantum University” with a useless, unaccredited ‘PhD’… who goes off to promote woo-bong herbalist healthcare as an alternative to science based medicine, does damage to us all by undercutting what it means to get healthcare and by putting crankery and quackery in all seriousness at the same level as scientific truth when there should be no comparison.

If everybody understood that there is no ‘alternative’ to the truth, joking about what is true would mean something totally different to me. But, we live in a world where ‘alternative facts’ are a real thing and where everyone with a soapbox can say whatever they wish without fear of reprisal. Lying is a protected right! But someone has to stand up for truth. That someone should be scientists and educators. That should include an ‘education doctorate’ like the Shaq. If he were an NBA numbskull without the doctorate, I would care less: Kyrie Irving is a joke. But he isn’t; he’s got a doctorate and he has a responsibility to uphold what that degree means! The only reason humor in irony can work is if it can be clear that one is being ironic instead of serious… and that is never completely clear in this world.

# How to learn Quantum Mechanics: not like this!

This particular topic never fails to get my hackles up. At breakfast this morning, I stumbled over an article about Willow Smith. This article linked to a profile on the same person.

Up front, Jaden and Willow Smith have both made their feelings about school well known. They are home schooled and actively decry spending time in the classroom.

The Smith kids are a master course on how to game the media. Every article about them comes off crooning over how smart and otherworldly they are. Jaden Smith opens his mouth and utters endless solipsisms with offhand references to ‘mathematics’ and ‘theoretical physicists’ and the tabloids bend over in awe about his perceived intellectual might. Never mind that for all his talk about ‘math’ and ‘physics’ he has not once pulled out any associated skill in a place where it’s clear that he doing anything but reading Deepak Chopra –which is a really bad way to learn anything about Quantum Mechanics.

When I think of Willow Smith, I will always think of this:

I went to school for one year. It was the best experience but the worst experience. The best experience because I was, like, “Oh, now I know why kids are so depressed.” But it was the worst experience because I was depressed.

Followed closely by this:

maybe even attending the Massachusetts Institute of Technology (MIT) one day. It’s why she hopped on a flight to tour the campus in Cambridge directly after Paris Fashion Week (where she excited a flashing mob of paparazzi with karate kicks at Chanel’s #frontrowonly show—NBD!). “It was nice to be able to talk to female students and professors about science and logic because that’s just such a man’s world,” she notes.

This pair of quotes is separated by a couple years. The first outlines why she won’t stay in school while the second is suggesting that she’s thinking about jumping into the iconic school of STEM education. Does she want to be in school or not? She’s been in school for only a year total in her life and doesn’t like the process, but she wants to jump into MIT??? If you can’t handle the classroom in a normal highschool, you are not only flunking out of a University, but talking about a place like MIT just for the name recognition is a complete joke. To get into MIT and make it meaningful, the bare minimum is not merely a GED, it’s excellent scores on ACT and SAT. You can’t just talk your way through that. Maybe money is enough to open all the doors, but what do you do when the professor has shoved a test in front of you and demanded that you either get an ‘A’ on it or fail? You can’t cry about gender discrimination if you are not capable of handling the task put in front of you… and it sure as hell won’t be a photo shoot with you dressed head to foot in swanky leather.

Now, it’s with me forever and not just words. The feeling and the vision are still there along with the addiction of cracking problems apart and seeing where they implode into order.

In truth, there are people in this world who are ‘that’ smart. There is a small chance the Smith kids are among them. I do believe them to be bright, but how bright? Not like you can actually tell something like that from a tabloid interview. I’ve met and interacted with a few of these people, though I wouldn’t qualify myself among them. These people are truly scary because no matter how hard you work, they do better than you on the same test without having seemingly put in the effort. On the other hand, when they talk, it’s clear that they know what they’re talking about… with the Smith kids, it’s endless alliteration and metaphor without any substantial verification of the background. They use the words, but shove them into metaphors as if they have no concept of what the words actually mean. I was completely capable of that myself at that age! I talked endlessly about hypercubes and event horizons when I was seventeen, but ask me now if I truly understood it.

This particular article about Willow Smith drove me to write something on this blog because of this:

Willow sews clothing, hosts underground teachings in quantum mechanics, and is studying how to produce songs from mathematical equations

And in the other article, this:

1. Willow Smith likes to sew.

2. Willow Smith is a self-proclaimed “STEM freak.”

3. Willow Smith chatted with female professors at MIT about science and logic, and might attend school there.

4. Willow Smith’s eyeliner philosophy is “all about emulating the colors you feel inside,” which is probably the best eyeliner philosophy, tbh.

5. This whole interaction between Willow Smith and Siri: “‘I see myself as a — hold on, let me ask Siri.’ The teenager whips out her iPhone and speaks into it, drawing stares from tables nearby. ‘Siri, define artisan.’ Everybody’s favorite robotic voice serves up a satisfying definition: Artisan is a worker in a skilled trade, especially one that involves making things by hand. ‘Ah, OK, yes!’ Willow allows. ‘I call myself an artisan.'”

6. Willow Smith is studying how to produce songs from mathematical equations.

7. Willow Smith “hosts underground teachings in quantum mechanics.”

A big portion of what’s written here is about some combination of science, physics and math… having never actually demonstrated a competence at any of these in a public framework! What does it mean ‘hosts underground teachings in quantum mechanics?’ Is she sitting around with a group of her friends learning how to derive Klebsch-Gordon recurrence formulas?  For all that the article applauds her for using the words, there’s zero demonstration of the substance. You can look back at my post about Quantum University to know what I think of that.

I’m all for STEM education in women. I’ve dealt with female physicists who pulled higher scores than me in my quantum classes. I have a deep respect for women in STEM and I know flat out that they are capable of wickedly cool things. Take Emmy Noether, for instance. General Relativity would not be the same as a field without her. The difference here is that Emmy Noether actually did it. She didn’t wear around the aura of doing it, she didn’t abstractly pay lip service to ‘quantum mechanics,’ she produced real mathematical topology results never having once wasted her time singing about it in a recording booth, going on photo shoots for whoever or beaming about Prana energy, Ayurveda or Osho. After they get to the level I’m at, most of these women stop worrying so much about how they dress or what makeup they wear because they simply don’t have the time to spend the effort. I respect them because of the bias they wade against in many fields and it blows me away when they dress just as comfortably as the guys and pull through tests neck-in-neck. They can certainly do what they want with their clothing, but with many of them, it’s clear where they put their budget of energy. Most stop troweling on the eyeliner or lipstick unless they feel like it. Give me a clean-faced, smiling woman in flat, comfortable shoes with a three second pony-tail talking competently about Fourier transforms over this paper-tiger with her photo shoots and nonsensical posing any day. Willow Smith is casting the image of what popular culture wants smart to be… not what it actually is!

This girl could be an incredible benefit to her generation: she could make it cool for girls to do well in engineering type disciplines (if she were actually doing that, of course, which is debatable). She and her brother could make it cool for kids to be science geeks like I was. However, in order to actually accomplish in these fields, you can’t just wear the aura. If you are divided in your path and can’t get behind the idea of sitting in a classroom learning how to tell when you’re wrong, and really being pushed into a territory where almost no one is just ‘comfortable,’ you aren’t making it. Don’t delude yourself, it’s never just the words! Anybody can sound smart.

Much ado is made about them ‘teaching themselves’ in the book of life and how much better that is than the classroom. The problem with self study education (autodidacticism at the extreme), is that it’s hard to learn how to error-check your own thoughts. There are not that many true autodidacts because of that. People don’t easily step outside of themselves to know whether the information they’ve picked up is correct or not. Adding to a library means sometimes knowing when to discard a book. For instance, reading Deepak Chopra is not going to take you anywhere in learning quantum mechanics, but you can’t necessarily know this without some external direction since Chopra actively works to make what he says look like a legitimate truth deserving of as much consideration as what the topic of quantum mechanics actually contains. If you’re spending too much time pondering such chaff, you go nowhere with the things that have substance which take huge amounts of time to understand, like real Quantum Mechanics. And, if you accept what Chopra says as a valid interpretation because of some eastern mystic mentality, you have sabotaged yourself from knowing what real quantum can give you. For something like this type of physics, which contains no close conceptual parallels in our workaday world, without some guidance toward where the field lies, there’s not any reason why anyone can teach themselves to sort out what’s truth from what isn’t.

I think that the path to deep understanding of something like quantum physics is not along the path she’s walking… if she were actually walking it, it wouldn’t be ‘learning how to make songs about mathematical equations’ it would be ‘learning math.’ You can’t go deep or far if you’re divided. Your purpose can’t be distantly around, it has to be directly through. For instance, you can’t really learn quantum if you’re wasting time pretending that Ayurveda contains some kind of equivalent truth. That would have you spending time on the Ayurveda and not on the math. Quantum is a handful all by itself, let me tell you! I wish very much for her to prove me wrong, to prove to me that she has some substance to go with the borrowed legitimacy from using the words ‘quantum’ and ‘math’ to describe half of what she does. If I were invited to one of her ‘underground quantum mechanics teachings’ believe me, I could knock the topic straight and make it real… but I doubt anybody like me is ever invited. Likely, it’s all Ayurveda and Chopra and 2% real quantum.

Prove me wrong, girl! In five years, when you’re 20, after you’ve scraped off the makeup and put away the toys, gotten the GED and dominated the aptitude tests, then spent enough real effort on learning higher math to know what an equation is, we’ll chat again about what you like at MIT.

Math is fun, but you’ve got to really do it!