Equations. Sharing experiences —one equation at a time.

Posts tagged engineering
signal-to-noise ratio.
















Picture of the entrance to Building 37 at MIT, below the image of Astronaut Dr. Ronald McNair is a signed copy of the first page of his dissertation.


Typically sophomore year an undergraduate studying Electrical Engineering* will encounter signal-to-noise ratio or SNR. A simple ratio, much more powerful concept. SNR = P(signal)/P(noise). Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful information) and the power of background noise (unwanted signal). So the larger the the noise (unwanted, non-meaningful information) the smaller, less clear the signal or the information you need. I told you it was simple yet powerful…

Thesis stories:

Everyone who has a doctorate has one. It’s almost like the “how did you meet story” for couples. I love hearing them, the good, the bad and the ugly ones. My favorite one is that of Dr. Ronald E. McNair

I have made it tradition to go to building 37, the McNair Building here at MIT, on January 28th, the day we loss one of the great one in the Space Shuttle Challenger disaster. I remember running around McNair Hall at NC A&T State University as a kid at summer camp unaware that the face on the sculpture in the front lawn would follow me throughout my life. I will never forget Dr. Shirley Ann Jackson telling the story of how he lost ALL of his experimental data (2 years worth!) for his doctoral thesis right at the end. He never complained, they said he just showed up the next day ready to start all over. He focused on the signal. He focused on the fact, that it all the experimental nuances and data analysis outcomes were fresh on his mind. The noise of the despair and despondency he had to have felt as one so close to the end of his journey, he minimized it! And he did start all over, and over the course of a year he replicated all of the experiments and ended up getting better data the second time around…and his PhD. He understood SNR. He focused on the signal.

My thesis story is a little more dramatic… If you follow me on Instagram, I’ve been sharing mine little by little. But if you haven’t, it goes a like this…my Dad, Kenneth Johnson, literally saved my life* and lost his life all in the course of the completion of my dissertation work. I was wrapping up my Ph.D. when he was diagnosed with Stage 4 lung cancer. He always taught me to finish WELL (thus my #finishWell hashtag everywhere) and the day he died, as God would have it, I received an email that my very first, first author paper was accepted and I’d been asked to give an invited research talk at ICPT in Grenoble, France. At the time I thought it was ridiculous, like God was mocking the nightmare that had become my life, I couldn’t even imagine going back to school much less functioning well enough to present a technical paper in another country. I was focused on the noise. But, I remember what my brother-in-law said in my father’s eulogy, he quoted the scripture from a conversation he had with Dad, “always be sober, endure suffering, do the work and carry out your ministry fully” 2 Timothy 4:6–8.

always be sober, endure suffering, do the work and carry out your ministry fully
— 2 Timothy 4:6–8.

And for an imperfect man, he sure finished his life SO WELL. He was sober and free of addiction for 25 years, he did the work not only creating a well-respected, waterproofing business for himself but that gave employment to those others found unemployable, he carried out his ministry fully as a loving and involved husband, father, grandfather and uncle. And to that I had no choice but to focus on the signal = FINISHING. I miss him like crazy but in honoring him, death has truly lost its sting.

McNair Building.png









Of course I held my thesis defense in the McNair Building. I would have had it no other place on the entire campus.

Now that I've shared my experience, if I may humbly give some advice on completing the doctorate, this would be it. Your ability to control the SNR in your everyday (every hour) life will positively correlate to the amount of time it takes you to graduate and how much hair (and sanity) you have left when you do. So, here’s my advice for focusing on the SIGNAL and keeping that SNR to unity:

  1. Take care of your mind daily, like you would your body. Cleanse it with meditation, nourish it with prayer & strengthen it with positive thoughts and laughter. {Here’s a bibliography of positivity1/2/3/4/5 & humor 1/2 (since your family will never truly understand why someone your age lives in a dorm & makes less than minimum wage)}
  2. Relentlessly ignore all distractions (aka NOISE). If it takes getting rid of your precious TV for a couple months, getting a flip phone or setting your phone to be contacted for emergencies only and fasting from email (except your advisor and committee!)/social media (here’s how!)/negative folks, naggers & naysayers (here’s how to politely say no). Sorry but you gotta get ruthless on this one.
  3. Set yourself up for success. Sunday is it! Meal plan , clothes plan (even if you have to wear the same thing every.single.day, it will save you precious time) & drown/schedule yourself into radical accountability (1 /2/3/4) and focused routine.
  4. Do it. Hour by hour, day by day, month by month…“Focus on the Signal” -Dr. Carol Espy-Wilson or as Aristotle put it (for my non-science doctoral students reading this blog) “Aristotle said, “Excellence is never an accident. It is the result of high intention, sincere effort and intelligent execution. It represents the wisest option among many alternatives.” He said, “Choice, not chance, determines your destiny.”

That’s all my advice for now, until you’re ready for the big day for which I have worked with the great folks at Kit http://kit.com/joyjohnson/dissertation-defense-day-kit

I cannot wait to call you Dr!


*(another story for another day but let’s just say a father can tell better than a Harvard board certified doctor when his daughter is bleeding out. An outpatient surgery that turned into a major emergency surgery with two transfusions, a weeklong hospital stay and almost 3 months of physical therapy & recovery….its just NOISE to a PhD student trying to graduate, focus on the SIGNAL (and get a second opinion;).)

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ohm's law.
Advertisement for a freshman circuits course, 6.002, at MIT.

Advertisement for a freshman circuits course, 6.002, at MIT.


Ohm’s law is the first law an electrical engineer learns. The model equation, I = V x R where I is current in amps, V is voltage in volts and R is resistance in ohms. Simply put as electrons (or little negative charges) travel through a “circuit” or a closed loop connected to a power source, their ability to travel is affected by elements along that loop which can slow them down (resistance) (current is just a form of speed or the rate of change in charge over time). Simple, right? Ohm’s law actually preceded the more rigorous Maxwell’s equations we all know and love😒, but simply put it suffices to solve most circuit problems on a typical undergraduate exam and is the foundation of complex circuit design..it will also help you understand a similar, linear equation I find myself in as a non-wealthy person of color in a tech startup.


It’s 10pm. I’m standing at the Boston Medical Center bus stop completely lost in my own thoughts.

Why is iOS9 completely incompatible with XCode?
Did I remember to do that last commit before I left the office? Is the intern syncing right now and causing conflicts in this production build😒😒😒
My knees. Are they still attached? This run got the best of these 30 year old knee caps. I can’t feel my knees. I can’t remember if I committed my changes. No memory, no muscle memory, boy I am getting….mature.

Until I hear someone yell “is THAT your wife? Hey man, is THAT YOUR wife? I said is THAT YOUR WIFE?” Me, being no one’s wife and someone who doesn’t typically respond to yellers continue to wade through the my thoughts and backtrack my steps before I left the office trying to remember one command and only one.. ‘gitcommit’.

After a couple minutes I notice out of the corner of my eye a man in the median of the perpendicular street frantically motioning in MY direction, I turn down the music in my earpods so I can hear what he is saying to the yeller. He’s yelling back “she’s not my wife, she’s not my wife. Leave her alone man, don’t hurt her she’s not my wife.” HURT!?!?! I look in the direction of the yeller and he’s coming down the street, quickly but clearly incapacitated by substance or illness, who knows which, but with a long silver object in his hand, still yelling. As he gets closer he starts to pick up speed and just as I look away I hear the man at the median say “just RUN, RUN babygirl”. Just then, I forgot about my kneecaps (and unsync’d code) and just took off running down Mass Ave. I was running so hard and so fast that I think after a couple blocks my legs were outrunning my torso and I was airborne like my dude in Juice. My forehead somehow hit the concrete first and as I tried to catch my fall, my hands were next. I didn’t let my legs and feet hit the ground for more than a couple seconds so that I could get back up and keep going. When I stood up I realized I had ran to Dorchester, I was almost home and thankfully the two men were no where in sight. And the hospital was but a collection of lights in the distance.

Walking home with bloody hands and sore limbs all I could think was “I could have died….I could have died….I could have lost my life…and for what?” At that moment I realized that entrepreneurship is not the glamorous, hipster lifestyle portrayed in the magazines and movies with the dope, modern co-working spaces fully stocked with free food and the freedom to work on cutting edge technologies with “friends.” I asked myself in that moment, “Who do I think I am that I think I can I afford to be in a startup?” I thought about the fact that me getting paid below market salary is an entirely different situation than that of my teammates in the startup company I work in. My mind immediately went to an article I’d read that week in The Atlantic. [Insert rant about the economic disparties between most minority millennials who help their families with necessities and/or monthly expenses and do not start life as a working adult with the proverbial ‘path of least resistance’ by not only having trusts and inheritances but the financial support of their parents like most of their non-minority colleagues]. But the fact of the matter is, if they got paid $0 from the company they could maintain a fairly comfortable lifestyle while I’d still be running from the deranged man at the bus stop bc I can’t afford to drive or not work a second job (and third job) since I do not solely support just myself, which is also the reason I’m out so late. The risk that they take and the one I take are astronomically different….whole dwarf planets away. Not just the safety risk but also the monetary ones. The resistance is orders of magnitude higher.

The article aforementioned describes how minority millennials “almost always talk about financial help they give family members. People come to them,” Shapiro said. But when he asked white interviewees if they were lending financial support to family members, he said, “I almost always get laughter. They’re still getting subsidized.” Don’t get me wrong, I consider it a high honor that I get to help my family financially. When my father left this earth, he did not leave me empty handed. He taught me how to make money, not how to depend on him for it. {He always told me that he could have made the small waterproofing company he created from a curiosity into a common moisture problem of his pest control clients into a million dollar franchise but he was happy to keep his sobriety and his wife by making enough to take care of us while still being there for us. But not franchising, meant making a 6 figure salary on a 6th grade education where he had to work to make money, no passive income only biblical.

Not having that cash cushion makes the free flow of electrons in this entrepreneurial circuit I am trying to travel through significantly harder as I have to add resistors like time consuming part-time jobs, longer commutes due to dependency on public transportation, creditor stress and other distracting inefficiencies to my day just to keep myself going financially.

What this means for me, and a lot of other millennials (minority or not) who do not come from wealth, who decide to join startups with little funding (like most in the real not the fictional Silicon Valley) means not only increased resistance on our own paths but on those who depend on us as well. It means potentially no longer being the person your family can turn to when they need to make ends meet. It means potentially taking out loans and credit cards on an otherwise pristine credit score once saved by part-time jobs, scholarships and fellowship funds. It means being the only person on your team with a part-time job…or two. It means your all-nighters on pitches to investors and code for demos doesn’t end when the task is done since you still have to go into your part-time job while the team sleeps in the next day. It means getting creative, really, really creative (but I’ll save for a post I’ll creative ways to make money quickly without involving a plastic bag…or plastic heels). It means that just when you thought “education” was your ticket out…out of subsidized housing, out of check-cashing lines, out of foodstamps, out of debt. Startup life may have just voided that ticket.

Welcome to startup life for the Young, Gifted and Black.#startupLife


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