A philosophy of circuits, systems, and signals in biomedical engineering

A final lecture delivered to the students of of BIOMEDE 211 on April 23, 2019

I sing the body electric

Circuits
In circuits there is repetition. Loops, paths, meanderings. Time and again we end up at the same place, having tread the same paths we have before, or those similar. Indeed many of our analyses require such circuitous wanderings. We must conserve energy, mass, charge. Summing things up, we are often left with a zero: a numerical nothing that still must go around in a circle — a circuit — to express itself. There can be meaning in repetition. 
 
Systems
Within systems we can broadly understand a slew of specifics quickly. Emergent behaviors can be quickly realized, adapted to, controlled, approached. To know how something will respond, how it will react, what its future holds, is the power wielded by those systemic thinkers among us. The ability to describe what a thing or a group of things will do with confidence is one of the few true powers available to we human beings. That we can do so, reliably and quantifiably across multiple planes of existence is nothing short of extraordinary. Simply to know if something will grow on forever, stay the same, or decay away into nothingness is know a great deal about the nature of Nature in your presence. To do it again and again, adds to our understanding.  There can be meaning in repetition.
 
& Signals
That meaning in motion is what we might call a “signal”. Data, information, something expressing something as a function of something to tell us just that little something more, that is what we are after in all of this. To go in loops to grow or decay, these are of local import. That such loops, such behaviors, can be captured, understood, and used to our desired ends is what makes this whole endeavor worth it. Perhaps a human, all too human, perspective in all of this can put thus: why describe what we cannot control? Indeed it was with the naming of things that humans first established their dominion. To name what comes of circuits and systems — namely signals — is the desire, implicit or explicit, to control them. Such powers of control are starting to come under yours.
 
in biomedical engineering
And this is because we have now spent approximately one hundred days studying the subject matter of circuits, systems, and signals within biomedical engineering. I have tried, at each opportunity I was afforded (from electrocardiograms to pacemakers), to ensure that what we learned was relevant and of specific interest to those studying biomedical engineering. 
 
Our choir is distinct in this regard. We, as the American poet Walt Whitman figured it, “sing the body the electric”. As the poem goes, Whitman explains
The armies of those [we] love engirth [us] and [we] engirth them, 
They will not let [us] off till [we] go with them, respond to them, 
And discorrupt them, and charge them full with the charge of the soul. 
 
Was it doubted that those who corrupt their own bodies conceal themselves?  
And if those who defile the living are as bad as they who defile the dead? 
And if the body does not do fully as much as the soul? 
And if the body were not the soul, what is the soul? 
Indeed, this may be as good a summary as any that may be given on the matter of why it is that we do what we do. We observe, understand, and wish to care for the bodies of others via, in this class at least, the laws of bioelectricity and principles of good engineering. To help others is the primary motivating factor moving most of through the class — to “charge them full with the charge of the soul.” 
 

The expression of the face balks account

Thanks in part to this class, we know that the time rate of change of those charges is called “current” and currently, I can see at least one or two faces around the room in which, to such notions as these,  “the expression of faces balks account”. Is this really what this class has been all about? Is this really the sort of class that can charge others with the charge of the soul?
 
I think it is.
 
Moreover, I think a good lot of you think it as well. When asked who you all were as engineering students on our recent quiz, many answer came back with just humanistic tendencies:  
  • I want to help people and solve problems (N. P.);
  • I will leave positive and constructive ideas and thoughts in the world and contribute to the betterment of life quality (M. A.);
  • Looking to […] make the world a better place by implementing […] those learned skills in the field (X.); 
  • Improv[ing] some aspect of mu field of study in order to contribute to the growing Bank of Knowledge we have built (A. S.); and
  • I’d like to do my best to understand how my actions affect others so I can do right by people (I. H.).
This is not to suggest that our minds are not periodically (often?) bombarded by thoughts of negativity, inadequacy, or uncertainty. For instance, some of us have taken to describing ourselves to that same prompt as “a mess”, “below average”, and noting there have been “a few tears”. But that “mess” is trying their best to be an engineer. That “below average” is passionate about what they want to do. Those “tears” have been accompanied by “figuring out what it means to learn how to think and explain [my] thoughts to others.” And that’s something. To try is something. It is often enough. And don’t you forget that.
 
Often we are our own harshest critics. But, if I may quote, with slight modification, another American poet of sorts, President Theodore Roosevelt:
It is not the critic who counts; not the [one] who points out how the strong [] stumble[], or where the doer of deeds could have done them better. The credit belongs to th[ose] actually in the arena, whose face[s are] marred by dust and sweat and blood; who strive[] valiantly; who err[], who come[] short again and again, because there is no effort without error and shortcoming; [] who do[] actually strive to do the deeds; who know[] great enthusiasms, the great devotions; who spend [themselves] in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if [they] fail[], at least fails while daring greatly, so that [their] place shall never be with those cold and timid souls who neither know victory nor defeat.
To try is enough sometimes.
 

Of wonderful vigor, calmness, beauty of person

To this point in our lives, school has conditioned us to focus on the workproduct and outcomes of school — the homework, the tests, the grade. Some pathologize this further, finding value only on what is assigned, assessed, and graded. Such souls mistake the exercise for the act, the picture for reality. But I am here to tell you that the world extends beyond the four corners of a given assignment. There are horizons, I would rather you have your eye on.
 
Here at this level of education, it is about developing you the person, not you the transcript. What matters is you the flesh and blood human beings here in this room, not some assembly of documents (resume, project portfolios, etc.). The hymnal does not sing, does not uplift, does not join in the human chorus of living, breathing, sweating, spitting, teeming collection of souls that make up our fine choir here. We must give voice to what we put on the page, we must provide the action. We must make ourselves capable, then make ourselves do.
 
Here at this level of education we are not necessarily training you for the job you get right out of college. (Here’s a dirty secret: you could/can get many such jobs with a decent public high school education and experience. It really is okay and even preferred to receive “on the job” training. Your employers, those paying you to do something, will let you know what they want.) We here are instead trying to prepare you for the job you will have half a dozen years down the line, when your experience must be tempered by judgment. We are here to shape that temperament, to form that judgment.
 
That one’s sense of competent judgment is not uniform nor steady is not something I must here preach. We know what it means to doubt. The general trajectory of your confidence in your own abilities often goes something approximately thusly: you go from knowing nothing in high school to knowing it all in college back to thinking you know nothing after college, then to something about nothing, something about a little, then a little about something. That’s progress. And it takes time. And it takes eyes toward summits, legs compelled to bring you there, and a steadiness of stride. You can have your doubts, as long as you make room for a little hope too.
 
You have to get there yourself, but you need not go it alone.
 

I have perceiv’d to be with those I like is enough

In another class, in another speech, I remarked that “Some of this, I think should understand, is artifice. I am not the one doing the teaching. Rather, we are all doing the learning.” In the less-than fifty hours I have up here to convey all that I know, think, and care about circuits, systems, and signals in biomedical engineering, I have tried in many ways to get us all learning from one another. This has included in-class worksheets where we have worked as individuals, pairs of individuals, and/or small groups to come to answers, we have shared those answers aloud with our colleagues, we have attended office hours and review sessions and study groups, we asked each other questions, we have facilitated each others knowledge, we have benefitted from mutual understanding.
 
That is because this University as a place on earth is something special. The halls are hallowed by lofty conversations, the rooms are charged with hope, expectation, ambition (thwarted or otherwise). But that is only because you all attend this fine institution. “The only thing special about this place is the people. And you are the people. Emptied of you, this place has the mere residue of wonder.” That is because you are all smart, talented, capable, driven, even if you don’t think you are, even if you don’t believe you are, even if you’d fight me on the subject! You all are a special lot, and our times here together are special by consequence. 
 
Whitman again reminds us
I have perceiv’d that to be with those I like is enough, 
To stop in company with the rest at evening is enough, 
To be surrounded by beautiful, curious, breathing, laughing flesh is enough, 
[…] 
I do not ask any more delight, I swim in it as in a sea. 
 

As I see my soul reflected in Nature

The seas we have sailed have at times been rough. Maelstroms of swirling doubt, thunderclaps of frustration, waves of exhaustion, all for what? What have we learned? To answer my own rhetorical question with my own rhetorical device, we have learned a lot in the class, including but not limited to the following topics:
  • what electricity is;
  • how charges move in space and time;
  • current, its direction, its possible deadliness, its “speed”;
  • potential differences;
  • power;
  • energy;
  • active and passive circuit elements;
  • Ohm’s law and what it means both physically and within our analyses
  • voltage and current sources;
  • resistors, resistance, resistivity;
  • capacitors, capacitance, their time- and frequency-dependent behaviors;
  • inductors and how they store energy as distinct from capacitors;
  • impedance;
  • equivalent impedance;
  • equivalent impedance for series and parallel circuits, for delta-wye circuits, for whole networks of components;
  • grounds;
  • conductors;
  • switches;
  • transformers;
  • operational amplifiers including their detailed operation, the rules governing their behavior, a few short cuts;
  • inverting amplifiers, non-inverting amplifiers, voltage followers, summing amplifiers, differential amplifiers, (instrumentation amplifiers);
  • nodes, branches, loops;
  • the Seven Bridges of Konigsberg;
  • the fundamental theorem of network topology;
  • Kirchoff’s current law (a reformulation of the conservation of charge/mass within an electric circuit);
  • Kirchoff’s voltage law (a reformulation of the conservation of energy within an electric circuit);
  • nodal analysis;
  • solving simultaneous equations via Cramer’s rule;
  • mesh analysis;
  • circuit analyses with controlled sources, requiring us to develop supernodes and supermeshes;
  • linearity;
  • superposition;
  • source transformation;
  • Thevenin and Norton equivalents;
  • Euler’s formula and identity;
  • the Laplace transform;
  • the Laplace transform of a constant, of an exponential, of a derivative, of an oscillating function; of RLC circuits;
  • the s-plane;
  • poles and zeroes;
  • the general form of just about all systems;
  • undamped, underdamped, critically damped, and overdamped systems;
  • inverting the Laplace transform;
  • representing circuits as ordinary differential equations;
  • source-free RC circuits;
  • source-free active circuits;
  • first- and second-order systems;
  • singularity functions such as the unit step function, the unit impulse function, and the unit ramp function;
  • pulses and impulses
  • convolution, mathematically, graphically, conceptually;
  • the relationship between convolution and the Laplace transform;
  • the stability of systems with bound inputs and bound outputs;
  • the relationship between stability and poles and zeros;
  • a bit about resonance;
  • the Q factor;
  • ideal inverting integrators;
  • a modification to said ideal inverting integrators that yield low pass filters;
  • ideal inverting differentiators;
  • a modification to said ideal inverting differentiators that yield high pass filters;
  • non-inverting variants of low and high pass filters;
  • combining different filters to achieve desired bandwidths. passing frequencies we want and attenuating the rest;
  • open-loop systems;
  • closed loop systems;
  • block diagram algebra to describe system functions;
  • feedback control;
  • PID feedback control;
  • the passive electrical properties of biological tissues as when we spent a good deal of time deriving their characteristic semi-circular arc in the resistance-reactance plane;
  • the active electrical properties of biological tissues stemming from the sodium-potassium pump, membrane capacitance, potassium ion channels, sodium ion channels, leakage channels;
  • electrocardiography’s underlying physiological basis, historical development, and measurement via the leads of Einthoven’s triangle;
  • the basic concerns of hardware and software engineers in the development of biomedical instrumentation;
  • electrophysiology briefly (as manifest in electroenecephalography, electrooculography, electromyography, and electrogastrography;
  • digital logic springing forth from the mouths of knights and knaves, those truth tellers and liars among us;
  • digital logic gates such as NOT, AND, OR, NAND, NOR, XOR, XNOR;
  • representing logic graphically in truth tables;
  • establishing functional completeness to show that all logic springs from a singular underlying truth;
  • silicon’s desirability as a semiconductor;
  • doping, diodes, transistors, and their accompanying terminology;
  • a brief, all too brief, electronics laboratory exposure where teams could build and test their own bandpass filters;
  • an overview of medical device regulation in the United States via the Food and Drug Administration;and
  • ascertaining the hierarchy of standards applicable to medical devices so that we might build that they might use.
I hope you have seen fit to incorporate some subset of that knowledge into your brain, into your being, into your soul. There is something human in all of this. “I see my soul reflected in Nature, // As I see through a mist, One with inexpressible completeness, sanity, beauty”. We are what we know of ourselves and of the world we inhabit. And of those two things we have learned much, with more yet to know.
 

All is a procession

Whitman goes on to parenthetically state that “All is a procession, // The universe is a procession with measured and perfect motion.” Time goes on in our world, but we have also learned to look at it askance, from a perspective not of time and order but of stability and decay. We have learned of ideal components — “measured and perfect” — but I hope too that we have gained some sense of the messiness of reality, the ambiguity of what is asked, answered, conveyed, understood. We are not perfect, we are but human.
 
And as each and every one of you were important to what this class was, I think I as your instructor ought to acknowledge that. What follows is an individual thought for each of you, comprising this philosophy. I have listed you here in the order in which you registered for my first class. 
 
  1. Number seven (7). A. L. In describing yourself on our recent quiz, you describe us all: “stressed, sleep deprived, ambitious, want to design medical devices in the future.” Pithily are we put. May you relieve your stress, find your rest, and ambitiously pursue your future.
  2. Number ten (10). A. R. One of the hitches that comes with having me as a professor more than once is that I can recall what I said of you last time. “You will be remembered by me’, I had said, “and likely by E. as being the fellow who swooped in for those [extra] points in helping with our [discussion regarding] dying with dignity laws.” I said it then and I said it now “I like your gumption”. May you keep it ever with you.
  3. Number nineteen (19). L. N. Describing your journey through this class you started as someone “who knew nothing about circuits” and now complete your journey “understand[ing] the importance/relevance to the world and [biomedical engineering] as a whole”. Such a trajectory is the arc toward which the engineering universe bends: to go from not knowing, to knowing, to wishing to know more. May you continue on your trajectory.
  4. Number twenty-one (21). B. P. Though I was unable to provide you with an official “B Glorious Quiz”, I believe you had the magic when you crossed out the “A” and put your own B. P. “B” on it, as you did quite well on this third quiz (as the others). This is but a minor example of the larger point here: you can change the world for the better. May you always make the world better, with a capital B.
  5. Number twenty-three (23). A. B. While it appears that our sausage casing idea to help with bone healing might not work, I suspect it will certainly not be the last of your thoughts the matter and hopefully not the last words we share. Thoughts, ideas, experiments, they require continuance, perseverance, and those with the desire to move them forward. May you persevere in your studies and keep sharing your thoughts.
  6. Number twenty-four (24). Y. H. “This class”, I have you down as saying, “has proved surprisingly interesting to me […] it’s insane how much we’ve learned in such a short amount of time.” Though I might wish to attenuate the surprise a bit (we should expect our subjects to be interesting!), I am glad to hear that you have learned a lot. May you continue to surprise yourself and learn intensely.
  7. Number twenty-eight (28). J. D. Poetry can be found everywhere. Though I have somewhat forcibly infused it here, you gracefully incorporate it into most of your actions. In your recent quiz the answer describing you was broken into lines of a stanza that I quote here
    someone who works hard to gain 
    a clear and deep understanding of everything 
    that I learn, even when the topic is not something I enjoy.
    May you continue in your poetic grace.
  8. Number thirty-three (33). E. B. Though at times you have been frustrated, I have never see you flag or waiver. You show up, you try, and you see what happens. Even more than a principled understanding of circuits, systems, and signals in biomedical engineering, such an approach to life — to \textit{try try try} — will count for something significant. May you always try your best.
  9. Number thirty-four (34). A. R. You have recently remarked upon the “many cool and crazy things you can do with complex circuitry.” And believe it or not it just gets cooler and crazier from here. All the same, may you keep your cool when things get crazy.
  10. Number thirty-seven (37). R. B. One of the chief joys in this profession of mine is the front-seat view of many minor eureka moments. I reminded here of one instance in which you attended my office hours, asked several keen questions, and upon realizing that you had done it all all right from the start, commented “oh, is that all it is?” Yep, this is all that it is. While there’s plenty yet more to learn, you have grasped well what I have put in front of you. May you ever realize what you know.
  11. Number forty-one (41). I. H. To go that extra step is one of the surest signs of the helpful. To share what you have learned is one of the surest signs of the charitable. To do what you can for others is the highest calling of the engineer. As it was you and Ryan put together one heck of a good tutorial on how to create an actual bandpass filter with actual circuit components in an actual circuit lab, we in this class owe you that debt of gratitude. May you continue on your engineering journey helpfully charitable to all you encounter.
  12. Number forty-two (42) E. L. I still find the words you wrote in my ENGR 100 ringing around my head every once and awhile: “nothing should go so beyond the way of nature that it goes against it”. As this philosophy has been an experiment in my conception of Nature and our natures, knowing where the limits lie in each is profoundly important. Thank you this poetry which has accompanied me ever since. May similar poetry accompany you the rest of your days.
  13. Number forty-eight (48). A. S. A personable sort, you have helped to humanize the subject for those around you. Perhaps they have not said so directly to you, but I have been told by others that you have been boon both in class and in study groups. For helping others, I thank you. May you continue to humanely serve.
  14. Number fifty-one (51). M. M. Sunny when skies are gray, chipper when others are dour, you have kept your head up in class and down in your studies. May you find yourself happy in every space you occupy.
  15. Number fifty-five (55). S. D. Not all this language must be so grand, so verbose. In describing yourself you simply stated that you are “[s]omeone learning new things to implement later in life to hopefully help people.” To do what you ought, for who you can, when you are able is the responsibility of each and every engineer. May you continue on in your education, humbly, nobly.
  16. Number sixty (60). D. J. At times, I have seen you doubt yourself. Allow me to allay your concerns: Simply put, you are precisely the sort of engineer I want to see more of in the world. You are thoughtful (as I’ve seen in our bioethics discussion), you are motivated (as I’ve seen in your laboratory research), and you are learning all you can (as I’ve seen in at least two classes now). May you doubt less your once and future success.
  17. Number sixty-eight (68). A. S. You aptly note that “[You and your peers] are the future of this field, which is super cool :)”. Beyond cool, it’s necessary for the continuance of our discipline here. The trick of it all is that you all go off and  design medical technologies that folks like me then convey to folks like you who go off and design medical technologies that folks like me then convey to folks like you who then… There can be meaning in repetition. May you find meaning, peers, and a future in this field.
  18. Number seventy (70). E. K. I find it easier to use the words of others when they are substantially better than own on a matter. To wit, of this class you have said that it “consists of many people w[ith] many different backgrounds and many different goals in life, all brought together in a single classroom at 12:30 every Tuesday and Thursday by the shared intent [of] contributing to the biomedical world. […] We all have chance at making an impact on the world.” I could not and dare not say it better myself. May you continue to find the words necessary to charge others full with the charge of soul.
  19. Number two-hundred ninety-two (292). M. A. I have written of you recently, “[b]eyond being an objectively good student, Matt is one of those driven types whose flame behind the eye is apparent to all who meet his gaze. He has spoken of his desire to pursue advanced education after college (an M.D., a Ph.D.), having planned so far ahead for that possibility that he sought out research experience as early as his freshman year, a dedicated spirit that is remarkable even in the fertile and competitive grounds of Michigan.” I meant every word. May you continue to keep alight that flame behind the eyes.
  20. Number three-hundred twenty-nine (329). S. P. I hope your recent trip to Champagne-Urbana as a manager of the University of Michigan’s Men’s Gymnastics team was enriching. As it turns out, there is more to learn and do and see than the confines of this class allow for. May you continue to learn and do and see more after our time here.
  21. Number three-hundred thirty (330). R. S. An honest person is worth more to this world than all the talents all the liars may muster. From the first homework to the last, you have written right at the top of your homework who it is you worked with during your attempts. Such forthright admission is admirable and I hope you continue on your path honestly and forthrightly.
  22. Number three-hundred thirty-one (331). R. R. I hope you have begun to appreciate that there is more to each subject than what a single class can say. You have gone from the briefest of glimpses of neural engineering in that incubator class to the slightly less brief view of the electrical engineering undergirding that discipline here. Yet, we were here only for a moment, however brief and wondrous. May you find more such moments in life.
  23. Number three-hundred thirty-two (332). W. C. Those students in the back of the room have the reputation of being the disengaged, the disinterested, the uninclined-to-do-well. Not so in your case. Consistently dominating the homework and the quizzes, you have shown that learning can happen anywhere in the room. May you learn where ever you are.
  24. Number three-hundred thirty-three (333). J. G. You striven greatly, learned immensely, participated fully. You have done each and everything I could ask you to do and you have done it well each and every time. Consistency of such efforts will take you far into the healthcare landscape. May you continue in your stride.
  25. Number three-hundred thirty-four (334). K. S. I have enjoyed and been thoroughly enriched by your independent research this semester. While almost wholly devoid of bioelectrical content, it has nevertheless enabled me to see your scientific mind in action and your experimental approaches on display. And though just the first steps of an endeavor that may end in heartbreak (experiments rarely go as expected), I know from your recounting the existential happiness you get from such Sisyphean efforts. May you continue stepping forward.
  26. Number three-hundred thirty-five (335). D. K. Though I am man of many, far too many words, I can appreciate when others have better words than I. Indeed I have found no better compliment of this class than in your recent comments on the subject . This “[c]lass”, to quote you verbatim, “was pretty fucking dope.” What more can I say, then to say, you’ve express all I ever wanted this class to express. May you continue to find the rights words and express yourself accordingly.
  27. Number three-hundred thirty-six (336). I. M. Some people quietly come in, crush their assignments, and walk out. You, in this case, are some people. As an aspiring doctor and/or engineer, you have deftly handled the material in front of you. Of the three quizzes you have been given, you have lost the fewest points. For that, you should be proud. For other things too. May you continue your competence deftly, developing confidence along the way.
  28. Number three-hundred thirty-seven (337). N. P. “Just a man” or so I have you saying “trying to excel at what he does  so he can make an impact in some way, shape or form […] to help people and solve problems.” The hopes and dreams of an engineer manifest. May you excel and help others while doing so.
  29. Number three-hundred thirty-eight (338). E. R. You have said that you are “here to learn [and] understand as much as I can and hopefully have some fun along the way.” Here, at the end of this class, I hope you have learned and understood as much as you could and had a little fun along the way. To know and to grow in the subject is the responsibility of every engineer. May you learn how fun it all be.
  30. Number three-hundred thirty-nine (339). H. S. Your consistent conceptual questions have aided you, the students around you as you ask them, and me as well! You have a mind structuring itself to reality. This positions you well to “ultimately save or benefit more people’s li[ves].” May you continue to ask good questions.
  31. Number three-hundred forty (340). M. W. Again, when I find others saying what I wish to say, I merely quote them. To quote you: “As an engineering student, this class has given [you] a basic understanding of circuits, system response, and many other topics along the way. Our methods of analysis and logic have improved [your] critical thinking. [You]’ve seen actual applications of the material we’re learning and [you] have a basis off of which [you] can learn more about things like instrumentation.” From such a description it is obvious to that you have understood the purview of the process: to learn, to know, to learn more. May you learn more to know more to learn more still.
  32. Number three-hundred forty-one (341). K. A. In my short time teaching I have come to discover that those saying few words are not those saying little. May we continue to hear more of what you have to say.
  33. Number three-hundred forty-two (342). M. B. I personally believe in mildly embarrassing the truly talented among us as humor is all the rest of us have. (Or tears.) To that end, allow me to state here for the record that earned the highest grade on the hardest test that I’ve yet put together. And that is one hell of an accomplishment. Join me in a round of applause. May you continue on with such an embarrassment of talents.
  34. Number three-hundred forty-three (343). F. H. You have described yourself as “optimistic, excited for the future, [and] interested in improving the quality of life for others.” May I say, I think you have found your calling here. Our glasses are fuller, our futures are brighter, our lives are improved by those driving to do so. May you keep your optimism as you excitedly dash into the future.
  35. Number three-hundred forty-four (344). S. J. Every year there is a student who comes in, says about half a dozen words, and collects one of the highest grades in the class. This year, you are that student. Though I may not have had the opportunity to learn about you in a more personal setting, your work speaks for itself. Talent needs few words to express. May you achieve all you want and say all you need.
  36. Number three-hundred forty-five (345). D. N. One of the things I genuinely appreciate is when someone in the back discusses the subject with me up here at the front. As we exchange words with one another, a few stray phrases find their way to ears that may benefit. Such indirect helpfulness often accompanies those honestly searching for the truth. May you continue to help others as you honestly search.
  37. Number three-hundred forty-six (346). M P. Though I think there is much that can be improved in your handwriting skills (as a lacker of those skills, I can identify their lack in others); I think you have learned just about all I can teach you with regards to electronic circuitry. May you continue to learn long after this class. And write it up well!
  38. Number three-hundred forty-seven (347). S. S. I have you as saying that you are “always on the verge of freaking out”. One of the lesser used definitions of a “verge” is a rod carried by a high official as an emblem of the office. Wear that badge of the engineering student “freak out” proudly. Just be sure those precarious steps along the precipice are accompanied by similar travelers. May you never walk alone.
  39. Number three-hundred forty-eight (348). E. S. Your submission to the GitHub modeling the the neuron via Python is downright fascinating and I would encourage everyone in this room to read it if they have not already done so. You go through a basic description of a neuron, establish a set of equations governing the openings and closings of various channels, and you code the whole thing up for us to see. Application of knowledge is ultimately what they pay us engineers for. May you continue to apply what you learn.
  40. Number three-hundred forty-nine (349). D. C. If no one has yet done so, I would like to thank you for your consistent participation in this class. Your questions are not the only ones in lying in the hearts of those here, yet you gave voice to them and asked what others did not, dared not. May you continue to give voice to the voiceless.
  41. Number three-hundred fifty (350). C. C. Rumor has it that you are interested in going into pediatric medicine. You may not know this, but that was what I wanted to do when I was younger, around middle school. But, upon learning of the mortality of babies, their finitude, I crumbled. I lack the bravery necessary to help those most vulnerable. I am humbled to see that you do not. May you have the courage to help the meek, the bravery to help the mild.
  42. Number three-hundred fifty-one (351). N. H. You have said that as engineering student you have to work hard. (I believe your actual quote was “I have to work a lot hard than the LSA kids”, but let us not compare ourselves to them!) But you noted that “it will be worth it when I am the reason people can stay alive.” Indeed, your tireless efforts here will prepare you for just worthwhile activities. May you keep your reason alive and help others in the future.
  43. Number three-hundred fifty-two (352). F. Q. I always appreciate when someone “gets” what I am after, when they pick up on what I am putting down. You have said that “this class has taught me so much more than I expected. Not only have I learned about the fundamentals of circuitry, but I also learned the importance of genuinely understanding material versus just getting correct answers.” If you have learned this much, then I have little else to teach you. May you continue to learn importance, genuinely understand, and always get out of this life more than you expected.
  44. Number three-hundred fifty-three (353). A. R. You have claimed to suffer from “mental blocks at times”. You could have and did fool me. I have seen you as hardworking, intuitive, and able to integrate what you have learned into your problem solving. May you continue to work hard, intuit well, and smash through each and every mental block foolish enough to get in your way.
  45. Number three-hundred fifty-four (354). C. S. It is a shame that I had to get to the penultimate-penultimate student of this to see my own philosophy stated better. To you, you have said, “being an engineer means holding myself to a certain standard and having the ability to solve problems directly by creating [] physical system[s].” Indeed, you must rise to your own standard. You must test your own mettle. You must measure the charge of your own soul. May you continue on with both high standards and high hopes.
  46. Number three-hundred fifty-five (355). J. W. Though obviously not your favorite subject matter in the world, you have shown up each day to this class to learn what you can. You participated early both in our board work and in our GitHub document. You have tried. And the fortitude of those who can try their best at what they like least is character-trait I dare say more important than electronics knowledge. May you continue to show up where there’s a challenge and face it, shoulders squared.
  47. Number three-hundred fifty-six (356). A. S. A late great addition to our class, showing up on day one without a seat to your name and continuing on here til, right up front, ready to learn. Tenacity does wonders for the tenacious. Often it is the tenacious that do wonders for the rest of us. May you continue tenaciously on in every class you find a a seat in.
 

In this head the all-baffling brain

That’s it. That was us. That was the class. 
 
Some at times refer to this sort of class as a “weed out” class. As one of the first (and toughest) engineering classes you take, the pace, the material, the concepts, it can all be so overwhelming. It can make you want to quit.
 
I myself subscribe to no part of that. This class is not meant to exclude, not mean to separate engineering wheat from non-engineering chaff. No one in this room doesn’t belong here. You have earned your seat.
 
“In th[ese] head[s] all-baffling brain[s], // in [them] and below [them] the makings of heroes.” What you feel, what you know, what you desire, each of these springs forth from a fount within you. Such waters may at times be stilled, spilled, or splashed all around, but may they never be depleted. 
 

If any thing is sacred the human body is sacred

“If any thing is sacred the human body is sacred”. We have learned but a small sliver of the circuits, systems, and signals necessary to measure that most sacred of electric bodies. There is still more to learn.
 
And if I can convey but one more lesson to learn it is that the measures heretofore applied to you and those measures which follow (grades, GPA, test scores, lines on a resume), these measures do not quite capture what is special about each every one of you. Though you should be proud of what you have achieved here — the grades you’ve earned, the knowledge you’ve gained — recognize still further that you are no taller at the summit, no shorter in the valley. We have many steps yet to take on our paths. Knowing who you are and what you like about yourself is the most important lesson I can convey.
 

I believe the likes of you are to stand or fall with the likes of the soul

Whitman concludes the final part of his poem by stating that “I believe the likes of you are to stand or fall with the likes of the soul”, as true here as it was in the Reconstruction Era when he first penned it. Find what makes you happy. Find what makes you challenged. Find what what makes you you. In this class and elsewhere.
 
With that, I thank you for the opportunity to dismiss this class one final time. I hope you all do well on your fast-approaching exams and on your ever-to-the-horizon journeys. I’ve done what I’ve can for you here and I trust that you can do more. Good luck.