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Thinking With a Fresh Mind

A brief anecdote.

Today, a student came to me with a question that their science instructor could not answer (the curriculum is mostly intro to chem with some classical physics). I am in no way, shape or form, a scientist or even a teacher of science, but the students know I’m interested in many odd things and like to reason through intriguing problems with them. The student asked:

“How can a photon – which has 0 mass – have 0 kinetic energy even though it is moving? If it does have mass, how can a photon go the speed of light?”

Now, I knew that the answer had to be explained via quantum mechanics and was fuzzily certain it was because particles did not behave as particles should in this scenario, but the ability to give a coherent and scientifically accurate explanation that related to the student’s current knowledge base was beyond me. I do not have a good enough grasp of the basics of quantum physics to lead the student to particles and waves through a series of questions. So, after complimenting him on his insightful question, I said I would contact an expert, Dr. Von, and get him a concise, equation-free, answer, which Von helpfully provided.

The point here, however, is not the answer (Newtonian physics is invalid at this scale and momentum is redefined in relativity theory which leads to particle-wave duality, uncertainty and other aspects of quantum mechanics) but the excellence of the student’s thinking that went into the question.

The student knew very little about physics except what was presented in the course – essentially, some laws of Newtonian physics, basic constituent parts of matter, simple atomic models etc. Given that information and having – this part is critical – no prior assumptions, having understood the “rules”, in a few minutes he identified a contradiction or paradox that undermined the authority of an elegantly constructed system of great explanatory power, conceived by the greatest genius to ever walk the Earth.

Not too shabby for a younger American teen-ager. Remember him the next time some loudmouthed fool opines how worthless kids are today or how they learn nothing at school.

Obviously, my student is quite bright, but his reasoning was also not polluted with the preconceptions we all pick up as we gain ever greater depth of mastery of a field. It was fundamentally new to him, so he did not yet have the kind of blind confidence in “the rules that everyone knows to be true” possessed by most adults and nearly all experts. He was still skeptical. Few content domain experts are innovaters for this reason. They are mostly overconfident masters with answers – not makers who create or discover the novel by asking questions. They are not skeptics, they are guardians of received knowledge.

We all need to step back, periodically, from the rush of life and our own pride and try to look at the things we think we know with a fresh mind.

23 Responses to “Thinking With a Fresh Mind”

  1. Cheryl Rofer Says:

    He was also trying to put together the facts he had to come up with a coherent answer. He came up with an apparent contradiction, and the question is about that contradiction.
    It sounds like it wasn’t an attempt to impress. That’s another bad habit adults get into. Ask a question to show how smart you are. Happens all the time in meetings and lectures. Another way to close your mind.
    So the kid is actually using his brain. We can hope he doesn’t close it down any time soon.

  2. zen Says:

    Hi Cheryl,

    No, he was not trying to impress, he was confused as to why the rules as he was learning them in class did not explain the situation. There’s usually very little exposure to physics in schools, unfortunately, until maybe the last couple of years of high school and none at all to modern physics ( I don’t think there’s even a textbook written yet for modern physics aimed at secondary students – too small a market to be profitable). That’s something I’d love to see changed but chances of that happening in education these days are about zero – states and Feds are moving in the opposite direction.
  3. J. Scott Says:

    Zen, Thanks for sharing; will second Cheryl’s closing comment: "We can hope he doesn’t close it down any time soon." A habit of skepticism can be healthy and enlightening. Our culture would be better-off if more people questioned the "dogma" we’re served daily; pick a topic: education, health-care, man-made global warming, terrorism—even COIN. Your student wasn’t simply asking "why;" your student processed the new data and found it wanting…May I suggest that we "step back" daily?:)) Thanks again!

  4. Shlok Says:

    So heuristic: Ignorance is the birthplace of Innovation?

  5. Cheryl Rofer Says:

    I didn’t  get to modern physics until my junior year in college – might have been sophomore year if I had been a physics major. I don’t think modern physics is much fun and is fairly incomprehensible – you have to take an awful lot on faith unless you really like the mathematics. That may just be a matter of temperament – I tend to be more comfortable with concrete things or things I can make pictures of.
    Shlok – I’d be really careful with that one. I’ve worked with people (physicists, some of them) who believed that not knowing what went before was helpful in innovation. They came up with an awful lot of useless stuff that had been thought of before. And that can crowd out innovation, too.
    Ignorance and a fresh mind are not at all the same thing. If this kid keeps thinking the way he is, he’ll maintain a fresh mind as he learns the material. And that’s the best basis for innovation – a fresh mind working on everything we know now.

  6. zen Says:

    Hi Shlok,

    Depends how you are defining "ignorant".
    The student’s knowledge of physics was certainly incomplete and his mastery level was that of a beginner but that’s not the same thing in terms of ignorance as, for example, equating witchcraft with the scientific method.
  7. Larry Dunbar Says:

    One thing they really don’t teach you in physics class, they are teaching two different classes. In one they are teaching the divergent lesson, as things are, but in the second class they teach the convergent lesson, as things really are. It is really hard to explain this, but if you actually think mass exist, then you are learning the lessons being taught in the divergent class. I mean in a way mass exists, but it is really just a sum of forces problem and that force comes from potential energy. That really creates a problem, because potentially it could or could not exist, i.e. there is just as great of potential in something not existing as existing. As we are all just created from potential energy, it means that we probably don’t exist. I am just saying he should keep his mind open, but don’t get bogged down in reality, only in what is real. It is really just a wave of velocity and force. If you can create something out of it like mass, then you are doing very well.

  8. Gray Hat Says:

    I realize your point had to do with psychology and curiosity, not physics, but (using only High School physics) I can’t see the contradiction that puzzled the student.  Kinetic energy is a product of factors, one of which is the mass of the moving object.  Any product one of whose factors is zero will be zero.  Now I grant that the idea of an "object" having "zero mass" may strain the imagination, but if you accept that, isn’t it self-evident that the object will have no kinetic energy?

  9. zen Says:

    Hi Gray Hat,

    Yes, but not if the "object" – in this case a photon – is also moving – that was the part causing the student’s difficulty.  Zero mass. Zero energy. Movement.
    Hi Larry,
    You’re right. It’s hard to introduce concepts at this level for students without unintentionally misleading them in an effort to keep things simple and clear. Ideally, it is a leaping off point to more nuanced understanding, but many students struggle with just grasping the concepts for the next few years
  10. Roy Lofquist Says:

    "If you think you understand quantum mechanics, you don’t understand quantum mechanics" – Richard Feynman. Nobody understands what really goes on at that level. A photon is said to have zero mass because it makes certain equations balance. There is a mathematical method in quantum mechanics called "normalization". It is, in essence, divide by zero and you get the right results. Ah, sweet mystery of life.

  11. Shlok Says:


    I’m with you. Rather than ignorance, a ‘fundamental but incomplete understanding’ is probably a better way to put it. In Taleb-speak, knowing enough to know that you don’t know.


  12. Antoinett Says:

    I love this blog….but as an organic chemist immersed with high school students; and, as a mother of two American college physic majors (junior and sophomore), I have to say to you, Mr. Zenpundit Extraordinaire,  keep the compliments to your students coming but please refer those questioning students to the ones who can answer their physics questions properly – their physics professors! Perhaps you will find a philosophical compatriot in the physics department.  I think you will be amazed at the Zenpunditness of those who teach physics.

    A loyal, appreciative reader.

  13. zen Says:

    Hi Antoinett,
    Gracias. I have to say though, in my defense, I  did refer my student to a physicist for a short answer ( see post) and also for the opportunity for a longer, in depth explanation, if he chooses to ask Dr. Von, who has years as a particle physicist at Fermilab under his belt, via email.  I also told the boy straight out that I could not effectively answer his question, so there’s no fear he went home today confusing me with Stephen Hawking 🙂

  14. karaka Says:

    Great anecdote. In my experience, either the act of questioning itself or putting the question to those who aren’t intimately concerned with the problem is often the difference between coming to a solution or struggling with a lack thereof.

  15. Andy Says:

    We all need to step back, periodically, from the rush of life and our own pride and try to look at the things we think we know with a fresh mind.

    Easier said than done, I’m afraid.   The sad reality is that most people believe they can look at things "with a fresh mind" but few are actually able to do so. 

  16. Ed Beakley Says:

    Few content domain experts are innovaters for this reason. They are mostly overconfident masters with answers – not makers who create or discover the novel by asking questions. They are not skeptics, they are guardians of received knowledge.

    "With a fresh mind" may be hard, but choosing a different"lens" or approach angle works well, I think.  As example Fourth Generation Warfare (4GW) gets much heat from some quarters for not having all its "i’s" and "t’s" nailed down historically, yet I submit if you really read the original by Lind et al, plus other well thought through pieces, it gives significant insight into warfare as it is today.  (And Von Clausewitz is still valid, suprise suprise). Debating whether 4GW is the crown prince of theory on warfare is fool’s erand.  To dismiss it’s approach is to be a "guardian"not someone digging for answers to messy problems however one can.

  17. Gray Hat Says:

    Let me try again.

    (kinetic energy) = .05   x   mass   x   (velocity squared)
    If mass = 0, it doesn’t matter that velocity is non-zero:  kinetic energy must be zero, because

    m = 0 –> mn = 0 for all n.

    What is the problem?

  18. Gray Hat Says:

    Oops.  Make that .5, not .05!  😉  Doesn’t affect the point, though.

  19. zen Says:

    hi Gray,

    Sorry, I understood your original point but didn’t explain my response well.
    The reason why the mathematical expression does not help in this situation is that, developmentally and demographically, it’s not an effective way to teach physics concepts to most students at this age level, though later, say AP physics and college physics, it’s the standard technique.
    Essentially, at an older age, physics is: 
     Concept—> mathematical proof —-> comprehension. 
    Sometimes there’s experimental demonstration but a lot of physics instruction relies on using higher mathematics.  That works because students are more physiologically mature and you are only teaching a much smaller, brighter, segment of the population in  that have passed the math prerequisites.
    At a younger age, with a more representative sample of the general population, the cognitive process probably looks a lot more like this ( assuming the quantitative element is present at all is being generous – but it is something some instructors will do):
      Conceptual narrative——-> Comprehension <——mathematical proof
    Providing equations does not mean the student automatically can integrate and connect them with a narrative description of the concept and acheive comprehension. Most of them will hold the two aspects separately or reject one they understand less well and cling to the other. If you look at textbooks for younger students, the equations given as examples are very few in number for this reason ( that and the fact that many science teachers are not teaching in their field of study). The reaction by many students will be a blank look even though they can perform the calculation perfectly well.
  20. Ed Beakley Says:

    IMHO you’re on point here related to a whole lot more (and for a completely different set of folks) than just "student" differential between high school and college and their "intel prep" for their current/ appropriate  "academic battlespace" – readiness to learn the subject at hand. As in confrontation/conflict/warfare/war in the 21st Century, No?

  21. critt Jarvis Says:

    > Conceptual narrative——-> Comprehension <——mathematical proof re: "intel prep"Conceptual narrative is critical, fundamentally sufficient…. up to the point where you need to measure something in the battlespace:)

  22. zen Says:

    hi Critt,

    Wisdom is knowing when not measuring (or not knowing how to measure) might kill you 🙂
  23. deichmans Says:

    Gray Hat,

    You’re only using part of the formula.  The 1/2mv^2 function is simply the first factor in a Taylor series polynomial for kinetic energy — and perfectly fine for non-relativistic speeds (i.e., Newtonian classical mechanics).

    But when speeds are a significant fraction of the speed of light (c), then the formula for relativistic kinetic energy is obtained by subtracting the rest mass energy (E=mc^2) from the total energy (E=[g]mc^2, where [g] is the Lorentz transformation function "gamma": (1-v^2/c^2)^(-1/2).)

    It’s refreshing that a student such as Zen’s was able to detect an inconsistency in the science that was presented to him — and even more refreshing that he didn’t simply hit the "I Believe" button, but dug deeper into his inquiry.

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