We will be featuring different members of the Brilliant community, so that you can get to know them better. For the ninth issue, we are featuring Michael Mendrin, who is a polymath that enjoys engaging with the community.
True to form, Michael has posed numerous thought-provoking questions. Here are some other of his 400 point questions: 1, 2, 3, 4, 5. Out of this problems, the one that I love most is about the sandpiper:
While walking on a straight path on the flat wet sand on the beach, you approach a sandpiper directly ahead of you in the line of your path. The sandpiper does not move until you are at distance \(X\) from it. Then it starts moving away from you at a constant speed in an arc, maintaining the same distance \(X\) from you, so that when you are at where the sandpiper was originally, the sandpiper is now at distance \(X\) from you perpendicularly to the line of your path. As you continue on, the sandpiper continues on the same arc around behind you, so that it eventually comes back to exactly where it was before you interrupted his feeding, and hopes you won't bother it again.
If you were walking at 1 meter per second, how fast did the sandpiper walk?
Michael has written over 300 solutions in the past 2 years, which makes it hard to pick my favorite. One of those that I (and the community) enjoyed, was the insight to solve the following problem, without the use of guessing / trial and error:
\[ \large \sqrt a + b = 7 \\ \large \sqrt b + a = 11 \]
Tell us more about yourself.
I was self-taught and pretty good with math when I was in public school, and started as a mathematics major in college. Physics was required, and when I tried to study it, it was ridiculous and so riddled with contradictions and lacking in rigor that I decided to switch to majoring in Physics --- and I haven’t stopped thinking about physics since.
Let’s see, I’ve been in and out of things since then, like programming at JPL, cold-heading and machine shop business, compact copper sulfate production, subsidized housing in South Central Los Angeles, drafting, surveying, construction, code compliance and structural design, accounting, trusts, estate and tax planning, collectible antiquities, theme park design, computer animation, real time image enhancement technology, film and live broadcast technologies consulting, and a miscellany of other things in-between with uneven outcomes. Then a sabbatical, back to real estate, and then recently drip system technologies for California farmers. Sometimes I’ve been able to put my math skills to work, much of the time not.
For fun, I like mountains, skiing, rock climbing, knocking over Brilliant problems.
What is one fun fact about yourself that the Brilliant community doesn’t know about?
When I was a high school senior, I was invited to one of Richard Feynman’s lectures at Caltech, and shook hands with him. At the time I had no idea of who he was or how famous he’d be. Or how much I’d end up thinking so much about his ideas, such as his observation that the Schrodinger equation is a diffusion equation with an imaginary diffusion constant. So, it’s about random walks in some kind of a complex space?
What do you want to accomplish?
I’m still waiting for irrigation companies in California to comply with the new laws to change their traditional ways of delivering water to the farmers. When that happens, then I hope to be ready to help the farmers, some of whom I know personally, to deal with the drought.
But in my free thinking time, I ponder Physics—it’s one of the few things I’ve not ever lost interest in since college. Questions like these are really hard to answer:
Is it possible to develop a finite element computer simulation (not prediction) of quantum behavior without specifically requiring a quantum computer, which Richard Feynman himself said was probably necessary? Feynman suggested this decades before physicists thought quantum computers would even be possible.
Is the existence of time a consequence of probability? That is, of all possible causal universes, the ones that makes possible having time as a parameter makes up the vast bulk of them through chance alone? “God has a passion for beetles”, so wrote the British biologist J.B.S. Haldane, because “there are nearly 300,000 species of beetles”, as compared to far fewer species of other insects.
Many laws of physics are consequences of symmetry. Might not “almost perfect symmetries” explain or give rise to other laws in physics? I often like to say, “Who needs infinity?” Related to this sentiment is, “Who needs perfect symmetry?” Too bad Emmy Noether is no longer around.
With stuff like this on my mind, my biggest goal in life is to live as long as I possibly can, because I sure would hate to go without having figured out some of them. I don’t want to miss the answer!
What do you wish for Brilliant?
I think Brilliant is a terrific place build math and science skills through problem solving, as well as authoring original problems, notes and collaborating on wikis. Ah, well, but I’d like more opportunity for dialogue. Some of my most fun moments were the times I’ve squabbled with the author of a problem or a note over some subject matter, or speculating on an interesting topic.
I’d like to see a lot more sharing of ideas, better featuring of the excellent wikis and notes being written. A true community, a forum, a noisy intellectual salon—rather than the squeezed experience of a math test room where nobody talks.