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Featured Member - Michael Mendrin

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.

Note by Calvin Lin
1 year, 7 months ago

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@Michael Mendrin Great to see you featured, Michael. I particularly enjoyed the long list of careers you've had. Theme park design? There must be a particularly interesting story to that one. :)

Any ideas on how to create "a noisy intellectual salon" environment on Brilliant? I always enjoy reading the 'conversations' you have with John Muradeli, (and have enjoyed participating in a few of those myself), but rarely do others get involved. I do feel a strong sense of community on this site, but I'm not sure how it can evolve into the more stimulating platform you envision. Few (if any) of us are at your level, especially in physics, so you're probably the cornerstone for any kind of 'salon' construct.

P.S.. What was the material covered in that Feynman lecture you attended? Brian Charlesworth · 1 year, 7 months ago

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@Brian Charlesworth Hey Brian. Theme park design? Yes, it is, not was, an interesting story, it's not over yet. Best argument for business ventures is that it can bring peoples as disparate as Dubai investors, Urantians, and the Egyptian government together with a common goal. Hippies used to say, "Make love, not war". Let's expand on this to include "Make money, not war".

Notes like this is one way to have a noisy intellectual salon. Solutions to problems pages is another. What I notice is that if I immediately post a perfect, clean solution to some of my problems, conversation comes to a dead end. So, should I try posting poor solutions? Technically incorrect solutions to some problems have led to interesting dialogue about issues involved. I think talk like that should be encouraged. Now that Brilliant wikis have a new feature that allows feedback and commentary, I hope people will take advantage of it for more such talk.

P.S. I have no recollection. It was the classic huge blackboard filled with...something. Sodium thiopental, anyone? Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin You were one of the first people I followed on Brilliant and for good reason. You depth of knowledge and range of knowledge is humbling. I agree with the others that I was looking forward to your feature. I am surprised to discover that your career choices havent included maths considering your abilities and your (assumed)passion for it. I look forward to more interactions with you(hopefully on game theory and probability). Have a good one Mike. Michael Bye · 1 year, 7 months ago

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@Michael Bye Michael, thank you, I am a little surprised that you were looking forward to this feature. Now, don't get me wrong--there have been times where I used applied math intensively. Like the time I built a small scale compact copper sulfate production plant, or like back in the 1990s when "real time broadcast image enhancement technology" was cutting edge and involved image analysis and fast Fourier transforms implemented by hardware. Perhaps you are thinking about work in theoretical physics, but that is a very difficult line of work to break into, and I was being a realist. Anyway, I'm hoping to collaborate with Josh Silverman about the 2nd Law of Thermodynamics and how statistical mechanics leads to that, and that does involve combinatorics and probability. Maybe we could have something to talk about,. Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin Why is it surprising? You are the kind of person the kids on this site should look up too. I work in finance so I utilize math daily but not in the fun way the site offers. I look forward to your and @Josh Silverman 's problems. Gambling and casinos are what started my interest into probability and game theory before I was old enough to be in that type of establishment(legally). From your short autobiography stated, it seems you have gone after passion projects and I am sure that has kept you happy(work wise). Michael Bye · 1 year, 7 months ago

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@Michael Mendrin Urantians? I had to look that one up. Apparently Jimi Hendrix, Stevie Ray Vaughan and Jerry Garcia were adherents. Far out. :) And yes, the "Make money, not war" notion, aka the peace dividend, is quite plausible; I recall getting my niece a book by that name authored by the cognitive scientist Steven Pinker.

When posting solutions, I often find that my more cryptic entries can prompt more dialogue, mostly of the "could you please elaborate" variety. (Not as cryptic as Gianlino's solutions were on Yahoo, mind you; those made my head spin sometimes.) The math questions that seem to create the most discussion are those involving \(0, \infty,\) tetrations and nested radicals, (oh, and logic problems, too). There's only so much material there, though, before things get repetitive. I've been negligent in checking out all the wikis, (I don't want to feel like I'm back at school), but that new commentary feature does sound promising.

I know many members were eagerly anticipating your profile being featured, so I have no doubt this page will generate plenty of discussion of one sort or another. :) Brian Charlesworth · 1 year, 7 months ago

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@Brian Charlesworth Oh, for sure I'll get my fifteen minutes of fame, Brian. Michael Mendrin · 1 year, 7 months ago

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So, at last.. My long wait is over. You are the one of the greatest minds of this community. Salute to you Sir! And congrats for being featured :-) Swapnil Das · 1 year, 7 months ago

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@Swapnil Das Thanks, I'm still a little surprised at the attention I'm getting. Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin Haha, you truly deserve it:-) Swapnil Das · 1 year, 7 months ago

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OMG! You're like Da Vinci! I see some nice sofas in your picture. I have the same kind. Sharky Kesa · 1 year, 7 months ago

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WHAAT? MICHAEL MENDRIN WAS FEATURED AND NOONE TOLD ME?!

Have I died around here or what? :/ ....

\[\huge{\text{CONGRATZ MR. MATHOPEDIA!!!}}\]

This list shouldn't even EXIST without you on it. Now I hope they make one for my other buddy Brian Charlesworth. What great people - without whom which I probably woulda dumped Brilliant long time ago due to its 100 updates/week progressive (rather, regressive) schedule.

You go!

(P.S. - lookin great. Do you lift bruh?) John Muradeli · 1 year, 7 months ago

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@John Muradeli I'd much rather climb than go lift stupid weights, but I have such a hard time finding qualified rock climbing partners. All of my former climbing partners are all grown up. Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin Well, I really liked what you want to accomplish, it's really a great work to do and it actually inspires me. And meeting Mr. Feynman, wow! I wish I could have been old enough to do the same, I'm jealous(just joking). By the way, "joking" reminds me does he really "jokes"? I mean you've attended a live lecture - what was it all about? any jokes?

And yeah, what about your thoughts on Banach Tarski Paradox - its physical significance, I mean? I think it would've been quite of an interest for you.

Finally, I wanted to ask one more thing. What can someone "achieve'' if he knows the physics and the mathematics - all(almost all, of course) the natural phenomenon and its expression? That I am asking because I am nowadays watching "Breaking Bad" in which it is shown how Chemistry - the study of matter, can change lives. Kartik Sharma · 1 year, 7 months ago

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@Kartik Sharma Kartik, the lecture by Feynman happened almost a half century ago. I wish I could remember what he was talking or joking about! In fact, I started to learn a great deal about his works after college, while I was doing work which had nothing to do with physics. But I can tell you that once you've developed ability and confidence in math, physics, and science--well, you do tend to feel like you can handle just about anything. I was ready for any engineering challenges that came in my way, and sometimes you never know what's going to come up. It's like having rock climbing skills--when you're up in the mountains, nothing really looks that formidable, you know you probably could handle it.

Let me preface my opinion about how the Banach-Tarski Paradox relates to physics by first mentioning non-Euclidean geometries. As you know, viable and consistent geometries can be had from three different ways of looking at the parallel postulate. Which one is "true in physical reality"? The answer is all of them. It would be a mistake to believe that while, mathematically, any of them can be "true", only one of them can be in nature. The Banach-Tarski Paradox depends on the Axiom of Choice, which is much like the parallel postulate--one can different versions of it, so that in other versions, there is no such thing as being able to make two identical balls out of one through dissection and rearranging a finite number of parts, or subsets of points. And yet we cannot say it has no relevance in physics! Yes, there are laws of conservation, and we are told tirelessly that "energy cannot come out of nothing", but in quantum physics it does come out of nothing, if only temporarily. And I've seen a number of speculative suggestions where the principles behind this paradox could apply. Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin Well, yeah the Feynman question was stupid. The Banach-Tarski Paradox seems really interesting and now that you say "... in quantum physics it does come out of nothing, if only temporarily", my interest has doubled. As you say you've seen a number of speculative suggestions where it can be applied, can you give some of them here?

BTW, I would like if you elaborate your views on physics and life. My question was - how does it matter in life to know how's nature behaving more than satisfying one's own self. I wouldn't be making a new nature of myself anyways so one's knowledge of physics wouldn't really change the nature itself. For example, if I say that I have discovered a new particle just like a neutrino but still different from it, how will it change the nature in itself? It will although change the our view of nature but that has not been significant for the people to know.

Above all, I am not at all critical of Physics and physicists as I myself might consider that as my profession, but it just seems quite absurd of how physicists couldn't have a significant effect on nature directly and they leave it for engineers etc. to take the credit. Kartik Sharma · 1 year, 7 months ago

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@Kartik Sharma It's called curiosity. Wanderlust. When faced with something that shrieks at you, "How can that even be possible!", you just can't put the mystery down until you have the answer. I suppose that for many people, they don't have the experience of having that kind of non-reality shoved right in their faces. Instead, it's something vague, something they heard somewhere---isn't it something already in the movies anyway? Movies are full of fantastical stuff, one amazing thing after another, with glib and easy explanations. But to someone familiar with evidence of experimental physics---well, sometimes that that even threaten one's sense of reality, because it isn't merely made up stuff, and there are no glib nor easy explanations. When trying to grapple with the incomprehensible, a theoretical physicist isn't thinking about how a better car or smartphone can result. Michael Mendrin · 1 year, 7 months ago

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@Kartik Sharma Breaking Bad!!!! :) Aditya Chauhan · 1 year, 7 months ago

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Oh gosh.....I wish I had half the passion you live with.... Arnav Das · 1 year, 7 months ago

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@Michael Mendrin it's great looking at your enduring love of physics and math. I may be misinformed but i wanted to ask you, there is this perception around(may be mine) that physicist and the likes tend to be indifferent to the subjects latter in life. For example feynman latter in life said 'Physics isn't the most important thing Love is' . Also one time at ATOM i met a nobel prize winning physicist who has retired from physics, and wasn't much interested in talking about it. From your perspective is the perception of physics and math volatile? Is it something in time you perceive as not much of the big picture in life?

Note-I am not referring to the decreasing love of the subject. I hardly believe there are people who switch fences in this regard. Beakal Tiliksew · 1 year, 7 months ago

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@Beakal Tiliksew I think there's such a thing as burnout. Also, have you noticed that when you're told to stare at a particular image, after a while parts of it seems to fade? I think maybe because my life has been a little bit eventful, "returning" to physics can be such a pleasure. Kind of like going back up in the High Sierras after a long absence. By the way, the High Sierras is another thing I have not ever lost interest in since I was young. Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin I won't stop pondering about math and physics till the end of my life! Swapnil Das · 1 year, 7 months ago

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You look as stunning without the sunglasses. Your problems have been the toughest and I have hardly solved any. Like you, my first love was also Physics. I settled for electrical engineering in the university for better career prospects. Didn't use much of math and engineering in my career. Nice to know that you have Richard Feynman. I like your tribute piece to John Nash. Wish to hear from you further on the latest developments in physics. Chew-Seong Cheong · 1 year, 7 months ago

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@Chew-Seong Cheong One of my regrets is not having known Feynman, I only met him briefly. And how did you find my comment on Nash? But you are a solid presence here in Brilliant, I know you've posted thousands of clear solutions. I merely look stunning with or without my sunglasses.

Edit: Oh, right, I remember now your tribute to John Nash. Pareto Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin How you be so cool? Congrats for being featured. Nihar Mahajan · 1 year, 7 months ago

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@Nihar Mahajan Secret is always having iced tea on hand. Michael Mendrin · 1 year, 7 months ago

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Congratulations for being featured!!! By the way, is that Ubuntu loaded on your monitor? Arulx Z · 1 year, 3 months ago

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@Arulx Z This is the first time I've even heard of "Ubuntu". Is it because Ubuntu has a screen-saver that looks like a beach? Michael Mendrin · 1 year, 3 months ago

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@Michael Mendrin Haha no. The icons on the left resemble the side bar. Arulx Z · 1 year, 3 months ago

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@Arulx Z They can be of mac too:

they also have a sidebar.

(a computer guy such as you will try to see all the app i bet) Aareyan Manzoor · 1 year, 3 months ago

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@Michael Mendrin Congratulations,sir! Well-the list of careers you've had is amazing. I'm about a year old on Brilliant, and given the very mediocre insight of mine into problems, might as well need your guidance. Looking forward to interactions with you. Salute ! :) Yuki Kuriyama · 1 year, 5 months ago

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It's good to see you featured in this ' Featured Member ', sir . \(\huge\ddot\smile\) Anish Harsha · 1 year, 7 months ago

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@Michael Mendrin u really awesome. I've seen some of your level 5 solutions. U r one of my true inspiration to keep balance between physics and Maths. Aditya Kumar · 1 year, 7 months ago

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@Aditya Kumar Yes, like keeping balance between having fun and having to be conscientiously polite. Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin Haha I didn't know that having fun and being polite were mutually exclusive events. :) Brian Charlesworth · 1 year, 7 months ago

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@Michael Mendrin That adds up to the things I learnt from u ☺ Aditya Kumar · 1 year, 7 months ago

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Personally, no matter how fun a tough question can be, doing a proof is (arguably) more interesting as you can go about proving a conjecture from many different angles . I think if we have more notes on here asking for proofs that might encourage the noisy intellectual salon sort of atmosphere you have described that you, and many people (myself included) really enjoy. Also, Congratulations on the feature, you really deserve it! (Level 5 for everything - WOW!) Raghav Arora · 1 year, 7 months ago

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The long wait for this post is over now. Yay! Agnishom Chattopadhyay · 1 year, 7 months ago

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@Agnishom Chattopadhyay Agnishom, I'm going to start my long wait for yours. Michael Mendrin · 1 year, 7 months ago

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Congrats lil old wildman. You are so a good inspiration for we lil' teens. We love your math and physics ability. You are like an all knowing expert to us. Sometimes, you act like a small child! We all love you! It's surprising me that you haven't ever published a paper on math or anything. C'mon do it! People would be just amazed by it. YOU ARE GREAT MIKE "WILDMAN" MEDRIN! This is a long awaited Feature!!! Kishore S Shenoy · 1 year, 7 months ago

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What are your thoughts on Schrödinger's cat ? Chinmay Sangawadekar · 1 year, 7 months ago

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@Chinmay Sangawadekar This is a huge subject and deserves its own note. Briefly put, this subject can be broken down into two sub-subjects, which are:

1) Schrodinger devised this thought experiment to drive home the point that the mathematics of quantum mechanics doesn't fundamentally distinguish between "the very small" from the "large". In other words, if subatomic particles can exhibit quantum behavior, so can cats. As ridiculous as it sounds. But nobody has been able to conclusively prove or show the impossibility of that, and, in fact, experimental physicists have steadily increased the size of objects that are shown to have quantum behavior, and there are now plans to come with a "Schrodinger's Virus". How and why this can even be possible is a massive subject, but I don't dispute the growing experimental reality of this.

2) The ever popular staple of science fiction, "Parallel Worlds", is from Everett's "Many Worlds Hypothesis" of explaining how there can be a Schrodinger's Cat (see above..."massive subject"). Anytime there is ever any superposition of states, whether of subatomic particles or cats, it's said that there's branching parallel co-existing worlds, each with their own observer witnessing different things, and "no communication" is possible between such parallel worlds. Not everybody is happy with this view, myself included, and there have been criticisms with this approach, and modifications proposed. I don't have a problem with the mathematics of it, I just think that the common science fiction interpretation of it is a bit misleading. Michael Mendrin · 1 year, 7 months ago

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Which can is it that is on your table ? Chinmay Sangawadekar · 1 year, 7 months ago

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@Chinmay Sangawadekar Cold Starbucks Doubleshot coffee. I like to start the day with one, while looking through what's new in Brilliant. Which is why I have it featured in the picture. Michael Mendrin · 1 year, 7 months ago

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I too love Physics Chinmay Sangawadekar · 1 year, 7 months ago

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Grandpa. Hi Nitesh Chaudhary · 1 year, 7 months ago

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@Nitesh Chaudhary Heh. May the youth be with you.

Michael Mendrin · 1 year, 7 months ago

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@Michael Mendrin This was the one on my screen when I was in Leicester. Lu Chee Ket · 1 year, 7 months ago

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