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11 hours ago, Rolig Loon said:

As a rather unimaginative mathematician myself, I learned a few basic rules along that way through my calc and diffEQ courses:

1. If you can integrate by parts, do it.

2. If you can integrate by substitution, do it.

3. If #1 and #2 don't work, ask a mathematician.

Like most scientific types, I learned the math tricks of my own discipline, honed them to perfection, and. left the rest for people who chase quarks and angels dancing on pinheads.

I'm in agreement with this, with emphasis on "tricks". One of the last projects I worked on before retiring involved collaborating with a wonderful fella who had a Phd in physics and MA/BA in mathematics. He could spin circles around me mathematically. His curiosity about how things worked was something I shared and we had great fun discussing them. We were faced with a control-systems problem which he approached with a mathematical rigor that I found impressive, over my head, and hopefully unnecessary. I told him I would have to look for a simpler (to me) solution because I couldn't possibly understand his.

We went off in our different directions and I returned with my implementation of the control loop first. He was skeptical that such a "bubble gum and rubber band" approach would work. It did, and well enough that he dropped his work and moved on to another aspect of the project. Over lunch one day, he asked how I had come up with such a "hillbilly" solution. It was the best I could do! It worked because the problem was just a bit more hillbilly than I, which was something he hadn't realized. He had a deep mathematical understanding of the problem, but no intuitive feel for it. He wanted the exact answer, I wanted a useable answer.

Mathematicians value perfection. Engineers value production. I have never found myself needing a mathematician, other than as a lunch partner for fun discussions of just how marvelous the world is... for it's perfection... and its messiness.

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Rhonda's thoughtful thought of the day: If you love someone, set them free.  You will know your love is true if they don't press charges.

Happy Wednesday folks! Four years ago today I brought this little guy home and snapped this pic. More current ones with his brother.

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41 minutes ago, Madelaine McMasters said:

Mathematicians value perfection. Engineers value production.

Scientists are somewhere in between. Or at least some kinds of scientists. My own grad school advisor had a healthy attitude about getting estimates which were correct "within an order of magnitude" well before he would spend valuable time on the messiness of mathematical precision. For physical chemists, an order of magnitude answer is often the best you can expect anyway, so it often saved him the work of unnecessary perfection. From him, I learned some valuable "almost" constants (like the number of seconds in a year = PI times 10^7) that have simplified my life immensely. 

On the other hand, there are times when a strict analytical solution is preferable, so there's no way to avoid getting into the weeds.  I remember struggling for the better part of two weeks with a way to represent a rather difficult kinetic process mathematically so that I could translate it into a numerical model. I was mulling it over one afternoon when a much more gifted friend wandered in to see what I was doing. He looked over my shoulder and made muttering noises for a couple of minutes, then finally said, "You know, this would be quite easy if you simply use a Green's function here and then drop a couple of those terms." Hence my third rule, above: "If #1 and #2 don't work, ask a mathematician."  There are times when it's definitely handy to have a friend with a more mathematical mind.  The trick to being a successful scientist is knowing when it's necessary to call that friend and when to settle for an order of magnitude.

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9 hours ago, Rolig Loon said:

Scientists are somewhere in between.

Yep. Your third rule is important, though not one that I've ever had to use. I would have enjoyed needing to call in a mathematician somewhere during my career, but I was never presented with a problem that wasn't more hillbilly than me. I did a lot of digital signal processing over the years, wading up to my chin in Fast Fourier Transforms and digital filters, but those are the tricks of any modern electrical engineer's trade and we have powerful tools like Matlab to help. I don't mind solving problems with heavy computing, but it's more rewarding to find simple solutions that make people slap their forehead. Coding in LSL gives you the motive and opportunity to find such solutions.

I have envied colleagues who were deeper into the science of something we were working on, because I find nature's mysteries far more intriguing than those we create for ourselves. Engineering is sometimes a little more removed from first principles than I like. On the upside, I got to watch my hillbilly algorithms run at breakneck speed inside little computers, doing things that amazed me. Sometimes being fast is as good as being smart.

In defense of hillbillies (and myself), I use the term to describe people who solve problems in unexpectedly simple ways, with perfectly acceptable results. And if the solution brings laughter... bonus!

Happy Peak of the Week, Kids!!!

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2 hours ago, Madelaine McMasters said:

In defense of hillbillies (and myself), I use the term to describe people who solve problems in unexpectedly simple ways, with perfectly acceptable results. And if the solution brings laughter... bonus!

Happy Wednesday Y'all and many thoughts and thanks to the D-Day invasion veterans on this June 6th.  Thank you for your bravery and sacrifice for our freedom.

Maddy, love your above sentence and the best thing about it is that they made a great TV show about that common sense problem solving!


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7 hours ago, Rhonda Huntress said:

I am wandering around Lil's part of the world this week. Well, more on the Mesa Verde side of Colorado but close enough to shout HELLO.


Hellllloooooooo over there.


7 hours ago, Rhonda Huntress said:

I hope you feel better soon.  Summer migraines can be horrible.

Luckily this one was more sinus pressure than migraine, so some meds eventually took care of it.

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