The Beauty Of Mathematics

February 15, 2014

A recent study published in the journal of Frontiers in Human Neuroscience found that mathematicians perceive the same degree of beauty in elegant equations as an artist does admiring beautiful architecture, or a musician listening to Bach.

“Many have written of the experience of mathematical beauty as being comparable to that derived from the greatest art. This makes it interesting to learn whether the experience of beauty derived from such a highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources. To determine this, we used functional magnetic resonance imaging (fMRI) to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae which they had individually rated as beautiful, indifferent or ugly. Results showed that the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources.”

The most elegant and beautiful equation was Euler’s identity.


We physicists spend so much time with mathematics, we also have this same sense of beauty.  Paul Dirac once said, “What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating.”

I spend so much time with mathematics these days, I now viscerally “feel” and “perceive” the beauty in equations.  It’s the same feeling I have when I look at the blue sky and think that the clouded dome above us is a realm of the gods.  Who could define exactly what it is that makes a group of big poofy white clouds so beautiful?  The same thing happens with mathematical expressions.

Topics: Physics, Psychology | 2 Comments »

Paul Dirac Lectures on Quantum Mehanics

February 11, 2014

I’ve just finished watching some really old lectures of Paul A.M. Dirac speaking on quantum mechanics and quantum electrodynamics.  Youtube is so neat.  Somebody found an old film spool, digitized it, and uploaded it to Youtube.

I find the end of the lecture on quantum mechanics very interesting.  He felt that the subject is full of problems, incomplete, and creates as many problems as it solves.  He was waiting for someone to come up with something to replace it.  Jump to time 49 mins to hear the discussion.

Topics: Physics | 1 Comment »

Dealing With Hate

February 9, 2014

From time to time I receive nasty emails from people who disagree with the things I say in my blog posts.  When I say nasty, I mean really nasty, with not a single shred of respect.  They insult me, call me all sorts of names, and tell me how terrible a person I am.  Some of you may notice that I never talk about it, and I don’t make posts like, “Reading my hate mail” or “Analyzing hate mail”.  Truth is, when I receive hateful criticism that doesn’t offer any sort of argument, and I’m unable to glean any new insight from it, I simply delete it and never think of them again.

I really enjoyed Ayn Rand’s movie The Fountainhead.   Personality wise, I have a lot in common with Howard Roark, the main character.  He’s an architect with a passion for building beautiful skyscrapers.  Another man, Ellseworth Toohey, runs a column in a popular magazine on architecture and acknowledges Roark’s excellence but is afraid of it. Toohey does everything he can to stop Roark because he knows that he will take business from his buddies.  Therefore he uses his column to attack Roark’s buildings, stirring up public controversy.

They end up meeting one day on the streets, with Toohey waiting for Roark at a building site.  Roark should have gotten the deal but didn’t due to insider corruption, in large part due to Toohey’s influence.  You should take note how Roark handles it.

You may easily misunderstand this scene, thinking Roark hates Toohey.  He doesn’t at all.   In fact, later in the movie, the owner of that very newspaper hires Roark to build several skyscrapers for him.  When they meet in his office, Gail Wynand, the CEO, asks him how  he could work for a newspaper which had spent so much time running him down.  Roark just makes a joke out of it, actually finds the good in Wynand, compliments him on it, and goes on to design them spectacular office buildings.   That’s how men and women of integrity deal with hate.

Topics: Personal | 3 Comments »

Political Correctness Is Out Of Control

February 8, 2014

I’m sure you’ve all heard of Jerry Seinfeld.  He was the star of his hit TV comedy Seinfeld throughout the 90’s, and now he does a web show called Comedians in Cars Getting Coffee.  In an interview, they were asking him about comedy and stand up routines.  He said, “if you’re not funny, I’m not interested. I have no interest in gender or race or anything like that.”  He said that comedy is the ultimate form of justice.  The audience laughs or they don’t.  That’s the only real factor.

Then they asked him why almost all of his web show guests have been white males.  Of course, they were implying that he doesn’t have racial diversity in his show.  Where are the asians, blacks, women, and everybody else?  I loved Jerry’s response, “What is this, the census?”  The left is now saying he’s a racist.

This stuff makes me sick.  Click toward the bottom right to get it to play.

I’ve never seen a group as intolerant in all my life.  See that woman in the interview?  “I used to be a fan of Jerry, but now… UGH!”  The third woman’s response is so telling.  Listen carefully to what she says, “He’s had so much success, and he’s had that success doing things his way…” 

God forbid he does things his way on his show.  Why should it be your way, or anyone else’s way?  It’s his show.  And what is the left’s problem?  He was just saying comedy should be based on merit, not anything else.  What’s wrong with that?

It’s his cameras.  His cars.  His equipment.  His guests.  He’s the one paying to advertise the show.  You know what?  That gives him the right to have whoever he wants as his guests.  Period.

And by the way, he had Chris Rock and Mario Joyner on his web show.  So much for your claims he’s a racist.  He’s also had Tina Fey.  They’re not all white males.

If you deal with these leftists, you have to have a politically correct statement  prepared in advance for every question they ask you, and if you say anything they don’t like or disagree with, they’re going to boycott you and cause a giant stir.

If you’re going to accuse a person of racism, why Jerry Seinfeld?  He’s the racist?  Really?  Give me a break. Go after real racists, not the rich white guy whose success you can’t stand.

I’ve had it with political correctness, in all of its forms.   This isn’t equality, this is control.  This is one group of people trying to tell another group of people what to do with their things.  I don’t respect that at all.

Topics: Politics | 2 Comments »

Happy Birthday To Me

February 2, 2014

Just a few days ago was my birthday.  I was on Youtube and searched for one of my old favorite bands, Matchbox Twenty.  I was thrilled to find out they still make music.

Isn’t that a great song?  I got to thinking about all the time I used to spend playing basketball with friends in the gymnasium, and we’d have the radio playing.  Matchbox Twenty was always coming on the air.  Real World, When You’re Gone, Bent, so many great songs.

I remember shooting around waiting for people to show up and Matchbox Twenty would come on and I’d stop, go sit on the bench, and just listen.  I feel really nostalgic when I hear music from the 90’s.

I still play basketball all the time, but those I used to play with are all fat and married.  They can’t jump, their knees hurt, and there’s no way they could get up and down the court.  Me?  I’m the same as I was all those years ago, though a little less nimble.  Just a tad  🙂

That got me to thinking how long ago that’s been – 1997.  In a few years, that’ll be twenty years ago.  Twenty years.

I guess I grew up fast, and even when I was young, people would joke that I’m an “old man”.  I actually am getting older now.  Still, in my mind, it all seems like the other day.

I suppose this is all on my mind because so few of my old friends seem happy.  Everyone was full of life back then.  After twenty years of boring jobs, big bellies, screaming bratty kids, and never having any time time for anything fun, they’ve just sort of slipped into this rut of “existence”.  Many of their wives, once sweet and fun, are now nags.

Greg and I went out for lunch the other day, and I was telling him about an old episode of Star Trek, the pilot actually.  The captain summons the doctor to his quarters and complains that being captain of a star ship is too much pressure.  He doesn’t want it anymore.  He has to send people on missions, putting their lives in jeopardy.  He never knows if he’ll return home.  He says he wants to find a nice girl, settle down in a cabin on some remote planet, and just relax.

The doctor looks at him and says, “You don’t really want that, Jim.  You do that and you’ll die.  You know as well as I do that those who stop taking life’s punches just slowly wither away, dying a little each day.”  When I heard that I thought, wow, that’s exactly what I see happening to people.

You won’t see it until you start getting older.  I’m at that point now where I actually see people’s life decisions and what it led them to.  There are those who invested in life, and now it’s paying off.  They might have earned a PhD in some science or form of engineering, and they’re now working in labs on the cutting edge.  One guy I know works at NASA on the Mars rover project.  It took him forever to get through school, but then boom, he loves going into work.  Others?  They work in dead end office jobs, or some factory, or wherever, no passion, just wanting to go back home.  And what do they do at home?  Watch TV.

You have to always be in a place where you’re uncomfortable, pushing yourself, bettering yourself, never sure if you’re even going to succeed.  Taking risks, being vulnerable, not sure how things will turn out.

The real key is to find something where you enjoy your work.  Where you don’t hate your job or find it boring.  You don’t live for a vacation or some other form of escape.  It’s not about earning lots of money, or dreaming of retirement.  That’s a tricky thing to do.

Maybe I’m fortunate to have found a passion with physics?  I find it amazing that I’ll go in to talk to my professors, many of them graduates from different Ivy league universities, and they’ll be in their late seventies but still going at it.  You’ll come into their office and they’re reading the latest research papers in their field.  Dr. Hale was once asked if she’s ever going to retire and she told them that she’ll die at her desk at work.  I thought that was awesome.

I’ve never found anything like physics.  It’s like a super hard puzzle game where the rules are really simple, and nobody is trying to deceive you, yet it’s extremely difficult anyways.  You deal with bazillions of small pieces doing the same simple things over and over, but trying to figure out how a bazillion little legos would snap together and behave in different situations is really difficult.

But when you do come to a higher level of understanding, you “see” it taking place all around you.  There’s this elegant, simple principle guiding everything around you.  You feel the wind blowing and you think of how you’re on this whirling ball in space, the sun is heating it at different angles, and the air is flowing from hot to cold.  Such a simple idea, but try modeling the weather!

When I was a teenager, I wanted to build a complex computer simulation of a virtual world of my own making.  I liked how it was only limited by what I could imagine and how clever I was with my programming.  Then I came to understand that I’m already living in a sort of simulation like that, where practically anything is possible.

I really enjoy the classes I take nowadays.  One of my classes this semester is an advanced course on plasma physics.  I have to research all the different ways in which we’ve built tokamak reactors and how well they’ve worked.  Also, our professor is a NASA scientist who builds ion thruster engines, so we literally go in his lab and he shows us how to build them.

As I go further into all of this, the class sizes get smaller and smaller, and the material is more and more specialized and interesting.  You take a course on particle physics and learn all the physics involved in the Large Hardon Collider, or take solid state courses and learn details in how we’re constructing nano-electronics or laser systems.

Just a while back I took a course on computational simulations.  We were using quantum mechanics to simulate chemical reactions, at other times using Einsten’s general relativity to simulate planetary motions and black holes.  Another was a nano-electronics simulation in magnetic materials.

In my plasma course, my current homework is to write a 3D simulation of charged particles within magnetic fields, just like a tokamak.  When I first enrolled, the classes were so basic and I couldn’t stand them.  But the further you get, grades matter less and less and it’s more just, “Let’s build this.  Let’s do this.  What do you guys want to study?”

When I hear young people say things like, “School is such a waste of time.  I’ll never use any of this.”  I feel pretty bad for them.  What they’re really saying is they’ll never build or do anything interesting, because everything that’s interesting these days requires lots of knowledge of math, science, and things like physics.

If you go to build artificial intelligence like Siri, you have to really understand programming and advanced probability theory, not to mention psychology.  If you want to build rocket engines used to thrust up the space station, you have to know tons of physics and mathematics.  Same goes for designing the next generation of touch screens and cell phones.  Everything that’s going on these days requires lots of education.  At least the fun creative jobs.

I love browsing different sites seeing people at the cutting edge.  Some are working on augmented reality glasses, like Google glass.  Some are trying to build nanotechnology where they can all be embedded in a thin contact lense.  Others are working on medical cures, building tiny robots which can swim into your body and destroy cancers.   There’s so much cool stuff going on.   As I was saying before, I’ve learned about all the cool things I could build and work on.

The other day I saw a picture of Nikola Tesla and all these arcs of electricity are flying across the room.  I thought, “I could build that.”  I understand how all of that works.  I can go online and read his old research papers and understand all of it.  That’s a really cool feeling.

But I have to stay active.  Working hard.  Challenging myself and my mind.  Recently I was trying to master some advanced areas of particle physics.  It slammed me back on my face and I was struggling to understand any of it.  But you don’t give up.  You ask questions, you find people who do understand it, and you hop in your car and go to them, email them, or find some other way to learn it.  Watch lectures online.  Always keep at it.

It’s neat that my computer programming skills are now being applied to different types of simulations and modeling.  Years ago I used to always lament how I was stuck writing boring business software.  Designing reports.  Databases.  Data entry screens.  I HATED that stuff.

I always found myself wondering how I could get involved in something more interesting.  Now I get job offer after job offer, and there’s so many things I could do.  It’s been a long dream of mine to work on all this sort of stuff, but I’m having a hard time deciding what I want to specialize on.  I’ve been working on solid state research in super-conductors used in quantum computers, but I still haven’t chosen which direction to go yet.

Lately I’ve had to build a device to do experiments on different metals used in car engines.  Lining the insides of the engines with special materials, you can extract thermal electricity to power the dash or charge the battery, energy that was just being wasted before.  Physicists are kind of jack of all trades people.  We can do just about anything.  We know how everything works.  It’s not really related to super-conductors or quantum computers, but the lab gets contracts from companies like General Motors, and we raise money to buy more equipment.  Research equipment is expensive.

Topics: Personal | 5 Comments »

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