Part 6: What is a Physics Model Anyway?
When we discussed the development of our EarSpring model for the loudness response of normal human hearing, it bore many similarities to the structure of our auditory system — a sensor, tuned to resonate at a particular frequency, with a negative feedback control loop from the brain.
We have known at least 3 things about human hearing, for more than 50 years.
1. The sensitivity to near threshold level sounds is approximately linear. That is to say, the loudness appears to grow in direct proportion to the stimulus.
2. The sensitivity to loud sounds is compressed by approximately 3:1. It takes an increase of nearly 10 dB in the sound intensity to provide the appearance of it being twice as loud.
3. As sounds grow louder, they appear to sound flatter. I measure almost 3/4 semitone flattening in my lab, near 1 kHz, as sounds grow from 40 dBSPL to 90 dBSPL.
Let’s digress a moment about fitting models to clinical data…
Nearly all studies to date have been based on fewer than 3 dozen participants in any single study. Participants are typically untrained listeners, who may have a lot of trouble discerning whether things sound like they are distorting from overdriven amplifiers, or from intermodulation distortion. (If you read that last sentence and you don’t know what I’m talking about, then point taken…) So our data for fitting is already somewhat suspect by way of self-reporting.
To be fair to the field of Audiology, their goals have likely never been the same as mine. Their goals are to help people understand human speech better. They are very concerned about helping children, especially, since growing up with a hearing impairment, if left uncorrected, could seriously hamper a child’s education.
When I was a kid in college, many years ago, I signed up for a course on “Mathematical Modeling”, taught by Dirk Hoffstedder at our college (Rose-Hulman Inst. of Tech.) Dirk was a rotund Dutchman who spoke with a very strong accent, and kept an unlabeled bottle of Scotch on his desk. Five of us signed up for the course — a special offering for the five of us who were the school’s only Physics Majors.
We set out to solve the mathematical physics of several problems that school term — a rolling coin, the inverted pendulum, a burning cigarette, and, one which stuck with me all these years, the modeling of the diffusion of oxygen across the capillary membranes into surrounding cells in the tissues of a human body.
Bioengineering was a brand new field at that time. The development of an artificial heart was the Holy Grail for them. There was a new Engineering Major for that field, apart from our Physics Dept. But I was struck that a field like biology could submit to physics. I went into physics because, unlike my physician father, I did not like biological substances very much — they are messy, smelly, frequently dangerous to your health, and often invoke a gag response. Rocks are more to my liking, but that’s just me. (Radioactive rocks can be dangerous, however)
Fast forward many decades to an era where my own hearing had deteriorated significantly. I once had amazing hearing abilities. In my work in Intelligence (both corporate and national security), I could sit in a crowded restaurant and listen to conversations as far as 5 tables away. But no more.
I went, at my wife’s urging, to get my hearing tested because she complained about my constant asking her to repeat what she just said. Sure enough, I had remarkably damaged hearing! 50-70 dB threshold elevation above 1 kHz !! I was shocked by the severity presented by the audiologist, and immediately took to her suggestions that I consider hearing aids.
Little did I know, at that time, that a threshold elevation of that much, really doesn’t mean that you need that much gain in a hearing device. I didn’t know anything at all about hearing physiology or hearing physics. (Turns out, none of the audiologists know anything about hearing physics either, but I wouldn’t discover that for several more years…)
But the way the hearing results were presented by the audiologist were very shocking indeed. So I put on a pair of hearing aids and went back to my recording studio. I could hear my own footsteps again, and I had the distinct impression of being merely 3 feet tall. I could understand what my wife was saying when she talked, and I didn’t need to have her repeat what she said.
Now back to music… and I got the most awful second shock of my life…. Prior to hearing aids, all my music compositions had migrated to the lower registers on the piano keyboard — down in the basement, so to speak. All my compositions began sounding like mud.
But when I listened to music with my new hearing aids, I knew something was terribly wrong. Musical tones didn’t sound right. A clarinet didn’t sound like a clarinet anymore. An oboe sounded like a muted trumpet. This was disgusting…
What’s going on here? Well, every musical instrument, in fact, every human voice, has a complex audio spectrum which is dominated by its fundamental pitch, accompanied by a series of harmonic tones at multiples of the fundamental frequency. Those harmonics roll off in amplitude in just a particular manner, such that a clarinet has its own distinct tone, as does an oboe, or a flute, or a trumpet, or a human voice.
The hearing aids were distorting the amplitude spectrum of the higher harmonics so that an oboe sounds like a muted trumpet. That’s very bad for listening to music. I’d rather not wear any hearing aids at all, if music were going to sound like that. Just awful…
So… what to do about this? I began to think about how to solve this problem. I had an amazing background in physics, signal processing (from my former life in National Security Intelligence), computer programming and architecture, DSP’s, you name it. I just didn’t know anything about how we hear things. Well, that’s easy, just go learn about the physics of hearing… simple, right?
Not so fast… it turns out there are darn few books about the physics of hearing. Audiology text books are useless and they are often incorrect. There was one book, a Dover Publication, by Dr. Arthur Benade, on “The Physics of Musical Insruments”. I always had a fondness for Dover books. Many great books, long past their original publication lifetime were resurrected by Dover. And, to top it off, I remembered meeting Dr. Benade at Case-Western University when I was a teen. This was great!! My uncle took me with him to this visit with Dr. Benade, to discuss the design of clarinet mouthpieces with him. My uncle was a professor of Musicology at Brooklyn College.
Dr. Benade’s lab was down in the basement of the building that housed the Van de Graf generator, located behind walls of thick concrete and lead bricks, to avoid radiation from the generator. On his lab bench was an array of instrument horns. He was investigating the effects of the flare of trumpet horns, using a microphone fed through a syringe needle to avoid affecting the measurements by the presence of the microphone pickup. His lab bench was truly fascinating to me. But this was a few years before I had yet decided to study physics.
In order to talk about the physics of musical instruments, you had to also know something about the physics of sound, and how we perceive sound. And Benade’s book is filled with discussions about loudness perception, historical facts about investigations that had failed, and so on. It is a great read, many times over.
So how could a field like Audiology completely fail to understand what was in Dr. Benade’s book? The mystery grows…
This is a continuation of my previous post “The Higgs Boson particle Explained: Part 1”
The Higgs Boson is that particle that is exchanged between the Quarks while they are bound to each other, and gives rise to the notion of particle Mass. A particle is called a “Boson” if it has integer spin values (0, 1, 2, …), while they are called “Fermions” if they have half-integer spins (1/2, 3/2, ….). Light (photons) has spin 1, so it is a Boson. Electrons have spin 1/2 so they are Fermions. The Higgs Boson (named jointly after Higgs and Bose) is also an integer-spin particle. [ BTW.. Bose is *not* the Mr. Audio we all currently know, but rather a contemporary of Einstein, named Satyendra Nath Bose (1894-1974) ]
Perhaps, with a 5-sigma announcement from CERN about the possible discovery of the Higgs Boson particle we are much closer to understanding Particle Physics. But my own hunch is that physics is far from being complete at this point. Beneath this table, I mentioned the existence of the Quarks, yet nobody has ever been able to isolate a single quark. Producing a single quark by splitting one of the Standard Model particles entails putting so much energy into the particle to stretch apart the constituent Quarks that by the time we have them separated far enough to see individually, the energy would have been converted into another Quark particle that immediately pairs with the potential lone Quark, producing another Meson or Baryon that is comprised of a pair of Quarks.
And more vexing, we still have to tie the (nearly completed?) realm of particle physics to the final frontier of tying all the natural forces into a unified field theory. Gravitation continues to evade all attempts to unify with other forces (electrical, strong nuclear, weak nuclear). The Higgs Boson may hold some answers there… we’ll have to wait and see.
Meanwhile, String Theory, has evolved as a possible explanation for all that we see in the universe, but evokes up to 10 or 11 dimensions to do so.
Modern physics is an amazingly fun fantasy story. It is so bizarre and yet so seemingly real. But it is only a story… The Astronomer’s Nightmare states that when we die and go to heaven, G-d takes us by the hand to give us a tour of the Universe and show us how it *really* works.
This is a “modern day Periodic Table” for elementary particles of physics. It was first postulated by Murray Gell-Mann, who was awarded the Nobel Prize in Physics for his work in 1969. Gell-Mann was often referred to as “the brightest kid in the class, and he knew it…”. An irascible character, he looked down on other fields of physics, once referring to “Solid State Physics” (the field that seeks to understand transistors and the basis of modern day computing devices), as “Squalid State Physics”.
I was just a kid entering college in 1969 when he was awarded his Nobel Prize. Quark Theory was a newly postulated theory to help explain the internal structure of elementary particles. It was simultaneously derided and admired at that time. But it sought to explain the internal structure of these particles of the Standard Model as being composed of even more elementary particles known as Quarks. In the past 30 years Quark Theory has gained broad acceptance, but had to evolve to encompass even more types of Quarks than originally postulated in the late 1960’s. Now we have “Up”, “Down”, “Strange”, “Charmed”, “Bottom”, and “Top”. The hope was that we could explain all fundamental forces of nature, the the particles we see and create, as composites of these various kinds of Quarks. It made a huge splash at the time, for it represented an experimental confirmation of the existence of the Charmed Quark. The discovery paper contained well over 100 co-authors.
The 1960’s-1990’s were a time when Particle Physics dominated the research funding for physics. My own field of Astrophysics was a bit starved for cash, and courses in physics graduate education featured particle physics at the expense of nearly every other major area. The Higgs Boson is the particle postulated to hold the Quarks together inside the particles of the Standard Theory. The W-boson (see image) was actually discovered in 1978. So in the interim, we have all been searching for confirmation of the veracity for the Quark theory. Since we can’t see individual Quarks, how do we know they really exist? And what holds them together? and how do their combinations form particles ranging in mass from an electron at 0.5 MEV to a proton at nearly 2000 MEV For more read “The Higgs Boson particle Explained: Part 2”
Interesting article from: http://ow.ly/cbARU
Atom-smashing physicists have just turned data for a newly discovered particle, likely the Higgs boson, into music. On July 4, researchers at the world’s largest atom smasher, the Large Hadron Collider (LHC), in Switzerland, announced they had seen a particle weighing roughly 125 to 126 times the mass of the proton that was consistent with the Higgs boson. The researchers used so-called data sonification to transform data collected by the experiment into sound. Essentially, they used a graph showing the data and turned the energies of collisions shown on that graph into musical notes. Each data point, or energy number for a collision, was always given the same musical note, with the melody changes following exactly the same profile (the ups and downs) of the scientific data.
“It offers the same qualitative and quantitative information contained in the graph, only translated into notes,” composer, physicist and engineer Domenico Vicinanza told LiveScience. The beats are not just music to the ears, as Vicinanza said; the melody could be useful for many reasons. “For example, it would allow a blind researcher to understand exactly where the Higgs boson peak is and how big the evidence is,” Vicinanza said. “At the same time, it could give a musician the opportunity to explore the fascinating world of the high-energy physics by playing its wonders,” added Vicinanza.
Here is another picture of the chaotic attractor basin, with more than 1-million cycles of vibration accumulated. Notice the beautifully intricate interior structure of the basin. Even within the solid trajectory region there are holes where the system never goes.