omenti

some recommendations

A few recent conversations led to some recommendations that may interest some of you so rather than a normal post here are a few books and a talk.

 

 Sound is something our brain generates - an interpretation of a periodic mechanical compression wave that travels through some medium.  Depending on your definition, it is possible to describe sound as something that only exists in the brain.   

 

An anthropologist told me that music is one of those human activities that is seen in all known societies.  Singing exists in all but a handful and a minimum of percussive music is universal.  Music and speech are processed in different parts of the brain and that makes them interesting.   Over the millennia people have become experts at conveying rich meaning acoustically and in the past few decades we've been putting together how it all works, although the neurology of music is still in its very early stages.

 

A few good books on the subject exist.  Musicophilia by Oliver Sacks, like his other books, is a delightful read and highly recommended.  Somewhat deeper and more interesting I think is This is Your Brain on Music by Daniel Levitin.  It is a bit dated now, but is a fascinating look into the subject offering a lot for contemplation.  Levitin has a companion website that should be used as you read.  Unfortunately it is not directly linked in the ebook version of the book.

 

A few months ago Aniruddah Patel of Tufts gave a fine talk on current research- Exploring the Impact of Music on Brain Function  While it is not a broad overview of the field it is at a high level and accessible to non-specialists.  From the introduction to his talk:

 

 Music reaches into our deepest self, or so Plato declared some 2,300 years ago. We’ve been wondering about music’s effect on us ever since. In the last decade in particular, a growing number of scientists have taken up the quest to chart music’s course in the body, starting at the top—the brain. According to Dr. Aniruddh Patel, associate professor of psychology at Tufts University, there’s no better time for music cognition research.

“What measurable impacts do musical listening and musical training have on brain function?” he asked May 13 in his talk for the National Center for Complementary and Alternative Medicine’s Integrative Medicine Research Lecture Series. “People have been speculating about music in the mind for millennia. Plato remarked that rhythm and harmony find their way into the inward places of the soul back in three or four hundred B.C.”

 

Highly recommended!

 

Feynman, by Jim Ottaviani and Leland Myrick is a fine little biography in the form of a graphic novel.  Even though it is mostly pictures, there is a bit of physics that is clearly explained by him.  If you get the ebook version and have an iPad, the iPad version is better rendered than the Kindle version.

 

It is difficult to recommend an introductory physics book.  There are any number of popularizations that will give an introduction to current and past thinking.    Learning a bit more takes a lot of work on the part of the student.  It is funny - as an undergrad you learn a bit about the subject, but very little about physics. Of course you think you're learning physics.  What you are doing is learning some mathematical technique and a bit of physics that has been learned over the centuries.  You learn to solve a few problems.  The first few years of grad school exist to refine technique, but you also start learning how to ask questions and hunt.  It is only then that you start doing physics and by the time you get your Ph.D. you are only starting.  Somewhere along the path you realize how little you know.  Getting out with the title means the training wheels are off, but you have a proper adult curiosity and are beginning to learn how to ask proper questions and are learning how to interpret the results.  This is probably the path for many other fields - there is a false sense that you know what you are doing early on, but then a wonderful realization that you knew so little that you thought you knew a lot.  

 

My favorite first year physics book is one that I would only recommend to those who have had a year of college physics already.  Although it is dated, the three volume Feynman Lectures on Physics is a real delight and was re-released in a set a few years ago.

 

A big hole in my education has been an understanding of the history of science.  I think it is important to understand the flow of the development of understand, something that has been very uneven and often dramatic. A few universities have great courses, but I never had any of it until after my formal education was over and I started reading books on the history of science.  I can make recommendations for bits and pieces as I've only scratched the surface.  I'll continue to make recommendations when I stumble across something notable.  Of course I'm always interested in interesting things you've uncovered as most of you are probaby much better read.

 

Finally a book on making things.  Making It by Chris Lefteri is not a how to book, but rather the best introductory guide to manufacturing techniques I've seen.  Be sure and get the recently released second edition.

 

Huge volumes are being written about 3D printing, but presently it only covers a very narrow range of what is possible and practical.  It is one of a large number of tools and techniques - even for single example custom work.   I find it exciting that there is a renewed interest in making things and this should be on the shelf of anyone starting down the path as well as anyone who is curious how the stuff around us was made and the different processes used for making one, a hundred, ten thousand or millions of an item.

 

With Summer here I note something fun you can do on your vacation.  Find out what is made in the places you'll be visiting and try to arrange a tour.  A lot of this went away after 9/11, but many companies are delighted to show what they do and often you run into boffins with deep knowledge who are just bursting at the seams to share bits of it. It is a world that touches all of us that is mostly invisible.

 

And for the last recommendation a fantastic book on flavor.  Neurogastronomy by Gordon Shepherd sorts out the current understanding of our perception of flavors.  One of those books I just couldn't put down.

 

on core questions - what are the real questions you need to ask?

Sukie recently had eye surgery which left her without the use of an eye for a few weeks.  She remarked that it was interesting that she still could judge depth - don't you need two eyes for stereo vision?

 

For years people have been building 3D displays.  The idea usually amounts to recording an image with two slightly offset lenses and then presenting the images to the eyes in such a way that you can detect the parallax.  As far back as the 1950s many of these were intended to revolutionize movies and then television.  Many are clever and the battle to put 3D everywhere continues today, but there are some serious technical problems that include the need to match camera lenses, screen brightness, lowered resolution and the fact that some cues required for vision are broken resulting in a less than quality experience for anywhere from 10 to 30 percent of viewers.  Combine this with the need to create and polish a different directing technique for live action like sports or post production with movies and it is easy to see why ESPN is dropping support for 3D sports.¹

 

It is important to think a bit more deeply about how the senses work.  To date the approach has been to deliver what is believed to be the right proxy for realistic 3D to a pair of retinas.  After all - this should fool the brain which should just assemble the right image.  The problem is that realistic vision doesn't work this way.  In fact the parallax information is only one of several cues we use to create images.

 

Several years ago I was given a talk at the Disney Animation Studio in Burbank, California.  A fabulous place complete with a Mickey Mouse Wizard's hat, the place is filled with history.  It was my first visit to the place and we got a great tour of the place, its people and some rather curious historical kit.  The piece that really interested me was the multipane camera.

 

I had too many questions, so the guide scurried off and brought back one of the older animators to explain.  You've probably noticed animations move a background relative to the foreground when motion is involved.  The technique gives one of the depth cues our brain uses to create images.  What you may not have noticed is the old Disney films use up to seven layers of depth and the motion is very smooth.  

 

The technique was mostly invented by Ub Iwerks - a legendary animator and director at Disney, although he was not with the studio at the time.  Several groups refined the technique during the 30s and the one I saw was invented by William Garity.  Its first movie won an academy award for an animated film. Disney was an interesting place at the time.  It did serious perceptual work and invented many of the tools of animation to use in-house - very much like Pixar does today.  If it is core to the business, there is a need to invent, own and perfect it.  

 

What I saw was one of the old production machines that was used in Bambi, Peter Pan,Fantasia and Pinocchio, but the film it was invented for was called Snow White and the Seven Dwarfs:-)   The technique is still used in computer animation and has been highly perfected at studios like Pixar and Disney Animation - I saw one of the tools in action one some preliminary work for Tangled. It is also used dramatically by Hayao Myazaki at Studio Ghibli.²

 

Here Walt talks about it

One of many things that impresses me about the film makers I know at Disney Animation and Pixar is the rich model they have for human vision.  This and subsequent discussions noted they see depth as coming from several cues - things like closer objects being larger than farther ones, the blurring of far away objects, relative motion, lighting cues, parallax (sometimes called stereopsis) and the focus of the eye (often called accommodation).  Regular movies and video can have all of the cues except parallax and accommodation.  3D movies only add parallax and in many cases it is broken as the camera optics are not well enough matched to the eye and some crosstalk is created.

 

Some studios have achieved a fair amount of success with current 3D technology, but they tend to use it sparingly - mostly on the foreground and using great care with the viewing box.  This is somewhat easier in animations and mixed mode films (like Avatar) where great control is possible, skilled artists are present, and there is a time and resource budget.  But it is not a real 3D effect and perhaps we are entering a form of uncanny valley.  The last bit - accommodation is really hard.

 

It is interesting watching the spec wars among 3D vendors.  They have metrics which they are optimizing and some fine work has been done, but they are only attacking part of the problem.  They are ignoring the full experience and, for many people, dropping an imperfect parallax leads to lower production costs and a better viewing experience.

 

You really need to consider the full experience.

 

In the late 80s the Japanese were taking over the tech world at the time and a huge effort was underway for the US to create a digital standard high definition standard that would be better than the analog version the Japanese were working on.  Bell Labs was part of this Hail Mary effort and some of the physical scientists and applied math folks were asked to make sure the tests made sense.  I was invited to be part of that critique.

 

They were doing all of the right engineering things and it was a lot of fun getting to see a bit of the future, but my experience was while the video signal was better than anything I had ever seen, what really blew me away was the audio.  Since then I've talked with a dozen other people who saw the demos and tests and everyone said the same thing - really good video, but mind numbingly wonderful audio!

 

The audio was there because it could be.  Digitally encoding the signal allowed for a lot of compression and there was space for a compressed multichannel audio signal.  The test videos were carefully made with a big budget and the audio guys were world class.  The demo room was set up to take advantage of this.  It dawned on me that the experience of watching a movie or television is much greater than the moving image ... the audio is important.

 

When you talk with some of the serious movie guys they'll sigh and note 3D is there to fill movie houses and first and second to save television makers.  Some good work is being done, but there is a lot of garbage and it is increasingly being viewed as a checklist item that only adds a tiny amount of value to the movie artistically at best.  The monetary value is rapidly dropping and there is historical precedence for this.  All of them said what they really want is better control of sound.  The problem of sound field reconstruction is a thorny one and doubly difficult if the listening stage is much larger than a single seat.  When it is done at a single seat level you get a dramatic response from the viewer that is much greater than any 3D effect that has been tried.  This, if and when it arrives, will probably require a new direction and post production language, but may well be worth the effort.

 

Multipane made animation dramatically advance.  3D hasn't had a similar effect on film.  You have to understand the limitations of an art deeply and have a good enough model of perception if it is to become art.  Techniques or may not easily jump from one art form to another.  And you have to ask yourself what is the full experience?  Is your little corner of the world inclusive enough?

 

Apple appears to have asked that question with iOS 7.  While the reception has been a bit polarizing, one thing they've done is multipane to add the illusion of depth.³  When I saw a video of their keynote demonstration I was immediately reminded of my tour of that building with a wizard's hat and William Garity's amazing machine.  I'm assuming they have probably learned at the feet of their friends at Pixar as a considerable amount of experience is needed to make this feel right.  I don't know how well it will work, but Apple is asking the right set of questions.

 

The right set of questions applies in so many disciplines.  I recently read a couple of great urban planning books and recommend them as examples of people who have thought deeply about core problems - Cities for People by Jan Gehl and Walkable City by Jeff Speck.  Sometimes a few questions outside the popular frame give a much deeper understanding of the real issues.

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¹ Sports is particularly difficult as scene transitions can be jarring.  ESPN is forced to use about 80% fewer transitions than best practice television uses.  This makes the experience worse for 2D viewers.  Fatigue is an issue for a significant percentage of their viewers and that gives advertisers something else to worry about with placement position.  Some viewers become more immersed, but many don't.  Both might have a negative impact on advertising.  Additionally it is very expensive and difficult to maintain precisely matched zoom lens pairs on multiple cameras.  

² Very convincing flying scenes can be created with it:-)  Animation is all about good enough immersion.

³ Apple's video showing the early beta of the interface.  You begin to see multipane a bit after a minute into the video and then around 2:15. (there are other depth cues)

 

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Recipe corner

 

I had a birthday recently and that means cherry pie.  Mine isn't too fancy, but demands high quality tart pie cherries.  If you don't have a source it is best to forget about baking one.  I won't go into crust building as that is religion.  I use a combination of crisco and butter and never lard (I'm a vegetarian).  A good flour is important as is chilling it.  I don't use the popular vodka trick as Sukie is allergic to potatoes.  

The recipe is for some good canned cherries I get from Michigan for off-season baking.  This is good for one 9" pie.  I like to lattice the top:-)

 

Tart Cherry Pie (assuming you have a the crust prepared)

 

Ingredients

 

° three 425g cans of sour pie cherries (about 5 yo 6 cups of pitted cherries if you have fresh)

° 150 g white cane sugar

° 3/4 tsp cinnamon

° 45g quick cooking tapioca or 100g of King Arthur Pie Filling Enhancer

° 1 tsp almond extract

° 1/2 tsp salt

° 30g butter

 

Technique

 

° line a 9" pan with pastry dough

° Drain the cans and reserve 2/3 cup of cherry water from one.  Put the cherries and water into a large bowl

° combine sugar, tapioca or pie enhancer and cinnamon and stir in the cherry bowl 

° stir in the extract and salt.  Let it sit about 20 to 30 minutes if you're using tapioca. 

° pour the filling into the pie pan and dot with bits of the butter

° work a lattice on top or just roll out a second crust.  If it is a second crust you need to cut some vents.  Get fancy with the design

° put it on a baking sheet (I put some parchment on the sheet to keep spills from burning in) and pop into a preheated 425°F oven for about 40 minutes until the crust is golden brown.

° remove and cool it on a rack.  You may have to defend it.

 

how much is enough?

It is remarkable when you think about it.   Put a pair of athletes on a field and give them a ball.  After a bit of tossing it back and forth, one might throw it well past the other.  Without using any equations she creates a model of its trajectory and starts it running as she turns from it and starts running down the field.  At some point she knows when to turn, makes a few corrections to her position and catches it.  Apart from the interesting sensor and computation problems there is the question of how accurate does she need to be? How bad can her mental model be and still allow her room for correction?

 

Knowing just where you are in position and time has been a traditional problem.  For navigation it is relatively simple to calculate your latitude to reasonable accuracy with 15th century tools, but longitude was a different matter as the Earth is spinning on its axis.  In 1707 this came to a head with a terrible naval accident that claimed four warships and perhaps as many as 2,000 sailors in British waters.  It was later blamed on the inability to compute latitude accurately enough and it lead to the Longitude Prize of 1714 - an Act of Parliament that offered a then huge reward to anyone who could create a practical solution.  

 

Clocks are still very important, but you need really good clocks.  In fact the trick is to orbit and few dozen of them, each with a radio that sends out a time stamp and location. Your phone has an antenna, receiver and some computational power to receive some of these signals and quickly give you a mostly good enough idea of where you are.  

 

The GPS system turns out to be simple in concept and difficult in practice.  It is one of those problems that you would normally discount as just silly - too expensive and impractical - unless you had experience in navigation.  A few years ago a few of us were asked to look at the problem of GPS denied navigation.  There are any number of ways you might learn where you are and it makes sense to re-visit these periodically for certain niche applications (this was navigating in caves), but in the end if you can see the sky and the GPS constellation is operational, it is far and away the best solution. 

 

An interesting feature of GPS is that relativity is turns out to make a difference.  The satellite's speed with respect to a stationary point on Earth makes the time noted by the satellite slow by about 7 millionths of a second a day - just special relativity.  But the satellites are farther from the center of the Earth than we are, so the general relativity tells us the clocks run a bit faster - about 45 millions of a second a day - these add up to a 38 microsecond per day correction and it is built into the location model along with corrections for radio propagation through the atmosphere, orbit determination and a few dozen other issues.  The model is thorny and has enough understanding of applied physics that it works well enough for conventional navigation.¹

 

So Einstein was important to a critical piece of our defense and economy.  But we rarely use special relativity in our normal lives.  Frequently it is claimed that Special Relativity replaced Newtonian physics.  It turns out special relativity reduces to Newton physics in the limit where objects are moving "slowly" with respect to each other.  For most practical purposes we can just go ahead and use the simple mathematics of Newton. One theory augments another rather than replacing it.

 

The same can be said for quantum mechanics.  What triggered the blog was hearing that Ken Wilson had died.  Quantum mechanics is elegant, but also very strange to our expectations - a bit kooky as Feynman would say - but that's the way Nature works.  When you get to a small enough scale it is time to throw out classical physics and use quantum mechanics instead.  Possibly no one understood quantum mechanics more intuitively than Wilson.

 

Quantum mechanics happens to be very important for us - numerous bits of how our electronics work depend on a rigorous understand for example and it drives many physics processes at the atomic and even the molecular levels.  But, like relativity, it has an influence in when you might think you can totally discount it.  Recently a beautiful little experiment showed just that.²

Now there are about a dozen directions I could go, so I'll just pick one and see where it leads.

 

A very interesting question is will new physical law replace relativity and or quantum mechanics and where will it be important?   Both are difficult, but I suspect classical physics will be just good enough for 99.99% of what we do as humans for a long time.  When you get to smaller sizes and much higher energies (temperatures) that we're used to you need to go to newer physics.  

 

It turns out there are four known forces in nature - gravitation, electromagnetic, strong and weak.  Three of them have been unified - the standard model was developed in the mid 1970s.  There are bits and pieces to nail down, but it is a remarkably solid and predictive model.  A problem, it turns out, is gravity.

 

Gravity may seem like a big thing to us, but we're pretty big at about halfway between the size of an atom and a star. There is a lot of mass in us and we tend to have problems falling on something as massive as the earth.  But gravity is weak - astonishingly weak.  If gravity has a strength of 1, the electromagnetic force has a strength of 1,000,000,000,000,000,000,000,000,000,000,000,000 (36 zeros if I counted correctly), the strong force is about 100 times stronger than electromagnetism.  The weak force only has 25 zeros after it, but still ...³

 

You've probably seen Feynman diagrams popular with particle physicists.  They are a shorthand notation that buries a boatload of math and allows you to examine a large class of fundamental interactions - electrodynamics with some quantum mechanics and relativity thrown in.   Usually time runs along one axis and position along another.  Particles collide, forces are represented by squiggles and so on.⁴

 

Imagine a particle that interacts with another particle through some force.  The top diagram represents two particles interaction with some force f between them (if it was electromagnetic the squiggle would be a photon).  One of the beautiful things about the theory is that if this is true, you can rotate the diagram 90 degrees and, if the energy is high enough in the collision between the particles labeled p, new particles labeled x are created.⁵

 

This turns out to be useful.  Physicists can do experiments and look for unknown forces. Perhaps the force is very very weak or it only works at very short distances.   The strange looking plot from a paper a few years ago that summaries searches for new forces (discover a new force and you get a Nobel out of it which can lead to amazing perks like reserved parking places).  It is possible to rule out new forces in much of the observable world, so it seems likely at our scale that we will never see much of a modification of what we have.  Any new force with a range on the human size scale would have to be more than 100,000 times weaker than gravity!  Of course finding new forces, even though they apply to odd conditions, can lead to a deeper understanding of what makes the universe tick, so lots of good stuff remains.

 

t is interesting to thing that, at the level of human observation, fundamental physics is largely solved.  That doesn't mean there isn't a huge amount of fundamental physics lurking out there, its just that we probably won't need the corrections for our daily lives.  now, this sounds like an absolute statement and they tend to fall, but there is a lot of confidence behind this.  There is also a huge amount of non-fundamental physics at our scale that needs to be done.  Our understanding of even simple amounts of complexity is poor at a deep level.  In theory we could work it out, but it is just too complex - we need new understandings.  

 

This is a natural pivot to emergent properties, but time is out.  sigh ...  such a wonderful topic.⁶

 

I strongly recommend finding a friend or your dog and playing around a bit with some simple classical physics.  It may not be at the edge, but it is still amazingly fun and even seemingly simple things (like the biomechanics of walking) are yet to be sorted out.

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¹ An applied physics discussion of relativistic corrections to GPS by Neil Ashby of the U of Colorado.  It turns out there are deeper relativistic corrections that would be necessary if we wanted a more accurate system.

² The introduction may give the impression this is new physics - it isn't.  It confirms what is expected.  This happens all the time in science.  People figure something is too difficult to measure and move on to other things.  Then someone comes along with real cleverness and/or better measurement tools and performs the experiment.

³ As an exercise calculate the electric force between the electrons in two gallons of water separated by, say, ten cm or so.  It turns out to be strong enough that it could easily lift the weight of the earth.

⁴ I'm not being precise, but just to give a rough description.

⁵ Being really caviler on particles and antiparticles here.  Generally think of a particle and its antiparticle colliding and creating another particle and its antiparticle..

⁶ It is wonderful to think that a room full of air molecules with someone on the order of 10³⁰ equations that would need to be solved in the simplest possible case, reduces to a couple of equations due to an emergent property of scale.  

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Recipe corner

The really good produce isn't here yet, so in the meantime this is a nice Summer soup that will improve as real corn arrives.

 

Corn and Avocado Soup

 

Ingredients

 

° 1 avocado

° 3 cups almond milk (could use regular whole milk if not vegan)

° 4 cups yellow corn (canned unless you can get it on the cob)

° 1 tbl finely chopped onion

° 1/8 tsp turmeric

° 1 tsp cumin

° some sea salt

° some freshly ground pepper

° coriander

 

Technique

 

° toss everything except the corn into a blender and blend 'til smooth

° add the corn and season to taste.  If you like try running about half the corn through the blender for a different texture.  You can also add chopped herbs if you like  -- experiment!

 

 

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Bonus section

A WNYC Soundcheck interview of the director of the Macaulay Library's extensive audio collection - about 150,000 samples



An amazing resource!

Also recommended is The Great Animal Orchestra by Bernie Krause.  I link to the iBook version which has higher quality audio than the Kindle flavor.  Of course it should be listened to with good headphones or speakers rather the internal speakers to hear the detail.  A downside is iBooks current doesn't work on laptops, although that supposedly chanages in a few months.

 

a galactic snack

We've all thrown balls for kids or dogs.  There is a point where you want to get them to run, so you throw as you can at a good angle and watch how far they have to go.  Our abilities vary a fair amount - it is embarrassing to throw with an athlete friend who has a 70+ mph fastball - she can get much more range than I can.  But there is a limit to what muscle power can provide.

 

Guns and canons take you farther.  Wind resistance limits the range, but some impressive results were possible.  The WWI German Paris gun had a 75 mile range and put the first manmade objects into the stratosphere.  This sort of gun was specifically outlawed by the Treaty of Versailles, which moved the Germans towards experimenting with rocketry in a big way.  But that is another story.

 

Now imagine what Newton did hundreds of years ago.  Put a canon on a very tall mountain where air resistance was small.  The canon was pointed parallel to the Earth's surface.  The shell would move out and fall to the ground.  More gunpowder was added for the next shot and the range would be farther out.  Repeat with faster projectiles and they would go further and further until they fell completely around the earth. They would go into orbit.

 

A bit more thought and you can imagine a speed that is high enough that the projectile can escape Earth's gravity entirely - no longer in orbit around the earth it is truly outward bound.¹  Increasing the mass and or decreasing the size of the body you want to escape increases the velocity.

 

We know that the speed of light is the universal speed limit.²  Only massless bits like photons go that fast, but it is natural to wonder if something can be so dense that light can't escape its surface.  You can plug in the speed of light into the escape velocity formula and come up with a number, but to do it properly requires General Relativity as conventional Newtonian physics breaks down.  Einstein's theory still had wet ink when Karl Schwarzchild did the calculation in 1915.   It is curious that the answer is the same even though the approach is different.

 

Schwartzchild now could think about objects that were so dense that light couldn't leave their surface.  The problem was imagining what would be so dense.  The critical radius, the Schwartzchild radius, was r_s = 2GM/c² or about 2.95 kilometers(M/M_s) where m is the mass of the object in question and M^s is the Sun's mass.  A bit of terminology - it technically isn't the same, but at this level r_s can also be called the event horizon.

 

So if you could shrink the Sun into something that was smaller than 2.95 kilometers in radius, light couldn't get out.  

 

You would have a black hole

 

This works out to an amazingly density of 18.4 million-billion grams per cubic centimeter (water is 1 and lead is about 11.4).  No one could imagine any physical mechanism that would permit this.  Note that the radius increases linearly with mass, but the mass only increases as the cube root of the radius.  Less massive objects would have to be much denser.  It seemed hopeless - stars could collapse, but there was always some internal pressure, sometimes exotic, that prevented it from reaching this number.

 

Time went on and the inner workings of stars began to become clear.  An aside - I'm struck by the elegance of looking at tiny points of light in the sky and sorting out what is going on inside of them.  Doing this has produced results that make the best science fiction seem completely unimaginative by comparison.  

 

Very massive stars, at some point in their evolution, could collapse into tiny spheres that were mostly tightly packed neutrons - tiny stars a few tens of kilometers across.  But there was a point where they could be massive enough to collapse into something smaller than the Schwartzchild radius.  A stellar black hole could form.

 

No light can escape from the object.  There is a lot of wonky physics that takes place as well as a huge breakdown.  Physicists have been successful at mostly unifying three of the four known forces of nature, but understanding how to link in gravity has been elusive.  What goes on inside the black hole in in the realm of quantum mechanics and general relativity - and we simply don't understand how to do that.  Using some interpretations you can talk about singularities - the mass collapsing to a mathematical point with infinite density, but that is out of ignorance - we simply don't know.

 

We've seen black holes - or at least evidence for them.  Great stuff, but I'm running low on time and have to talk what black holes  eat.

 

It turns out enormous black holes exist at the centers of most galaxies.  About 26,000 light years from use is one at the center of the Milky Way.  Properly known as Sagittarious A*, it has a mass of 4.3 million Suns and it is by no means the largest.  Some of these supermassive black holes are surrounded by gas which is attracted to them.  As it falls in, it accelerates to near the speed of light giving off light in the process - often strongly in the X-ray range.  But these are rare.   Most SMBHs simply sit at the center of their galaxies adding enough mass to make the orbiting stars move a little faster.  

 

The center of the Milky Way has a high density of stuff - stars and little clouds of gas.  Objects close to Sagittarious A*  are moving very quickly - so quickly it is possible to watch their positions change yearly from Earth -  and, every once and awhile, one of them will get too close.  

 

The density of Sagittarious A* is not as high as that of a stellar black hole - more mass makes the event horizon grow more quickly than the radius of the massive object inside.  Our black hole has a radius of a little under 13 million kilometers - a bit under a tenth of the Earth's distance to the Sun.

 

Now the question is what happens if something gets close.  If it is a gas cloud some of it may strip off and fall in creating a nifty fireworks display probably including a couple of brilliant x-ray jets.  But if the object is solid there is a radius where the tidal forces are so great that the body is ripped apart.³  This limit, for a star like our Sun and a SMBH with a mass of about a million solar masses, is about half the radius of the Earth's orbit.  The star would be ripped apart and a good deal of it would fall into the black hole giving off a capital show in the process.  It may be that one of these events was recently observed.

 

Now imagine a really huge SMBH - say 100 million solar masses.  The Schwartzchild radius is now about the same as the distance where the star would shred - about twice the radius of the Earth's orbit.  The SMBH would simply gulp the star whole.⁴

 

All of this turns out to be interesting as an object with about three times the mass of the Earth in close orbit around Sagittarious A* will be getting very close later this year.  it is likely it is a gas cloud and perhaps there will be some fireworks.  It won't get close enough to break apart if it was a solid body.  A lot of astrophysicist are really curious about the feeding habits of our neighborhood's black hole.  Stay tuned!  A fair amount of energy may be liberated.

 

If anyone wants to talk about black holes I know a bit and am always up for a conversation.  There are so many rich topics - primordial black holes,  frame dragging, do black holes have hair, gravity waves, the evaporation of black holes and frontiers where we lack any clue - like what happens to information that drops into a black hole.  I hope I know enough to not be completely opaque.  To go deeper check into popular sources like Scientific American.  They've had a few great articles in the past decade that are well written by experts. Getting to the level where you can them is like many things  - some background and effort is required.⁵

 

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¹ Escape velocity is  sqrt(2GM/r) where M is the mass of the massive body and r is its radius and G is the gravitation constant.  It is the speed where the kinetic energy of the projectile (or rocket:-) exceeds its gravitational potential energy.  1/2 mv²  = GMm/r and a little rearranging gives the answer.  I won't go into the physics of orbital velocity, but for a circular orbit close to the surface of a sphere it is the escape velocity divided by the square root of two. 

² I had an old tshirt that said c - not just a good idea, its the law.

³ Tidal forces arise when the gravitation force on one side of an object are different from those on the other side.

⁴ I sort of lied ..  if the black hole is spinning the event horizon is smaller - about half the radius for the fastest spinning black holes.  This and the radius at which a Sun rips apart allows a SMBH of about 700 million solar masses.

⁵ I'm fond of Gravitation by Misner, Thorne and Wheeler.  It came out in the early 70s, but reignited the field.  Clear and written with humor and at two different levels.  The easy part of the book is probably accessible to anyone who has taken junior level physics courses and has a foundation in differential geometry and topology.  The advanced part is more at the level of a first year graduate course.

There are newer books and much of the field is in journals.  To sink your teeth in you need a combination, but Gravitation is excellent for teaching some of the fundamentals.

 

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Recipe corner

 

Nothing formal - just an idea that worked out well.  

 

Quinoa stuffed pepper.

 

Cook some quinoa and add sautéed onions, carrots and mushrooms.  Now add currents nuts and some tomato sauce.  Cut the tops off some green pepper and clean out.  Stuff them and bake in a covered casserole dish for about a half hour.