omenti

beyond 88

Yesterday Om pointed out that it was piano day - the 88th day of the year honoring the 88 keys of most pianos.  I read his post a day late, but there's still hope for another celebration with the same name. An obvious choice might involve the Bösendorfer grand where options include 92 and 97 keys in addition to the normal 88.  Music has been written for these beautiful instruments, but why stop there? 

 

Press a key on the piano and a hammer strikes one or more strings which begin to vibrate producing a sound.  The frequency of the vibration depends on the length of the string with longer strings vibrating at lower frequencies.¹  The left most key causes the longest string to oscillate 27 times per second - 27 Hertz (Hz) - while the right most key produces a 4,186 Hz frequency.  In between the keys are divided into 7 octaves, each composed of 12 keys.  Each octave doubles the frequency so the C above middle C has a frequency twice as high. The notes are evenly divided so each key has a frequency 2^1/12 times - just under six percent higher than the preceding key. 

 

Now we're ready.

 

Let's say you wanted a piano with the range of human hearing - usually given as 20 to 20,000 Hz in young children.   Going from 4,186 to 20,000 Hz, after a bit of arithmetic, requires 27 extra keys on the right.  Five keys on the left will get you to 20 Hz..   One hundred and twenty keys and some long arms would be sufficient to entertain young children to the limit of their range.

 

But what about dogs?  Canine hearing goes up to about 40,000 Hz.   All  we need to do is add an octave, or 12 keys, to cover their range.   Other mammals can hear even higher pitches.  Bats top out around 160,000 Hz so we add two more octaves giving us a 156 key instrument.  We don't have to go much higher as the atmosphere strongly attenuates higher frequencies. A bat can produce a very loud noise, but even their sensitive ears are only good for a 20 meter range.²

 

We've left out elephants which go down to about 12 Hz - that works out to 9 keys on the left. We've grown the beastmaster piano to 165 keys.   I won't cover whales because pianos don't work underwater. 

 

The game can go on.  There are any number of natural sounds of lower frequency (infrasound), but we'll leave it at that..  

 

Well - almost.  There are very faint sounds in the universe - ripples that move compress and expand space-time itself.  They come across a wide range of frequencies, but exquisitely sensitive instrumentation is required for some of the loudest - like colliding black holes where the energy that goes into the resulting gravity wave can be the equivalent of several solar masses.   It turns out the frequency of the first one detected was a chirp that went from about 35 Hz up to about 250 Hz (close to middle C).  You can play the signal as audio.

So much information there, but it may not be pleasing so let's end with one of the most demanding pieces for the human voice - in this case a coloratura soprano.  The Queen of the Night in Mozart’s  Die Zauberflöte. 

I'll leave you to find some good piano music today.  Perhaps Om's list is a place to start. 

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¹ It also depends on the mass of the string, its diameter and tension.  Additionally a rich set of other frequencies are produced giving the louder central frequency richness and character.  There's a good deal of art in the design and construction of a fine piano and none of the sound the same. 

² It's a feature.  Longer range would confuse them with signals from other bats, plus they tend to work a few meters from their prey.

 

the cost of knowledge is a great deal of ignorance

a mini-post

First a caveat - I have almost no background in the social sciences.

This week a few people have written about information overload. It’s certainly been with us since the beginning of the 16th century in the Western world and one can make arguments that extend further back. The rate of new knowledge, as opposed to raw information, has increased in many fields, doubling or more every decade and causing many fields to fission into new subfields. It’s a major cause of the imposter syndrome I feel when I’m trying to hack through a paper in low temperature physics for example … sixty years ago there wasn’t a problem thinking about both.

We deal with the information increase by specializing and creating what are often rich traditions. I’ve been able to carry on rich conversations with people where I have no Mandarin and the other person had almost no English by jotting abstractions and drawings of our shared tradition on a blackboard (slate blackboards are another tradition in my field) .

But these traditions blind us to the greater knowledge around us. .. It reminds me of the early experiment where you train a dog to respond to a bell. When you measure the brainwave of the dog you get a clear signal when the bell is rung. Now put a piece of juicy meat before the dog and ring the bell. The bell signal is nowhere to be found - it’s been overridden by the sight and/or the smell of the meat.

It’s funny - we don’t make progress without tradition, but it can also blind us to the greater world.. My belief is it’s important to communicate across the boundaries of the many traditions. I think this is an area where the arts are very powerful. We’re resorting to mechanisms we don’t have a real grasp on.. machine learning comes to mind.. to deal with some of this. There are many views on the subject, but I’m guessing it isn’t as useful as many suggest.

Finally there's an issue in traditions where knowledge doesn’t increase rapidly. How to be kind, how to be a good person, love, peace. Areas where people a long time ago had figured things out within the context of their tradition and arguably we haven’t made progress..

anyway .. just random thoughts on a rainy Spring evening. There are so many issues here that are interesting to think about.

Enjoy the Spring and listen to some music and enjoy some art. And some of you are creatives so create rather than sit back!

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A note on ignorance .. that's a complex subject in it's own right, but the title seems to fit.

 

things aren't always what they seem

I was asked why I didn't do a Pi day post. Sadly I didn't have any pie to celebrate, but  I'll try and make up for it a bit late.

 

π is a wonderful number. Deeply related to so much as well as being irrational and transcendental. But it turns out I’ve never needed more than five or six digits. Randall Munroe (xkcd) nails it:

 

 

 

My sophomore quantum mechanics professor liked to add a few math problems to homework assignments. Nothing deep, but unusual to encourage critical thinking. On the 14th of march he gave a pop quiz. We had twenty minutes to calculate the probability that the ratio of two random numbers x and y, where each is between 0 and 1, is even.

 

It turned out this was his Pi day fun. (he was Swedish where Pi day would be the 22nd of July, but he used the American date convention). He didn’t grade it - either you saw it immediately or 20 minutes wasn’t long enough.  He served apple pie afterwards. Apple, of course, for Newton although I’ve though cherry more appropriate as Einstein loved cherry pie and the 14th of March was his birthday.

 

Here's how I approached it:

 

 

I’m summing the areas for regions for ratios closest to even integers for all even integers by measuring triangles. The area for the region closest to 0 is 1/4, 2 is (1/3 - 1/5), 4 is (1/7 - 1/9) ... there’s a clear pattern. The pattern is almost the expansion of the arctangent of 1 which happens to be π/4.   Adding 1 gets us there.   The probability the ratio is even is 1/4 + 1 - π/4 or (5 - π)/4.  

 

A more important point is things aren't always what they seem.  Not only does π turn up, but our intuition about the answer was wrong.  The component for 0 isn't symmetrical and that leads to a 46.46% percent probability rather than 50%.    

 

Obvious first guess are often wrong and can lead to enormous problems.  We're bad at probability and risk analysis.  Not exactly a good thing given technology.

 

good, good, good, good lunations

minipost

The Earth and Moon are gravitationally locked with the Moon rotating around its axis in the same time it takes to travel around the Earth.  The result is we only see one side of the Moon ..   Well... sort of..    The Moon doesn't orbit the Earth.  Instead both Earth and Moon orbit a common point known as a barycenter which is about 1,700 km below the surface of the Earth.  The Moon's orbit is also  elliptical which turns out to impact how much of the Moon's surface you can see.

 

The Moon moves slower when it's farthest away and faster at its closest.  You see a bit more of the Eastern side when it's moving slower and more of the Western side when it's speeding.  Added together we can see about 59% of the Moon's surface over the course of a month.  (There's also a smaller effect due to parallax, but it's mostly the elliptical orbit.)

 

You learn this right away when you start looking at Moon, but seeing a visualization is dramatic.  Andrew McCarthy took two million photos over nearly a full lunar month and put together a wonderful video of the effect.

 

 

 

building blocks

Watching Apple's Mac Studio announcement yesterday took my mind to something Carl Sagan said in the Cosmos series.

The Mac Studio's underlying technology goes far beyond the many tens of thousands of person-hours Apple has invested.  The semiconductor industry that stands on the shoulders of Bell Laboratories back to the fundamental work of James Clerk Maxwell and before.  Apple and others are able to come up with advances that strike us as dramatic as they make an impact on our lives.  The impact of some innovations like the electric light, the telephone, the automobile, powered flight, radio, the atomic bomb and the Internet have changed how we see ourselves.   But take a look and they're all built on long chains of invention and innovation that are often forgotten.

 

This comes to mind with the horrors going on in Ukraine.  Russia has always had brilliant minds.  They've made stunning advances in physics and math, but they haven't been as successful as the West in building on that.  A good deal of their technology is derivative.  In the past 25 years this may be by design. Most of the export value comes from extraction - oil and other natural resources. These industries seem to fall under the direct control of Putin's friends.  More technical industries are still under oligarchs, but these aren't super high profit.  As long as the core players can control them, the real focus of the economy is what can be run by shear force and power rather than technology and sound business practices.  (note - this is speculation as I'm certainly not a Russian expert..  so take it with a grain of salt).  

 

High tech industry is required for the military and some consumer use.  Although that is supposed to be home-brew there is a lot of importing and rebranding. I've seen that in electronics used in physics experiments and am told is standard operating procedure.

 

So imagine you can't important and rebrand the CNC tools necessary to make jet engines.  Can you make the tools yourself. What if you can't even make precision bearings?  What if China doesn't allow electronics into the country (they probably will, but now they can be the Mafia dons)?  Sanctions can make a medium and longterm impact.  

 

You don't need to make your Apple pies from scratch - we have our universe - but few companies or countries have the capability to build objects of the modern world without technologies that exist outside.  All of these long threads few of us think about until they aren't available.  Think about all of those high value products waiting for fifty cent ICs that were designed twenty years ago...

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PS - I'd love a Mac Studio, but it's way beyond my budget. 

 

 

on nuclear winter

Talks and discussions on the impact of nuclear war - even small exchanges.  It's an important, but potentially triggering, subject. If the current situation in Ukraine is keeping you up, please skip this one for awhile.

 

The first two videos are short TED talks from the last decade. 

 

The last is an excellent discussion lead by Andy Revkin.