I love music. I love singing. I love playing the piano. I love listening to music. Certainly not most important, but also among my loves, is understanding the science behind music.
Among the most basic understandings for western music is how harmony works. Harmonics is the physics (and, by necessity, the maths) behind the sounds. If you pick a note, say C, and designate its frequency (the 'speed' with which its sound wave oscillates) as 1, then the C exactly one octave above that will have a frequency of 2. Moving up an octave is defined as doubling the frequency. This higher C is called the second harmonic of the lower C, which itself is called the fundamental.
(By the way, the norm is to define the A above middle C on a piano as 440 Hz and to build all of the other notes off of that, but we'll stick to a C-to-C scale, which more people are used to dealing with).
The third harmonic is the note whose frequency is three times that of the fundamental. That note is one octave plus a fifth above the original C. In this case, it is the G above the upper of the two Cs we've defined so far. To get the G that resides in the octave between our two Cs, we have to divide the frequency of the third harmonic by two to bring it down an octave.
Having built the two Cs and the G, we can move in both forward and backward directions in the 'circle of fifths' to build the rest of the scale. For instance, D is a fifth up from G. A is a fifth up from D, etc. Similarly, F is a fifth down from C. B♭ is a fifth down from F, etc.
The entire sequence of fifths (with C in the middle) is:
Since G♭ is the same as F#, the sequence becomes a circle. But wait, although we're used to G♭ and F# being the same note, that is only because most of us learn music with a piano or guitar - fixed pitch instruments that use the modern even-tempered scale, which we'll come to in a bit.
Actually, building the scale based on pure harmonics does NOT give us a G♭ equal to F#. Without boring you (perhaps I'm too late) with the steps that get us there, the notes and their relative frequencies end up working like this:
C - 1; D♭ - 256/243; D - 9/8; E♭ - 32/27; E - 81/64; F - 4/3
F# - 729/512; G♭ - 1024/729
G - 3/2; A♭ - 128/81; A - 27/16; B♭ - 16/9; B - 243/128; C - 2
You can use your calculator (!) to confirm that those F# and G♭ fractions are not equal.
Despite the dizzying array of fractions, the progression from the lower C to the higher one is relatively, if not perfectly, smooth. The percentage increase in frequency for any semi-tone move up the scale is either 5.35% (for C-D♭, D-E♭, E-F, F-G♭, F#-G, G-A♭, A-B♭ and B-C) or 6.79% (for D♭-D, E♭-E, F-F#, G♭-G, A♭-A and B♭-B).
Because the steps are not of uniform size, a song can sound quite different in different keys (i.e. depending on what note the song starts on). Different musical eras have used different approaches to get round this 'imperfection'. Bach would have written his pieces for a specific key because of the 'feel' that key had.
Now, back to the piano and guitar (and all other fixed pitch instruments) of today. For some time now, the music world has been using what is called an even-tempered scale. One in which the sizes of the steps from the lower C to the higher one are all the same. As it turns out, to double the frequency over the course of twelve uniform steps, each note needs to have a frequency 5.95% greater than the note below it. Unsurprisingly, this interval lies between the sizes of the two intervals (5.35% and 6.79%) in the 'pure' or 'perfect' harmonic scale.
There is a cost to this simplicity, but one only borne by the most sensitive of ears. None of the intervals / harmonies produced by the even-tempered scale is perfect. Each is slightly off what physics calls for. These days, nearly all of us are attuned to this minor blemish, but we should all recognise that the harmonies we hear, while undeniably beautiful, are sadly not perfect.
Originally posted 5 Oct 2003. This predated the birth of social media and its enhanced 'echo chamber' effect. Looking back now, I think that it also, perhaps, underestimates the care and work required at the practical level to 'see' the stories through which we interpret the world.
I dreamt I was emperor of the Earth. From my glass palace, I set out law and pronounced on every dispute. But I could not leave my palace. I had at my disposal ten deputies, each of whom had ten assistants who in turn had 10 observers each. Through this network, I learned of the goings on in my kingdom, heard of the wishes of my people.
My deputies did not always agree. I was presented with accounts so different that I could hardly believe both described the same event. I suspected that my deputies, rather than wishing to pursue the Right, sought to advance their own interests. In this nightmare I knew that I did not and could not rule my kingdom, for I knew not the first thing about it.
Where is the truth?
In the run-up to the recent invasion of Iraq, I was struck more strongly than ever by the belief that there was no way I could ever really get to the bottom of the 'facts' behind the cases for and against the war. Now, the Hutton inquiry and other investigations in the UK (and serial scandals in the States) roll on, and the debate continues about both the justifiability of the invasion and its concrete costs and benefits. I feel that truth will always be beyond my grasp (unless I reach it through good chance), and I can't help but draw a parallel with well-known problems caused by sceptical challenges in 'formal' philosophy.
The philosophers' problem
Descartes famously embarked on a programme of doubt that included viewing himself as a mental entity whose access to the external world relied completely on his senses, all of which were subject to error. We've all been introduced to interesting optical illusions in which our visual sense was duped. We can take one hand from the fridge and the other from the radiator, place both in the same bucket of water, and register cold sensations from one and hot from the other. We've thought we heard things when others swore there was no sound. Our taste buds are fooled by clever food product engineers into reporting that a mix of synthetic liquids is cranberry juice.
Pushed to its logical conclusion, this collection of uncertainties might lead us to doubt whether the 'real' world resembled our model of it in any regard. It might lead us to doubt whether a physical world exists at all. In the end, Descartes, like Berkeley and others after him, relied on the existence of a benevolent God to secure the existence of a world that 'tracked' with our senses. Some today take solace in the same belief, but others cannot.
Hume, William James and others, in different ways, effectively threw in the towel and said that all we can do is adjust our 'model' when we encounter new, awkward evidence, trying to find a way of incorporating it with as small an adjustment as possible to the old system. Much of this is done based on what was then called human nature - what some would now call our general genetic and cultural 'programming', which tells us which inputs to trust most at which times, etc. At some cost to human pride, we could dodge the question rather than bang our heads against the wall to secure a route to Knowledge of the Truth.
The citizen's problem
This image - of a mind forced to make do with a collection of error-prone (perhaps even wholly unreliable) senses to collect information from the world with which to predict how best to act within that world - has an obvious parallel on a political level. The Cartesian mind becomes the citizen, man-on-the-street, would-be pundit. The unreliable senses become the competing editorial lines of the media, the jousting press-conferences of the governments, the mass prattle of the chattering classes. This modern, practical example poses new problems, because we all know that each source of information is not only imperfect but also driven by an 'agenda'. Truth may not be what these sources seek at all.
We all need to sift through the overabundance of information, choosing which data to attend to - to pay attention to. Most of us don't have time to go to primary sources in Iraq, Afghanistan, the Pentagon or Whitehall. This selection in itself goes a great way toward determining what we will believe. Of course, I would be oversimplifying if I asserted that readers of the (leftward-leaning) Guardian or the (conservative) Telegraph will have beliefs that wholly conform to the editorial line of their chosen newspapers, but the correlation is certainly non-zero.
Most of us have access to and pay attention to multiple, often competing (or even contradictory) sources of information, so we have the luxury of a second challenge - choosing what to believe from among the information we take in. Obviously, we can reject some claims, assertions, stories out of hand. They fly in the face of too much that we take to be unshakably true. Or perhaps we know from experience that the source of the information is not to be trusted. This certainly helps. Yet, given that intelligent, reasonable people can and do disagree passionately, not only about moral principles but also about the facts of the cases in which principles must be applied, our reason cannot take us to a universally accepted answer.
Our senses have developed over millions of years so as to provide information to our brains that can be (generally) trusted - trusted in that decisions based on that information have tended to result in longer life and greater reproductive success. For the most part, I trust my senses. At a practical level, I am not unsettled by Cartesian doubt.
Our political institutions and media corporations have evolved over a much shorter time span. The individuals within them have learned within a lifetime all that helps them rise to 'the top'. Entertainment value aside - the drive of this evolution and learning is not reproductive achievement but rather success in being believed. We get our information from a collection of finely honed experts in the field of belief generation. At this level, I do feel overwhelmed by sceptical doubt. How can I possibly work out who to trust?
Bush? Bin Laden? NY Times? Le Monde? UN Weapons Inspectors? MI6? David Kelly? Al Jazeera? Amnesty International? The Vatican? Michael Moore? I do hope you didn't expect a post about scepticism to come to any answer...
A post originally from 26 Sep 2003. Clear weight given to the role of conditioning (without calling it that) in life. Reality is all matter and no spirit. I'm probably closer to the opposite these days.
I am made of stardust. My body's materials and the way they behave at a fundamental level are basically the same as the stuff that makes up the entire universe. That these building blocks, created in solar fusion furnaces and spread via the explosion of supernovae, exist at all is pretty impressive, but in me they come together in an awe-inspiring display of order.
I am a vehicle for my genes. This matter is all put together according to a genetic programme, constructed of DNA and resting at the core of each of my trillions of cells. That programme evolved through many generations, so my programme was shaped by the fact that my ancestor's programmes were successful in getting themselves passed on hereditarily. Its complexity is hard to imagine, with 3 billion 'bits' of information; yet it is written using only four different characters. It shows acres of common ground between me and the rest of the life on earth, yet my specific programme is unique.
I am a product of my environment. The programme is written to be responsive to different environmental inputs, so the 'me' that has resulted flows from my accumulated interactions with the external world and how those interactions have switched on and off different parts of the programme. Some of those interactions are physical, some involve the exchange of ideas. Many of them directly involve other people.
I am a part of nature. I have no soul, no mind that is not ultimately traceable to the physical activity of my brain. There is no 'I' free agent that somehow stands aloof from the causal laws that affect everything else in nature. At any moment, I am wholly defined in natural terms. Embedded in the divine organisation of my material lies not only the genetic programme but also an entire history of thoughts, actions, accidents and events that define potentials for future decisions and actions. Complex? Yes. Astounding? Yes. Supernatural? No.
I am moral. I define the good, the right. Nature's weave does not contain it. There is no God to command it.
I am a unique instantiation of Life, Sentience and Self-Consciousness, uniquely placed in this time, navigating a unique set of gates and hurdles, sharing with a unique collection of other persons. My causes reach back to the beginning of time. My effects flow to its end. I am a special knot in the infinite and eternal web of Being.
Originally posted 7 Oct 2003. A story of undivided wholeness, but in strictly material terms and in linear time, with a definite beginning and an open end. My life is in a tiny segment of that time. These days, my sense is that neither reality nor I have a beginning or an end.
I like to think of myself as a very special little collection of stardust. Before you back away slowly, avoiding eye contact, let me explain. The story below is my layman's understanding of the condensed history of the universe up to the earth's formation…
Nearly 90% of my body is made of just five elements - oxygen, carbon, hydrogen, nitrogen and calcium. This is good old run-of-the-mill physical stuff. Atoms of these elements and their brothers and sisters from the periodic table are what make up all of the things we see on Earth and across the universe. Sure, in you and me, these things are put together in pretty special ways, but we are still made of the same building blocks as the rest of existence.
The material in me is pretty old. It didn't just pop into existence as I grew in my mother's womb. It's been around longer than the Earth, because the earth was formed from it. So I'm not talking 37 years old here, but something somewhere between 4.5 billion years and 15 billion years old.
It was 4.5 billion years ago that the sun and the earth formed as the gravitational force of clumps of matter pulled those clumps together and attracted more matter, which in turn made the ever-growing clumps more massive.
All of the raw material for this clumping came from massive explosions of other stars. The earliest stars formed just the same way as the sun, from the accumulating effects of the gravitational force between specks and clumps of matter. The matter for these first stars was all very light - having burst onto the scene in the Big Bang that gave birth to space and time in our universe (which we think happened 10-15 billion years ago). Maybe early editions of our hydrogen atoms were there, but not the other elements I've listed. The stars basically transmuted the light material into increasingly heavy material.
That's what fusion is. Stars are just huge fusion furnaces. Under their immense gravitational force, matter is compressed tightly at their centre - sufficiently tightly that the nuclei of light atoms there are 'mushed' together to form heavier atoms. The weight of the each resultant heavier atom is ever-so-slightly less than the weight of the lighter ones that made it. Einstein's E=mc2 tells us that the 'missing' matter shows up as a huge amount of energy, which counterbalances the gravitational force to keep the star from imploding upon itself.
Over time, these early stars fused atoms into heavier and heavier configurations, creating the elements of the periodic table up to and including iron. Yet all of this matter was still 'trapped' in the star. The next step came when the balance of the energy released from the fusion reactions and the gravitational force of the star's huge mass was lost, at which time the star exploded in a huge supernova. This did two things.
First, it splattered much of the star's matter, composed by then of many different elements, far and wide. Second (and simultaneously) the huge force of the explosion fused some of the matter into even heavier elements than iron. These elements were and are all unstable - radioactive. The energy baked into them in that huge explosion is released slowly over time as the atoms 'decay' back towards the stability of the structure of iron.
Anyway... some of that material ended up in a clump we now call earth, and a tiny portion of it gets recycled constantly by geological and biological (read life) processes. Right now, some of that stardust is bundled up into a happy, if twisted, little living thing - me. I was made from a single fertilised cell of it and grew to 8 lbs of it by building additional cells from material passed from my mother through the placenta. Over the course of 20 years, I ate and digested huge amounts of previously living matter (all made of stardust) to grow to a healthy 170 lbs. I now try not to add even more mass (!), but I still ingest large amounts of it to gain energy and replenish dying cells within my body.
When I die, I will relinquish the remains of my borrowed stardust to the common pool, from which at least some of it will take life in new forms - grass, rabbits, cows and persons. Eventually, and sadly, the Earth will die - scorched then frozen. And the stardust of this little corner of the universe, having so valiantly created order against the raging tide of entropy, will just continue to be.
This piece is from 23 Sep 2003. Time and matter are the main characters. These days, they are not in my cast. Funny that even then I tied the birth of a separate "I" to pain.
BANG. From nothing, from a black hole in another universe, from God? Being springs forth in triple extension and one-way time. Perhaps among infinite others, lucky universe.
Hot but cooling. Expanding. Clumping - gravity's thing. A star is born. Fusion furnace and factory - building heavier atoms. Supernova sprinkles elemental blocks, compressing energy above iron, to be released in half-lives thereafter. Might not have been - different velocity, uniformity, elementary relations. Lucky universe now celebrating 15 billionth anniversary.
New clumps, sub-critical, circle certain star. Goldilocks-style: not too hot, not too cold, wet enough, abundance of H, N, C, O and other players. Within a cubed infinity, lucky Earth will grow to see at least 4-1/2 billion years.
Shallow pool? Lightning strike? Complexity barrier breached. Local anomaly. Non-equilibrium small print in contract of second law. Order's march makes massive leap forward. Being sprouts life. Lucky life.
No life is an island. Interdependency also drives the train. You scratch my organelle... Partnerships, coalitions, division of labour, division of cells.
Success survives. Reproducers win. Clever molecules, laddered programmes, recipes. DNA, RNAs, proteins dare all. Little errors, random mutations. Quantum cause? Innumerable niches. Countless millennia. Success survives. Reproducers win. Ecology explodes. Life breathes deep. No brains yet for dear old ancestors.
Chinese whispers 'ATCG, pass it on'. Danger out there. Limited resources, unlimited need. Unexpected turns, changing environment. Need some flexibility here. Nerves build a centre. Nested if-thens grow, twist, intertwine. Organic central processor, RAM, I/O. Life's computations evolve.
On this path, subjective perspective emerges - adaptive, or emergent and redundant? Some life now feels like something. Pain, satisfaction, keeping it simple at first?
Pain exists when this body is hit, but not that one. Birth of 'I'. Sentience and feelings bear self-consciousness, emotions, thoughts. The mental takes true flight. This I exalts and thrills to think about a memory of a dream about an idea whose time has now come.
Wheat from chaff thousands of times over. Man expands into and fills the computational niche. The differentiated brain is our trunk.
Whispers now take spoken form. Driven by and driving mutual reliance. Language is born. But how to anticipate, predict, measure, remember, learn from how words and actions relate. Trust? Suspect? Reward? Punish? Language and reciprocity demand more powerful, more subtle synaptic stuff.
Floods rage, diseases strike. Strong seek justification. Weak seek comfort. Where is the agent, where is the guarantor, where is the giver of hope? Gods spawn, proliferate. Owned gods, reflexive 'Thou shalts'. Gods of the insiders - outsiders be damned.
Passing of primary evolutionary baton from biology to technology. Tools enable, reward. Tools improve. Man masters his environment, spreads throughout all environments. Too good for those who didn't co-evolve with him - Australian large beasts exterminated. Others manage to hold on in shaky equilibrium. Tools help and tools harm. War begins its mutation from ritual to extermination.
Culture, social forces. The individual, already ruled by the molecule, increasingly cedes power to the collective. A drop in a stream. Norms, calls to conform. Sweeping forces, powers unnamed drive masses.
The Universe begins to understand itself. Man as agent, vessel. Revolutionary method takes root, proves worth. Science first in support of, then beside, now supplanting other gods. But who can eradicate confusion? Accurate predictions do not escort firmer understanding - quantum weirdness.
Forget not form. Perfection of a different sort - music, image, tale. Man seeks ecstasy and beauty as much as truth. These are the crowning glory and most effective tools of culture.
Particles, information, actions, circumstances swirl in special confluence. This I is born, takes temporary prominence as the one accessible subjective view. Being, life, sentience, self-consciousness surface in this instantiation. I am here, at this time, in this place, with all of you and our shared world to engage.
My name is Doug Fraley, and I live in the UK, in a bit of London called Richmond. I moved to this fair country in 1998 after growing up in Ohio and living in different parts of the U.S. and Europe.
Three wonderful teenage boys call me Dad, not without justification. Their lovely mother and I split a few years ago, after 19 years of marriage. They all live a mile down the road. My amazing partner, J, lives just around the corner from my one-bedroom flat, with her dog, Jack.
Aside from these super people, my interests include music, cycling and travel. On the music front, I sing and play piano - mainly to myself. With cycling, my days of competitive sportives and gritty urban commuting have largely given way to short, bracing rides in Richmond Park, occasionally punctuated by longer ones in the Surrey Hills. The cycling overlaps with the travel as well. J has a VW camper van, and we travel around Europe with the bikes (and kayaks) on the back. Wherever we stay, we look to take in the scenery at human-powered pace.
But all of these interests, and my whole life, take place within a fundamental curiosity I have. I guess you could say that it's a curiosity I live. Some would call it philosophical, others spiritual, some even religious. Fewer would call it scientific, but it is certainly empirical, based in my own experience.
I've had and still have a working life. I won't go into that here. Anyone who wants to find more about that can do so on LinkedIn or at my company site, P3 Leadership.
I've taken to writing more about where my curiosity leads me, and this site is one of the places I do that.
I've been thinking. So I've got that going for me...
I went through a phase earlier in life, when I wrote down a lot of what I was thinking in a blog. I've decided to do a bit of that again, and here you have it. The Blog is called 'What Is Happening.' You'll notice that there is a period, not a question mark at the end. It is about What Is Happening, right now - literally, as I type these words, literally as you read them.
The original blog I wrote has disappeared from online view, but I still have all the material, much of which I'll re-post here, always making clear when it is old material / past thinking. My 'answers' to the questions I think about have changed since those earlier days, and it might be interesting for you to see that.
A lot of what you will read in this blog will be about Big Questions: What is reality? What is good? What is right? Why am I here? How am I meant to live? Is there a God? If so, what is She like? There will also be a bit of background from my life, for two reasons: 1) I like talking about myself and 2) that background is inseparable from what I thought 10-15 years ago and what I think now.
What this blog won't include, because I can't bear it, is my adding yet another layer to the angst about the likely departure of the UK from the EU or about the person who currently occupies the office of the President of the United States. My views on those topics are just as one sided and ill-informed as yours, so I won't waste time reinforcing your echo chamber effect or violently disagreeing with you.
Plus, believe it or not, I think that we have more important things to concern ourselves with...