Tag Archives: Science

Global Warming Canaries, Anyone? A short intro to why most scientists are worried about climate change…

The current state of arctic sea ice (see graph below) sends a chill down my spine.


So what it says is that the ice is melting furiously, and looks like it’s not yet slowing down even though the days have started to draw in.

However, any scientist will tell you that no single data point can be used as evidence of global warming, there are simply too many fluctuations for anything to be concluded over anything but the longest timescales. We cannot simply look at the mean temperature for a hot year and say, there you go, global warming!

Now, the issue is, there are well-known cycles over pretty much all timescales – this pretty much undermines all serious attempts at prediction.

So, what to do? Well all is not lost; there are still some clever little leading indicators we can look at to give us that sobering wake up call.

#1:  CO2

Firstly, we know CO2 concentration is up, no doubt or argument, this can be seen in the famous Hawaii data above, complete with the seasonal ‘breathing’ by global plant-life. The argument is about whether the greenhouse models that say this will result in warming will turn out right. I honestly don’t know, but I wouldn’t even have to wonder if the CO2 levels weren’t going up, would I?

#2: A Record Breaking Rate of Record Breaking

Secondly, rather looking at averages or ‘new records’, we can look at the frequency of records. So rather than saying, “we just had the hottest summer ever in some parts of the US, there’s the proof” we can look at how often records are set all over the world – hottest, coldest, wettest, dryest and so on. This approach creates a filter; if it shows there are more records being broken on the hot side than the cold side, could this be an indicator? I hope not, because there are.

Again, it could be part of a long-term cycle that could bottom out any time now. But on the other hand, if it was going the other way, I wouldn’t have to hope, would I?

#3: Sea Ice

Now the sea ice. The sea ice is another proxy for temperature. The reason it’s interesting to climatologists is because it is a natural way to ‘sum-up’ the total warmth for the year and longer; if ice is reducing over several years, it means that there has been a net surplus of warmth.

CryoSat – The European Space Agency’s Sea Ice Monitoring satellite launched in 2010 – (Image credit ESA)

Today we are seeing a new record set for minimal northern sea ice. And not only is there less area of ice, but it is thinner than previously realized and some models now suggest we could be ice-free in late summer in my lifetime.

Now if that does not strike you cold, then I didn’t make myself clear. This is not some political posturing, not some ‘big-business’ spin, nor greeny fear mongering. It’s a cold clean fact you can interpret for yourself, and it could not be clearer.

So is it time to panic?

Well it can still be argued the melting is part of a cycle, it could of course reverse and hey, no biggy. After all, what does it matter how much ice there is?

Well, yet again, I hate to rely on the ‘hope’ that it’s a cycle. Because if it continues, the next effect will be felt much closer to home…

Sea Level

Sea level is the ultimate proxy for warming. Indeed, sea level change can be so serious, maybe it is the problem rather than the symptom. If the ice on Greenland and Antarctica melt, the rise in sea level would displace hundreds of millions of people and change the landscape so dramatically it’s a fair bet wars and famine will follow. Now that is serious.

So have we seen sea level rise? Well, yes. Here’s the plot:

Now, it looks pretty conclusive but hold the boat. Some say’s it’s proof of warming but not everyone agrees. It’s true it could again be a cycle. Also, the sea level rise is fairly gradual; what people are really arguing about is whether we should expect it to speed up. If temperature goes up a few degrees it could go up 5 or 10 times faster. The speed is the issue. Humanity can cope if the level goes up slowly enough, sure, countries like Tuvalu will be in big trouble either way, but countries like Bangladesh and cities like New York and London will only be in real trouble if the rate increases.

Actual Canaries

Canaries taken into mines in order to detect poisonous gases; the idea being they would suffer the gas faster than the people and if the canary dropped, it was time to vacate. Do we have systems that are hypersensitive to climate change?

Yes! There are many delicately balanced ecosystems that can can pushed over a tipping point with the lightest of touch. Is there an increase in the rate of species loss, or an increase in desertification? Yes!

We can also look at how far north certain plants can survive, how high up mountains trees can live or how early the first buds of spring arrive.

Again, these indicators fail to give solace. Everywhere we look we see changes, bleached coral, absent butterflies, retreating glaciers.

The conservative approach is to ascribe these changes to the usual cut and thrust of life on earth; some take solace from the fact that humankind has survived because we are the supreme adapters and that the loss of species is exactly how the stronger ones are selected.

Yes, we are great at adapting, however, to kill any complacency that may create, consider the following: for humans just ‘surviving’ is not the goal, that’s easy, we also need to minimize suffering and death, a much tougher aim. We’ve also just recently reduced our adaptability significantly by creating ‘countries’. Countries may seem innocuous, but they come with borders – and mean we can no longer migrate with the climate. Trade across border also needs to be of roughly the same value in both directions.  While some countries will actually see productivity benefits from global warming, most will not, and without the freedom to move, famine will result. Trade imbalances mean inequality will become extreme. The poorest will suffer the most.

So for now changes are happening, and advances in agricultural technology are easily coping; however, because ecosystems are often a fine balance between strong opposing forces, changes may be fast should one of the ropes snap.


Looking at the long history of the earth we have seen much hotter and much colder scenes. We have seen much higher and much lower sea levels. We are being wishful to assume we will stay as we have for the last 10,000 years. It may last, or it may change. Natural cycles could ruin us. And mankind is probably fraying the ropes by messing with CO2 levels.

Can we predict if we are about to fall off of our stable plateau? No, probably not. But is it possible? Heck yeah.


If you liked this, you may like these earlier posts on the subject of global warming:

  1. What does the earth’s history tell us about climate? And how can we find out if our house will be one that sinks should sea levels rise? Find out here!
  2. Can we  change the planet’s dangerous behavior? Read my call for a study in mass behavior.

Tilt shift miniaturisation, giving away the family jewels…

After seeing this impressive video by Robert Weber about a town near where I used to to live, I decided to give tilt-shift photography a try…

I never tire of that video, and the music grew on me too.

Anyway, so here is the straight dope on tilt-shift…

What you’re supposed to do is take a picture with the lens tilted along a horizontal axis relative to the photographic plate (or CCD for newfangled cameras). This means only a strip across the middle is in focus, and the picture gets gradually more blurry towards the top and bottom.

Now this sounds wasteful of good focus, but is actually something the eye is very used to seeing whenever it looks as a horizontal plane, such as a table-top (one that’s pretty close). Of course, for bigger things, like a football fields, you can usually focus on entirely, especially if you’re seated where the tickets are cheaper. Anyone who has tried to take a photo of small things, or used a microscope, knows this.

So basically, the brain associates this blurring with ‘close’ things, and uses it as one of its tools to guesstimate the size of things.

So you (yes you!) can fool the brain into making things look smaller by adding blur to your photos!

Aside for my science readers…

You can actually create true focal depth blur by using a very wide aperture in your camera; however, even the widest apertures struggle to create much miniaturisation – to get true blur at significant distance, you really need to scale-up the camera proportionally with the distance. To make a warehouse look like a microchip, you really need a camera big enough that its microships are the size of warehouses 🙂

Now, when I was researching this, I was probably thinking what you’re thinking. Mile-wide camera’s are probably a custom job, and even cameras where the lens can be tilted never fail to confuse the nice people at Wal-Mart.

Needless to say, Photoshop (other brands are available!) can add the blur.

Before we dive in, another other top-tip is that air tends to add blue and wash out your colour saturation; you can remove the faraway mountain look by bigging up the red and green saturation. So here was an early attempt of mine:

Here I took a fairly plain photo, added progressive more blur toward the top and bottom, but taking care to mask the tree on the right from the blur. I also greened it up a bit 😉 – I like how it makes the destiny of the golf ball sort of mysterious. Like most of my golf balls.

Of course, touch-ups like the tree are tedious, you really need a photo that has the faraway stuff at the top and the things at the bottom to avoid such issues. Or you can just ignore them and it usually works out fine:

So I blurred the treetop. Most viewers (test subjects in my experiment) did not notice this until I explained what I had done.

Here is one last example; the photo just asked for it…

Enjoy trying it out, and please do add links to your own work – though not to ones you find by googling “tilt-shift photography”, I already did that, and heartily recommend it 😉

Big Pharma: Heroes or Villains?

What is ‘Big Pharma’?

Many people have argued that alternative and complimentary medicines are suppressed because they threaten the status quo for ‘big pharma’.  Before we accept this claim, let’s unpack the idea of big pharma a little to understand the incentives at play and when it may be right not to trust big pharma.

Let me start by making it clear – big pharma, as a label for the largest pharmaceutical companies, deserves a healthy dose of outrage; but before we toss the baby out with the bathwater, but lets see when – and why.

Big pharma is just another name for ‘big business’: a big business is an organism that has grown beyond the people that founded it, such that rather than having emotions, conscience or guilt, it has KPI’s like turnover, cashflow and return on investment. Big pharma is in the business of making money and as such should generally be expected to default to that option unless constrained by law. The collective conscience of shareholders only tends to kick in when dirty laundry is put out on show. Ok, so firstly, I think we can agree, a business is not a charity.

Next we take this lack of compassion and combine it with size and complexity – we see we now have an organism susceptible to plain outright crookery – from the white collar sort, like insider trading – to the very tangible – such as the dumping of toxic waste. These practices usually require the corruption of people – but not always – it is very easy for companies to do bad things without any individuals having malicious intent; it could simply be negligence or incompetence, or it could simply be that profit sometimes comes before fairness.

Take for example the problem of selling DVD’s in the world market. They are small and lightweight and easy to ship worldwide. This usually means that the price would be similar worldwide, if dealers in one country were to raise prices, residents would simply import the product. However, the enormous wealth differentials that exist between, say, the USA and Mexico, mean that the company could set a high price to extract maximum value from the US market, but then essentially price themselves out of the Mexican market. If they lowered the price, they would sell more product but with much reduced profit margins.

This problem is thrown into stark relief in the case of drugs, where the most profitable option is often to cater to the richer countries. This is sound business – set your price high, keep your factory trim, reduce shipping costs, keep high margins. However, if the drug can radically improve health outcomes, this policy could be seen as unethical.

This is the sort of problem big pharma face routinely; they are not selling entertainment, they are sometimes selling life itself, and often find they need to play profits against ethics in they way I describe above. It is thus hardly surprising that the general public have a distrust and general suspicion toward Big Pharma. In addition to drug import controls, there are many other situations where governments have had to step in to ensure the pharmaceutical companies ‘do the right thing’, such as the case with antiretroviral drugs (for HIV) coming into Africa.

Now think for a moment on this thought experiment: what would happen if a small publicly traded company discovered a cheap and easily reproducible cure for cancer? Would they really be able to hold on and extract full value for their shareholders? History actually suggests they wouldn’t – the drug would become public property, or would simply be nationalised if the company tried to resist. Inventions like the major vaccines and the first antibiotics were often not patented, and we see if we look at the pharmaceutical industry that their biggest profits come predictably not from miracle cures but from drugs that cater to the maladies of the richer classes. The top targets are heart disease, heart-burn, stroke, mental health and asthma. Once you  add disorders like diabetes you have accounted for the most profitable chunk of the industry.

This trend raises fresh concerns, because there are many severe ailments that are simply not attractive to profit making operations, the poster-boys being malaria, TB and HIV/Aids. Drug companies can be bullied into doing work in these areas, but it tends to fall to governments and charities to fund research in the afflictions of the poor, or on the so-called ‘orphan diseases’ – ailments that affect too few people to ever make a profitable market.

Economists will also argue that profit making businesses, being creatures under the strict control of incentives, will be unlikely to aim for ‘cures’ because cures are ‘one-offs’. While this criticism has some sad validity (in the board-room if not in the clinic), we have to remember that the big drug companies only exist because they make profits; in an imagined world where the first dollars were always spent on the most dire diseases and we only get to do botox and erectile dysfunction once those are all solved we would have no private industry at all, so far fewer trained scientists, far less public knowledge and certainly no map of the genome. We have to remember that to some extent at least, the aging american taking their cocktail of pills every day for the last 50 years has in some sense subsidized the field doctor in rural Africa. Yes, they also subsidized Wall Street excesses, but perhaps it’s a deal worth making.

Publication Bias

Another area where drug companies increasingly in need government intervention is in drug trials; specifically, they are presently allowed to pick and choose what to publish; this sounds OK at first, because, surely, you assume, the drug company has to make a bulletproof case before the drug is licensed? Well, if you do 100 trials, you may well find 50 good results, and publish those, and simply sweep the duds under the carpet. What’s more is those duds could have revealed possible side effects or interactions that could actually turn out to be real issues later on down the road. This is going to be a big one in the next few years.

The Big Picture

When criticizing the pharmaceutical industry it is easy to get caught up in the weeds, for there are weeds, but let’s also try to remember that this century has seen unparalleled improvements in life expectancy world-wide, and the improvements in child mortality in the third world do owe a lot to the sometimes cold-hearted business models intrinsic to western medicine.

Before I move on, and being a scientist, I wanted to make another point about big pharma. While it’s true that big money is involved, we have to remember that the Pareto principle applies here too – the majority of the profits come from the minority of the research. There are legions of perfectly good people, motivated by no more that the desire to help people in distress working in healthcare all around the world. Drugs are highly integrated with other therapies at the clinical level and the people actually running trials ‘in the trenches’ face-to-face with the patients (and often dealing with terrible trauma)  are rarely shareholders in big pharma, and many would not even think for a second they are part of what people would call big pharma. Yet it is they who have gradually built up our current understanding of the human body, not the men in suits.


To me, the idea of executives at the top 5 drug companies has become conflated with the idea of the ‘canon’ of western medicine. The idea that the whole world of ‘proven medications’, the result of countless years of hard graft (and the learnings from millions of deaths), can be dismissed because it’s under the control of ‘fatcats’ is a sick tragedy. Western medicine is simply a name for ‘what has been statistically been proven to help’, and the idea that even a tiny fraction of the scientists who developed it would be working to suppress good ideas from outside the ‘fold’ sounds frankly paranoid. Yes big pharma has some warped incentives that cause it to focus on the wrong things and leave the poor out in the cold, but all for-profit publicly-traded businesses do that! Ask yourself for a minute – even if a cure for heart disease were found that threatened the profits to Pfizer and friends, could they really recruit a worldwide network of conspirators who think a cure for cancer is something worth selling their very souls for to suppress?

It hard enough to run a real business, let alone running one so effectively in complete secrecy in the face of so much scrutiny. If they have that much skill and power, they should go legit, they would make a real killing!

Musical Notes Explained Simply

Have you ever wondered how the musical notes we use were chosen?

I mean when I was growing up I was learning one thing in music class  (do-re-me-fa-so-la-ti-do!) and another in science class (440Hz) and never the twain did meet…

So what gives? I always suspected the musical community were being scientific, but their language was all Greek to me.

Years passed and only rarely did I get the chance to wonder at this question – and meantime my science education was getting the upper hand – I learned how sounds travel through the air and how the ear works – how deep, low notes are the result of compression waves in the air, perhaps a few meters apart, while higher pitched sounds where compression waves much more tightly packed, perhaps millimeters apart. I also learned a note could have any frequency, and so no reason to pick out any ‘special’ frequencies.

However,  just recently I realized, in a flash of light, that with an infinite number of notes to choose from, musicians had very deliberately selected only a few to make music with, and I suddenly wanted to know why. Was it arbitrary? Was it the same in different cultures? Why did some notes seem to go together and others seem to clash? And of course, as The Provincial Scientist, I wanted to know if our early musicians had done well in their choices.

As it is now the era of the internet I set about to find out more and thought it was so interesting, it would be a crime not to report what I learned on my blog. So here is what I learned…

In Search of Middle C

The best place to start is probably a vibrating string. The vibrating string is clearly key to pianos, harps, guitars and, of course, the entire ‘string’ section of an orchestra. If you stretch a string and pluck it, you are starting an amazing process – as you pull on the string, you create tension, you literally stretch the string and store energy in the fabric of the string. When you let go, the string shrinks under that tension, which pulls it straight. Alas, when its straight it has picked up some speed and the momentum keeps it going until the string is stretched again – thus the string swings back and forth – and it would continue forever were it not for frictional losses – energy is lost in heating the string, but some is also lost in buffeting the air around the string. The air is pushed then pushed again with each cycle creating compression waves that ripple out into the room – and into our ears. Thus we hear the string.

You can see the vibrating string doing it’s magic here:

You can see in the video that the string swinging back and forth is an awful lot like a wave moving up and down the string! Indeed it is!

The speed at which the wave moves (or string vibrates back and forth) – and thus the note we hear – is determined by a few simple factors – the tension in the string, and the weight of the string and the length of the string. The greater the tension, the greater the force trying to straighten the string, but the greater the weight, the more momentum there is to make it stretch out again.

It is therefore easy to get a wide range of notes from a string, start with a long, heavy wire and only tension it enough to remove all the slack. The note can then be gradually increased by decreased the length or the weight of the wire, or by increasing the tension. These are the tricks used in pianos, guitars and so on.

So far so good. But if you have several strings to tune up, what notes should you pick – from infinitely many – to make music with?

The human ear is an amazing device and can hear notes ranging anywhere from 20 to 20,000 compressions per second (the unit for per second is called Hertz or Hz for short). That is a lot of choice!

As I am sure you guessed, the key is to understand why some notes seem to ‘go together’, and the answer lies back in the vibrating string.

Overtones of Overtones

Firstly, it turns out that when you pluck a string, you actually get more than one note. While the string may swing back and forth in one elegant sweep, it may also get shorter waves, with half or a third or quarter the wavelength hiding in there too. This video shows how one spring can vibrate at several speeds:

Although the video shows the string vibrating at one speed each time, it is actually possible for a string to carry more than one wave at a time (this amazing fact deserves its own blog posting, but we will just accept it for now).

So when a string is plucked, the string ‘finds’ ways to store the energy with vibrations – it finds a few frequencies that carry the energy well, these are called ‘resonant frequencies’, there will be several, but they will all be multiples of one low note. As these higher notes are all multiples of a single low ‘parent’ note, they also have consistent frequency relationships between one another, 3/2, 4/3, 5/4 and many many others.

String Harmonics

So clearly, once you have one string, and you want to add a second, you could tune the second string to try to match some of the harmonics of the first string. The best match is to pick a string whose fundamental note is at 2x the frequency of the first string. This string’s fundamental note will match the first string’s 2nd harmonic (also called its first overtone). The second string’s harmonics will also perfectly match up with pre-existing harmonics from the first string. The strings are what is called consonant, they ‘go together’.

Now although the second string will have some frequencies in common with the first string, it turns out that there is an even stronger reason why these notes will go together – it is because when you play several strings at once, you are no longer just playing the strings, the instrument you are playing is the listener’s eardrum. The eardrum will vibrate with a pattern that is some complex combination of the wave-forms coming from the two (or more) strings. When you add two notes together, it is like adding two waves together and you get an interference pattern – the interference may create a nice new sound:

If we add a low note (G1) to a note one octave higher (G2) we get a totally new sound wave.

If, as in this example, one string vibrates at exactly twice the frequency of the other, the two notes will combine to make a handsome looking new waveform, with ‘characteristics’ from both the original waves – but if the frequencies are not a neat ratio, you will get something a bit messy:

This waveform may not repeat, and is unlikely to be consonant with any other notes you may care to add.

Sometimes, when your second string is fairly close in frequency to the first (say 1.1 x the first string’s frequency) then a second phenomenon rears its head, beating. This leads to the creation of entirely new (lower) frequencies that the ear can hear [click here to listen to a sample]. The sum now looks like this:

Beating can sound awful, though of course, the skilled musician can actually use it to create useful effects.

Beautiful Ratios

We have seen that once you have selected one note, you have already greatly reduced the ‘infinite’ choice of other notes to use with it – because only some will be consonant. Although the best consonances are at exactly 2x the first frequency, we see that once you have picked two strings, the choice for the third string is more limited. Should you be consonant first the first string or the second? Can you be consonant with both? You can be fairly consonant with both, but only by being 2x and 4x their respective frequencies. If you picked all your strings as multiples of the first string, the ‘gaps’ between the notes would be very big, akin to playing a tune with only every 12th key on a piano. So how can we fill in the gaps?

Well, early thinkers quickly realized that you can’t actually select a perfect set of notes – some combinations will mesh well, others will be just a little bit odd. This realization was probably a bitter pill for early musician-scientists to swallow.

In the end, they came up with many competing options, each designed  to maximise the occurrence of good ratios  – a good example is the just intonation scale:

Note: C D E F G A B C
Frequency ratio to the first note: 1 9/8 5/4 4/3 3/2 5/3 15/8 2

Here, the musician picks two notes that are consonant (C and the next C one octave higher) and then divides the gap into seven steps. Each note is a special ratio of the lower note – we get neat ratios of 5/4, 4/3 and 3/2 showing up which is good, however the ratios between adjacent notes are much less pleasing!

Aside: You will also see that the steps from B to C and E to F are rather small! Now take a look at your piano and note these notes correspond to the white keys on the keyboard that have no black keys between them! This is no coincidence…

Is the ‘just intonation’ division perfect? No, the notes are not all consonant! Remember than with 8 notes in this group, there are 7+6+5+4+3+2+1=28 ratios (or note pairs), and there is no known way to choose them to all be consonant. That is why, although most musical cultures divide their music notes into ‘octaves’ (nicely consonant frequency doublings), there have evolved many different ways to make the smaller divisions.

Western music has tended to divide the octave into 7 notes (the heptatonic scale) , you could really use any number. Let’s stick with 7 for now.

Another popular way to divide the octave is the Pythagorean tuning:

Note: C D E F G A B C
Frequency ratio to the first note: 1 9/8 81/64 4/3 3/2 27/16 243/128 2

This scale is based on prioritizing the 3/2 overlap of harmonics and moves three notes very slightly.

It is key to remember there are dozens of ways to do this, depending on what you are trying to optimise – do you want to match the greatest number of harmonics, or some smaller number of stronger harmonics? It may even be that personal taste could come into play.

The Wonderful Piano

Have you ever wondered why you hear someone is playing something in C-minor or F-major? What is the deal there? Well, these are also ‘scales’ – alternative ways to cut up the octave, but from a specific family that lives on the piano.

You see, the piano could also divide the octave into 7 notes, and indeed it was once so divided, but with time musicians realised they could open up more subtlety in their music by adding in more notes. So they decided to add the ‘black notes’, the extra black keys on the keyboard!

So in addition to the 7 notes A,B,C,D,E,F & G, they added C#, D#, F#, G# and A# – they called them ‘half tones’ or accidentals. Of course, there are already two half steps (B-C and E-F) which is why there is no B# or E#. These extra notes gave us 12 smaller steps, and of course choosing 12 consonant notes was even harder than choosing 7!

So, after some hard thinking by scholars including  J.S. Bach, a very sensible decision was made – to divide the octave into 12 ‘equal’ steps, which gives us the so-called ‘equal temperament‘, the most popular way to tune a piano. To do this, each note is 21/12 or 1.05946… times higher in frequency than the last one, such that twelve steps will eventually give you a doubling.

However, our musical notation is older than the piano and generally only allows for 7 notes per octave, so how do you write music for 12?

Despite that there are 12 notes, composers have tended to still feel some combinations of 7 notes ‘go together’ better than others and so have persisted to write music using only 7 notes, though of the many hundred’s of ways you could choose the 7 notes, they have selected 12 combinations, the 12 “Major scales“:

The Major Scales (down the left). Each uses only 7 of the 12 notes on the piano keyboard. The shaded vertical lines correspond to the black keys on the piano.

Personally, realising what these scales were was a breakthrough for me. Looking the above map helped me to realize several things:

  1. Many long pieces of music will completely ignore nearly half (5/12ths) of the keys on the piano! To play a tune based on a certain ‘scale’ is sometimes said to be played in that ‘key‘.
  2. The scale of C-Major ignores all the black keys, and is probably the oldest/original scale.
  3. Each scale is displaced 5 ‘steps’ from the previous scale (there is a #1 beneath each #5)
  4. The empty squares occur in vertical groups of 5, and move up 5 spaces each time you move a column to the right.

Aside: Note that there are also the 12 “minor scales“. These scales actually use the same 12 subsets of keys as the major scales, but are ‘shifted’  – they have a different starting point (base note, or ‘tonic‘).  This may seem a trivial change, but because the gaps (steps in frequency) are not all evenly sized in these scales, the major and minor scales have their two ‘small’ steps in different places, which is supposed to change the feel or mood of the music (or even the gender!)

The Number 5

The number ‘5’ in the pattern we saw above was noticed by musicians long before me, and it shows up in other places too.

For example, we saw in the ‘just intonation’ scale above, that the note G had a frequency ratio of exactly 3/2 with the note C. This means that when you hear both together, every third vibration of the higher note will coincide with every second vibration of the lower note. They are thus highly consonant – and they are 5 steps apart on the stave.  This relationship is called the ‘perfect 5th‘. It is again no coincidence that the 5th note of each scale is the base note (tonic) of the next scale. Stepping in 5’s (ratios of 3/2 in frequency) 12 times takes you through exactly 5 octaves and eventually back to the first scale.

Of course, the scales repeat for every octave, so you don’t really need top go up 5 octaves! This cycling behavior allowed the invention of a learning tool called the ‘circle of fifths‘, which helps us to understand  the relationships between the scales.

Yet another aside: The ‘perfect fifth’ is called perfect if it is truly a ratio of 3/2 – but recall that pianos have their 12 notes ‘evenly spaced’ (a geometric progression) so the ratio of G to C on the C-Major scale will not be exactly 3/2 – it is actually 0.113% off!

But What About Middle-C?

Ok, so we have seen how some notes ‘go together’, and how once you have one note, you have clever ways to find families of notes that compliment that note – but that leaves just one question – how do we pick that first note?

The leading modern convention is use the note A that comes after (above) middle-C, and to set it at 440Hz exactly.

The question is, why?

Well firstly, I shall point out that the 440Hz convention is not fully accepted. For example, anyone who wants to hear, for example, the Gregorian chants the way they originally sounded, would need to use the conventions of the time. Thus there are pockets of musical tradition that do not want to change how their music has always sounded.

However, when it comes to performing a concert with many instruments, it is useful if they all adopt the same standard. The standard is thus sometimes called the concert pitch, and though 440Hz for A is common, this number has been seen to vary from 423Hz to as high as 451Hz.

So the short answer is, there is no really good reason; the choice of 440Hz really just ’emerged’ as a more common option, and when they standardized they rounded it off. While this answer is ultimately trivial, I find a little amusement in the fact that all the music we hear sounds the way it does for no particular reason!


Before I go, there is a video I want you to look at. I think it shows beautifully how 12 different frequency oscillations can exhibit some beautiful harmony (or harmonics!)

All Done! Ready to Read Some Music?

The next step is to learn to read musical notation – luckily someone has already written an excellent tutorial with pretty pictures.

All I can hope is that the weird things they teach you in this tutorial will be a little less weird now we have covered the baffling origins of the notes!

Jarrod Hart (Los Olivos, CA, October 2011)


A couple more useful references:




Exceeding the Speed-Of-Light Explained Simply (and the Quantum riddle solved at no extra cost)

It has recently been in the news that some particle may have exceeded the legal speed limit for all things : 299,792,458 metres per second.

Of course, this will probably turn out to be a bad sum somewhere or perhaps waves ganging up, but the whole hubbub has raised my hackles, and here’s why.

Because Albert Einstein at no time said what they say he said (see here for example). They misunderstand relativity! Things can move at any speed we want, and I will try to explain the fuss now.

So let’s get to it!


First, we have to consider the way space warps when we move.

The problems started when people realised that light always seems to have the same speed, regardless of the speed you were moving when you saw it. This seems to be a contradiction, because surely if you fly into the light ever faster, it will pass you ever faster?

Well the tests were pretty clear, this does not happen. The speed is always c.

For several years, people were unsure why – until they were told by Einstein in 1905. In the meantime, another ponderer of the problem (Lorentz) decided to write down the maths that are required to square the circle.

The so-called Lorentz equations show, unequivocally, that space and/or time need to warp in order for relative speeds of c not to be exceeded, even when two items are going very close to c in opposite directions to one another.

So something needed to give, and it was space and time!

So, newsflash! it was not Einstein that first published on space and time warping. His contribution (along with Henri Poincaré and a few others) was to explain how and why. His special theory showed that because there is no ‘preferred’ frame of reference, a speed limit on light was inevitable. The term ‘relativity’ come from this – basically he said, if everything is relative, nothing can be fixed.


Ok, so we have some nice observations that nothing seems to go faster than the speed of light  – and we have a nice maths model that allows it. So why do I persist in saying things can go faster than the speed of light?

Let me show you…

There is a critical difference between ‘going’ faster than light and being ‘seen to be going’ faster than the speed of light, and that is where I am going with this.

So lets take this apart by asking how we actually define speed.

If a particle leaves point a and then gets to point b, we can divide the distance by the time taken and get the mean speed (or velocity to be pedantic).

The issue with relativistic speeds are that the clock cannot be in both point a and point b. So we need to do some fancy footwork with the maths to use one or other of the clocks. So far so good. This method will indeed never get a result > c.

The nature of space forbids it – if the Lorentz transformations that work so well are to be taken at face value, then for something to exceed c by this method of measurement, is much the same as a number exceeding infinity.

So all is still well. Until you ask, what about if the clock is the thing that travelled from a to b?

In this case, the transformations cancel! The faster the movement, the slower time goes for the clock, and you will see its ticks slow down, thus allowing its speed to exceed c.

The clock will cover the distance and appear to have tavelled at c on your own (stationary) clock, but the travelling clock will have ticked fewer times!

If you divide the distance by the time on the travelling clock, you see a speed that perfectly matches what you would expect should no limit apply. Indeed, the energy required to create the movement matches that expected from simple Newtonian mechanics.

The key point here is that while the clock travelled, the reader of the clock did not. If you do choose to travel with the clock, you will see it tick at normal speed, and see the limit apply – but see the rest of the universe magically shrink to make it so.

Some have argued that I am not comparing apples with apples, and that by using an observer in a different frame to the clock I am invalidating the logic.

To those who say that, I have to admit this is not done lightly. I have grown more confident that this inference is valid by considering questions such as the twin paradox over and over.

The twin paradox describes how one twin who travels somewhere at high speed and then returns will age less than his (or her) stationary twin.

Now if we consider a  trip to Proxima Centauri (our nearest neighbour) the transformations clearly show that if humans could bear the acceleration required (we can’t) and if we had the means to get to, say, 0.99c for most of the trip, that yes, the round-trip would take over 8 years and no laws would be broken. However the travellers themselves will experience time 7 times slower (7.089 to be precise). Thus they will have aged less than 8 years. So, once they get home and back-calculate their actual personal speed, it will exceed all the live measurements.

This has bothered me endlessly. Although taken for granted in some sci-fi books (the Enders Game saga for example) this clear ‘breakage of the c-limit’ is not discussed openly anywhere.

Still uncertain why people were ignoring this, I read a lot (fun tomes like this one) learned more maths (Riemann rules!) and also started to look at the wider implications of the assertion.

On the one hand, the implications are not dramatic, because instant interstellar communication is still clearly excluded, but that whole issue of needing a 4 years flight to get to Proxima Centauri is just wrong. If we can get closer to c we can indeed go very far into the universe, although our life stories will be strangely punctuated, just as in the Ender books.

But what about the implications for the other big festering boil on the body of theories that is physics today – quantum theory?

Well, if one is bold enough to assert that it is only measurement that is kept below c and not ‘local reality’, then one can allow for infinite speed.

In this scenario, we are saying measurement is simply mapping reality through a sort of hyperbolic lense such that infinity resembles a limit. Modelling space with hyperbolic geometry is really not as unreasonable as all that, I don’t know why we are so hung up on Euclid.

With infinite speed at our disposal, things get really interesting.

We get things like photons arriving at their destination the same tme they leave their source. Crazy of course… but is it?

Have we not heard physicists ask – how is it the photon ‘knows’ which slit is blocked in the famous double slit experiment? It knows because it was  spread out in space all the way from it’s source to it’s final point of absorption.

If you hate infinities and want to stick with Lorentz, you can equally argue that, for the photon, going exactly at c, time would stand still. Either way, the photon feels like it is everywhere en route at once.

If the photon is indeed smeared out, it probably can interfere with itself. Furthermore, it is fitting that what we see is a ‘wave’ when we try to ‘measure’ this thing.

A wave pattern is the sort of thing I would expect to see when cross sectioning something spread in time and space.

Please tell me I’m wrong so I can get back to worrying about something useful. No, don’t tell me – show me – please! 😉

Energy Drink Misinformation

Zero calorie ‘energy’ drinks piss me off. Why?

A zero calorie energy drink is a flat-out contradiction. 

Think about it. What is a calorie? If you don’t know, look it up. Yes, exactly, it is a measure of… energy content! WTF?

What I want to know is this: how come we let big business redefine our language to their own greedy ends? I mean the people who make low-calorie energy drinks know they have no energy in them, so why are they called energy drinks?

I think its because energy is a misunderstood concept and they are taking advantage of this.

Understanding what energy is (and more importantly isn’t) will allow people to more accurately decide things correctly – like whether it’s a good idea to try hike 100 miles across a desert armed only with zero calorie energy drinks.

So for background, please take a look at my article on energy designed for people with too little time to read a whole book, or even a pamplet.

Now, the specific issue here is that people are confusing energy sources with stimulants. Sure, the sugary versions do actually supply some energy, but no more than a can of Coke – but these guys are not charging those absurd prices for sugar – those prices, and claims, are for the drugs. Compounds like caffeine affect our nervous system and interfere with our built-in protection systems, systems that make us feel tired after effort, mechanisms that force us to get the sleep we need in order to rest our muscles and reboot our brains.

The issue here is that the word stimulant is not as easy to sell as ‘energy’, and the English language does allow us to mix up feeling ‘energetic’ with feeling alert and ready for action.  The nerdy scientific truth issue here is that tired people actually still actually have plenty of energy (especially if they are prosperous about the middle) it is just their inclination to use that energy that changes.

So next time you feel tired but need to keep going, by all means get a ‘so-called’ energy drink but remember it is mainly just a drug. The next time you hit a wall 20 miles into a marathon, remember to get some real energy.




So is messing with you body’s tiredness systems bad? Not necessarily! We must also resist overreacting and committing another crime – resorting to the naturalistic fallacy that messing with nature is fundamentally a bad idea. I quite like it when medical science messes with natural things like smallpox and malaria for example. Stimulants are not all bad, keeping alert can keep us safe when driving, and used in moderation can actually help us focus through tedious study or exams.

Fun Physics Questions: Does time flow in baby steps?

Question: is it possible time flows in little steps?

At some small scale, could it be, that time is simply a ‘symptom’ of a sequence of events, or states, that there is no actual time passage ‘between’ those states?

This scenario has interesting implications – it suggests life is a bit like a movie – a series of pictures on a strip of celluloid, or pages in a book, and like a book, while the story may unfold to you at whatever speed you read it, it does not matter how fast you read the story itself still has its own pace.

This doesn’t mean the book has to be pre-written, it can still unfold with utter unpredictability, the book is unfinished if you like – the important point is that we are stuck experiencing the passage of time at a rate determined internally – by the rate of chemical reactions in our brains. The drum beat of those reactions would feel the same no matter how fast or slow they seems to an outside observer. They could even be paused for a few minutes – we could not tell!

Now physicists studying energy balances of sub-atomic particles have seen that energy often seems to come in little chunks (the ‘quanta in’ quantum), and that can imply that time may also be chunky (maybe Planck time?); alas, time chunking has contradictory implications – contradictory to common sense anyway- like infinite energy flux, not to mention infinite speeds, but hey if you can just get your head around some of the workarounds physicists have dreamed up (quantum tunnelling for example) everything’s all right again. I am personally highly suspicious of workarounds, and that is what I think they are!

Anyway, even if you try to get away from quantum weirdness, you get sucked back in – take for example this geometrical example. Consider the relative positions of three point objects (small particles?) moving freely in space: they could, for an instant, line up perfectly, but if your measurement were infinitely accurate, this could only occur for an infinitely small duration so long as the particles are moving. If you try to explain this by saying space is divided up into chunks (like ‘snap to grid’ in MS Powerpoint) you get into geometrical issues that three points cannot always be integer increments apart  (nor even rational increments apart) without breaking the most basic number axioms.

So even if space isn’t chunked, it turns out you can appeal to the uncertainty principle, which handily says you can only measure the position of anything infinitely accurately if you allow its momentum to be anything at all, including infinite – and infinite momentum is exactly what you (temporarily) need if you are bold enough to let time ‘leap’.

So none of these issues with time chunking turn out as solid proofs against the possibility, they just make things more slippery!

Aside: rather than a book, I like to think of our universe as being a bit like a computer program  – I like to think about Pac-man when it plays itself in ‘demo mode’ – in demo mode, used to allure people at the arcade, the computer controls both the ghosts and pac-man. In the computer, a sequence of commands is run in the CPU and the speed of the computer (like the reader of the book) controls the rate at which we ‘see’ the ghost-chase on the screen, but this speed is invisible to pac-man himself – yes the ghosts chase faster across the screen, but he can run faster too.

Question: Does a time-increment universe allow time travel?

Well I don’t think we can ‘skip’ events out (we have to experience them all), but if we can go somewhere where events are more or less ‘dense’, maybe we can. We will not feel the difference, we will not get any extra life-span, our cells will age just the same – but if a friend had gone to another place is space-time, where events have bigger gaps, he may have aged at a different rate, and when you meet your friend again one of you will have time travelled forward and the other backward relative to one another.

Is this really possible? Well, yes, I think so – this model ties in very well with relativistic time travel: if you assume events are more spaced out (less dense, with bigger ‘leaps’ between them) in areas with more mass nearby. or when moving vary fast, it maps perfectly.


That’s it for now! Of course, maybe time does not leap, I don’t know, but its something I love to think about! Please let me know your thoughts…

Confirmation bias: confirmed as bias.

I have this theory that ‘confirmation bias’ is a load of BS, so I looked on the net and found, after careful search, some people who clearly agree with me. Most don’t, but they must be idiots.