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“Plurality must never be posited without necessity”
-William of Ockham
People prefer simple solutions to problems. This is pretty obvious – it takes less unnecessary hard work. So, does this idea apply in science? Welcome down the rabbit hole of the history and philosophy of science.
Ockham’s Razor is a hugely influential heuristic (rule of thumb) in science. The Razor provides a way to decide between competing explanations that are equally supported by the evidence at hand. It suggests that the favoured explanation is that which posits fewer variables.
However, we all know that science is not often ‘simple’. How do we translate this position to science? This is where ‘falsifiability’ comes in, a concept made famous by Karl Popper in “The Logic of Scientific Discovery”. If you cannot falsify a hypothesis, then it is not scientific. The famous example is “all swans are white”. By inductive logic, no amount of white swans can prove this statement; instead it is supported until a single black swan is found.
Falsifiability alone does not, however, reduce possible explanations to one. Competing theories may all be falsifiable, thus scientific. Having established that swans can be black or white, we propose three competing ideas: 1. All swans are either black or white. 2. All swans are either black or white, but location determines which. 3. All swans are either black or white, but location and the season it is in December determine which. Having taken samples from Australia and England to test these hypotheses, you would see that all statements are supported, however number 2 has an extra variable, and 3 has two.
Strict application of the Razor would suggest you accept hypothesis 1. However, the extremely strong correlation between location and swan colour suggests that 2 is also acceptable. In this case, you decide that the ‘simplest’ hypothesis is the weaker, because it has less explanatory power. That is, even though clearly swans are either black or white (hypothesis 1), the black swans are all in Australia, and so hypothesis 2 suggests an explanation determined by geography. What about hypothesis 3? Well, seasons are dependent on location, and so the seasons variable is superfluous, regardless of how well supported it is by the results. We take hypothesis 2 and move on, because that result has thrown up new hypotheses (e.g. around species and evolution) – the very fodder of science.
Thus science aims to explain, rather than simplify. Ockham’s Razor is really about how to prefer an explanation, rather than about the most simplistic explanation. Sometimes the best explanation is very complicated, the point is that it is no more complicated than it needs to be to do the explaining. Many ‘conspiracy theories’ fall foul of the Razor for this reason–they introduce extra variables without improving the explanatory power – that is, the non-conspiracy hypothesis can explain all the evidence.
Things get interesting when a contradictory result is found by a new experiment. Does it really falsify the hypothesis, or should we modify the hypothesis? Should hypotheses be ‘backward modified’ like this to explain new data? Doesn’t this contradict everything I’ve just said? How the hell does science really work? This will be a tale for another day, where we meet people like Thomas Kuhn and Imre Lakatos, and encounter the anarchist, Paul Feyeraband.
This article first appeared in print in my column in Woroni, the student newspaper of The Australian National University, No. 8, Vol 65, 23 July 2013.
We do seem to be heading in dark direction. A world where we seek not evidence but instead opinions from friends and talk show hosts, a world where argument is all that is needed. A world, in short, where anything can be true if we only believe it.
In an attempt to keep the post short, I first observe that the Cassini spacecraft has taken its final look at Earth, an event mostly ignored despite its poignancy given its status as one of the last great exploratory missions to Space.
People, and the politicians who represent them, seem determined to look at short terms goals, especially financial, in the face of species-threatening climate change. (I wanted to link something there then realized there are too many examples…)
‘Journalists’ of science and technology seem comfortable to be creationists (apparently because the story is better).
Elections are contested as a race to the bottom for votes, rather than as a conversation on ideals, goals and aspirations for society.
In the face of this, the collective advancement of society’s knowledge seems to be localized to the ‘nerds’, and clearly the popularisation of nerds has done nothing to raise the status of their work. I’m glad I was never a fan of that American show, ‘The Big Bang Theory’ (somewhat more of a fan of its namesake though).
I remember laughing at a movie a number of years ago called “Idiocracy”. I now actually can see a day where humans attempt to feed crops with Gatorade and puzzle at why that doesn’t work.
We seem to have lost sight of the days when we looked to the stars and imagined how much more we could know, how much better we could be and pictured a glorious future for humankind.
I don’t know, perhaps I am prematurely a grumpy old man. Still, I do wonder how we can combat the level of unreason in society, and I fear where it will lead.
Simply because everyone else is raving on about the recent AAS survey, I thought I would too. How depressing it is to find that not the entire population of Australia knows that a year is measured by the time it takes for the Earth to do a lap of the Sun! And fresh water makes up what percent again of total water resources? How much of that is potable? Wait, that wasn’t one of the questions (probably would have require knowing what ‘potable’ means anyway).
Like many science commentators out there (and I won’t even try to list them all, but this is an excellent one, and this is an excellent one from the last time they did this survey), I breathed a sigh of “so what!” After which I sort of just found the whole thing depressing.
I tweeted earlier today that all I think it says is that 30-40% of Australians are not ‘natural naturalists’. That is, people who take a broad interest in scientific topics and fields and who tend to remember lots of the gory details. At the top level, these people are known as ‘polymaths’ – that is, they operate at near genius level in more than one scientific field. At the other end, they could be your average Joe who loves a good documentary (and is probably a fan of David Attenborough). In other words, they quite possibly are not scientists. And THAT is the point. Knowing certain facts about the world does not make you a scientist.
Others mentioned above have pointed out that science is about such things as approach to problems and method and application of analytical techniques. Generally, it is about concepts and thinking, not about facts. The facts fall out of the conceptual tree when you shake it hard enough.
So why does it depress me? Well I guess I am a bit of a ‘naturalist’ – I love to know about the world and how it works. Knowing why a year is as long as it is is part of that, to me. Finding out about natural phenomena is exciting! And even though my specialist field is geology, I am very interested in a range of things, some scientific, some not quite (like philosophy) and some not at all (art). So I consume all manner of things, and along the way I happen to remember a few things (although I will be the first to admit I have a terrible memory). I suppose I find it hard to understand why anyone else would not be the same.
So perhaps I am weird? Or perhaps not! Lurking in the 60% odd of people who knew stuff for the survey will be people like me! And some of them will be in or go on to scientific careers. I think Australia is pretty safe for now.
[But come on, people should know how long it takes for the Earth to go round the Sun, I mean, really?]
“What do we want? Scientific Certainty! When do we want it? Within a certain timeframe!”
The public, the media and especially politicians like to make a big thing about scientific uncertainty. For scientists, it’s just a fact of life. So what is this ‘uncertainty’ and how does this affect our lives?
We scientists perform research just so that we can understand the world around us. To do so, we use various scientific and statistical techniques, and especially where the latter is concerned, these result in ‘measures of confidence’ in the data (and thus conclusions drawn there from). It means that we present data with ‘error bars’, which are designed to show a range of values within which the ‘reality’ may lie. These error bars represent upper and lower limits that are determined on the basis of our confidence in the results. This is largely a statistical calculation, and it results in mind-bending statements such as “plus-minus 6% with 95% confidence”. What does this all mean?
Three concepts: Confidence, Error and Likelihood.
Imagine this scenario: you decide to determine whether the morning light is a result of the rising of the Sun in the morning (hear me out, this is going to be scientific!).
You’ve noticed that it seems to get quite light at around about the same time as when the Sun rises, but you’re not sure that it’s actually related to the Sun rising (stay with me!). So you hypothesise that the morning light is due to the Sun rising. To test this, you take a series of measurements over numerous days – the amount of light, the time of day, and the position of the Sun with respect to the horizon.
Your data looks a bit like a curve when you plot it – that is to say, there is no definite point at which dark becomes light (anyone who’s been up before it’s light will know this, but for the benefit of an undergraduate audience…).
So you do the statistics on it (yes, there is a point to paying attention to those stats classes!). This shows that there is a correlation between the position of the Sun and the amount of light (durrr, I know…), but wait! There is variation in the data. Not every day is the same! How could this be? Well, it could be that your instrument is near some artificial light sources, it could be that the very light of God is shining upon your scientific research (hey, appealing to all audiences here). How do you decide?
To the rescue – the null hypothesis!
For this you decide to generate a completely random version of the sunlight data (even your phone could do that these days). And then you compare, statistically, the random set to the experimental set. Sure enough, it tells you that only a percentage of the data could be explained by the random data. The rest could be considered to be explainable by the hypothesis (that the amount of light is a result of the position of the Sun).
Now, just say you decide you want to know what 95% of the data is saying. It is telling you that the light patterns match to the Sun position patterns to within, say, plus or minus 2 minutes every day. That is to say, the middle 95% of the light data matches within the same times plus or minus 2 minutes every day. What have you learnt? Well, you’ve probably confirmed that the position of the Sun is the dominant factor in the amount of light in a given place at a particular time of day (yes, yes, assuming you are outside, etc). That is, your 95% Confidence Interval.
But why all the scary stats and numbers? Why should we be only 95% confident of this match, plus or minus 2 minutes? Well, because we have measured things in the real world, with human-made devices and their associated problems; nothing is infallible. But also because there might actually be other factors at work – street lights, machine error, etc. But if we take that null hypothesis test we did before, we’ll see a pattern. In the above example, had we taken the middle 99% of data, we may have had a result that was plus or minus 30 minutes in the time data. That’s starting to sound a bit dodgy. Had we taken the middle 66% percent of the data, we may have been within plus or minus a few seconds, but that would have left a third of the data unexplained. What’s going on here?
Well, fortunately, these numbers I’ve been picking relate to ‘standard deviations’ (SDs), a highly statistical term that essentially means the amount to which the data show ‘weirdness’. A small SD means the data is pretty tight – it’s all showing the one thing. One full SD is around 66%, which we’ve agreed is a pretty poor test of the data. 2 SDs however, is 95% of the data, “almost all” in most people’s parlance. 3 SDs puts you in the 99% category, which is ridiculously definite!
Imagine a diagram of confidence versus error; the Y-axis shows Error, measured as a percentage deviation (that is, how much it differs from the average), while the X-axis shows the confidence level, measured in those Standard Deviations. Remember, we choose our confidence level, then see what the error level is. Choose your confidence interval, and then see where your error margins plot. This will give you an idea of how strong your result is. This is, the likelihood that you have made an observation of reality; your science has revealed a ‘truth’ about the world around us.
So, those studies that have low error margins at high levels of confidence, those are the ones we can be pretty darn certain are likely to represent the real world. The ‘Nobel Committee’ area of certainty represents experiments that start to demonstrate ‘theory’ – that summit of science where things are considered to be the closest thing that science has to ‘fact’.
Examples of things that fall in to that ‘Nobel’ area: gravity being responsible for the apple falling from the tree; the Sun rising in the east and causing ‘daytime’; human influence on climate causing global warming. Yes, I said it. Ask the climate scientists – this is where the data lies.
We’re never certain, we’re just certain within certain error bounds, at a confidence level of X.
This article published at Woroni, the student newspaper of The Australian National University: http://www.woroni.com.au/features/scientific-uncertainty-a-certain-certainty/
Students of the 70s and 80s enjoyed a certain freedom in their tertiary academic education – it was fully funded by the government. All they had to do was put a roof over their heads and feed themselves (which of course is a challenge when you’re a student), but they did not end up with a significant debt to the government afterwards as students do these days. Concurrent with this ‘golden age’ of tertiary education was a booming era of scientific research in Australia. Everything from medical research to planetary science got a gong, and Australia has its fair share of Nobel medals to show for it. Between all of this, these people found the time to agitate for progress in society. Before one’s eyes get misty with nostalgia, it can be summed up by saying that from the 50s up until probably the early 90s, Australia was one of the most progressive places in the world to be in research.
Something happened in the 90s though, politics changed, people switched off and governments no longer felt the need to invest so heavily in fundamental societal values, like research and innovation. The boom in private wealth probably lulled everyone into thinking that capital markets had developed a momentum to help carry this burden. The shifting ground of popular politics also helped sideline exciting fields of research, and science in general. It simply wasn’t news any more, and it was too easy to sit back in suburban comfort and say, “the money should be spent elsewhere, what’s the value of nerdy scientific research?”. This coupled with a growing conversation around elitism versus egalitarianism, which in the Australian context was read as “academics in their ivory tower are wasting money”, laid the groundwork not just for cuts to funding, but for those cuts to go largely under the political radar.
Fast forward to 2013, and we are in a situation in which federal funding for research and higher education faces cuts and deferrals of $3.8 billion over the next four years. Anyone familiar with the research grant process in the country will know that it is a back-breaking, time consuming exercise, a process that takes valuable time from research efforts, without any certainty of success. And it has to be done at least every few years. But don’t take my word for it, here is the process put beautifully in metaphor by Professor Suzanne Cory, the President of the Australian Academy of Science in her address to the National Press Club today:
Imagine you decide to build a house – you go to the bank and borrow enough money to buy 1000 bricks, and you lay them. And then you have to go back to the bank to ask for another loan, to buy another 1000 bricks. Having laid them, you then once more have to stop building and spend time convincing the bank to lend you enough for the next 1000 bricks and they only lend you enough for 600. When you know you are working with so much uncertainty, how far do you dare plan?
That is the current situation in research funding in Australia, has been for years, except now it is against a backdrop of a shallower pool of funds (and getting shallower).
The consequences of this for Australia will be simple: Research and innovation will decline, our brightest minds will leave the country, and Australia will lose status as an innovation powerhouse. Following that will be a negative flow-on effect to the economy, the scale of which will dwarf the cuts currently being made. This will be a sad state of affairs for the country to find itself in, the country which produced WiFi, flu vaccines, cervical cancer vaccine, the cause (and cure) of common peptic ulcers, the Atomic Absorption Spectrometer… the list goes on.
For the future of Australia, for it to have a prosperous, innovative future; scientific research needs to be funded as a central national priority. Indeed funding should increase, and the onerous short timelines of the grant process need to be reviewed to take into account the natural process of scientific research; to let academics and students evolve their work. Governments on both sides of politics cannot afford not to provide this support.
This article first seen at ABC News Australia’s ‘The Drum’ Opinion and analysis: http://www.abc.net.au/unleashed/4798960.html
Time to rekindle this blog. I’ve returned to science, somewhat officially, now being involved in geological research at a major university. And I’m living on campus. So I get to pretend to be a pimply student again. This also gives me time to think about science in general and I suspect that this will result in me writing here again… so, it’s been a long time, but please do come back!
See you soon!
Traversing the Razor 