IT IS not obvious what connects a falling apple and the rising sun. It took a genius to realise these two effects are the product of a single hidden cause, one that also explains the stars鈥 positions and the fact that our feet are firmly planted on the ground 鈥 the invisible pull of gravity.
That genius was Isaac Newton, a man gifted with 鈥渢he power of holding continuously in his mind a purely mental problem until he had seen straight through it鈥, in the words of economist John Maynard Keynes. We could use a few of his stamp now more than ever. While Newton鈥檚 successors stutter as they try to find further unifying laws of the cosmos, the world at large grapples with problems on unprecedented scales 鈥 economic instability, poverty and disease, climate change.
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Finding solutions means doing what Newton did with gravity: asking the right questions, teasing out causes and effects, and so building an intellectual framework to explain the puzzle. But how do we do that with the sheer quantity of data sloshing around in today鈥檚 world? It鈥檚 this problem that has led some to think we need to think seriously about the way we think. Only by rebooting our powers of logic and going beyond what nature has hardwired into our brain can we hope to grapple with problems that are far bigger than any of us. It鈥檚 time to install Thinking 2.0.
For most of us, Thinking 1.0 is taxing enough. We humans love to sideline logic in favour of the easy answer. We might make life decisions based on newspaper horoscopes, champion medicines that don鈥檛 really make us better or follow the same diet that didn鈥檛 work last year. Collectively, we convince ourselves we can put off making hard decisions about tackling climate change until tomorrow, and stake our futures on economic models that bear no resemblance to the real world.
鈥淭he potential to find answers is greater than ever before 鈥 but the possibility of finding the wrong ones rise鈥
杏吧原创s, those supposed guardians of cold logic and rational thinking, are by no means immune. Here the most acute problem lies in statistical analysis 鈥 used correctly, the best way to extract meaning from a large amount of data, but all too often prone to oversimplification or flawed claims.
鈥淪tatistics is presented as a way of being careful about the world and not making claims that aren鈥檛 supported by the data, but it ends up being a licence for people to believe things that they would never otherwise have believed,鈥 says , a statistician at Columbia University in New York. 鈥淚t鈥檚 an excuse for people to turn their brain off.鈥
He cites findings from recent eye-catching studies with statistical flaws that good-looking parents are more likely to produce female children, or that women tend to wear red clothing when ovulating. Back in 2005, researcher John Ioannidis, now at Stanford University in California, claimed that sloppy statistics could mean that more than half of scientific papers reach flawed conclusions. Neuroscience and psychology are areas that have come under particular scrutiny recently for possibly flawed assignments of cause and effect.
Now, as never before, screeds of information are logged digitally every day and stored in perpetuity, from government records to ocean surface temperatures. Couple that with the relentless rise of cheaply accessible computing power and it鈥檚 clear that the potential to find answers is greater than ever before 鈥 but the possibility of finding the wrong ones rises.
The challenge starts in asking the right questions, says social scientist of Harvard University. 鈥淥ften the question isn鈥檛 well posed, or there isn鈥檛 a direct answer but there is another question that鈥檚 of interest.鈥
In the world around us, cause and effect are often unambiguously defined, and the right questions and answers are similarly clear. I kick a football, the football moves. The question 鈥淲hat made the football move?鈥 is as obvious as the answer 鈥淚 did鈥. But then take a cock鈥檚 crow before dawn. An incautious statistical analysis might show that the one precedes the other sufficiently often that the crowing causes the sun to rise. We only know that is nonsense because independently acquired knowledge tells us we live on a rotating planet 鈥 an entirely different assignment of cause to effect.
Big and messy
Often we don鈥檛 have that independent knowledge. Say a clinical trial involving a large group of people shows that a new drug is effective at treating an illness. Break things down, though, and it turns out that the recovery rate is lower for men who got the drug compared with those who didn鈥檛 鈥 and it is also lower for women. 鈥淚f you try to interpret this in a causal fashion, it seems paradoxical,鈥 says , a physicist at the Perimeter Institute in Waterloo, Canada. This is an example of what鈥檚 known as Simpson鈥檚 paradox, and the reason is that the drug does not cause better recovery 鈥 it鈥檚 actually your sex that does (see diagram).
In a structured environment such as a clinical trial, such potential pitfalls can generally be circumnavigated through means such as control groups, in which some people take no drug or a placebo. But often controls aren鈥檛 possible, and the waters may be muddied by irrelevant, confusing or missing data. The UK鈥檚 , for example, followed a segment of the population throughout their lives to assess their health, wealth and happiness. But how do we tease out cause and effect from what will always be incomplete information, and so draw conclusions that help others improve their lives? 鈥淏ig data are messy data,鈥 says Gelman. Such data might show that quantities A and B shrink or grow together 鈥 but does that mean A is causing B? Or that both A and B have a common cause in C 鈥 or in D or E, about which we have no data?
Even professional problem-solvers fall down in such a situation. of Carnegie Mellon University in Pittsburgh, Pennsylvania, recalls a researcher who came to him convinced his data showed that religious practices reduced stress and helped overcome depression. A more detailed breakdown, however, showed that stress was causing depression, and depression was causing people to turn to religion 鈥 and it was not clear that anyone was getting better anyway. 鈥淗e was very disappointed,鈥 says Scheines.
This, then, is the rub as we attempt to bring our homespun logic to bear on big problems. 鈥淧eople know that correlation does not equal causation, but they don鈥檛 grasp the depth of it,鈥 says , a computer scientist and philosopher at the University of California, Los Angeles. 鈥淵ou simply cannot grasp causal relationships with statistical language.鈥
Pearl has spent the past few decades pioneering more reliable tools. These are founded on a mathematical language that for the first time enables causal relationships such as 鈥渢he rooster crow does not cause the sun to rise鈥 to be coded directly into a computer program. Algorithms built using this language enable researchers to reliably find the cause-and-effect relationships between the variables in a problem. Rather than combing a data set for things you think might be cause and effect, the algorithms instead create a hypothetical set of relationships and see if they fit with the data in every instance. In a similar way, a physicist would construct a model of a real-world situation and see if its predictions match with reality in all cases. Depending on the number of variables, building such a 鈥渃ausal structural model鈥 can be a mammoth task 鈥 but it provides an independent logical template into which you can see if your data fits. 鈥淚t gives you mathematical guarantees,鈥 says Pearl.
鈥淲e know that correlation does not equal causation, but we don鈥檛 grasp the depth of it鈥
This is seminal work, says Scheines, who is also a co-founder of the University of Pittsburgh鈥檚 , created in 2014 to exploit the new insights. 鈥淧earl has been monumentally important to the revolution in causation,鈥 he says. Most science, he points out, involves coming up with a model of causes and effects, testing it, and modifying it when it fails 鈥 a wearying process. 鈥淲e can now look to a computer to search billions and trillions of different models at the same time,鈥 he says.
Slowly, the new techniques are gaining adherents. One early success came in 2012, when biologists and statisticians at the Swiss Federal Institute of Technology (ETH) in Zurich used causal discovery algorithms to . 鈥淭hey got it down to nine candidates from 25,000 genes,鈥 says Scheines. Others are applying the methods to understanding causal relationships in cell signalling, and between genetic mutations and tumour development, as well as to tease out differences in the workings of autistic and neurotypical children鈥檚 brains. 鈥淭his work is starting to penetrate the mainstream,鈥 says Scheines 鈥 just as ambitious programmes such as the UK鈥檚 are beginning to crunch gigantic swathes of data to find correlations, and perhaps causations, between people鈥檚 genes, diet, lifestyles and health, and the onset of cancer.
of the Holon Institute of Technology in Israel also thinks the new logical tools could be a game changer. 鈥淚t is truly revolutionary,鈥 he says. 鈥淚t has shown that causal reasoning works and provides clear, reasonable and systematic answers to important questions.鈥
Together with of the University of Texas at Austin, Bochman is boring down to the next level. They have been working to reformulate Pearl鈥檚 mathematical notations into the more basic language that formal logicians use, enabling them to explore ideas of causality within logical frameworks that contain assumptions 鈥 and understand what happens when those assumptions are found wanting. 鈥淎ssumptions are just beliefs, so they should be abandoned when we learn new facts that contradict them,鈥 Bochman says. If we find the grass is wet, we might assume it has just rained, for example 鈥 until we learn that a new sprinkler system has just been introduced.
The 鈥渘onmonotonic reasoning鈥 logic scheme that he and Lifschitz have devised allows a user to keep track of their assumptions, and update a chain of reasoning if those assumptions change. This provides a surer way to work with incomplete or changing information 鈥 a boon in interpreting 鈥渢he vast range of vexed questions about causation and its role in science and beyond鈥, says Bochman.
Spekkens is approaching that same problem from a different angle. He is a quantum physicist 鈥 and there is no field of human enquiry in which questions of cause and effect are more vexed. Quantum theory describes with perfect accuracy phenomena that occur on atomic and subatomic scales, but only at the price of particles existing in two places at once, for example, or seeming to influence each others鈥 properties without any physical connection.
Physicists explore this last phenomenon of 鈥渆ntanglement鈥 using an experimental set-up known as a Bell test, which aims to exclude the possibility of standard, 鈥渃lassical鈥 cause-and-effect influences being responsible for what is observed. Bell tests generally show that the experimental apparatus obeys our familiar classical causal rules, while the measured particles seem to be obeying a different, unfamiliar set. There are two responses to that: say 鈥渋t鈥檚 weird鈥 and carry on 鈥 or try to work out what the rules of quantum causality are, and whether they might give us a deeper insight into logic in the wider world.
What Spekkens and his colleagues have teased out so far is that the way causality works in the quantum world allows a cause-effect relationship to be distinguished from a common-cause relationship 鈥 something nigh-on impossible in the classical world without using a control group (see diagram). In other words, it allows us to sidestep those Simpson鈥檚 paradox-type situations ().
鈥淓ntanglement seems to be based on a causal relationship outside physical space and time鈥
That could have direct consequences in fundamental physics. Entanglement seems to be based on a causal relationship that lies outside our conventional conception of physical space and time, phenomena dealt with by Einstein鈥檚 general relativity. Find out more, and we might find a common cause that could unify relativity and quantum theory, two stubbornly incompatible theories. But Spekkens thinks it could also feed back into more rigorous logical analysis in the real world. There are undoubtedly more classical causal algorithms waiting to be discovered, he says, and perhaps the quantum analyses could allow us to discover ways to distinguish cause and effect from common cause in the classical world, too. That could potentially be of great interest, say, for clinical trials in which randomised controlled experiments can鈥檛 be carried out for cost, technological or ethical reasons. In precise evaluations of the comparative effectiveness of end-stage cancer treatments, for example, it would be unethical to deny a control group any treatment at all. 鈥淚f one could deliver on this promise, it would be an interesting example of the field of quantum foundations having applications in other fields,鈥 says Spekkens.
Spekkens is keen to point out that such tools complement, rather than compete with, conventional tools from classical logic. Pearl for one welcomes any synergy between quantum and classical thinking, and any approach that can increase the rigour and effectiveness of our approach to crunching data to solve the messiest of human problems. Rather than relying on presumptions of cause and effect made by often politically compromised economists, for example, he thinks we might use new thinking tools to crunch through all conceivable combinations of economic variables to work out which should be tweaked and under what circumstances, say to bring about more equality while not strangling economic growth. 鈥淭here鈥檚 a lot of research in this direction and it looks promising,鈥 says Pearl. 鈥淲e haven鈥檛 yet discovered the cause of poverty, but we鈥檙e moving in the right direction.鈥
If we can go beyond Thinking 1.0 to frame better questions and process data more reliably, we might all reasonably become geniuses 鈥 a cause that could mean a better future for all of us. 鈥淢aybe we will begin to think in more complex and subtle ways,鈥 says Gelman. 鈥淭hat would be great.鈥
This article appeared in print under the headline 鈥淭hinking 2.0鈥
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