7. How to achieve your goals
Quantum physics, network theory and goal setting
It was my first heartbreak. I was eight years old, and he was the thing I felt the closest connection to, other than my dad’s fried noodles. You may remember him, as he was quite the name in science. I’m talking about Stephen Hawking.
It would be hard to overstate my childhood hero worship for the greatest physicist of my lifetime. From the way I ate to how I looked out of a window and sat in a chair, I tried to copy him. It even got to the point of me emulating him as my chosen hero in drama class. I told you, I was in deep.
But then my hero disappointed, confused and upset me. I was reading his most famous book, A Brief History of Time, specifically the second chapter which deals with space and time. Here, he explains how the historic belief of space and time as fixed entities has given way to an understanding that both are dynamic, shaping and being shaped by the objects that pass through them. Space and time are neither fixed, infinite nor independent of each other. To understand the universe we must visualize them together as four dimensions: the three of space, and one of time.
Hawking uses the image of a light cone to visualize this concept of ‘spacetime’, and demonstrate how past and future events are connected. When light is emitted it spreads out like ripples in a pond, forming the cone shapes. Because nothing can travel faster than the speed of light, every event that contributes to (past), or stems from (future), the present moment must therefore be happening within these cones: at or within the speed of light.
Events that take place outside the cones are said to be elsewhere: therefore they cannot change the present, nor be changed by it. To illustrate, Hawking offers the scenario of the sun suddenly dying: this has not happened in the past light cone, and it does not affect the present because of the eight minutes it takes for light to reach us from the sun. Only at this point, some distance into the future light cone, does it intersect with and change our reality: we acknowledge the event not when it actually happens, but at the moment it starts to cross our consciousness.
Reading this for the first time, I did not feel my customary rush of excitement at a new concept I could explore and use. I was used to science illuminating my world and helping to explain it. Now I was faced with the cold, diagrammatic reality of a vision that clashed with mine. Here was the future as a fixed, quantifiable entity, sketched out in solid lines, while my vision was all about wobbly boundaries, interlinked outcomes and adaptable possibilities. This incongruence was like suddenly finding that your house key no longer fits in the door. Instead of feeling comforted and intrigued, I felt choked and my anxiety kicked in hard. It was as though my vision for the future had been whitewashed. What was happening beyond the boundaries of time in this model? What if I ended up out there, outside the cone and blinded beyond the light?
This was a scary moment but it was also a galvanizing one. It was when I realized that I couldn’t get all the science I needed from other people’s books and theories. To make the world make sense, I had to use my individual perspective. It was from this point that I started writing down notes in my own words, combining what I was learning with reality as I experienced it. I was oblivious to what the use of this might be, but it felt right and necessary. Now it’s the book you are holding in your hands.
And I couldn’t have started my journey with a more important topic than this. Thinking about how the past shapes us, how we experience the present, and how we can shape our future, is as fundamental as it gets.
We are all looking for ways to learn from what has happened to us, and influence what might happen next. We want certainty but also opportunity: to feel safe about our future but also to be inspired by the possibilities. While accepting that there are things we cannot influence, we want to know about the ones we can change. We want better ways to set goals, make judgement calls and fine-tune our priorities. We need a way to live in the moment as well as tools to plan effectively for the future.
The good news is that these aren’t just questions we ponder while lying awake at night, or when we sit at the beginning of each year to write down our goals and resolutions. Theoretical physics has done a lot of the heavy lifting for us. It shows there are ways of visualizing the events in our lives that can help us to plot a path forward and maximize the possibility of a desired outcome. Even better – as I would have liked to reassure my eight-year-old self – these are methods that don’t rely on the binary model and harsh boundaries of the light cones. By using the ideas I will introduce in this chapter – network theory, topology and gradient descent – we can all use methods to plan our lives and set goals that are as flexible and changeable as we are.
The big question: now or later?
When it comes to life planning and goal setting, perhaps the biggest question we face is what to focus on. Should our emphasis be on the present or the future? Is it about gratification now or pleasure deferred? Does constantly planning for the long term inhibit your ability to enjoy the here and now; or does too much focus on the present mean you will be ill prepared for what comes next?
Or, is it possible to have it all: a life well lived in the present along with one ideally planned for the future?
If you’ve ever worried that you struggle too much with this dilemma, quantum mechanics – the study of subatomic particles, the smallest we know about, and a subset of theoretical physics – is here to reassure you. Heisenberg’s Uncertainty Principle tells us that the more precisely we can measure the position of one of these particles, the less effectively we can track its momentum. And the same applies in reverse. In other words, physics tells us that we can’t measure location and speed of movement with accuracy at the same time. The more we focus on one, the less precision we can achieve with the other.
Sound familiar? Heisenberg may have been writing about quantum particles, but the same principle seems to apply at the macroscopic level of our everyday lives. Just as precision measurement equipment has its limitations, so too does our ability to concentrate and prioritize. You can’t be a great host at the same time as enjoying the party: you’re either thinking about it, or experiencing it, having a great time yourself or worrying about whether other people are. One detracts from the ability to do the other. Especially if, like me, you’ve had to prepare by googling, ‘How to have fun.’
This is the dilemma of adulthood, where we’re constantly aware of two contradictory needs: to live in the moment and to plan for the future. The desire to do both at once eats away at the capacity to properly achieve either. We’re either dragging ourselves away from enjoyment by worrying about what comes next, or having such a great time that we never get around to organizing things for the future. Even as someone who relishes taking an information-driven, research-based approach to life, there are times when I just want to unlearn everything and be a kid again – basking in the bliss of being ignorant about the world, and the ability it engendered to truly live in the moment.
Alongside the diligent researcher, there lives a part of me that yearns to return to family holidays in Cornwall, the time in my life when I felt most liberatingly, unrestrictedly alive. Even the car journey to get there was an event. After three hours of driving, two packets of crisps and fifteen games of I Spy, we would finally reach the point of peak anticipation: when Devon gave way to Cornwall, marked by ecstatic screams from the back of the car as my dad drove us across the Tamar bridge. ‘We are in Cornwall . . . NOW!’ With the county boundary behind us, there was nothing in the way of a week of Cornish pasties, fishing in rock pools and trips to Padstow.
These are some of my happiest and most colourful memories, a time and place where I knew how to enjoy myself without reservation. Cooking fish dishes in the kitchen with my dad, playing outside in the garden, making as many sandcastles as the heart and mind desired, sitting on ‘Millie’s rock’ on Looe beach in my awesome, multicoloured swimming costume. My penchant, aged seven, for gingham, re-enacting scenes from films using my mother’s Blue Denmark crockery, and imagining my future with my heartthrob: none other, of course, than Stephen Hawking. The colour, taste and smell of every memory remains clear in my mind, twenty years later. It was a time of doing whatever I wanted, not even considering what other people might think. The good life.
This mixed bag of hobbies might have been random, and seemed shapeless, but all form part of the past light cone that has led me to this point: an accumulation of experiences that reinforce my interests, identity and individuality. They remind me of a time when the fear of missing out, and worries about what will happen next, simply didn’t cross my mind.
As children, we see time as endless, even boring: to be filled with whatever fun, colourful and interesting things we can lay our eyes or hands on. In adulthood, time narrows into a currency: something to be measured and parcelled up, and jealously guarded. By the time I was doing my degree, there hardly seemed to be any room for relaxation. There were final exams to prepare for, and beyond those, application deadlines to meet and a future to plan. My life seemed to have become an endless to-do list, leaving me with little time or choice but to keep ticking off the next item. In this context, trying to find a present moment just to exist and enjoy myself felt almost sinful, even if I could have achieved it. In these months, I lived almost on autopilot, numbing myself to emotion and denying myself the exploration and enjoyment that my inner child craved. Daydreams about Cornwall’s beaches were interrupted by a voice that told me to focus on my studies, and the next planned unit of time, including the ones I had allocated to relaxation. Try as I might to escape, the voice kept commanding me back to the medical science library, out of the rock pools and back to the air-conditioned, lithium-lit hallways.
In my efforts to get the balance right, I have taken inspiration from another subset of quantum mechanics – the study of how waves move through space and time. This presents a classic Heisenberg problem: you can either pinpoint the way a wave is moving, or its position at a certain moment in time: try to put your finger on both at once and you lose track. To get around the problem we create what are called wave packets, grouping and visualizing lots of different waves together so we can study their aggregate behaviour. A single wave is hard to pin down, where a ‘packet’ of several can be studied more effectively. Setting goals and making life plans are not so different: in isolation, it’s hard to see if any one decision or goal is the right one. We need the entire ‘packet’ – the full picture, and all the context – to understand if we are making the best possible choice, relative not just to the immediate moment but to our best impression of what the future as a whole looks like.
As we try to create these virtual wave packets, we have to strike another balance, between two different ways of thinking about our lives. There is momentum thinking, in which we live through time, going from one thing to the next, with our happiness defined by what we achieve and plan to do (the adult world of responsibility). And there is position thinking, in which we live for this time, captured by the present moment and the sensation it offers, blocking out everything else and simply being, including the feeling of guilt. This is hard, since it goes against the grain of what we are told it takes to be a ‘functioning adult’. But it’s also vital. Standing still doesn’t mean you’ve stopped. Rather, it allows us to be more creative, reassessing our progress, living through the forces of our senses, and exploring more possibilities for the future.
Embracing position thinking gets harder as you get older, but it’s still possible. My best moments are in yoga classes, where there is no noise, nothing to concentrate on except the posture you are trying to hold, and the opportunity to let all other thoughts and concerns dissipate, creating precious mind space. By the end of a class, as we are instructed to take on the shavasana (corpse) pose, I am too tired for any other thoughts to intrude. Often it leads to a cat nap on my yoga mat. Yet this rare moment of bliss doesn’t come for free. Invariably, the next morning I feel sad: future thoughts and worries are again tugging my mind out of present harmony, even harder than before, sometimes to the point of self-punishment, be that via the withdrawal of food or cancelling social events to do something ‘constructive’. I became a real a-hole – with myself as the main victim.
I needed a way to break the cycle of momentum thinking, preoccupations of what’s next, intruding on almost every aspect of life, denying me the joy of present moments. I wanted to recover my ability to live in the moment, without sacrificing my endless need for clarity about the future. So I tried an experiment, one inaugurated with a special batch of pancakes, just before Lent 2013: a socially acceptable moment to implement change. My own forty days and forty nights would be divided into two sections: half spent living in the world of momentum thinking, being completely rigorous about ticking every box and addressing every priority; and the second half basking in position thinking, trying to enjoy every single moment and not giving a thought to the future.
By now, you probably know me well enough to guess this didn’t go particularly well (another of the all-important failed experiments that have made me the person I am). I couldn’t avoid the thought of what I was missing out on – present enjoyment or future clarity – intruding on the experiment. I was hosting the party, but unable to stop thinking about the washing-up afterwards. I fell victim to another tenet of quantum mechanics, the observer effect: merely by observing a process, you inherently influence and change it – the classic example being that to observe an electron under a microscope, you rely on projections of photons that will change its course. Observing my own experiment, by definition, had skewed its outcome. I was too busy thinking about what I wasn’t doing to enjoy what I was.
Since the failed experiment I have reached something of a compromise between position and momentum, present and future. At different times in a typical day, I will iteratively switch between the two, seeking to shift into whichever one I need the most at that particular moment. I battle my ADHD – which wants everything now, and has no concept of time – to try to manage the dance between living now and planning ahead. Just being aware of the Uncertainty Principle is a helpful way of achieving the right balance. As I discovered, it’s impossible to completely compartmentalize the two, but even the simple act of accepting their incompatibility is liberating. It helps us to worry less about the one we’re not doing – realizing that there will be time for it later, and we shouldn’t feel guilty about an afternoon in the sun (or one indoors planning, when everyone else is having fun).
But it’s not enough to be conscious of how living in the moment differs from planning for the future, and trying to mesh the two mindsets. We also need a mechanism to visualize how present and future are connected, giving us clear choices about how to set goals and reassurance about the pace at which we are travelling. This is where network theory, one of my most trusted allies in life, comes into its own.
Network theory and topology
Ever since reading A Brief History of Time, I have been searching for a predictive model that suits my needs better than the fixed boundaries of the light cones. I was caught in the classic human contradiction – between the need for certainty and a frustration with setting limitations. Other than not knowing what happens next, nothing freaks me out more than actually having the limits of a plan imposed on me. I need flexibility: to turn those thick, straight lines into wobbly ones that I can navigate around and bend to my needs.
I needed a method of planning that understood both my need for endless preparation, to the point where it can take me five hours just to leave the house, and my tendency to tear up hours of careful thinking in a burst of intense impatience – a sort of psychological brain freeze, when the lemon sorbet you thought your day was going to be is turning into more of a vanilla ice cream. My Heisenberg struggle to reconcile present and future is sharpened by the time warp of my ADHD senses, with my mental accelerator constantly pressed to the floor.
In dealing with all this, network theory has been my salvation. This is a very straightforward concept: the study of how we represent connected objects via graphs, visualize the network they collectively create, and learn from what the connections tell us. It’s what allows us to analyse complex, interrelated and dynamic systems by using the related techniques of graph theory.
A network is simply a series of objects or people connected together. You and your friends and neighbours are connected by a series of social networks. The London Underground is a network of stations connected by the different service lines. The electrical circuits in your toaster plug are networks. The smartphone sitting next to you is probably part of a network right now, connected to Wi-Fi and part of a WLAN (wireless local area network). The Internet itself is a mega network of computers connected both physically and wirelessly, moving vast volumes of data around.
Networks are everywhere, from the physical to the digital, the social to the scientific. They are the tangible and intangible structures that affect everything from how we build a career over decades to how we can get connected to the Internet right now.
They also provide the ideal mechanism for visualizing and mapping out our lives, over both the short and long term. We are all being affected by so many different things, pushed and pulled in a hundred different directions, that we need a more complex, iterative and adaptable model than a to-do list to plan ahead. Network theory provides this, especially when it comes to topology – how the different components (nodes) of a network are connected together, and the structure they form. Topology is what turns those inflexible, straight lines into a mobile network of possibilities: bringing some that had been shrouded in darkness back into light, and easing my anxiety of its pinch. It’s what allows you to recognize that logic that may once have helped you no longer applies, or that an idea that has been germinating is now ready to flourish.
The nature of topology is crucial. If I gave you six buttons to arrange into a pattern, you could make a line out of them, or a circle, or a V-shape. This topology determines how the network will function: its capabilities and limitations. When we make decisions and set priorities in our lives, we are doing the same things: arranging the available evidence and choices into patterns that will determine both short- and long-term outcomes.
Thinking of our future life as one big network – with its nodes being everything from the people in it to our hopes, fears and goals – is the best method I have found for making plans that isn’t either too simplistic or uncomfortably restrictive. It’s helpful because it’s dynamic, capable of adapting as your circumstances do. It’s clarifying, helping us to understand what is and isn’t truly important. And it’s focused on connectivity – allowing us to see the things that are linked, which nodes are influencing or being influenced, and where a certain path may lead.
A network allows us to think as Hawking shows we must – in the context of both space and time – without being restricted by the tramlines of the light cones. It helps us to navigate proximity and distance – between people, specific goals, and stages of your life – across the dual canvas of space and time: what you need to happen, and when, and where you need to be for it to take place. Over time I have realized why the lines of Hawking’s diagram exist, because we need directionality to create signal from noise, and overcome the anxiety of losing our way – becoming lost in our own life. But a network softens those lines into squiggles, turning the fixed cone into a leaf shape that can fold and curl up on itself as time evolves, exposing different sides of it to the light. It gives us structure, a path to follow, and also the flexibility to move around.
So the next time you are sitting down to write a plan, or worrying about what’s going to happen, try replacing your to-do list with a network diagram. Treat every important person and goal as a node, and establish the connections between them: which people can help you to achieve which goals. Try to be realistic (in relative terms) about space in your drawing: which people or goals are most proximate, and which are distant? This is important, because you are looking for the junctures between different nodes as your path forward. The points where different components on your network come together are where you start to understand the unrecognized connections, and glimpse potential pathways ahead. You’re looking for hubs – where lots of nodes are close to each other – and for potential elbows – where one path intersects with another, giving you a route. Also think about establishing an order of preference, for instance by colour-coding your objectives. A high-priority goal surrounded by lots of enabling nodes suddenly starts to look both desirable and achievable. In this way, the network begins to illustrate the things you want, the order of priority and what you can do to move closer to them.
Because – unless you are Stephen Hawking – it’s incredibly difficult to think and draw in four dimensions, it’s worth creating different networks for different points in time. One that shows where you are now. And two more that take you a few months, and then potentially a few years into the future. You might want separate ones for your professional and social networks too. This is something I do with my sister, Lydia, and we regularly help each other to set and refine our plans. We’re ideal partners in this, because she is a perfectionist who is brilliant about pinpointing the immediate future, which I find scary, whereas I am good at looking into the more distant future, which she finds hard to fit into her closely controlled vision. I am able to help her think more flexibly about her long-term goals, and she helps reassure me about what is going to happen tomorrow – and what to wear that day. Because let’s face it, I’d be happy wearing the same thing every day until instructed to burn it. We are both very happy and adept in our contrasting worlds, Liddy’s where networking means the art of being well connected and meeting people, and mine where it means plotting nodes on a graph and establishing the probability of various outcomes.
In these conversations, something she has often said to me is, ‘I want to do everything.’ That fear of missing out is something many of us face. Surrounded by social media’s hall of mirrors, we’re more conscious than ever of the parties we haven’t been invited to, the goals we haven’t yet achieved, the ‘gap yah’ mountains we haven’t climbed, and the feeling that our lives and our peer group are passing us by. What I always say in response is that she can do everything, but only by understanding how the different nodes are connected, and what should take priority, based on nothing other than what you want for yourself. It’s simply not possible to do everything at once – but you can plan for how to achieve all the things you want. Over time the well-networked tortoise will outlast the frantic, fickle hare.
We need this ability to map across space and time – creating clarity about what needs to happen next – to avoid both overwhelming anxiety about the present, and gnawing fears over the future. A list of goals on its own doesn’t help us, because there is no context, no sense of interconnection and no mechanism to establish preference. It can be good for the linearities of life, but to make decisions you need a network that plots your goals alongside people and places, something that doesn’t have to adhere to any shape but your own. None of this, however, guarantees that we won’t get anxious and envious as we overlap and compare our own topology with those of our friends and peers, wondering about all the would-haves and could-haves, and worrying about being left behind. Network theory can’t save you from this feeling of FOMO, but at least it gives you a direction and a purpose, one you can shape flexibly and evolve over time.
Once you have your networks, you need to start navigating them: determining from the mass of information and components what represents a viable path forwards. How can you both identify and develop the optimum layout, and then continue to shuffle the moving parts as your situation evolves?
To answer that I want to look next at another machine-learning technique, and how it can help us to set a course from now to what happens next.
The gradient descent algorithm: finding your path(s)
Once you have your network sketched out, you can start to see the options in front of you. There are always different paths you can take, and you would be forgiven for being unsure about which is the quickest route to goal. Fortunately, machine learning is on hand to help. These questions of optimization – how to find the quickest and most efficient path – are the heart of computer science. Algorithms thrive on burrowing through data sets to discover how to do things more quickly, efficiently and cost-effectively. And we can borrow their techniques to optimize our own path through life – after all, they are based on human logic in the first place.
The algorithm used in machine learning to answer this question is called gradient descent. This is an approach used when trying to optimize a process and minimize its cost function (error). The analogy is of someone trying to climb down from a mountain into a valley. The goal is to get to the lowest point (minimum error) as quickly as possible. So the algorithm, which can’t see all the paths at once, is programmed to navigate by gradient: continually finding the steepest downslope and reassessing with each step. As long as it keeps finding the path with the highest negative gradient overall, it’s going to reach the bottom fastest. Just like people, algorithms of this kind vary in their attitude and approach. There are greedy ones, which choose the most rapid, immediate route – a bit like a politician trying to fit everything into a fixed term of government. And there are explorative ones, which persist with patience, allowing more routes and solutions to be tested out along the way. The latter is something I’m still trying to learn from – counterbalancing the greediness of ADHD to focus all attention on one thing while forgetting about everything else (which explains why I’m writing this in bed, in the middle of the night, still wearing my waterproof jacket).
Gradient descent is one of the most fundamental techniques in machine learning, and it’s a concept with several lessons for us all as we navigate our own life networks. The first is that you won’t be able to see the whole path, or even much of it, in advance. You can connect nodes and identify clusters, but ultimately our view gets hazier the further down the path – into the future – we look. And that’s OK. Because the second lesson of gradient descent is that your immediate context tells you everything you need to know, right now. Just as the algorithm tests the gradient to determine its progress, we should judge the value of a particular path by our own metrics – is it making us happier, more fulfilled, more purposeful? We can’t predict how something is going to work out in the future, but we can absolutely test the direction of travel, and go towards the one that minimizes our cost function in life – developing our sense of value and purpose, fulfilling the upper layers of Maslow’s hierarchy of needs – which states that, once we have fulfilled our most basic human needs such as food and shelter, our focus shifts to more ephemeral matters, such as the ability to feel achievement, find respect, solve problems and be creative.
And if that direction starts to become less favourable – the gradient is tailing off and you have less momentum and feel stagnant, numb or just not quite right – then change it. A gradient descent algorithm isn’t sentimental about its choices: it is happy to take two steps back if that means re-routing back onto the steepest path of descent. We should do the same. We need to be iterative in how we choose and adapt our pathways, changing course whenever we feel as though we are moving away from our goals and happiness rather than towards them. And we need to accept that there is no such thing as the one perfect path forwards: there’s only the path we have the willingness, interest and patience to discover and then pursue. Your ultimate route is always going to depend on factors other than objective perfection: the time you have available to explore options, and how perfectionist you are as a person.
The gradient descent algorithm teaches us to identify a path experimentally, through trial and error, constantly assessing and responding to our environment, and not being afraid to retrace our steps. Its last important lesson concerns not the direction of those steps, but their length. This is a problem known as the learning rate. For the most accurate results, you program an algorithm to take the equivalent of tiny steps, inching its way forward and slowly accumulating findings. By contrast, a higher learning rate means you may reach the valley more quickly, but because the steps are less precise you may simply step over the lowest point. Fine-tuning the learning rate, so you get the best results as quickly as possible, is one of the biggest challenges of gradient descent. An especially difficult thing to do with ADHD, where time warps, context blurs and you end up making the most important life decisions while sitting on the loo.
There is no perfect answer to this, because it can change, just as there is no one optimum path through life. Everything is subjective, and you need to pick the right balance between speed and precision. The perfect path does not exist – in our life or anyone else’s. From the available data, as represented in our network, there are numerous potential routes. As long as we let the evidence guide us, and keep hunting for the steepest gradient, we will find a way – in fact, I encourage you to have many ways. Just make sure they are ones which make you ‘tick’, and that you are equipped to do them.
Setting and pursuing our goals in life can be one of the most difficult things. There are so many considerations: should we pursue this ambition or that, optimize for the short or long term, do what makes us feel happy or what we think is most important? How do we create a vision for the future that is uniquely our own, and not beholden to those of other people? (One of the hardest things for a social, communicative species, but also one of the most important: living according to someone else’s benchmark is a bit like eating with their spoon – it never tastes right.)
All this is enough to induce an anxiety attack, as I should know, having been through more than my fair share. And it’s not just about the big, scary decisions in life. Last year I even failed to get my Mum a birthday card, as, having been to fifteen different shops, I couldn’t decide which one she would like best. I got too anxious about the decision and ended up not getting one at all. This is explorative thinking, a testament to my love for her that inevitably left me empty-handed, and in the dark. Maybe I should have drawn the line at shop number seven?
But being anxious about the future – or ‘not knowing’ what to do next – can be a strength and not a weakness. Quantum physics and machine learning demonstrate that uncertainty, and a willingness to change course, are assets rather than liabilities. Not being sure about our progress in life is a simple facet of our innate inability to effectively measure momentum and position in parallel. While the willingness to change course is machine-learning best practice – where ‘suck it and see’ is key.
So if you worry that you haven’t made enough progress in your life, or don’t know what comes next, allow science to reassure you. Those fears are natural. And the anxiety is helpful, acting as a lens through which to simulate any number of different potential paths. I have always seen it as my supercomputer, allowing me to make links and see possibilities that others cannot. People have told me not to be silly, or that I’m off my trolley, but I wouldn’t want to live without my anxiety and the ability it provides to scan the landscape, as well as the momentum it creates to learn more.
Setting and pursuing goals may be intimidating, but like any climbing challenge (a sport I love), it is just a matter of having the right equipment and personal endeavour. Heisenberg provides our belay, network theory our rope and gradient descent the route.
And remember, you’re trying to climb down the mountain, not up it.