I’ve always loved mathematics. It is such a beautiful tool for solving difficult problems. Eventually I realized that I could apply mathematics to the problem of achieving happiness. The result has changed my life and started me on an incredible journey. I have a long way to go, but I’m happier and more compassionate than I’ve ever been before. I hope this post can help others be happier as well.
Becoming a State Space Traveler
Imagine that life and the pursuit of happiness is really an optimization problem. Imagine that we spend our lives traversing a gigantic endless landscape full of mountains and valleys. The landscape represents the space of all different possible beliefs, values, and experiences that you can have at any moment: your state. And the height of the landscape represents how happy you are at that state. Imagine that the lower you are in the landscape, the happier you are.
That’s why most people take the path of least resistance. They spend their lives walking straight down hill or squatting at the bottom of a valley; because that’s the most comfortable place to be. But this presents a problem: when you’re at the bottom of a valley, you can only see places that are higher up than you, in this case, states where you would be less happy.
So it is easy to make the mistake of thinking that there is no point in exploring your landscape. It’s hard to imagine that there might be deeper valleys beyond the ridgeline of your own.
Here is a common example of how we get stuck in local minima: many people spend their lives in ‘the valley of money,’ where the local minimum is defined by having as much cash as possible. When you consider the ultimate goal of the money valley, you realize the futility of such optimization. Whether you have ten dollars or ten billion dollars, you are no closer to your ultimate goal of infinite money. Consider that most people who win the lottery end up no happier one year later. They’ve got the money, fame, and freedom, yet they can’t get themselves any closer to being truly happy. Why is this? Why can’t they escape the valley of money?
Our ancestors evolved to optimize for local minima such as sex, security, and resources. Once we have settled into local minima, we grow comfortable and see no reason to leave. And it doesn’t help that we are all automatically born into the local minima that our parents occupy. That is why the vast majority of the world believes in the same religion as their parents and holds the same cultural values. These local minima are vast and very difficult to escape. Most of us have no idea that a great landscape even exists beyond the walls of the local minimum into which we were born.
Leaving the comfort of your local minimum is unsettling. Even though taking that step requires confidence, you appear less confident to the outer world because you are not sure what you believe in. You lose your values and your convictions. You no longer know what is right and what is wrong. You can no longer make yourself feel superior by passing judgement on others. You lose your sense of identity and must expose your ego directly to the fact that you don’t actually know everything. Many people who have been through this share a common shocking experience: “I suddenly realized that I actually knew nothing.”
But for those of us trapped in a local minima, once we decide to climb out and ascend a high ridge of uncertainty and discomfort, we will see a whole beautiful world that was invisible to us from the valley, a vast landscape full of far deeper valleys than the one you came out of. And you will also see even higher mountain ranges in the distance that stretch up into the clouds. And you will know that to find out what is beyond them, you must climb their steep cliffs. When you occupy these high places of discomfort, you feel lost and exposed. It is windy and cold. But from there it is much easier to descend back down and ultimately reach deeper valleys and get closer to finding your global minimum: true enduring happiness.
Simulated Annealing: A Mathematically Proven Way to Find True Happiness
So we’ve established what you have to gain by leaving your current local minimum. But you also can’t spend your whole life exploring randomly through the state space because one day you’ll drop dead. So given the constraints of the human life time, what is the best strategy for traveling the state spaces and achieving true happiness?
1. First of all, give yourself as much time as possible.
In other words: exercise regularly and don’t eat crap food. The longer you live, the more exploring you can do, and the more time you can spend enjoying the benefits of your exploration and changing the world. And maybe you will live forever.
2. Increase the size of your state space.
This means consider every possible idea, belief, and value no matter how crazy or wrong they seem at first. Think about how many great scientific discoveries came from mistakes in the lab, or how many great companied evolved from bad initial ideas. People with the largest state spaces change the world. They are the ultimate creative types and big dreamers whose singular visions define humanity’s achievements. These people are always open to the newest experiences and cherish the craziest ideas. They surround themselves with people from diverse backgrounds and don’t let their egos blind them to critical feedback.
3. Use simulated annealing to search your state space.
Simulated annealing is an algorithm that can find the global minimum of a state space. Which, in our case, means finding ultimate happiness. In fact, it has been proven that under certain conditions simulated annealing can always find the global minimum of any arbitrarily large state space. This is a very exciting idea but how does it apply to our lives?
To answer that we need to know how simulated annealing works. Imagine that there is a ping pong ball and you want to get it to the lowest point in a landscape. To perform simulated annealing, you would heat up the temperature of the landscape so that the ping pong ball starts bouncing around crazily and randomly between all the different places. After heating up the ping pong ball to very high temperatures, you slowly lower the temperature. As the temperature lowers, the ping pong ball bounces around less energetically and slowly starts to settle down in lower parts of the landscape.
It has been mathematically proven that if you heat up the landscape to an infinite temperature and lower that temperature slowly enough, the ping pong ball will always end up in the global minimum of the landscape. Even for an infinitely large landscape.
So how can we apply this mathematical proof to living our lives? Well if we heat the ping pong ball up to an infinite temperature, this means it randomly moves around the landscape at an infinite speed and is simultaneously at all locations and also no location. The ping pong ball doesn’t occupy any single state. For us, this means we must do the same and completely clear our minds of all beliefs and values. This is very hard since from birth we’re inundated with belief systems. However, meditation is a powerful practice for emptying our minds and releasing ourselves from preconceptions.
From this place of clarity, we are completely free to explore any part of the state space without bias and beliefs that were embedded in us as children. This is the part where you slowly cool down your state space and start considering new beliefs and values. However, given that our state space is very large, this must be a very careful and slow process. But if we live long enough and chose those values slowly and carefully enough, we will eventually reach ultimate happiness. It is a mathematical certainty.
Firstly, try this on for size: http://en.wikipedia.org/wiki/Paradox_of_hedonism
You will find that J.S. Mill and other philosophers would reject the underlying premise of your post, specifically that a “strategy” to achieve happiness would ever result in happiness.
A few suggestions:
A. Define “ultimate happiness” – without a working definition your post is irrelevent and hopeless.
B. Your entire post is steeped in”belief systems” “preconceptions” – once you realize this you will realize the hopelessness of your project to “empty” your mind of these.
C. The fact that as a recent college grad you are even attempting to answer/give advice to the question you posed, “what is the best strategy for traveling the state spaces and achieving true happiness?”, is mindbogglingly arrogant.
It’s nice that you like Mathematics……and I appreciate your attempt.
thanks i liked that.
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Thanks for the link, Anonymous. And for sharing your interesting thoughts. I don’t appreciate the ad hominem comments but, on the other hand, I’m just really excited to have my first two comments ever on my blog!
To answer your points:
a. I don’t define happiness explicitly because each person has their own state space and their own definition. The idea behind the model is that it’s very abstract and relies on very few axioms. All you need are states (define however you want: values, beliefs, experiences etc…) and a heuristic for valuing those states (happiness, physical pleasure etc…). You can choose your own specific definitions.
b. I agree somewhat. It is paradoxical. But that is the point. Dealing with paradoxes forces us to question everything and clears our mind. Emptying your mind is not hopeless. I’m not great at it, but through meditation you definitely notice a big difference.
c. I’m sorry you find it mindbogglingly arrogant. This approach made me significantly happier and other people I’ve explained it to said they found it very helpful and said I should write about it. I’m sorry it didn’t help you. I think my only qualification for writing this is my own happiness that I’ve experienced as a result of eating my own dog food. Just because I’m young doesn’t disqualify me. There are many older people who are very unhappy
Thanks for the comment though. Having a blog is really exciting…
This is awesome!!!! really made me think and explains why people fall into class systems so easily.
“Anonymous” from the posts before sounds like a huge dick. He is probably just super unhappy…
I more or less agree with Anonymous. This whole idea is a nice attempt, but it’s fundamentally just too naive and relies on several bold assumptions, such as:
(1) We have an accurate model of our local “happiness terrain.”
(2) Happiness always lies “upward” and unhappiness always lies in local minima.
(3) Happiness is a function of a set of variables and can even be thought of in terms of state space.
(4) Meditation is an effective way to rise above local minima. (Clearing your mind does not necessarily open your eyes.)
(5) Our inborn biases and cultural assumptions are barriers to our happiness rather than tools for reaching happiness.
(6) The cost of searching the state space is negligible (hint: only in pure mathematics can search cost negligible…because you don’t actually worry about carrying out the search).
(7) That the global maximum of “ultimate happiness” is significantly “taller” than the local minima that are easily reached.
(8) And finally (and this is the biggest assumption of all), that people are happier when they are given more choices.
I think everyone should count for themselves how many of these assumptions they are willing to accept. Number 8 has actually been disproven by psychologists and is sometimes called “the paradox of choice.”
I like mathematics too, and I use state space concepts on a weekly basis, but generally speaking mathematics has little to say about human feelings or life in general.
Irrefutable truth. The proof is in the pudding. Math and happyness baby.
ultimate happiness is intuitive — if someone has to define it for you then it will forever elude you (even with a technical definition firmly in your grasp)
great post
True happiness lies within. When we stop searching for it in external objects or expectations, happiness is the natural state of being. Seekers will always be seekers, and finders will always be finders.
Mathematics is a beautiful thing, and it can be a metaphor for the internal as well as the external. Mind made belief systems, ego identities, and thought patterns are like abstract parameters in an infinite dimensional space. Annealing can be thought of as metaphor for transcending these mind made hindrances to ultimate realization. This is a creative piece of work.
Wisdom doesn’t know time or age. It finds those who are ready, youth and aged alike. Let us all respect one another, whatever stations in life we may occupy!
Be healthy, happy and loving,
Miro
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Awesome blog Carter and agree with some of the comments from Miro: this shows mathematically through simulated annealing that happiness is not found it's a process of you being in the moment and the moment taking you to the global minimum
hey. I like your formulation of the problem of happiness. “A mathematically proven way to find..” is a bit deceptive though, I think you mean “a mathematically justified technique…”
In either case, I think you are throwing away some useful information though. If you wanted to know your future happiness with some new situation in life, looking at a person in a similar situation would be a better predictor than your own guess for yourself. Since one thing we, as people, have that ping-pong balls do not is the ability to communicate, we do not have to undergo this search alone. There are actually many many slightly different ping-pong balls and they can more or less tell each other about their local space. (In fact their spaces may even be a partially relative or interdependent property…)
In reality if you wanted to find the lowest (or highest) pt. in a conventional physical geography, you probably wouldn't just bounce around, exploring. You would see where other people have been and you would make or get a map of the terrain. Why can't you do this with happiness?
Actually I am trying to do this. I have only just started, but please look at my sight and tell me about your space or how you think this map could be made… 33dsoul.com
Yes, it's very true that to model our state space more accurately we could
add in properties such as communication. Another very important property
that we have which ping pong balls don't is memory.
But of course all these additional properties come at a cost and complexify
our model.
Instead, the actions of communicating with people and the property of memory
can instead be considered as components of a state. So instead of adding
more rules to our state space, we just redefine our state space as taking
into account these actions and these properties.
So for example, the action of observing other people and asking them why
they're happy means you have explored into different states that correspond
to these actions.
In this way we have re-mapped our state space, and are now back to the
.
simple original problem of solving for the global minimum. The beauty of
abstraction
Interesting post — reminded me very much of http://cdixon.org/2009/09/19/climbing-the-wrong...
Both similar and powerful ideas on applying math to life philosophies.
http://www.ted.com/talks/daniel_kahneman_the_ri...
I am a monk living in a bhakti-yoga ashram in India.
Interesting thoughts my friend. Because landscapes in the world are so variegated, this provides a rich metaphor with a lot of possibilities.
Regarding trying to come to full happiness within this lifetime, I agree we should strive for that. Of course, I'm sure you're aware, being interested in meditation, that the general consensus in the eastern part of the world is that this is not our only life, and that just as we sleep every evening and renew our activities the next day, we die at the end of every life and continue the trend of our activities in the next. According to this conception, we can continue our work within our consciousness in our next life where we left off in this one. (although being born again is said to be a bit of a hassle)
Thank you for your insight, Venu. I can't tell you how exciting it is to garner reactions and perspectives from such interesting places. I can feel my own state space expanding as a result
.
I'm curious how you find out about this blog?
Regarding reincarnation, I think that it is a great way to view life, since we should always be trying to create value for the world to inherit once we are gone. Likewise with karma, I think it is the optimal framework for how we treat others. However, beyond using these concepts as a way to make decisions in life, I see no evidence that reincarnation is physically possible. Is that what you're suggesting? I'm curious to hear your thoughts.
Nice read.