Understanding the mathematics of scaling towards a sustainable future for humanity.

There are some truly pressing problems in our times. These concern the survival of humanity. They can range from environmental to socio-economic such as climate change, world poverty, migration and gender inequality. These are problems which are prevalent in every city around the world. 

Today, the world is urbanizing at an alarming rate. The population is reaching unsustainable levels, especially since resources are finite. Growing population brings with it growing rates of crime, inequality and pollution. Thus, it is now more urgent than ever that we model and understand our cities better. 

While cities can be the problem, they can also point us towards a potential solution. They can be facilitators of social interaction leading to innovation. Due to their multi-variate and highly non-linear nature, cities have evaded a quantitative understanding until now. However, recent insights in the field of complex adaptive systems could be the key to solving these important problems.

A key feature of complex adaptive systems is the scaling properties they follow. These scaling properties are underpinned by predictive mathematical frameworks and can be written as power law equations. Such an equation looks like:

Y = A * X^k, 

The value of the exponent k determines the type of growth in the system. Linear growth — where if X doubles, Y doubles, and so on — results if k = 1.

‘Sub-linear scaling’ is the case where k < 1, in which changes in X result in less-than-proportionate changes in Y: if X doubles, Y will increase by less than double.

In physics, such scaling is observed in things like Kepler’s Laws, which relate the time period of a planet orbiting the sun and its radius. (In this case, k = 2/3.)

Biological systems, on the other hand, are continuously evolving, which makes them difficult to predict. But nonetheless, despite the extraordinary complexity and diversity of life, many of its most fundamental metrics follow similar scaling laws. This can be true of systems as small as cells and as large as ecosystems.

For example, comparing metabolic rates and body mass across species gives k = 3/4. Nature exhibits an inbuilt economy of scaling.

The problem arises when we have k > 1, which is known as ‘super-linear’ scaling. This implies unbounded growth and is unsustainable in the presence of finite resources. Unfortunately, as we will see, cities are systems which follow this kind of growth.

According to studies by complexity expert, Geoffrey West, the origin of such power laws lies in the dynamics of the underlying networks which constitute such complex systems. Every system  needs energy to survive. Networks help deliver energy in a system efficiently. In this way, they enable interaction between seemingly unrelated parts of a system leading to an emergent large scale behaviour. This is the field of complex adaptive systems. 

In the biological world, such a network is the circulatory system. The total (finite) amount of input energy is allocated between maintenance and the growth of a system. As the system grows, a larger volume requires higher allocation of energy towards maintenance which implies less energy for growth. This is what leads to bounded growth and eventually death.

West and his collaborators observed that there is a similarity between growth in the biological world and growth in our cities. Cities, like living systems, are continuously growing and evolving. More importantly, cities, just like biological systems require energy to survive and grow. However, unlike biological systems, cities seem to avoid senescence!

Studying the growth of infrastructural measures in a city, such as numbers of gas stations and lengths of roads and electrical cables, with population size, we see that these follow the same sub linear scaling (k < 1) as in the biological world. However, cities are much more than just infrastructure! In fact, the growth of socioeconomic quantities involving human interaction, such as wages, patents, AIDS cases, and violent crime with respect to increase in population size, follows a super-linear scaling (k >1)! This is a new and surprising class of phenomena separate from anything observed in the biological world. It also implies unbounded growth which explains why cities never stop growing! 

What is even more interesting is that despite their unique histories, cities all over the world exhibit universality by obeying the same scaling laws. These regularities have led to the beginnings of a quantitative framework of cities in terms of their underlying networks. In this case, these are social networks or transportation networks which are universal features of every city. Unfortunately, on earth, resources are finite. And thus, such an unbounded growth is unsustainable and predicts a collapse of the system once resources are depleted. This is known as a finite time singularity. 

Interestingly, human beings have avoided such finite time singularities by making a drastic paradigm shift after regular finite time intervals. Or in other words, we have had to innovate continuously in order to use our resources more efficiently. Examples of such paradigm shifts have been the discovery of coal, the industrial revolution, the discovery of clean energy sources, the IT revolution, digitalization of technology and discovery of automobiles. However, there is a catch. Each subsequent interval is smaller and smaller which implies that in order to survive, humanity needs to innovate faster and faster. Thus, it is important to understand what drives innovation in cities. The answer, perhaps unsurprisingly, lies in diversity. The more diverse a city, the more adaptable and resilient is it. Again, this has parallels in the biological world.

Thus, the need of the hour is this: Can we come up with a recipe for a sustainable future? The answer might lie in combining insights of complexity theory into concrete and smart implementable policies. 

Tricksters in the Sky.

Following my last post on black holes, I want to write a small post focusing on what other kinds of objects could be in the sky. A more specific question is: What other objects does General Relativity (GR) predict?

Also, physicists have long known that GR as it stands currently, cannot account for all the matter in the universe. In fact, 85% of the universe must be what we call “Dark Matter“. Now, whether Dark Matter could be made up of many possible things. And it could very well be made up of “dark” bosonic particles.

Turns out there are many possible “compact” objects in the sky. Schwarzschild metric is the metric which describes the space-time around a spherical symmetric static object and turns out it can be applicable to different kinds of stars such as normal stars (Luminous stars made up of hydrogen and helium), which could turn into red and white dwarfs, neutron stars and some other hypothetical stars known as Boson Stars. Mind you, here we are assuming that the Standard Model of Particle Physics is the only valid model for these stars.

My personal favourites are called Boson Stars, especially because they can mimic black holes. So what are these stars and how are they different from the usual stars as we know them?

Boson Stars (BS) are stars which are made up of elementary particles called “Bosons”. They are solutions to Einsteins Equations which can be found using numerical GR. One of the simplest kind of Boson Stars would have no self interaction force between the bosons other than being held together by gravity. However, in order to stabilise them, you would probably require some kind of repulsive potential between the bosons in order to stabilise them against gravitational collapse due to gravity pulling everything in.

Such a simple BS, would not have any electromagnetic radiation or light being emitted which would make them very hard to detect. In fact, they can have masses close to masses of black holes and without having any light emission, might not be indistinguishable from them! And this is why they caught my interest. They are like silent dark spies in the night sky, steadily spinning around without any one knowing about their existence. How exciting is that!

In a recent paper, me and my collaborators modelled a very simple Boson Star with a repulsive potential which could be made up of “dark” Bosons. Since these do not have any electromagnetic coupling, when two BS which are in a binary system, rotating around each other, finally collapse, they will radiate energy in the form of gravitational waves, just like black holes. We calculated the amount of gravitational wave radiation would be emitted from mergers of binary Boson star systems in the universe such as this one and we discussed whether detectors such as LISA and EPTA would be able to detect them or not. Turns out in certain ranges LISA might just be lucky!

Here a few favourite things about Bosons Stars that people have said on the internet and some lists it has found a place on:

All I can say is, if you exist, you go girl!! I am rooting for your existence!

Black Holes!

As a kid, I used to look up to the sky and try to count the number of stars. But I wasn’t as intrigued by what happened inside of them till I heard the story of black holes. For the first time, I was super intrigued by these seemingly super mysterious points in our universe. What are they? How are they made? What happens inside of them?

While the question of what happens inside of them might be the subject of another upcoming post, if scientists manage to crack that code, I did manage to learn about how they are theoretically predicted as well as experimentally formed. Lo and behold, stars had a lot to do with it!

In Einstein’s General Relativity, we can write down the Einstein’s equations and calculate the solutions to these equations. A particular class of solutions which are called as Vacuum Solutions, exist, among which the “Schwarzschild Solution” is a special one. This is a metric which describes the space-time around a spherically symmetrical mass in the universe and it looks like this:

If we calculate the poles of this equation, we find that the equation predicts an event horizon as well as a singularity! If a star many times the mass of the sun goes through the whole chain of nuclear fusion events and ends up quite heavy, it would at some point collapse under its own weight and would form a blackhole if it is trapped inside it’s own event horizon! At this point, the mass and gravitational force of this star becomes so high that not even light can escape the confines of the event horizon! And thus, we do not have a direct probe for the inside of this hole due to which it looks black to us!

And thus, it is a black hole!! And to top this post off, here is a picture of a blackhole swallowing a star!

Taken from here.

Diversity in Constructions: Who are our cities built for?

In this blog post, I will touch upon a not often thought of topic. How do architecture and physical details add to the lack of diversity in our workplaces?

I have been thinking about this for a while because for a long time, ever since I have been in cold countries, for example, Canada, UK, US and have been in a shared office, I have had to have an extra of 4-5 layers always on the back of my chair handy in case I needed them. And I inevitably needed them. Sometimes, the overall office temperature was just too low, otherwise my office mates (inevitably males) would get really hot and open the window. Now, this very innocent sounding details can be very very mischievous. Here is how. Every day, I would ask if I could close the window, once and then twice and would be too embarrassed the third time since it is hard to repeat the same things over and over again, and of course, their problem of feeling too hot was also legitimate. However, the age old adage of compromise for females usually clicked into my brain and even though I would try to push hard to stay there and work, the cold temperature would not allow me to after a bare half an hour and I would make some or the other excuse and go home for the day.

I was also very aware that this made me feel/seem like I was working less than others, so I worked weekends and week nights leading to a high level of mental stress. Not being in the office at strategic times also made me feel a little disconnected from many people who would eventually come to matter by the time I needed recommendations. This in a larger picture eventually leads to gender gaps. The gender data gap is both a cause and a consequence of the type of unthinking that conceives of humanity as almost exclusively male.

So, while I was thinking this, I never actively tried to look for data to see what that problem was and how to address this problem which was clearly structural. And a few days ago, I stumbled upon this article which presented the following data:

“The formula to determine standard office temperature was developed in the 1960s around the metabolic resting rate of the average man. But a recent Dutch study found that the metabolic rate of young adult females performing light office work is significantly lower than the standard values for men doing the same activity. In fact, the formula may overestimate female metabolic rate by as much as 35%, meaning that current offices are on average five degrees too cold for women. This leads to the odd sight of female office workers wrapped in blankets in the summer, while their male colleagues wander around in shorts.

Not only is this situation inequitable, it is bad business sense: an uncomfortable workforce is an unproductive workforce. But workplace data gaps lead to a lot worse than simple discomfort and inefficiency. Over the past 100 years, workplaces have, on the whole, got considerably safer. In the early 1900s, about 4,400 people in the UK died at work every year. By 2016, that figure had fallen to 135. But while serious injuries at work have been decreasing for men, there is evidence that they have been increasing among women. The gender data gap is again implicated, with occupational research traditionally focused on male-dominated industries.”

The link to the whole article is here for those of you curious cats who want to know more.

But here you go! Now, this is an example towards a very very important realisation. I was once told by a physicist, “if you are feeling confused about something, it’s because there is something new to learn there. It’s not invalid. ” And it applies to life! If you are uncomfortable, then it is probably because of a reason, and often it might be structural and wide spread. So talking and researching about these things might actually lead us to build more diverse, inclusive and efficient workplaces rather than blindly following data. As always, the question to ask is what are the possible causations towards a correlation?

And a more immediate question. What are the ways we can go towards unbuilding our gendered city and work spaces and work towards more contemporary inclusive architecture?

Complexity of Gender in Academia and how it adds to the Leaky Pipeline.

Hello everyone. Today, I have been talking to a collaborator of mine regarding the complexity of factors that adds to gender skewness in the workplace. Often I have attended workshops, conferences and events where participants focus on one aspect which leads to the “leaky pipeline” of academia, so to say. Now, just to put it here, I am not a big fan of the phrase “Leaky pipeline” but we will come to the nuances of language in another post.

Last year, I was invited as a Key note speaker to the WomenBeing Conference in Edinburgh where gender studies students presented their work on various topics ranging from how drug abuse rates are different in different genders, the rate of microaggressions faced by various genders, the power distance between supervisor and supervisee relationships, statistics on how race/gender/age determines who are victims of certain kinds of behaviours to domestic abuse and a variety of other factors. This was a wonderful conference full of great ideas and statistics, however, one thing which leapt out to me was how often we miss the intricate complexity of this topics and the interaction they have with each other. For example, a woman who is being abused at home and has a baby, and is also on her periods and in a lot of pain, would be highly prone to having low self esteem. If an interaction happens with an uncooperative boss, that puts her at a risk of aggressions that she would otherwise be able to handle better. This would inevitably lead to depression and anxiety, low performance and then become a self fulfilling prophecy of certain genders low rate of success if she drops out.

I have often believed that the metrics by which we measure success in our workplaces around the world are lacking in their depth of understanding the feedback loops of how each seemingly separate cause feeds into another one and eventually comes back a full circle. This is also the same principle as to how the rich become richer and the poor become poorer, not withstanding how “hardworking” each of these individual people are.

It is common knowledge that once you have one house, you can get loans to build more. And some more. You can rent the rest of the houses out and make more income and so would have a lot more property to show as collateral for your next loan. A tiny difference in the initial amount is often what separates an escalation of wealth from a downward economic spiral. Many other micro-factors add to this. We have all heard the age-old adage of “The First Impression is the Last Impression”. Now, let us compare someone who has money to splurge on “Smart office wear” and is not irritated by not eating a healthy diet, has enough money to spend on child care or has a live-in spouse (often female) at home and so is not distracted at meetings and is able to commit to his work fully while looking dapper to someone who has to juggle multiple shifts, does not have enough money to splurge on a comfortable work wear and has to rush back home to take care of the baby. The strain on their face would show, making people view them as less trustworthy and motivated. This would eventually lead to loss of opportunity. And such examples can be many and varied.

However, in the conference, I decided to take the opportunity to sketch an interaction slide showing the interaction between seemingly disparate topics and how each of them eventually add to the Leaky Pipeline of Academia. The problem is not motivation which can be easily proved by a multitude of statistics. The problem is the lack of proper infrastructure and the delegation of microaggressions and unpaid (often emotional among others) labour onto certain demographics. Here is the slide which provides a (incomplete) list of many tiny details which add to the low percentage of women in high positions.

The conclusion here is that there is an intricate relationship between poverty, comfort, economics, brain power, psychology which overlap with gender, race and privilege. I will pick small topics and go on to talk about these in more detail in my future posts.

Cool Animations and Softwares to use for them.

Recently I have been obsessed with cool animations as I described in my last post. I then went around searching for even more and the world of tumbler and pinterest did not disappoint! Check these bad boys out (all of them are from Pinterest and Tumbler):

These look like some of the simplest ones to start with I am guessing, and I am going to use Processing and Blender which are open source softwares to learn how to start making these. The goal would be to move on to the following type of animations in the near future:

I am really excited to see what the next few weeks bring!

Beautiful Animations

Recently, when I was revamping my website, I was searching for cool animations to satisfy the sci-fi junkie inside of me and also to motivate myself to learn how to create some of those. I will post some of these amazingly funky animations here for your entertainment. Note that none of these animations belong to me or are created by me. I stumbled upon them in random google searches using random keywords.

How cool are these, huh!!

Inclusive Logic

A little bit about debating and privilege. It would be great to have the privilege to debate on everything as an academic and an ideal world exercise, but it is important to recognise that doing so, validates violence as a trickle down effect into the present day lives of many. Most debates I have seen in present day facebook are mostly by demographics who are not directly affected by the consequences of their so called academic enquiry. For example, a whole thread on abortion laws, where after the first five arguments, the women have disappeared. A whole thread on the Strumia comments, when (sometimes straight) white males (or people from a privileged background) argue about how no-platforming is not an option, and it continues, so on and so forth. If you have not faced a certain issue, it makes sense to learn from demographics who actually do face it rather than debating with/about them to satisfy one’s emotional satisfaction for a debate. In the search for an ideal world, we must be careful not to build an “ideal world” upon the broken skeletons of those demographics who do not fit into your neat pursuit of logic. Rather, inclusive logic is that which takes into account how things are in reality. In all of our realities. 

Can we, as humans, refrain from turning debate into a colonialism of someone else’s humanity and an invalidation of their self. Can we stop treating silence as assent? Or powerlessness? But rather recognise our own ability of eloquence as privilege?

This is in solidarity with something I saw on facebook written by someone called Sarah Maddux :

“When you debate a person about something that affects them more than it affects you, remember that it will take a much greater emotional toll on them than on you. For you it may feel like an academic exercise. For them, it feels like revealing their pain only to have you dismiss their experience and sometimes their humanity. 

The fact that you might remain more calm under these circumstances is a consequence of your privilege, not increased objectivity on your part. Stay humble.


Inclusive STEM, it’s time to stop being Hypocrites.

Last weekend, I was at Amsterdam representing the University of Sussex as a part of our equality and diversity team. My team comprised of Claire, who is the Vice-Chancellor of Equality and Diversity, Nicola, Katy and finally Daniel .. whose project “Grapheel/IRIS” we were showcasing. The team got ready to deploy after a lot of brain storming and a slide show showcasing all the different initiatives that have been applied and have been really successful at Sussex. But Grapheel/IRIS, was a completely different project to be showcased in the conference than any others, because IRIS is a community app designed by Daniel, who is a blind physicist, for other vision impaired researchers like himself to have the resources to understand scientific figures better. How amazing is that?

Claire started her talk talking about how Sussex has been going about building a more inclusive Sussex, not just for people who have everything “normalised” going for them in the world, but for everyone who our ancestors should have taken into account before designing the structures of this world and the essential tangible and intangible structures in the work place. This includes women, LGBTQA people, people with a wide range of disabilities, carers, people who are trying to remake themselves such as ex-prisoners with a record, less-economically able people, racial minorities and so on. Claire focussed on how we can use our research expertise and our brain power to take these steps to completion and ensure their execution and at the right moment, Daniel jumped in to talk about how he lost his vision some five years back and how he did not want to let the various frustrations push him away from his passion to do research and he combined “Be my eyes” and “Citizen Science” to create a love child called “IRIS”. You can check it out here and sign up to become one of their esteemed ambassadors here.

For me, the conference was really really amazing. And in this blog post I would like to summarise the various things I took away from this conference and what I in turn, contributed to it. The conference was amazing in the way it brought together university policy makers, university professors and researchers working on the best way forward for an inclusive atmosphere.

  1. Inclusivity in AI training. We were shown the video clip of the AI humanoid Sophia
    as well as extensively discussed how easy it has been to past and present AI’s to learn from human bias on the internet and perpetuate this much faster. AI safety and AI governance has become a big issue, however I propose that we call it AI education to start from the bottom up approach of educating AI’s on diversity and inclusivity principles, starting them off with the right questions and data sets rather than go back and correct mistakes we see in retrospect.
  2. Redefining the definition of excellence in academia. Excellence is a spectrum which should potentially include normalisation to include challenges specific demographics face. This picture says a thousand words.
  3. Inclusivity in architecture (toilets, temperature) geared towards all genders, orientations and disabilities.
  4. Using our own scientific research to further an inclusive STEM.
  5. How to take into account invisible “disabilities” such as sexual abuse, or family responsibilities, emotional abuse, even pain during menstruation and fertility treatments which certain demographics undergo as opposed to other and how a lot of this and more certainly contributes to a power distance ( along with how it depends on the culture).
  6. How to make sure we go beyond unconscious bias but also consider and address conscious bias.
  7. How to overcome bias against ex-convicts in academia and the responsibility the media has.

There was a lot of debate and discussion on how to make sure we, as human beings can fluidly put ourselves in some one else’s experiences rather than denying them as something “foreign” and “lies” since we did not experience them firsthand. Related to this is the issue of addressing backlash against liberal movements and understanding since the losing of privilege does not come easy to people.

Would an AI government be able to fix these things? Apparently not, since the present day AI technology is spearheaded by straight white men who form only the creamy layer of a certain demographic. And the question remains, how do we go ahead?

If you wanna talk to me, I would very strongly argue that we need to go beyond and above, calling all of these “women”/minority issues since this is just excuse culture. As Claire says, these are things which should have been normal in humanity since time immemorial. We have screwed up and are forced to do error correction and so, let us all call these measures as “Ecosystem management” and make it everyone’s responsibility since we all share the same ecosystem.

Here are some slides from things that sussex has done in strive towards an inclusive STEM policies which I put together and you can find here.


Equality in STEMM Conclave

So, I am thrilled to be representing Sussex tomorrow at the Equality in STEMM conclave at Amsterdam as part of the Equality and Diversity Group. In the light of that, here are some amazing slides I made showcasing all that Sussex is working for. ❤ Let’s all move towards building a more inclusive STEM!

Find the slides here!