Infinite in All Directions: Knowledge’s Demesnes, Cybersec Games, Langton’s Ant

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Credit: fdecomite/Flickr, CC BY 2.0

Credit: fdecomite/Flickr, CC BY 2.0

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We begin.

Rationalism v. empiricism

Last week, The Wire published a story about the ‘atoms of Acharya Kanad‘ (background here; tl;dr: Folks at a university in Gujarat claimed an ancient Indian sage had put forth the theory of atoms centuries before John Dalton showed up). The story in question was by a professor of philosophy at IISER, Mohali, and he makes a solid case (not unfamiliar to many of us) as to why Kanad, the sage, didn’t talk about atoms specifically because he was making a speculative statement under the Vaisheshika school of Hindu philosophy that he founded. What got me thinking were the last few lines of his piece, where he insists that empiricism is the foundation of modern science, and that something that doesn’t cater to it can’t be scientific. And you probably know what I’m going to say next. “String theory”, right?

No. Well, maybe. While string theory has become something of a fashionable example of non-empirical science, it isn’t the only example. It’s in fact a subset of a larger group of systems that don’t rely on empirical evidence to progress. These systems are called formal systems, or formal sciences, and they include logic, mathematics, information theory and linguistics. (String theory’s reliance on advanced mathematics makes it more formal than natural – as in the natural sciences.) And the dichotomous characterisation of formal and natural sciences (the latter including the social sciences) is superseded by a larger, more authoritative dichotomy*: between rationalism and empiricism. Rationalism prefers knowledge that has been deduced through logic and reasoning; empiricism prioritises knowledge that has been experienced. As a result, it shouldn’t be a surprise at all that debates about which side is right (insofar as it’s possible to be absolutely right – which I don’t think ever will happen) play out in the realm of science. And squarely within the realm of science, I’d like to use a recent example to provide some perspective.

Last week, scientists discovered that time crystals exist. I wrote a longish piece here tracing the origins and evolution of this exotic form of matter, and what it is that scientists have really discovered. Again, a tl;dr version: in 2012, Frank Wilczek and Alfred Shapere posited that a certain arrangement of atoms (a so-called ‘time crystal’) in their ground state could be in motion. This could sound pithy to you if you were unfamiliar with what ground state meant: the thermodynamic condition wherein an object has no energy whatsoever to do anything else but simply exist. So how could such a thing be in motion? The interesting thing here is that though Shapere-Wilczek’s original paper did not identify a natural scenario in which this could be made to happen, they were able to prove that it could happen formally. That is, they found that the mathematics of the physics underlying the phenomenon did not disallow the existence of time crystals (as they’d posited it).

Credit: Kenneth C. Zirkel/Wikimedia Commons, CC BY-SA 3.0

Frank Wilczek. Credit: Kenneth C. Zirkel/Wikimedia Commons, CC BY-SA 3.0

Shapere and Wilczek turned out to be wrong.

By late 2013, rigorous (formal) proofs had showed up in the scientific literature demonstrating that ground-state, or equilibrium, time crystals could not exist – but that non-equilibrium time crystals with their own unique properties could. The discovery made last week was of the latter kind. Shapere and Wilczek have both acknowledged that their math was mistaken. But what I’m pointing at here is the conviction behind the claim that forms of matter called time crystals could exist, motivated by the fact that mathematics did not prohibit it. Yes, Shapere and Wilczek did have to modify their theory based on empirical evidence (indirectly, as it contributed to the rise of the first counter-arguments), but it’s undeniable that the original idea was born, and persisted with, simply through a process of discovery that did not involve sense-experience.

In the same vein, much of the disappointment experienced by many particle physicists today is because of a grating mismatch between formalism – in the form of theories of physics that predict as-yet undiscovered particles – and empiricism – the inability of the LHC to find these particles despite looking repeatedly and hard in the areas where the math says they should be. The physicists wouldn’t be disappointed if they thought empiricism was the be-all of modern science; they’d in fact have been rebuffed much earlier. For another example, this also applies to the idea of naturalness, an aesthetically (and more formally) enshrined idea that the forces of nature should have certain values, whereas in reality they don’t. As a result, physicists think something about their reality is broken instead of thinking something about their way of reasoning is broken. And so they’re sitting at an impasse, as if at the threshold of a higher-dimensional universe they may never be allowed to enter.

I think this is important in the study of the philosophy of science because if we’re able to keep in mind that humans are emotional and that our emotions have significant real-world consequences, we’d not only be better at understanding where knowledge comes from. We’d also become more sensitive to the various sources of knowledge (whether scientific, social, cultural or religious) and their unique domains of applicability, even if we’re pretty picky, and often silly, at the moment about how each of them ought to be treated (Related/recommended: Hilary Putnam’s way of thinking).

*I don’t like dichotomies. They’re too cut-and-dried a conceptualisation.


Game theory + cybersec

Say Ashley hacks into Bismillah’s computer and steals some information – a.k.a. perpetrates a cyber-attack. Depending on whether Bismillah can defend against the attack, has the ability to attribute the attack to Ashley, punish Ashley or will simply have to tolerate her, a group of American researchers have been able to use game theory and elucidate four questions relevant to cybersecurity policymaking in the process. It’s a fairly simple method with an ability predict outcomes quite in line with we’ve actually seen happen in reality. The four questions that arise from analysis of this fashion are:

  1. Under what conditions will peace (i.e., ‘no attacks’) be possible?
  2. When will a mischievous third party or accident destabilise the ‘no attacks’ situation?
  3. When should cyber-attacks be tolerated?
  4. What are the consequences of asymmetric technical attribution capabilities?

These arise, according to the researchers, when Ashley and Bismillah square off over their knowledgeability (k) and vulnerability (v). Knowledgeability is the precursor to attribution whereas vulnerability dictates the susceptibility to attack, so between them, they represent the offensive and defensive sides of cybersecurity.

Key to the researchers’ analysis is a real-world consequence attributed to each of these outcomes – as, for example, representing these possibilities:

  1. Ashley is vulnerable and Bismillah knows;
  2. Ashley is invulnerable and Bismillah knows;
  3. Ashley is vulnerable and Bismillah doesn’t know;
  4. Ashley is invulnerable and Bismillah doesn’t know.

In other words, depending on Ashley’s and Bismillah’s positions at the beginning of each game, these are the four types of possible games. Secondly, the series of games are Bayesian, which means the outcome of each game is dependent on the outcome of all the other games before it. Though this isn’t evident from the four combinations presented above, it’s relevant in each of their aftermath.

For example, if Ashley is vulnerable and Bismillah doesn’t know (outcome #3), then Bismillah will blame Ashley if he is (wrongly) confident that Ashley is vulnerable based on how she’s responded in previous games. Similarly, if Ashley is invulnerable and Bismillah knows (outcome #2), then he will blame her if he has accrued a cost of inaction. Inaction’s value often outside the technical game and within politics.

In these circumstances, the researchers figure that a ‘no attacks’ situation can arise if both players are vulnerable and if both of them are aware of each other’s vulnerability. However, if they’re unaware, then the researchers say that Ashley and Bismillah will both hold back if the rewards for attacking are lower than the gains.

Although neither knowledgeability nor vulnerability are as out in the open in the real world as they are within the researchers’ equations, the game theoretic approach appears fairly robust – and simple – in being able to model how cyber-attacks are likely to play out, especially in relation to the foreign policy sphere of two nations in conflict.



India has a shortage of astronomers, according to an article hosted on the Vigyan Prasar website. This is not something I thought would be the case: India has AFAIK been an astronomy powerhouse, with a slew of satellites observing the universe in the gamma-ray, X-ray, infrared, UV and visible parts of the spectrum. The country is home to some powerful telescopes, such as GMRT, GRAPES, MAST, MACE and PACT – as well as ASTROSAT. But the Vigyan Prasar article, by Dinesh C. Sharma and P. Sunderarajan, quoted astronomer Sheo Kumar Pandey to write:

A country of 1.2 billion people has just 500 to 700 professional astronomers who are engaged in research. “We need at least ten times this number in the years to come to handle all scientific work and data emanating from these mega science projects,” Prof Sheo Kumar Pandey, President of Astronomical Society of India, said on the sidelines of annual session of the society here on Tuesday. “It is good that there has been a profusion of big projects. It is highly welcome. But there is a major shortfall of manpower. The new opportunities would generate lot of data. These needs to be analysed and made use of,” Prof Pandey added.

I thought the last bit was true only in the context of ASTROSAT, and more so in the case of the Mars Orbiter Mission, since ISRO’s data-processing pipeline is not as good as it needs to be. But if it is the case that we don’t have enough astronomers working on post-observation capabilities, then we’re in trouble because our telescopes are always passively competing with others of their kind around the world in terms of being able to deliver data ASAP, and latency can be a strong disincentive for international collaborations.

“We also need to develop data centres and a networks to handle and analyse data that be flowing from mega science projects,” Prof Pandey said. Dr G C Anupama, dean of faculty of sciences at the Indian Institute of Astrophysics, Bangalore said that engineers – civil, mechanical, electrical – capable of handling projects in astronomy were required, in addition to those trained in software and electronics.


Langton’s ant

If you haven’t played Conway’s Game of Life (CGL), you should. It’s endless hours of fun and is among my favourite video-games of all time – even if it doesn’t exactly fit that category. CGL is basically a cellular automaton. Its canvas is an infinite grid of cells, or boxes, and each box has two conditions: live and dead. Imagine it like this: a live cell is coloured in, a dead cell is left uncoloured. Now, to the rules (which I’ve just copied from Wikipedia):

  1. “Any live cell with fewer than two live neighbours dies, as if caused by underpopulation
  2. Any live cell with two or three live neighbours lives on to the next generation
  3. Any live cell with more than three live neighbours dies, as if by overpopulation
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction”

These rules are implemented in steps beginning with step 0 (i.e., the initial conditions). So based on the configuration of cells at each step, the next step evolves – like all living things. People have been able to create all kinds of things using the CGL, including representations of blinkers, spaceships, ‘glider’ guns, pulsars, trefoil knots, a 48-step oscillator and even a full-blown Turing machine. Seriously, the possibilities are endless.

My favourite CGL is much simpler, however. It’s called Langton’s ant and operates with a different set of rules. From Wikipedia:

  • “At a white square, turn 90° right, flip the colour of the square, move forward one unit
  • At a black square, turn 90° left, flip the colour of the square, move forward one unit”

So, start with an arbitrary configuration of live cells on the CGL grid and drop the ant on any cell. Then, the magic begins. For the first few hundred steps, the ant moves around in small, almost symmetric patterns, and then it goes berserk. It begins to trace a larger, more irregular pattern for the next 10,000 or so steps with no apparent long-term predictability of what’s going to happen. And then, around 11,000 steps, something awesome happens: the ant begins to form a repeating 104-step ‘highway’ (see image below) that keeps going infinitely.

Screen Shot 2017-03-13 at 8.52.53 AM

Try it out.

While researchers have been able to show that, no matter what the initial configuration of live and dead cells on the CGL grid is, Langton’s ant will always play out the same way: a short period of symmetry, a long period of chaos and ultimately an infinite highway. As a result, the highway is referred to as an attractor: a general term for the conditions into which a chaotic system eventually settles. However, researchers have no clue why.

Anyway, I didn’t just write this out of the blue. A few days ago, I spotted that someone had built a digital clock – a DIGITAL CLOCK! – on CGL. Each change of the seconds number requires a whopping 11,520 steps, so infinite props to the person who built this beautiful beast.




Other bits of interestingness

(Lots this week)

  • Poetry: Small insects and their place among main-sequence stars
  • More evidence that Mars had a water-rich history
  • So what do we know about Mars so far?
  • If you use Google Chrome and are often looking up scientific papers, I very highly recommend this extension. If you land on a page with a paywalled paper, it automatically looks for OA alternatives on the web and provides the link.
  • Book review: Global Warming Primer
  • Do scientists lack empathy? A short essay
  • On the place of naturalism and instrumentalism among quantum mechanists (“Perhaps the great scientists all want to be philosophers in secret, since the utilitarian value of instrumentalism seems hollow and ultimately a dead end”)
  • NASA (Numerology Astrology Sastra Administration)
  • It’s been 50 years since the Outer Space Treaty was opened for signatures
  • The tortoise whose sex drive saved his species
  • Tutorials on how to spot and call bullshit in statistics
  • Researchers in Germany are trying to measure the background noise of vacuum

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