..Being a follow up to the glorious 42 (earlier post) in being two times 42 (almost?) – strong, weak and electromagnetic (but not gravitational) at the same time! eh?
After I published 42, Fred, a physicist colleague commented that 42 is important in some very fundamental physics and he was disappointed that more hadn’t been made out of this. He also sent some evidence of this grave atrocity!
From my amateur interest in theoretical particle physics (I was a student of Murray Gell Mann, after all 😉 (Well, I can keep that suspense for another blog post) – I know that the search for the Grand Unified Theory (GUT) made some great progress (with ideas such as string theory). Basically, there are 4 fundamental forces – strong, weak, electromagnetic and gravity. It seems like while others have agreed to be unifired, gravity has been a b*** and has refused to be unified – Any UK/EU readers reading this post? 😉
Well, getting back to 42, apparently, at a particular high energy, the three ‘friendly’ forces become equal in energy of 1/42 (behold, 42 makes an appearance). If you go to the wikipedia page on 42 – you’ll find a number of entries of the importance of 42 – In fact, exactly 42 total entries under Mathematics, Science, Technology, Astronomy and Religion!! – wow, was that intentional?
Q: For a given number x, can I find x interesting things to say about it? I suppose there may be a way to do that!
Now, what about 88! Of course, 88 is two fat ladies! – that’s it! If you’ve ever had the honour to play Tambola! – I remember as a kid being carted around to Tambola games with my mother and family. At least, that adds to interesting things one can say about the first 90 numbers as listed on this Tambola nicknames site. Now, clearly the nicknames site has an Indian bias – where else would the nickname for the number 83 be India wins Cricket World Cup?
PS: ‘R u sure that 9 time 6 equals 42? My child has a different answer.’ – another comment from a careful reader! I hope you caught that in the last post! My answer, of course, would have been to ask Douglas Adams (if he was alive) or to query his faulty super duper computer yet again!
What are the distributed algorithms behind cell communication? Stuck in a sandpit, I and colleagues at QUB gather up some ideas which will hopefully also find some applications.
Ever been in a sandpit? When I was asked to be in one (called the Applied Maths Sandpit at our new EPS faculty.) I was not sure what it would be. It could be an innocent fun activity in the sand as in the first picture, an unlikely dream holiday at a golf course (as in the second picture), or, most likely, a grueling day which I was not forewarned of (third picture). As it turns out, it was rather nice and, ultimately, useful. There was no sand around, of course! (and neither was there much warm Sun, unsurprisingly for here).
PGA Golf Club, Port St. Lucie
A U.S. Soldier roughing it out in a sandpit! [http://www.defense.gov/Media/Photo-Gallery?igphoto=2001253076]
For a start, I met a few brilliant colleagues I did not know existed. Then, in a day of real intense cut-throat Dragon’s den like competition, we pitched our, mostly half-baked, ideas (btw, I am joking about the ‘cut-throat’, after all, we were (applied) mathematicians, not MBA enterpreneurs at the gathering!). Amazingly, at the end of it, our emergently formed motley crew of me, Fred Currell, Thomas Huettemann, Dermot Green and Alessandro Ferraro (All except me from QUB Maths and Physics) have been given resources to recruit and spoil a PhD student for a proposal that makes up the ideas of this post.
So, here comes a very high level, sparse, ambitious, and rough sketch:
Living organisms can be thought of as clusters of cells in communication (typically at gap-junction interfaces). Within interacting communities new cells are born and old ones are removed, through (sometimes programmed) death. There is a strong environmental influence on these processes. On a much smaller scale, quantum-mechanical processes are at work within cells, complicating the picture further. We think real life processes are efficient, fault-tolerant, self-healing and scalable, leading us to hypothise that there must be powerful distributed algorithms somewhere in these networks of cells waiting to be discovered.
Networks are often modelled as a graphs: the cells are nodes and a common surface between two cells facilitates communication. In biological systems, things change and this dynamism in networks is often addressed by failure models, including adversarial and accidental (random) death. The network can react to these changes in various ways and we seek a mathematical framework in which to formulate and analyse the various questions arising.
The team thought of three systems which could be of interest (some of the team already work on these though I know little about them at the moment):
- Volvocine green algae — These capture the evolutionary emergence of multicellularity, including what is believed to be the simplest multi-cellular eukaryotic organism: Tetrabaena socialis.
Rough outline of phylogenetic relationships in volvocine green algae.
- Light harvesting in photosynthetic organisms — the mechanism whereby living organisms harvest energy from light is believed to be one of the clearest biological systems countering the view that life is too “warm and wet” for quantum phenomena to be relevant.
A quantum machine for efficient light-energy harvesting (from the paper)
The tumour spheroid — a simple multicellular mimic of a tumour, this system is amenable to direct laboratory study and is known to show many of the hallmarks of cancer, including the lack of growth regulation mechanisms, meaning it seeks to grow avidly.
A study showing effects on size, shape and growth rate of tumours (from the paper)
The PhD advertisement is here (if you know of suitable candidates): http://www.qub.ac.uk/schools/eeecs/Research/PhDStudy/PhD-2016-17-65/
Talking of Maths sandpits, somebody is already working putting them to work: MathsSandPit.co.uk
Hunting for the ultimate questions and answers a la ‘hitchhiker’s guide to the galaxy’, and some rather ‘useful’ algorithms!
Might as well begin with the answer to the ‘Ultimate Question of Life, the Universe, and Everything’. I would have titled my blog ‘The Algorithm’ if I knew how to reach the answer! Of course, the answer is deduced by the supercomputer, Deep Thought, afterr 7½ million years of computation. Deep Thought then points out that the answer seems meaningless because the beings who instructed it never actually knew what the Question was. So, when asked to produce The Ultimate Question, Deep Thought builds an even more powerful computer (the planet Earth) to do so, which is supposed to run for 10 million years to find the question and so on…(and you know the rest). Of course, independently, the answer is also discovered to be 9 times 6 (equals 42)!
So, to begin with, here’s an algorithm ….
Question: Are you aware of other such fundamentally useful algorithms?