Recently there has been a little buzz around the new paper by Erik Verlinde (excellently reported by Natalie Wolchover) on the new theory of emergent gravity that apparently can take a shot at explaining the phenomena attributed to dark matter in a different (and fascinating) way.

I must admit that I am overly excited by theories like this, since they hit right at my sweet spot. I have been fascinated by emergence of a complex structures from more basic rules ever since I first learned, as a teenager, about the Conway's Game of Life and Mandelbrot set (it is not a coincidence that both can be found in the examples in my assembler packages). These are purely mathematical constructions and I then studied theoretical mathematics myself, but later I started to appreciate more and more the emergent mechanisms that show up in other disciplines, like physics. I now hold the statistical mechanics in high regard, as it shows how a things like temperature and thermodynamics naturally emerge from the microscopic structure of matter through the statistical regularities. (I have once written a couple of texts for a friend where I tried to explain the emergence of temperature and pressure to someone with only very basic knowledge of physics. I though I could even share them here, but since they were written in Polish, they would probably end up being read through some kind of automatic translator - after a quick look at the maimed text that Google Translate made out of one of them I concluded that it is not the right direction.)

We have been discussing such topics many times with Ender (usually over a coffee) and we played with idea that things like gravity, space and time might also be an emergent phenomena. But neither of us is proficient enough in physics to actually try pursuing such ideas on the current frontiers of science. All that we are left with then is to get excited when we see the works of people like Verlinde.

Even when such ideas fail to provide a complete model of observed reality, they still may give an interesting insight when they demonstrate how some of the regularities found in real word can be generated from simpler constituents as an emergent feature. It then hints that the same mathematical structures may also show up in a different framework and produce similar regularities in other model.

The other day I saw a brilliant MinutePhysics video which uses a well-chosen example to demonstrate how the same mathematical regularities may show up in a different models. When there is an idea how a given complex behavior may emerge from something simpler, it is highly probable that any better model would also contain a similar mathematical emergence in some form. I was never impressed by the modified Newtonian dynamics, since it was just trying to find an equation that would produce the results consistent with observation (though I understand the mindset that leads to such approach) - but when I see that Verlinde was able to derive the same equation as an emergent feature of some model, I am suddenly fascinated.

The video I brought up above mentions the Bohmian mechanics and this is another topic that recently got my attention, mainly thanks to Veritasium and the "bouncing droplets" experiments that show some interesting analogies with quantum mechanics. The droplets provide only an incomplete analogy for selected quantum phenomena, but it is very refreshing to see how a previously mysterious behavior can be modeled as emerging from something simple. Seeing how a probability density similar to quantum mechanical can show up in a completely different setting makes one wonder if there is a mathematical emergence mechanism common to both of them. And the full-fledged Bohmian mechanics provides an interpretation of quantum mechanics that also is based on some emergent features. To give the predictions consistent with experiments, Bohmian mechanics rely on the so-called "quantum equilibrium", a property of statistical "mixedness", which would be reached naturally through a chaotic motions of the particles in a process similar to thermodynamics. This detail really made me pause and think that I should perhaps keep an eye on this theory.

Our world is made from incredibly huge numbers of building blocks, perhaps everything that we observe is statistical to the core.

Bohm wrote in one book: "Analysis creates the parts."

God only knows how much coffee have been poured over these talks!
This really is a very fascinating stuff. And it keeps me wondering: can any systematic method of finding an "underlying model" for any emergent behaviour exist?
A system, roughly speaking, capable of reducing the pattern of Conus textile to, let's say, a particular cellular automata.
Well, my hunch tells me this thing would be darn uncomputable...

A new paper follows that demonstrates at least some agreement between Verlinde's theory and the experimental evidence. This is not much, as it is still applied to just one simple case for which Verlinde provided a mathematical model. For anything more complex, a much more complicated models would need to be derived. But perhaps such ones will also come.

I also found on the web a nice mathematical explanation what is an entropic force. This one is able to really stir the imagination. Though the example of the elasticity of polymers in the original Verlinde's paper was also very illustrative.

Thanks for sharing the links Tomasz! very interesting info.
I would love for somebody like Veritasium, minutePhycisc, VSauce to make a video about this otherwise I don't think I am really able to comprehend fully the fine details of this theory.

I think it's more likely to end up on PBSSpaceTime, but yeah it would be lovely, I need visuals/animation to intuitively visualize this stuff...