Revolution vs incremental change

I think that the dysfunction and animosity we currently see in the US political system and election is partly due to the underlying belief that meaningful change cannot be effected through slow evolution but rather requires an abrupt revolution where the current system is torn down and rebuilt. There is some merit to this idea. Sometimes the structure of a building can be so damaged that it would be easier to demolish and rebuild rather than repair and renovate. Mathematically, this can be expressed as a system being stuck in a local minimum (where getting to the global minimum is desired). In order to get to the true global optimum, you need to get worse before you can get better. When fitting nonlinear models to data, dealing with local minima is a major problem and the reason that a stochastic MCMC algorithm that does occasionally go uphill works so much better than gradient descent, which only goes downhill.

However, the recent success of deep learning may dispel this notion when the dimension is high enough. Deep learning, which is a multi-layer neural network that can have millions of parameters is the quintessence of a high dimensional model. Yet, it seems to be able to work just fine using the back propagation algorithm, which is a form of gradient descent. The reason could be that in high enough dimensions, local minima are rare and the majority of critical points (places where the slope is zero) are high dimensional saddle points, where there is always a way out in some direction. In order to have a local minimum, the matrix of second derivatives in all directions (i.e. Hessian matrix) must be positive definite (i.e. have all positive eigenvalues). As the dimension of the matrix gets larger and larger there are simply more ways for one eigenvalue to be negative and that is all you need to provide an escape hatch. So in a high dimensional system, gradient descent may work just fine and there could be an interesting tradeoff between a parsimonious model with few parameters but difficult to fit versus a high dimensional model that is easy to fit. Now the usual danger of having too many parameters is that you overfit and thus you fit the noise at the expense of the signal and have no ability to generalize. However, deep learning models seem to be able to overcome this limitation.

Hence, if the dimension is high enough evolution can work while if it is too low then you need a revolution. So the question is what is the dimensionality of governance and politics. In my opinion, the historical record suggests that revolutions generally do not lead to good outcomes and even when they do small incremental changes seem to get you to a similar place. For example, the US and France had bloody revolutions while Canada and the England did not and they all have arrived at similar liberal democratic systems. In fact, one could argue that a constitutional monarchy (like Canada and Denmark), where the head of state is a figure head is more stable and benign than a republic, like Venezuela or Russia (e.g. see here). This distinction could have pertinence for the current US election if a group of well-meaning people, who believe that the two major parties do not have any meaningful difference, do not vote or vote for a third party. They should keep in mind that incremental change is possible and small policy differences can and do make a difference in people’s lives.

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7 thoughts on “Revolution vs incremental change

  1. one can also look at china and vietnam—both now are semi-capitalist countries after communist revolutions (some of my relatives have been to both places).. i dont think they have much of what one could call a democracy however.

    thomas kuhn had ‘structure of scientific revolutions’; S J Gould had ‘punctuated equilibrium’. Nonlinear dynamics has ‘ bifurcation theory’, phase transitions.
    there is also ‘simulated annealing’—its sort of like shaking a cereal box, when you only want the raisins and not the cereal. I dont know how that fits into the framework above —it seems to be a form of gradient descent with shocks to knock it out of local mimima. (sherrington-kirkpatrick-hopfield)

    i personally am a registered green party member (but in dc it doesnt really matter—its dominatly democratic , and voting here doesnt matter, so i have only voted a couple times for local issues—-eg weed legalization partly so we dont have people getting locked up). i am not that impressed with people who run for green party–many seem to be ‘self-promoters’.

    I also have known quite a few people who want ‘revolution’ and see voting for ‘the lesser evil’ as impure, but many of them live very comfortable lives so actually it sometimes seems that the worse things get for many people , the better their lives get—‘another war means i get another international speaking tour’.

    (if there were a revolution, i’d probably be like a squirrel, and sit in the tree and watch it and collect acorns. maybe beg for food from both the revolutionaries and their opponents.

    ‘dimensionality’ is always interesting empirically and theoretically. eg Poincare sections —eg for lorentz attractor. There are all kinds of approaches to reducing high order systems and high dimensional manifolds to lower order forms Flatland tries to visulaize 4 dimensions in 3 or 2. S Smale in J Math Bio in 70’s had a sort of universal form for coupled multidimensional equations. S Jones has approaches to the ‘universal diophantine equation’ (hilbert’s 10th problem–davis, robinson, matijevitch (sic) —one can vary degree or number of variables. “Center manifold theorem’ is another approach.

    it would be hard to know what dimensions of politics are. (one can note that while some current fairly stable and democratic societies which have incremental positive changes exist—i see some of these in terms of better public transit (with all its flaws) and better food choices (one can get healthy vegetarian food now for same prices as junk food which used to be the only thing conveniant) —one has to remember that these systems were built using ‘tools’ like colonialism, slavery, empire buidling etc. The ‘democratic west’ had WW2 which was only 80 years ago.

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  2. Not that I’m trying to draw a parallel to the current US elections, but it seems that the idea that England’s revolution paving the way for the current system was all smooth and civilized is actually debatable (see Steve Pincus revision of the “Glorious Revolution”). Besides, don’t you think that, with the common history of England France US and Canada, the events happening in one wouldn’t affect the other? In other terms, I do not think that these are examples of separate algorithms to be evaluated separately and compared …

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  3. @Zeina You are absolutely correct that we have no idea what would have happened in England absent the American and French revolutions. England may have reformed because they feared a revolt. However, Russia did not liberalize and thus was subjected to its own revolution, which took a very different course. In any case, revolutions in other states may be necessary for motivation perhaps but the path internally does not require a revolution per se.

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  4. Certainly not advocating any kind of ‘revolution’, but there are important contextual differences between the process of social change and the mechanisms by which they were enacted in each of those revolutions.

    There are no democratic systems like the US. That’s why it’s the US.

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  5. @Hosam That’s exactly the point. The path to the end was very different in all cases but the end result was basically the same. This is just like deep learning. You are not guaranteed to get the same parameters each time you train but the end result performs about as well.

    @Kevin Thanks.

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