A research programme after Leibniz for a future physics

In "Einstein’s Unfinished Revolution", Penguin Books, 2019, Lee Smolin introduces principles through which to develop fundamental physics. So, they are not mathematical or logical principles but founding elements for thinking about and then formulating physical theories.

Introduce five closely related principles for a future physics:

1. The principle of background independence 
2. The principle that space and time are relational 
3. The principle of causal completeness 
4. The principle of reciprocity 
5. The principle of the identity of indiscernibles.

These are all aspects, claims Smolin, of what Leibniz called the principle of sufficient reason (PSR). he interprets the principle as follows: 

Every time we identify some aspect of the universe which seemingly might be different, we will discover, on further examination, a rational reason why it is so and not otherwise.

 This is not quite standard but then, if we even go back to Leibniz, we have a number of versions. We shall examine the formulation and the five principles in light of their origin in the philosophy of Leibniz and then go on to discuss them as principles for developing physics especially in dealing with quantum mechanics and theories of space and time.

The promotion of the principle by Leibniz

Although the PSR is most closely associated with Leibniz there is an earlier formulation by Spinoza

Nothing exists of which it cannot be asked, what is the cause (or reason) [causa (sive ratio)], why it exists.

The version given by Smolin has an epistemic flavour while that of Spinoza is ontological. As Smolin is defending a realist view of physics an ontological formulation may be preferred. Leibniz provided a mixture of logical, ontological and epistemic formulations. The modern recovery of the reputation of Leibniz is based on his achievements as a logician and here is the version from the Monadology (not Leibniz's title)

31. Our reasonings are based on two great principles, that of contradiction, in virtue of which we judge that which involves a contradiction to be false, and that which is opposed or contradictory to the false to be true.
32. And that of sufficient reason, by virtue of which we consider that we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise, although most of the time these reasons cannot be known to us. 

Ergodicity and investment growth

The status of Ergodicity Economics as a minority topic in mathematical economics may be about to change due to the profile it has achieved through a special 'perspective' article published in Nature in December 2019 authored by Ole Peters of the London Mathematical Laboratory.

The article itself provides a clear introduction that presents sufficient mathematics without being overly pedantic. The main point has been well known and put on a rigorous foundation in mathematical physics for several decades. The point being that the time average of a dynamical variable is not equal to the static expectation value over the associated probability distribution over that variable. The claim that this ignored in main stream economics seems incredible given the repeated claims that mathematics has too tight a hold on the subject currently. However the effects that Peters claims does seem to stand up to scrutiny.

The model that is used to illustrate is a simple gamble where with equal probability you can increase your pot (wealth) $W$ by $A$% or lose $B$%. If $A > B$ then the expected outcome is positive and traditionally the gamble is considered acceptable. In general the outcome is
$$<\Delta W> = W \frac{A - B}{2 \times 100} .$$
This simple game of chance could also be thought of as the outcome of a risky investment or a purchase that has associated unknowns.

However when the stakes are high most people are disinclined to accept the such a bet. High stake would mean something like betting your house. A bad outcome would leave you with significantly reduced  total wealth. The rejection of the gamble is often declared irrational as  you are rejecting an expected win.  But something slippery is going on; "expected" is being used in two distinct ways. The ordinary language use means what is likely happen and what is very likely to happen is that either your wealth increase significantly or it decreases significantly. The technical meaning is that it is the average over the probability distribution; Equation for $\Delta W$, above is that average for the gamble discussed.

Now one way to day with a large one off loss is to spread your bets over time. That is iterate the game. So what is the expected win if the game is played $N$ times? To address this we will have to introduce a more formal mathematical model. Let $s(0)$ be the initial stake and let the stake to iteration $n$ be
$$s(n) = \prod_{i=1}^{n} r_i s(0) $$
where $r_i = a$ with probability a half and $b$ with probability a half, where
$$a = 1 - A/100$$

and
$$b = 1 + B/100$$.
A further technical assumption is that each gamble is independent of the previous one, which gives for the expected stake:

$$<s(n)> = \prod_{i=1}^{n} <r_i >s(0) $$

$$<s(n)> = <r_i>^n s(0)= <r>^n s(0) $$

$$<r> =\frac{a+b}{2}$$
where we have used the fact that each gamble has the same probability distribution.

As long as $<r>$ is greater than one the stake will grow. Is the calculated expectation value what is to be expected? To test this we will look at what happens over time to $s(n)$, that is as $n$ increases. For large $n$, noting that the order in which $a$ or $b$ is randomly selected does not affect the value of $s(n)$. Therefore
$$s(n) = a^{m} b^{n-m} s(0) $$
\[\lim_{n \to \infty} s(n)^{1/n} = \hat{s} =\sqrt{ a b} s(0)\].

So this increases exponentially with rate $\sqrt{ a b}$ if $ab > 1$. Let us first consider the example with parameters used by Peters. The result for $a=0.6$ and $b=1.5$ is shown below for $100$ histories. This case shows that for these parameters playing the game leads to almost certain loss, amounting to ruin or almost complete loss of stake, but the expectation value estimate predicts an exponentially growing gain. For these parameters $\sqrt{ab} < 1$ so the analysis has told us to anticipate this. Here anticipation and expectation are not the same.

Lets keep $a=0.6 but now let $ab$ be greater than 1. This gives

 This give most histories growing, just, after $25000$ iterations. As  $\hat{r} =1.0003$ and now $,r. = 1.366$. By making   $<r>$ slightly bigger we get into a situation where the game becomes almost always favourable to the player.

A more realistic gamble such as investment in carefully chosen stock it likely to vary only a few percent between iterations. This is the situation shown below.

Here when $a$ and $b$ are close there is less uncertainty and the expectation value is not such a terrible estimate as in the previous examples. Perhaps the positive return is unrealistically high. An iterated sample with a 4% loss and 5% gain is shown below.

Energy Science and Technology priorities to achieve "net-zero" GHG emissions

I am no expert on energy and the environment, having spent the latter half of my career in information systems engineering; especially security, safety and automation. However, I have also worked as a trouble shooting systems generalist and it is this experience that I want to try to bring to the energy challenge in tackling climate change.

Grangemouth refinery

The government is committing to  “Net Zero” greenhouse gas (GHG) emissions by 2050. This is good news but the means of achieving it are critical. To tackle climate change innovation is still urgently needed and it must come quickly because implementation time scales for new technology in complex systems are so slow. Often implementation to operation requires more than a decade to get on-line, as can be seen from the proposed Small Modular Reactor power plant that will not see operation before 2030. However,  even at this stage, given that the best scientific opinion has been clear on climate change for decades, there is still no consensus on the mix of energy solutions required and priorities. There is a continuing environmental movement opposition in principle to nuclear energy, despite its zero GHG emissions when in operation. Ensuring that the identified priorities are the right ones means recognising those environmental and societal factors that contribute to global warming and disentangling them from the real but different concerns on air quality and pollution of oceans and waterways.  The concerns about species extinction would also benefit from the clarity afforded by distinguishing between what is and what is not a due to GHG emissions.

Rolls-Royce consortium concept Small Modular Reactor facility

We need to unblock the system to act with urgency but remain focused on a plan. All this requires an increase in tempo. Suggestions on how to do this have been provided in a report prepared for the Aldersgate Group: Accelerating innovation towards net zero emissions. They identify six (not five) key actions for government policy to accelerate low carbon innovation in the UK :

1. Increase ambition in demonstrating complex and high capital cost technologies
2. Create new markets to catalyse early deployment and move towards widespread commercialisation
3. Use concurrent innovations, such as digital technologies, to improve system efficiency and make new products more accessible and attractive to customers.
4. Use existing or new institutions to accelerate critical innovation areas and co-ordinate early stage deployment.
5. Harness trusted voices to build consumer acceptance.
6. Align innovation policy in such a way that it strengthens the UK’s industrial advantages and increases knowledge spill overs between businesses and sectors

The report says that implementing these lessons will require a further increase in government support for innovation – through both research, development and demonstration and through deployment policies to create new markets. Government doe snot have good record in implementing complex infrastructure projects. As well as policies to create new markets, regulation and market correction should be implemented to channel the the infrastructure and engineering capabilities of the the oil and gas, as well as the defence and petro-chemical industries. As has been argued persuasively by the Nobel Prize winning economist William Nordhaus, many problems should be solved by robust carbon pricing, preferably through a carbon tax. This will release current market potential and create new market opportunities as well as generating funding for innovation.

If cost was no obstacle, land and material resources available, then current renewable energy technologies and storage methods would be sufficient. But this is not the case; there are trade-offs with costs and benefits of any course of action need to be weighed. There are many challenges and perhaps the greatest are political in both needing to convince the populations of almost all countries in the world to sacrifice their current quality of life to mitigate a predicted greater cost but one that will impact grand children and finding ways to ensure that the free loader effect does no disrupt the good intentions achieved through the Paris protocol. However if this political challenges are achieved further innovation will still be required and if the political challenges are not addressed or only partially then innovation become the only hope. However, the International Energy Agency (IEA) identifies a bottleneck in innovation. The investment in R&D for low carbon technology is not growing. IEA are tracking key technologies and of a set of 39 only 7 are on track to meet Paris targets, 20 need remedial action and 13 are off track. Those that are on track are: solar photovoltaics (PV), bioenergy for power, energy storage, electric vehicles (EVs), rail, lighting  and data centres. It must be emphasised that these are on track, not complete, further investment and maintained efforts are required. To concentrate on the power domain the following technologies are tracked by the IEA:

•  On track: Solar PV and  Bioenergy;
• Need remedial action: Renewable power, Onshore wind,  Offshore wind, Hydropower and  Natural gas-fired power;
•  Off track: Geothermal, Concentrating solar power, Ocean, Nuclear power, Coal-fired power and CCUS in power.

Now, not all are equally critical but there are systemic dependencies so that the full benefit of net-zero carbon energy generation can be delivered through efficient power transmission with capacity for storage. Obviously the problem with coal fired power is that we are still using too much of it and this can only be solved by replacement technologies. For wind the key problem is not primarily technical, although there are improvements to be made, but regulation, planning and consultation. In those areas that are difficult to de-carbonise there will need to be compensating carbon capture technology. In nuclear technical work to increase modularisation and scalability is required as well safety and security by design. The major objections to nuclear of waste, safety, security and cost are being addressed but efforts must continue.

We need a short to medium term boost in funding to achieve the needed acceleration. This could be provided as a dividend from imposing a carbon tax or other robust form of carbon pricing. As well as providing revenue for R&D it also provides a steering mechanism because the tax will help correct for the failure of the energy market and provide path to exploitation for the innovations. Speed of exploitation remains a challenge with a quagmire of regulations, permissions and consultations to wade through in addition to the technical challenges that are always present in scaling up form proof of concept to operational system. Eventually an emergency situation will require emergency powers but climate change is a slow motion emergency both in the climatic development in response to increased green house gas concentration and in the climates response to mitigation. In the end it will come down to whether there is the social and political will to carry through an emergency response.

Preclusive action: liberty and the state of emergency

A good few years ago when reading "Terror and Consent" the notion of preclusive action struck me as a key concept Philip Bobbitt's together with the interpretation of security in what he referred to a the Market State. An aspect of the book that is especially relevant today is the treatment it gave of pandemics although its main concern was clearly terror. Except for fringe conspirationalists nobody thinks the current pandemic was terror instigated but Bobbitt also discusses naturally occurring pandemics in the wider context of the role of the state in protecting civilians. 

The outline below adapts freely from sections in Bobbitt's book. In addition to preclusive action the other key notion introduced by Bobbitt is the Market State - the affordable successor to the Welfare State. I hope this slight essay will encourage others to read or re-read his book.

A market state, as the term is used by Bobbitt, take up the challenge of protecting civilians and places that protection at centre stage in the life of the State. This protection  embraces not only policing and defence but also health and security of supply (food security for example). The stakes can be high. We do not know the cost of the current pandemic but an avian flu epidemic—whether engineered by a state and given to terrorists or created by them directly (the genetic code of the 1918 avian flu that killed 50 million persons has now been posted on the Internet) or naturally occurring (as is currently the case) — strikes globally with a velocity that leaves little time for reactive measures. Similarly, leaving pandemics for the moment to consider an extreme terror act, a nuclear device detonated in a major twenty-first century city could dwarf the casualties at Hiroshima. These vulnerabilities have important implications not just for diplomacy, but also for precautionary interventions and anticipatory preemptions. In addition to deploying these preclusive tactics, market states (if our current sluggish nation state ever evolves completely into one) should be able to marshal many assets—relative nimbleness and dexterity in adapting to technological change, devolution, the use of private entities as partners, and global networks of communications and cooperation—that are denied to reaction oriented nation states in their struggle against terror.

At the outset, we should be clear that anticipatory warfare is not the result of the development of WMD or delivery systems that allow no time for diplomacy in the face of an imminent reversal of the status quo. That might have been President Kennedy’s justification for threatening a preventative war against Cuba to prevent it from deploying ballistic missiles with nuclear warheads, but it would have been folly to have made a similar argument for action against the Soviet Union. Rather it is the potential threat to civilians — a market state concern — posed by either arming, with whatever weapons, groups and states openly dedicated to mass killing or a naturally occurring rapidly developing catastrophe that collapses the distinction between preemption and prevention, giving rise to anticipatory action whether war or emergency powers. 

Examples of failing to act preemptively and its consequences abound. For example, the USA  could have stopped the genocide in Rwanda had it acted preclusively; by the time the killing was imminent it was too late. Those inspectors who were shocked by the progress of the Iraqi nuclear weapons program in 1991—by some accounts Saddam Hussein was a year away from deployment—must have been quietly thankful for the Osirak raid ten years earlier. Had Saddam Hussein acquired nuclear weapons before he invaded Kuwait, the option of disarming him would have been infeasible. Michael Walzer once asked whether “the gulf between preemption and prevention has now narrowed so that there is little strategic (and therefore little moral) difference between them.” The last Irag war is still devisive but Bobbitt's main point is that if the community of developed states had had the will and means to carry out appropriate preclusive action then the war need never have taken place. Acting well prior to the actual development of WMD or before a full blown pandemic is underway will give rise to weighty moral considerations. As with all moral questions, one would have to know a good deal about the facts of the case under consideration. 

Therefore to understand the changing nature of victory in our wider context we must first review the shift, over the last few centuries, in the constitutional order that determines the war aim. The "war aim" must be extended now with the reach of the state extended to more  general protection of the civilian population.To simplify, the sixteenth century princely state sought to aggrandise the personal possessions of the prince; the seventeenth century kingly state attempted to enlarge the holdings of the ruling dynasty; the eighteenth century territorial state tried to enrich its country as a whole (and its aristocracy in particular) by acquiring trading monopolies and colonies; the nineteenth century state nation struggled to consolidate a dominant national people and sought empire; the twentieth century nation state fought from 1914 to 1990 to establish a single, ideological model for improving the material well-being of its people. To put it in slightly more technical terms, victory achieved in pursuit of these various (and sometimes overlapping) goals could be characterised as perquisitive (princely state), acquisitive (kingly state), requisitive (colonial territorial state), exclusive (imperial state nation), and inclusive (nation state). In all cases what is considered victory is defined by the "war aim". The victory sought by twenty-first century market states will be preclusive because damage to the civilian population is unacceptable as that wil be the nature of the effective contract between the state and the population.

If market states are indeed emerging, such states’ terms for victory in warfare and protection can best be described as preclusive. The market state comes in at least two distinct forms. According to Bobbitt, one is a state of consent and the other is a state of terror and coercion. The goal, whether for the market state of consent or for the market state of terror, is to preclude a certain state of affairs from coming into being. For the state of consent, it is terror itself that must be precluded, chiefly by the protection of innocent civilians. For the state of terror, it is individual self-assurance that must be prevented from spreading within a society, for once enough people refuse to be cowed it will be difficult to return them to a condition of submission. The line can be fine, of course, between protecting someone and preventing them from developing as they wish (as we know in our current situation).

When we consider the paradigmatic case of preclusive humanitarian intervention to prevent genocide or ethnic cleansing, we must consider these two elements, domination and responsibility. To the person, or the peoples, for whom others would assume responsibility, the exercise of that duty sometimes looks like simple authoritarianism and even exploitation (as indeed it often is).  This is one legacy of nineteenth century imperialism; and there were many beneficiaries of the altruistic late-twentieth century humanitarian interventions in Somalia or Haiti or Kosovo who seethed with resentment. The authority (often self appointed) preempted the right of the suffering people to act for themselves. Though this may have been justified on the grounds that without outside intervention these peoples would have had no real alternative in their circumstances, yet a preclusive victory has inadvertently stimulated resistance, even hostility, to the authority. Given the time when it was published, Bobbitt's focus is on terror. The dilemma will not play out in the same way in reaction to state measures to preclude a pandemic but it will put considerable strain on civil liberties and trust. It will also potentially disrupt the international cooperative order.  

To return to the current situation. We may be just at the peak of the Covid-19 pandemic. Reaching that peak has been bought the price of unprecedented modern peace time restrictions on personal liberty. Indeed, in some ways the measures are even more restrictive than during war time because of the nature of the threat. But as the nature of the threat is an evolving but dumb virus there is no need fall back on war time instincts to restrict information or act secretively. To maintain and nurture the consent of the population the state must act with openness, fairness and exemplary competence.

Review: Human Compatible by Stuart Russell

Stuart Russell is a very influential figure in the Artificial Intelligence (AI) community. He is co-author of a widely studied text book on the subject, Artificial Intelligence: A Modern Approach, that was key to moving the subject from being dominated by a formal logic approach to one that focused communities of artificial agents operating and cooperating to maximise rewards in uncertain environments.

His most recent book, Human Compatible, is written for a general audience. It helps if you are a reasonably informed member of the general public but the book rewards the effort with not only an overview of the current successes of AI but also addressing the technical and ethical challenges with novel, constructive  proposals. It is highly recommended.

Russell takes the challenges to human purpose, authority and basic well being seriously without being unnecessarily alarmist. Even with current and immanent applications of AI there are threats to jobs but also real gains in efficiency and cost effectiveness in medicine and production.

The aim of what Russell calls the standard model of AI has been defined almost since its inception as

Machines are intelligent to the extent that their actions can be expected to achieve their objectives.

However the major challenge comes with an anticipated major step forward. That is the creation of  general-purpose AI (GAI). In analogy with general purpose computers, that is one computer can carry out any computational task,  GAI will be able to act intelligently, that is plan and act to achieve what it needs to achieve, on a wide range of tasks. This would include creating and prioritising new tasks. Currently AI produces highly specialised agents but many of the algorithms  can be put to diverse uses; learning different skills but once learned that skill is exercised narrowly. For example, Deepmind's AlphaGo can play the board game Go very well, better than any human, but that is it. Related underlying techniques, however, can be applied to a number of applications such text interpretation, translation, image analysis and so on.

The major breakthrough that would enable the AI to escape from the constraint of narrow specialism has yet to be made. As indicated above, GAI would be a method that is applicable across all types of problems and would work effectively for large and difficult tasks. It’s the ultimate goal of AI research.  The system would need no problem-specific engineering and could be asked to teach sociology or even run a government department. A GAI would learn what from all the available sources, question humans if needed, and formulate and execute plans that work. Although a GAI does not yet exist, Russell argues that a lot of  progress will results from research that is not directly about building "threatening" general-purpose AI systems. It will come from research an the narrow type of AI described above plus a breakthrough on how the technology is understood and organised.

It is the mistake to think that what will materialise is some humanoid robot. The GAI will be distributed and decentralised; it will exist across a network of computers. It may enact a specific task such as cleaning the house by using lower level specialised machines but the GAI will be a planner, coordinator, creator and executive. Its intelligence would not be human it will have significant hardware advantages in speed and memory it will also have access to an unlimited number of sensors and actuators. The GAI would be able to reproduce and improve upon itself. It would do this at speed. 

And the role for the human? None that the GAI requires. The GAI would be able to construct the best plan to tackle climate change, for example, but on its terms  and in a way that maximised its utility. And to maximise its utility it will find ways to stop itself being switched off.

This danger, according to Russell, comes from the aim that has guided the whole research programme so far. That is, to give an AI objectives that become the AI's own objectives. A GAI could then invent new objectives such as self replication or inventing better information storage and retrieval to speed up its own actions. A GAI could then be said to have its own preferences and effectively is a form of person. It need not be malevolent but equally it need not be motivated by benevolence to humans  either.

In short, the solution proposed by Russell to the problem of human redundancy is to engineer the GAI so it cannot have preferences of its own. It is engineered to enact preferences of individual humans. The final third of the book is devoted to exploring the ramification around a set of principles for benevolent machines:

1. The machine’s only objective is to maximise the realisation of human preferences. 
2. The machine is initially uncertain about what those preferences are.
3. The ultimate source of information about human preferences is human behaviour.

These principles are there to inform design but also regulation and the formulation of research programmes. Russell deals with these and the societal efforts and cooperation that will be required to deal with unintended consequences as well as the actions of some less than benevolent humans who may want to create a GAI that has a goal other than to satisfy human preferences.  The discussion addresses the challenges of multiple artificial agents and multiple and incompatible human preferences. Of course Russell does not definitively solve any of these but indicates routes to resolution.

It is important that this book shows there is an approach in which humanity can reap the benefits of AI research without being subjugated to a superior intelligence or being forces to implement an AI ban. It is a positive vision that I hope informs and shapes our approach to this technology. But there is urgency, because we do not know when or where the break through to GAI will take place. If it happens within the current standard model pattern of research and application then disaster threatens.