Helgoland
Recently, my eldest son presented me with the book “Helgoland” by Carlo Rovelli. Like many people I’ve long been fascinated by quantum theory, always failing to understand it, yet always returning to it. Rovelli tells the story of its conception in exceptionally clear language. He recounts how young Heisenberg, beset by hay fever, flees to Helgoland and ponders a scientific enigma on that wind-swept rock in the Baltic sea.
This is the problem: Niels Bohr captured many experimental observations of the frequencies of light emitted by various elements when heated, in a neat scheme. This scheme related frequencies to electrons that were presumed to jump from orbit to orbit. A jump from one orbit to the next would cause a certain frequency of light to be emitted; a jump to an orbit further away would cause emission of another frequency. Picture the results as a table with orbits on the rows and columns and frequencies in the table cells.
Successful as the scheme was, it could not explain the energy that was measured, just the frequency. Clearly the scheme was incomplete, yet without being completely wrong. But by far the biggest problem was that there was no explanation why electrons would orbit at fixed distances in the first place, nor why they would suddenly jump from one orbit to another.
Now physicists at the time relied on formulas derived from Newtons classical laws to explain their experimental observations. These formulas have variables for the speed of an object, its position, its energy and so on. In other words, the very formulas that structured their thoughts, led physicists to conceive of the phenomenon they studied in terms of a moving object, like a falling apple or a planet circling the sun. Having discovered ever smaller units of matter, they’d arrived at a picture of electrons circling a nucleus of protons and neutrons. They applied those laws to electrons — but failed to explain their observations. So the enigma was: how do the elementary forces, governed by Newton’s laws, explain the sudden jumps of electrons?
Heisenberg first tried to think of a new kind of force to explain the jumps, but failed. He then tried to come up with new laws for movement. But this failed, too. Then, in a stroke of genius (or maybe a fit of despair) he realised there is a third part to the picture: the electron itself.
Heisenberg realised no one had ever actually seen an electron.
Ernst Mach had taught him and his contemporaries to think in just terms of things that can be observed. Clearly, electrons do not qualify! So Heisenberg tried to escape the mental picture of electrons as tiny planets circling a mini-sun. After all, all the physicists had actually seen, was light emitted by some substances under certain circumstances. He literally replaced the single-point variables in the formulas (that implied objects) by matrices of these measurements: the relation between orbits and the frequency and energy measured for a jump between them. And this turned out to work beautifully (though requiring a new and difficult mathematics). Quantum theory was born.
AI and Representation
We were trained in Artificial Intelligence in the 1980s. This was before the rise of AI as we know it today: neural nets that need to be trained on extremely large collections of data. The Good Old Fashioned AI (GOFAI) we studied, relies on symbolic representations and hand-crafted algorithms. We were encouraged to question the representations we used in our programs very, very critically. The same puzzle could require either a fiendishly difficult algorithm, or a very concise and elegant one, depending on the representation chosen for the situation at hand.
To get a taste of the impact of representation, consider this situation: you receive simple instructions on where to find things on a kitchen shelf. Because you’ll have to pass that information on to someone else, you decide to take notes. Now, at this point you have to choose a representation, meaning that you have to decide on the form you’ll use to capture your new knowledge about that kitchen. Let’s say that you discard all options but two: a picture and a written text. We’ll explore both.
Here is the first instruction:
the salt is next to the pepper on the shelf.
The textual representation is easy: just write down the instruction in a concise form, e.g. “salt next to pepper”. Drawing a (schematic) picture of salt and pepper on a shelf is not difficult either, but you’re forced to put the salt either on the left or on the right of the pepper. You arbitrarily pick the right.
This is the next instruction:
The sugar is immediately to the right of the pepper.
Damn! At this point, your picture is a dead end: you’ll have to erase it and draw it again, this time with the salt on the left. In contrast, the textual representation can just be extended.
Does this mean that text is superior to pictures? No. A picture can be very intuitive. It is immediately accessible and easily holds massive amounts of information. In many cases, it is superior to a textual representation. But it cannot represent a lack of knowledge of the position of things — something that is easily expressed in natural language. The picture requires you to be over-precise when some things are unknown. In such cases, a textual representation is to be preferred.
Physicists in Heisenberg’s time found themselves in a situation where they had to erase their picture, too, as it were. Their representation (mental image) of the light-emission phenomena they studied, required them to be over-precise. Their mind’s eye saw electrons moving with a definite position and speed around a nucleus. They tried to explain the observation tables in these terms — but it cannot be done. Heisenberg gave up on the electron as a tiny moving ball and replaced it by a matrix of observed values. By sheer luck (I suppose) just replacing one part of the representation opened the door to a solution.
How is a matrix of observations less precise than a moving ball? Well, the matrix represents attribute values at certain points only, whereas a ball should have attributes at every point. Something like that. By introducing the matrix, Heisenberg introduced quantas.
Things and Thoughts
In the Western world, we all stand in a tradition of things versus thoughts, body versus mind (or soul if you’re inclined that way). To reconcile our experiences across this great divide has puzzled the greatest minds.
In Heisenbergs time, electrons were thought by physicists to be very real. In fact, for these physicists, trained to reduce phenomena to ever smaller parts, they were more real than the touchable parts of their experimental setup.
A number representing the outcome of an observation, however, is clearly more in the domain of the mind, than the domain of things.
Cast in this light, Heisenberg moved electrons from one category to the other, from things to thoughts. That is truly mind-boggling!
Heisenbergs epiphany had epic consequences. Quantum physics has literally changed our world. An insight so influential is very rare. But suddenly seeing things in a new light is a much more common experience. Sometimes, this is because of teaching. Often it happens on revisiting a subject after a long pause. Discovering a way of seeing reality that is really new, however is a rare occasion that should be treasured.
Perspectives
Rovelli’s book caused me to scour our work on Perspectives. Did we have our Heisenberg moment? Have we found an important reconceptualisation? There is one way of telling the story of its development that puts it in a similar light. Now, to prevent misunderstanding, nothing we did is on par with Heisenberg’s genial move! Yet, there is a story to tell I am proud of.
Consider a program that supports people in running an organisation, for example an online bookshop. Many individuals will use it. IT specialists like to group these users into roles. A role will have access to a particular subset of the data stored by the program, and it will be allowed to execute some but not all functions. Roles might include: a client, a financial controller, an order picker, etc. This facet of program development is called Access Control.
The meaning of ‘role’ is similar to the role of an actor in a play. It allows us to make distinctions based on context: in the context of the play, a person might be a butler; but when the play is over we think of him as an actor, or a father, a brother, or, indeed, a client in a bookshop.
A role is played by a person. In terms of things versus thoughts, a role belongs in the realm of thoughts while persons belong in the realm of things (arguably, however, persons, as conscious beings, straddle the divide in some way!)
In Perspectives, we’ve declared context and role to be mutually dependent but otherwise undefined concepts. ‘Context’ is not used extensively in contemporary IT (in contrast to role). Recognising context
as an important structuring concept is one of the distinguishing features of Perspectives. But if we left it at that, Perspectives models would be unorganised sets of contexts with roles.
Now roles turn out to relate contexts to one another. To a first approximation, consider that there are restrictions on who can assume a role. Often, such restrictions must be expressed in terms of other roles. For example, in a meeting, only a Participant can assume the role of Chair. This we could capture in a requirement on the role of Chair: to play the role of Chair, one must also play the role of Participant. This requirement could be enforced in runtime.
Another example. Only employees of a company are allowed to drive its trucks. One is an Employee in the context of a Company; but one is a TruckDriver in the context of a Delivery. So, relations between roles may cross the borders between contexts.
At this point we have Perspectives models contain
— a list of contexts
— a list of roles in those contexts
— a list of requirements on filling a role in terms of other roles.
The requirements do not sit easily with the graphical representation given above. They are more naturally expressed as rules, written as a text. This cripples the usefulness of the graph.
One of us (Cor Baars) had the insight that we could re-think role playing. Instead of considering a role to be played by a person, we could just as well declare that roles can be played by other roles. Employee (from the Company context) fills (plays) TruckDriver (from the Delivery context).
Suddenly, we could draw the entire model as a graph, ditching the rules:
This turned out to be very fertile. For example, we were able to conceptualise paths through the graph as queries. A query pulls roles in from remote contexts, as it were. As user roles have perspectives on other roles in a context, queries allow them to look across a context’s border into other contexts. This allows for very natural modelling of many situations. Importantly, the restrictions that formerly only did something in runtime, now suddenly contribute to modelling itself.
In retrospect, we see that the idea that a role must be played by a person (an idea borrowed from drama) turns out to be over-specialised. It hampered our efforts to model real life situations, just like conceptualising the material reality underlying the light-emission experiments as tiny star systems hampered understanding the observations in Heisenberg’s time. In both cases, the ill-fitting representation brings in assumptions that are invalid.
And there is another similarity. If we conceive of role-filling as we do in drama, a thing (person) fills a thought (role). It is the thing in reality that does the filling. Not so in Perspectives, where we can do the filling with a non-real entity: another role. So we move the idea of the filler from the realm of things to the realm of thoughts: Heisenberg moved the electron in the same direction.
However, tongue-in-cheek we might ask: what is real? How unreal is a thought that moved the world and how real is a thing that cannot be seen?!
This is the twelfth column in a series. The previous one was: Big Tech Loves Privacy — as a Frame. Here is the series introduction.
Post Scriptum. Harry Pinxteren drew my attention to a letter by Gerard ‘t Hooft). ‘t Hooft makes the — in the light of the above — interesting point that physicists may have hidden assumptions in their theories that might be questioned, much as Heisenberg successfully stepped back to regain a wider perspective on the ‘forces — laws of motion — electron’ ensemble and found hidden assumptions that precluded understanding. Let me give you some quotes:
“Both the proof and its dismissal showed that the authors understood the mathematical nature of the equation, but missed the point that the physical world might be much more complex than just this one abstract equation, in which all sorts of possible complications were suppressed.”
Here he writes about John von Neuman’s ‘proof’ (later refuted) that ‘that quantum mechanics cannot be explained in terms of hidden degrees of freedom, which would restore some deterministic interpretation of Schrödinger’s wave function’. The point of interest to notice here is that ‘t Hooft explicitly alerts the reader to the fact that the equation is not (all of) reality.
A little further on he elaborates:
“What the Schrödinger equation is describing is not exactly what is happening; it merely describes the tip of a gigantic iceberg, in which most processes happen far beneath the waterline.”
He then becomes more specific as to what (in his opinion) has escaped theorist’s attention for a long time: the choice to build on real numbers.
“Those real numbers used now are so powerful that it is easy to forget that they are manmade.”
Manmade, as opposed to nature itself, we presume.
“Is this really the correct way to indicate distances, velocities, and so on?”
So here ‘t Hooft questions, very critically, some elementary representational choices that have been made by physicists. Choices that import assumptions that might be questioned.
“It could be that all positions and all velocities eventually only require integers to specify their values.“
I have no independent meaning on the merit of the alternative put forward here — integers. I am not a physicist and I cannot even begin to understand the implications of what ‘t Hooft is alluding to. But it would be nice if the fact that reals were constructed to represent continuous phenomena and the fact that a primary characteristic of quantum phenomena is discreteness, points in the direction of where new and better representations could be found!