Transforming the world with intellectual objects
The power and the cost of objectifying
There is no such thing in the real world as frictionless planes, classical genes or atoms, or rational consumers. These are intellectual objects, which transform things “out there” into a mentally manageable number of features, which can then be manipulated and transformed within an abstract intellectual space that doesn’t exist in the material world. In this abstract space of mental operations, the intellectual objects can be linked to other intellectual objects, and we can derive the consequences and relationship between the two using logical reasoning or mathematics.
In Re-Assembling Reality #27a, we talked about the world of cosplayers. Every single cosplayer is different. Every single cosplay outfit is different. Every single cosplay event is different. “Cosplayers” aren’t even a single, palpable “thing”. But to get a handle on cosplayers as a group, we need to turn them into a single intellectual object, that we can pick apart and work with inside our minds. And this intellectual object will always be a gross simplification compared with the reality of cosplayers — even if the description is written by an anthropologist who has spent two years hanging out with cosplayers and writes a 500-page thesis trying to capture all the nuances and complexities of their world.
The insights gained from such simplifications can be powerfully illustrated by looking at the physics of two-level systems.
In a two-level system, the system can be in one of two states, much like a switch that can either be “on” or “off”. A prime example of a two-level system is electron spin. An electron has a property called spin and, when an external magnetic field is applied to the electron, the spin will either align itself with the magnetic field (spin up) or against the magnetic field (spin down). These are the only two options, just like a simple switch can either be on or off.
Theoretical physicists went away and developed extensive mathematical formalisms for how to treat spin. If you want to know how an electron’s spin changes when you perform various actions, you just pull the maths down off the shelf, turn the handle, and get the answer.
Significantly, however, the maths does not appeal to the fact that the electron has spin, but to the fact that it is a two-level system. This means that the maths that has been developed can be applied to any other two-level system, regardless of the particular details. Atoms, for example, have many different levels. But they often only have two levels that we care about. So we ignore the fact that they are complex multi-level systems, and act like they only have two levels. Then we take all the maths that we developed for electrons and apply it to atoms. We don’t care that atoms are not really two-level systems. And we certainly don’t care that they are not fundamental spin-1/2 particles in an external magnetic field. It does not matter. Because the maths works all the same.
The same trick can then be played throughout physics, whenever you find something that looks like a two-level system. A photon? An interferometer? Coupled quantum-harmonic oscillators? Solid-state dispersion curves? Whatever you want. Once you have solved the behavior of one, you have solved them all.
In the real world, however, these entities are far more complicated and cannot be fully extracted from their environment. The real world only approaches these idealizations when we create artificial environments and experimental setups — an artificial reality designed to externalize all factors that are not included in the intellectual model.
Something strange has happened here — the work of science involves turning things into intellectual objects, ideally mathematical ones, that can be manipulated in a purely abstract, non-physical space that doesn’t exist. Only when we have constructed something that doesn’t actually exist, can we say that science has taken place!
Through applied sciences and engineering, the process is then taken in the opposite direction: the intellectual objects can be given a physical existence, albeit one which does not and cannot exist outside of a man-made experimental apparatus. Once understood in the abstracted but physical situation, these can be converted into physical objects that can return into everyday reality.
By this process, something that had no material existence is converted into a material thing.
I start with an electron. Then I abstract it and create an intellectual object in mathematics which treats two-level systems. Then I imagine a two-level atom: a beautiful idea. If only I could create it in the lab, I have the maths to model it. So I return to the lab and create a two-level atom. A real atom, with many levels, but so isolated from the world around it that it only behaves in the way that a two-level system would. Then I measure it and abstract it and create an intellectual object in mathematics which treats crystals. Then I imagine a pure silicon crystal: a beautiful idea. If only I could create it in the lab, I have the maths to model it. So I return to the lab and create a large, defect-free crystal of pure silicon. This process of abstraction and realisation continues until I hold in my hand a solar cell.
High-efficiency solar cells never appear in nature. And no human would ever happen to make one by chance. They were created by a methodical process of moving back and forth between intellectual objects and physical objects. Looking at what exists and abstracting it. Creating in our minds a thing which does not exist and then concretising it. Calling into being a thing which would never have existed, but for this back and forth process between intellectual and physical objects.
Similarly, the social sciences create abstract intellectual objects that model society, social groups, or social forces. Applied social sciences, or “social engineering”, then aim to turn intellectual models of society into social realities. In order to do so, they often need to create artificial environments, similar to laboratories, in which humans are molded to align themselves with the intellectual objects.
Modern education as a form of social engineering, for example, creates the artificial environments of schools, in which children and youth are fashioned into good citizens and producers, in line with the intellectual objects usually known as theories of education, theories of politics and citizenship, theories of economics, and so on.
The cost of objectification
Objectification is a marvelous process that is at the root of the power of modern science. But there is a cost to it.
No intellectual object can capture all of reality or all of the truth — the moment we create one intellectual object to get a better handle on one aspect of reality, we block out the possibilities of getting a handle or insights on some other aspect of reality. Think of the cost of objectifying a dog for vivisection, as we discussed in Re-Assembling Reality #18 — not only were the researchers (and dog) depersonalized, but most of the dogs died. The cost of some kinds of objectification is life itself.
Remember that creating an object means to extract it from where it was embedded (as discussed in Essay #18). By cutting off and carving a stone and a branch in a particular way, not only have we lost out on many other potential ways of cutting and carving — we have also lost out on knowing about the bigger thing that the stone and the branch were part of.
Similarly, scientific research projects need to focus on constructing manageable objects. The two hunter brothers we met in Essay #18 would be unable to turn the entire ridge, with its forest and meadows, into a single object. Some things are overlooked because the size and scale of the object would require too many resources to construct — and other things may be overlooked because, by their very nature, they cannot be objectified.
Mathematics is often the preferred language for scientific intellectual objects, owing to its precision and complex calculatory power in relation to certain things. But other things can neither be counted, nor calculated, nor modelled mathematically. If we only trust mathematical objects, however, we will only trust and value those aspects of the world that can be mathematically objectified. We will stop valuing those things that can’t be turned into mathematical objects. Or, we will change those things in order to make them mathematically objectifiable.
You think wealth needs to be measured? You can come up with a metric for “wealth”, and maths will do it. But this could destroy the other meanings of wealth, because they aren’t amenable to maths, and will replace them with a single, monetary metric.
You want to come up with a metric for education? Maths will do it. You want to optimize trade-offs between the number of teachers, the amount of money spent, the number of pupils educated to a given standard and the economic and social impact of that? Maths will do it.
But on the way, we will redefine what is meant by “teacher”, “pupil”, “educated”, “standard”, “economic”, “social”, and “impact”, because maths cannot deal with many aspects of teaching, learning, wealth, relationships, and so on. So we change the definition of “teacher” into someone who executes quantifiable teaching and learning objectives. We change the definition of “learning” into quantifiable knowledge. Thanks be to maths for giving us better definitions — the definitions that maths can deal with.
Do you want to come up with a metric for Beauty? Happiness? Effectiveness of parenting? A mathematical metric can surely be found — provided you don’t care about beauty, happiness, or effective parenting.
 McCauley, Why Religion is Natural and Science is Not, Oxford University Press, 2011, pp. 99–100.
 Neil Postman, Technopoly: The surrender of culture to technology. New York: Vintage Books, 1993.
This essay and the Re-Assembling Reality Medium series are brought to you by the University of Hong Kong’s Common Core Curriculum Course CCHU9061 Science and Religion: Questioning Truth, Knowledge and Life, with the support of the Faith and Science Collaborative Research Forum and the Asian Religious Connections research cluster of the Hong Kong Institute for the Humanities and Social Sciences.