Monomorphic

We distinguish between inventions and discoveries. You can own the intellectual property rights to an invention, but not to a discovery (you can’t patent the discovery of mercury or selenium, for instance). Inventions are meant to be created, and discoveries are meant to be sought for. But sometimes, the line between invention and discovery is blurry.

We cannot own the rights to mathematical structures or theorems, since they follow directly from axioms. Anyone with a mathematical education would come to the same results within the same axiomatic system. The creation of a mathematical theorem can be said to be a search process, hence the term “discovery” and not “invention”.

We can own the rights to music and paintings, since these are considered to be inventions. But isn’t the process that leads to a painting or work of music being created also a search process? Doesn’t the artist search for possible combinations that work together, in a — albeit very large and continuous — search space? But this is considered to be creation/synthesis rather than search.

The software developer is, at least sometimes, somewhere in between. A vision of a user interface that interacts with end users in a certain way can perhaps be said to come from the same large, continuous space as music and paintings come from. But given the constraints imposed by such a vision, and by the platform on which the system is to be built, the available libraries, the languages, etc, I would say that the construction of much of desktop/consumer software is a search problem. We look for combinations of components that fit the constraints, and when we have decided on this combination, we must connect the pieces together correctly. The space of possible solutions here, at least for someone who follows good design principles, is in essence much smaller than the music/painting search space. Of course there are considerations of taste and style, but they are completely irrelevant to the compiled product. They are a programmer aid.

Artificial intelligence problems are defined as search problems. But what are search problems, and what are “creational” problems, precisely? Is it merely a question of the size of the search/design space?

Today an oppressive, passivizing heat covers Tokyoites like a massive woollen blanket. Summer is here. In a feeble attempt to defy the heat, I follow up on my previous post on languages and automata.

That post ended with the suggestion that we can apply these concepts to interactions in society. But can we? As a starting point, let’s think about stateless and stateful interactions in a system. Stateful interactions involve a change of state, in some sense. Stateless interactions involve no such change. What counts as stateful depends very much on how detailed the model is – these might be examples:

• You make a purchase in a convenience store – the obvious changes of state are the balance in your wallet/bank account, the amount of items you possess/carry with you, and the corresponding opposite changes on behalf of the store.
• You greet somebody you know on the street and exchange some small talk. Even though no actionable information is exchanged, you both feel happier afterwards and in a better mood because you were acknowledged by someone else. This is a change of state. The precondition is that you are in a state where you know the other person – this interaction would not be possible with a random person in a random state. (On a different level, a typical such exchange goes through at least three discrete states in itself – “greeting”, “exchange of information”, “goodbye”).
• You go to your job in an office, read some documents, write some reports and leave. We can think about the wear and tear on the furniture and the building, the carbon dioxide-oxygen exchange in the air, and the changes to your company’s total body of information as changes of state. Which to choose depends, again, on the model.

Are there any stateless interactions then? Within the context of a particular model, yes. If we only care about monetary and material transactions, the meeting on the street might be stateless. If we only care about “mood” states, the purchase in the store might be stateless, and the office job might have a negative effect on accumulated mood.

In software engineering, we always try to hide state as much as possible. State makes the system far harder to understand and reason about.  We like immutable objects, whose state never change. If we look at reality through abstractions, maybe such things can exist, but in the physical world I don’t believe they do (I’d have to ask a physicist to know the answer though).

The most complex interactions in society, I think, take place among people and organisations that have long lasting relationships. These entities can modify each other’s state over a long period of time. If I’ve known somebody for years, there’s a very large number of possible states a conversation with that person might be in, a large number of topics I might possibly bring up and discuss. But the limitations of societal norms and my own knowledge imply that a conversation with a stranger might be a very small state machine indeed. (On the other hand, maybe this is why getting to know a new person can be very satisfying – the newness of building a new structure from scratch in your head to represent this person’s states). Companies that interact with customers in short, anonymous relationships almost never present them with complex interactions (convenience stores, taxi drivers). With other companies we have more complex interactions and longer relationships (doctors, banks).

These transitions of state are, again, like words that make up sentences in formal languages. We all live these languages every day. How many states do you have?