I recently wondered about the value of the concept of presumption of innocence. I mean that in the legal sense. We base our justice on a presumption that the accused is innocent, that the burden of proof is on the accuser to prove the accusation beyond a reasonable doubt to a jury of peers. It is a concept that I learned at an early age so that I have such a firm conviction of its rightness that it seems to me to be a truth that can’t be challenged.

Now that I state that I’m sure there are philosophical writings that do challenge the notion in some form. For this post, it doesn’t matter that I’m ignorant of the arguments for or against the notion. I am not going to argue the legal merits or demerits of the concept, but I’m going to start with the contrary notion, that it is better to presume guilt and place the burden on the guilty to prove their innocence. Proving innocence beyond a reasonable doubt to a jury of peers is far harder than proving guilt. For instance, to prove a negative, one would have to document every moment of the relevant period to show beyond a reasonable doubt that the accused could not possibly have committed the crime.

It is hard for me to envision that this would ever be practiced in anything outside of fantasy novels, but I suspect it has existed in other cultures or in other times. I can’t imagine living under such a system, and certainly can’t imagine that I would retain my sanity under such a system. That’s just because I haven’t really considered the possibility. If legal systems that presumed guilt existed, I’m sure people learned how to live within it. I simply can’t imagine what such a life would be.

My motivation of this post is to consider some unintentional consequences of believing in the supreme rightness of the presumption of innocence. I think it has an impact on the broader social reality, far beyond the legal system.

A presumption is a safe default conclusion because we have found to to be true most of the time, or a presumption is something that we credit as being the cause of many benefits to society. Again, I believe this, but only because I this is what I was taught to believe as naturally true. I never have really considered the rational justification for it. It just makes sense to me.

In the legal context, the presumption of innocence is a protection against unjust convictions or punishments by the state. In this context, the presumption of innocence is merely a mechanism to put the full burden of the proof onto the prosecution. Failing to prove guilt results in a finding of not-proven-guilty and such a finding has the same weight on a person’s life as being innocent. Underlying the legal concept is that we accept that some truly guilty people may be found not-guilty, but this is price worth paying to avoid as much as possible from punishing the truly innocent. I’m confident we still end up making the mistake of convicting innocent people, and to be honest I’m not sure our justice system is very good about avoiding this error. But I’m also convinced the system we have is closer to being able to make a correct judgment than other other system.

But here, I want to talk about the non-judicial aspects of society where innocence is the absolute truth. This is not a failure to be proven to be guilty but instead that the innocence is not even questioned in the first place. This presumption implies a notion that innocence is naturally true. I want to explore the merits of this idea that people are naturally innocent so that it is the safest presumption.

I am aware although not well educated of the debate about whether humans are by nature good so that any failing is something that must be learned. This to me seems to be an ultimate presumption of innocence. The alternative is that any goodness has to be learned through culture so that a reasonable presumption may be that everyone is guilty because we can’t be sure they learned the appropriate lessons. I should study up more on this topic to discuss at some other time. My point here is to use this as a way to branch away from the legal concept to a more general concept.

Getting closer to the topic I want to address is another analogy of a presumption of ignorance we grant to people. More precisely we presume people are unqualified for something unless they can prove otherwise. I guess this analogy could work as a presumption of guilt since unqualified is closely associated with being a fraud, but I’m associating this presumption as similar to the presumption of innocence.

In this case, the natural state of humans is to be incompetent at the start of their lives. They need to prove their competence though various tests. This plays out in our education system where we start off teaching children rudimentary mental and physical skills needed to qualify for further training that eventually ends up with a level of skill that is valuable enough to society that the person can earn a living performing that skill.

When I started thinking about this, I was thinking of a college course that covered how to work with boundary value problems, that was particularly relevant for certain electromagnetic problems. Although I never had a job that required using this skill, I was proud to get through the course. It felt like an accomplishment at the time, when I was around 22 years old.

Looking back on that now, I can see what made it feel like an accomplishment. It was the result of a 12 year education that started with arithmetic, then progressed to algebra, then to geometry, then to calculus, then to differential equations, then to linear algebra, then to partial differential equations, and finally to boundary value problems.

It seemed like a reasonable progression of education at the time.

It is also necessary because each successive step required more specialized training where it is important that the teacher not waste time on students who were not qualified to for the more advanced topic. The earlier courses were primarily for qualification for later courses although they did train new skills.

What made me think about this now is why did it require 12 years to learn how to solve boundary value problems. What if the ability to solve such problems was something that was in high demand by society and that there were not enough qualified people available to perform it?

In other words, how long would it take to train a 10 year old to become competent in this mathematical skill, with the full implications of all the underlying skills from algebra through calculus. I don’t think it would take 12 years even for a mediocre intelligence such as my own. I think I could have learned it by my 12th birthday if that was what was needed.

What interests me here is that that was never an opportunity. By the time I was 12, I had no skills that could earn a living for myself. I suppose if I had to make it on my own, I could have learned some skills, but the opportunities for such learning were in more manual tasks like being a farm hand, or a laborer of some sort.

To be clear, even now I could see myself being content in a career of such labor even though my body would have been far more broken down by now than it is. To me, I’m content to be anything that others find valuable. I often imagine I probably would have been happier with my life if I had not gone to college and sought a trade instead.

My point here is whether we could treat academic training, especially in the science and mathematical disciplines similar to training for trade skills like welding or carpentry. With very rare exceptions, teenagers are not skilled at advanced calculus. We simply don’t expect it to be possible absent some rare precociousness.

That is when I thought about the idea of the presumption of incompetence and how it might be related to the presumption of innocence. A student must prove his competence.

I wonder whether it is useful to society to presume that everyone, especially young people, are incompetent. I think it may be more beneficial to presume competence, or at least to presume that capacity to become competent with accelerated training.

Assume we needed the skills to solve partial differential equations with known boundary conditions. Would it be possible to train this skill backwards? We could start with the problem that we really want to solve, and then train the necessary background skills to get this problem solved. The result could be a young person having a full mathematical skill that delivers value to society to the extent that he could make a living.

Clearly that training will not cover the breadth of skills that result from the 12 year training where each early stage results in a broad range of skills applicable to many different applications. Most people will make their living with a tiny faction of the breadth that they learned. This seems a waste.

Another waste is that we lose a lot of potentially competent students because they are bored with silly simplified examples of unrealistic scenarios because those are the only ones that can be solved with the skills learned to date. We wouldn’t lose these students if their first project were real world problems that society would immediately reward in some form to show their gratitude for the achievement.

The question is whether this is realistic. We presume that this is unrealistic. We presume that young people are incompetent. We even make stories about how their brains are still forming and that they will not be ready for the higher skills until their brains develop further. While their brains are developing, we make the best we can by training simpler skills generalized to be relevant for a range of future occupations.

I wonder whether we are missing the opportunity that could be possible by assuming that 10 year old people can begin learning advanced mathematics. Realistically, it will still take a couple years to get to marketable skills in this area, but I am confident it can be done in a lot less than 12 years. I speculate that an marketable mathematical skill can be learned before the mid-teens for even students with average intelligence.

We never give them a chance.

I started thinking about this as a contrast to our expectations from machine learning. Machine learning involves mathematical models based on a very simplified concept of a neuron. With a very few of these simplified neurons, we expect machine learning to learn some very complex tasks. Surprisingly these incredibly simple brains are able to solve some very difficult problems. While deep-learning neural networks may be very complex to comprehend, they are trivial compared to the networks available to 10 year old humans.

We can expect a simple neural network to learn a complex skill with a moderate number of training examples. Meanwhile we can not expect the same from a young human.

While the boundary value problem described above is a mathematical problem, I see an analog to what we expect from big data analytics. While there is no differential equation that connects the data, we ask the analytics to come up with some kind of solution that matches the observations in the data. The observations in big data represent a boundary for an unknown system that we want to predict that we want to see what is going inside where we can’t observe. Analytics and machine learning tackles this kind of problem (frequently successfully) by providing the answers we seek. They satisfy our needs without our understanding of skill required to come up with that solution.

We understand the math behind analytics or machine learning, but we don’t understand the solutions involving internal data sets too large for humans to interpret directly. The machines have a skill that can only come from training but they are fully capable of learning this skill quickly despite access to only very small networks of simple models.

I wonder if our preoccupation with the presumption of innocence has over time distorted our view of younger people. We transform the innocence into some idealization of life so that we are motivated to prolong childhood in a misguided attempt to postpone exposure to guilt.

Behind this messy argument is a deeper concern I have that we are doing a disservice to young people by presuming that they really do need more than a decade to learn advanced skills. We can subject young people to more intense education than we are now, and that they could have college-graduate level skills before they become 18 years old. Yet, we think that such an expectation is unwise as if it risks losing something more valuable. Perhaps we fear the young person’s loss to easy access to the presumption of innocence.