The limits and applicability of knowledge

Miss McInerney has asked for principles, or “touchpaper problems“. Well, here is my two-pence worth.

It is a well known phenomenon that as we cool substances their density increases. Liquid is denser than gas, solids are denser than liquids. We know this. Water is a good example. Liquid water we drink is denser than steam or water vapour. And ice is denser than liquid water which we can obviously see because ice sinks when… hang on, thats not right. Ice doesn’t sink. It floats. Well it does on my Gin and Tonic.

Water is a strange substance. Few others (silica being one of them) have this property where the solid state of the substance is less dense than the liquid state. And it’s very important that it is. Cold water rises in an ocean and in small bodies of water ice forms on the top providing an insulating layer, creating year round conditions for life to thrive. If ice sank then ponds would freeze in the winter killing all life within. So, if water did not have this property either there would be no life on earth or there would be life, but not as we know it. Jim. For more information about what happens to water as it freezes see here.

Water has other interesting properties. It is known as the universal solvent. There are few common liquids that act as a solvent for so many other substances. Of course, some substances dissolve in spectacular ways. Which is a really good excuse to show this:

Of course, not all substances do this when thrown into water. Salt for example, forms brine, which again helps with the whole not killing everything in the water thing. It also help increase the oxidising power of water.

So we know all these things about water. We know about these effects. In order to make use of these properties, or to design around them, do I need to know why they happen? That depends on who I am and why I am interested in the effect. If for example, I am designing a structure in water I obviously need to know these effect exist, and which substances I can safely use. So, no submarines made out of Caesium, for example. It’s enough that I know about the effects, that they are predicable and consistent. It is also important that I know which groups of substances react in which way. But I don’t, if I am just building a structure in water, need to know that the density effect is due to the nature of the bonds being formed in the cooling liquid and how the crystals are packed.

So a lot of this information resides in the periodic table. The columns and the rows mean something, they are different classifications of substances. For a simple description of this classification look here. This tells us a lot about how different substances will react in different circumstances. There are more detailed sub-classifications but for most everyday uses the periodic table is sufficient.

Ok, to the point.

Well, two points.

First one is that before we look to work out what we want to know, we have to to establish how much we need to know. Do we need to know how the hydrogen bonds are shortening which is causing the packing density of the ice crystals to change, or do we just need to know that ice is less dense than water? In an educational context, do we need to know exactly how the brain encodes memory engrams before we can establish the most effective way for students to memorise information, or can we just try a few ways of memorising and use the one that turns out to be more efficient?

Simply put, is there a limit to how deep our knowledge has to be about something before we can just accept that it is as it is and use that knowledge to our advantage? This approach has obvious risks. For example, imagine if the builder of a structure on water had tested the density of water at different temperatures but had stopped before getting to 4C? They would not have found the area where the problem exists. So the approach is OK as long as we define the bounds of applicability of any methodology. E.G. method X works with students between the ages of Y and Z. This also places us nicely in a scientific context. We can accept that we know what we know, and also that at some point in the future we may know more which might lead us to do things differently  – we could currently be wrong. There is no shame in accepting this. No one ever criticises Newton for not knowing his Laws of Motion don’t work at close to light speeds.

Which brings us nicely onto the second point.

Some things work with some groups and not with others. Dropping iron into a basin of water doesn’t make the basin explode. Caesium does. Method A works with Group J but not with Group K. Here’s the touchpaper question. What are the groups? Into what identifiable groups can a cohort be subdivided so that interventions (designed for that group) can be applied with (an acceptable level of) certainty of success. The number of groups should be as small as possible (to be manageable) but there need to be enough groups to increase the level of confidence that effects will apply. It is also important that the ‘rules’ for membership of the group be able to be consistently and easily applied. So reasons for group membership will need to be objective rather than subjective. This is not about dividing into sheep and goats. An individual could be a member of more than one group.

So to summarise, I want to know how much is it we need to know, and who we can apply what we have learnt to. In one sense these could be considered to be issues that underpin any other touchpaper problem. Without knowing those two things (i.e. setting bounds on the applicability of our knowledge) we will continue to see arguments about what works best because we can always find different sets of conditions where different interventions can be used and claimed to be the best.



@a_weatherall was kind enough to suggest the post reminded him of Richard Feynman talking about magnets. I’ve never needed much of an excuse to post videos of Feynman talking, so here’s that one:




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