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problems with quadraxials - was: designing a glaze - stephani

updated sat 7 jun 03


Ian Currie on sat 7 jun 03

Hi Stephani

Firstly, thanks for this...
>>I like Ian Currie's method,

But this....
>>which I surmise is an adaptation of
>>quadraxial blends, because it shows me some observable relationships.

.... definitely needs some qualification. This comes up many times,
because it can be hard to get one's head around the relationships....
but in brief, my grid is NOT a quadraxial. It has been called as such
even by experts, and all the blending, recipe calculation etc. works the
same as if it were a quadraxial, but there is a vital difference...

In a quadraxial experiment you can put whatever you like on the 4
corners, which means that you can blend 4 random variables (glazes in
this case).

In my grid the 4 corner glazes have a fixed relationship to each other
so we end up with a rectangular experiment with silica increasing to the
right and alumina increasing to the top... 2 variables, not 4. (It
could be square if you prefer - I won't go into why I chose 5 X 7 here...)

My grid is actually a 4-sided part of the flux-kaolin-silica recipe
triaxial... the part that melts, more or less. If you have a copy of my
book "Stoneware Glazes..." you will see this on Diagram 8.1 on page 46.

Four variables may seem better, but there are 2 major problems with true
quadraxial experiments that in my mind rule it out as a useful tool, in
comparison with for example a triaxial. (And I say this knowing the
extent to which the true quadraxial has been used in ceramics and other
disciplines... they still have the same problems...)

The first problem with trying to fit 4 variables onto a "flat"
experiment is that it is not possible to get all possible combinations
of the 4. The combinations you get depend on the order in which you
place the 4 around the diagram. Imagine for example trying to find the
glaze that is a 50/50 combination of the two glazes from opposite
corners. That glaze does not exist on that quadraxial.

The second and more serious problem is that, except for along the
outside edges (which are simple line-blends) it is not possible to say
unambiguously what is causing what. I know you understand clearly the
power of separating out the variables... you said:
>it shows me some observable relationships.

The reason my grid does this is because it is laid out so that you can
go one way across the grid and say... "this way only silica is changing"
and you can go another way and say "this way only kaolin is changing".
You are looking at cause and effect. This is basically what causes the
lights to come on when the grids come out of the kiln at my workshops.
Bring too many variables into the "flat" experiment and this becomes at
the very least clouded, sometimes hopelessly confused.

By the way, you can do higher orders than 4-axials. It is easy to do
6-axials, 8-axials etc. The more variables you use the less and less
you see all the possibilities, and the more confused the results are if
we are seeking cause-and-effect information. I suppose an 8-axial is a
useful ordered way of throwing 8 glazes together at random and seeing if
anything interesting comes out. But if you are going to do that much
work, you also want to go for the big prize... There are two things you
can get out of this sort of experiment... 1. some useful glazes, and 2.
understanding. Long term the big prize is understanding, as it
facilitates useful glazes.

So, how many variables can we accomodate unambiguously on a "flat" or
2-dimentional experiment? If we lay it out like an x-y graph with the 2
variables x and y at right angles to each other we can achieve two
independent variables maximum. By independent I mean they can vary
completely independently of each other. We can however put three
variables on a flat experiment if we use the triaxial format. Here the
3 variables are INTERdependent in such a way that the total of the 3 is
kept constant. And if I had you in front of a piece of paper I could
show with diagrams how the triaxial and x-y graph can both be used to
represent the same experiment. However text like this has its
limitations, and I probably should have given up several paragraphs
back, but Ivor will read this far even if nobody else does! Hi!!

A message from the sponsor... you can buy my books on glazes at my
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