Monthly Archives: May 2024

Mistakes and Innovation

Innovation is often brought about by pressure. You can do something a certain way and it is expensive, so cost pressures you to find a cheaper way. The expense can be time, material, monetary currency, complexity, reliability, lack of beauty. The expense does not even have to be real to pressure you towards innovation. It just has to be perceived.

Early on in my development of my current light installation I had to have a way to turn up and down the levels of light on Red Green and Blue LEDs. The light levels built into my RGB chip that I am using are 0-255 . There are only 256 levels. The problems are that there is nearly no difference between 254 and 255, the lowest levels are not visible, 0,1,2, and sometimes 3, cannot be seen, and the difference between 3,4,and 5 are pretty coarse and that the three colors have different properties. Some seem more linear at lower levels than others. The lowest visible level on each of them is different. Each time you want to adjust one of the levels you change the code and then load it up to the chip. Getting it to look smooth was not difficult, but at the start it was time consuming.

When using a bigger chip with more memory I used three lookup tables for the levels. This is a table that might start like this, [0,2,3,4,6,8,10,13,16, etc.] But for this piece I only had ATTiny 85 chips during the development. Others were becoming available again. The ATTiny has got “Tiny” in its name for a reason. At $1.59 its memory is limited.

Using the lookup tables I started to get “out of memory” type errors when trying to “compile” the program. Compiling is the process where what you have written gets translated into the code your computer, in this case the ATTiny can use. I had to come up with another way. The errors made no sense to me, my program did not use that much memory. But I am not a computer scientist, no degree, no deep expertise. “Live with it, find a new way”.

So, instead of using a lookup table I used multiplication and division of integers. But because numbers with decimal points use more storage, I would multiply by 106 and then divide by 100 then add 1 on the way up . So 30 stepped would step to the integer portion of 30*106/100 +1, or 32. 100 steps to 107 and as you get higher the steps get bigger. Coming down I multiply by a number less than a 100, say 94 and subtract the 1. This does not use that much less memory as far as I could figure, but it worked. Maybe there was something I did not know. I cannot know everything, sometimes I just let things be if they are working.

Well turns out I had tried to compile my software with the settings set for an ATTiny 25, not an ATTiny 85 and it has much less memory. However, the new method is much easier to tweak and keep track up so I have stuck with it. It produces numbers very similar to my lookup tables, mostly because my lookup tables were done by mostly approximating the formula in my head. The formula has a softer top or bright range and I like the way it looks. I ran a single strip of lights back and forth the old lookup table way and the new way. I like the new way. If I go back to a lookup table for some reason I will likely calculate the steps.

The chips I am talking about using in the next piece have four times as many steps. I am about to start working with them. But I think that the properties of LEDs will stay the same so the formulas will stay similar. Since the communication time with the new LEDs is also faster there should be less jitter and flicker. I am excited to see them. With more steps lookup tables become even less efficient and more difficult. The multiplication and division for indexing is much easier.

Air Bubbles

Unfinished.
There are a lot of oversimplifications. In some ways any statement can seem one. Sometimes oversimplifications contain truths but fail at conveying understanding.

“Air bubbles cause explosions” is an example of an oversimplification common in my field of clay work. Often this is explained as “just untrue”, “air bubbles do not cause explosions”. Unfortunately, to me these examples both are partial truths and partial falsehoods. It makes me uncomfortable to write them down. 

In order to understand how air bubbles encourage explosions you have understand what an explosion is, and when it takes place, why. I am going to leave out explosions in air, in many ways they are a separate case.
Clay explodes not because of steam. Steam is part of the picture in most clay explosions. The clay explodes when the wares ability to contain the pressure of the gas inside is exceeded. Strength is important. It is the most important reason why it is harder to explode bisque. Bisque is stronger and can contain, hold, withstand more pressure. Porcelain may be easier to explode because of less pore space, but it is also because it tends to be weaker as greenware. Paper clay may explode less because of pores letting the pressure dissipate, but also because the paper fiber vastly increases the tensile strength of the greenware.
If you think of a quarter inch slab of clay 4 inches square, you can also think of it as two 1/8 inch slabs connected where they touch. Each of these slabs is stronger because of the other. When you think of them disconnected they are less strong. The reason that air bubbles preferentially explode is because of the weakness in the wall that the air bubbles create.

Things that decrease pressure from steam

  • open pores from grog, course clay, pinholes, other inclusions.
  • slower heating
  • dryer clay

Things that increase strength

  • lack of air bubbles or other strength reducing imperfectionsor inclusions
  • fibers
  • stronger clays. Some ball clays are chosen in industry to increase dry strength.

Clay can also explode because of organic inclusions and water of hydration of clay and other minerals. Colemanite chunks in your clay can cause explosions. So can plaster. Likely there are other theoretical causes.
—
— additions in response to questions
-Evaporation in a closed vessel (or one with small holes) is a complicated dynamic. I will try and explain it all in a way that can easily be understood. I have not tried before.
-Standard pressure is the pressure of air at sea level. It varies some,,, but it is a good place for a standard.
-I am going to leave out discussions of partial pressures. They do not seem needed at this point. But really understanding this might require it. One step at a time.

As water evaporates or turns to steam it absorbs energy. The molecules in water become more energetic and “bounce around more” so they act as a gas rather than a liquid. This is a substantial amount of energy. So, it takes a while to increase the heat past boiling to evaporate much water. The temperature of a pot of water in air essentially does not raise above the boiling point until all the water is  gone.  This is why your pot of water on the stove does not all instantly evaporate when you get it boiling. You have to add more heat to it. To make things simple, it takes 70 calories to bring 1 gram of water from 30 degrees to 100 (One calorie per gram per degree C). But it then takes 540 calories, at room pressure to evaporate it. Until you add the extra heat it will remain a liquid. So this process is not instantaneous. In a kiln at that temperature you are mostly transfering heat to the ware via convection. It is a slow process. This is part of why you can have explosions when the kiln is at 250˚C. The water has not had the heat added to it yet in order to evaporate. Convection is slow unless the temperature difference between the ware and air is high.
At sea level water boils at 100˚C (212˚F). As you go down in pressure, as happens as you gain elevation, the boiling point goes down.
As you increase pressure the boiling point goes up. This is most of the reason pressure cookers cook faster. They cook at higher pressures and hence the water in them gets to higher temperatures. The pressure comes because the water has enough energy to become a gas but is constrained by the volume.
So as you make steam in your clay by heating above 100˚C the pressure increases. If it is small enough to not explode the work, this increased pressure slows the evaporation because you now need to climb in temperature as well as add the heat of evaporation. Hopefully the steam leaks out through the pores fast enough that the pressure does not get greater than the clay can hold.

I hope that this is clear enough to make sense.

In glazed near vitreous ware that has gotten water into nearly closed cells traditional drying below boiling is not very effective.
Consider a long very narrow tube connected to a small container of water where the tube is the only opening to the outside. Just for an example lets chose 95˚C . My numbers are approximate.
Lets also assume that the tube starts completely saturated with water vapor. This is about 80% steam.
There is no great force moving the steam out of the tube. The way it leaves is via diffusion into the atmospheric air. As the water is creeping out via diffusion the air is creeping in. In a long narrow tube this happens very slowly. Until the percentage of steam over the water drops, no more can evaporate.
Bringing the temperature to just under the temperature of boiling does not help this dynamic. It just raises the percentage of water in the gas in the tube closer to 100%
Two things do change as you raise the temperature. The viscosity drops and the surface tension drops. These two properties do change the dynamics of drying in clay. As they drop the water is more able to spread out on surfaces providing more opportunity to dry, and also to spread more evenly through an object. But with really small pores it likely does not help enough to make much of a difference. Very little water will close off the pore.
It is my opinion, I do not treat this as fact, and I am not responsible if you blindly accept the ideas of some retired clay dude and blow up refires, that the best way to dry out refires is to get them near boiling, hold them at that temp until they are uniformly hot and then slowly raise the temp past boiling. I use 113˚C as the top temp if things are very thick and have soaked in water. I have used 2˚C per hour,, I suspect it is excessive.
The problem is that thermocouples and meters are not particularly accurate, even type R pr S unless you calibrate them and spend big money. Consequently you need a buffer for error.
As you add heat above 100˚C (assuming sea level) you will boil some of the water. This will increase the pressure in the container and force water and steam out of the tube. So long as the container, your clay body can withstand the pressure (better not be to high) the water will be expelled. Just before I retired I used a slow rise rather than a hold at ~110˚C to finish drying stubborn items and take care of cold spots.
The last couple of years I have thought that a long dry below boiling was a waste and that trying to get just above boiling would be more productive. The problem here is that kilns are not even in temperature and as they get older and leakier they get less even.
—
This discussion parallels high temperature drying. Once your ware is leather, unless it really is close to not being able to hold itself up, drying at a high temperature is superior. The low surface tension and viscosity of water at higher temperatures allows the clay to remain more evenly wet. How slow it dries is based on how fast you bleed humdity out of the container holding it. This might not be particularly good for kilns, but I think that its problems are over-rated and the real problem with corrosion is from the organic acids from organic matter. Somewhere I have something written on this process.
[answers to questions and clarifications added]

Where is the Functionality in Students Learning Calculus in High School When Few People Use Calculus in Real Life?

-a tribute to Mr. Alvin Mayes who taught Calculus to me 50 years ago, and an unnamed graduate student who taught Calculus at the University of Michigan a year later-

Some of this will not be understandable by those that do not understand calculus. None of it will be understood by those who do not try.

Calculus is a language and way of thinking, a way to describe properties of the real world and to learn about them. It was first discovered by Newton and not published and then discovered by Leibniz. Although it is used for other things it provides a language for describing the properties of curves, an advanced vocabulary for some properties of solids, and ways to understand the cumulative action of forces on the movements.of objects. It has its little fingers in every aspect of our life.

I cannot say that I use calculus as much as I could or even should, but it does get used when I press the accelerator of my car. I think about it as I turn the water down as I am filling a container so that it won’t overflow. Acceleration, and deceleration are topics covered in calculus classes. When you leave a stop sign do you depress the gas pedal at a constant rate? I don’t. I press my foot down rather quickly at first because I want people to know quickly that I am moving and then slow the depression of my foot with the rate moving towards a steady state when I am at speed. I am sure that how I do this is not optimal for gas savings. How I do this is a compromise between safety, speed of travel and gas. I also try not to tax my brain too much as I drive. My understanding of this is informed by my understanding of the curves that describe the motion and its affects.

I have taught a lot of pot making over the years. It might not be the most effective way to teach about form, but for some people the discussion of form is best done classically by breaking it up into pieces that can be described. There is more than one way to cut a cake, and really you do not always even need a knife. But one of the ways I do this is to talk about how the radii that are tangent to the pots curve at different places change in length. I should be clear for the mathematically inclined that I do not discuss slope as described by my Geometry teacher Mr. Waldman as “der rise über der run” because it is not as useful as talking about a more linear seeming property, the rate of change of the angle of the slope. (By this definition a vertical line has a slope of infinity, a horizontal line 0 and a 45˚ angle one. The difference between horizontal and 45˚ with this concept is 1 and from thereto vertical is ∞ -1. This is not intuitive.) I talk about change of angle. With this a tight curve in any orientation has the same description. The radius of a curve at any point in the curve is a basic concept that I use in most other concepts about curves.

Studying calculus you look at a lot of curves, think of them in terms of rates of change, or acceleration, deceleration. When you push down the gas pedal at a constant speed your car accelerates, but there are competing properties at work. It is easiest to talk about in a manual transmission once the car is moving. At the low end, when the pedal is only depressed a little bit your car accelerates but as the pedal moves down further, if it does it fast enough you car starts to accelerate faster and faster. At some point near the “pedal to the metal” point, fully depressed, your car may still accelerate, but does so slower and slower. I have slightly redefined some concepts in calculus so that I can use them in life without having to work too hard.

If you are trying to get your car to say 60 kilometers per hour and do so quickly, you may push the pedal down rather quickly and find that you have to ease off when the car reaches sixty. At some point driving like this your foot stops going down and starts easing off. This is an inflection in the depression of your foot. Knowing where you should do this makes your driving smoother and probably reduces gas consumption. I suspect that not having an inflection at all probably saves more. Knowing where to depress your foot to to achieve a steady state and easing up on how fast your depress the pedal as you approach it also likely improves mileage. It also keeps your passengers happy.

An adult I used to drive with complained that the dog only threw up in the car when they were driving. This is because they used the accelerator similar to an on and off switch with no idea that a steady state might be better. That they used to teach calculus did not help them understand its application in driving. So it goes.

As a curve gets tighter its angular rate of change accelerates, it changes more and more quickly. As it gets broader this decelerates, changes slower and slower. When a curve goes from being concave to convex the mathematical description is that its second derivative goes from being a positive number to a negative one. The mathematical concept may not of much use to the casual user of calculus concepts. But the point of change between the concave and convex is a critical point in the description of some “complex curves” (my phrase, meaning a piece of a curve with a discontinuity in the first or second derivative or a curve that goes from concave to convex ) . This point, again where the curve goes from concave to convex is called an “inflection point”. Knowing precisely where this is in change from the belly to the neck in some jars or jugs makes recreating the object much easier.

A “first order discontinuity” (an abrupt change in the first derivative) is a place where two curves join producing a sharp angle. A “second order discontinuity” (second derivative) is a place where the radius of a curve abruptly changes. So if you take a 3 inch diameter arch and attach it directly to a 5 inch diameter arc so that there is no corner , this is a second order discontinuity. If one is concave facing up and the other is convex facing up,,,, going from concave to convex,,,,, then this is also an inflection point. A first order and inflection together is really quite unusual but does happen at the intersection of bellies of bottles to the shoulder. it can have a very different look and feel than the second order kind, you have to keep this straight. While I think about third order changes, I do not think that I can perceive them in products. I let them be as just abstract thoughts.

In throwing on the wheel the axis of rotation is always vertical. But a dear departed teacher Victor Babu, used to talk about taking a curve and slightly tipping this axis. He did not use the phrase axis of rotation. His way of describing this was in some ways better. He tipped the curve to be rotated. Not having a good phrase to hold the concept made this sometimes difficult to describe to some people.

In high school I did very little homework. This is in part because I hated writing anything. ADHD likely played into it. The “write it over stuff but make it neater earlier in my education made homework as a topic very unpleasant.” The only time I can remember completing homework regularly was when studying with a friend. I did learn. In 11th grade I was in the semifinals for the Michigan Math Prize competition. I think that this changed my standing in the eyes of Math teachers, but they already knew I was smart. I had not studied enough to have a chance at the finals. My high school owned this competition back then. It was a great place to go to school.

Because of not always getting all the concepts and not doing homework, not practicing, and errors in basic processing of numbers I got mostly B’s and C’s in math. I did get a D in 10th grade (might have been 9th grade) and my mother made me take a course over the summer. To the best of my knowledge I was the only person ever to pass Mr. Waldman’s Geometry class without doing my homework. I read the textbook over the summer before it. At the end of the first few days I took the first test and got 100 percent, then took another quiz . A few days later I took the final. Despite his policy of failing the course if you did not do homework, I got an ‘A’. Its fortunate, because if required to do homework I would have failed. Unaccommodated dysgraphia can be a disaster.

After my first class in Calculus with Mr. Mayes, a class I believe I got a ‘B’ in, I got a ‘3’ on an advanced placement test. This was not a high enough grade to earn credit for Calculus at The University of Michigan Engineering School. It did show that I knew much of the content. I had not memorized formula and rules for doing some problems. The class despite being difficult. I can remember the good nature of Mr. Mayes. He had an incredible smile an patience. But the ‘3’ meant that I had to take calculus in college. The TA was a joy. Starting at the beginning again it all quickly came into focus. I did not do the homework, but easily aced the class.