I recently received an email from a former student (Class of 1965) whom I stay in touch with on an occasional basis.  She and her husband own and operate a B&B in the Yucatan, The Flycatcher Inn.  Kris is a former high school art teacher and very successful professional  jewelry designer.  The following represents what I believe teaching is all about.  It has very little to do with test scores and a whole lot with the development of an inquisitive spirit that may not surface for many years.  Here is the exchange.  Note that it continues beyond this post.  Not bad for 45 years later!

Kris-

Dr Bob. I am delighted to hear that you are still “agitating”.  Someone needs to do it!! My daughter Clair in Eugene seems to do the same. She is still at North Eugene high school, and loves it. We are currently in Puerto Vallarta, checking out this side of this amazing country. We still have the Inn, but for the first year in many, we are not building so we are taking advantage of the time spaces and traveling more. I think I should have been an architect…. next life.

Do give our best regards to your lovely Marie. I will check out the new website you have. Enjoy the Joseph country.

Good to hear from you!  Cheers, Kristine and Santiago

Kris-

Hi Dr. Bob. I have a question that you may be able to answer, but first I will have to explain where the question came from.

We were recently in Puerto Vallarta, on the Pacific coast side of Mexico, and there was a man doing “beach exhibitions”. There is a section of beach there, near where a fairly good sized creek runs into the sea, composed of large relatively smooth rocks instead of coarse sand. These are small to large boulder size, and aside from being in quite a few diverse lovely colors, have quite a diversity in shape also from long thin ones to bigger ovalish ones. This strip is not terribly wide, maybe 6-8M, from ocean to sidewalk. The tides seem not to change much here either.

The first time we passed this area, there were some amazing sculptures made from these rocks, maybe 8 or so, and none more than three rocks high. Most were just two rocks, one balanced perfectly on top of the larger base, but in some the top rock was actually larger than the base. Sometimes it was MUCH larger than the base. All these were balanced on a point, and sometimes the point was on a fairly steep angle of the side of the base rock.

Depending on how you looked at them, from what angle you saw them, they would look like they were balancing on no more than a point as slender as your finger. If you moved to a different perspective, then you would see that the balance area was actually wider than just a point, but from any direction it was hard to believe. There was a young mexican man doing these. Not a large man, and not terribly muscular looking. Sometimes he would use a smaller roundish rock between the two larger rocks, the top rock being balanced on this smaller one.

NONE of these rocks were flat, nor had any real flat surfaces, but they were generally quite smooth, like river rocks are, so there was no real porosity to give him an edge that way either.

First he had to balance the base rock, which wasn’t all that easy as it was resting on the rest of the rocks in this section. Then after establishing that to his satisfaction, he began looking for the next rock to balance on this base. And it wasn’t just any old rock. He was very picky as to color and shape. And they were just wonderful! I thought at first that they had been glued and it was a permanent exhibition, but the second time we passed, there he was putting one together, and it just intrigued the heck out of me.

These top rocks were around 50-60K, and the base would have been more. He could barely wrestle the bases into position, and some of the balancing ones, he really struggled with. The top rocks were something like 40-60 cm high, and 30 wide. This is really general because none of them were the same, but the type of rock was of a similar nature.

We stayed and watched for a long time each time we passed. Finally when he took a break, I talked to him. He just does it because he wants to. I asked him how long each one will stay up, do people knock them down, does the wind knock them down, etc. He said that they don’t stay up too much longer than 2 hours (if there is no climate element adversely affecting them) when the sun is full on them. When the sun is full on. they last longer in the early AM, or in the evening. (He says sometimes he knocks them down, just for the heck of it and sometimes people passing knock them over because they think they are glued). But he says most of the time, after about 2 hours of direct sun, they just begin to fall. He starts all over each day and never uses the same combinations.

So my questions is, why would the direct sun affect them so much? The sea doesn’t reach them, but they are sitting on damp rocks from the spray, the slight change in tides, and the afternoon rains, so the stones must be slightly damp when he begins to work with them. I would then suppose that once they are balanced, they then no longer are in contact with anything damp and obviously begin to dry out. As they dry out and lose moisture, wouldn’t that affect this delicate balance? Because although a slight wind doesn’t affect them, a stiffer wind would. Their balance is pretty precarious, but each day none had fallen in the time period that we watched, and passed by later, although it was never more than about and hour or so. There would be none standing by the next morning.

The balance was just incredible. To watch him decide, he would study the bottom rock for a long time, and from every angle. And he wasn’t a showman either. it was like he was completely unaware of anyone watching him, he was so concentrated. Then when he actually lifted the top rock, he embraced it the whole time, until he settle it into balance, which sometimes was many many minutes. This was not a fast process, and sometimes it was off and the top one would fall, but not often.

It was like he was talking to the rock while he was working.

So why would they fall?

Bob V-

You know me, I have a theory about what might cause the tipping, but really want you to figure it out.  Remember the boxes with hidden contents I would never let you open?  Anyway, my theory has to do with expansion and contraction due to temperature differentials and with where the fulcrum of the lever is placed.  I will keep thinking about it and hope you do too.

Kris-

I see… silly me to think you would just give me an answer!!

Yes, I now remember the boxes.

I was thinking of expansion and contraction too, and climate, as well as wondering about the placement (fulcrum, thank you. I now forget words in english). And wondering if salt water would have any stronger effect than plain old river water. If we had been there longer, I would have put some of my theories to test, and asked more questions of the guy!

You may know that once something intrigues me, as this did, it doesn’t leave me mind until it is solved. might take awhile. We don’t have any such rocks to experiment with.

We took some pictures. I will try to send you some.

I thought about the salt water, but the weight would only change by the amount of water that evaporated and I assume it would evaporate ll over the rock in 2 hours.  How much did the temperature change over the course of the 2 hours required to fall?  Did one side of the rock receive more sun than the other?

Bob V-

Amazing what we can call back from our memory if the appropriate situation arises.  What is happening here is one of the reasons I am so upset about paying teachers based on their students standardized test scores as is being proposed here in the States.  I think it is more valuable by far that you can recall things from class 45 years later that were designed to make you a better thinker than to remember in 3 months on a test some “fact” that might even be disproved at a later date….Sorry about the soapbox!

Sorry about the typos.  I am working on my laptop (literally) and my fingers keep skipping keys

Do you mind if I use this exchange in my blog (Either http://valetc.com or http:// ksdcitizens.org)?

Kris-

I don’t mind if you would find it useful.

The sun was pretty much direct overhead during this whole time, and the temperature there changes little during the day. It was around 96º this whole time, with almost no change. There was no shade from surrounding trees, nor buildings. There was almost no wind to enhance the evaporation either.

The sun comes up behind the low mountains well behind the sea area, passing straight overhead, and sets in the sea. Thinking about it, most of the sculptures seem to have the top rock balanced on what would have been either the south or north sides, or faces, of the base rock, but this might be because of the east/west slope of the beach.

Very few of the sculptures had a small, roundish rock as the balance point between the two larger rocks, but I didn’t think to ask if they would stay up longer than those without.  It would be logical to assume they might.

I am assuming that it has to do with the moisture that must have penetrated the rocks during the night, and especially if it rained which is typical of this time of year, evaporating as the sun is directly overhead, drying out the rock to the point that it upsets this very delicate balance.

Since it did rain almost every night, and the tide didn’t come in far enough to cover the rocks, then most of this moisture would not contain salt. And maybe that is a factor as to why they fall soon also. Salt when it evaporates leaves a crust and maybe that would help it stay up longer. One would have to make one using sea water, and one without to check that out, but it probably would be minimal anyway.

I am also going back over what the colors of the rocks actually were. None were really dark in color, so one wouldn’t absorb more sun and dry faster than another that was much lighter in color. But would it make a difference if the balancing rock was a darker tone than the base rock? Or vice versa? And yes, they created their own small shadows from the top rock to whatever was below which would mean that that area would dry slightly slower than the face exposed to full sun. But since the time period he indicates that the rocks begin to fall would be with the sun directly overhead, the shadowed area would only be that of the fulcrum area, and pretty much the same all around. At this latitude, there is very little change in the sun between noon and 2 PM.

We have 4 photos, taken two different days. I will send them to you. As you can see by blowing them up as much as possible, some of these rocks are definitely more porous than others, such as the red top rock in the last two photos. You can also see the man working these and how large they are in comparison to his stature. I would assume that the more porous the rock, the easier it would be to balance and that it would retain moisture in it’s pores longer than the smoother rocks. So one would have to be there when they started to fall to see which falls first as I now see that several factors should influence how fast they fall.

You always taught concepts, Dr. Bob, not just “memorize this”. I completely agree with your views on testing. What you pass on a test within a short time period is not a good indication of what you have really LEARNED.  Big difference.

Bob V-

Do you know the direction in which the rocks fell?  My theory predicts they would fall toward the sun.

Kris-

Assuming that falling in the direction of the sun means that they would fall west, this would be in line with the slope of the beach, and the direction any below surface water/moisture might be moving, making this direction slightly less stable as the water evaporates. The side facing the sun would be losing moisture the quickest on the stones themselves, as well as the ground in front of it thereby making it the side with the least resistance, that would seem feasible. Possible gravitational pull?

On a blowup of the first two photos, it appears that many of the rocks have fallen in a slight east/west pattern, moreso than a sideways, north/south pattern. (you also note porosity on these blowups whereas where we were there, one is far enough away for it not to be as apparent).

However, I have to say that I don’t know which way they fell. We just saw rocks lying on the beach seemingly haphazard. I also thought that possibly he used the same combinations making it known to him which would fit together making less guesswork than one would think, but we never saw an obvious combination repeated while we were there.

It rather seems as if I am going to have a very good excuse for returning to Vallarta!

So why does Dr. Bob think that they fall in the direction of the sun… what else could influence this that I am not thinking of?

Bob V-

Hey Kris, at this point your theory is as good as mine.  We would have to develop some tests of our theories to carry this much further.  For example, I would like to see what would happen to rocks stacked at night or in the shade of some large screen.  What about you?