The Silent Knight- In a fight to the death with "conventional" wisdom

A Decompression Chamber For Deep Water Fish

Bruce, an old friend of ours, once built a decompression chamber to use when collecting tropical fish from deeper than in 50 feet. Freshwater And Marine Aquarium Magazine published the article he wrote about it in June, 1988 (Volume 11, Number 6). That magazine is no longer with us, and the information is not available online. Although he no longer collects fish, Bruce claims that based on more recent conversations he’s had and his online research, he hasn’t found anything like it (or better) since. We offered to post it for him here.

This post is adapted from that article. The original illustrations were created by the magazine staff based on the drawings Bruce sent with the article. We’ve helped him enhance them a bit where he thought appropriate. He also sent new photos of whatever equipment he could still find. At our suggestion, he even added more information on how to use this equipment and made other editorial changes. Consequently, this article is much better than the original. The following is in his voice and perspective. The prices mentioned herein are still in 1988 dollars. [Based on the CPI of 116 for 1988 and 325 for 2026, expect current prices to be about three times as much.]

Why a Chamber?

Few fish can be collected from deeper than fifty feet without some kind of decompression. Some people tie their collection bucket to the anchor line and bring it up a little at a time. This technique has three disadvantages.

First, you can’t see the fish, and won’t know until it’s too late whether they are going to make it.
Second, some of the fish I’ve caught need a couple of days to decompress.
Third, if it’s not your boat, you could have trouble convincing the skipper to stick around, even for a much shorter time. And even if it is your boat, who wants to bounce around at anchor for so long?

Some people claim to “needle” their fish. Apparently, they bring the fish straight up. Then they stick a needle into its air bladder to release the gases. We don’t like that idea.

My Solution

I have the perfect decompression chamber. It is easy to build, cost me less than fifty dollars, and is even easier to use. We use it as the collection bucket. At the end of the dive I seal it and bring it straight to the surface. Once there I can raise or lower the depth/pressure at will, and can even bubble air through at any pressure/depth. If you build a second chamber, you can use it to make water changes and even feed the decompressing fish (in the first chamber) as needed.

I got a few of my ideas from talking with experienced members of the Florida Marine Aquarium Society, who have each collected deep water fish here in Miami. The rest is a result of my own experimentation. I was constantly refining some of my techniques, especially the decompression times for different fish at different depths. I’ll discuss my preliminary findings at the end of this article. But first I’ll tell you how to build this chamber, and then describe how to use it.

Description

Illustration of components of my fish decompression chamber — Figure 1: Showing the components of our fish decompression chamber. None of these illustrations are to scale.

We made the chamber from a five-gallon stainless steel cola syrup canister — the kind that you find under the tap of your finer soda concessions everywhere. The chamber has two ports on top for passing gasses and/or liquids. One is attached to a metal tube that feeds off of the bottom of the chamber and the other feeds right from the top of the chamber. The quick-disconnect fittings for the two ports look alike, but are not interchangeable. As you can see in Figure 2, the one leading to the bottom of the tank has 3 nubs. The other fitting has 2 nubs.

The cola syrup container that we used for our decompression chamber — Figure 2: Original syrup container

The original lid for the cola syrup cannister we used for our decompression chamber — Figure 3: Original lid

In the original application (dispensing cola syrup), the tank was pressurized by inserting a gas (CO₂ or air?) into the top of the tank, which would force liquid out from the bottom of the tank. When we circulate air in our application, we put it in through the bottom tube and remove it from the top. But when we do a water change, air enters from the top and water leaves from the bottom. So instead of referring to the ports as “in” and “out”, we will arbitrarily call the one with three nubs and the long tube “red”. We will call the other one, with two nubs and no tube, “green”. This is not because they actually come in those colors, but to match my illustrations.

In the decompression chamber, you connect the green side to your buoyancy compensator (BC) inflator hose. The other side can be hooked to a pressure gauge. On the inside of the chamber is a large tube around the opening which traps air up around the shoulders of the tank. This trapped air is crucial to maintaining pressure in the chamber and also keeps the buoyancy constant. The final innovation is a clear plexiglass lid so that you can see into the chamber.

Details

The Container

First, the canister. I got mine for about $20.00 (used) from a local wine and brew shop. These chambers hold up to 130 psi pressure, which is equivalent to over 280 ft. depth. The quick disconnect fittings that go on the two ports cost me about $15.00 more.

The Gas Input Plumbing

The essential pieces to the “green” side assembly (connecting to the long internal tube), as shown in on the left side of Figure 1 are:

the fitting that connects to your particular BC inflator hose (which you can get at your local dive shop for roughly $4.00), which then it goes to
a simple brass valve, which then goes to
your quick-connect fitting.

The assembly for adding air to the decompression chamber — Figure 4: Gas input assembly

These three pieces are linked by rubber fuel line hose and stainless steel hose clamps, and whatever adapters are necessary. You can get these pieces, except as noted, at any well-stocked hardware store for less than $2.00 a piece. Note how this assembly attaches to the three-nub port. If your “green” port connects to a flexible hose inside, instead of a rigid pipe going to the bottom of the tank, then you can attach a cheap air wand or long air stone on the end for an added touch (as long as it’s not the fragile kind).

“Red” Gas Outflow Plumbing

On our gas outflow assembly, connected to the “red” port, we go from

the quick-disconnect fitting to
a T-fitting for the pressure gauge and then to
(some sort of variable over-pressure relief valve (optional and untested), and then)
another valve.

This looks like the photo in Figure 10, but without the BC connector. Again, these pieces are connected by adapters, hose, and clamps. On all threaded connections I used Teflon tape.

Between the pressure gauge and the valve, I thought it would be cool to have some sort of variable over-pressure relief valve so that it would be easier to aerate the chamber, but I have never actually used or really needed such a device.

My pressure gauge only reads up to 60 psi (or about 135 ft.) and cost me about $12.00 at a boat hardware shop. It does not have to be waterproof since you leave it on the boat during your dive. And no matter how many decompression chambers you build, you will only need one set of these “green” and “red” side assemblies.

The Shoulder Tube

Now for the hard part — fitting the tube on the inside of the chamber. I used a large (half gallon) Rubber Maid pitcher (suggested retail $1 .99). Cut off the top inch to get rid of the spout, and cut off the bottom, and the handle so that you have an almost perfect cylinder about 4″ in diameter and 6″ or 7″ long. Whatever you use must be just flexible enough to fold in half and cram down the entrance hole, after which it returns to its original shape and is fairly rigid.

Glue this tube to the roof of the container with silicone sealant (just like you used on your aquariums). With the tube back in working shape and resting on the bottom of the container, my technique was to tie one end of a long string (3′ or 4′) to the middle of a 6″ stick. Then apply the silicone sealant to the roof of the container (apply liberally). Drop the stick through the tube and hoist it into position. Tie the string snugly to some higher object until the sealant dries.

Closeup illustration of features near opening of fish decompression chamber — Figure 5: Close-up from Figure 1 showing details around the entrance hole of the decompression chamber.

The Lid

For the lid you could use the one that comes with the container (shown in Figure 3), but then you couldn’t inspect your fish. I made a lid out of plexiglass. These lids seal from the inside (hench the elliptical shape instead of circular). They use interior gas pressure to maintain the seal. Use the standard lid as a pattern. Use a router to get the lip for the O-ring. I use the O-ring from the original lid (lubricate this O-ring sparingly with silicone grease periodically, as you would on your underwater cameras).

My lid is about 5/8″ thick with a contoured lip that gets thinner than 3/16″ along the bottom. I used super glue to attach a couple of small pieces of plexiglass to hold the lid in place until it seals (see Figure 6). My simple wood handle is held on by a couple of suction cups (with a diameter of more than one inch) instead of being permanently attached. That way you can remove it when not needed. Otherwise it would obstruct your view.

Acrylic lid for decompression chamber — Figure 7: Our plexiglass lid (without O-ring and handle)

As noted in Figure 6 (and shown in Figure 7), the pivot hole on the movable lid arm was drilled off-center to restrict its range of motion. Another way to do that would be to just glue a plexiglass stop next to it when it is in its straight-out position. This restriction is for convenience, but not absolutely necessary.

Also keep in mind that these two acrylic add-ons are only needed until you raise far enough off the bottom for the internal pressure difference to seal the lid in place. But at the end of your dive when you are low on air and have captured some real nice (meaning rare and exotic) specimens, having your lid fall into the chamber before you get it sealed tends to really increase your anxiety level. Or so they tell me. 😉

The Entrance Net

As I mentioned earlier, we use our decompression chamber as a collecting bucket. My wife is the ace fish collector (sometimes I help herd the fish, but mostly I’m just the caddie). Anyway, she made a double-compartment net out of plastic window screen and Velcro (see Figures 1 and 8), which we attach to a Velcro ring around the outside of the mouth of the decompression chamber (see Figure 5).

The net on our decompression chamber — Figure 8: Decompression chamber entrance net

As shown in Figure 8, the Velcro openings to each compartment come with a tab on each side to help pull them open. On one of those tabs, there is a lanyard to tie the net to the chamber before your dive.

The outer (top) opening is just wide enough to go around my wife’s collecting net. We transfer the fish from the collecting net to the decompression chamber in two stages, so that the fish already in the chamber don’t escape. Remove the net from the tank Velcro (but keep it tied to the decompression chamber) at the end of the dive when no longer needed.

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Collecting Net

This isn’t a part of the decompression chamber, but since we mention it in this article, it may have aroused your curiosity.

By now you probably realize that those “slurp guns” are worthless. My wife built this net. The sides are plastic. The bottom is plastic window screening (like the one on the decompression chamber). All of this goes around a ¹/₄” aluminum rod. The ends of this rod fit into shallow grooves (wide enough for the rod, but less than ¹/₄” deep) cut for this purpose along opposite sides of one end of a ⁷/₈” wooden dowel. They are secured by three stainless steel hose clamps. A wrist strap is tied to the other end of the dowel. She has attached her galvanized probing rod (maybe a little thicker than ¹/₁₆” diameter) by carving a short groove under the third hose clamp for one end, and a ring of bungee cord around the dowel at the other end.

Using this net, she generally catches only one fish at a time. When they go in the net, she collapses it at the mouth. Then we quickly transfer it to her collecting bucket or decompression chamber. Her collecting bucket is just a one-to-three gallon plastic bucket with the two-compartment entrance net (similar to Figure 8) permanently attached.

This collecting net works well on everything except for Blackcap Basslets (Gramma melacara). She designed a special collecting net for them, but that is well beyond the scope of this article.

Another method to collect fish would be to put your catch in tote tubes small enough to fit into the chamber (with numerous small holes to allow water circulation). This technique could also hamper your inspections later. But how you catch the fish is your problem.

Pressure↔Depth Conversion Table (Optional)

Figure 9: A Pressure/Depth Conversion Chart.

We discuss the making and displaying of this chart in the “Testing” Section below.

A pressure-to-depth conversion table for our fish decompression chamber

Testing

Before actually using this chamber, you will test it thoroughly at home. Put it in a trash can and fill both the can and the chamber with water (except for the air in the shoulders of the chamber). Add weight until the chamber is neutral. It should take less than a couple of pounds. Later you can bolt that weight to the rubber boot on the bottom of your chamber. Remember that salt water is heavier than fresh, so a chamber that is neutral in fresh water will require about 5 ounces more to be neutral in the ocean. If the chamber sinks before you add any weight then your shoulder tube wasn’t long enough.

The next test is the pressure test. Put on the lid and add air slowly from your BC inflator hose. Check for leaks in the plumbing. If you have a clear lid you can also calibrate your pressure gauge by placing your depth gauge in the chamber and comparing the two gauges at different pressure levels. I have my pressure/depth conversion chart (see Figure 9) taped to the side of the chamber (as shown in Figure 1). If you don’t have a clear lid you can make the chart by remembering that every 33 ft. of depth corresponds to 14.7 psi (with the surface being 0 psi, not 14.7).

Using the Chamber

On the Dive

Now to use this contraption. I’ll talk you through a typical dive. Before you suit up, connect the gas inflow assembly to the chamber’s green port. Also tie it and the net to the chamber. Put the lid in your BC pocket or your goody bag. Put the gas outflow assembly in the cabin of the boat where it can stay dry.

The Descent

When you enter the water, let the chamber fill up with water. Keep it as upright as possible so that air gets trapped in the shoulders. The chamber should be neutrally buoyant (or else make a mental note to adjust the weights before your next dive trip). As you descend the anchor line, the chamber will get a little heavier as the air inside gets compressed.

When you reach the bottom, attach your entrance net to the chamber by mating the Velcro (leaving it tied to the chamber). Remove your inflator hose from your BC and connect it to the chamber. Turn the valve to blow air into the chamber. When it is full it will again be neutrally buoyant and bubbles will come pouring out the mouth of the chamber. Turn off the valve and return the hose to your BC. You shouldn’t have to play with it again for the rest of the dive. I often disconnect the quick-connect inflow assembly (but keep it tied to the chamber). Minor fluctuations in pressure during the remainder of the dive are inconsequential.

Collecting Fish

One of the benefits of the shoulder air and the base weights is that the chamber is very stable. You should be able to rest it atop a pinnacle and have it remain upright and in place (under conditions of moderate currents). You may add fish to the chamber whenever you get the chance.

The Ascent

At the end of the dive, I put the lid in place by carefully taking it through the net, and hold it in place as I start my ascent. After rising only a foot or two, the pressure inside the chamber will hold the lid in place. I remove the net (still tied to the chamber). The chamber will remain neutrally buoyant during the ascent.

On the Surface

Keep the chamber out of direct sunlight; you don’t want to heat the water too much. You may start to decompress the fish as soon as you get your diving gear off.

To Raise the Fish

To decompress the fish, attach the gas outflow connector (make sure the valve is closed) to the “red” port. Open the valve and slowly let air out until you reach the desired pressure. Close the valve and remove the connector. Inspect the fish. You usually get a more useful view of the fish by lying the chamber on its side. Of course, you need to bring it upright again before conducting other operations.

Lowering the Fish (Increasing Pressure)

If a fish appears distressed (symptoms are discussed below), you may need to increase the pressure in the chamber. Connect the gas inflow assembly to the “green” port and a SCUBA tank to that assembly. Add air slowly (by controlling with the valve) until you reach your desired depth.

Aerating the Fish

Aerating the fish is just a matter of connecting both assemblies to their respective ports at the same time and opening both valves so that they are balanced. The gas inflow assembly may be connected to either a SCUBA tank or oxygen bottle. I open the gas outflow valve first, but put my thumb over the hole. Then I open the other valve slowly, keeping a sharp eye on that pressure gauge. After a little practice, you’ll see its not that tough. Of course here is where that over-pressure relief valve might come in handy.

Surprisingly, you don’t need to bubble the fish as often as one might think. I’ve left fish in the chamber at least a day and a half without aerating. Fish left in a bucket at sea level for that time would be long dead. Apparently, the 20% oxygen from your SCUBA tank dissolves into the water much better at four atmospheres. Some fish suck up oxygen faster than others. Pygmy angels (Centropyge argi) and Jack-knives (Equetus lanceolatus) will not last as long as other fish. I usually don’t bubble the chamber until I reach twenty feet. Then I use pure oxygen (from an emergency oxygen unit I carry on the boat) every four to eight hours. Air from your SCUBA tank will also work, but more frequently.

Making a Water Change

As mentioned near the top of this article, this operation will require two chambers. You will also need three new fittings.

The New Gear

The assembly used to pressurize the chamber holding clean water for a water change — Figure 10: Gas input assembly for making water changes

The new inflow assembly, like your first one, starts with a BC connector and a valve. Downstream of the valve is a pressure gauge, similar to the one on your first outflow connector. (In fact, you could just add a BC connector to your existing outflow connector when needed.) Then it terminates with a quick-disconnect fitting which attaches to what we’ve been calling the “red” (two-nub, no tube) port – the opposite of the connector on your original chamber (compare Figure 1 to Figure 11).
The connector between the two chambers is an assembly with a “green” port quick-connect fitting on one end and a “red” port quick-connect fitting on the other end. Between them is only another valve.
The third assembly, your new outtake connector, has only the “green” port quick-connect fitting (the one that attaches to the three-nub port that has the long tube) at one end, with a valve at the other end. Again, check Figure 11.

Illustration of components needed to make water change while decompressing fish — Figure 11: illustration of components needed to make a water change while decompressing fish

How it’s Done

Add good water to the spare chamber. Before connecting the two chambers, use your original outtake assembly to record the current pressure in the fish chamber. Then remove the pressure gauge. Connect the two chambers with that new chamber-connect fitting, making sure the connecting valve is closed. Bring the spare chamber’s pressure up to match that of the first chamber (the one with the fish) with your new inflow assembly. Close that “Intake” valve. Connect the new outtake assembly to the “green” port of the chamber with the fish (after making sure its valve is closed). Slowly open the connecting valve all the way to equalize pressure between the chambers. Now you can add water to this system in a manner similar to the one used to aerate a single chamber under pressure – by slowly pumping air into the clean-water chamber while removing water from the fish chamber. Close intake and outtake valves regularly to check and maintain pressure. And be sure to finish before the clean water runs out.

Feeding Your Fish

Start as you would for making a water change. But after putting clean water in the spare chamber, add some brine shrimp, similar small live food, or even flake food to the water. Proceed with the water-change instructions to completion. The brine shrimp will still be alive when they enter the fish tank (but probably not for long).

Removing the Fish

To get the fish out of the chamber, first siphon the water to within an inch or two of the bottom of the chamber.

You could do this while the chamber is still sealed, perhaps at the beginning of the operation that finally brings the chamber to the surface pressure, by adding air to the chamber via the green port in the usual fashion while removing water from the red port in the same way you use for making a water change.

Or, after they are at surface pressure with the lid off, you could just syphon out the water with some sort of hose.

Don’t take too much water. You want just enough water to keep your fish afloat. Then use a fine mesh net which has been attached to a 3-ft handle. Don’t try to just reach into the chamber with a short handled net; you won’t` see what you’re doing.

Decompression Schedules

So how long should you decompress your fish? I make a decompression stop every ten feet (although sometimes I skip the first stop). For fish caught deeper than 100′, I start at one hour per stop until I get them to 50′. Then I go two hours per stop until I get to 20′. There I stop four hours, and at 10′ I stop six hours.

For sensitive fish like Blackcap Basslets (Gramma melacara), I will (instead of the 10′ stop) make a stop at 12′ for six hours and another at 6′ for eight hours. The last 20′ are the most crucial. For fish caught shallower than 100′, I just go an hour per stop all the way up.

Again, watch the fish every stop, especially when you reach 20′. You might need to stay longer on those last two stops. Now if one of my scheduled stops should end after say 11:00 p.m., I frequently prolong it until around 7:30 a.m. It doesn’t hurt the fish, and it does make my trip more enjoyable (you might sleep better if you bubble the fish first). You can’t make up any extra time spent on one stop by cutting time on future stops, however.

I have invented other schemes, like the 10% rule, where you make all the stops for the same interval (say two hours), but each time drop the absolute pressure 10%. From a 110′ dive, your stops would be at 96, 83, 71, 60, 51 , 43, 35, 28, 22, 17, 12, 7, and 3 feet. And I have glanced at the Diving Decompression tables for clues. So far my experience has been mainly to raise the fish 10′ at a time and see how long it took for him to look comfortable.

Symptoms

The first signs of sickness are of course rapid breathing and swimming with a bow down attitude. More severe symptoms may include the inability to swim away from the surface, small bubbles under the skin, usually near the fins or around the eyes, and a bloated belly. To complicate matters, the fish don’t always show symptoms right away. A few of my fish looked okay when I got them out of the chamber, but the next morning had to be taken to 20 or 30 feet. And when they do show symptoms while in the chamber you may have to back up several stops before they recover. Not all fish need the same amount of time to decompress, either. As a rule of thumb, younger fish seem to handle it better than older fish. Invertebrates may not need decompressing at all.

In Conclusion

Well, that’s all there is to it. If you have any ideas for improvement, let me know below. I think you’ll find that this chamber is as good as you could want. One thing I’m interested in particularly, is refining the decompression times. Let me know how you do.

A Better Solution to the Blue-eyed Monk Problem

The Problem

There are variations to this problem, but we will go by the XKCD version discussed in www.xkcd.com/blue_eyes.html. It goes:

“A group of people with assorted eye colors live on an island. They are all perfect logicians — if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.”

“On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.”

“The Guru is allowed to speak once (let’s say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following: ‘I can see someone who has blue eyes.’”

“Who leaves the island, and on what night?”

The Traditional Solution

The traditional/standard/irrefutable solution is described everywhere, including in xkcd.com/solution.html. Basically, if there were only one blue-eyed monk (BEM), then he wouldn’t see any. He would realize he must be it, and leave that night. If there were two, they would each see only one and would assume the other guy would leave that night. When they saw each other the next day, they would both leave. And the people who were worried that they might be Number 3 would all breathe a sigh of relief. And so on. For the case described above, all 100 would leave on Night 100.

Disclaimer (and Personal History)

There is a reason why I was never invited to Logical Island. When I first read this problem, decades ago, I didn’t even figure it out on my own. I cheated and read the solution. But then I thought, “That’s pretty slick”! When I ran across the problem again, a decade or two later, I remembered the answer and still thought it was pretty cool. But I thought it was too bad that there wasn’t a quicker solution. The third time I ran across it, another decade or two later, I became obsessed with finding that solution. It wasn’t going well, but a few nights later it occurred to me that the answer might involve modular arithmetic^Explained. A test using Mod 6 was effective.

To see the Note click here.To hide the Note click here.

In the Mod 6 Method, the “proof” proceeds normally up through five BEMs. Those seeing four leave on Night 5. But for the case of six BEMs, those seeing five (you know what that means) would await their findings on the morning of Day 5 to decide their fate. Those seeing six BEMs, however, would leave the first night since six is 0 (mod 6). Their first clue as they approached the dock would be the dozens of other monks at the dock instead of the six others they were expecting. Even more important, perhaps, is that none of them had blue eyes. They would all have a good laugh (probably against the rules), and then quietly go back to bed. Those who originally saw five (a.k.a. 5 mod(6)) were sleeping when all of this happened and wouldn’t know anything about it. The problem would take care of itself four days later.

The next logical question would be “Why is six so special?” If all of the monks can’t agree on the same base/modulus without communicating, the scheme fails. I introduced my idea on a different forum. (I posted a couple of blog articles here as the plan developed, but they have been superseded by this one.) One commenter quipped (sarcastically), ‘if that scheme is even legal, what’s to stop you from just having everyone who sees an even number of BEMs go to the ferry on Night One?’ I thought that was way too extreme, but as I was typing “ridicul . . .”, a bell went off in my head. Of course. That’s it! Mod 2. But that commenter wasn’t buying it.

The Fastest Answer

In my plan, everyone who sees an even number of BEMs (remember, zero is an even number) goes to the dock the first night. If when they got to the ferry, everyone else there had blue eyes, they would all board the ferry. Otherwise, having non-blue eyes, they would all quietly return home. If the problem isn’t solved that night, everyone that sees an odd number of BEM’s (everyone else) leaves on the second night.

Let’s say there were 99 BEMs (or 101). They would all see 98 (or 100) BEMs, and they would (as in the case of one BEM) get on the ferry the first night. That would be that. But if there were 100 BEMs, those seeing all 100 would all go to the ferry the first night. They see nothing but non-BEMs and all go home quietly. The next morning, those seeing 99 and hoping that those seeing 98 acted accordingly, would realize that wasn’t the case. They would all leave that second night (as in the two BEM case). End of story.

Advantages

If there are 200 monks between the ages of, say, 19 and 85, with minimal turnover, you can expect three deaths each year. That means there is about a 50% chance that the number of BEMs will mysteriously change while the 100-day clock is ticking. (I’ve heard no discussion about how the traditional method handled such things. But a similar situation is addressed in the next-to-last paragraph [Go]). My new method virtually eliminates that possibility. Even if nobody dies, there is over three months of meticulous counting that can be avoided.

Other Concerns and Considerations

More About the Technique

As we’ve discussed, this method is actually based on the traditional method, but folds the number/time line into the smallest possible segments using modular arithmetic. For a monk that sees 100 BEMs, there are only two possibilities. Either there are 100 BEMs (which all see 99) and he is among the 100 others, or he is one of 101 BEMs. Nobody seeing 100 thinks there might be 102 or 99. If you see 100 and think you might be one of 101, then you don’t care what the non-existent monks that see 102 BEMs think. For those seeing 100 BEMs, this scheme folds the other monks from both possibilities – those seeing 99 and those seeing 101 – into heading to the ferry the same day.

As mentioned, the solution must be so logical as to be adopted unquestionably by all monks without discussion. First, remember that they were able to come up with the original method without discussion (something I couldn’t do). Why would they stop at the first answer they came up with when they can clearly see the disadvantages to that approach. This answer adds another simple mathematical concept for the next logical step. But if you know of another logical solution candidate, even completely unrelated to these techniques, speak right up.

I mentioned that there are variations to this puzzle. This technique would not work in variations that require the monks who discover their eye color to quietly commit suicide in their homes. And it is the ferry part, not my new technique, that would minimize the damage of an oracle mistakenly (or maliciously) claiming he saw a BEM when there were actually none.

Questions Answered

Even if based on the original method, doesn’t the mod 2 math allow two possible answers? Why wouldn’t they have those seeing an odd number of BEMs go first? Because the “let odd go first” plan is not the direct result of simple mod 2 math. And the first two cases (1 and 2 BEM’s) in my technique are exactly the same as the original method.

I’ve heard that the inductive method proves that the original technique is the only one possible. Nonsense! All mathematicians know there are commonly more than one way to solve or prove anything. Just a couple years ago, two teenage girls found a new trigonometric proof to the Pythagorean Theorem^Article.

I’ve heard that these monks are illegally communicating information. No, they are giving the same information at night as they were giving during the day – no more information than in the original approach. In either case, when the lone BEM disappears the first night, he is telling every other monk (that was worried that he might be Number 2) that they can stand down.

But what would happen if some of the monks stuck with the old technique? Well, I guess all monks weren’t perfectly logical. But if there were an odd number of BEMs, for example, and only some of those seeing an even number go to the ferry, as my plan dictates, then they would see other BEMs and leave as required. The next day, those who chose the traditional solution would notice that there were far fewer BEMs. Regardless of whether the new number of remaining BEMs was odd or even, they would realize what happened and leave the next night.

(If they still couldn’t figure it out, they could at least proceed with the traditional plan using the new BEM count at the original starting point. [Return to Advantages]

Would they be allowed to take action without knowing their eye color? Nothing in the rules restricts their access to the ferry dock or prevents them from noticing the eye color of those they meet. I would expect logical monks to be curious and willing to conduct simple experiments that could benefit themselves and the group.

Any questions?

Another Solution For Legislative Voting Systems

Our forefathers, in creating a new nation, were concerned about a democracy’s capability to degenerate into “mob rule” through “the tyranny of the majority.” James Madison, who later became our fourth President, in Federalist #10 and in debates in 1787, argued that the government should protect “the minority of the opulent against the majority”.

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According to vocabulary.com, “opulent” means rich and superior in quality (but contains connotations of pretentious). Our forefathers, like Madison, were considered wealthy.

Yet Lord Acton’s belief that “. . . absolute power corrupts absolutely”^A can be seen in states like Florida with supermajorities controlling their government. In 2023, legislatures with veto-proof majorities in both houses^A control 29 states. Florida’s governor, Ron DeSantis, with no resistance from the legislative branch, has waged a culture war of tyranny against “the woke” – Democrats, women, minorities, and anybody that publicly disagrees with his policies – in his bid for President of the United States.

In my article “Two Political Parties Are Not Enough”, I address some of the problems of our current two-party system (promoting polarization, guarantying an instant majority). I propose a solution (more political parties). But then I also discuss obstacles to that solution. While waiting for changes, I’ve come up with a simpler solution.

My New Solution

I propose adding a requirement to the only existing rule of securing a majority vote (or 60% in the Senate, or . . .) when state and national legislatures vote on bills. It should also be necessary to secure at least 25% of the vote from each minority party. This would fight polarization and encourage collaboration, compromise, and bi- or multi-partisanship to find solutions at least partially acceptable to all constituents.

Is 25% the right number? We can tweak it. It might not take that much to be effective. And as the rule is stated, it can be combined with other solutions (including those we’ve not previously discussed). Could it get in the way of passing laws in an already dysfunctional government? Well, yes, but that’s actually the point until we can elect representatives that represent all the people while trying to solve problems instead of just making sure the other team doesn’t score any points. They apparently can’t do that individually, but maybe they can collectively.

By now I shouldn’t have to tell you that we accept opposing view and solutions. Start the discussion in the comment section below. Thank you.

I’m Back – Are You Still Interested?

No, I’m not a red-eyed monk (see our last post, Will 2020 See The Extinction Of The Red-eyed Monks?). And just like Samuel Clemens, any reports of my death were greatly exaggerated. Nor did I run out of material to write about. The truth is that my day job grew increasingly hectic. Just as we started to get that under control, first COVID and then personal issues began to occupy a lion’s share of my time.

I haven’t yet cured all of that. But I will try to commit to at least four posts a year until I finish getting my act together, so to speak. My next article could be a new idea for how congress passes laws. Also look for an article about what our forefathers meant when they said we were created equal, maybe some comments about our Supreme Court. Possibly other constitutional issues, and probably an explanation of math concepts used/exploited in places like advertising. To review our previous articles, see https://thesilentknight.info/. There will be some formatting changes soon, starting most likely with my code for reference links.

I’ve had to upgrade or replace software, etc. to conform to new standards. In line with some of those new standards, I need to get you to reconfirm whether or not you are still interested in being notified by email about any new post to this blog. As part of the changes, all users must now re-subscribe. Those who do not reconfirm their interest will have to be erased from our records.

To reconfirm, fill out the form at https://thesilentknight.info/please-reconfirm-your-subscription/. Hope to hear from you soon. Thank you.

Will 2020 See The Extinction Of The Red-eyed Monks?

For those of you not familiar with what has been called “the hardest logic puzzle in the world”^Link, The Blue-eyed Monk problem or Blue-eyed Islander problem (Another version), check out the above reference links. For what it’s worth, that “hardest” title is probably an exaggeration. But my new version, inspired by recent events, might be harder.

In this version of the famous logic problem, there are a number of monks on this remote island. All of them are “perfect logicians”. Every monk sees every other monk every day, but they are rugged individualists who never talk to each other or communicate in any way. They also take full responsibility for their actions and obey all rules and protocols. (Yes, this problem is entirely fictional.) Strangely, there are no mirrors or reflective surfaces on the island. The ferry visits the island every night to drop off supplies. It would take the monks to the mainland, if necessary. But none of the islanders wants to leave and no strangers are allowed on the island. In this version of the problem, all of the monks have red eyes.

One day, all but one of the monks noticed that one of their peers had blue eyes. But they all continue to go about their lives. Many days later, almost all of them notice that two of the monks now have blue eyes. Still, life goes on. This trend continues with a slowly increasing frequency until many, many days later, the first monk to have developed blue eyes is found dead. Doctors on the mainland soon discover that some as-yet-unknown, but contagious pathogen hit the island. The number of monks infected has been growing 2% every day for quite some time. The only visible symptom is the changing of eye color from red to blue. The disease is not contagious until the eyes go blue but then remains contagious until the infected person dies. How it spreads is still unknown, but obviously, direct contact or even close proximity is not required.

By the time the doctors figure all of this out, red-eyed monks have started changing eye color at the rate of one every other day and the second blue-eyed monk has just died. If a blue-eyed monk gets to the mainland in time, they can be cured. but the ferry does have a limited capacity. The monks are pacifists, so there will be no shooting of blue-eyed monks (yes, I might have a personal stake in this directive). All of this information was left on a large sign at the ferry dock the next day.

So what do the monks do? Will they go extinct? Will 2020 see the end of all logical thought on this planet? Only you can answer that question. Good luck! Leave your answers in the comment section below.

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In the interest of full disclosure and transparency, I have addressed the original monk problem before. After much fumbling, I did come up with a better (faster) solution, which was widely regarded as cheating (see A Better Solution to the Blue-eyed Monk Problem.

A Pair Of Perspectives On Pearls

Several Sundays ago, our pastor began his sermon by talking about the world’s largest pearl.

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This pearl, which was just recently revealed after being hidden for ten years, is 26 inches long and 12″ wide, weighing 75 pounds. That’s over 2½ times longer and five times heavier than the previous record-holder, which was found in another giant clam near the same Philippine island in 1934 (both the diver and the clam lost their lives in the earlier case).

Filipino Fisherman Reveals 75-Pound Pearl He Kept Hidden For A Decade.

Our preacher used the pearl as an example of how God can take an irritant and help you turn it into a treasure. I believe that is a common way of looking at this from a human perspective. But for some reason, I saw the issue differently.

Another Possible Moral To This Story

Turning trash into treasure – is that what the clam was actually trying to do? Does the clam even know that the old irritant now has such great value (estimated to be over a hundred million dollars)? Was this 75-pound object, which started as a gain of sand and had been growing for over a hundred years^A, actually less irritating to the clam than the original grain of sand? I suspect not!

The preacher could have used this as an allegory, showing how man, because of pride, will try to solve a problem by himself but fail, despite putting a great deal of effort and time into it. And, as is often the case, he could even make the situation worse, not better. “But look how pretty I made it.” Can’t you just see that giant clam trying to sing Frank Sinatra’s “My Way”^video, but failing, of course, because it has a 75-pound lump of calcium in its mouth?

Is There A Third Possibility?

One of the beauties of life is that some situations can share many lessons. Reality is like that. Even as I was writing this, a third perspective began taking shape in my mind. Of course, I ignored it. But if you found another pearl of wisdom in this parable, please share in the comment section below. Thank you, and thanks for listening.

Truth In Advertising: An Unborn Baby’s Beating Heart

Above is one version of a common billboard along the interstates in Florida and across America. The problem for me is that the spokesman didn’t look anything like that when he was 18 days from conception. He would have been barely visible and a lot less cuddly. Below, I’ve taken the liberty to replace him with his earlier self, which would have been about half the size of a pea or just able to fit through the pupil in the eye of his older self as shown in the background of the revised billboard. His heart would have been larger than a grain of sand. He still has no eyes, arms, or lungs, and I’ve found no information on brain function. I don’t think he’s feeling any pain. Now ain’t that cute?

His Odds Of Success (Birth)

While I have touched on this subject before (in my article Save Your Birthday – Vote For Clinton), this time I dug deeper in order to put things into a more serious perspective. Here’s what I found:

According to ABORT73.COM, abortions have been decreasing slightly every year for the last decade. 879 thousand occurring in the United States in 2017.
The Statistica website says that the number of births in this country has been fairly stable. There were about 3.86 million of them in 2017.
The attrition rate of fertilized human eggs is not as well known. Comparing articles on spontaneous abortion in humans and Early embryo mortality in natural human reproduction, it looks like only 25% of fertilized eggs actually make it to birth (± at least 10%).

Here’s what that means: if you start with 18 fertilized human eggs, 13 will die from natural causes before birth, and one embryo or fetus would be aborted. Both forms of attrition are “front-loaded”. 2/3 of abortions happen by the 8th week^A1, while 2/3 of fertilized eggs will die in their first 11 weeks^A2.

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A common mistake would be to compare the number of abortions with the number of births directly but to compare apples to apples, as they say, you need to use the same reference point. Here’s the math:

3.86 million births divided by 25% (or 0.25) gives 15.4 million fertilized eggs. That would be the common reference point. Divide that by 879 thousand abortions and you get the total number of fertilized eggs there are for every abortion (17.6 – let’s round to 18). To find the number of those fertilized eggs that would die naturally, simply multiply the same 18 by 75% (or 0.75).

One thing that is not clear is “what are the odds that the aborted “child” would have died from natural causes anyway?” The easy answer (and my best guess so far) is 75%. That means there are a lot of self-righteous people out there (many being middle-aged white males with nothing invested) who are willing to throw a woman in jail for long periods of time without even caring about the circumstances of her case to protect something that probably wasn’t going to make it anyway. I guess for the pious, any excuse is a good one for beating up on your neighbor.

At least that’s the way I see it. Any comments?

Has the Republican Party Become a Ponzi or Pyramid Scheme?

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Definition of a pyramid scheme.

As a teacher, I didn’t heartily endorse “the Curve.” I didn’t believe that just because a student could find five friends who were either stupider or lazier than they were they deserved a free pass. (I’m sure that for some of my students that was no trivial feat). This also tied into a theory I developed early in my teaching career^Article (which turned into a prophesy). Unlike doctors, who are said to be able to bury their mistakes, if teachers were to make mistakes, and for political or social reasons were unable to correct the system to reduce the number of those mistakes, then non-educated people could eventually reach critical mass. They could then elect enough unqualified politicians to negatively affect the education process (with budget cuts, for example). This would be the beginning of a feedback loop that could put American education and thus American society on a death spiral. But that could never happen here, right?

Now that Mr. Trump has been elected president and his conduct, unchecked by congress, has become more and more outrageous, I find it interesting to watch some of his supporters as they have to warp their world (or the principles by which that world is defined) to greater degrees in order to be able to justify His actions within that small world. To do that successfully, they need other people (their five friends) to be dumb enough to fall for those contorted explanations. As time goes on, those friends need to recruit their own set of even dumber friends so that they don’t look like the fools that they are . . . and so on. But even now, dumb and foolish people are not an unlimited resource in this country. And Trump’s actions will continue to test that resource like no other leader in the history of the Earth. So as in all such schemes, the buffoon bubble is bound to break. The only question is – will that happen before the next election? I’m not so sure it will. Any comments?

From Your Crew: Why We Ask “How High” When You Tell Us To Jump

When bragging about their leadership skills, most of you have probably heard someone you know tell you “When I tell them to jump, they ask ‘How high?’”. You are supposed to assume that the jumpers do it to satisfy the most particular nature of the speaker’s demands. This implies that the speaker holds such power that their workers spend extra effort meeting even his or her most detailed or trivial requests. The speaker doesn’t expect you to wonder why their workers assume s/he has a need to micromanage every task. To keep your mind from wandering too far down that path, let me explain not the speaker’s mind, but go right to the true motives of their crew.

As a crew member, I know the speaker (let’s just call him or her “fearless leader”, or even “fearless” for short) has the financial resources and personal or political connections to hold his/her current position. But they got their leadership skills from studying Hollywood blockbusters or listening to other wannabees further up the chain of command. S/he hasn’t taken the time to learn the capabilities of their team. They don’t understand the complexity of the problem at hand. They really do like to bark orders, however. As a member of fearless’ crew, my motives are simple. I want to stroke his or her ego and get out of serious work. I may have been on my school track team, but if fearless is satisfied with me jumping four inches off the ground, that’s fine with me.

If fearless had a hangover, and I was asked to stand in for them one day, my crew would know not to ask frivolous questions. If one of them did ask “How high?”, I would be tempted to stop and have him or her jump as high as they could many times while other members of the crew documented the results. And if the last jump didn’t measure up? . . . .

My crew would know two things:

I expect them to give 100%. If he was on the track team, I would expect him to excel. I would have assigned it to someone else if the situation only demanded a 4″ jump. If the job demanded a spacecraft to be built, I’d give the job to my rocket scientist (which would probably be a different person than my track star).
I expect my crew to understand the nature and needs of the assignment in front of them and work it out. Whether the job demanded a 36-inch or a 24-inch high jump, I would expect my track star to be able to figure it out and complete the job without further guidance. At the same time, I expect my team members to know their capabilities and understand their limitations, as well as the other capabilities within the team so that if there is a mismatch, we, as a team, can effectively deal with it.

Is any of this too much to ask?

Not Quite Clear On The Concept “Innocent Until Proven Guilty”

Listening to discussions on Facebook about the Brett Kavanaugh nomination, I was surprised and disappointed to see the “innocent until proven guilty” principle so often misapplied (and in two different ways). It became clear to me that a lot of people just don’t understand the concept.

A Larger Doctrine

When something is being awarded to somebody, whether it is good, bad, large, or small, most people would like to think the recipient deserved the award. It is the presenter’s responsibility to make sure that’s the case. The more extreme the action, whether reward or punishment, the more effort the presenters should take to see that the award has been earned.

The Bad

When the award is a punishment, this doctrine takes the form of “innocent until proven guilty”. If the death penalty is under consideration, for example, we need to go to great lengths to be sure we aren’t making a mistake. I’ll save the discussion of the two types of possible errors – letting a murderer go free vs. hanging an innocent person – for another day.

The Good

When the action under consideration is a reward, one would expect some law of symmetry to apply, and it does. In this case, the slogan “innocent until proven guilty” has no place. Whether it is the Mega Millions jackpot or the Nobel Prize, one does not assume a prospect is ‘innocent’, or deserving, until proven otherwise. It is up to the claimant to prove they deserve the award. For the Mega Millions jackpot, that would be by showing the winning ticket and some form of identification. The Nobel Prize has even more stringent requirements. Republicans have no trouble applying this principle to welfare recipients but seem to get tripped up when it comes to Presidents and Supreme Court nominees.

The Ugly

In either of the above cases, it is well understood, as stated above, that the candidate will be fully vetted. And the more significant the award, the more serious the investigation. For someone to insist that a candidate is “innocent until proven guilty”, especially for a reward, and then refuse to hold a meaningful investigation into any evidence of guilt is the height of duplicity. But that seems to be the current state of the Republican Party. It hasn’t always been this way.

Anyone with a logical alternate interpretation of the facts is welcome to share. You can be sure the civility of this discussion will be maintained.