Inspired by Jaby's work on large scale microbe distribution, I've been testing the small scale distribution changes in my camp. By small scale, I mean the distribution from within 1 coordinate, up to tens of coordinates.
Testing at intervals of 2 coordinates, going North South, I found a relatively slowly changing microbe population. Going East West, the slow change was interrupted by a sharp change at coordinate 2368. This change was a major reshuffle of the microbe population. It occurred within a fraction of a coordinate, and there was no warning dropoff of microbe entry times before the transition. This transition boundary was tracked through RSO, and showed up in single sample tests in Sinai and Karnak. Jaby noted that coordinate 2364 was divisible by 64. This led to a search for a power of two pattern. Transition lines were found to occur on 32 x 32 coordinate grid. Limited sampling indicates the pattern persists throughout Egypt.
Knowing that microbe populations change, sometime dramatically, at specific boundaries should be helpful to brewers. Personally, I found the sudden unexpected transitions confusing. Now I have found a pattern to them, I'm hopeful finding the mix of microbes I am looking for will be easier.
Introduction
I started with a NE to SW diagonal run across camp, at about 10 coord intervals. It was clear some microcrobes were persisting, and others changing, but I couldn't see any obvious pattern. I decided on a more methodical approach. First I set up my six kettles at 2 coordinate intervals, along a North South Axis, and did an open kettle yeast test. I recorded the top eight microbes. I developed a numeric score for the rate of microbe change between samples, called Total Shift. Total Shift is calculated as follows. Comparing sample 1 to sample 2, if a microbe is in the same place in the list, its shift is zero. If the microbe has moved one space either left or right, its shift is 1, if it has moved 2 spaces, its shift is 2 etc. Microbes that dissapear from the sample are assumed to have moved to position 9, and new entries are calculated as having come from that position. This slightly underestimates the shift, but is not that significant. The third column in the following tables is the Total Shift from one sample to the next.
North-South variation
Results at 2360e
| 3330n | Y50, Y24, L12, Y32, Y98, Y2, L13, A54 | - |
| 3332n | Y50, Y24, L12, Y32, Y98, Y2, L13, A54 | 0 |
| 3334n | Y50, L12, Y24, Y32, Y98, L13, Y2, A54 | 4 |
| 3336n | Y50, L12, Y24, Y32, Y98, L13, Y2, A54 | 0 |
| 3338n | Y50, L12, Y24, Y32, Y98, L13, Y2, L92 | 1 |
| 3340n | Y50, L12, Y24, Y32, Y98, L13, Y2, L92 | 0 |
On this scale, steps of 2, going north south, there is only a gradual variation in microbe order. To confirm that the order does give at least some approximation to microbe enter time, I did a closed kettle microbe test. Kettle closed at 1200 secs remaining.
| 3330n | Y50, Y24, L12 | 0 |
| 3332n | Y50, Y24, L12 | 0 |
| 3334n | Y50, L12, Y24 | 0 |
| 3336n | Y50, L12, Y24 | 0 |
| 3338n | Y50, L12, Y24 | 0 |
| 3340n | Y50, L12, Y24 | 0 |
This shows that microbe order can be at least a rough proxy for microbe entry times.
East-West variation
I repeated a similar 2 coordinate spaced test going West to East. I was surprised to discover at 2368e a sharp change in the microbe population. I focussed in on the discontinuity, and spaced my 6 kettles closer together. Below is the amalgamated results of a series of runs. The decimal points on coordinates are of course my own estimation. The world map does not give finer than unit coordinates.
Results at 3330n going East
| 2360e | Y50, Y24, L12, Y32, Y98, Y2, L13, A54 | - |
| 2362e | Y50, Y24, L12, Y2, Y32, L13, Y98, A54 | 6 |
| 2364e | Y50, Y24, L12, Y2, Y32, L13, Y98, A54 | 0 |
| 2366e | Y50, Y2, L12, Y24, Y32, L13, Y98, A54 | 4 |
| 2367e | Y50, Y2, L12, Y24, Y32, L13, Y98, A54 | 0 |
| 2367.5e | Y50, Y2, L12, Y24, Y32, L13, Y98, A54 | 0 |
| 2368.0e | Y50, Y2, L12, Y24, Y32, L13, Y98, A54 | 0 |
| 2368.3e | Y24, L12, Y98, L92, L77, Y32, M47, Y50 | 48 |
| 2368.6e | Y24, L12, Y98, L77, L92, Y32, M47, Y50 | 2 |
| 2368.9e | Y24, L12, Y98, L77, L92, Y32, M47, Y50 | 0 |
| 2369e | Y24, L12, Y98, L77, L92, Y32, M47, Y50 | 0 |
| 2370e | Y24, L12, Y98, L77, L92, Y32, M47, Y50 | 0 |
| 2371e | Y24, L12, Y98, L77, L92, Y32, M47, Y50 | 0 |
| 2372e | Y24, L12, Y98, L77, Y32, L92, Y50, M47 | 4 |
| 2373e | Y24, L12, Y98, L77, Y32, L92, Y50, M47 | 0 |
Investigating the Transition Point
I was curious if there was any indication of the upcoming transition point. In particular, did the microbe entry times change smoothly but steeply near the transition point, or was the change a sharp discontinuity? I got some feel for this by recording the microbes entering sealed kettles. The same set of six closely spaced kettles was used for all tests. The kettles were laid out in an East West line with about one kettle width between each one. The times indicated are the seconds left till the end of fermentation.
| Location | Open | @1200 | @1150 | @1100 | @1000 |
| 2367e | Y50, Y2, L12, Y24, Y32, L13, Y98, A54 | Y50, Y2 | Y50, Y2, Y24, L12, Y32 | Y50, Y2, Y24, L12, Y32, L13 | Y50, Y2, Y24, L12, Y32, L13 |
| 2367.5e | Y50, Y2, L12, Y24, Y32, L13, Y98, A54 | Y50, Y2 | Y50, Y2, Y24, L12, Y32 | Y50, Y2, Y24, L12, Y32, L13 | Y50, Y2, Y24, L12, Y32, L13 |
| 2368.0e | Y50, Y2, L12, Y24, Y32, L13, Y98, A54 | Y50, Y2 | Y50, Y2, Y24, L12 | Y50, Y2, Y24, L12, Y32, L13 | Y50, Y2, Y24, L12, Y32, L13 |
| 2368.3e | Y24, L12, Y98, L92, L77, Y32, M47, Y50 | Y24, L12, Y98 | Y24, L12, Y98 | Y24, L12, Y98 | Y24, L12, Y98, L92, L77 |
| 2368.6e | Y24, L12, Y98, L77, L92, Y32, M47, Y50 | Y24, L12, Y98 | Y24, L12, Y98 | Y24, L12, Y98 | Y24, L12, Y98, L92, L77 |
| 2368.9e | Y24, L12, Y98, L77, L92, Y32, M47, Y50 | Y24, L12, Y98 | Y24, L12, Y98 | Y24, L12, Y98 | Y24, L12, Y98, L92, L77 |
There seems to be pretty sharp change in entry times at the transition point, with no significant change in microbe entry times before that. At least at the resolutions I am measuring at. Note also the change in the order of the Y24, L12 microbes at location 2367. Despite being in the same kettle, they have swapped order from a previous run. Perhaps a time of day effect? I noticed that on a few other repeat runs. The effect seemed small though compared to the larger location dependent effects.
Tracking the Transition Line
The next obvious question was, does this transition zone form a line? And if so, how far does it extend? To answer this question, I developed a portable line testing kit. This consists of
which weighs under 500 deben, so even a weakling like me can carry it. For more distant experiments, I would substitute a sharp axe for the wood, and forage locally.
To test for a North to South Transition Line at coordinate x East, proceed as follows
If the Transition line passes through coordinate x, the Total Shift across the x -1 to x + 1 should be significantly higher than across x -3 to x -1 or across x + 1 to x + 3.
Here are the results tracking the line at 2368e northward through RSO
at 2250n (RSO chariot area)
| 2365e | Y88, A70, Y82, A38, Y25, L85, L13, M63 | - |
| 2367e | Y88, A70, A38, Y82, Y25, L85, M63, L13 | 4 |
| 2369e | Y88, A38, L13, A70, Y96, L85, Y25, M71 | 15 |
| 2371e | Y88, L13, A38, A70, L85, Y96, Y25, M71 | 4 |
at 2410n (RSO chariot area)
| 2365e | Y64, Y96, M15, L68, Y51, A86, Y81, Y40 | - |
| 2367e | Y64, Y96, M15, L68, Y51, A86, Y81, Y40 | 0 |
| 2369e | Y64, M15, L68, Y96, Y51, Y40, M79, M31 | 9 |
| 2371e | Y64, M15, L68, Y96, Y51, Y40, M79, M31 | 0 |
at 3180n (northern RSO)
| 2365 | Y50, L60, Y24, L29, Y11, Y3, Y72, A14 | - |
| 2367 | Y50, L60, Y24, L29, Y11, Y3, Y72, A14 | 0 |
| 2369 | Y11, Y24, Y50, L29, Y43, Y3, L60, M7 | 14 |
| 2371 | Y11, Y24, Y50, L29, Y43, Y3, L60, M7 | 0 |
at 3320n
| 2365 | M7, Y99, Y50, Y11, Y10, Y72, L92, Y90 | - |
| 2367 | M7, Y99, Y50, Y11, Y10, Y72, L92, Y90 | 0 |
| 2369 | Y99, L61, Y91, Y72, Y10, M7, Y25, L92 | 25 |
| 2371 | Y99, L61, Y91, Y72, Y10, M7, Y25, L92 | 0 |
at 3350n
| 2365 | Y50, L12, Y24, Y32, L13, Y98, Y2, M23 | - |
| 2367 | Y50, L12, Y24, Y32, L13, Y98, Y2, M23 | 0 |
| 2369 | Y24, L12, Y98, L92, Y32, L60, L77, A70 | 24 |
| 2371 | Y24, L12, Y98, L92, Y32, L60, L77, Y50 | 0 |
Tests in Sinai and Karnak indicate the line runs the length of Egypt
at -980s Karnaki)
| 2365e Y81, Y67, L69, A14, Y34, M87, M47, Y9 | - |
| 2367e Y81, Y67, L69, A14, Y34, M87, M47, Y9 | 0 |
| 2369e Y34, M87, Y81, Y67, Y57, M95, Y99, Y19 | 24 |
| 2371e Y34, M87, Y81, Y67, Y57, M95, Y99, Y19 | 0 |
at 5500n (Sinai)
| 2365e | Y34, L92, L61, M63, L85, Y19, Y27, L28 | - |
| 2367e | Y34, L92, L61, M63, L85, Y19, Y27, L28 | 0 |
| 2369e | L85, Y27, A62, Y34, L61, Y19, Y50, Y32 | 23 |
| 2371e | L85, Y27, A62, Y34, L61, Y19, Y50, L28 | 0 |
Negative Tests
A good theory should also predict what won't happen. In this case, that we won't see these kind of abrubt transitions outside of the Transition Line. Picking a couple of spots in RSO leads to these results.
at 2250n (RSO chariot area)
| 2377e | Y88, A38, L13, A70, L85, Y25, Y96, Y40 | - |
| 2379e | Y88, A38, L13, A70, L85, Y25, Y96, Y40 | 0 |
| 2381e | Y88, A38, L13, A70, L85, Y25, Y40, Y82 | 4 |
| 2383e | Y88, A38, L13, A70, L85, Y25, Y40, Y82 | 0 |
at 2250n (RSO chariot area)
| 2351e | Y88, L13, A70, Y82, A38, A62, M63, L93 | - |
| 2353e | Y88, L13, A38, A70, Y82, A62, L85, M63 | 10 |
| 2355e | Y88, A70, A38, L13, Y82, A62, L85, M63 | 4 |
| 2357e | Y88, A70, Y82, A38, L13, A62, L85, M63 | 4 |
The transition at 2351 to 2353 was a fair size and warranted further investigation. At a later date, I put kettles at 2351 and 2353, then inserted two kettles in the space between.
| 2351 | Y88 L13 A70 Y82 A38 A62 M63 L93 | - |
| 2352.4 | Y88 L13 Y82 A38 A70 A62 L85 M63 | 7 |
| 2352.8 | Y88 L13 A38 Y82 A70 A62 L85 M63 | 2 |
| 2353 | Y88 L13 A38 A70 Y82 A62 L85 M63 | 2 |
At this "higher resolution" the transition show up as an area of particularly rapid change, but not the abrupt edge of a Transition Line.
32 x 32 cell theory
At this point, Jaby very helpfully observed that the coordinate 2368 is divisible by 64. This suggested a possible power of 2 spacing in the transition lines. A 16 coord grid was eliminated by the data on hand, but a 32 x 32 grid looked possible. I first tested for a Transition line 32 coords East.
@ 2400e = 75x32 (3330n)
| 2397e | Y24, Y50, L12, L77, Y97, Y32, Y98, Y41 | - |
| 2399e | Y24, Y50, L12, L77, Y97, Y32, Y98, Y41 | 0 |
| 2401e | Y24, L12, Y50, Y97, L77, L13, Y32, Y35 | 9 |
| 2403e | Y24, L12, Y50, Y97, L77, L13, Y35, Y32 | 2 |
Bingo! What about an East-West line?
@ 3328n = 104 x 32 (2360e)
| 3325n | M7, Y99, Y50, Y11, Y10, Y72, Y90, L92 | - |
| 3327n | M7, Y99, Y50, Y11, Y10, Y90, Y16, Y72 | 5 |
| 3329n | Y50, Y24, L12, Y98, Y32, Y2, A54, L92 | 31 |
| 3331n | Y50, Y24, L12, Y32, Y98, Y2, A54, L13 | 3 |
@ 3360n = 104 x 32 (2360e)
| 3357n | L12, Y24, Y50, Y32, Y98, L13, Y59, M23 | - |
| 3359n | L12, Y24, Y50, Y32, Y98, L13, Y59, M23 | 0 |
| 3361n | L12, Y24, Y98, Y50, Y32, L60, L92, M47 | 10 |
| 3363n | L12, Y24, Y98, Y50, Y32, M4, L60, L92 | 5 |
Looking good! So I hopped on a chariot to test if the transitions showed up where predicted in other parts of Egypt
On arrival at the Chariot Stop, I tossed a coin to determine if I would look for a North South (NS) or East West (EW) Transition Line. Then I headed for the nearest patch of open ground, calculated the next available Transition Line, and verified its existence.
Sinai NS
@ 2624e = 82 x 32 (5496n)
| 2621e | A6, Y35, A30, Y66, Y64, Y34, Y3, L21 | - |
| 2623e | A6, Y35, A30, Y66, Y64, A30, Y34, Y3 | 5 |
| 2625e | A30, A6, A62, Y66, Y35, L61, Y3, Y34 | 23 |
| 2627e | A30, A6, A62, Y66, Y35, L61, Y3, Y34 | 0 |
Nile Delta EW
@ 7072n = 221 x 32
| 7069n | A54, Y89, A62, Y40, A46, Y74, Y67, Y91 | - |
| 7071n | A54, Y89, A62, Y40, A46, Y74, Y67, Y91 | 0 |
| 7073n | A54, Y40, A62, Y89, Y74, A46, Y73, L84 | 15 |
| 7075n | A54, Y40, A62, Y89, Y74, A46, L84, Y73 | 2 |
Pharaohs Bay NS
@ -960w = 30 x 32 (7658n)
| -957w | M87, Y82, Y18, M15, M63, Y64, Y56, Y9 | - |
| -959w | M87, Y82, Y18, M15, M63, Y64, Y56, Y9 | 0 |
| -961w | M87, M63, Y82, Y18, Y9, Y67, A6, Y64 | 16 |
| -963w | M87, M63, Y82, Y18, Y9, Y67, A6, Y64 | 0 |
Fools Paradise NS
@ -2112w = 66 x 32 (-422s)
| -2109w | L52 Y98 Y59 L28 A94 Y74 Y11 Y56 | - |
| -2111w | L52 Y98 Y59 A94 Y74 L28 Y11 Y56 | 4 |
| -2113w | L52 Y11 A94 Y56 Y59 Y74 Y50 Y98 | 21 |
| -2115w | L52 Y11 A94 Y56 Y59 Y74 Y50 Y98 | 0 |
Not a lot of samples, but it looks like the theory is a good predictor
Some suggestions