Layer Cake and Planets

Ok, I got to admit sometimes I see pattern in things that might not actually exist, but hey, if it is for the sake of "finding out" the truth, it might worth the time analyzing the data it provides and say "yup, there's definitely a pattern there.." and so I can use that as an analogy for a concept that is slightly tricky to grasp. 

What now? 

The other day when my brother and his girlfriend traveled to Jakarta, part of the souvenirs he got us was a package of layered cake. Without notice, my mother packed that delicate dessert into my luggage when I move back to my campus after recent general election. 

So when I opened that box, besides the delicious aroma of cinnamon, I saw this:

The cake were craftily layered with its dark lines laden with cinnamon powder (verified upon tasting). Well, from first glance, it seems that the top layers are thicker compared to layers at the bottom. Logic tells us compression from the upper layers during the process of baking forces the still-soft layers at the bottom being pressed into a denser and thus able to "sink" more. 

So, I cut up another thin slice and laid them on a clean white plate while ready my camera for shooting. Assuming the camera was aimed perpendicularly to the plane of the cake, simple measurements can be done to find out the thickness of each layer by the units of pixels (they are digital picture of course). And I have to confess among the excitement to publish a blog post after the idleness from preparing my doctoral thesis proposal, I actually re-sized the photo for publishing before actual measurements were made. Ok, so we lost some resolution, but statistical analysis almost always prove itself useful to solve this kind of problem. 

What I did was quite simple. There are 22 layers in a slice and because the thickness of each layer varies locally i.e. different thickness at different points of the same layer, I measured them from 4 different points. One from the left-most edge, two around the center of the cake and the last from the right-most edge. The arithmetic mean was taken as the average thickness per layer and I plot a graph of thickness of each layer against the layer count where 1 is the top-most layer and 22 is the bottom-most. Here's what I got:

It is (not-so) obvious that the result produced a general trend of shorter layer as it is more bottom compared to the layers on top. Linear regression shows poor coefficient of determination (R squared at 0.22) meaning it is difficult to use this analysis to predict thickness after layer-22 based on this statistics. Nonetheless, some of the error bars (which are contributed by the absolute deviation of points from the mean) are huge denotes the big difference of measured values in the local layer thickness. 

What did we get from the simple analysis? The work was not entirely in vain when we see a general pattern of decreasing thickness over depth of layers: it tells us the layers at the bottom are being compressed by the layers after it and that gave us an insight on how the cake was made. i.e. how patient was the cake-maker in perfecting his/her cake by waiting until each layer has completely solidified from baking before pouring another layer into it. 

So, the idea is about compression: where under the influence of (earthly) gravity, the same substance (of same cake batter) on top is capable of compressing the bottom layer into a thinner and thus more dense state. You can see this more evidently with few soft pillows stacked up to a few layers where the bottom-most pillow will turn out flatter compared to the ones on top. 

This concept has astronomical importance. The structure of planets, how stars get its heartbeat and how because of this eventually lead to its death, are governed by similar mechanism. Without going too far, I'll just take planet Jupiter as an example:

The picture above was taken from NASA's public domain (photo ID: S89-44035) 35mm film taken by mission STS-34 by Galileo entitled "Labeled Drawing of Jupiter Showing its Core and Composition" taken in 9th July 1989. It described: "Labeled drawing of Jupiter identifies fluid molecular hydrogen, transition zone, fluid metallic hydrogen, and possible core and the composition of its atmosphere - cloud tops - aerosols, ammonia crystals, ammonium hydrosulfide clouds, ice crystal clouds, and water droplets."

What I want to emphasize here is the difference between the "hydrogen" evident in layers called "fluid molecular hydrogen" and "fluid metallic hydrogen" in the NASA photograph. Compressed by gravity in a fashion similar to the layers in the cake, hydrogen which constitutes to 90% of Jupiter's mass has been split into two types. Notice the "metallic hydrogen" exist only when it is highly compressed, in a place exceeding 40,000 kilometers beneath the surface of the gas planet! The usual hydrogen "float" on its surface freely as gas while the "special" hydrogen, being compressed, thus with higher density sinks towards the heart of the planet. 

Now this metallic hydrogen is in a special state of the same thing that floats on top of it. It is "strange" because the extremely high pressure caused by the upper layer (about 250 thousand times pressure of our atmosphere) has pressed the usual hydrogen gas into liquid and at this state, this strange hydrogen is able to conduct electricity hence it is dubbed "metallic"!

Currently, there are few literary works that theorizes the existence of such a state and experimentally (on earth), it has been proven difficult to achieve such a state of matter due to the requirement of extreme pressures unlike so conveniently provided by the self-compression of Jupiter's mass. Hydrogen is abundant in our planet and they are mostly locked as a form of water in the oceans (H20) and also there are some parts of it in our upper atmosphere. If anyone manage to make a vial of those amazing fluid, it would definitely hit the newsstand as  "NEW HYDROGEN FOUND AFTER BOYLE IN 1670".