Cartography and Et Cetera Stuff

Cartography is a subject much larger than many may think. It is usually solely dependent upon how accurate you want your maps to be.

An Example: Google Earth, Google Maps was having major problems with distance measures across their maps when users wanted the distance from A to B. Google gave a challenge to the universities across America. The team me professor chose me to lead worked on this problem. Only three days into our investigation, I had thunked a Wild Tangent.

“What geoidal model are they using for the Earth?”

Found out they were using a perfect sphere with R = 6371 kilometers. Earth is spheroidal, but not a sphere. Geoidal is the preferred term. Additionally, Google was ignoring terrain. All those ups and downs of terrain add additional distance from PntA to PntB.

Author’s Note: The images below were actually drawn with me finger on my Notebook/PADD.

 

 

A Simplied Terrain Model
SimpleTerrainModel

In image above, LengthA + LengthB > LengthC. Comprendez-vous? Use ANY triangle and the sum of any two sides will ALWAYS be greater than the remaining side. I am referring to length (distance), remember? Additionally, the way mountain roads are made adds even more distance as shown below.

A simplified Mountain Road Model
MntnRoadModel

The mountain road (black) is quite longer than the straight horizontal measure. Comprendez-vous, maintenant?

The road goes to and fro so as to maintain a climbable slope. Cannot just drive straight up the side of the mountain.

 

 

 

 

Areal Features

Terrain also adds more area than a flat measurement.

Flat Terrain Area...
FlatVsTerrain-flat

... versus !Flat
FlatVsTerrain-trrn

The greyscale image is an actual DEM from somewhere in Colorado, USA. I have a fairly hi-res DEM of the 48 contiguous on a Terabytes data drive. Or, is it PB? As one measures the area of the hillsides, it will be greater than the area in full-black flat map. Kind of like the AreaA + AreaB > AreaC depicted above with the triangle representing a cross-section.

Now think of unfolding that 3-D DEM into a 2-D plane. It would vastly increase in size, and would no longer be rectangular. Fractal perimeter. Know about the Koch Snowflake? Take an equilateral triangle. Now take 3 one-third sized triangles on each face. Keep doing this ad inifinitum. You end up with a finite area, defined by an infinite perimeter.

Slope Area versus Flat Area Example (drawn with finger)
SlopeArea

I know the lines are messed up, specifically blue, but what do you expect, I ain’t exactly conversant with drawing with a finger. Much prefer a stylus pad which I need to purchase. If you know trigonometry, then you know the red line is longer that the blue (bottom grey) line. If this is a prism cross-section, the area of the plane shown measured along the red facia is greater than the area of the bottom face shown measured in blue. The blue is if one were using a straight-down area measurement from above which would be incorrect when compensating for terrain. The plane measured in red would the correct method.

Some interesting facts:

There are three things any cartographer must remember. Projecting a 3-D surface onto a 2-D surface causes distortion in direction, distance, AND area. ALWAYS. Unfolding anything from a higher dimension into a lower dimension will cause distortion. As Agent Smith would say, “It is... Inevitable.”

On a 2-D map, you can only preserve one of those, but never two. You have methods to alleviate the other two, but only one can be preserved. Most often Cartographers, as me self, will try to preserve area, while alleviating distance and direction distortion as best can. An Areal Preserved map to me is always the best to use. If I have a Professional Compass, then I would rather use a UTM style map. UTM = Universal Transverse Mercator. A much better Mercator than the original. And as long as you know Magnetic Declination for your region, you cannot get lost. Unless something else disrupts the compass.

Historical Magnetic Declination Viewer. You can even download past MagDev maps.

Remember those infamous Mercator maps long ago? The Mercator Projection Map preserves direction only, badly distorts the other two. Thus, no matter how long the line across a Mercator map, it stays in a constant heading. However, the distortion it creates making Greenland look larger than USA or Europe, when it is actually only slightly larger than Texas or France. The Mercator Map distorts distance and area worse the further you go from the equator, its Point of Tangency.

The Plate-Carrée projection in aspect is equidistant along any meridian and the equator. Shape, scale, and area distortion increase with the distance from the equator, its Point-of-Tangency. What makes the Plate-Carrée projection a great tool for mapping is it can be wrapped onto a spheroid with no distortion, except for polar pinch. As long as YOU account for the distortion in the Plate-Carrée projection. In other words, as you go away from the equator, you will need to compensate for the East-West width of the land.

    

The image on left is a flat Plate-Carrée map. Duh. Right is the map wrapped onto a spheroid. Duh. And notice the polar pinch effect. As long as you calculate for the distortion effect when making the flat map, only the polar pinch effect causes distortion, and truly shows once poleward from 45° latitude. Also notice the land appears thinner east-west on the globe as compared to the flat map. I shall be the first to admit the northernmost coastline could have been smoothed to account for the pinch effect.

That crop of the Plate-Carrée projection is from a wall-map I had printed 8 feet by 4 feet. Plate-Carrée projection will always be 2× width as height. The Equirectangular Projection is 1.7:1 ratio, not 2:1. It will not wrap very well on a spheroid.

Thus, you end up with three categories of map projections which preserve one of those three: Distance, Direction, or Area. The Lambert Conformal Projection for the United States is the best if you wish to see areal features. Usually, the USGS uses UTM style Quad-maps.

Example of some Worldbuilding

For this example I shall use Liu Cixin’s Remembrance of Earth’s Past trilogy: https://en.wikipedia.org/wiki/Remembrance_of_Earth%27s_Past. Now a damned good show on Netflix: 3 Body Problem. I recommend it with 6★ out of 5. ★★★★★★

Imagine a species that evolves both True Genetic Memories (if one survives, all survive) and Mental Thought Communication (communication amongst all is made as soon as the thought is generated). That would be the only way the Trisolarins could advance their science. If just one of them survived, they have all the previous knowledge. However they reproduce, the Trisolarin would make more so as to get the work of more advancement before the next Age of Instability before the planet gets wiped out in recurring cataclysmic disasters. But how kewl is it that if only “one” survives, they all survive? All needed is a setup that preserved one and could sense when an Age of Stability was present. Then automatically “rehydrate” them. And I think it ain’t what we think of as rehydration. The Trisolarins used the best word us humans had, but it means something far greater and quite different than “rehydrate”.

Honestly, I feel the Ages of Stability were rather short. Some perhaps only a few millennia. Which is fine because look at how far we advanced from 1900CE to 2000CE. The Ages of Instability could last for millions of years. It could even have taken the Trisolarins a billion years before they could go from hunter-gatherers to constructing an interstellar fleet and their Sophons.

Earth, on the other hand, has had a largely stabilized orbit for at least a billion years. Advancement continues without the disruption of cataclysmic near-extinction events. Us humans by comparison could only take 200,000 years to achieve the same TechLvl as it took the Trisolarins millions of years. And they sacrificed virtually all resources for that “leap of faith”. Think about that...

Think on this. How long did it take us humans to go from sticks and stones and bone clubs to the TechLvl today? No more than about 200,000 years. Homo sapiens have only been around for about 200,000 years. How long would it have taken the Trisolarins? Millions of years? Dare I say billions? Then it will take the Trisolarins 400 years to reach our stellar system. How far will we have advanced by then from today? Provided we can get rid of the religion bullshit. Currently, it is still religion doing its damnedest to disrupt our science advancement. The Trisolarins do not need Sophons to hinder our science advancement. Religion will do it for them. Think on that.

7734, we could build our own Sophons to send against the Trisolarin fleet before it got here. Remember how Sword Lady Sophon explained how a superduperhypercomputer can be imprinted onto a single higher-dimensional proton? (Provided you have seen 3 Body Problem.)

With the cartography example above, when you unfold higher dimensional objects into lower dimensions, there shall always be distortion, and an increase in size in that lower dimension. We see this by modeling a 3-D Earth onto 2-D object. If truly depicted, the 2-D map would have a much larger area. That higher dimension object will become larger in the lower dimension. This happens with each unfolding into lower dimensions. A 3-D object (by area) unfolded into 2-D would be larger than its original 3-D version. Now imagine taking a 13-D proton and unfolding it 10 times into our 3-D Realm of Existence. That proton could grow to be larger than the Earth. Then easily imprinted with a superduperhypercomputer and refolded. Easily launchable at near lightspeed velocites, say 0.999986c? By then, we could probably hit 0.99999999999c with a proton. Get to the Trisolarin fleet still a few decades away. Use Sophons against them. What a battle that would be: Sophon vs. Sophon.

Then Liu Cixin used the Dark Forest Hypothesis. Say we knew of an extrasolar invasion on its way. We know how long it will take. We broadcast a signal they cannot stop, announcing not only our location, but the learned location of their homeworld to the universe. The hypothesis is that there may well be other advanced civilizations out there, but they are exceptionally xenophobic and have ceased broadcasting their location for fear of invaders. Here come the Klingons...

That is also how I based the Intraspatial Folding of several rods that form a geodesic dome into just one rod. Those people use the Power (“onaviu”; that within all) to simply fold many into one.

IOW, a plausible scientific explanation for how the “magic” worked. Just as the Original Arakish intended for his role playing system. But also remember those atoms are composed of huge amounts of “empty space”. Who knows what other higher-dimensional objects could be folded within?

Can a 0-D Realm of Existence exist? Yes. It can. It would be a singularity. A black hole. MECO: Magnetic Eternally Collapsing Object. What about negative dimensions? I know, you cannot have a negative length. But what if you could? OOoof...

Assuming survivability, that may be the core of a black hole. A 0-D realm of existence. A dimension with no dimensions. Kewl.

String Theory

In String Theory, the size of a “string” is given as: a comparison of a 15 meter tall tree compared to the entire cosmos/universe, compared to one electron. If so, those Strings are DAMNED small. Well below Planck Length. Thus, it would take what, 1081474 “strings” to make an electron? And many more to make a proton or neutron. I just do not partake of the String Hypothesis. To me it shall stay forever as a simple fantastical idea. Kewl, and, Highly Fascinating. But. It could very well be true. We do not have the technology to test such things. Yet. Thus, like M Theory, both remain hypothetical ideas.

Remember the test that determines hypothesis from fantasies? And answers given for both String and M Theories.

  1. Is IT testable? — No. Need more advanced technology, if possible.
  2. Is IT falsifiable? — Yes. But since cannot Test, cannot falsify. Thus, No. Not falsifiable.

Then there is the hypothesis (idea) of M Theory. M Theory hypothesizes there are 13 dimensions. String Theory 11. I like both because they are Prime Numbers. I feel that if this universe IS multidimensional, then the Number of dimensions shall always be a Prime Number. Do not ask me why. It is just an intuitive leap of faith. Even I cannot explain why I would feel it to be true.

Yes, scientifically contradictive. But I WAS correct when I assumed that the die-hard religious were mentally retarded. Science proved it about 25 years later. PROVED it. Sometimes us scientists have this intuition that something is correct, although we cannot explain how, nor prove it.

I had first-hand experience growing up. One of my childhood friends had parents that were mentally retarded. He was fine. In fact, very intelligent. Like me, found science more acceptable than religion. Thus, I grew up young knowing how to spot mentally retarded methods of thinking. His mom was worse. His dad phazed away sometimes.

Michio Kaku is full of these kind of scientific hypotheses of multi-universes and et alia, but they forever stay as fantastical ideas. As one TV character used to say, “Verrrrrrrrrrry Interesting.” They are kewl ideas. But that is all they are. Even I have an idea to explain how the universe is infinitely old. Has no beginning or end. A kewl idea, but just an idea because IT cannot be tested, nor falsified.

Back to N-Body Problem and ITS major malfunction.

One FACT about the N-Body Problem is that there is NO solution for N ≥ 3. The N-body problem is completely unstable for N ≥ 3. Our stellar system is unstable. However, it is enjoying the period of stabilized equilibrium of a Mature stellar system some n-body problems can achieve. But in the long run, our stellar system will become junk floating through the galaxy in different directions. But do not worry. That is billions (trillions?) of annums from now...

How can the universe be Infinitely Old?

No Beginning? No Ending?

Simple. We have our Big Bang Model. Okay. No problem. Does the universe continue expanding forever? Never stopping? Does it suffer the “Heat Death” of 0K? A cosmos filled with junk floating every which direction? Here is a bulleted list:

Especial Note: I reverse the Pop-I to Pop-III stars as defined by the IAU.

Furthermore:

Easy. Peasy. And yes, it is based on the old (1960s) idea of Big Bang... Big Crunch...Big Bang... Big Crunch...Big Bang... Ad infinitum...

The above now kind of Begs the Question: “Which Iteration of the universe are we currently in?”

First?

Second?

Millionth?

You would go wonko just attempting to figure that out.

Thus, the universe IS infintely old in MY Cosmological Model. Since we cannot look into past iterations, nor future ones, how could we even know which Iteration we are currently in? In my cosmology, the cosmos remains. Always has. Always shall. Get over it. It is the universe that goes crunch, bang, crunch, bang, ... Thus, ultimately there is no beginning. There is no ending. It just always has been. And always shall be. Make sense? And O! how incorrect I am.

ADHD. These ideas come faster than I can type. Thus, I snag one, type it. Wait. Snag another. Et cetera. Et alia.

Planetary Overall Density

This is a great consideration for the planet of your world. If you wish for metals, then Overall Density of your world’s planet should be close to Earth’s: 5515kg/m3. Maybe 4500 AT lowest. According to some models I have played with, it seems the break point for having a strong enough GMF is about 5000kg/m3. Maybe 4500 at minimum. Otherwise, life may never complexify. Too much Insolation reaching the surface. And without as large an iron core, gravity will be less, and the planet will have trouble holding an atmosphere thick enough.

Then, with lower density, the planet must be larger to equalize around 1g. Just determine the lower density, use a larger VMR, then calculate mass and gravity. May have to play around a little bit with the VMR. Say density is 4300kg/m3. Its VMR would need to be around 7200km? I am guessing. But it may be close enough to 1g.

ADDENDA: I have plans to provide some simplified algrebraic equations and formulas. Debated it amongst the Three of Me and decided Yes.

For Overall Density of my worlds, I usually choose a overall density of 5000 ≤ OD < 6200 kg/m3. I feel that is a very good range of Overall Density for terran type planets and complex life.

And remember this about Overall Density. An Earth-denser planet would mean it would also be somewhat larger than Earth. More gravity to pull in more material. Thus, a greater overall surface gravity.

Basically, I use Earth’s Overall Density of 5515kg/m3 to guage where I may want the OD for my world. Slightly greater is OK as long as you do not go overboard, say an OD of 8000kg/m3. This would be indicative of a rock ball very rich in the actinidic elements. A radioactive fireball wasteland. Carbonic life would never have a chance to develop. Radioactive Life?

Technically: I will always limit the above to a range of 5200 ≤ OD < 5800. That also tends to give me a surface gravity of 0.85 ≤ g < 1.25.

With what I know of Nuclear Physics, I cannot plausible see how radioactive life could exist, except as an energy-based life? With my understanding of energy physics, I cannot see that either. Hmm...

As with the Titanverse (nt), if radioactive life, it would be within the Earth. Deep where it is much hotter. More pliability for movement. Basically a rock life form that feeds on the actinides. But on the surface of the Earth, they would definitely go after everything “nuclear”. And the frigidity would drive them back into the interior of the Earth. As said, “cold” is relative. Compared to a molten, yet solid, state, Earth's surface would feel like Absolute Zero for us. Hmm...

How could an energy-based life develop intelligence? We know our intelligence comes about from chemical reactions in our brain. Chemical reactions may produce some energy, but they are not energy.

Thoughts I Thunked. How could energy develop intelligence? Energy pulses? Would have to keep them constant, else intelligence is lost. That would require the consumption of more energy. A requirement for life: Consumption of fuel. Could even consume enough extra energy to replicate itself. Another requirement for life: Replication. Yes, us humans even replicate, through a process of Bisexual Reproduction. However, energy would be Asexual Reproduction for its replication. Until, said energy life developed Bisexual Reproduction. Two pieces of energy becoming One? Hmm...

Furthermore, I am only trying to qualify IT as life. Not intelligent life. That comes later.

So...

And think on this. Even us humans replicate through bisexual reproduction. And there is always Asexual Reproduction. The first and simplest method of replication. Viruses do not qualify as “life” since they only replicate. They do not consume. They do not excrete.

Would not the three above be the only requirements for determining Life? For intelligent Life, even with Animal-Training, that requires a bunch of other stuff. So... Could there be an energy-form Life? 7734, could there be mineral, metallic, cerami-alloy Life? Here inside Earth? Down where it is much hotter, thus easier for them to move about? Hmm...

Could even the magma that floats to the surface of the Lithosphere be their excreted waste material? Ooo... Yuck! We are living ON their Poopoo.

How is that for Science Fantasy attempting plausible feasibility?

I still see scientists use the wrong term. It is replication. Life replicates itself through two different reproductive processes. Life does reproduce in a sense, but the actual proper term is replication. In mine opinion only.

What about an overall Hive Mind intelligence within a group of nanites? Then replication (reproduction) becomes imperative. Much like the Replicators in the Stargate franchise.

— The Unknown Atheist

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