Top ten

The ‘Spherical’ Earth

In this blog post we will talk about the ‘spherical’ earth that we are all living in. Some people have a common misconception that the earth is flat, and for millennia this has been a carefully discussed topic especially in the middle ages where religious beliefs ruled the entire society.

We will try and debunk utilizing state-of-the-art photos, mathematics for describing our ’round’ earth and finally come with some facts about the earth and common misconceptions which people should be careful not to fall against.

Is the earth flat?

Before starting off on our talk about our beloved earth lets try and answer one of the simplest questions most people have asked themselves: Is the earth flat? To start off with, it certainly seems flat to the naked eye, as the horizon on which you can steer out into creates a seemingly straight line as expected with a flat earth. One interesting video about the flat earth is the ‘Vsauce’ video titled: “Is Earth actually flat?” A contribute to debunking the flat earth society.

Video 1: Vsauce video about the flat earth society and whether or not the earth is a flat disc.

For centuries this fact has puzzled human kind who believed to be the center of the universe and the earth to be a flat plate swimming alongside the back of a turtle, or in some cases, a flat disc where the sun has been placed on a curved space with a stationary earth.

Fighting the ‘Globe’ Theory

One of the latest’s and most famous examples of such a phenomena is the 1893 drawing by Richard Ferguson, a firm believer in the flat earth theory constructed the ‘plausible’ drawing of how the earth might be a curved square space with a stationary centered earth against the entire solar system and how this revolved around the earth system. He constructed this in order to ‘combat’ the dominant ‘Globe’ theory.

The 'square and stationary earth' theory proposed by Orlando Ferguson meant as a fight against the dominant 'Globe Theory'
Figure 1: The flat earth fighter Orlando Ferguson in 1893 fighting against the ‘Globe Theory’ the square space contains numerous biblical passages which is used to justify the wrong assumptions.

Even to this day with our photographic evidence from satellites and space missions, there exists people who remain members of the so-called flat-earth society, a society of firm believers in the flat earth theories that exist.

Photographic evidence of ‘Globe’ earth

After the invention of satellites in the 20’th century we now have photographic evidence of the so-called ’round’ earth as can be seen in Gallery 1. Here a collection of pictures of our blue ’round’ earth have been taken showcasing clearly that the earth is round.

This earth looks a lot like a sphere and surely this is a way better approximation of the shape of the earth rather than the flat earth society experienced. The following shows how to calculate the spherical earths volume, circumference and surface area based on a supplied radius of the earth.

Related read: Top ten misconceptions about ChatGPT, Top ten misconceptions about Earthquakes, Top ten misconceptions about Tsunamis

The Spherical earth

Now lets dive down into the mathematical description of our spherical earth. A sphere is most easily described by its radius, r, from which you can calculate the volume, V, and surface area, A, along with the two-dimensional circumference S.

(1)   \begin{align*} V &= 4/3 \cdot \pi \cdot r^3 \\ A &= 4 \cdot \pi \cdot r^2 \\ S &= 2 \cdot \pi \cdot r \end{align*}

For the determination of the radius of the earth there exist multiple values based on a variety of methods a great overview over the different methods is given in a Wikipedia article:

The most common values ranges between 6.384 km – 6.528 km for a radius of the earth. This quite different range details the differences in roundness that the earth resembles, as the mountains and sea-floor valleys aren’t accurately mapped in a perfect spherical world.

The non-spherical earth

The spherical earth which we live on is therefore not exactly round as first expected as the mountains valleys and later realized poles of the earth aren’t accurately mapped in a spherical system. The

In fact when mathematicians worked on theories of spherical earths and tidal forces, wind speed generations, Coriolis forces to mention a few. These are facts about the earth which a full perfect sphere cannot perfectly answer.

The slight variations in shape and size of the earth have significant impacts on the way our planet behaves. For example, the mountains and valleys affect wind patterns and ocean currents, and the non-uniform distribution of mass leads to variations in gravity, causing fluctuations in the Earth’s rotation.

Despite these complexities, the spherical model of the earth has proven to be incredibly useful for navigation, satellite communication, and understanding the world around us. But it’s important to recognize that the earth is not a perfect sphere and that its imperfections have real-world effects.

Mathematical description of imperfections

The description of the deviations from the spherical shape is mathematically described through the flattened ellipsoid equations where an ellipsoidal disc can be described simply through two different equations concerning the radii typically described in the equations of state.

The equations used to describe the surface area, volume and in a similar format as that of a spheroid except for the fact that the parameters; a, b and c are introduced instead of the value of r.

Ellipsoids for describing the Globe type earth which is more accurate than the spheroid version.
Figure 2: Illustration of the three typical ellipsoids with different values of the radii parameters a, b and c. For the special case where a=b=c we have a spheroid. See source.

(2)   \begin{equation*} (\fraq{x}{a})^2 +(\fraq{x}{b})^2 + (\fraq{x}{c})^2 = 1 \end{equation*}

Now for the cases where surface areas of ellipsoids need to be calculated the expressions are quite a bit more complicated as the surface integrals depend on the chosen parameterization of the different values of a, b and c among others.

The parameterization typically found used in spherical projections correspond to spherical coordinate systems utilized in many different aspects of life and engineering in general. The parameterization follows to be the following:

Volume of an ellipsoid:

(3)   \begin{equation*} V = \frac{4}{3} \cdot \pi \cdot a \cdot b \cdot c \end{equation*}

While the general formula for spherical coordinates and therefore parameterized surface area of the ellipsoid is the following:

(4)   \begin{equation*} \begin{bmatrix}   x = a \sin(\delta) \cos(\theta) \\   y = b \sin(\delta) \sin(\theta)\\   z = c \cos(\theta) \end{bmatrix}  =  R \cdot  \begin{bmatrix}   \cos(y)\cos(\lambda) \\   \cos(y)\sin(\lambda) \\    \sin(y) \end{bmatrix} \end{equation*}

Where -1/2 \leq y \leq 1/2 and 0 \leq \lambda \leq 2 \pi. The definition of R is described as

(5)   \begin{equation*} R = \frac{abc}{\sqrt{c^2 (b^2 \cos^2 \lambda + a^2 \sin^2 \lambda) \cos^2 y + a^2 b ^2 \sin^2 y}}, \quad -\pi/2 \leq y \leq \pi/2, \quad 0 \leq \lambda \leq 2 \pi \end{equation*}

These equations are used in various applications from satellite tracking systems to navigation systems for vessels and ship, to map creation and transformations utilized for creating specific map types.

Now that we have established that the earth is round one may consider approving of this theory and buying a globe to support the ‘globe’ theory. This helps the website and content creator if you decide to click and buy one of the recommended globe spheres below.

AI conquers the world Top ten

ChatGPT – Top 10 misconceptions

The Chatbot, “ChatGPT”, (Generative Pre-Training translator), has recently been the new kid on the block raking in millions of new users breaking records for first to market.

In this blogpost we discover 10 common misconceptions about ChatGPT and trust me there is more to this chatbot than meets the eye.

OpenAI logo. Original company who created the chatGPT chatbot
Figure 1: OpenAI’s logo

1. Using ChatGPT to replace software developers

People fear new and revolutionizing technology. They are afraid to lose their job and therefore be unavailable to financially support themselves.

A tale of horses and automobiles

This was the case with the introduction of tractors suppressing the use of horses. Historically speaking, horses was used to plow fields, drag harvested crops and equipment across the farmland. They were indispensable on farms and used heavily in cities.

In cities horses was used for everything from driving carriages with people, postal services, public transportation and transportation of goods and services. This required a stable amount of draft horses that needed horseshoes, saddles and brushes as maintenance for the draft horse stables.

With the advent of the automobile all jobs in relation to the horses got replaced by automobiles. This replaced horseshoe makers, saddle makers and similar jobs with mechanics and factory workers.

New horizons and beginnings

Consequently, the innovation of the automobile replaced previous job-types and was initially met with extraordinary resistance and fear from the people. For fear that, the unknown new ‘dangerous’ technology was generally a big problem for the general public which reacted with civil unrest and demonstrations.

Now one may wonder, is that a better way of life for the general public? As it turns out people are smart and adaptable. They are able to adapt to their surroundings. The horseshoe makers changed their professions in accordance with the advent of automobiles. Consequently new jobs are created ensuring that people innovate and so the cycle continues.

ChatGPT – Replacing modern day horses?

In this case, I believe that ChatGPT won’t revolutionize standard software architecture jobs. The chatbot cannot fully abstract to the level which humans are capable of.

Necessity is the mother of invention and software architects/programmers will either specialize or new jobs will be created which they adapt for. The innovative capabilities of ChatGPT will compete against software programmers and possibly free up resources to be allocated towards more challenging tasks.

2. ChatGPT will conquer the world

The invention of new technology embraces the welcome feeling of new and untested territory which brings forth emotions of excitement and joy. However also feelings of discomfort and uncertainty, moral dilemmas and ethical considerations are keystones of the modern innovation space.

Specifically the feelings of fear with the unknown must be dealt with effectively. The spurious thoughts spawn from fear. These include feeling of disempowerment, and include the fear that ChatGPT will conquer the world.


The irrationality of such thoughts are difficult to comprehend for the isolated individual. Especially if that person surrounds itself will people of the same belief systems. Such scenarios exist causing so-called echo champers. Echo-champers are ideological abstractions which encourage radicalization of ideas. This enables users to develop own beliefs of impeding doom.

AI-generated image of an abstract cheese bell shaped echo-champer
Figure 1: A ‘cheese’ bell echo chamber sketch of a person -AI generated

The lack of evidence is neglected and becomes evident when attacked by critical thinkers from the outside. To clarify, ChatGPT will not conquer the world. Neither will it enable terrorists to try and capture key infrastructure from scripts developed by ChatGPT.

Related read: top ten misconceptions about Tsunamis, Top ten misconceptions about Earthquakes

3. ChatGPT will replace google

One of the ChatGPT – top 10 misconceptions, is that it will replace google as we know it. Google is the well-known search-engine answering all questions which people might wonder. It is basically an indexed table of the internet where users can post and question all of the naturally happening world.

On the other hand, we have ‘ChatGPT’ which according to the creators themselves (OpenAI source: is an optimized conversational language model. The ChatGPT language model is based on reinforcement learning models, supervised learning and specifically Reinforcement Learning from Human Feedback (RLHF-models). The chatbot is therefore able to make informed conversations with its users remembering what the conversation is about and admitting mistakes underway.

ChatGPT-diagram about the reinforcement learning methodologies utilized
Figure 2: ChatGPT diagram over the structure of the reinforcement learning models.

A profoundly different methodology than the index based search engine which is google. Unlike google, ChatGPT generates answers utilizing its AI engine. However these answers credibility is up to the individual users interpretation while general credibility for source material indexed from the users of google searches is based on source material written by other humans.

4. ChatGPT will replace writers

Another of the ChatGPT top 10 misconceptions is that ChatGPT will replace writers. This is a misconception which has partial credibility. Specifically ChatGPT is a chatbot that can generate paragraphs of text. This text is readable by humans and is somewhat easily comprehendible.

With this being said, ChatGPT might actually replace human writers with written blog material, news agencies or similar types of material. This is particularly different than writers of novels, books or poems which are profoundly different abstraction levels than commonly used material.

Consequently, ChatGPT will most likely not replace common writers or writers as we know it to exist. However it can likely make people writing for news agencies and similar unable to accurately make jobs.

5. ChatGPT will develop new languages

One common misconception about ChatGPT is that it will create new languages. In the world today there exist more than 5000 languages worldwide, not counting professional programming language syntaxes such as C++, Fortran and Python.

Creation of new languages

To make a new language you would have to have thousands of people using it on a day to day basis with its own history, culture and verbal/non-verbal communications.

Therefore it is not possible to correctly characterize the new chatbot ChatGPT, as a new language, nor does it actually invent new languages by replying to prompts through an interactive fashion.

The conversational logic behind ChatGPT might trick the users into thinking that it is a sentient being, thus passing the Turing test, however this is not yet the case and certainly the conversations you are having with the chatbot is based on trained neural networks, not actual sentient thinking.

6. ChatGPT will automate life as we know it

In our top 10 misconceptions about ChatGPT, this is one of the more spacey statements. To start off let’s characterize what the capabilities of ChatGPT is.

ChatGPT is a conversational reinforced learning network, answering to prompts received by human consoles. Similar to modern pc’s it can calculate and respond to a given set of instructions supplied via a prompt.

Similarities to a regular pc

The deviations from a regular pc, comes both from the fact that it is software algorithmically driven and that it therefore fundamentally runs on similar binary logic as a regular computer.

Secondly and more importantly, ChatGPT is unable to communicate with existing infrastructure and hardware meaning that it is unable to actually take control over old machinery or similar.

It can thus easily respond to prompt and provide answers and corrections to questions. However when trying to solve real world problems such as supplying hungry people with food and clean drinking water, it falls sort and will be unable to plan and perform changes in the real world for people.

7. ChatGPT will change everything

The changes which will be incurred from the world wide usage of ChatGPT lies more when trying to answer questions which we already have answers for and need people to execute.

In these regards ChatGPT might very well change common work principles and routines for people working with software and it-infrastructure.

Old fashioned ways

However when it comes to complex labor tasks such as; harvesting of crops, processing of clean drinking water and planning for road constructions, the old fashioned ways with project leaders and workers will remain unchanged going forward.

There will constantly be a need for people with a plethora of skills solving complicated pieces of work all within the same puzzle. This type of work with a mixture of manual and knowledge driven work, will be key when trying to fundamentally change the way of lives of regular people.

ChatGPT will change a small fraction of these tasks and most likely create new jobs along with it.

8. ChatGPT will replace humans

This misconception might actually have some grain of truth within itself. It is likely that ChatGPT will replace human interactions on a certain level come it to be scripting, coding or answering regular questions as a chatbot in public service infrastructure.

Boring jobs and uninteresting work

The replacement of boring, unchallenging, uninteresting work of humans by machines is a constant when innovating. It is important for people to feee up more of their time to do stuff which they want to do, such as art, music and creation of innovations.

However to think that ChatGPT will actually replace humans as we know it and make us obsolete in the workforce is fear mongering at best.

9. ChatGPT will replace doctors

Second to last on our top 10 misconceptions about ChatGPT is one of the more controversial topics, medicine and particularly doctors.

Big tech response replacing doctors

Recently, big tech giants like google, Microsoft and similar have invested quite a substantial amount of money into developing an artificial doctor capable of accurately provide diagnosis of sick people.

Their job is trying to effectively remove the old traditions of booking appointments with doctors to get diagnosis but rather take tests and answer questions by a chatbot.

Conversations as therapy

This last part respond well with ChatGPT however it won’t replace the regular doctors as we know it. The conversational chatbot ChatGPT is unable to read and process tests delivered to a computer and although the response to answers from patients might have a therapeutic effect it won’t replace hardcore blood samples.

ChatGPT is built with responsive language models and conversations in mind, not difficult deep-learning neural network tasks such as eliminating possible diseases.

10. ChatGPT will posses emotions

Last on our top 10 misconceptions about ChatGPT is that it will poses emotions. on a more abstract level, emotions are quite subjective feelings arising from a complex network of neurological connections whose interactions aren’t fully understood.

Emotions are defined as human characteristics best expressed when subjected to extreme circumstances. They are not possible by definition to invent into machinery and especially not ChatGPT, as feelings are universally inherent in human nature and thus cannot be prompted by a mere chatbot.


Now as a final bonus for this blogpost consider the paragraph below which have been entirely generated by an AI talking about ChatGPT misconceptions. In my personal view, not an entirely bad addition to our humanly written content above, but what do you think? Will ChatGPT be the end to human life as we know it?


ChatGPT can entirely simulate a human-to-human conversation, replacing actual humans in the chat lounge. Despite its AI-backed capabilities, ChatGPT does not yet possess the capacity to completely replicate the nuances of a person-to-person conversation due to its programming.

References – link to proper ChatGPT chatbot


Earthquakes – Top ten misconceptions

In this blogpost we explore top ten common misconceptions about earthquakes.

Related read: Top 10 misconceptions about Tsunamis

1. Earthquakes cause violent ruptures of the earth

We all know the scenario from movies, the hero’s try and escape the rupture from the earth. The crack keeps running all the way up to the hero’s foot where it suddenly stops. This common misconception arises since when movies need to be more spectacular.

In fact, earthquakes tremble the earth for up to multiple minutes based on the severity of the earthquake. Earthquakes do not cause earth ruptures as illustrated by an AI below in meme 1.

Thus you shouldn’t be afraid that the earth will split underneath you during an earthquake.

2. It is better to run outside than staying inside during an earthquake

Often times people believe that running outside during an earthquake is safer than staying inside.

By going outside you risk being hit by falling debris, rubble and subduction zones while if you stay inside the building most likely will absorb the earthquake shaking.

It is therefore better to seek shelter inside sheltering yourself from above by hiding underneath tables, beds or sturdy furniture.

This way you are protected by the solidly built walls and ceilings of the building while simultaneously ensuring you are safe from falling books, chest of drawers, fridges, wardrobes and book shelf’s.

3. Earthquakes are predictable events

Unlike most other natural phenomena which we have extensively researched, the predictability of earthquakes still remain a resounding problem in science and engineering.

Top tier researchers still struggle with methodologies and theories to explain and provide early warning systems for earthquakes.

Typically sounding equipment is placed on locations around the globe, allowing the triangulation of epicenters to be calculated.

Related read: How do you calculate an earthquakes epicenter?

4. Earthquakes only happen during warm weather

In ancient greek, they believed that earthquakes were mystical events caused on warm sunny days where the earth opened up underneath their feet and closed again later on, see reference for more information.

Unlike the ancient Greeks, people today have a misconception that earthquakes happen during warm sunny weather.

Although this would be convenient allowing us to better estimate the eminent occurrence of an earthquake, sadly this isn’t the case.

Earthquakes are driven by deep earth dynamics governed by mass and heat transfers indifferent to top-earth weather phenomena.

Thus earthquakes can happen during sunny, rainy, snowy, foggy or stormy weather indifferent to other phenomena’s driving mechanisms.

Related read: Tsunamis the what, when and where

5. The initial shaking is defining a marked ending to the earthquake

A common misconception about earthquakes is that once the initial shaking stops the earthquake is over. This is however not the case. As aftershocks of earthquakes always accompanies the initial shaking and the higher on the Richter scale the earthquake is, the larger and long-lasting the aftershocks become.

Related read: Effective investment strategies for climate adaptations

This means that the danger after the initial shaking recedes unfortunately still resides. The dangerous aftershocks are critical to be vary off, since the initial shaking can loosen and damage buildings while the aftershocks cause weakened structures to collapse or loose debris to fall down on people below.

The Richter scale and aftershocks

The power of the aftershocks and the initial shaking follows a logarithmic scale naturally distributing with powers of 10 in magnitude. This scale, called the ‘Richter scale’ is widely used to describe the severity of experienced earthquakes, see Figure 1 as an example. This scale defines the magnitude of the initial shaking and also defines the aftershocks strengths.

In order to understand the distribution of aftershocks researchers have compared the temporal extent of the number of observed aftershocks with number of days since the main shaking event, see Figure 2. They have found that the distribution of aftershocks with number of shaking events follow an exponentially declining function with time since main shock.

An illustration of the Richter scale with examples of the logarithmic nature of the magnitudes of earthquakes. Examples of historic earthquakes are exemplified
Figure 1: Illustration of the Richter magnitude scale with the logarithmic scale with example earthquakes.
Aftershock duration based on observations and theoretical best fit on days after main earthquake shock
Figure 2: Illustration of the observed aftershocks of the Honshu, March 11´th 2011 Earthquake hitting Japan. The theoretical best fit is shown with a black line.

6. Earthquakes only happen in Japan and USA

Another common misconception about Earthquakes is that they only happen at specific locations around the earth such as Japan and USA.

One of the driving mechanisms behind earthquakes is plate tectonics. Plate tectonics is theoretical framework that is the movement of continents and countries located on drifting (large timescale) plates at different parts of the world.

Plate tectonic

By indexing the world in tectonic sections each within its own plate see Figure 3. It is possible to explain most of the historic movements of continents throughout earth eras and develop theories for the occurrences of earthquakes whose likelihood depends on the locations of fault-lines of the different types such as subduction, lateral sliding and spreading.

Illustration of the plate tectonics of the earth with naming and three different types of fault line zones illustrated.
Figure 3: Tectonic Plates world map vector diagram and tectonic movement illustrations showing subduction, lateral sliding and spreading process.

The Western Mediterranean – a new example

As a newer example lets take a closer look at the interesting fault-lines which are the located at the Western Mediterranean towards the Gibraltar strait. This area is interesting because of the differences within the topographic and bathymetric features clearly shown in Figure 4.

Figure 4 and 5 include locations and markings of fault-lines together with recorded magnitude earthquakes. Arrows show the measured movement of the tectonic plates given as a yearly movement in mm’s. Corresponding to roughly 4.5 mm’s per year for the North African continental crust.

Scientific explanation of the development of a possible new fault-line within the Wester Mediterranean sea. Location of earthquakes with magnitudes, zoomed in area of interest and fault-lines are marked along bathymetric features, topographic terrain and movement arrows.
Figure 4: Reproduced from Figure shows the magnitude earthquakes, strike-slip fault-lines, normal fault lines and the proposed development of a new tectonic plate located near the end of the western Mediterranean sea.
Zoom in of the Wester Mediterranean. fault-lines and figure markings with other zoomed in areas are shown.
Figure 5: Reproduced from Closeup of the investigated area encircled with a white rectangular box. The given fault-lines are shown accordingly.

7. Drills can negate earthquake damages

To battle the damages of earthquakes we incorporate drills that explain to children that they should run for cover and hide underneath tables. This way of providing false hope to children can be dangerous if not correctly addressed.

Knowing when to run outside and when to seek cover inside is important as a means of preventing human injury during an earthquake. The damaging forces from earthquakes are not influenced by people running away from them.

In order to mitigate the damaging effects of earthquakes it is therefore necessary to continuously invest sturdier building materials, equipment and tuned mass dampers for high-risers. Such that buildings resistance towards the damaging shaking of earthquakes are continuously improving.

Preemptive investments are key to ensure that future disastrous events are accounted for and mitigated as much as possible.

Related read: Effective climate adaptation strategies

The drills are an important supplement which allow people to react quickly in the event of an earthquake. This must be accompanied by smart investment decisions enhancing the existing building mass for everyone benefit.

8. Building codes == safe buildings

Strict building codes lead to safer buildings. This is a common misconception present across the globe.

In fact, the foundation for safe buildings is strict building codes mixed with the efficient quality assurance. High-quality building work with proper quality control, safe building environments and senior-staff controlling junior is key.

The senior staff must check work carried out by junior laborer, allowing for the detection of faults and errors early on in the building process. The early detection of errors is critical for ensuring high-quality work and consequently safe buildings according to the strict building codes.

9. The implications of earthquakes are local

The effects of earthquakes can cause other dangerous events such as Tsunamis. Implications of earthquakes and the resulting consequences of their generated Tsunamis are dangerous and possibly globally covered.

The Tsunamis can spread from epicenters across the globe causing massive damages all because of earthquakes are displacing large amounts of water.

The damages on energy infrastructure such as nuclear powerplants can potentially damage the environment of the entire globe. These powerplants are vulnerable to earthquakes happening in the vicinity. History tells us that nuclear waste as a result of earthquake disasters can spread across the globe and pose a real threat for the environment and the people living in it.

10. Earthquakes are all the same

A common misconception about earthquakes is that all of them are the same in the fact that they are developing similarly across the globe regardless of the fault line types.

This is incorrect since earthquakes are dynamic phenomena whose development depend on the different instances of the boundary conditions as well as the soils initial state before the shaking starts.

The marginal effects of earthquakes are essentially changing with the initial state of the soil, plate tectonics and recent geological activity. These effects are difficult if not impossible to accurate describe throughout the three-dimensional medium.

Geophysical surveys make it easier to try and estimate tectonic plate composition. The survey depths of intrusion are however sufficiently deep to fully explain the plate tectonic behavior.

Bonus: Earthquakes can change the length of a day

In fact earthquakes are not only powerful destructive events, they can actually (in theory) change the length of a day on earth.

By releasing an increasing amount of energy through the shaking events, it is possible for the most powerful earthquakes to change earths rotation and thus the length of a day.


Gómez de la Peña, L., R. Ranero, C., Gràcia, E. et al. Evidence for a developing plate boundary in the western Mediterranean. Nat Commun 13, 4786 (2022). Used under creative commons license 4: