Posts for Tag: interactive

Interested in Early Retirement or FIRE (Financial Independence to Retire Early)?

Here are some interactive and educational planning tools that I developed to help you understand the concepts of FIRE and calculate how long it will take to achieve retirement and how likely you are to survive retirement. Click on the tools below to try them out.

Financial Independence Calculators

Regardless of where you are on your path to FIRE, there are several types of tools that are useful:

These tools all focus on the concept of FIRE. FIRE is the concept that revolves around saving and investing to achieve Financial Independence (FI) and to potentially Retire Early (RE). One of the core concepts is that once you can save up enough money, you can retire by withdrawing a fraction of this money annually to cover your living expenses. Other important topics related to this core concept have to do with reducing spending so you can save money and investing so your money can grow and sustain your retirement over many decades.

Other visualizations and tools related to Financial Independence

These tools relate to taxes and stock market returns.

 
Data Sources and Tools:
See the individual tool to learn more about how it was made.
 

See which words follow and break the “i before e” rule

I wanted to see how often there were exceptions to the spelling rule “i before e, except after c”.  I found a website (wordfrequency.info) that had a list of the 5050 most common english words and decided to do some analysis on it to see which words followed this rule and which did not. Below is a treemap graph that shows the words that follow the rule in green and those that do not in red. The size of the box represents how common the word is in regular American English usage (based on the frequency that it shows up in the Corpus of Contemporary American English).

What we see is that while 81% of the 158 most common words with ‘e’ and ‘i’ adjacent to one another do follow the rule, when you take into account how frequently these words are used, the weighted percentage of words following the rule drops to around 60%.  This is because some very commonly used words do not follow this rule and if you were to count how many times you use words from this list, it’s likely that about 40% of the time you’ll be using words that don’t follow the rule. For example, the two most commonly used words with ‘e’ and ‘i’ adjacent (their and being) do not follow the rule, since then have the ‘e’ before the ‘i’ but aren’t after a ‘c’.

I was inspired to look into this after seeing a tweet about the rule in the comic Pearls before Swine by @stephanpastis.

Perhaps the most unhelpful spelling rule ever. pic.twitter.com/sW0aud6rA3

— Stephan Pastis (@stephanpastis) March 9, 2021

I asked my kids but they had never heard of the rule so perhaps this isn’t taught in schools anymore.
 

Sources and Tools:
I downloaded the word list from wordfrequency.info. The wordlist comes from the Corpus of Contemporary American English (COCA), a collection of English works across a wide variety of genres (spoken, fiction, popular magazines, newspapers, academic texts, and TV and Movies subtitles, blogs, and other web pages between 1990 and 2020). This word list was then analyzed using javascript to categorize the word as fitting or breaking the rule. The visualization uses the plotly.js open source graphing library and HTML/CSS/Javascript code for the interactivity and UI.

The code has been updated to allow for multiple chunks of icebergs now, which can occur via melting if you draw an iceberg a certain way.

Draw (or choose) an iceberg and visualize how it will float and melt

I was so impressed with the interactive Iceberger tool that Josh Tauberer (@JoshData) made that I had to modify it and add some additional features. Click here to see the original. My additions allow you to conjure up pre-made “icebergs” to see how they float and also allow some interaction. Try “poking” the icebergs you make.

Josh and I were both inspired by a tweet by Megan Thompson-Munson (@GlacialMeg).

Today I channeled my energy into this very unofficial but passionate petition for scientists to start drawing icebergs in their stable orientations. I went to the trouble of painting a stable iceberg with my watercolors, so plz hear me out.

(1/4) pic.twitter.com/rtkCYub38b

— Megan Thompson-Munson (@GlacialMeg) February 19, 2021

Instructions
You can choose between 3 different iceberg creation options:

• Draw Iceberg – the original Iceberger option. Choose this option and draw any shape you want and see how it floats.
• Select State – Choose this option and select from one of the states of the United States to see how it will float.
• Select Shape = Choose this option and select from one of the premade shapes to see how it will float.

Once the iceberg has been created, you can also affect it in a couple of different ways:

• Click on the Iceberg – This lets you push on the left side of the iceberg to induce some rotation and see if there are multiple stable orientations. Click it several times in a row if you want to flip the iceberg over. If you push on the right size it will rotate the iceberg clockwise and if you push on the left size, it will rotate counter clockwise. if you push in the middle third of the iceberg, it will push it straight down.
• Melting – You can select between different options – No melting, slow medium and fast. This took awhile to code correctly. Previously, I’d just scale parts of the iceberg but this new code actually takes material away from the surface of the iceberg in a uniform way. It works more like you would expect melting ice to behave.
• Changing the Sky – You can change the colors of the sky between sunrise, midday and sunset colors.
• Showing forces – You can toggle whether to show the center of buoyancy (B) and center of gravity (B) of the iceberg.

Some Physics – no equations
The force of gravity (G) affects the entire body regardless of where it is or how it is oriented. If you show the forces, the red dot labeled G shows where the center of mass of the iceberg is. The blue dot labeled B shows where the center of buoyancy is. This is the center of mass of the part of the iceberg that is submerged. The force acting on the submerged part is equal to the volume of water displaced. If the center of buoyancy is below the center of gravity, then the forces will be equal and object will be in stable equilibrium. If the center of buoyancy is somewhere other than under the center of gravity, then the buoyant force will be pushing up on a different place than the gravity force and this will induce a rotation until they are directly over one another.

The code has been updated so that multiple icebergs are now allowed. Melting can separate a single piece of iceberg into multiple pieces, just as in real life. The melting process was a bit difficult to program because of the complexity of shapes that could be produced.

If you have additional suggestions for shapes or countries to add to the list or other improvements to make, let me know in the comments. Also if you are using this as a teaching tool, I’d love to hear how you are incorporating it into your curriculum.

Sources and Tools:
This visualization uses HTML/CSS/Javascript code from the Iceberger app to simulate the buoyancy of icebergs. Melting was accomplished with the help of code from the turf.js, polygon-offset and simplify.js javascript libraries. Additional elements of the UI and other features are also made using HTML, CSS and javascript.

How do current California rainfall and precipitation totals compare with Historical Averages?

If you are lookin at this visualization, it’s likely winter in California and that means the rainy season (snowy in the mountains). I wanted to visualize how the current year compares with historical levels for this time of year. I used data for California rainfall totals from the California Department of Water Resources. Other California water-related visualizations include reservoir levels in the state as well.

There are three sets of stations that are tracked in the data and these plots:

• Northern Sierra 8-station index
• Tulare Basin 6-station index
• San Joaquin 5-station index

These stations are tracked because they provide important information about the state’s water supply (most of which originates from the Sierra Nevada Mountains). Data from the CDEC website appears to be updated at around 8:30am PST each day.

The visualization consists of two primary graphs both of which show the range of historical values for precipitation. The top graph is a histogram of water year precipitation totals on the specified date (in blue) as well as the precipitation total for the current water year in red.
The second graph shows the percentiles of precipitation over the course of the historical water year, spreading out like a cone from the start of the water year (October 1). You can see the current water year plotted on this to show how it compares to historical values. It also shows the present precipitation level and its percentile within the historical data for the day of the water year.

You can hover (or click) on the graph to audit the data a little more clearly.

Sources and Tools

Data is downloaded from the California Data Exchange Center website of the California Department of Water Resources using a python script. The data is processed in javascript and visualized here using HTML, CSS and javascript and the open source Plotly javascript graphing library.

We can compare the sizes of countries and continents to planets and moons by projecting a map of a specific country onto another planet. Select a country and planet or moon to find out.

In one of my kid’s favorite books, there’s a picture demonstrating how Pluto is the same size as Australia. It has a satellite image of the country and an image of the former ninth planet superimposed on top as if it were hovering above the country. That image has stuck with me and I thought it would be interesting to see how other countries would compare with other planets and bodies in our solar system. As I’ve been working with javascript graphing/mapping library, D3.js and making maps/globes, I realized I should try to “project” individual countries onto these planets to see what they looked like.

Instructions

This visualization should be pretty self explanatory. You can select a country or continent and a planet or moon (or the sun) in the solar system. The visualization will then project the land onto the body and you have a simple visual comparison of the size of the country/continent and the planet or moon. You can drag on the visualization to rotate the planet.

There are some combinations that are not possible because the country/continent is too large to be projected onto the body without overlap. In these cases, the planet or country will be greyed out in the selection menu. You can click the “Get URL” button and share a specific map combination (country and planet) by copying the address in the url address bar.

The visualization also displays the area of the country/continent and the surface area of the planet or body. In some cases, the percentage may not look correct but remember that you can only see half of the planet surface and that it’s actually a hemisphere (half a sphere and not just a circle). It becomes clearer if you draw the surface of the planet around.

Calculations

The calculations to project a country onto another body involves starting with a set of coordinates (made up of longitude and latitude values) which define the border of the country, in the geojson format. To display them on Earth, the coordinates are modified so that the center of the country is centered at the intersection between the equator and prime meridian [0 deg latitude, 0 deg longitude].

To display them projected on a different planet or moon, it is necessary to change the latitude and longitude values of each point of the polygon country border so that it represents the same distance away from the polygon center. I used the Haversine formula to calculate the distance and bearing between two points on a sphere and then used the inverse to find the coordinates that were that distance and bearing from the center point on a sphere of a different size. These formulas can be found here. The main idea is that the distance representing one degree of latitude on Earth will be half as large on a planet that is half the size of Earth (like Mars). Thus, the distance between the center of a country and a point on the border will be a different number of degrees latitude and longitude from the center point on a different planet than on Earth. And this calculatin is done using these formulae.

Sources and Tools:
This visualization was made using the open-source, d3 javascript dataviz library and UI are made using HTML, CSS and javascript.

What does it look like if you center a map on a specific country? Click on a country to find out.

World maps are used to show the geographic relationships between the countries and regions of the world. Their design shapes our perception of the world and those relationships. Two of the important aspects of map design are the choice of map projection and what is centered in the map. The idea for this map dataviz is to let users create their own country centered map by centering the map where you choose (on a country of your choice or a specific point) and the map projection.

As discussed in my real country size mercator map, there aren’t any perfect map projections as you try to represent the 3-dimensional surface of a sphere on a 2-dimensional map. Each map projection has advantages and disadvantages.

Instructions

• Click on a country or point on the ocean to center the map projection onto this area

You can choose between the following map projections:

• Orthographic (globe) – a map projection that looks like a globe
• Mercator – a very common cylindrical map projection used in many web maps which expands sizes of land near the top and bottom edges
• Mollweide – a pseudocylindrical projection that maintains equal area of land masses. Areas near the top and bottom edges can be distorted
• Equirectangular – another cylindrical projection but latitude lines are kept equidistant. Areas near top and bottom edges of map are wider than in reality.
• Gall Peters – an equal area cylindrical projection that stretches shapes vertically at the equator and shrinks shapes vertically at the poles.

In addition, you can:

• Rotate the map in increments of 45 degrees using the ⟲ and ⟳ buttons.
• Share maps of your home country, chosen map projection and rotation by clicking on the share button (and copying the URL).

The number of different maps you can create is quite large and will give you a different and often unusual perspective on the world. If you choose the cylindrical projections (Mercator, equirectangular, Gall Peters) you will see some interesting distortions when you focus on different countries or regions. The reasoning is that because the map is rectangular (i.e. the longitude lines are kept parallel on the map, while in reality longitude lines converge at the poles), land masses near the top and bottom of the map will grow as they are widened (and in the case of the Mercator, made taller) to accommodate the map projection. Because the Orthographic and Mollweide projections have converging longitude lines, they do not exhibit the same level of distortion.

If you are interested in map projections, they are described in this wikipedia article. For a cylindrical projections, you can think of it as encircling the globe with a rolled surface which forms the side of a cylinder. See this image from wikipedia.

In the standard projection, the globe is touching this cylinder at the equator, but this map lets you move any country or point to the place where it intersects the cylinder and then projects the land masses onto the cylinder. Land masses at the top and bottom of the sphere in this orientation will be more distorted at top and bottom of the map projections in these cylindrical projections.

Sources and Tools:
This map was made using the open-source, d3 javascript dataviz library and based on Mike Bostock’s observable maps notebook.