Trying too hard

Today, I return to the life expectancy graphic that Antonio submitted. In a previous post, I looked at the bumps chart. The centerpiece of that graphic is the following complicated bar chart.

Aburto_covid_lifeexpectancy

Let's start with the dual axes. On the left, age, and on the right, year of birth. I actually like this type of dual axes. The two axes present two versions of the same scale so the dual axes exist without distortion. It just allows the reader to pick which scale they want to use.

It baffles me that the range of each bar runs from 2.5 years to 7.5 years or 7.5 years to 2.5 years, with 5 or 10 years situated in the middle of each bar.

Reading the rest of the chart is like unentangling some balled up wires. The author has created a statistical model that attributes cause of death to male life expectancy in such a way that you can take the difference in life expectancy between two time points, and do a kind of waterfall analysis in which each cause of death either adds to or subtracts from the prior life expectancy, with the sum of these additions and substractions leading to the end-of-period life expectancy.

The model is complicated enough, and the chart doesn't make it any easier.

The bars are rooted at the zero value. The horizontal axis plots addition or substraction to life expectancy, thus zero represents no change during the period. Zero does not mean the cause of death (e.g. cancer) does not contribute to life expectancy; it just means the contribution remains the same.

The changes to life expectancy are shown in units of months. I'd prefer to see units of years because life expectancy is almost always given in years. Using years turn 2.5 months into 0.2 years which is a fraction, but it allows me to see the impact on the reported life expectancy without having to do a month-to-year conversion.

The chart highlights seven causes of death with seven different colors, plus gray for others.

What really does a number on readers is the shading, which adds another layer on top of the hues. Each color comes in one of two shading, referencing two periods of time. The unshaded bar segments concern changes between 2010 and "2019" while the shaded segments concern changes between "2019" and 2020. The two periods are chosen to highlight the impact of COVID-19 (the red-orange color), which did not exist before "2019".

Let's zoom in on one of the rows of data - the 72.5 to 77.5 age group.

Screen Shot 2022-09-14 at 1.06.59 PM

COVID-19 (red-orange) has a negative impact on life expectancy and that's the easy one to see. That's because COVID-19's contribution as a cause of death is exactly zero prior to "2019". Thus, the change in life expectancy is a change from zero. This is not how we can interpret any of the other colors.

Next, we look at cancer (blue). Since this bar segment sits on the right side of zero, cancer has contributed positively to change in life expectancy between 2010 and 2020. Practically, that means proportionally fewer people have died from cancer. Since the lengths of these bar segments correspond to the relative value, not absolute value, of life expectancy, longer bars do not necessarily indicate more numerous deaths.

Now the blue segment is actually divided into two parts, the shaded and not shaded. The not-shaded part is for the period "2019" to 2020 in the first year of the COVID-19 pandemic. The shaded part is for the period 2010 to "2019". It is a much wider span but it also contains 9 years of changes versus "1 year" so it's hard to tell if the single-year change is significantly different from the average single-year change of the past 9 years. (I'm using these quotes because I don't know whether they split the year 2019 in the middle since COVID-19 didn't show up till the end of that year.)

Next, we look at the yellow-brown color correponding to CVD. The key feature is that this block is split into two parts, one positive, one negative. Prior to "2019", CVD has been contributing positively to life expectancy changes while after "2019", it has contributed negatively. This observation raises some questions: why would CVD behave differently with the arrival of the pandemic? Are there data problems?

***

A small multiples design - splitting the period into two charts - may help here. To make those two charts comparable, I'd suggest annualizing the data so that the 9-year numbers represent the average annual values instead of the cumulative values.

 

 


Visualizing composite ratings

A twitter reader submitted the following chart from Autoevolution (link):

Google-maps-is-no-longer-the-top-app-for-navigation-and-offline-maps-179196_1

This is not a successful chart for the simple reason that readers want to look away from it. It's too busy. There is so much going on that one doesn't know where to look.

The underlying dataset is quite common in the marketing world. Through surveys, people are asked to rate some product along a number of dimensions (here, seven). Each dimension has a weight, and combined, the weighted sum becomes a composite ranking (shown here in gray).

Nothing in the chart stands out as particularly offensive even though the overall effect is repelling. Adding the overall rating on top of each column is not the best idea as it distorts the perception of the column heights. But with all these ingredients, the food comes out bland.

***

The key is editing. Find the stories you want to tell, and then deconstruct the chart to showcase them.

I start with a simple way to show the composite ranking, without any fuss:

Redo_junkcharts_autoevolution_top

[Since these are mockups, I have copied all of the data, just the top 11 items.]

Then, I want to know if individual products have particular strengths or weaknesses along specific dimensions. In a ranking like this, one should expect that some component ratings correlate highly with the overall rating while other components deviate from the overall average.

An example of correlated ratings is the Customers dimension.

Redo_junkcharts_autoevolution_customer

The general pattern of the red dots clings closely to that of the gray bars. The gray bars are the overall composite ratings (re-scaled to the rating range for the Customers dimension). This dimension does not tell us more than what we know from the composite rating.

By contrast, the Developers Ecosystem dimension provides additional information.

Redo_junkcharts_autoevolution_developer

Esri, AzureMaps and Mapbox performed much better on this dimension than on the average dimension. 

***

The following construction puts everything together in one package:

Redo_mapsplatformsratings.002


Displaying convoluted indices

I reviewed another batch of projects from Ray Vella's class at NYU. The following piece by Carlos Lasso made an impression on me. There are no pyrotechnics but he made one decision that added a lot of clarity to the graphic.

The Rich get Richer - Carlos Lasso

The underlying dataset gauges the income disparity of regions within nine countries. The richest and the poorest regions are selected for each country. Two time points are shown. Altogether, there are 9x2x2 = 36 numbers.

***

Let's take a deeper look at these numbers. Notice they are not in dollars, or any kind of currency, despite being about incomes. The numbers are index values, relative to 100. What does the reference level of 100 represent?

The value of 100 crosses every bar of the chart so that 100 has meaning in each country and each year. In fact, there are 18 definitions of 100 in this chart with 36 numbers, one for each country-year pair. The average national income is set to 100 for each country in each year. This is a highly convoluted indexing strategy.

The following chart is a re-visualization of the bottom part of Carlos' infographic.

Junkcharts_richricher2021_2columns

I shifted the scale of the horizontal axis. The value of zero does not hold special meaning in Carlos' chart. I subtracted 100 from the relative regional income indices, thus all regions with income above the average have positive values while those below the national average have negative values. (There are other challenges with the ratio scale, which I'll skip over in this post. The minimum value is -100 while the maximum value can be very large.)

The rescaling is not really the point of this post. To see what Carlos did, we have to look at the example shown in class. The graphic which the students were asked to improve has the following structure:

Junkcharts_richricher2021_1column

This one-column structure places four bars beside each country, grouped by year. Carlos pulled the year dimension out, and showed the same dataset in two columns.

This small change makes a great difference in ease of comprehension. Carlos' version unpacks the two key types of comparisons one might want to make: trend within a given country (horizontal comparison) and contrast between countries in a given year (vertical comparison).

***

I always try to avoid convoluted indexing. The cost of using such indices is the big how-to-read-this box.


The gift of small edits and subtraction

While making the chart on fertility rates (link), I came across a problem that pops up quite often, and is  ignored by most software programs.

Here is an earlier version of the chart I later discarded:

Junkcharts_redofertilitychart_2

Compare this to the version I published in the blog post:

Junkcharts_redofertilitychart_1

Aside from adding the chart title, there is one major change. I removed the empty plots from the grid. This is a visualization trick that should be called adding by subtracting. The empty scaffolding on the first chart increases our cognitive load without yielding any benefit. The whitespace brings out the message that only countries in Asia and Africa have fertility rates above 5.0. 

This is a small edit. But small edits accumulate and deliver a big impact. Bear this in mind the next time you make a chart.

 

P.S.

(1) You'd have to use a lower-level coding language to execute this small edit. Most software programs are quite rigid when it comes to making small-multiples (facet) charts.

(2) If there is a next iteration, I'd reverse the Asia and Oceania rows.

 


Election visual 3: a strange, mash-up visualization

Continuing our review of FiveThirtyEight's election forecasting model visualization (link), I now look at their headline data visualization. (The previous posts in this series are here, and here.)

538_topchartofmaps

It's a set of 22 maps, each showing one election scenario, with one candidate winning. What chart form is this?

Small multiples may come to mind. A small-multiples chart is a grid in which every component graphic has the same form - same chart type, same color scheme, same scale, etc. The only variation from graphic to graphic is the data. The data are typically varied along a dimension of interest, for example, age groups, geographic regions, years. The following small-multiples chart, which I praised in the past (link), shows liquor consumption across the world.

image from junkcharts.typepad.com

Each component graphic changes according to the data specific to a country. When we scan across the grid, we draw conclusions about country-to-country variations. As with convention, there are as many graphics as there are countries in the dataset. Sometimes, the designer includes only countries that are directly relevant to the chart's topic.

***

What is the variable FiveThirtyEight chose to vary from map to map? It's the scenario used in the election forecasting model.

This choice is unconventional. The 22 scenarios is a subset of the 40,000 scenarios from the simulation - we are left wondering how those 22 are chosen.

Returning to our question: what chart form is this?

Perhaps you're reminded of the dot plot from the previous post. On that dot plot, the designer summarized the results of 40,000 scenarios using 100 dots. Since Biden is the winner in 75 percent of all scenarios, the dot plot shows 75 blue dots (and 25 red).

The map is the new dot. The 75 blue dots become 16 blue maps (rounded down) while the 25 red dots become 6 red maps.

Is it a pictogram of maps? If we ignore the details on the maps, and focus on the counts of colors, then yes. It's just a bit challenging because of the hole in the middle, and the atypical number of maps.

As with the dot plot, the map details are a nice touch. It connects readers with the simulation model which can feel very abstract.

Oddly, if you're someone familiar with probabilities, this presentation is quite confusing.

With 40,000 scenarios reduced to 22 maps, each map should represent 1818 scenarios. On the dot plot, each dot should represent 400 scenarios. This follows the rule for creating pictograms. Each object in a pictogram - dot, map, figurine, etc. - should encode an equal amount of the data. For the 538 visualization, is it true that each of the six red maps represents 1818 scenarios? This may be the case but not likely.

Recall the dot plot where the most extreme red dot shows a scenario in which Trump wins 376 out of 538 electoral votes (margin = 214). Each dot should represent 400 scenarios. The visualization implies that there are 400 scenarios similar to the one on display. For the grid of maps, the following red map from the top left corner should, in theory, represent 1,818 similar scenarios. Could be, but I'm not sure.

538_electoralvotemap_topleft

Mathematically, each of the depicted scenario, including the blowout win above, occurs with 1/40,000 chance in the simulation. However, one expects few scenarios that look like the extreme scenario, and ample scenarios that look like the median scenario.  

So, the right way to read the 538 chart is to ignore the map details when reading the embedded pictogram, and then look at the small multiples of detailed maps bearing in mind that extreme scenarios are unique while median scenarios have many lookalikes.

(Come to think about it, the analogous situation in the liquor consumption chart is the relative population size of different countries. When comparing country to country, we tend to forget that the data apply to large numbers of people in populous countries, and small numbers in tiny countries.)

***

There's a small improvement that can be made to the detailed maps. As I compare one map to the next, I'm trying to pick out which states that have changed to change the vote margin. Conceptually, the number of states painted red should decrease as the winning margin decreases, and the states that shift colors should be the toss-up states.

So I'd draw the solid Republican (Democratic) states with a lighter shade, forming an easily identifiable bloc on all maps, while the toss-up states are shown with a heavier shade.

Redo_junkcharts_538electoralmap_shading

Here, I just added a darker shade to the states that disappear from the first red map to the second.


Unlocking the secrets of a marvellous data visualization

Scmp_coronavirushk_paperThe graphics team in my hometown paper SCMP has developed a formidable reputation in data visualization, and I lapped every drop of goodness on this beautiful graphic showing how the coronavirus spread around Hong Kong (in the first wave in April). Marcelo uploaded an image of the printed version to his Twitter. This graphic occupied the entire back page of that day's paper.

An online version of the chart is found here.

The data graphic is a masterclass in organizing data. While it looks complicated, I had no problem unpacking the different layers.

Cases were divided into imported cases (people returning to Hong Kong) and local cases. A small number of cases are considered in-betweens.

Scmp_coronavirushk_middle

The two major classes then occupy one half page each. I first looked at the top half, where my attention is drawn to the thickest flows. The majority of imported cases arrived from the U.K., and most of those were returning students. The U.S. is the next largest source of imported cases. The flows are carefully ordered by continent, with the Americas on the left, followed by Europe, Middle East, Africa, and Asia.

Junkcharts_scmpcoronavirushk_americas1

Where there are interesting back stories, the flow blossoms into a flower. An annotation explains the cluster of cases. Each anther represents a case. Eight people caught the virus while touring Bolivia together.

Junkcharts_scmpcoronavirushk_bolivia

One reads the local cases in the same way. Instead of flowers, think of roots. The biggest cluster by far was a band that played at clubs in three different parts of the city, infecting a total of 72 people.

Junkcharts_scmpcoronavirushk_localband

Everything is understood immediately, without a need to read text or refer to legends. The visual elements carry that kind of power.

***

This data graphic presents a perfect amalgam of art and science. For a flow chart, the data are encoded in the relative thickness of the lines. This leaves two unused dimensions of these lines: the curvature and lengths. The order of the countries and regions take up the horizontal axis, but the vertical axis is free. Unshackled from the data, the designer introduced curves into the lines, varied their lengths, and dispersed their endings around the white space in an artistic manner.

The flowers/roots present another opportunity for creativity. The only data constraint is the number of cases in a cluster. The positions of the dots, and the shape of the lines leading to the dots are part of the playground.

What's more, the data visualization is a powerful reminder of the benefits of testing and contact tracing. The band cluster led to the closure of bars, which helped slow the spread of the coronavirus. 

 


Deaths as percent neither of cases nor of population. Deaths as percent of normal.

Yesterday, I posted a note about excess deaths on the book blog (link). The post was inspired by a nice data visualization by the New York Times (link). This is a great example of data journalism.

Nyt_excessdeaths_south

Excess deaths is a superior metric for measuring the effect of Covid-19 on public health. It's better than deaths as percent of cases. Also better than percent of the population.What excess deaths measure is deaths as a percent of normal. Normal is usually defined as the average deaths in the respective week in years past.

The red areas indicate how far the deaths in the Southern states are above normal. The highest peak, registered in Texas in late July, is 60 percent above the normal level.

***

The best way to appreciate the effort that went into this graphic is to imagine receiving the outputs from the model that computes excess deaths. A three-column spreadsheet with columns "state", "week number" and "estimated excess deaths".

The first issue is unequal population sizes. More populous states of course have higher death tolls. Transforming death tolls to an index pegged to the normal level solves this problem. To produce this index, we divide actual deaths by the normal level of deaths. So the spreadsheet must be augmented by two additional columns, showing the historical average deaths and actual deaths for each state for each week. Then, the excess death index can be computed.

The journalist builds a story around the migration of the coronavirus between different regions as it rages across different states  during different weeks. To this end, the designer first divides the dataset into four regions (South, West, Midwest and Northeast). Within each region, the states must be ordered. For each state, the week of peak excess deaths is identified, and the peak index is used to sort the states.

The graphic utilizes a small-multiples framework. Time occupies the horizontal axis, by convention. The vertical axis is compressed so that the states are not too distant. For the same reason, the component graphs are allowed to overlap vertically. The benefit of the tight arrangement is clearer for the Northeast as those peaks are particularly tall. The space-saving appearance reminds me of sparklines, championed by Ed Tufte.

There is one small tricky problem. In most of June, Texas suffered at least 50 percent more deaths than normal. The severity of this excess death toll is shortchanged by the low vertical height of each component graph. What forced such congestion is probably the data from the Northeast. For example, New York City:

Nyt_excessdeaths_northeast3

 

New York City's death toll was almost 8 times the normal level at the start of the epidemic in the U.S. If the same vertical scale is maintained across the four regions, then the Northeastern states dwarf all else.

***

One key takeaway from the graphic for the Southern states is the persistence of the red areas. In each state, for almost every week of the entire pandemic period, actual deaths have exceeded the normal level. This is strong indication that the coronavirus is not under control.

In fact, I'd like to see a second set of plots showing the cumulative excess deaths since March. The weekly graphic is better for identifying the ebb and flow while the cumulative graphic takes measure of the total impact of Covid-19.

***

The above description leaves out a huge chunk of work related to computing excess deaths. I assumed the designer receives these estimates from a data scientist. See the related post in which I explain how excess deaths are estimated from statistical models.

 


Reviewing the charts in the Oxford Covid-19 study

On my sister (book) blog, I published a mega-post that examines the Oxford study that was cited two weeks ago as a counterpoint to the "doomsday" Imperial College model. These studies bring attention to the art of statistical modeling, and those six posts together are designed to give you a primer, and you don't need math to get a feel.

One aspect that didn't make it to the mega-post is the data visualization. Sad to say, the charts in the Oxford study (link) are uniformly terrible. Figure 3 is typical:

Oxford_covidmodel_fig3

There are numerous design decisions that frustrate readers.

a) The graphic contains two charts, one on top of the other. The left axis extends floor-to-ceiling, giving the false impression that it is relevant to both charts. In fact, the graphic uses dual axes. The bottom chart references the axis shown in the bottom right corner; the left axis is meaningless. The two charts should be drawn separately.

For those who have not read the mega-post about the Oxford models, let me give a brief description of what these charts are saying. The four colors refer to four different models - these models have the same structure but different settings. The top chart shows the proportion of the population that is still susceptible to infection by a certain date. In these models, no one can get re-infected, and so you see downward curves. The bottom chart displays the growth in deaths due to Covid-19. The first death in the UK was reported on March 5.  The black dots are the official fatalities.

b) The designer allocates two-thirds of the space to the top chart, which has a much simpler message. This causes the bottom chart to be compressed beyond cognition.

c) The top chart contains just five lines, smooth curves of the same shape but different slopes. The designer chose to use thick colored lines with black outlines. As a result, nothing precise can be read from the chart. When does the yellow line start dipping? When do the two orange lines start to separate?

d) The top chart should have included margins of error. These models are very imprecise due to the sparsity of data.

e) The bottom chart should be rejected by peer reviewers. We are supposed to judge how well each of the five models fits the cumulative death counts. But three design decisions conspire to prevent us from getting the answer: (i) the vertical axis is severely compressed by tucking this chart underneath the top chart (ii) the vertical axis uses a log scale which compresses large values and (iii) the larger-than-life dots.

As I demonstrated in this post also from the sister blog, many models especially those assuming an exponential growth rate has poor fits after the first few days. Charting in log scale hides the degree of error.

f) There is a third chart squeezed into the same canvass. Notice the four little overlapping hills located around Feb 1. These hills are probability distributions, which are presented without an appropriate vertical axis. Each hill represents a particular model's estimate of the date on which the novel coronavirus entered the UK. But that date is unknowable. So the model expresses this uncertainty using a probability distribution. The "peak" of the distribution is the most likely date. The spread of the hill gives the range of plausible dates, and the height at a given date indicates the chance that that is the date of introduction. The missing axis is a probability scale, which is neither the left nor the right axis.

***

The bottom chart shows up in a slightly different form as Figure 1(A).

Oxford_covidmodels_Fig1A

Here, the green, gray (blocked) and red thick lines correspond to the yellow/orange/red diamonds in Figure 3. The thin green and red lines show the margins of error I referred to above (these lines are not explicitly explained in the chart annotation.) The actual counts are shown as white rather than black diamonds.

Again, the thick lines and big diamonds conspire to swamp the gaps between model fit and actual data. Again, notice the use of a log scale. This means that the same amount of gap signifies much bigger errors as time moves to the right.

When using the log scale, we should label it using the original units. With a base 10 logarithm, the axis should have labels 1, 10, 100, 1000 instead of 0, 1, 2, 3. (This explains my previous point - why small gaps between a model line and a diamond can mean a big error as the counts go up.)

Also notice how the line of white diamonds makes it impossible to see what the models are doing prior to March 5, the date of the first reported death. The models apparently start showing fatalities prior to March 5. This is a key part of their conclusion - the Oxford team concluded that the coronavirus has been circulating in the U.K. even before the first infection was reported. The data visualization should therefore bring out the difference in timing.

I hope by the time the preprint is revised, the authors will have improved the data visualization.

 

 

 


Three estimates, two differences trip up an otherwise good design

Reader Fernando P. was baffled by this chart from the Perception Gap report by More in Common. (link to report)

Moreincommon_perceptiongap_republicans

Overall, this chart is quite good. Its flaws are subtle. There is so much going on, perhaps even the designer found it hard to keep level.

The title is "Democrat's Perception Gap" which actually means the gap between Democrats' perception of Republicans and Republican's self-reported views. We are talking about two estimates of Republican views. Conversely, in Figure 2 (not shown), the "Republican's Perception Gap" describes two estimates of Democrat views.

The gap is visually shown as the gray bar between the red dot and the blue dot. This is labeled perception gap, and its values are printed on the right column, also labeled perception gap.

Perhaps as an after-thought, the designer added the yellow stripes, which is a third estimate of Republican views, this time by Independents. This little addition wreaks havoc. There are now three estimates - and two gaps. There is a new gap, between Independents' perception of Republican views, and Republican's self-reported views. This I-gap is hidden in plain sight. The words "perception gap" obstinately sticks to the D-gap.

***

Here is a slightly modified version of the same chart.

Redo_perceptiongap_republicans

 

The design focuses attention on the two gaps (bars). It also identifies the Republican self-perception as the anchor point from which the gaps are computed.

I have chosen to describe the Republican dot as "self-perception" rather than "actual view," which connotes a form of "truth." Rather than considering the gap as an error of estimation, I like to think of the gap as the difference between two groups of people asked to estimate a common quantity.

Also, one should note that on the last two issues, there is virtual agreement.

***

Aside from the visual, I have doubts about the value of such a study. Only the most divisive issues are being addressed here. Adding a few bipartisan issues would provide controls that can be useful to tease out what is the baseline perception gap.

I wonder whether there is a self-selection in survey response, such that people with extreme views (from each party) will be under-represented. Further, do we believe that all survey respondents will provide truthful answers to sensitive questions that deal with racism, sexism, etc.? For example, if I am a moderate holding racist views, would I really admit to racism in a survey?

 

 


The Periodic Table, a challenge in information organization

Reader Chris P. points me to this article about the design of the Periodic Table. I then learned that 2019 is the “International Year of the Periodic Table,” according to the United Nations.

Here is the canonical design of the Periodic Table that science students are familiar with.

Wiki-Simple_Periodic_Table_Chart-en.svg

(Source: Wikipedia.)

The Periodic Table is an exercise of information organization and display. It's about adding structure to over 100 elements, so as to enhance comprehension and lookup. The canonical tabular design has columns and rows. The columns (Groups) impose a primary classification; the rows (Periods) provide a secondary classification. The elements also follow an aggregate order, which is traced by reading from top left to bottom right. The row structure makes clear the "periodicity" of the elements: the "period" of recurrence is not constant, tending to increase with the heavier elements at the bottom.

As with most complex datasets, these elements defy simple organization, due to a curse of dimensionality. The general goal is to put the similar elements closer together. Similarity can be defined in an infinite number of ways, such as chemical, physical or statistical properties. The canonical design, usually attributed to Russian chemist Mendeleev, attained its status because the community accepted his organizing principles, that is, his definitions of similarity (subsequently modified).

***

Of interest, there is a list of unsettled issues. According to Wikipedia, the most common arguments concern:

  • Hydrogen: typically shown as a member of Group 1 (first column), some argue that it doesn’t belong there since it is a gas not a metal. It is sometimes placed in Group 17 (halogens), where it forms a nice “triad” with fluorine and chlorine. Other designers just float hydrogen up top.
  • Helium: typically shown as a member of Group 18 (rightmost column), the  halogens noble gases, it may also be placed in Group 2.
  • Mercury: usually found in Group 12, some argue that it is not a metal like cadmium and zinc.
  • Group 3: other than the first two elements , there are various voices about how to place the other elements in Group 3. In particular, the pairs of lanthanum / actinium and lutetium / lawrencium are sometimes shown in the main table, sometimes shown in the ‘f-orbital’ sub-table usually placed below the main table.

***

Over the years, there have been numerous attempts to re-design the Periodic table. Some of these are featured in the article that Chris sent me (link).

I checked how these alternative designs deal with those unsettled issues. The short answer is they don't settle the issues.

Wide Table (Janet)

The key change is to remove the separation between the main table and the f-orbital (pink) section shown below, as a "footnote". This change clarifies the periodicity of the elements, especially the elongating periods as one moves down the table. This form is also called "long step".

Mg32190402_long_conventional

As a tradeoff, this table requires more space and has an awkward aspect ratio.

In this version of the wide table, the designer chooses to stack lutetium / lawrencium in Group 3 as part of the main table. Other versions place lanthanum / actinium in Group 3 as part of the main table. There are even versions that leave Group 3 with two elements.

Hydrogen, helium and mercury retain their conventional positions.

 

Spiral Design (Hyde)

There are many attempts at spiral designs. Here is one I found on this tumblr:

Hyde_periodictable

The spiral leverages the correspondence between periodic and circular. It is visually more pleasing than a tabular arrangement. But there is a tradeoff. Because of the increasing "diameter" from inner to outer rings, the inner elements are visually constrained compared to the outer ones.

In these spiral diagrams, the designer solves the aspect-ratio problem by creating local loops, sometimes called peninsulas. This is analogous to the footnote table solution, and visually distorts the longer periodicity of the heavier elements.

For Hyde's diagram, hydrogen is floated, helium is assigned to Group 2, and mercury stays in Group 12.

 

Racetrack

I also found this design on the same tumblr, but unattributed. It may have come from Life magazine.

Tumblr_n3tbz5rIKk1s3r80lo3_1280

It's a variant of the spiral. Instead of peninsulas, the designer squeezes the f-orbital section under Group 3, so this is analogous to the wide table solution.

The circular diagrams convey the sense of periodic return but the wide table displays the magnitudes more clearly.

This designer places hydrogen in group 18 forming a triad with fluorine and chlorine. Helium is in Group 17 and mercury in the usual Group 12 .

 

Cartogram (Sheehan)

This version is different.

Elements_relative_abundance

The designer chooses a statistical property (abundance) as the primary organizing principle. The key insight is that the lighter elements in the top few rows are generally more abundant - thus more important in a sense. The cartogram reveals a key weakness of the spiral diagrams that draw the reader's attention to the outer (heavier) elements.

Because of the distorted shapes, the cartogram form obscures much of the other data. In terms of the unsettled issues, hydrogen and helium are placed in Groups 1 and 2. Mercury is in Group 12. Group 3 is squeezed inside the main table rather than shown below.

 

Network

The centerpiece of the article Chris sent me is a network graph.

Periodic-bonds_1024

This is a complete redesign, de-emphasizing the periodicity. It's a result of radically changing the definition of similarity between elements. One barrier when introducing entirely new displays is the tendency of readers to expect the familiar.

***

I found the following articles useful when researching this post:

The Conversation

Royal Chemistry Society