#venndiagrams — Public Fediverse posts

Discussed Venn diagrams with a couple of friends this morning, especially in the context of illustrating the utility of including all 3 or 4 of a specific set of design principles when creating certain kinds of things, and learned about the difference between Venn diagrams and Euler diagrams.

In short:
* a Venn diagram shows ALL possible relationships between different sets
* an Euler diagram shows only some relationships between different sets, typically focused on conveying relevant or the more important relationships

If you want to dive into their history and why these differences matter, bookmark (or open new tab) this Scientific American article to rabbithole later:
* https://www.scientificamerican.com/article/venn-diagrams-history-and-popularity-outside-of-math-explained/

In pop culture and media, nearly any diagram of overlapping circles with labeled regions is (errantly) referred to as a “Venn diagram”.

This is imprecise at best, outright incorrect in many cases, especially diagrams of four circles.

A classic example is the “Ikigai” diagram:


Many (examples below) call this a Venn diagram. It is not a Venn diagram. It is an Euler diagram.

The Ikigai diagram fails to express two specific relationships between different sets, the two that contain opposing side circles but neither of the other two. The missing Ikigai sets relationships in particular:
1. only “you are good at” AND “the world needs” (with neither of the other two)
2. only “you love” AND “you can be paid for” (again with neither of the other two)

If you Google web search for "examples of four circle venn diagrams", Gemini gets this wrong:


And so do the majority of articles that Google shows in top results (which I’m not helping by linking here, but hey it’s Google’s job to fix its search quality, not mine. I was able to use Internet Archive links for two of them at least.)
* https://web.archive.org/web/20260823204717/https://boardmix.com/knowledge/4-circle-venn-diagrams/
* https://miro.com/templates/4-circle-venn-diagram/ (Miro’s own top template there is wrong, though others have contributed proper 4 set Venn diagrams)
* https://web.archive.org/web/20260823205434/https://www.istockphoto.com/illustrations/venn-4-circles-diagram
* https://www.educationworld.com/tools_templates/EW_venndiagram_4

This has interesting implications for expertise and trust.

Clearly by this one example search result, we cannot trust the expertise of "design tool" websites (boardmix, miro), nor stock photo websites.

Nor can we trust educationworld as a place to be educated.

Nor can we trust Google Search (or Google Gemini) to surface expertise above popular misconceptions.

Perhaps a good example of when to use Wikipedia search instead of Google (or other generic) web search.

Personally I generalize this example to “all proper nouns”, that is:

* Wikipedia search proper nouns instead Google or other general web searching.

You can make this more convenient by setting up “w” as a search shortcut for Wikipedia: https://tantek.com/2024/287/t2/setup-search-shortcuts-firefox

For reference / more reading on Venn diagrams and Euler diagrams:
* https://en.wikipedia.org/wiki/Venn_diagram
* https://en.wikipedia.org/wiki/Euler_diagram

#Venn #diagram #diagrams #VennDiagram #VennDiagrams #EulerDiagram #setTheory #relationships #Ikigai #fourCircles #fourCirclesVenn #fourCirclesVennDiagram #misconception #popMisconception #Google #GoogleSearch #GoogleWebSearch #webSearch #search #Gemini #GoogleGemini #GeminiWrong #expertise #trust #webTrust #Wikipedia
#Blaugust #Blaugust2026

And now: the Venn diagram you've been waiting for...
#musichumor #venndiagrams

The insane factions running the US government now

#us #usPol #usPolitics #doge #maga #trump #musk #vennDiagrams #fascistAmerica

What better way to represent the best animated movies of 2024 than in a handy-dandy Venn diagram? @polygon explains the sweet spot.

https://flip.it/p57VZs

#Movies #Animation #Entertainment #VennDiagrams

Santa Claus v Garmin, Venn diagram

#garmin #santaclaus #venndiagram #venndiagrams

Nobody:
My brain: let's make a Venn diagram of salad
#salad #VennDiagram #VennDiagrams

(If anyone has examples I can add to the intersections without any, feel free to chime in)

Given there's been a lot of love for Venn diagrams this morning.... if you've never seen Venn that Tune, you'd likely find it also raises a smile.

here's a sample - you can find more & the book here:

http://www.vennthattune.com/mainmenu.shtml

#music #venndiagrams

From Trump and Vance to falling asleep on public transport: #EdithPritchett’s week in #VennDiagrams – #cartoon | Life and style | The Guardian

https://www.theguardian.com/lifeandstyle/picture/2024/aug/12/from-trump-and-vance-to-falling-asleep-on-public-transport-edith-pritchetts-week-in-venn-diagrams-cartoon

If you know an engineer, are an engineer or even worse, are MARRIED to an engineer, you should watch this comedian. To quote Stefon, this comedian has EVERYTHING. #Powerpoint, #flowcharts, #statistics, #BadMath, #GeeksVsNerds, #VennDiagrams, #MarriageAdvice, you name it. (Sorry about the ads.) https://youtu.be/kwz-Md6OoyA

#Politicians trying to seem relatable and uncanny #robots: #EdithPritchett’s week in #VennDiagrams – #cartoon | Life and style | The Guardian

https://www.theguardian.com/lifeandstyle/picture/2024/feb/26/politicians-trying-to-seem-relatable-and-uncanny-robots-edith-pritchetts-week-in-venn-diagrams-cartoon

#Humour

The #HardRight of the #Toryarty meets StarAnise: #EdithPritchett’s week in #VennDiagrams – #cartoon | Life and style | The Guardian

https://www.theguardian.com/lifeandstyle/picture/2024/mar/04/the-hard-right-of-the-tory-party-meets-star-anise-edith-pritchetts-week-in-venn-diagrams-cartoon

#Humour

This is definitely up there with the best Venn diagrams I've seen.

#Excel #Venn #Funny #VennDiagrams #Humor #Humour

@errantscience #VennDiagrams #BarGraphs #PieCharts etc… ✅

But to restrict depiction of #MolecularStructure (including Bader et al.’s #MolecularGraph ⬇️) to two-dimensions would take #science back 150 years, when chemists were ridiculed for believing molecules had a three-dimensional structure!
#MolViz #SciComm #DataViz

https://pubs.aip.org/aip/jcp/article-abstract/70/9/4316/88468/Quantum-topology-of-molecular-charge-distributions?redirectedFrom=fulltext

Perhaps valid criticism is best suited for sentences with capitalization AND punctuation with emphasis placed in WRONG capitalization? /S

#BlameTheSoftKeyboardsMeme #meme #BlameStorming #SoftKeyboards #MavisBeacon #typing #Generations differences via simple #VennDiagrams of indifference A / B / U

An Educated #infosec #ecosystem is a vibrant #ecosystem full of wonder and enjoyment regardless of the day to day machinations of the #VennDiagrams for which you will be engulfed by in your travels through the vast and #limitless #imdb of #irl

#infosec_jcp 🐈🃏 done differently 📡🛰️📺📰🗞️🕵️‍♀️🕵️📊☣️😳😋😏🤜👽🤛

Ah, the old cat vs inkjet printer Venn diagram!

#CatMemes #CatsOfMastodon #humor #Catstodon #VennDiagrams

[source unknown]

#venndiagram #venndiagrams #vampires #vampire #transfems #transfem #transfeminine #transwomen #transwoman #transgirls #transgirl #trans #transgender #transsexual

#DifferentialPropositionalCalculus • 7.3
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

Figure 10. #VennDiagrams for #SingularPropositions on 3 Variables
• https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2-p-q-r-e280a2-singular-propositions.jpg

Rank 3. The cell \(pqr.\)

Rank 2. The 3 cells \(pr\texttt{(}q\texttt{)}, qr\texttt{(}p\texttt{)}, pq\texttt{(}r\texttt{)}.\)

Rank 1. The 3 cells \(q\texttt{(}p\texttt{)(}r\texttt{)}, p\texttt{(}q\texttt{)(}r\texttt{)}, r\texttt{(}p\texttt{)(}q\texttt{)}.\)

Rank 0. The cell \(\texttt{(}p\texttt{)(}q\texttt{)(}r\texttt{)}.\)

#Logic

#DifferentialPropositionalCalculus • 7.2
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

In a #UniverseOfDiscourse based on 3 #BooleanVariables \(p,q,r\) there are \(2^3=8\) #SingularPropositions. Their #VennDiagrams are shown in Figure 10.

\(\text{Figure 10. Singular Propositions} : \mathbb{B}^3 \to\mathbb{B}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2-p-q-r-e280a2-singular-propositions.jpg

Related Subjects —
#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#CactusSyntax #MinimalNegationOperators
#DiscreteDynamics #QualitativeDynamics

A nice short read on #VennDiagrams and #Logic about the strengths/weaknesses of simple conceptual tools when applied as practical tools: https://statmodeling.stat.columbia.edu/2022/11/26/when-a-conceptual-tool-is-used-as-a-practical-tool-venn-diagrams-edition/

#DifferentialPropositionalCalculus • 6.2
• https://inquiryintoinquiry.com/2020/03/02/differential-propositional-calculus-6/

Figure 9. #VennDiagrams for #PositivePropositions on 3 Variables
• https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2-p-q-r-e280a2-positive-propositions.jpg

Rank 3 (Top). The #BooleanProduct or #LogicalConjunction \(pqr.\)

Rank 2. The 3 #BooleanProducts \(pr, qr, pq.\)

Rank 1. The 3 #BasicPropositions \(q, p, r.\)

Rank 0 (Bottom). The #ConstantFunction \(1 : \mathbb{B}^3 \to \mathbb{B}\) or the #ConstantProposition expressed in #CactusSyntax by the form \(\texttt{((}~\texttt{))}.\)

#Logic

#DifferentialPropositionalCalculus • 6.1
• https://inquiryintoinquiry.com/2020/03/02/differential-propositional-calculus-6/

In a #UniverseOfDiscourse based on 3 #BooleanVariables \(p, q, r\) there are \(2^3 = 8\) #PositivePropositions. Their #VennDiagrams are shown in Figure 9.

\(\text{Figure 9. Positive Propositions} : \mathbb{B}^3 \to \mathbb{B}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2-p-q-r-e280a2-positive-propositions.jpg

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#CactusSyntax #MinimalNegationOperators
#DiscreteDynamics #QualitativeDynamics

#DifferentialPropositionalCalculus • 6
• https://inquiryintoinquiry.com/2020/03/02/differential-propositional-calculus-6/

The #PositivePropositions \(\{p:\mathbb{B}^n\to \mathbb{B}\}=(\mathbb{B}^n \xrightarrow{p}\mathbb{B})\) may be written as products:

\[\prod_{i=1}^n e_i~=~e_1 \cdot\ldots\cdot e_n~\text{where}~\left\{\begin{matrix}e_i=a_i\\ \text{or}\\e_i=1\end{matrix}\right\}~\text{for}~i=1~\text{to}~n.\]

To get a sense of this family's structure we'll next draw the #VennDiagrams for the 3 variable case.

#Logic #LogicalGraphs #DifferentialLogic

#DifferentialPropositionalCalculus • 5.5
• https://inquiryintoinquiry.com/2020/02/29/differential-propositional-calculus-5/

The third row of Figure 8 shows #VennDiagrams for the 3 #LinearPropositions of rank 1, which are none other than the 3 #BasicPropositions, \(p, q, r.\)

For example —

\(\text{Figure 8.3. Venn Diagram for}~p\)
• https://inquiryintoinquiry.files.wordpress.com/2020/02/venn-diagram-e280a2-p-q-r-e280a2-p.jpg

Related Subjects —
#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#CactusSyntax #MinimalNegationOperators
#DiscreteDynamics #QualitativeDynamics

#DifferentialPropositionalCalculus • 5.4
• https://inquiryintoinquiry.com/2020/02/29/differential-propositional-calculus-5/

The second row of Figure 8 shows #VennDiagrams for the 3 #LinearPropositions of rank 2, expressed in terms of #MinimalNegationOperators by the following 3 forms, respectively:

\[\texttt{(}p\texttt{,}r\texttt{)},\quad \texttt{(}q\texttt{,}r\texttt{)},\quad \texttt{(}p\texttt{,}q\texttt{)}.\]

For example —

\(\text{Figure 8.2. Venn Diagram for}~\texttt{(}p\texttt{,}q\texttt{)}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/02/venn-diagram-e280a2-p-q-r-e280a2-p-q.jpg

#Logic #LogicalGraphs

#DifferentialPropositionalCalculus • 5.2
• https://inquiryintoinquiry.com/2020/02/29/differential-propositional-calculus-5/

In a #UniverseOfDiscourse based on three #BooleanVariables \(p, q, r\) the #LinearPropositions take the shapes of the #VennDiagrams shown in Figure 8. Equivalent verbal & variant logical expressions are given in the next few posts.

\(\text{Figure 8. Linear Propositions} : \mathbb{B}^3 \to \mathbb{B}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/02/venn-diagrams-e280a2-p-q-r-e280a2-linear-propositions.jpg

Related Subjects —
#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions

#DifferentialPropositionalCalculus • 5
• https://inquiryintoinquiry.com/2020/02/29/differential-propositional-calculus-5/

Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general. We can do this by recruiting our visual imaginations and drawing up a sufficient budget of #VennDiagrams for each family of propositions. The case for 3 variables is exemplary enough for a start.

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions

#memes #venndiagrams

Something to think about…and think about…

#VennDiagrams #recursive

Logical Graphs, Truth Tables, Venn Diagrams • 1

Re: Peirce List • Mauro Bertani • Helmut Raulien

Dear Mauro, Helmut,

I’ll be focusing on logical graphs, especially the duality between entitative and existential interpretations, for quite a while longer, so this doesn’t address your questions about modal logic, but you might find it useful to compare the representations of logical operators by means of truth tables with those using logical graphs.

You could start with the top eight entries in the section headed “Logical Operators” on the following page.

• Logic Syllabus

There’s also a page bringing all eight of those Truth Tables together in one place.

• Truth Tables

I had been meaning to include the corresponding Logical Graphs and Venn Diagrams — I’ll spend some of my pandemic time working on that — It looks like it would be worth the candle reviewing their properties as representations of basic operations and going over their relative utilities for various logical purposes.

The following two pages also contain useful synopses of the boolean basics.

• Zeroth Order Logic
• Minimal Negation Operators

Resource

• Survey of Animated Logical Graphs

cc: Cybernetics • Ontolog Forum • Peirce List • Structural Modeling • Systems Science
cc: FB | Logical Graphs • Laws of Form

Can you solve it? The enduring appeal of #VennDiagrams | #Science | The Guardian

https://www.theguardian.com/science/2019/jul/29/can-you-solve-it-the-enduring-appeal-of-venn-diagrams

#Mathematics