The What

About the Lesson

Purpose

Introduce methods for handling jargon, definitions, metaphors and analogies, applications, examples, images, folk knowledge, citations, characters, locations in mathematical communication

Goals and Outcomes:

Participants will be able to assess the level of jargon in communication and determine if it is reasonable for its audience
Participants will be able to describe how to write a good technical definition
Participants will gain experience in using black boxes for technical terms
Participants will create a metaphor or analogy for an aspect of their work
Participants will practice creating in-depth examples related to their research
Participants will discuss the importance of images, folk knowledge, citations, characters, locations in mathematical communication
Participants will employ the employ the methods discussed to draft a new summary of their research

Tools Used

For sharing ideas and best practices we use Scrubmlr

Lesson Notes

What are we sharing technical information What are the potential roadblocks not having the background not understanding the language

The Big Questions
for all Communications

What is your Point?
What is your Goal?
What does success look like?
Who are your audience?
Always keep these in mind!

Jargon

What is it?
- Words that are specific to, or with specific meaning to, a group or profession
Jargon is Good
- Allows for faster communication
- Allows for very specific communication
- Creates an in-group where knowledge is shared
- What happens when there is no jargon?
  - Up-Goer Five
Jargon is Evil
- Jargon creates an out-group where people are gatekept from knowledge
- Jargon keeps people from understanding things
- Jargon can really take people out of a piece of communication
  - It is jarring to see a word you don’t know or a word that you thought meant something else
- Same word can mean many different things depending on field
  - Speaking of field, in this room how many different definitions can we come up with?
- What happens when it is all jargon?
  - All About the Brain
Jargon is Neutral
- Context and Audience Matter
- Have to hit the right level for your audience
  - ML Five Levels of Difficulty

De-jargonize Activity

Using De-jargonizer, The Up-Goer Five Text Editor, or Hemmingway App to:
- compare the levels of jargon from your two technical summaries
- remove all, or as much as possible, jargon from a sentence from one of them.

Definitions

Definition Definition
- The term
- the class to which it belongs
- the things that make it different from the other things in the class
  - (Purdue OWL)
Definitions are critical in all technical fields
But Mathematical Ideas only exist because of definitions!
- This is why undefined is so important in mathematics
Jargon is Cumulative
- Be careful your definition is not adding unnecessary jargon
- Match the depth of your definition and the terms it contains to your audience
When to Define
- Is the term important for your point or goal?
  - Define it!
  - Importance is transitive
    - Also define the terms you need in order to define your important terms
- Does the term mean something different from what almost everyone in the world thinks it means
  - Define it!
  - For example:
    - Real
    - Normal
    - Magic
    - Map
- Otherwise?
  - Skip past it
    - Your audience CAN look things up if they want to know more
    - Your audience doesn’t have to understand everything
      - Especially the math
  - Put it in a Black Box
    - Name the term and tell the audience that it is/does X without explaining exactly how or why it is/does X
      - The Black Box can use metaphors and analogies as the vehicle to get the more technical concepts across (more about this soon)
      - Example:
        
        Two shapes are topologically equivalent is they have the same number of holes. This is why topologists think coffee mugs and donuts are the same thing
Definition Level Examples
- 1
  - A curve 𝛼 that is parametrized by arclength is a geodesic if and only if for any two points and on 𝛼 that are sufficiently close, all other arcs joining P and Q are at least as long as .
  - A geodesic is the shortest path between two points.
- 2
  - Let and be two negatively curved Riemannian metrics on a compact surface . If then is isometric to
  - The collection of lengths of the shortest closed curve in each homotopy class is enough to determine the geometry of a negatively curved compact surface.
- 3
  - The collection of lengths of the shortest closed curve in each homotopy class is enough to determine the geometry of a negatively curved compact surface.
  - If we agree that we’re looking at the same shaped object, and you tell me how long it takes to walk around all the holes in it, I can tell you the exact dimensions of the object.

Definition Activity

Read through your technical summaries and identify the terms.
Determine if they are needed to make your point or achieve your goal.
Of the ones that are, choose one that is not defined in your summary, and write a definition of it
From the others, choose one and create a black box for it

Metaphors and analogies

Starting with Bacon, Locke, and Hobbes there has been the idea that technical communications should be plain and communicate with direct language devoid of ornamentation
Metaphors and analogies are essential to STEM, not just communications
- Solar System Analogy of the Atom
- A computer’s Desktop
- Particle-Wave Duality of Light
- Eddystone lighthouse
- Mathematics itself
  - Benjamin Pierce on a proof by Euler, “is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it must be true.”
- (Sides and Giles)
Examples
- For limits it’s really about the journey not the destination
- A proof by induction is setting up the dominos and then tipping the first one over and watching the rest fall down
- Asymptotes are like getting closer and closer to the edge of a cliff without falling off
- Fair Division is cutting a cake in a way that everyone is happy
- Imaginary numbers rotate vectors (ArchitectofAges)
- According to the Yoneda Lemma you are who your friends say you are (reddit (author deleted))
- When talking about Big O complexity 99 Bottles of Beer is and 12 days of Christmas is Frum

Metaphors and Analogy Activity

Choose one of your important terms and create a metaphor of analogy for it

Examples

The Running Example
- Set up an example in the beginning and keep building on it throughout
- Example:
  - Route Optimization
    - As the Crow Flies
    - No Stops
    - Defined Stops
    - Arbitrary Stops
One Example for Many Approaches
- Use multiple approaches to solve the same problem
- Example:
  - Traversing a Graph
    - Depth-First Search
    - Breadth-First Search
    - Dijkstra’s Algorithm
The Multi-Level Example
- Explore a single example at multiple levels of difficulty to reach different audience segments
- Example:
  - Billiards
    - Geometry
    - Trigonometry
    - Topology

Examples Activity

Outline how you could create a Running, Many Approaches, or Multi-Level example for your summary

Applications

Applications can help your audience:
- Understand abstract theory
- Develop an intuitive sense of your research
- Engage with the technical material
  - Especially if relevant to their lives

Images

Images are worth a 1000 Words (without Jargon make that 10,000)
If you have an image use it!
If you do not have an image make one!
If you do not know how to make one, ask a collaborator to make one.
If they say it is not possible to make the image you are asking for, ask them if they can make a simplified one.
If they still say no, that is ok. You did your best, and there is no more anyone can ask for.
Image Example - Area of a triangle on the sphere
- More Observations
1. The union of the three double wedges is the whole two-sphere
2. The intersection of the three double wedges is our triangle and its antipodal copy - this means that the sum of the areas of the double wedges trips counts each triangle. That is,
Let’s find the area of . Rotating so that vertex is at the northpole, we have a picture like the one on the left. The ratio of to should be the same as the ratio of to the total angle. That is, We know the area of the unit sphere! So we can then write the area as

This holds for any of the angles we shose, and so we know that and . Now, we can go back to the formula from earlier and plug these values in.
- Or you can use these pictures
  - The triangle on the bottom is the intersection of the three wedges above
  - Adding up the areas of all three wedges is the area of the sphere + counting the triangle 4 extra times

Using Numbers

Using numbers in media increase trust (Koetsenruijter)
But people are not always equipped to properly evaluate the numbers as presented (OECD)
A number in communications is an iceberg
- Most of the information it contains is hidden away under the surface
Example
- Take this medication and reduce your risk of heart attack by ⅓!
- Yay!
- Just a second, what is my risk of having a heart attack?
- 3%
- And what is the timeframe for this risk reduction?
- 5 years
- So, what you are saying is that in 5 years I will decrease my risk from 3% to 2%?
- Yes! Isn’t that incredible?
- Does this medication have side effects?
- Of course, all medications do. Nothing terrible just possible liver damage, joint pain, constipation, diabetes, nausea, diarrhea, headache, dizziness…
- So, what you are saying is that if 100 people take this drug for 5 years, with all those side effects, 1 fewer of us will have a heart attack?
- Exactly, isn’t that incredible?

Folk Knowledge

Information that is accepted and circulated by members of a community but is not published
Role as a Gatekeeper
- Case of Olivia Caramello Caramello
Does everyone really know?
Where did you learn it?
Who might now have had the chance?

Citations

This is the historical record for knowledge
When in doubt do it!
It especially helps audiences from other fields
Put yourself in their shoes
- Would you want credit?
- Would you want to know where information came from?

The Human Aspect

It is easier for audience’s to connect with your communication if they have someone to connect to
Characters provide that connection
- Yourself
- The person who developed the problem
- A person whose life has been impacted by the work

The Real World

The technical details may be abstract but your work took place here
Your audience may not understand where you did your work or what it looks like
- Not understanding is a relative of not believing
Share a picture, describe it, make it REAL for them

Summary Activity

Write a new summary of your work that includes at least one metaphor, example, character, and real world location, as well as black boxing or skipping terms which are not needed to make your point or achieve your goal

Acknowledgements

The definition and images examples were created by the wonderful Noelle Sawyer
Much of the best practices material was developed in collaboration with Sadie Witkoswki, Kenna Hughes-Castleberry, and Noelle Sawyer.

References

ArchitectofAges. (2011, March 18). _The best intuitive metaphors, analogies, etc. For mathematical concepts you’ve heard:_ [Reddit Post]. R/Math. Link to Resource

Caramello, O. (n.d.). _Unifying theory—Unification programme_. Retrieved July 11, 2024, from Link to Resource

Frum. (2011, March 18). _This one isn’t purel…_ Reddit Comment. R/Math. Link to Resource

Green, M. C., & Brock, T. C. (2000). The role of transportation in the persuasiveness of public narratives: Journal of Personality and Social Psychology. _Journal of Personality and Social Psychology_, _79_(5), 701–721. Link to Resource

Koetsenruijter, A. W. M. (2011). Using Numbers in News Increases Story Credibility. _Newspaper Research Journal_, _32_(2), 74–82. Link to Resource

OECD. (2019). Adults’ proficiency in key information-processing skills. In _Skills Matter: Additional Results from the Survey of Adult Skills_. OECD Publishing."Link to Resource

Purdue OWL. (n.d.). _Definitions—Purdue OWL®—Purdue University_. Retrieved March 27, 2024, from Link to Resource

reddit (author deleted). (2011, March 18). _The Yoneda Lemma: Yo…_ [Reddit Comment]. R/Math. Link to Resource

Sides, T., & Giles, C. (2016). _Motives for Metaphor in Scientific and Technical Communication: Large Type Edition_. Routledge. Link to Resource