Harvard students comment on "Uncertain Risks"

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

For non-quantitatively inclined readers, the discussion around risk and uncertainty can be made more illuminating by focusing on relatable scenarios and everyday decision-making contexts. Instead of delving deep into numerical calculations and statistical models, emphasizing the practical implications of uncertainty and how it affects personal decision-making could resonate more with such readers.

2. Suggest another framing of the issues discussed that would be more effective.

Another framing could involve using analogies or anecdotes that simplify complex concepts. For instance, likening uncertainty to navigating through foggy weather, where you can't see what's ahead clearly, but you still have to make decisions based on limited information. This analogy could help convey the essence of uncertainty without delving into technicalities. Additionally, using real-life examples, such as deciding whether to wear a seatbelt while driving or choosing between different healthcare options, could make the discussion more relatable and accessible to a broader audience.

I would assume the most challenging aspect of the article for students unfamiliar with quantitative prediction in general is likely the section discussing the detailed calculations of risk and uncertainty related to COVID-19. Here, the article introduces concepts like fractions, percentages, and the factors affecting these calculations, such as numerator, denominator, and uncertainty range. This involves mathematical reasoning and understanding statistical measures that can be quite complex for those not comfortable in quantitative methods. Understanding how these calculations relate to real-world risk assessment, particularly in a public health context, requires a grasp of both statistical concepts and their application to everyday decisions and policy-making.

I thought the discussion about applying the risk and uncertainty to COVID-19 would probably be illuminating to non-quantitatively inclined readers since it uses the framework on an issue that has affected everyone. This portion of the essay provided concrete examples such as calculating the risk of deaths and the uncertainty around the risk estimate, which would allow people to specifically grasp the interplay between risk and uncertainty in a situation that is easily explained/applies to many. The explanations of certain activities as being high risk/low risk also helped contextualize the concept in a way that deals with everyday tasks.

The part of the essay which could be most illuminating for non-quantitatively inclined readers is the discussion of COVID at the end. Because we all experienced COVID, especially the first few weeks when uncertainty about the lethality of the virus was at its highest, I feel like the distinction between uncertainty and risk is intuitive. When the virus began spreading globally we were only somewhat certain about the risk of death. Nobody knew the long term effects of the virus, the sample size of infected individuals was small, and the data was new and sometimes difficult to verify. Despite this, a ballpark estimate of the risk of death was still achievable. We knew that the death rate was not 100%, or even 10%. As the pandemic went on, uncertainty declined rapidly and people were able to take a slight sigh of relief as more information was available to the pubic. When you think about it, the risk of death from the original COVID-19 virus never changed over time, only our certainty of the figure.

The essay's discussion of deer hunting and Russian Roulette is likely the most illuminating component to non-quantitatively inclined readers given that it takes a relatively uncomplicated situation and explains the interplay between risk and uncertainty in either scenario. Each example serves to emphasize the importance of estimating odds in related situations, more common in daily life. Furthermore, the comments made by Dan Gilbert regarding humans' outlook on likelihood further contextualize the differences between risk and uncertainty as well as its manifestations in subsequent human action.

The parts of the essay that give actual, quantitative examples about each scenario would likely be the most helpful for non-quantitatively-inclined readers. Simply telling someone what the difference between risk and uncertainty is not very useful in a vacuum, but having one control "variable" (i.e., the level of risk) helps to illustrate it greatly. That is to say, showing how the moon landing has high risk because the astronaughts might die in any number of ways, and how a rare disease would have low risk if it doesn't kill often, but both have high uncertainty due to the large unknowns of a moon landing or the disease's erratic behavior, provides extremely helpful contrast for demonstrating the difference between the terms.

In the essay, the part that was most illuminating was explaining that uncertainty is inherent in risk assessment, and it's not just about whether something will happen or won't happen, but also about the degree of certainty regarding the outcome. In thinking about COVID-19, the uncertainty associated with the pandemic relates to some of the other notable events mentioned in the essay. Some of those examples used were Russian Roulette, lying on a couch, and the Apollo 11 mission, which helped illustrate the different levels of risk and uncertainty people encounter in their lives.

I expect the following parts of the discussion to be the most illuminating for non-quantitatively-inclined readers. First, the contrasting examples given of high risk/low uncertainty (Russian roulette), low risk/low uncertainty (lying on the couch), high risk/high uncertainty (Apollo 11), and low risk/high uncertainty ( a new disease that behaves erratically), illustrate how the concepts of risk and uncertainty work together clearly. I think another part of the discussion that provides further useful information to readers is how the COVID-19 mortality risk is put into perspective by comparing it to the overall annual death rate in the US, and to past pandemics. This helps readers understand the true risk level of the pandemic, and does not raise as much of an emotional reaction to the statistics of death tolls presented, although we should still be wary of them. Understanding how we have gotten used to a low-risk world and the way in which people misunderstand uncertainty is crucial to non-quantitively-inclined readers. 

The part of the discussion that was most illuminating for me (a non-quantitatively-inclined reader) was the clear way uncertainty and risk - and the differences between them - were explained. Using examples like the Apollo missions (high risk AND high uncertainty) and russian roulette (high risk, low uncertainty) really put things into perspective. Therefore, the high uncertainty nature of the COVID-19 projections became much more understandable in this framework.

Hello,

I found this reading to be thought-provoking. Many people in society will spew random statistics they saw or heard on the news without considering the factors that may influence this data. This is what non-quantitative thinkers will look at; due to this, they do not grasp the true complexity of the situation and what it takes to resolve such an event. For the Russian roulette analogy, many people may think, "Yes, there is a 17% chance of a round being fired, causing almost certain death," but those are not the true odds. I say this because the essay mentioned that revolvers misfire or malfunction, which can affect 1 in 6 chances of a live round going off. This is uncertainty because we are, in a sense, in the dark about the millions of factors that could have affected the weapon, person's hand movement, etc., which means without this information, we will never know the true odds of death in any given Russian roulette round. 

Best,

Joey Cano

For non-quantitatively-inclined readers, I would expect the introduction to be the most illuminating. The analogy to Russian Roulette and the deer hunting were helpful for setting up the conversation on risk and uncertainty. By bringing up this example throughout the post, the article provides a relatable way to understand these complex concepts. Using the Apollo 11 voyage as an example for high-risk and high-uncertainty was another helpful analogy made for non-quantitatively-inclined readers. Using COVID-19 was also another good example that grounded the reader in the concepts of data and uncertainty.

I think that the discussion on the uncertainty around the risk of COVID would be very helpful for non-quantitatively-inclined readers. When you are estimating something like risk, you have an average estimate of the risk and some degree of uncertainty around your estimate. This article’s discussion on COVID risk does a great job of illustrating how with few data points, we can still find an estimate of risk but we will have a larger uncertainty. This is because we did not know enough about the virus (early in the pandemic) to be certain if our best estimate of risk is close to the true value. As we see more cases of COVID, we can say with more certainty what the actual risk of the virus is since it is far less likely that we are just seeing a non-reflective sample of how dangerous COVID is. Knowing this concept is important in statistics since all estimates have some degree of uncertainty and understanding that uncertainty can help a lot in interpreting the statistical values we see in the world.

Readers who are not as familiar with quantitative concepts probably would find the section distinguishing "risk" and "uncertainty" especially helpful and insightful. This part of the discussion demonstrates how risks can be quantified, whereas uncertainties often cannot. Using accessible scenarios, such as playing Russian Roulette versus encountering unpredictable challenges in hunting, would help readers clarify the implications of each in real-world decision-making. Understanding this distinction can profoundly impact how individuals and organizations prepare for future challenges, emphasizing the importance of flexibility and resilience when handling unknowns.

The parts of the discussion that I expect would be the most illuminating for non-quantitatively inclined readers would be the introduction with analogies and the description of human perception of risk. The initial introduction, comparing the certainty of outcomes in hunting and Russian Roulette, can help non-quantitative readers grasp the fundamental differences between risk and uncertainty because analogies provide a relatable way to understand complex concepts. The section discussing how humans typically perceive risk, categorizing it into "it will happen," "it won't happen," and "it might happen," can resonate with non-quantitative readers because it calls awareness to something that they do without thinking.

I found this essay to be extremely accessible to those non-quantitatively-inclined, simply because hardly any numbers/math are mentioned -- when they are, they're (usually) representing a probability (essentially a well-know fraction with which most are familiar). On the difference between risk and uncertainty, the Deer Hunter "one shot" example versus the Russian Roulette game was a perfect example used to highlight such differences. The reason for this is that both examples fall on the opposite ends of an uncertainty spectrum, so their differences are easier to recognize. Its fairly straightforward to understand you risk an almost 1/6 chance of death from Russian roulette, and most people can understand how the uncertainty of this event is practically zero. This is simply because most people understand that if you shoot yourself in the head with a loaded gun, you'll most likely die. On the other hand, in the case of deer hunting and killing a deer with one shot, most people understand that there are higher levels of uncertainty associated with each risk. This is because there are more factors (weather, area, skill of hunter, rifle type, etc.) involved when it comes to hunting, rather than simply holding a gun to you head and pulling the trigger.

For non-quantitatively inclined readers, the discussion on how fear and uncertainty shape perceptions of risk, especially in the context of COVID-19, would be particularly enlightening. It delves into how the novelty and invisibility of the virus, coupled with initial data scarcity, led to heightened anxiety and exaggerated perceptions of risk. By highlighting the emotional reactions triggered by the pandemic and their impact on public responses and policy decisions, it provides valuable insights into the complexities of risk assessment. This segment underscores the importance of clear communication about known risks and uncertainties, as well as the need for transparency in decision-making processes, to navigate uncertain situations more effectively. Ultimately, it offers a pathway towards fostering resilience and informed decision-making in the face of uncertainty.

In order to better understand a high-risk high reward situation, you can change the framing to one of a roller coaster simulation. Imagine A new type­ of roller coaster gets introduce­d at an amusement park. It promises safe­ty and excitement. Be­ing the first of its kind, predicting safety is difficult. Ride­s can break down sometimes. Without past e­xamples of this specific ride, calculating risks prove­s challenging. This lack of information makes trying the ne­w ride uncertain regarding pote­ntial risk. Trying a new rollercoaster and being an early reviewer can be fun, but it may also come with alot of dangers

I believe that the distinction between risk and uncertainty will be the most illuminating for the quantitatively non-inclined; especially the example of a (essentially) 0 uncertainty game with known risk odds. Obviously, the example of Russian Roulette in The Deer Hunter is a grizzly way of conveying such truths, but given the statistical principles of the game are very transparent and easy to conceptualize, its use allows the reader to focus on the math behind risk as opposed to spending time understanding the specific mechanism of a hypothetical example.

As a non-quantitatively inclined reader, I found the example from The Deer Hunter to be the most illuminating. Although I had no prior knowledge of the movie, these simple and easy-to-understand examples helped me comprehend the difference between risk and uncertainty without a high understanding of statistics or data science. Simple examples like this make the essay more accessible to a broader audience that does not need to be an expert in the topic to understand the message the writer is trying to send.

1. I believe the parts that were most illuminating for non-quantitatively-inclined readers was the comparison between the low-risk low-uncertainty situations in contrast to the high-risk in general (both high uncertainty and low). But, for this example, let's keep it at high-risk low-uncertainty. People are generally good at making judgements on things that are obvious, so, when presented with the option of lying on a couch, versus participating in a round of Russian Roulette, then people would be highly inclined to take the couch option, even though they know the uncertainty of Russian Roulette. Even without knowing exactly the "odds" as the essay mentioned, non-quantitatively-inclined people will be good at measuring risk without the need to pay too much detail for uncertainty.

1. As a non-quantitatively inclined person myself, I think the use of the film The Deer Hunter was a good rhetorical device for breaking down the difference between uncertainty and risk and then walking through what different combinations of these concepts entail. For example, it made a lot of sense to me that the Russian Roulette game had a high amount of risk, but a low amount of uncertainty. The risk refers to the chance of dying while playing the game, while the uncertainty refers to the chance of the risk calculation being off. Because of how close of a shot the Russian Roulette game provides, it is unlikely that there will be much uncertainty. Continuing with this line of thinking, the hunting of a deer could be viewed as a high risk, high uncertainty situation. If we assume the hunter is pretty good and only takes shots that they have a good chance of hitting, as from my understanding most hunters do, then we say there is a high risk. But, similar to the Apollo example, there is high amount of uncertainty, over a longer distance with more variables, it becomes much more challenging to evaluate the exact risk.

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

I think that throughout the discussion, many clarifying points are made to make the piece more accessible to non-qualitatively-inclined readers, such as clarifying the fraction's numerator and denominator, or expliciting that 1-in-a-hundred is 1%. Also, the mathematical calculations that are written out are very useful and help the reader follow along and not feel lost.

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

I think the examples used for high-risk and high-uncertainty versus low-risk and low-uncertainty situations are helpful for illuminating the concepts herein for readers who are not quantitatively oriented. While numerical summations of risk and uncertainty may be opaque to these readers, I suspect they would have a strong reaction to their comfort level in playing Russian Roulette versus lying on the couch. I also think the example of Covid-19 is very effective for evoking these feelings as well — people can likely viscerally recall how they felt about the uncertainty of that situation, putting into context the importance of grasping uncertainty when dealing with potentially dangerous situations.

2. Suggest another framing of the issues discussed that would be more effective.

I wasn’t familiar with the Deer Hunter, honestly, and I think a large chunk of the potential audience for this paper likely is not as well. A fun example for risk that is familiar to younger audiences might be Avengers: Infinity War, in which Thanos’ famous snap wipes out half of all life. Here, as in Russian Roulette, there is extreme precision in both uncertainty and risk — you will without exception die should you be “selected” by the snap, and you have an exactly 50% chance of being selected. This might not be the perfect example, as technically you are not opting into this, but perhaps you could put the reader in the shoes of Thanos, who himself had that same level of risk and uncertainty when he chose to take the snap. Maybe this is a bit cheesy, but I do think it could be a fun and accessible way of explaining these concepts!

The essay on ‘uncertain risks’ provides qualitative and quantitative insight on risk vs uncertainty. Here, risk is defined as the fraction of number of people affected divided by the people that could have been affected. The part of the essay that would be most illuminating for non-quantitatively-inclined readers is the discussion about uncertainty in the case of russian roulette. Here, uncertainty is illustrated through a very logical way, as a percentage of times a gun would not work or a person would not die. This is a non-quantitative explanation of a usually quantitative-heavy subject of uncertainty.

Another framing that might be more effective in its own way is diving deeper into how figures for uncertainty are arrived at, how the uncertainty of 370k people is arrived at. Is it constructed based on previous similar pandemics or current, ongoing data?

I thought most of the article was geared well to non-quantitatively-geared readers. Throughout, it uses examples, never getting too theoretical without concrete, real-world examples. The movie reference was particularly helpful, although the article left me on a cliff hanger because I don't know whether or not the guy survived Russian Roulette or not (and I didn't click on the link because the movie sounds like it has some upsetting themes, so I didn't want to read the full plot). The one example that I think would be a bit hard to follow if you were not used to quantitative thinking was the Covid one. Since Covid is so recent, it makes it hard to look back on in the ways that I could with the other examples, and my mind got bogged down with so many connotations of Covid risk that it was hard to focus on learning the content. However, overall, I thought the article did a good job of providing information to a non-quantitatively-geared audience.

1. For non-quantitatively-inclined readers, the discussion of uncertainty in the real-world examples of Russian roulette and deer hunting might be most illuminating. Readers who have little or no background in statistics or data science will already be looking to connect the ideas in the article with something they are familiar with. If those familiar everyday examples are already available to break down the subject in simpler terms, then the whole learning process is expedited. 2. Similar to my discussion in the first question, I think another effective framing of the issues would be sharing the specific stories of individuals and their outcomes when dealing with this issue. These stories would provide more real-world examples for the readers as well as an inside look at the numbers to see how the outcome of one person contributes to the overall data. Every additional small part of the discussion that the readers can comprehend exponentially increases their understanding of the data and the uncertainty if they are non-quantitatively-inclined.

(1) The explanation of how humans typically categorize likelihood into three broad categories (it will happen, it won’t happen, and it might happen) might be particularly  illuminating for non-quantitatively-inclined readers. This section helps bridge the gap between everyday thinking and the more precise, numerical approach used in risk assessment. This leads into the second point, which is that (2) Instead of framing the discussion around the cold, hard statistics of risk and uncertainty, it might be more effective to frame it in terms of personal stories or case studies. For instance, discussing how different individuals perceive and react to the same statistical risk could provide insights into the emotional and psychological aspects of risk assessment. This approach could make the statistical information more relatable and less intimidating.

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

I think the most illuminating part for non-quantitatively inclined readers would be the parts that illustrate concepts with concrete examples. For example, the death problem was a good way to demonstrate the difference between risk and uncertainty. Risk is calculated by looking at the percentage of people that die, and uncertainty is how sure we are about that calculated percentage. I think this is a simple way of deconstructing a seemingly easy to understand, but commonly misunderstood concept. It is a good explanation for those who are less quantitatively inclined because even though there are no numerical examples, it is very direct. Additionally, it provides a clear contrast between the two terms which makes their definitions easier to grasp. I would imagine this is a good way to explain the two to even young children.

To answer Prompt 1—"Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?"—I would say that the example connection to Deer Hunter / Russian Roulette would be the most illuminating for non-quantitatively-inclined readers. Giving these real-life examples make the discussion super clear since most people are familiar with the nature of these games, and they also take the spectrum of risk/uncertainty to the absolute extremes. For example, in Russian Roulette, it's super easy to see how it is very high risk, since the prospective outcomes are either life or death, and the uncertainty is also clear to see since the nature of the game is based on the 1 in 6 outcome of a revolver chamber. Thus, these are great examples that underscore the difference between risk and uncertainty in that context.

2. Suggest another framing of the issues discussed that would be more effective.

Reframing the issues by focusing on practical strategies for individuals and policymakers to navigate risk and uncertainty can make issues that are difficult to tackle more effective. This would involve offering actionable advice, such as following public health guidelines and expert recommendations, to empower individuals to make informed decisions in their daily lives. Additionally, highlighting the importance of clear and transparent communication from public health authorities and policymakers can help convey risks and uncertainties effectively, fostering trust and cooperation among the public. Addressing psychological factors, such as cognitive biases and emotional responses to uncertainty, would be crucial, along with providing strategies for individuals to recognize and mitigate these biases.

Among the keywords that were discussed in this essay (uncertainty, risk, prediction, and decision), another word that I would add is consequence and/or outcome. The discussion of how uncertainty plays into outcome was not necessarily made explicit but was implicitly discussed in the context of Russian Roulette and how even though the outcome (death) is very dire, that doesn't affect our knowledge of the mechanism or our level of uncertainty. I also found the discussion of the quantification of risk to be very interesting. In the context of finance for example, the concept of risk-adjusted returns is incredibly important as it helps investors determine their optimal strategy. There are many different ways of quantifying risk in investments. While the volatility of an asset is often people's natural intuition for risk quantification, considering the amount of money you could potentially lose is probably a better measure. In the context of COVID-19, I think there are a few different ways of quantifying the level of uncertainty. Tracking people's decisions about whether or not they would attend non-essential activities such as a movie theater, shopping mall, or other places might reveal how people assess the severity of COVID-19 and how certain/uncertain they are about its effects.

Suggest another framing of the issues discussed that would be more effective.

A framing of the issue of risk, uncertainty and covid-19 that I think would be interesting, is to consider how a more quantitative (and less visceral) understanding of risk will affect an individual person's behavior, as well as policy decisions. The article states that risk of death from covid-19 is relatively low (about 100 times lower than that of the Spanish flu), and that people are mostly afraid of the uncertainty involved. However, it does not discuss how humans would choose to act if they focused purely on the numbers. A completely utilitarian approach towards disease and death does not necessarily seem to be the correct path either and I wonder if it is really beneficial for humans to be entirely rational. How we can best present ideas of risk in order to give humans an informed and balanced understanding of issues such covid?

1. For non-quantitatively-inclined readers, the most illuminating part of the discussion would be the representation of risk and uncertainty through the examples of deer hunting and Russian Roulette. Indeed, the concepts of risk and uncertainty are often intertwined and difficult to disentangle; however, these examples do an excellent job at showing how although they are not mutually-exclusive concepts, they are fundamentally different. The effectiveness of these examples is due to the reason that the readers are familiar and comfortable with these examples, and thus, through the lack of quantitative calculations to represent the concepts, the readers are able to understand them in a more efficient manner.

2. In order to frame these issues in a more effective manner, I would argue that using visual graphs would be extremely useful, especially for non-quantitatively-inclined readers. For example, by using simple bar graphs that compared the risk of Covid-19 to some other disease, such as the Spanish Flu, the public would be able to better understand the true risk of the virus. Furthermore, we could either add a confidence interval to the risk bar graph or create an entirely new bar graph to compare uncertainty among diseases. Undoubtedly, visual graphs allow the public to understand information more efficiently, and thus, I propose would be a proper alternative to explore.

For non-quantitatively-inclined readers, I believe the most illuminating discussion was the consideration of fractions, rather than a raw integer, as important in assessing risk. It might be scary to hear, for example, that 100,000 people died of X cause. However, if 1,000,000,000 people are engaging in such an activity, then the fear can be mitigated by the proportion. Adding uncertainty to that estimate, which grants an upper and lower bound to that risk, can also change how a person feels about it. One could be more risk averse, making them inclined to believe the upperbound, and another could be a risk taker, making them okay with the lower bound.

The section that was most illuminating for non-quantitatively inclined readers is about the discussion on COVID-19 risk and uncertainty. By framing the pandemic within the context of daily life and historical events like the Spanish flu, it showcases the significance of understanding risk in real-world terms. The comparison between COVID-19's projected death rates and those of past pandemics, along with the explanation of uncertainty surrounding these projections, offers a way to grasp the complexity of assessing risk. Through this lens, readers can appreciate the importance of interpreting risk and uncertainty beyond visceral reactions, empowering them to engage with information critically and make informed choices amidst uncertainty.

The section that I think was most illuminating for non-quantitatively inclined readers was the section which gave concrete examples to explain the uncertainty and risk distinction. That is, using Russian roulette and Apollo 11 as examples to explain this axis. Humans are really bad generally at assigning probabilities intuitively and as such assigning concrete examples makes it much more accessible.

In terms of framing, I always really like when communicating risk, similar statistics of equally understandable situations are used to convert fractions into intuitive metrics of risk. For example, the unit “microlives” - 1 “microlife” = 30 minutes of life expectancy. We can use this unit to communicate the outcomes of various behaviors. e.g Smoking two cigarettes reduces life expectancy by around 1 microlife. Exercising for 20 minutes extends life expectancy by 1 microlofe. This is a cool way of framing risk in a way easily digestible by non-quantitatevely inclined readers.

I really appreciated the deer hunt and Russian Roulette analogy to demonstrate uncertainty. I think it uses two situations that are very simple and very easy to understand. Everyone is familiar with the game Russian Roulette -- in fact, everyone is familiar with the certain risk associated with the game. Therefore, comparing this to a deer hunt where it is common to use multiple shots to take down a deer or to miss altogether is a good comparison. I think I would have appreciated a little more imagery on the deer example to hammer the point home, however.

As a non-quantitatively-inclined reader, I found the analogies comparing high/low-risk situations, like Russian Roulette and lying on a couch, to be the most illuminating part of the discussion. These examples effectively explained the concepts of risk and uncertainty without much math. The Russian Roulette analogy illustrates a low-uncertainty, high-risk situation, while the couch example represents a low-risk, low-uncertainty scenario. The essay also explains that humans typically group likelihood into three categories: "it will happen," "it won't happen," and "it might happen," with the word "might" capturing everything between "will" and "won't." This categorization helps non-quantitatively inclined understand how people often think about risk in everyday life, without attaching specific numerical odds. By using this kind of categorization and analogies, the essay was able to connect technical risk assessment and intuitive understanding. 

I found the framing examples in this article very useful for understanding and compartmentalizing the different kinds of risk and uncertainty. Considering the risk and uncertainty in Russian roulette compared to the risk and uncertainty in hunting makes these concepts more accessible for non-quantitatively-inclined readers and allows them to grapple with these complex topics in familiar contexts. By contrasting the risk and uncertainty in these two scenarios, the difference between them is made obvious. The only thing I think could potentially make this framework stronger is a visual like the one we looked at in section, with a scale from low to high risk and a scale from low to high uncertainty on the x & y axis. Positioning Russian roulette and hunting on this visual might further clarify these concepts and help to strengthen the explanation overall.

Suggest another framing of the issues discussed that would be more effective.

Another framing of the issues discussed could focus on storytelling and real-life scenarios to engage readers emotionally while conveying the significance of risk and uncertainty. Instead of diving straight into numerical examples, the piece could begin by narrating relatable scenarios where individuals are faced with decisions involving risk and uncertainty. These narratives could then transition into discussions about the importance of understanding risk in decision-making, drawing parallels to everyday experiences. By using storytelling as a framing device, the piece could capture the attention of readers who may not be naturally inclined towards quantitative analysis and provide them with a more accessible entry point into the topic.

Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers? The part of the essay investigating the uncertainty and fear surrounding COVID-19 risk assessment could be particularly effective for non-quantitatively inclined readers.  It breaks down the complex global issue into understandable terms while highlighting how a mathematical perspective on risk and uncertainty can provide clarity amidst fear and hysteria cultivated in the media. By encouraging readers to think critically about the media and official responses to the pandemic we can gain a more nuanced understanding of risk in the context of current events.

I guess I did a little bit of a combination of the assignment by touching upon both questions. For one, I think the most illuminating part of the discussion for non-quantitatively-inclined readers would likely be the discussion how humans perceive risk and uncertainty in various scenarios. The article touched upon examples like Russian roulette and the Apollo mission with regards to risk and uncertainty, which were extremely relatable and made the article a lot more personal. This leads into my answer for the second question, which is to potentially continue to expand on some cool ideas of the evaluation of risk and uncertainty. I think some small, funny examples that most humans interact with on a regular basis could also help a non-quantitatively-inclined learner to understand/think about the material. One quick example that I could think of is lottery tickets/gambling in general. Examples that are even more personable can help students learn about the core concepts of uncertainty and risk that we talked about extensively in class.

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

For non-quantitatively inclined readers, the discussion about the uncertainty surrounding the risk of COVID-19 could be most illuminating. Using examples like the Apollo 11 mission and the uncertainty around a new disease, the passage highlights how uncertainty can make risk assessment challenging, especially in situations where there is limited prior data and understanding of the mechanisms involved. The comparison of COVID-19 to the Apollo 11 mission helps to contextualize the concept of uncertainty. Just as the first lunar landing carried significant risk due to the lack of prior experience and understanding of space travel, COVID-19 presents uncertainty in terms of its transmission, effects, and overall risk to individuals and populations.

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

I believe the most illuminating part of the discussion for non-qualitatively-inclined people would be the introduction paragraph which compares Russian roulette to deer hunting. I think this analogy serves its purpose in showing the difference uncertainty plays in leading to the same outcome (death). I have never been a very quantitatively-driven person and find that the deer analogy is a very strong one in that it shows how much goes into uncertainty as opposed to something with so little uncertainty like Russian roulette. Roulette also provides the most easily understandable quantitative metric for uncertainty as it is a practice which is not influence by any external factors. Hunting for a deer offers such a high level of uncertainty that it cannot almost not be quantified, this is very realistic as the human brain often prefers to not quantify uncertainty and instead draw conclusions using its "fight or flight response".

Most illuminating for non-quantitatively-inclined readers:

The most illuminating part of the discussion for non-quantitatively-inclined readers is when Professors Goodman and De Vivo illustrate risk and uncertainty through observable examples. By translating statistical numbers into comparisons of real-life scenarios, readers can visualize the concepts in a tangible way. This approach helps demystify the quantitative analysis by using everyday language to describe what risk and uncertainty look like in practical terms, thus making the abstract more accessible. This method is especially effective when discussing complex topics like COVID-19, where understanding the nuances of risk can impact public perception and behavior.

Another framing of the issues discussed that would be more effective:

An alternative framing that might enhance the discussion's effectiveness is to broaden the focus beyond COVID-19 to include a variety of risk-related scenarios. By comparing and contrasting these scenarios, the article could explore how different levels of uncertainty affect decision-making across diverse situations. This approach would highlight the universal importance of understanding risk and uncertainty, not just in the context of pandemics but in everyday decisions as well. Additionally, incorporating insights into how the public perceives and reacts to statistical data could deepen the conversation about the interplay between information, emotion, and action in the face of uncertainty. This could provide a richer understanding of why people react differently to similar risks and how this shapes public policy and personal choices.

Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

I think the discussion on what uncertainty means was the most illuminating. The analogy and comparisons between lying on a couch and Russian Roulette helped make the "risks" of uncertainty very clear; we can be highly certain, but that doesn't tell us too much about the risk of the result. Thus, in order to better express predictions, it's critical that different scenarios are given when summarizing results. Although the best method would to directly display a distribution, this is obviously difficult because it probably carries too much data. Thus, including something like the 2.5%, median, and 97.5% result is probably succinct yet expressive enough.

Suggest another framing of the issues discussed that would be more effective.

A good reframing of these issues could focus on how the public interprets data and information given to them. This could be discussing the challenges in communicating uncertainty effectively, especially in a context where information is constantly evolving (like in the COVID case). By highlighting the uncertainty in presenting data, acknowledging uncertainties, and explaining the process of scientific inquiry, the public can gain a deeper understanding of information and make better informed decisions.

The essay by Professors Goodman and DeVivo was filled with enlightening analogies that are very useful for readers who are not quantitatively inclined. In particular, the analogy having to do with the Apollo 11 voyage and “extremely high-uncertainty experiences.” This was especially insightful because the pandemic itself was an experience that was full of high -uncertainty and possibly one of the most uncertain times most people had experienced. In this case it was important to distinguish the risk from the uncertainty — something that people were not necessarily doing during the times of the pandemic. The thorough description of uncertainty because of lack of information was important to parallel with the lack of data from COVID-19 outcomes. On the other hand, the high risk factor was an additional factor for Apollo 11 whereas it was not necessarily the issue for COVID-19. Goodman and DeVivo debunked this worry that the issue with COVID-19 was risk of death in comparison with other threatening illnesses like the Spanish flu. This discussion brings to light the fact that COVID-19 was not like Apollo 11 and that panic confused uncertainty with risk. 

The parts of the discussion that would be most illuminating for non-quantitatively-inclined readers may be the explanation of the "fraction of people having the experience being evaluated die." I liked that the author drew on familiar analogies and real-world situations, such as Russian Roulette and couch-lying to help us understand how risk is calculated. I.e. that the number of of deaths is in the numerator, and the number of people having the experience in the denominator. This made it accessible for those without a mathematical background to understand.

An effective reframing could focus on the idea of "navigating uncertainty". Rather than getting technical about risk assessment, the article could focus on the psychological and emotional impact of uncertainty. Perhaps the article could begin with a personal story that reflects a situation where risk and uncertainty is significant, grounding the discussion in a human experience to make it more relatable.

Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers? I believe the most illuminating part of the discussion is the distinction drawn between Russain Roulette and deer hunting to explain uncertainty. The two scenarios have a common outcome that we are trying to measure: likelihood of death. The distinction between the scenarios is the isolation in which they occur. I anticipate that looking at the Russian Roulette vs the deer hunting situation helps explain uncertainty very well because the Russian Roulette situation is so isolated. The outcome that we are interested in estimating has very little uncertainty, as there are very few things that can change the outcome based on the action that ends up happening. With deer hunting, one can fire their rifle at a deer and still not kill the animal. I believe this concept of isolating circumstances helps to explain the contrast between risk and uncertainty very well.

Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

I found that the Russian Roulette story and the laying on the couch example are the two parts of the discussion that would be most illuminating for non-quantitatively-inclined readers. The two examples display the difference between uncertainty and risk. The uncertainty of risk in Russian Roulette is very low or zero and similarly the uncertainty of risk when lying on the couch is also very low, but the actually risks of death when engaging in the activities are very different. Russian Roulette obviously has a high risk of death while laying on the couch has a low risk of death.

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers? I expect the discussion on how people often misunderstand the terms "risk' and "uncertainty" to be the most illuminating for non-quantitatively inclined readers. We use general terms like "safe" and "risky" daily, therefore adding specific numerical values to these words can be challenging and a new concept.

   
   

2. Suggest another framing of the issues discussed that would be more effective. Another framing could be linking these concepts to familiar, everyday scenarios. For instance, financial planning, health, or even routine choices like commuting. This could help brideg the gap between abstact statistical concepts and practical ones.

   
   

I think one aspect of this article that might be most enlightening to readers who are not quantitatively inclined is the connection between uncertainty and psychology. It helped me a lot when reading the article to understand that in some scenarios, humans are actually prone to error in estimation. Highlighting how humans interpret information and subsequently make predictions is just as important as looking at how machines or other rigid systems make predictions since in many cases it is human behavior that is modeled. Given this context the subsequent examples that involve more computation might be easier to understand for readers.

I found the metaphors discussed to be the most illuminating for non-quantitatively inclined readers. Highlighting the differences between Russian roulette, hunting, sitting on the couch, and the Apollo 11 voyage emphasizes the difference between risk and uncertainty. These examples make the concepts more tangible and easier to understand for readers who may not be familiar with technical or mathematical terms. By then applying these concepts to the COVID-19 pandemic by breaking down the risk of contracting COVID-19 and the associated uncertainty, it provides insights into why people may be afraid and how uncertainty can be quantified and understood. Another framing of the issues discussed might be a graphic with axes of uncertainty / certainty and risky / not risky. The examples discussed in the article could then be placed in a quadrant depending on the level of uncertainty and risk.

For non-quantitative readers, I believe the contrast between the risk of Russian Roulette and the safety of lying on a couch will be the most informative aspect of the conversation. With a one-in-six possibility of death, Russian Roulette poses a clear and imminent danger.  This contrasts strongly with the near-zero risk of injury associated with lying on a couch. The simplicity of these examples conveys the idea that some risks, such as playing Russian Roulette, are obvious and significant. In contrast, others, such as resting on a couch, are almost nonexistent. Understanding these extremes allows readers to appreciate risk assessment without specific numerical estimates.

I think the discussion about Russian Roulette and compared to laying down on a couch would be most illuminating for non-quantitatively-inclined readers because it was broken down in a way that was very simple to understand without prior knowledge of these terms, and the examples were common enough for the average person to imagine in their head. Another framing of the issues discussed that would be effective could potentially be the risk of drowning in the middle of the ocean if a person can't swim versus the risk of drowning in a 1ft tall pool with a swim vest and life guard nearby.

For non-quantitatively inclined readers, I believe that the discussion that focuses on the emotional aspects of risk and uncertainty would likely be most illuminating. An example is the exploration of why people fear certain risks more than others, even when the actual likelihood of occurrence may be low. By delving into the psychological and emotional factors that influence our perception of risk, people can better understand their own reactions and decision-making processes. Additionally, highlighting real-world examples, like the comparison between COVID-19, the Spanish flu, and Russian Roulette, can help people grasp the relative risks and uncertainties involved in different situations.

1. For non quantitatively inclined readers, I believe the portion with the Russian Roulette and couch analogy is quite intriguing because it displays two scenarios that are on two ends of the spectrum. The Russian Roulette describes a high risk situation, whereas the lazy couch scenario describes a low risk, and low uncertainty situation. It makes a clear distinction between two cases.

Suggest another framing of the issues discussed that would be more effective.

I think the issues talked about in this essay were presented in a fairly digestible way, such that it would be quite straightforward for people who aren't super well-versed in prediction and risk assessment to follow along with relative ease. I think that another way this essay could've been framed to make it more effective would've been to introduce each different topic in a narrative/more personal format. Personally, I find it easier to understand a lot of concepts when they're framed in a personal way that I could potentially find relatability in. Of course, a lot of the topics presented were relatable and every day -- lying on the couch and dealing with COVID-19, for example -- but I think adding another element of personality, for example describing each topic as if it were a story following one person or a group of people, or maybe the authors describing the topics through more personal lenses, could've made the discussion of these issues a little more effective.

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers? I feel that the Russian roulette and hunting examples in the introduction are incredibly effective at explaining risk for non-quantitatively-inclined readers, such as myself. I appreciated the visuals to make more abstract concepts involving risk and uncertainty more tangible. The hunting/life parallel was also particularly illuminating; in other words, life has a tendency of throwing curveballs when you least expect it, just as a hunter is likely to experience unpredictable conditions in action.

Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers? I think non-quantitatively inclined readers will benefit most from the attribution of the words “risk” and “uncertainty” to phrases such as “odds” and “how sure we are about those odds” respectively. Without ever calculating the risk or uncertainty of an event, a non-quantitative reader will be able to understand that an example of risk is just the fraction of people who died having contracted a disease and uncertainty is how certain we are about that fraction.

Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers? I think the comparison between Russian Roulette and deer hunting effectively highlights the differences between easily quantifiable risks and those that are more complex and uncertain. These examples, while dramatic, are very clear; some risks can be precisely measured, like shooting yourself in the head, while others involve many factors, like hunting. The abstract concepts of risk and uncertainty become more tangible.

Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers? I think that the discussion of risk and its relationship to extremely high uncertainty was quite interesting! I thought that the example of the Apollo voyage provided a really world-relevant (and thus interesting) example of risk in the case of high uncertainty experiences, and would help explain the concepts and relationship well. Specifically, I love the proof-like structure where the givens (factors that cause high risk of death) then lead into the conclusions. I also love how this seamlessly leads into the discussion of COVID-19 and connects the examples well! I think that a similar event to the Apollo example is the risk of dying in a self-driving car - the risk of death is high if the car makes a mistake (since car crashes are often fatal) and the uncertainty of whether it will is also high (since we haven't tested them very much).

I think that by far the most easily understood aspect of the essay when it comes to making complicated information digestible for people who are less quantitatively inclined was the uncertainty and risk examples of Russian Roulette and the Apollo 11 expedition. These two examples provide very real situations in which the risk can be understood in a simple way (as risk of death) and the uncertainty can be boiled down to basic principles of probability and likelihood. The framing of these issues allows the outcomes and odds to be summarized by an action or event rather than by a series of complex percentages linked in some complicated table to what someone might expect to happen and how.

It could never hurt a discussion like this that could be easily misinterpreted to have more examples, whether they be even more mundane or even more impactful-- either way, the more summarized information that creates a wider net of relatability the better for the understanding of the general public.

I think the best example from discussion to help explain uncertainty to people who are less quantitatively inclined was of Russian Roulette. Rather than diving into lots of complex math and probability associated with uncertainty, the Russian Roulette example exhibits low uncertainty in a very simplistic way. We can very confidently say the odds of dying from roulette with 6 bullets in the chamber is extremely close to 1/6. This is because there are not very many unknown factors that could influence the odds. I also think the couch example did a great job explaining the uncertainty of dying when simply lying on a couch. Both examples exhibit very low uncertainties in easy to understand ways but with drastically different probabilities of death.

I think discussing risk in the context of the Covid pandemic provides an interesting opportunity, given how much the perception of risk affected life during the pandemic. I believe that describing risk in terms of the question: "what percentage of people afflicted with this condition have died" is really enlightening. Upon hearing that a certain disease has a percentage rate of p, I think that humans / the general public are inclined to believe that their own chances of survival may essentially be equated to flipping a coin with probability p of heads. However, framing it in terms of the most general definition sets the stage for a more in-depth understanding of the reality of the disease and also allows for further understanding of more advanced topics, such as conditional probability.

Without fail, I believe, words can always translate to numbers; anything that is qualitative can easily be quantified. For example, the color spectrum can be converted to numbers; and feelings, too, can be translated into numbers. Thus, the most illuminating element of this essay that may resonate most with non-quantitatively-inclined readers would probably be Gilbert's claim that "humans typically group likelihood into three categories: it will happen; it won’t happen; and it might happen." In my opinion, words/sentiments/feelings are equally as impactful as numbers/statistics/probabilities. What may be more accessible to one person may be the opposite to another. Language and articulation is key when conveying the probability of events. Sometimes the more "statistical/numerical/accurate" numbers is not always the most effective way to convey data.

I think that contextualizing the uncertainty and the percentages with more observed historical factors is likely to be the most illuminating of this piece. Humans are generally terrible at quantifying probabilities, and have a deep instinct to overreact to uncertainty and the unknown. By contextualizing it with known data, we can make the message come across more usefully. 

It could also be useful to expand into discussing how fractions are often more easily conceivable to the general population than probabilities. I really like the quality of low uncertainty event examples that were given.

I thought the real-world scenarios that Dr. Goodman utilized to explain low-uncertainty experiences were excellent choices to appeal to a non-quantitative audience. The Russian Roulette example vividly demonstrates a situation in which there is a high risk of death and low uncertainty. A reader that is unfamiliar with statistics can still easily understand the certainty embedded within a system where the bullet will kill with only "one shot."

Conversely, the "lying on a couch" example showcases an everyday activity with an extremely low risk of death, but high certainty as well. This pair of scenarios demonstrates quantitative, statistical truths, in a way that translates the abstract concept of uncertainty into concrete examples.

I think the most illuminating part of the discussion would be the part which discusses how us humans are bad at estimating nuanced risks, and I think that plays into a lot of decisions we make, especially for those of us who are non-qualitatively inclined. This is why people allow their anxiety to take over, and not make rational decisions (it is safer to fly than drive a car, but people seem to think there is more uncertainty with flying, and less within their control, so they do not).

I think another way to frame it would be to state conclusively what we know (I.e. how many ppl have died, and how that will affect the future). I think the discussion here looked a bit more about what happened in the past and could we have predicted it, and the answer of its complicated is I think to some readers more confusing. I understand is designed to highlight the uncertainty, but I think some people could get bogged down in what they think they know even though as the article attempts to demonstrate, they do not. So I would approach of this is what we know, this is what our prediction would be, and this is our uncertainty and other factors.  

After rereading “Uncertain Risks” by Professor Goodman and Professor De Vivo, I expect their emphasis on understanding how many people were evaluated in a study to be most illuminating for non-quantitatively-inclined readers. Understanding the context for data is essential and can often be overlooked by the public. For example, it can be helpful to think about the fraction of how many people died to the number of people who could have died. As Professor Goodman and Professor De Vivo explain using COVID-19 as an example, the number of deaths by COVID-19 is striking—350,000 deaths in the U.S. in 2020. Nonetheless, when looked at as a 0.1% death rate (deaths/total population), the statistic is nowhere near as concerning to the public, especially with 1% of the population dying every year. Overall, I think Professor Goodman’s and Professor De Vivo’s article on uncertainty is extremely helpful in encouraging the average person to reframe how they look at statistics. When news sources are trying to grab your attention with a very high number, you should always ask “but what was the total number of people evaluated?” to gain more context. 

Another way that might be useful to frame the discussion would be the shape of the variance and how that matters in terms of real-life context. For example, if there were two strategies for fighting Covid-19, a high-variance one (where different samples of people were saved or died based on certain characteristics such as age) or a low-variance one (the death rate is exactly the same for every sample), they might have the same overall mean and expected number of deaths but the outcome would be very different depending on the strategies used. A high variance might be along the lines of taking a more lax response to Covid, meaning that more elderly people die of Covid. A low variance response might be along the lines of taking a strict response to Covid and saving more elderly but losing more young people to mental health consequences of being quarantined. Overall these strategies and variance in the overall discussion have an understated impact on how outcomes play out.

I found the discussion of the interaction between risk and uncertainty within the Russian roulette example to be the most simplistic and helpful. It clearly laid out to the reader how risk is the odds something happens while uncertainty acts as the first derivative of risk. Namely, it essentially sets the bounds for which our measure of risk is accurate. This framework for understanding how the two measures relate, applied to a very simplistic and understandable example, made the two concepts very digestible.

I enjoyed the real world example and graphic about where covid fits into the uncertainty and risk spectrum was helpful to visualize a lot of how our discussions fit into our current lives, especially how we all went through the pandemic. One of the other comments above mentioned the lack of stem classes at Harvard and I agree that this was a very helpful introduction to data science and prediction that I would not have otherwise had.

I think the inclusion of the Deer Hunter and Russian Roulette analogies throughout the article prove to be helpful to non-quantitatively inclined readers. As is addressed early in the article, misunderstanding or confusing the words "risk" and "uncertainty" can be dangerous, and doing so is a key reason why many misunderstand COVID-19. I think the first paragraph of the article does a great job of defining these words through the easily-understood analogies of hunting a deer and Russian Roulette. The article addresses all of the variable factors involved in determining the odds of killing a deer in a single shot which perfectly defines uncertainty, and the blunt 1 in 6 chance of dying in Russian Roulette which defines the other extreme, nearly complete certainty. These examples clearly differentiate risk, the chance of death, from uncertainty, how sure we are about the amount of risk, which I think is really helpful for non-quantitatively inclined readers.

1. Which part(s) of the discussion do you expect would be most illuminating for non-quantitatively-inclined readers?

I really like how the article suggests we put uncertain events into four "buckets" - high-risk high-uncertainty (Apollo 11), high-risk low-uncertainty (Russian roulette), low-risk high-uncertainty (getting COVID-19), and low-risk low-uncertainty (driving). While this approach applies "stereotypes" to uncertain events, it's often much easier for humans to think about things when using categories as compared to the raw numbers.

2. Suggest another framing of the issues discussed that would be more effective.

One method I love for evaluating risk of death is the micromort along with confidence intervals. In keeping with conventions for metric units, one micromort is a 1/1,000,000 (one in a million) chance of death. For example, skydiving comes with a risk of 8 micromorts per jump (8 in a million chance of death), while traveling 230 miles by car comes with a risk of 1 micromort. This unit lets us convert risk from a hard-to-understand fraction into a nice, low, round number, which is much easier to comprehend.

Additionally, micromorts let us use error bars that make sense on our numbers. For example, skydiving has a risk of 8.4 micromorts per jump, with a 95% confidence interval between 7.7 micromorts and 9.3 micromorts - a low-risk low-uncertainty activity. But going to space, by contrast, we now know has risk of 32,000 micromorts (not taking into account modern advances in spaceflight technology), with a 95% confidence interval between 21,000 and 49,000 micromorts - far less certain than skydiving.

As someone who wasn't entirely sure of the difference between risk and uncertainty, I found the example of the gun and Russian roulette extremely enlightening in differentiating the uncertainty of death -- which is almost 0 in the case of a bullet entering the brain -- and risk, which is the probability that the bullet will be in the chamber fired; in this case, 1/6. I also appreciated the examples of other easily visualizable isntances of different uncertainty/risk tradeoffs, such as the living room couch for low risk/low uncertainty and space exporation (Apollo 11) for high risk and high uncertainty. These examples really helped flush out the concepts before they were applied to the low risk, high uncertainty scenario of COVID-19

As someone who has never taken a rigorous stem course at Harvard nor considered themselves a quantitatively inclined reader, this essay was surprisingly helpful and clear for me when it came to understanding the difference between risk and uncertainty. Even though the risk/uncertainty matrix professor Goodman supplied was a qualitative representation of the issue, the quantitative aspects of things like covid modeling help us understand why mitigation is important in cases of high uncertainty particularly due to the human factors at play. I thought the article blended these two perspectives really well through the numerical examples provided in the covid examples in particular.

I think for non-qualitatively inclined readers, the covid risk discussion is the most useful. Particularly, when it says that the average deaths from the United States are only estimated to increase by 10%. I think that most people think that a relatively low number of people die each year, and so just one more person dying per 10 estimated deaths in a normal year would not concern them greatly. As such, I think they would be able to understand the chance of dying from Covid is not necessarily that great, and they can view the risk with more of a probability assessment rather than a "might happen" assessment.

2. Another way I might choose to frame this discussion has to do with another way to think about uncertainty. Rather than think about where the “real odds” may be, one can think of it in terms of how much you should be willing to adjust your odds. For instance, one can be very certain in a prediction that a coin flip will be heads exactly 50% of the time. Because we can have high certainty, it would take a lot of information to change your opinion. If someone told you “they knew” heads only came up 30% of the time you wouldn’t believe them; and if you flipped a coin 10 times and got 8 heads it wouldn’t really change your opinion on the probability. But let’s say you have a weighted coin, but you don’t have any idea how it is weighted. Now if you flipped the coin 10 times and got 8 heads, you would believe that the coin is probably a little weighted towards the head. Thus, one can have a real understanding of what uncertainty in prediction means through a more application-based explanation.

I found this essay very engaging and provided the reader with commentary and discussion that could be more easily digested than trying to interpret lots of statistics and quantitative evidence about this subject. Personally, I would consider myself a non-quantitatively-inclined reader and find that my best understanding of topics comes from broken down discussion and interpretation that is focused on the topic rather than trying to interpret all of the numbers that support that topic. In this essay, I appreciated the lens that deconstructed the complexities of these ideas; even in the first paragraph, there was a quote from a famous movie that one might know and then some explanation that was connected to common known activities like hunting and Russian roulette. From that point, I already had a better grasp of the knowledge trying to be conveyed than if I had tried to read a daunting quantitatively focused essay. The fact that the Deer Hunter Russian Roulette story returned to the conversation to describe the differences in uncertainty and risk which was also very illuminating and grounded my understanding. The reader is then able to connect the examples at the beginning of the essay to how it all relates to COVID-19 and epidemiology, which was a great way to help the reader to best understand the basics of risk and uncertainty and then more easily apply it to their uptake of this knowledge surrounding the current pandemic.

I think using the example of the One Deer Hunter Russian roulette story throughout the explanation and then weaving different components of the topic to be understood using the same example is something that non-quantitatively inclined readers would find to be most helpful. Especially since it allows them to apply this knowledge to a real-world working scenario and view the different definitions of the risk and uncertainty can be more easily applied. The example is used in the first paragraph to compare more complex odds with many factors playing a role such as deer hunting to the easily calculate odds when playing Russian Roulette. By then using these same scenarios to explain low uncertainty and high experiences we are able to better understand the details behind them.

I believe the main takeaway of the essay for non-quantitatively-inclined readers should be the discussion of why consider uncertainty in the first place. Humans are not perfect and when we attempt to theorize, experiment, or evaluate observable phenomena there is no way our results will hold 100% of the time. However, having a notion of 'error-spread' or uncertainty is crucial to make this idea transparent and thus make better science and even everyday decisions.

The section that I expect would be most illuminating for non-quantitatively inclined readers would be the part two situations with different uncertainties. In this section it looks first at a low-uncertainty situation (Russian Roulette) then at a high uncertainty situation (Apollo 11). I think it is very important to apply these easily comprehensible examples towards two drastically levels of uncertainty because it makes it a much easier access point. Jumping straight into numbers with little context can lead to people just giving up and tuning out the rest of the information. However, using these tangible situations and very little, simple math it is much easier to get a foot in the door of this information. Once that ground layer of understanding people can feel calmer and more confident that they will be able to comprehend the rest of the information. Also, having two different examples with different levels and factors of uncertainty allows the coinciding information about COVID-19 much easier to comprehend.

I believe that the thoroughness and the many examples given when exploring what risk and uncertainty mean at a fundamental level are extremely helpful for non-quantitively-inclined readers. One of the main objectives of the essay is exactly giving a quantitative look at a problem many people view only qualitatively (will happen, may happen, won't happen). Considering there is no escape from the quantitative analysis, I believe the way the essay handles it is excellent, by explaining at a basic level what is risk and uncertainty, using several examples along the way, in a way that almost all readers paying attention and that understand the basics of fractions and percentages will be able to understand. I also believe that the connection back to the pandemic will be specially illuminating for readers who hadn't considered uncertainty in risk from a quantitative POV before, as it equips them to better think about the numbers and predictions that are being shown to them in the media, and reflect on what they really mean, and what would be a reasonable response.

Unequivocally, the passage in this essay on COVID statistics was eye-opening to read for someone "non-quantitatively-inclined" such as me. While the language of low-uncertainty and high-uncertainty experiences was highly interesting and illuminating, I can't imagine organically changing behaviour based on these discoveries. When the statistics are set out in such a way that they are in the essay though; in plain language, and particularly in comparative context; to the average annual death rate, to the death rate of the Spanish flu, etc., I feel like I'm being introduced to a coherent narrative, based in fact, which will tangibly impact my thoughts, opinions, and thus behaviours.

The content, then, I think is excellent! It sounds silly, but perhaps a good way to impart it other than in essay format would be through a TikTok. While a short, tiktok format videos starts off mostly being watched by the younger demographic that likes the app, I see the videos being shared now frequently on other platforms, such as Twitter and Facebook, which have a larger reach for broader swathes of the population!

I surely agree, @vincentli -- these are the draft images we ultimately didn't include, but clearly should!

I appreciated the real-world examples of the combinations of risk and uncertainty (whether high or low for each). They concretely demonstrated the difference between risk and uncertainty in a way accessible for all readers. Perhaps including a graphic with the example scenarios (e.g. 2x2 table of risk on horizontal axis and uncertainty on vertical axis, similar to a Prisoner’s Dilemma table) would be a quick way to reference the difference between risk and uncertainty. Overall, I thought the essay addressed an important topic, since risk and uncertainty are often used interchangeably in everyday conversation but have different meanings.

So for example, if we see the coronavirus is infecting people in the United States, the known known is that it affects older people more and people with certain preexisting conditions. We also might have some sparse data and some rudimentary understanding of the mechanisms that lead to the spread of the virus and the way it leads to hospitalizations and deaths. From this, we might calculate a risk (or the odds) of death and hospitalizations. However, this risk may have a large uncertainty because we know that we do not know a whole number of things like does it spread through inanimate objects or how capable is the government in withstanding public anger when initiating lockdowns or how many people will actually wear masks. This might give us an initial range of uncertainty but then we also have the unknown unknown items such as we have no idea if another natural disaster occurs or if another country invades another country or how and when will the virus mutate. These are all unknown unknowns that further exacerbate the uncertainty. If there is good reason to worry that tail-risks can have dramatic impact on the outcome of the pandemic on # of deaths, then we might model with fat tails to represent the unknown unknown and we might keep a large range to model the high uncertainty reflected in the known unknowns.

Similar to Daniel, I think the most illuminating part of this article for non-quantitatively-inclined readers is the discussion comparing low-uncertainty experiences and high-uncertainty experiences in our lives. This comparison of events that we can relate to, allows us as readers to imagine our decision-making in these situations. Thus, we are able to evaluate the way we actions we make in our lives, and the way in which uncertainty affects them.

Similarly to what Will has written, I think that the part of the article most illuminating for non-quantitatively inclined readers would be a very number-heavy paragraph. In the paragraph that begins with "What fraction of people....", Prof Goodman and Prof De Vivo clearly spell out the calculations for what the fraction of people having the experience being evaluated die from COVID-19 is. Because this solution is prefaced with step-by-step arithmetic, this part of the discussion will be most illuminating for non-quantitatively-inclined readers such as myself.

I think the most illuminating part of the discussion for non-quantitatively-inclined readers is the part discussing the difference between low-uncertainty experiences and extremely high-uncertainty experiences. This part illustrates a good idea of what uncertainty is without using numerical data. Furthermore, the comparison between hunting and russian roulette prior gives a good explanation of the difference between risk and uncertainty.

The part of the discussion that I think would be most illuminating to non-quantitative readers is this idea of understanding risk and uncertainty and how that relates to the news. As we know, the new channels are fighting for attention and in order to increase eyeballs they usually use misleading titles or data because the crazier it looks, the more likely they are to lure someone in. I think regardless of how quantitative someone is, they can always think about the uncertainty of these news article predictions and understand that no matter what there’s always a chance that these numbers are misleading. I think this could help people take a step back and stop immediatly forming life decisions or actions based on a quick glimpse of a news title or graph.

After reading Profs. Goodman and de Vivo's article titled "Uncertain Risks," I believe that paragraph six (beginning with "The fraction scientists seek") is the most effective section of the piece at developing understanding of risk and uncertainty for non-quantitatively inclined readers. Primarily, it conveys very clearly the different methods of quantitatively communicating risk and uncertainty. Although it may be obvious to some, parsing out the quantitative synonyms—like "1-in-a-hundred" and "1%"—and commonly misunderstand concepts—like "5% uncertainty"—is incredibly valuable.

As a non-quantitatively inclined reader myself, there are a couple of aspects of this impactful article that most clearly break down the reality of risk and uncertainty as it relates to the coronavirus pandemic. First, the distinction between the four high/low-risk and high/low-uncertainty categories earlier on in the article is helpful. Even if the reader is fuzzier on the exact numbers, they can easily conceptualize the relative risk and uncertainty of the common sense examples for each category. Following this discussion with the implication that the pandemic lies closer to space missions on the uncertainty spectrum, but closer to lying on the couch on the risk spectrum, makes the argument easy to follow. An additional strength is framing data as "prior observations." Like the previous example, this part of the discussion relates the quantitative to something non-quantitative that is perhaps recognizable to a wider audience. Finally, the explanation of uncertainty as "how well we know the odds" is a concise but effective way to drive home a key point from this class, that just because there is uncertainty does not mean that scientists don't know what is going on.

The most illuminating part of this article is the part where readers can actually relate to. The discussion on the Covid-19 pandemic. These are prime examples of uncertainty we've been living in for years now, whether that be the actual transmission of the disease, the effectiveness of masks, timeline for vaccine distribution, variants etc. There is so much uncertainty involved here which the readers can relate to. Uncertainty about the upcoming academic year widespread. Will it be hybrid? Part in person? All in person? Who knows

After reflecting on “Uncertain Risks” by Profs. Goodman and De Vivo, I found the paragraph that compares the COVID-19 pandemic to the Spanish flu most illuminating as a non-quantitatively-inclined reader. Readers who are not quantitative-focused may be more willing to listen to articles and reports that compare COVID-19 to the Spanish flu. However, the authors explain in this paragraph that there is a 100x lower chance of dying from COVID-19 than dying from the Spanish flu. It is easier to visualize how much lower the risk with COVID-19 is when explicitly compared to the Spanish flu. The quantitative points in this paragraph also clearly show why the two events are not necessarily comparable without focusing on specifics that would confuse someone who is not quantitatively inclined. This paragraph is also illuminating because many media articles compared COVID-19 to the Spanish flu when in reality this comparison is not as strong as initially presented.

I think that the three paragraphs starting with "Looking at current projections for March 1, 2021--likely just before widespread vaccine distribution--" and ending with "and people misunderstand uncertainty" are the most illuminating paragraphs for non-quantitatively inclined people. This passage breaks down raw pandemic data and contextualizes it using jargon-free language and historical examples that most lay readers could understand. One of the biggest sources of misleading information were sensational news articles that provided raw statistics and "what-if" scenarios without contextualizing the data in terms of certainty, historical examples, or warranted level of concern. This article demonstrates that one can explain risk and uncertainty to lay readers in a digestible format that fully acknowledges the danger of the pandemic without causing undue anxiety about possible but exceedingly unlikely scenarios.

As a non-quantitatively inclined reader, I found the paragraph that contains the most numbers, in which you discuss the current uncertainty in the risk of dying from COVID-19, most interesting and helpful. In this paragraph, you describe different projections for COVID-19 related deaths and what that means for the uncertainty in the risk. Ultimately, this kind of reasoning relies on very simple, straightforward math that I find easy to follow. I haven't come across a clear description of what uncertainty means in terms of risk of dying from COVID-19, even with all of the articles I've read since the pandemic started. I think news outlets might shy away from this type of mathematical reasoning about risk because it could scare off readers. This essay shows that the math involved in calculating uncertainty in risk can be quite simple to explain and understand.

I think the most interesting aspect of our discussion would be the general differences between risk and uncertainty, as discussed in the essay. As someone who isn't quantitatively inclined (despite the valiant efforts of this course), the essay did an excellent job in highlighting the distinction between these two concepts in a way that can be followed by those who struggle with mathematics. I think what will also be interesting is discussing how these concepts relate to decision making. If you have a low risk but high uncertainty situation, your choice of actions can go in a divvy of directions. While prediction to decision seems to be the most straightforward way of seeing things, I think risk and uncertainty play into our decision making in a way that is more stressful than predictions.