How to Make Good Presentations

Transcript

00:00

Hey everyone, my name is Sydney Katz. I'm currently a posttock here at Stanford and I'm going to be talking today about how to make good presentations.

00:15

In the process of putting this presentation together, I looked up what some of the most common phobias in our society are. And on this list of common phobias is one that's particularly relevant to the topic today.

And that is one called glossophobia which is the

00:33

fear of public speaking. And the reason that I bring this up is because I actually want to introduce an extension to this phobia which I call metaglossophobia which is the fear of public speaking about public speaking.

So this might be

00:50

a very niche phobia but think about like how terrifying that is. I'm about to try to make a presentation about making good presentations.

So, you can imagine that, you know, that presentation seems like it must have to be like the best presentation of them all. And so, um,

01:06

I'm experiencing a little bit of metal glossophobia right now. But despite that, I'm going to try to give you a presentation on how to make good presentations.

So, I hope you'll stick around in this video, at least for the entertainment of me trying to do that. Uh, but I also hope that it will give you some tips and tricks for how to make

01:24

your presentations more effective in the future. Um, I also just want to acknowledge that I know there's a lot of resources already out there on this topic and many of them are very good and I'll actually link to some of them later.

But I do want to say that I think what I'm about to show you here is a very unique perspective on the things

01:40

that you should keep in mind when you're creating presentations and will hopefully make you more effective at making them in the future and give you some new ideas. So with that, I want to motivate you a little bit about why it's even important to make good presentations in the first

01:55

place. And to do that, I'll go through my presentation journey.

So my presentation journey started out probably similar to many of you where you know in middle school I was like introduced to Microsoft PowerPoint and I was like oh there's all sorts of like fun themes and different things I can

02:12

try out and like there's pretty dots and I can try to make things look pretty like this. But then at some point kind of towards the end of high school towards the beginning of undergrad my idea of what a presentation should look like shifted a little bit and that was when I started doing some internships at

02:27

engineering companies. So I got really great experience.

I got to work with really cool engineers. Uh but there was one problem which was that pretty much all the slides that they were presenting to each other looked something like this.

So they were kind of black text on a white background, tons of bullet

02:42

points, huge wall of bullet points. Um very very difficult to parse.

U maybe sometimes they'd have like the company logo at the bottom. Of course this is not like an actual slide from an engineering company.

I had chat GBT generate me their best impression of it, but this is generally what it would look

02:58

like. And you know, I was young.

I was super impressionable. I was like, these are super cool engineers.

I want to be like these super cool engineers. And so then all of my slides after that started looking something like this.

Uh so these are actually two slides from a presentation that I gave with a design

03:14

team that I worked with in undergrad called Wu, which stands for water out of thin air. Uh, and it's not super relevant here what exactly we were doing, but essentially we were competing in these various competitions in order to try to win funds to continue developing our product.

Um, and so these

03:30

slides are actually from the semi-finals of a competition that we were trying to uh participate in in order to win $25,000 for further development of our product. And again, these were our slides for the semi-finals.

And unfortunately, we actually came in dead

03:46

last. So that was kind of a bummer.

Uh but we did get lucky in that they allowed everyone who participated in the semi-finals to move on to the finals. And in between the semi-finals and the finals, there was actually not very much time at all.

So we didn't have any new

04:02

time to like make a new prototype, to talk to new people, to come up with any new ideas. Uh literally all we did in the time between the semi-finals and the finals was make our presentation better.

So our new slides looked something like this. um where they were much more

04:18

compelling. They told a much better story.

And it turns out that just making this change was actually enough to bring us from dead last uh all the way to first place and we won the competition and got the money for further development. And so I think this is actually like the exact moment where

04:33

things sort of like clicked in my mind and I kind of said, "Okay, wait. We don't have to make these really boring presentations with like bullet points on a white background.

And really, if we can actually spend the extra effort to make a presentation that tells a compelling story, we can actually allow

04:49

our ideas to go a lot further. And so, I hope that this convinces you that like, you know, you can have the best idea in the world, but if you can't communicate it properly, it's not going to go as far as if you could.

And so, you know, you might spend a ton of time developing your research idea or your new product

05:05

design or a new engineering idea. Uh, but it's not going to go as far as if you could just put in this little extra time to ensure that you can communicate it properly.

So, that's been really important to me ever since then. And along the way, I've picked up lots of tips and tricks in doing this.

Uh, and I

05:21

will say I've really never regretted putting that extra time in to make a good presentation. It's always been worth it.

So hopefully that convinces you that we need to make good presentations. And now I'll spend the rest of this presentation trying to give you some advice for how

05:37

to do that. And I want to start by talking about what the optimal presentation might look like.

So in my research and in my lab, uh we're often very interested in optimization and we tend to try to formulate things as optimization problems. So I'm going to talk about what the optimal presentation

05:53

looks like by formulating it as an optimization problem. So, we're going to be maximizing here.

And first, I want to talk about what objective we want to maximize. And over the years, I've been watching lots and lots of presentations throughout my PhD, for example.

And I've

06:09

been doing a little bit of inverse reinforcement learning. I've been trying to infer the objective that people are optimizing for when they give presentations.

And I've actually seen quite a few of them. Um, one of the ones I've seen often is looking smart.

That's not the right objective. Another one

06:26

that I often see is getting it over with. Also not the right objective.

Um, we've probably all seen a presentation like this. Proving you know math, definitely not the right objective.

Um, explaining every detail of your paper, also not the right objective. And really

06:42

the objective that we want to aim for here is just communicating your ideas to an audience. So I know sometimes you might be giving a presentation to like persuade people or win money or get a job, for example.

Um, but really you can't do any of those things if you don't effectively communicate your ideas

06:59

to the audience. So this is really what you should have in mind and the objective that you should be optimizing for when you create presentations.

There are some constraints that go with it. Um, the first one which people tend to ignore way too often is a lot of time.

Uh, this is one that you really

07:16

shouldn't ignore. So you shouldn't, you know, try to take a 20 minute presentation and and shove it into 15 minutes.

You should really custom design every single presentation you make for the amount of time that you're given because it never looks good if you're like rushing towards the end. If you have to skip your last section of your

07:31

presentation because you didn't get through it, uh people are not going to learn your ideas that way. So, it's really worth paying attention to this one.

The second constraint is the audience level of prior knowledge. So, this is one that you've probably heard before.

um you know of course you would give a different presentation to a set

07:46

of high schoolers than you would to for example a group of professors that's intimately familiar with your field of research. Um so that's just something that you should keep in mind when you give your presentation.

And then the final one is just audiovisisual constraints. So you should know like what type of computer you're

08:02

going to be running your slides on. Um is it able to run PowerPoint?

Is it able to run Keynote? Um will you have control over your slides?

These are all important things to take into account when creating your presentation. But that's literally it.

So there's no constraint here that says that you need

08:19

to have a white slide with a title and bullet points on every single slide. There's nothing that even says that you need to have slides at all.

You should really do whatever you think is going to maximally communicate your ideas to the audience subject to those few constraints that I put there. For

08:34

example, you can even have like funny animations like fireworks. uh when I taught some lectures uh a few months ago at Stanford, the students really enjoyed like fireworks uh animations and things like that to kind of keep people engaged.

Um and so every time I show you a tip in this presentation, it's

08:51

actually going to come with a fireworks animation. Um and my first tip here is that you should keep text to a minimum.

So this is probably something that you've heard before. Um, and then also like if there does need to be a lot of text for some reason, so for example, the slide I just showed you is maybe like the maximum amount of text I would

09:07

go for, but if you're going to do something like that, it's really helpful to just build it up one statement at a time using animations. And this should be something that's really easy to incorporate already into your slides.

So, for example, on the slide I just showed you, I started with the objective function and then I introduced each

09:22

constraint kind of one at a time um in order to kind of iteratively build it up so you could follow along. So you might think of this sort of similar to like maybe when you're in lectures and you see professors writing on the blackboard.

Sometimes I feel like that's a little bit easier to follow because they can really only introduce ideas at

09:39

the speed that they can write. You want to kind of mimic that cadence with your slides.

Another tip here is that kind of related to that there should be nothing on your slides that you do not explain. So your slides are really just tools for you to

09:56

maximally communicate your ideas to the audience. And so there's no reason to have anything extraneous on them.

And if you do want your audience to be able to reference extra things, you could always provide a link to some sort of reference document that you created or like for

10:11

example if you're presenting a paper, people can always go and look at your paper. Uh so for example, the link that I'm providing here is like a reference document that summarizes all the tips and tricks that I'm going to be talking about today.

Um, okay. And then before we move on, I just want to say one more thing about

10:28

this optimization problem and particularly about this objective. And really what I want to do is introduce a proxy objective for this objective.

And that is to minimize cognitive load for the audience. So the easier that you can make it for the audience to understand

10:44

the things that you're saying, the more things that they can understand and then the more ideas you'll be able to communicate to your audience. So when you're creating a presentation, you should have this idea of maximizing communicating your ideas in mind.

Uh but you can also at the same time sort of be

10:59

thinking of that as minimizing the cognitive load for the audience. And doing both of these things will help you create a better presentation.

Okay. So with that, I'm now going to give you a running example on what I think is a good presentation.

So this is even more terrifying because now I'm trying to

11:14

show you a good presentation inside of the presentation on good presentations. But here we go.

Um, but before I do that, just one tip here. In general, a running example is a really good way to minimize cognitive load for the audience.

So, when people are watching your presentation, it's much easier for

11:30

them to kind of grasp quickly anyway, like a concrete example as opposed to an abstract idea right away. So, if you can give them some sort of concrete example to follow along with, uh, then they can more easily move into the abstract or reason about how it might apply to other things later.

But to minimize that

11:47

cognitive load, it's much easier for people to understand like a concrete example as you're going along. So if you can find one of these running examples, it's really really helpful.

And also before I get into this example, I just want to show you a graph here. And on this graph, on the x- axis, we're going

12:03

to have the amount of information that you include in your presentation. And on the y-axis, we have the amount of information that gets learned by the audience.

And so I'd say initially it actually starts off as kind of this proportional relationship where the more

12:18

information you tell the audience the more things they learn. But at some point we reach a point where the audience has learned the maximum amount that they can.

And then this plot begins to level off a little bit. And then you might reach a point where you've actually told the audience so much that they just get completely lost and they

12:35

probably tune you out at this point. And so I would say it's actually a pretty steep drop off after that.

to the point where you could actually tell the audience so much that they literally learn nothing. So, it's really important to keep this in mind when you're creating presentations.

But I would

12:51

argue that there's actually kind of a problem here because I really love important sampling, which is the topic of our running example. And so, this is actually the amount of information that I want to tell you about important sampling.

So, it's like way to the right of that x-axis there. Um, and so the first thing I want to say about this is

13:07

like actually this is good. So, you should be excited about what you're talking about.

If you're not excited about what you're talking about, your audience isn't going to be excited and they're probably not going to listen to you. So, it is a good thing to actually be all the way over here on this plot.

But, we need to then make a conscious

13:23

effort to avoid TMI or too much information. So, this part of the plot here, I call the TMI zone.

You can see like where I'm at, I'm even out of the TMI zone. I'm in like the probably don't even start talking zone.

And what we really want to

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do is try to make this conscious effort to aim for this zone in the middle here where the audience is kind of learning the maximum amount that they we can tell them uh given maybe like the a lot of time constraints to reference back to the constraints from before or like the

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their level of prior knowledge. So this is something that you need to make a conscious effort to do when you're creating presentations.

And I know it's a conscious effort because I just told you like I'm all the way to the right on this axis. I want to tell you way more things about important sampling.

And so what you need to do when you're actually

14:09

sitting down to make your presentation is like resist this urge to tell the audience all the things you want to tell them because if you did do that, they would probably get absolutely nothing out of it. So it's really worth trying to aim for this zone in the middle here.

Okay, so with that said, we're going to go into our running example on what is

14:27

important sampling. So this is kind of a presentation within a presentation real quick.

So to talk about important sampling, I'm going to use another running example of aircraft collision avoidance. So basically the idea here is that we have this blue aircraft and it's trying to avoid this red aircraft using a

14:43

collision avoidance system. And what we want to make sure is that the blue aircraft does not enter within some region around the red aircraft.

And this would be called a near midair collision. And as long as it doesn't do this, we're good to go.

But if we were to simulate

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this system multiple times, we won't always get this outcome because, you know, there could be things like sensor noise, maybe the pilot doesn't always respond in the same way or other like various environmental factors. And so it's possible that we could actually get a simulation where things don't go quite as well and we do actually have this

15:15

near midair collision occurring. And this is of course something that could be quite dangerous and have quite catastrophic consequences.

So we don't want this to happen. So then you might be interested before deploying a system like this in the real world.

Well, what is the probability

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that this actually happens? What is the probability that a near midair collision occurs?

And so to figure out what this probability is, you might imagine we'll just simulate this system a whole bunch of times, we'll see how many of those simulations resulted in near midair collisions. And then we'll just take

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this number, in this case it was two near midair collisions, divide it by the total number of simulations, in this case 60 total simulations, and we'll get an estimate for the probability of a near midair collision. So in this case, our estimate is around 3.3%.

Uh this might be like setting off

16:05

some alarm bells in your mind, like I would certainly hope that every time I get on an aircraft, I don't have a 3.3% probability of a near midair collision. Uh and no worries that is absolutely true.

In real aviation systems this probability of near emitter collision is much much lower. And in fact if you were

16:22

to simulate a real aviation system you would probably get something that looks more like this where we actually don't observe any near collisions which is of course a good thing. But then now if we try to calculate the probability of near collision we see that we have zero near

16:38

collisions divided by 60 total simulations. So then our estimate is zero which seems a little bit strange and I would say yeah not exactly it's not exactly true that the probability of failure is zero and what actually happened here is just that 60

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simulations was not enough for us to find any near midair collisions to the point where we could actually get a good estimate of our probability of near collision. So then you might come to me and you're like okay well no problem let's just run a whole bunch more simulations.

But the problem with that

17:10

is that simulations tend to be expensive. And if failures are very very rare, then it might require us millions or even billions of simulations to actually observe enough failures to get a good estimate for the probability of failure.

And so I'll come back to you and I'll say but this is expensive. We

17:27

actually can't do this and we need to look for some other solution. And that solution is important sampling.

So the idea with important sampling is instead of simulating the real world environment that we want to estimate the probability of failure for, we'll simulate some different environment that's actually

17:43

more likely to cause failures. So for example, maybe we'll simulate that first environment that I showed you before showing you the real world.

But there's of course a problem here because we want to estimate the probability of failure for the real world environment, not for this extra simulated environment that we

18:00

came up with to induce more failures. And so what we do with important sampling is we actually rewe all of these simulations according to how likely they were to occur in the real world.

So now instead of having two near midair collisions, it's more like we

18:15

observed for example like 0.15 near midair collisions and we divide that by our total number of simulations and now we can get a more accurate estimate for the probability of failure. In this case around 02%.

Again no worries the real probability of failure is still even

18:30

much less than that. This is just a notional example.

And so you may still be wondering though like where did this 0.15 come from exactly? Like reweing happened.

What's going on here? Uh the answer is this 0.15 comes from these things called importance weights.

Uh and if you're interested in the exact way

18:46

that they're calculated, you can check out a chapter of a textbook that I worked on on this topic. But uh in general, I just want you to have the intuition that basically reweing these samples according to how likely they were to occur in the real world allows us to get this number that allows us to

19:02

accurately estimate the probability of failure. And so then using the same number of simulations, we're actually able to get a more accurate estimate of the probability of failure.

And in general, this is exactly what important sampling does. So important sampling allows us to efficiently estimate the

19:19

probability that a rare event occurs. Okay, so step back step back out of that.

We're now out of the presentation within the presentation back to the regular presentation. That was my overview of important sampling for you.

And now what I want to show you is we're

19:36

going to have to make a bit of an assumption here for the rest of the presentation. And that assumption, which I hope isn't super crazy, is just that what I just showed you was a good presentation.

And so going on that assumption, we can talk about what exactly made it good. And you might come

19:52

to me and you're like, oh well, it was of course those beautiful and effective slides. Uh to which I say, a thank you very much.

But I would argue there's actually one thing that's even more important than fancy slides. So you do not necessarily need fancy slides to make as good presentation.

As much as it

20:08

pains me to say that because I love making fancy slides, I would argue there's actually one key element that's worth even more than these pretty fancy slides. And that element is the story.

So the story that you tell is actually extremely important for how your

20:24

presentation comes off to the audience. You might be thinking right now like what do you mean?

Like I'm a researcher, I'm an engineer, I'm an academic, like I don't tell stories, like what are you talking about? Um, but it turns out like us as humans, it's just much easier for us to process things if they're told to us in the form of a story.

We'll be much

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more engaged. Uh, we'll understand more and we'll probably be more likely to actually remember what we're told.

So, it's really important even if you don't necessarily think that what you want to present is a story, you want to try to tell it like a story anyway. And so, you might be thinking like, okay, but like

20:56

what does that even mean? What does it mean to tell something like a story?

And this is something that I've actually been thinking about quite a bit over the last few years because I think a lot of times people will ask me after I, you know, make presentations like, "How'd you come up with that story?" Like, "How do you get that storyline? How do you

21:12

make it compelling like that?" And I always like never really had a super great answer for this. Um, until recently, I think recently I've come across kind of the best answer that I've seen to this.

And to introduce this to you, I'm actually going to tell you a story. So, the story starts like this.

21:29

was um giving teaching a class uh at Stanford a few months ago and for all of the lectures for the class throughout each lecture I try to have like some humor every you know 5 10 minutes or so to keep students engaged and humor is a very powerful tool that we'll talk about a little bit more later um but basically

21:46

you could imagine it's like really hard to keep up a steady stream of jokes over like an entire 10-week quarter uh throughout my lecture. So I was always like the night before the lecture struggling to think of like some jokes to to put in my lecture.

Um, and so I would often the night before like consult my husband for some help. Um,

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and to make the story make sense, one thing you need to know about my husband is that he basically lives his life through references to episodes of the TV show South Park. And so of every time I would ask him for advice, it would go something like this, like, "Hey, I need some help uh coming up with some jokes

22:17

for my lecture tomorrow." And then he would reply back, "Okay, well, like what's the topic?" And I would, you know, tell him some topic about algorithmic safety validation. And then he would come back to me and he would already have his phone out and he'd be pulling up YouTube and he'd be pulling

22:32

up an episode of South Park and he'd be like, "This is perfect. This is this is a joke.

This is perfectly align with everything you just said." Um, and it always drove me crazy because I was like, "I'm not including an episode of South Park in my lectures. I'm sorry.

This is not going to work. I need some other joke that I can actually use." And so I started to get very annoyed by

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this. But one day I started telling him about how I like really want to master like this art of storytelling.

And I feel like there's really something here that helped you make better presentations. And I just really want to be able to explain that and have a good way to explain it.

And of course, he's

23:04

already pulling out his phone. He's going to YouTube and he's like, "I have this perfect video for you.

It's the creators of South Park." And I'm like, "No, not more South Park." But it turns out, I'm really glad he forced me to watch this video because the creators of South Park, I think, got it absolutely right. So here's what they say about

23:20

storytelling. So they're talking about when they create their episodes, for example, they'll have an outline that maybe they write on a whiteboard and they have these beats of their outline and they say if the words and then belong between those beats, you're

23:35

cooked. Basically, they use a different word than cooked, but I won't repeat it here.

Uh, you've got something pretty boring. And what should happen between every beat that you have written down is either the word therefore or but.

And I think that this actually describes

23:50

everything super brilliantly. So here they were talking about creative writing, but I think that this actually very equally applies in an academic setting or in an engineering setting or a setting where you're trying to pitch an idea.

Uh all of these things are extremely important to take into account

24:06

when you're making these presentations. And so to help you understand like what this looks like and how I think it applies, let's go back to our running example.

So let's see if we can create one of these outlines for the running example I just showed you. So we basically started by saying okay an

24:23

aircraft collision avoidance system is there to help you avoid collisions. So then I showed you an example of that but sometimes it fails.

So then I showed you an example of a failure.

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Therefore we want to calculate the probability of failure. Therefore, we simulate a whole bunch of times in order to try to calculate this failure probability,

24:54

but failures might be rare and so we might not actually observe any failures. So then I showed you what this is like in the real world and how we might not actually observe any simulations of failures.

25:11

So then I had you come and say well therefore we just simulate more and I said but simulation is expensive. Therefore we want to simulate from a different environment that's more likely

25:27

to produce failures and this is important sampling. But we actually want to calculate the probability of failure for the real world, not for this set of trajectories from a different scenario.

Therefore, we rewe the trajectories.

25:45

Therefore, we get an unbiased estimate of the probability of failure and important sampling is super cool. Okay.

So, if we look at this outline that we've created here and we look at each of the beats, you can see there was no like and then there. Everything flowed from one thing to the next to the

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next. And I think many research problems or engineering ideas, anything that you're presenting on, they can almost always be put in a format like this.

You just have to like make a conscious effort to do it sometimes. And I think this is really how you tell a compelling story.

And this is how you get people to

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pay attention to your presentations. So, I would just encourage you if you want to know next time you're sitting down to make a presentation, if you want to know whether or not it tells a compelling story, you can put it to the test by creating an outline like this and checking whether or not the words therefore or but belong between the

26:34

different points that you have on your outline. Okay, speaking of outlines, let's talk for a minute about outline slides.

And this advice actually comes from my PhD adviser, Michael Kokanderfer. Uh, one of the first things he told me about making

26:49

presentations is that you don't want to jump directly to an outline slide. You should always try to start with some sort of attention grabber.

So, for example, my attention grabber for this presentation was about my presentation journey. There's lots of different things you can think of to put there.

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And sometimes you might actually not even need an outline slide, I would argue. So, if you're telling a compelling story and you keep people engaged the whole way through, they may not even need an outline to know where you were going.

Um, however, it is okay to include one if you want to. Uh, but if you are going to, do not put an

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outline slide that looks like this. This does absolutely nothing for you.

We've probably all seen this before. You go like introduction, background, motivation.

Um, this is just completely useless. There's no reason to have anything like this in your presentation.

And I would say if you are going to include an outline slide, you can

27:35

actually use this as an opportunity to check the story that you're trying to tell in your presentation. So, you could actually just make your outline slide a preview of the story that you're about to tell.

And this even gives you like the perfect opportunity to check whether or not each point that you have in your

27:51

outline flows from one thing to the next. So, you can actually check, again, going back to what the South Park creators recommend, checking if the words therefore or but belong between those points.

Um, okay. While we're on the topic, I'll just give one more piece of advice that my PhD adviser gave me.

28:07

Uh, which is that you should often try to have some humor towards the beginning of a presentation and throughout. So, I mentioned this before with like my lectures.

I was always trying to have some humor just to keep people excited. And I also want to add one thing onto this, which is just to say like it's okay to show people that you have a

28:22

personality. So, you know, you're human.

The people you are talking to are human most likely. And so, um, it's worth, you know, relating to them in that aspect.

It will allow people to be more engaged and also make them probably more likely to pay attention to you, which again

28:37

helps you maximize communicating your ideas. So, it's okay to show that you have a personality.

In fact, that's a good thing to do. Uh, you can tell funny stories.

You can incorporate humor. You can talk about how much your husband loves South Park as long as you know, of course, you have permission.

Um, and any

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things like that to keep people engaged. Okay, so I'm almost to the end here, but at the risk of having some and thens in my presentation, here's just a few other tips that I wanted to show you that I found useful.

Uh, one tip related to this slide is that a single sentence in

29:09

the middle of a slide is a really nice way to emphasize a point. Uh, next tip is related to the writing example I gave.

Uh, it's really nice if you can make a cartoon version of your problem. So, for example, I made like a

29:26

cartoon version of this aircraft collision avoidance system. This is of course not what it looks like in in real life.

You know, it's more than two-dimensional. There's lots of other environmental things going on.

But what you want to do is try to abstract away everything you can into a cartoon cartoon version and just leave the the

29:43

specific things that the audience would need to actually grasp the core concept that you want to give to them. And then later on they could always like try to extrapolate that to all the other like uh finite details that are going on.

Okay. Next uh you always want to try

29:58

then to show the naive solution first. So this can help a lot with your storytelling because you kind of present the problem and you say okay so therefore the simplest thing that you might do is whatever.

And so, for example, in the running example I used, I showed you how maybe the simplest

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thing you do is you just simulate the system a whole bunch of times and you see how many of them result in near emitter collisions. Um, okay.

Then, keeping along with the story, you say, "But it doesn't work." And you show why. So, for example, I showed you how this doesn't work when

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failures are very rare. Uh, and so therefore, you show how your solution fixes the problem.

Uh so I showed you how important sampling can allow us to get an estimate for the probability of failure using the same number of simulations. Okay, so

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those all help with the story line. Um another thing that I wanted to talk about related to this slide and some of the other slides I showed is that you should always explain every part of every single equation that you show.

So for example, I had very few equations in this presentation, but the ones I did

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have were just kind of like the ones on this slide where I had the number of near midair collisions divided by the total number of simulations and then I had an estimate for the probability of failure. So I was able to explain where every single thing in that equation came from and I had enough time to to allow

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you to digest that. But if you are finding yourself in a situation where you actually don't have enough time to go through everything that's in an equation, then that means that your equation is probably in the tmi zone.

So, one thing I would say that you should check every time you want to put

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an equation in is it's okay to have equations, but that means you need to explain every single variable, how they relate together, and what the overall equation means. And if you don't have time to do that, then your equation is in the tmi zone to reference back to what we were looking at before.

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So, for example, for important sampling, here's the actual equation for calculating the probability of failure using important sampling, I didn't really have time to explain like essentially any of the things that are going on in this equation, at least in terms of the notation that's used here.

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And so, I didn't include it. Um, even though, you know, I really wanted to because of course, like I showed you, I'm all the way to the right on that axis.

I love important sampling. I think this equation is beautiful.

But I had to resist the urge to put this equation into my slides. So it's really a conscious effort that you have to make

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and every time you want to include an equation sometimes it's okay to do that but you just need to check whether or not it actually uh you actually have time to sufficiently explain it. Um because if you don't you're probably just going to confuse people and you want to minimize the amount of opportunities people have to get

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confused and then tune you out. And so another thing that I want to say along those lines is for example I told you like we rewe all of these trajectories and we get this 0.15 And then I told you like don't worry exactly where the 0.15 came from.

I want

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you to just have the intuition that it comes from this like reweing according to how likely they are in the real world. But I didn't tell you exactly where it came from.

And I think that's actually a really important thing to do. So if there's like some sort of magic that seems to happen in your presentation because you don't have enough time to explain it, uh that's

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okay. You can always, you know, link people to more information, which is what I did.

Uh, but it's actually really important to call that out for people because if you don't, if I just had this 0.15, you might look at it and be like, oh, I don't know how she got that number. Like, I'm confused.

Okay, I'm lost now. I'm just going to tune out for

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the rest of the presentation. And you don't you want to avoid that.

So, you want to be able to say like, it's okay that you don't know exactly where that came from. I don't expect you to.

Here's how you can look it up, but stay with me for the rest of the time so that we can kind of continue on um without that information. And so that kind of brings

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me to one of my last points, which is that you can always link the audience to more information. Uh, and you should especially do this if it seems like there's some sort of magic happening.

Uh, you want to explain that to the audience so that they stay with you for the rest of the time. Um, okay.

So, linking to more information I'm going to

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use as a segue into, uh, my wrapping up of this presentation. Uh, so here's actually a link to a summary of all the points that I talked about in this talk and also some more links on some good resources.

And yeah, I really hope that you got uh some nice tips and tricks so

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that the next time that you sit down to make a presentation, it's one easier for you and two, it ends up being more effective.

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