Making Connections

Joanne Egner News & Announcements

isee systems is proud to have sponsored the 28th International System Dynamics Conference held in Seoul, Korea last month.  We especially enjoyed supporting the conference again this year through the Barry Richmond Scholarship Award.   The scholarship was established in 2007 to honor and continue the legacy of our company founder, Barry Richmond.  Barry was devoted to helping others become better “Systems Citizens”.  It was his mission to make Systems Thinking and System Dynamics accessible to people of all ages and in all fields. 

I first met Barry 20 years ago, when I had to trudge through the snow to get to his small wooden office.  I was building a discrete event model using STELLA and I wanted him to make some changes to the software so I didn’t have these “egg timer“ structures everywhere.  Barry was horrified with what I had done with his software and said words to the effect that it’s not meant for that, it was created to spread the gospel of System Dynamics.  Despite the fact that I was a civil engineer, he encouraged me to take a look at SD.  Such was his passion and conviction that 20 years later I’m still attending this conference.”

Tony Phuah accepts Scholarship Award from Mark Heffernan

Through most of his career Barry saw education as the key to spreading Systems Thinking.  As a teacher and a mentor, he dedicated much of his time to developing tools and methodologies for learning.  It is fitting therefore that this year’s award was presented to Tony Phuah, a Master’s student in System Dynamics at the University of Bergen.

Tony’s work includes an experimental study that explores the question: How can we improve people’s understanding of basic stock and flow behavior?  His experiment uses two different methods for teaching stock and flow behavior — the standard method (using graphical integration) and a method he calls “running total”.  Tony presented his paper at a parallel session during the conference and it can be downloaded by clicking here.  Although the results of his study favor traditional methods for teaching stock and flow behavior, we all should be encouraged by the work being done to try to improve Systems Thinking education and communication.  In Tony’s own words:

Speeding up ‘Systems Thinkers beget more Systems Thinkers’ growth will make us one step closer to Barry Richmond’s vision of a systems citizen world.”

Congratulations Tony and thank you Mark for helping us to celebrate Barry’s passion!

Applications for the 2011 Barry Richmond Scholarship Award will be available on the isee systems and System Dynamics Society web sites.  Check those sites for more information.

Barry Richmond, conferences, scholarship, System Dynamics Society

Nat Pierson Modeling Tips

After reading Karim Chichakly’s recent post on Integration Methods and DT, I was reminded that delta time (DT) has always been a tricky modeling concept for me to grasp.   Beginning modelers don’t usually need to think about changing DT since STELLA and iThink set it to a useful default value of 0.25.   But once you progress with your modeling skills, you might consider the advantages and risks of playing with DT.

The DT setting is found in the Run Specs menu.

By definition, system dynamics models run over time and DT controls how frequently calculations are applied each unit of time.  Think of it this way, if your model was a movie, then DT would indicate the time interval between still frames in the strip of movie film.  For a simulation over a period of 12 hours, a DT of 1/4 (0.25) would give you a single frame every 15 minutes.  Lowering the DT to 1/60 would give a frame every minute.   The smaller the DT is, the higher the calculation frequency (1/DT).

Beware of the Extremes

A common tendency for modelers is to set the calculation frequency too high.  Without really thinking too hard about it, more data seems to imply a higher quality model – just like more frames in movie film make for smoother motion.  If your model calculates more data for every time unit, its behavior will begin to resemble the behavior of a smoothly continuous system.  But a higher frequency of calculations can greatly slow down your model’s run performance and more data does not directly translate to a better simulation.

Beware of Discrete Event Models

Another situation where DT can often lead to unexpected behavior is with models that depend on discrete events.   My eyes were opened to this when I attended one of isee’s workshops taught by Corey Peck and Steve Peterson of Lexidyne LLC.

One of the workshop exercises involved a simple model where the DT is set to the default 0.25, the inflow is set to a constant 10, and the outflow is set to flush out the stock’s contents as soon as it reaches 50.   This is how the model’s structure and equations looked:

Stock = 0

inflow = 10

outflow = IF Stock >= 50 THEN 50 ELSE 0

I would have expected the value of the stock to plunge to zero after it reached or exceeded 50, but this graph shows the resulting odd saw-tooth pattern.

The model ends up behaving like a skipping scratched record, in a perpetual state of never progressing far enough to reach the goal of zero.  (Click here to download the model.)

What is happening in the model?  In the first DT after the stock’s value reaches exactly 50, the outflow sets itself to 50 in order to remove the contents from the stock. So far so good, but now the DT gotcha begins to occur.   Since the outflow works over time, its value is always per time.  To get the quantity of material that actually flowed, you must multiply the outflow value (or rate) by how long the material was flowing.  When DT is set to 0.25,  the material flows 0.25 time units each DT.  Hence, the quantity of material removed from the stock is 50*0.25 = 12.50.

Suddenly we are in a situation where only 12.50 has been removed from the stock but the stock’s value is now less than 50.  Since the stock is no longer greater than or equal to 50, the outflow sets itself back to 0 and never actually flushes out the full contents of the stock. 

So what do we do?  One solution to this problem would be to use the PULSE built-in to remove the full value from the stock.   Here’s what the equation for the outflow would look like:

outflow = IF Stock >= 50 THEN PULSE(Stock) ELSE 0

(Note: This option will only work using Euler’s integration method.)

Further Reading

STELLA and iThink have great help documentation on DT.  The general introduction provides a good explanation of how DT works. The more advanced DT Situations Requiring Special Care section focuses more on artifactual delays and the discrete model issues mentioned in this post.  Delta time and resulting model behaviors are reminders that system dynamics models run over time, but they achieve this by applying numerous discrete calculations in order to simulate the smooth behavior of actual systems.

DT, iThink/STELLA

Karim Chichakly Modeling Tips

The simulation engine underlying STELLA® and iThink® uses numerical integration.  Numerical integration differs from the integration you may have learned in Calculus in that it uses algorithms that approximate the solution to the integration.  The two approximations currently available are known as Euler’s method and the Runge-Kutta method.  All algorithms require a finite value for DT, the integration step-size, rather than the infinitesimally small value used in Calculus.  On the surface, it may seem that the smaller DT is, the more accurate the results, but this turns out not to be true.

Compound Interest:  Euler’s Method over Runge-Kutta

To introduce Euler’s method, let’s take a look at the simple problem of compound interest.  If we have $100 that we invest at 10% (or 0.1) compounded annually, we can calculate the interest after N years by adding in the interest each year and recalculating:

1st year:  interest = $1000 × 0.1 = $100; Balance = 1000 + 100 = $1100
2nd year: interest = $1100 × 0.1 = $110; Balance = 1100 + 110 = $1210
3rd year:  interest = $1210 × 0.1 = $121; Balance = 1210 + 121 = $1331

And so on up to year N.  We have just seen the essence of how Euler’s method works.  It calculates the new change in the stock for this DT (in this case, interest) and then adds that to the previous value of the stock (Balance) to get the new value of the stock.  In this example, DT = 1 year.

By noticing we always add the existing balance in, we can instead just multiply the previous year’s balance by 1 + rate = 1 + 0.1 = 1.1:

1st year:  Balance = $1000 × 1.1 = $1100
2nd year: Balance = $1100 × 1.1 = $1210
3rd year:  Balance = $1210 × 1.1 = $1331

And so on up to year N. We can further generalize by noticing we are multiplying by 1.1 N times and thus arrive at the compound interest formula:

Balance = Initial_Balance*(1 + rate)^N

Checking this, we find our Balance at the end of year 3 is 1000*1.1^3 = $1331.  In the general case of the formula, rate is the fractional interest rate per compounding period and N is the number of compounding periods (an integer).  In our example, the compounding period is one year, so rate is the annual fractional interest rate and N is the number of years.  However, if interest is compounded quarterly (four times a year), the interest rate has to be adjusted to a per quarter rate by dividing by 4 (so rate = 0.1/4 = 0.025) and N must be expressed as the number of quarters (N = number of years*4 = 3*4 = 12 for the end of year 3).  We can use this formula in our model to test the accuracy of Euler’s method.  Note that for quarterly compounding, we would set DT = 1/4 = 0.25 years.

To explore the differences between Euler’s and Runge-Kutta, the following structure will be used for all of the examples in this post.  This structure models the compound interest problem outlined above.

The equations change for each example and can be seen in the individual model files (accessed by clicking here).  For this example, the actual value is calculated using the compound interest formula, Initial_Balance*(1 + rate)^TIME.  The approximated value is calculated by integrating rate*Approx_Balance (into Approx_Balance).

In addition to the actual and approximate values, three errors are also calculated across the model run:  the maximum absolute error, the maximum relative error, and the root-mean-squared error (RMSE).  The absolute error is:

ABS(Actual_Balance – Approx_Balance)

The relative error is:

absolute_error/ABS(Actual_Balance)

and is usually expressed as a percentage.  The RMSE is found by averaging the values of the absolute error squared, and then taking the square root of that average.

Read more…

DT, Euler, Integration, RK4, Runge-Kutta

Chris Soderquist Systems Thinking

Editor’s note: This is a guest post by isee’s consulting & training partner Chris Soderquist

It’s been a little over 10 weeks since the Deepwater Horizon oil rig explosion that has resulted in a constant flow of oil into the Gulf of Mexico.  Oil is now beginning to impact the economy of the Florida coast.  Some estimate that the disaster could cost nearly 200,000 tourism jobs.   Efforts  to remove the impacts on the environment, including a massive rescue of manatees could cost billions.  The ability to truly restore the environment to pre-April 20 conditions is beyond that of mere mortals. It is an event truly unprecedented.

Who’s to Blame?

The current media focus has centered on an activity I refer to as the Find the Knucklehead Game. The idea is that there must be someone out there to blame, tar and feather, and that if we just remove the idiot from the system we’ll never have this problem again. Finé. Complete. Case closed! (And there was great rejoicing…)

However, if we begin to apply the systems thinking paradigm, there’s another analysis that might suggest we are in a long-term trend that is still just ramping up – and that if we don’t take action soon the impact on the economy and environment may be much worse.

A Systems Thinking Perspective

Two of the skills required to practice systems thinking are Dynamic Thinking and 10,000 Meter Thinking. If we look at the history of oil extraction from the balcony, as a long-term trend over time, we see something that may be quite useful. Let’s apply a concept developed by Charles Hall (SUNY-College of Environmental Science and Forestry) called EROI (“energy return on investment”).  EROI is the ratio between the energy we receive – to run our transportation system, heat our buildings, run electricity generators – and the amount of energy required to get the raw material out of the ground and process it into usable form. In the early 20th Century, oil was easy to extract. In many places it was just below the surface in the wide open fields. The EROI was 100:1 in 1930 – 100 units of energy received for 1 unit of energy extracting/processing. Since then there has been a marked decline, and as the United States passed peak oil production (the maximum production rate) in the early 1970s, and as we’ve begun importing most of our oil, the EROI for oil in the US is approximately 20:1.

Charles Hall's Energy Return on Investment Graph

Why the marked decline? Because the purest, easiest to extract/process oil has likely been found and burned (leading to too much in our atmosphere, but that’s another point). We now need to go to more distant places (no longer fields) – offshore, into the Arctic – to find oil. Often the oil is no longer in purest form; converting the “oil goo” from the tar sands in Alberta, Canada is a prime example.

Continuation of a Trend

Using the systems thinking perspective, we may conclude that the “event” of Deepwater Horizon is an inevitable continuation of a trend (that includes the Exxon Valdez). And that the trend is likely to get worse as our need (thirst) for oil increases – which will occur as developing nations continue trying to catch up to the developed world, and as we hope for “economic recovery.”

This leads to several questions in my mind.

1. If it’s true that the easiest to extract and process oil has been found and used, what’s this indicate about the risks we’ll incur as it requires increasing effort to get oil in the future? More deepwater drilling? Environmental degradation/damage to get oil like tar sands extracted?
2. How much oil really is left – how long will we continue to have this cheap resource?
3. Further, if we are facing increasing risks and costs for every unit of oil we acquire, when will that begin to have severe impacts on our economy (as the per unit cost of the stuff we love – iPods, cars, flying to Europe – increases, the profit margins of our globalized corporations will decrease)?
4. And when will we decide that we need to develop a way of living that is independent of this resource? To recover from our “addiction to oil.”

How Much Oil Is Left?

I’ve developed and published an isee NetSim model that you may use to explore questions regarding how long the resource will last and the implications of the economy on that length. You may explore it here.

Ultimately, we need to stop the Find the Knucklehead Game and instead recognize that it is we – in the collective sense – that are responsible. Not just for the recent disaster, but the long-term trend and its consequences (including the unintended consequences of climate change). The system is behaving as it is designed. It is up to us to design a different system!

environment, oil production, peak oil

Joanne Egner News & Announcements

Barry Richmond was the founder of isee systems and pioneer in the field of systems thinking.  When his life was cut short by a sudden fatal heart attack, Barry was in the prime of his career and the systems thinking community experienced a collective sense of loss and grief.

Barry was fully engaged in bringing systems thinking to everyone.  He saw how this powerful way of thinking could help people to better understand society’s most pressing issues and make the world a better place.  Barry saw K-12 education as one of the keys to creating a better world.  He spoke often about educating young people to become ”systems citizens” and preparing students for the complex problems they would have to face.  Much of his time was devoted to training teachers to incorporate systems thinking into curricula and pedagogy.

A couple of years ago, Barry’s daughter, Joy Richmond, began spearheading an effort to create a book in honor of her father.  Joy invited a group of us together to talk about some ideas for the book and come up with a plan to make it happen. The first idea we discussed was writing the book that Barry himself had intended to write.  Barry left plenty of notes and even had a working title for a book about systems thinking called Traces.   We all agreed that it would be much too daunting to try to write a book for Barry, so we decided to have a book written in tribute to Barry by friends and colleagues who share his passion for systems thinking.

Steve Peterson, Corey Peck and Khalid Saeed were all part of that original discussion and eager to contribute by writing a chapter.  Each had a story to tell about using Systems Thinking in their work and why it is so important in an increasingly interdependent world.  What better way to honor Barry than writing a book that helped get the word out about systems thinking!

Shaping the Book

Lees Stuntz, Executive Director of the Creative Learning Exchange, was also in on the discussion and excited about asking educators influenced by Barry to contribute their stories. Before we invited other authors however, we wanted to provide some guidelines that would tie the book together and give it a more meaningful context.  I think it was Steve who came up with the idea to use the critical thinking skills first outlined in an article Barry wrote for the System Dynamics Review titled “Systems Thinking: Critical Thinking Skills for the 1990s and Beyond”.   We agreed the systems thinking skills would provide a good foundation for the book and each author could then choose a few of the thinking skills to emphasize when telling their story.

Countless hours of writing, editing, and designing later, Tracing Connections: Voices of Systems Thinkers was born.  Published in partnership with the Creative Learning Exchange, proceeds from the book will fund scholarships that offer learning opportunities for educators to use systems thinking and system dynamics in K-12 education.  The response so far has been excellent and we are pleased to be funding scholarships to help educators attend the ST/DM Conference later this month.

A Chapter for Everyone

What is especially nice about the book, is that you don’t need to read each chapter in sequence.  Since the authors’ experiences range from education and research to business and public policy, there’s sure to be a chapter for everyone.  Click on the link below to view the chapter by Frank Draper titled “Teaching by Wondering Around: Learning About the World Naturally”.  Frank tells a wonderful story about how Systems Thinking has transformed the way he teaches science to high school students.  After reading it, you’re going to wish you could enroll in one of Frank’s field science classes at Catalina Foothills school district in Tuscon, Arizona.

Teaching by Wondering Around by Frank Draper

Animal Temperature Model

Table of Contents with full list of chapter titles and authors

For more information or to order a copy of Tracing Connections, visit http://www.iseesystems.com/tc

Education, Systems Thinking

Karim Chichakly Modeling Tips

Conveyors are useful model elements for representing pipelines or processes that take a certain amount of time to complete.  However, adding a leakage flow to a conveyor can make it difficult to initialize a model in steady-state.  The following discussion will explain how to initialize conveyors with leakage in steady-state.  Please refer to the model structure below while reading this discussion.

These additional variables will be also used:

transit_time = TRANSTIME(conveyor)
conveyor_length = transit_time/DT
leakage_fraction = the user-specified leakage fraction

Linear Leakage

The default leakage is linear in behavior.  The total amount that leaks across the length of the conveyor is directly proportional to the inflowing amount.  The leakage fraction is the constant of proportionality.  Thus, the fraction of inflowing material that makes it to the conveyor’s outflow is exactly

1 – leakage_fraction

Given the sample model structure above, to achieve equilibrium, conveyor_outflow must equal outflow.  For this to happen, we need to set the inflow as follows:

inflow = outflow/(1 – leakage_fraction)

The conveyor’s steady-state value is then:

conveyor = transit_time*inflow – (conveyor_length – 1)*leakage*DT/2

where the initial value of leakage is:

leakage = leakage_fraction*inflow

This must be calculated outside the program and entered as a constant into the conveyor as conveyors cannot be given equations (they can, however, be set to a the value of a single converter, but you must be careful how you calculate this to avoid circularity).

Exponential Leakage

Optionally, leakage can be made exponential.  The amount that leaks each DT is proportional to the amount remaining in the conveyor.  In this case, the leakage fraction is the fraction that leaks each unit of time so, for long conveyors, a lot of material can leak away.  Given the transit time, the fraction of inflowing material that makes it to the conveyor’s outflow is approximately

1 – (1 – leakage_fraction)^transit_time

Given the sample model structure above, to achieve equilibrium, conveyor_outflow must equal outflow.  For this to happen, we need to set the inflow as follows:

per_dt_no_leak = 1 – leakage_fraction*DT
inflow = outflow/(per_dt_no_leak^conveyor_length)

For steady-state, the conveyor itself must then be set as follows:

conveyor = (inflow*DT)*(1 – per_dt_no_leak^conveyor_length)/(1 – per_dt_no_leak)

conveyor, leakage, steady-state

Jeremy Merritt isee NetSim

Last week, we released version 1.1 of the isee NetSim software.  isee NetSim enables iThink and STELLA users to publish their models online so anyone can run them in a web browser.  Version 1.1 introduces several new features.  In this post I will share a couple of those that I am most excited about.

Forio Simulate—Like YouTube for Simulations

Since the debut of the isee NetSim software we have collaborated with Forio Business Simulations to provide free hosting for models published online.  Last year, I saw a demo of Forio’s new simulation service, Forio Simulate, in the early development stage.  It was awesome.  I couldn’t believe it—they added all of the Web 2.0 features I’d been dying for, and a slick, fun to use interface.  I knew we had to make isee NetSim work with it.

The new service is social by nature—it features keyword tagging, ratings, comments and built-in model sharing.  It’s like YouTube for simulations.  You can browse simulations and games that others have created, find similar ones by keyword tags, and embed simulations on blogs or web pages.  So you don’t have to be actively publishing your own simulations, or even be a modeler to get a lot of value from the site.  In fact, it’s a great way to introduce people to modeling and simulation.  Just post a link!

And if you are a modeler, you can get even more out of the service.  Most of the simulations published to Forio Simulate allow you to download or copy the underlying model that powers it.  Here at isee, we’ve uploaded the original iThink and STELLA models used to create all of our sample isee NetSim simulations.  That way anyone can run the simulation online in a browser and download the source model to dig into if they want more.  Take a look at isee systems’ models published on Simulate by clicking on the screen shot below.

The simulation overview page allows anyone to download the source model, rate, comment, add tags and embed the simulation on other web pages.

Anyone can use free hosting on Forio Simulate if the model contains 400 or fewer equations and is shared with other users of the service.  If you want to protect the model, resell a simulation, use a custom URL, etc., you can sign up for a premium hosting plan.  It’s easy to select a hosting plan when you upload your model with isee NetSim.

Graphical Input Device

Use the GID to change the price assumption

One of the most requested features for isee NetSim has been the graphical input device, or “GID” as we like to call it.  GIDs offer a simple way to allow people running your simulation to change the model assumptions.  Often it’s easier to sketch a curve of the behavior of a variable than to input numbers directly.

For example, the model below is a generic renewable-resource model that enables you to experiment with yield and price of a renewable-resource via GIDs.  The model is from our “Thinking in Systems” online course.  I published the model to Forio Simulate and then embedded it here.  Click the “Review model” link to take a brief tour of the model.

You can change the price elasticity and “yield per unit capital” curve by first clicking on one of the GIDs.  A window will pop open that displays the details of the curve.  Click and drag within the grid to draw a new curve.  Press “Ok” to apply the changes.  Take a few moments to play around with the model below.

[Editor's note:  If you cannot see the embedded model below because you are reading this post in a feed reader or email, please visit the post page here]

What I find interesting after playing with this model is what happens when you start to push the yield up.  At some point the efficiency improves to the point where the renewable-resource gets completely wiped out.  Sometimes the inefficiencies of harvesting a resource can be a good thing—it gives the resource time to “catch up”.  This may be a useful point to consider when thinking about sustainable systems.  What happens when you make the resource inexpensive?

A GID for the web

You may have noticed that the GID within isee NetSim does not allow a user to type numbers to define data points or change the x and y ranges.  We decided this simpler version of the GID was a good fit for models published to the web and would cover most use cases.  The GID allows users to easily change the assumptions by sketching a behavior pattern and not really concern themselves with the data.

If you’ve been dying to publish models with GIDs online, now is your chance.  While you’re at it, check out Forio Simulate and start contributing to the growing simulation community.  You can download a trial of isee NetSim 1.1 here.  If you already own isee NetSim, visit your “My Software” page on the isee systems website to download the upgrade.

embedded, Forio, GID, graphical function, graphical input device, netsim

Chris Soderquist Systems Thinking

Editor’s note: This is a guest post by isee’s consulting & training partner Chris Soderquist

Background

The April 26, 2010 article in the New York Times titled “We have met the enemy and he is PowerPoint” has created quite a stir. It is particularly telling that three days after its publication, it is the most emailed article on their website! The most interesting aspect of the article to me, as a system dynamics practitioner, is the publication of a system dynamics map on the US Counter-insurgency strategy as the example (i.e. visual sound bite) demonstrating why PowerPoint is so problematic. This is actually a poor example of the author’s point, since it is not PowerPoint, and because the map was shown out of context.

Although the diagram doesn’t portray how or why PowerPoint is misused, it does demonstrate some reasons why system dynamics maps and models are not more broadly used to communicate systemic issues. In this post, I will describe what issues a PowerPoint paradigm creates and how system dynamics can address those issues; more importantly, I will show why the STELLA and iThink software have features such as storytelling and web publishing in order to help people develop deeper, more systemic understanding of the complex problems humanity must address.

The Problem with PowerPoint

I don’t have anything against using PowerPoint. Those of you who have taken one of my webinars for isee systems know that I rely heavily on the software in my instruction and facilitation. I think there are inherent software limitations that combine with a cultural paradigm, that lead to its misuse. Currently, I see it promotes the following approaches to problem solving:

1. Narrow focus in space and time – due to limited screen real estate
2. Passive absorption of information of data – lazy learning, not experiential
3. Simplistic bullet point thinking – linear thinking, focusing on factors in a non-operational way

This all creates confusion between reducing complication and simplifying complexity. The world is a dynamically complex place, and thank goodness for that! Picture the blandness of a world that is simple, where everyone thought and acted the same, where you always knew exactly what would happen because it was so simple. Boring! On the other hand, dynamic complexity makes it difficult to resolve what currently appear to be intractable problems, such as environmental degradation, poverty, global economic turmoil. Living in a dynamically complex world necessitates finding ways to simplify complexity to its essence, making manageable and useful mental models.

That’s why people are drawn to lists (e.g., bullet point and linear thinking), believing it simplifies complexity; just give me a list of what’s wrong or what to do! What lists do well is remove complication, but they also remove the dynamic essence of reality, often making mental models that are less than useful.

System dynamics

System dynamics is an approach to building understanding that expands boundaries, looks at the world as comprised of feedback loops, uses a visual language that promotes operational thinking, and creates active learning. It’s a terrific approach to counter the many problems inherent in applying PowerPoint paradigm!

All of the above helps develop useful mental models that are both simplified and still capture the essence of reality. However, taking a map out of context – even one much simpler than shown in the article – and including it in PowerPoint will not create understanding, only confusion! When I’m in front of a group and have enough time, I will always draw it up on a flipchart or board, to bring the group along with its unfolding. The rapid feedback creates an engaged group capable of learning. But in the absence of time, or if you need to communicate to people “on their own time” you will find features in STELLA and iThink invaluable!

I’ve published a map to the web with the isee NetSim software to demonstrate how you can use system dynamics to create online experiential learning labs. Take a tour of the map below to see how the stock/flow language and Storytelling can overcome the passive absorption of bulletized information that PowerPoint facilitates.

Click on the image below to make sense of the map

Another interesting perspective from Linda Booth Sweeney on the New York Times article can be found on her blog.

COIN, counter-insurgency, New York Times, Powerpoint, storytelling