You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


Q:

How can I plot with 2 different y-axes?

I would like superimpose two scatter plots in R so that each set of points has its own (different) y-axis (i.e., in positions 2 and 4 on the figure) but the points appear superimposed on the same figure.
Is it possible to do this with plot?
Edit Example code showing the problem
# example code for SO question
y1 <- rnorm(10, 100, 20)
y2 <- rnorm(10, 1, 1)
x <- 1:10
# in this plot y2 is plotted on what is clearly an inappropriate scale
plot(y1 ~ x, ylim = c(-1, 150))
points(y2 ~ x, pch = 2)

A:

update: Copied material that was on the R wiki at http://rwiki.sciviews.org/doku.php?id=tips:graphics-base:2yaxes, link now broken: also available from the wayback machine
Two different y axes on the same plot
(some material originally by Daniel Rajdl 2006/03/31 15:26)
Please note that there are very few situations where it is appropriate to use two different scales on the same plot. It is very easy to mislead the viewer of the graphic. Check the following two examples and comments on this issue (example1, example2 from Junk Charts), as well as this article by Stephen Few (which concludes “I certainly cannot conclude, once and for all, that graphs with dual-scaled axes are never useful; only that I cannot think of a situation that warrants them in light of other, better solutions.”)  Also see point #4 in this cartoon ...
If you are determined, the basic recipe is to create your first plot, set par(new=TRUE) to prevent R from clearing the graphics device, creating the second plot with axes=FALSE (and setting xlab and ylab to be blank – ann=FALSE should also work) and then using axis(side=4) to add a new axis on the right-hand side, and mtext(...,side=4) to add an axis label on the right-hand side. Here is an example using a little bit of made-up data:
set.seed(101)
x <- 1:10
y <- rnorm(10)
## second data set on a very different scale
z <- runif(10, min=1000, max=10000) 
par(mar = c(5, 4, 4, 4) + 0.3)  # Leave space for z axis
plot(x, y) # first plot
par(new = TRUE)
plot(x, z, type = "l", axes = FALSE, bty = "n", xlab = "", ylab = "")
axis(side=4, at = pretty(range(z)))
mtext("z", side=4, line=3)

twoord.plot() in the plotrix package automates this process, as does doubleYScale() in the latticeExtra package.
Another example (adapted from an R mailing list post by Robert W. Baer):
## set up some fake test data
time <- seq(0,72,12)
betagal.abs <- c(0.05,0.18,0.25,0.31,0.32,0.34,0.35)
cell.density <- c(0,1000,2000,3000,4000,5000,6000)

## add extra space to right margin of plot within frame
par(mar=c(5, 4, 4, 6) + 0.1)

## Plot first set of data and draw its axis
plot(time, betagal.abs, pch=16, axes=FALSE, ylim=c(0,1), xlab="", ylab="", 
   type="b",col="black", main="Mike's test data")
axis(2, ylim=c(0,1),col="black",las=1)  ## las=1 makes horizontal labels
mtext("Beta Gal Absorbance",side=2,line=2.5)
box()

## Allow a second plot on the same graph
par(new=TRUE)

## Plot the second plot and put axis scale on right
plot(time, cell.density, pch=15,  xlab="", ylab="", ylim=c(0,7000), 
    axes=FALSE, type="b", col="red")
## a little farther out (line=4) to make room for labels
mtext("Cell Density",side=4,col="red",line=4) 
axis(4, ylim=c(0,7000), col="red",col.axis="red",las=1)

## Draw the time axis
axis(1,pretty(range(time),10))
mtext("Time (Hours)",side=1,col="black",line=2.5)  

## Add Legend
legend("topleft",legend=c("Beta Gal","Cell Density"),
  text.col=c("black","red"),pch=c(16,15),col=c("black","red"))

Similar recipes can be used to superimpose plots of different types – bar plots, histograms, etc..

A:

As its name suggests, twoord.plot() in the plotrix package plots with two ordinate axes.
library(plotrix)
example(twoord.plot)

A:

One option is to make two plots side by side. ggplot2 provides a nice option for this with facet_wrap():
dat <- data.frame(x = c(rnorm(100), rnorm(100, 10, 2))
  , y = c(rnorm(100), rlnorm(100, 9, 2))
  , index = rep(1:2, each = 100)
  )

require(ggplot2)
ggplot(dat, aes(x,y)) + 
geom_point() + 
facet_wrap(~ index, scales = "free_y")