Challenge 7: Ciphers (Finally)

The postponed and long-awaited cipher challenge is finally here! I recommend you guys work in groups or as a class for this to save some time.

In case you don’t know, a cipher is a disguised way of writing — it’s an encoded message. This challenge isn’t directly related to Leonardo da Vinci (though he did use mirror-writing and was pretty secretive about his notes, so it’s not entirely unrelated either), but I think it’s an interesting (and fun, if you like puzzles) way to practice looking at things differently! It all leads to becoming more creative. So, let’s get started!

One of the earliest and simplest forms of encryption is something called a Caesar/shift cipher. It’s about what you’d expect from the name. Here’s an example:

Let’s say you want to encode this message: Leonardo da Vinci was a cool dude. With a Caesar cipher, you’re “shifting” the letters a certain number up or down the alphabet. So, to keep things simple, let’s say we want to use a right shift of two. Therefore, A=C, B=D, C=E, D=F, and so on.

With a right shift of two, “Leonardo da Vinci was a cool dude.” becomes “Ngqpctfq fc Xkpek ycu c eqqn fwfg.” You know you’re on the right track when it looks like a lot of gibberish.

This type of cipher is easy to decode because all of the words stay intact, and one can easily just use brute force to go through all possible combinations. It might be a little dull and time consuming, but you can get the answer eventually. A good technique is to think of some of the most frequently used letters in the English language (e, a, r, i, o, and so on) and try to find a pattern in the encryption by looking at the most common letters. You can also look for words that are 1-3 letters because those are fairly easy to match up.

If you’d like to practice, here are some encrypted messages using a Caesar cipher that you can try out:

•  Gwadzwqwhm wg hvs izhwaohs gcdvwghwqohwcb.
•  D cvqz vgrvtn azgo do dn ht yznodit oj wpdgy v hvxcdiz ocvo rjpgy vggjr hvi oj agt.
•  Zk yru cfex jzetv tfdv kf dp rkkvekzfe kyrk gvfgcv fw rttfdgczjydvek irivcp jrk srtb reu cvk kyzexj yrggve kf kyvd. Kyvp nvek flk reu yrggvevu kf kyzexj.

If you think you’ve got it, feel free to skip these and move on. They’re all quotes by a certain Renaissance man, if you’re curious.

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Another interesting type of cipher is the transposition cipher. It’s a lot less straightforward because it doesn’t use substitution. Let’s take our example from earlier, “Leonardo da Vinci was a cool dude.”, and I’ll try to explain it.

First, we’re going to remove the capitalization, punctuation, and spaces, which leaves us with “leonardodavinciwasacooldude”. It’s important to note that we have 27 letters here because now we’re going to write the message in three rows composed of nine letters each, like this:

l e o n a r d o d
a v i n c i w a s
a c o o l d u d e

From that, we finish the encryption by reading the letters in order down the column to get “laa evc oio nno acl rid dwu oad dse” and then removing the spaces “laaevcoionnoaclriddwuoaddse”. As you can see, it’s a lot more intimidating.

So, how do you solve it? Well, it involves a little math.

First, you’ll want to count up the characters. We have 27. 27 characters can be encoded in grids of 1×27 and and 3×9. A 1×27 grid is just going to look like the original message, “laaevcoionnoaclriddwuoaddse”, so that’s not helpful. Therefore, it has to be a 3×9 grid. Just write the first three letters down as a column, the next three as the adjacent column, and so on. This particular message was pretty easy!

But, it’s not always going to be simple like that. You might get a message with 24 letters, which could make grids of 1×24, 2×12, 3×8, and 4×6. In that case, you’d have to try writing all possible grids until you get to the one that spells everything out correctly!

Here are some examples for you to try:

• cnosnygotuastoullvaetdiiot  (26 characters)
• ioaihunnohagpamdevaavezy  (24 characters)
• ryoeteahvlieinrzgyecttohhnianntegecevtlessrte (45 characters)

That’s all I have time to write for today unfortunately — I hope these didn’t turn out to be too tedious. Best of luck solving them!

The examples here were mainly meant as short practices to learn different cipher techniques. I would’ve liked to write a more in-depth post with a compound cipher or something at the end (a cipher using multiple techniques), but fourth quarter has started off pretty strong for me so there’s not as much time to write. 😦 If you’d like, feel free to check back tomorrow because I’ll probably edit this post and add more content later today! I really want to try my hand at creating a compound cipher of some kind because I think it’d be fun for classes to collaborate on and solve.

Until then, happy decoding! See you again tomorrow or next week. 🙂

Welcome back!

Hey there — welcome back from spring break! (It was far too short, I know.)

For those of you who are still with us, challenges are going to pick back up this Thursday (March 23rd). I wanted to take today to give you a rundown on how the rest of the da Vinci Challenge will go.

Like I mentioned, this week I’ll be putting up a challenge about ciphers on Thursday, and for the week of March 27th, we’ll be wrapping things up with the rest of da Vinci’s principles. The week after that (April 3rd-7th) will be the grand finale of this whole endeavor. I don’t want to spoil the surprise for you guys, but it’ll consist of a single, week-long challenge that’s a lot more hands-on and interactive than all of the previous challenges. (I’ll be reaching out to teachers later this week or early next week to discuss it, so be on the lookout for that.)

Thanks to everyone who’s participated, commented, and stuck with me this far! I really appreciate it. This has been a lot of fun to create, and I’ve loved all of the amazing feedback.

So, two more weeks to go! See you again on Thursday, everyone. c:

Week 4: Postponed

I thought about following through with the Wednesday/Thursday challenges this week, but I think we all need a bit of a break instead. I’ve decided to just push what I had planned for this week back until after spring break. With midterms going on, there just isn’t very much time to devote to these things! Posts will start back up after spring break (March 20th), and since I’ve decided to skip this week, the challenges will now end the week of April 3rd.

Thanks for your participation so far, and have a great break! (Until then, good luck with your midterms of course.)

Challenge 7: Postponed!

Hey everyone —

I just wanted to apologize in this post because Challenge 7 is being postponed until tomorrow (Wednesday, March 8th). Afterwards, the second challenge will continue on Thursday as usual.

Hopefully this doesn’t cause too many issues, and thanks for your patience! It’s the week before break, so my work has caught up with me a bit. I appreciate that you’re still participating!

–Carly

Challenge 6: Embracing mistakes

Continuing with our study of dimostrazione (“demonstration”), today we’re going to talk about making mistakes. Often in school, many students are afraid to speak up in class because they’re afraid of saying the wrong answer — we’re afraid of making mistakes because we don’t want to be ridiculed. Throughout all of my classes, I’ve never seen anyone ridiculed for speaking up with a “wrong” answer (if anything, the rest of the class is thankful that they don’t have to answer since that person took the blow), but it’s still an irrational fear that’s very common.

This fear of making mistakes is really harmful to the learning process, however. Making mistakes is one of the best ways to learn a new subject (especially when it deals with problem-solving) because you’ll usually remember the mistake you made and won’t repeat it. Leonardo da Vinci made a lot of mistakes throughout his work. He often doubted himself and questioned the value of what he was doing, but the important thing is that he kept working through all of that. He would write little “affirmations” throughout his notebooks, like these:

• “Obstacles do not bend me.”
• “Every obstacle is destroyed through rigor.”
• “I shall continue.”
• “I never tire of being useful.”

Those are really simplistic, but they’re important because they motivated Leonardo to persevere despite his adversity.

Affirmations

Since this is third quarter and midterms are coming up (sorry about the reminder), I’m sure that we’re all feeling pretty stressed out and exhausted right now. I thought it’d be nice to take a day and just write some of these affirmations to serve as motivation for getting through this next week. It’s a good way to strengthen your resilience and help you get through some of your biggest challenges, and it ties in nicely with this week’s da Vincian principle.

I’m not going to give you too many guidelines for these affirmations because I want you to be creative, but they seem to work the best when you frame them in more of an emotional way. For example, try saying “I feel patient with myself.” rather than “I am patient with myself.” The response is going to be slightly different. Michael J. Gelb recommends this because he states that it helps you “access your heart center.” I think that’s kind of excessively sentimental, but it’s worth giving it a shot. If you’d rather not, feel free to just write any affirmations that come to your mind. Here are some examples to get you started, again from Michael J. Gelb’s book:

• I trust the knowledge to be here when I need it. (Maybe embody this one for those midterms!)
• The brilliance of my mind manifests in ways that surprise me. (This one is a bit pretentious sounding, but I’m including it anyway.)
• I acknowledge my ability to learn intuitively.
• I feel curious on how to… (solve this problem, learn this subject, etc.).
• I feel worthy in my contribution to class/school/the world.
• I feel pride when others view my work.
• I trust my inner self.
• I feel deserving of happiness.
• I feel joy in the happiness of others.

So, I know that a lot of those are pretty sappy, but maybe they’ll give you a head start with this. When I do this challenge, I’m probably going to take my inspiration directly from Leonardo since his affirmations sound a lot cooler, so feel free to do that as well! If you’re a more emotionally-minded person, the ones I just listed might work better for you. It all really comes down to your personality and the nature of whatever challenges you’re working through right now.

Anti-Role Models

One other really good way to learn from mistakes is to let others make them for you. This bypasses a possible fear of making mistakes while still giving you all the same benefits.

We all have role models in our lives, but we don’t often think about “anti-role models” as well. I’m sure that we’ve all known some person, whether it be teacher or a coach or someone else entirely, who’s done things in a way that we don’t like. In the context of school, it could be a teacher who ignores questions and just lectures on in a monotone voice or a coach that humiliates players. From these people, we can learn what not to do in our own lives.

Take a moment to think about some people who have made mistakes that you’d like to avoid. One tricky thing about this is that sometimes these “anti-role models” also have positive qualities, and that’s to be expected. Everyone makes mistakes at times, including the best and nicest people. What you need to do is figure out which aspects of your role models you’d like to emulate and which aspects you’d rather avoid.

And of course, I don’t think I have to tell you this, but don’t go up to people and tell them that they’re your “anti-role model.” This activity isn’t meant in a malicious way at all, and that would be such a mean thing to say. Whether it’s learning from mistakes that you’ve made or that someone else has made, it’s important to remember that we’re all human and that we all make a lot of mistakes that we can learn from. We just need to support each other through these things and help everyone make the most of their situation.

Happy Thursday!

Here’s a dimostrazione survey as well that you can take if you have the time! It’s 11 questions that should only take about two minutes, and it’d really help me with the presentation that I’m preparing on this project. Thank you!

Also, make sure to check back next Tuesday if you can! I’m planning on briefly departing from these writing/thinking exercises to do a really cool “cipher challenge” because ciphers are super interesting and fun to work with. I’m excited to see how you guys do.

See you next week.

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Challenge 5: Objective opinions

This week we’re moving on to another one of the seven da Vincian principles, Dimostrazione. Demonstration. Michael J. Gelb defines dimostrazione as “a commitment to test knowledge through experience, persistence, and a willingness to learn from mistakes.” One quality that I think makes a teacher great is the ability to help the student learn for themselves, and this principle is really the key to doing that — it embodies the idea that we should learn from our mistakes and stay determined to continue learning and exploring new things.

Before going on, here’s a “dimostrazione self-assessment” that I’d be super appreciative if you took. It has 11 yes/no questions (save for the last one) that should take two minutes. From now on, I’ll put a survey like this before the challenges and after them to see if there’s any improvement over the week.

For this challenge, I’m mainly going to be focusing on the “commitment to test knowledge.” One of the most significant aspects of the Renaissance was the transformation of what seemed to be fundamental knowledge, assumptions, or beliefs. Leonardo was willing to challenge these widely accepted ideas and as a result, made several revolutionary breakthroughs. However, he knew that challenging the ideas of others first meant challenging your own views and stated, “The greatest deceptions men suffer is from their own opinions.” So, why not examine some of our own opinions, assumptions, and beliefs?

It’s easy sometimes to become so rooted in our opinions and fundamental ideas about the world that they can deceive us or limit our originality. We all have opinions about a wide variety of topics: human nature, ethics, politics, sexuality, religion, medicine, the meaning of life, art, marriage, parenting, history, foreign affairs — you get the picture. We have an opinion on nearly every aspect of our lives, even if it’s not fully conscious. Some of us have stronger opinions about things than others, but an opinion is an opinion. However, often we don’t stop to think about how we formed our opinion on that topic. Where did our information come from? Was it biased? Did we grow up in an environment that fostered these beliefs?

To start off, choose at least three topics that you’d like to examine further — you can take those topics from the ones that I’ve listed above or choose any other topics that you’re passionate about or have strong opinions on. Afterwards, I’d like you to write down at least three ideas, opinions, assumptions, or beliefs for each of those topics. Here’s an example from Michael J. Gelb’s book:

Human Nature

• “I believe that people are basically good.”
• “I believe that behavior is predominantly determined by genetics.”
• “It’s human nature to resist change.”

After you’ve done this for each of your chosen subjects, ask yourself this:

• How did I form this idea?
• How firmly do I believe it?
• Why do I maintain it?
• What would make me change my belief?
• Which of my beliefs inspire the strongest emotions?

Afterwards, you can consider the role of these sources in forming your beliefs:

• Media: books, online sources, television, radio, newspapers, magazines
• People: family, teachers, physicians, religious leaders, bosses, friends, and associates
• Your own experiences

Try to determine which sources you get most of your information from — these are going to be the most influential to your personal beliefs. And, see if any of the beliefs you’ve listed above have no “verification” or aren’t backed by any of these sources! It’s interesting to see if some beliefs we hold are simply taken from quickly reading something or hearing something in passing.

You can stop here if you’d like, but if you have time, here’s another interesting part to this challenge:

Write down one of your original beliefs from the previous exercise that you have the most emotional investment in. Back when we were studying curiosity, we learned how to reframe questions from different perspectives. We can do that with our opinions and beliefs as well! It’s all part of Leonardo’s quest for objective knowledge. So, try the following:

1. Make the strongest possible argument against the belief you wrote down.

2. Try reviewing your belief from a distance by asking yourself: would my views change if I…

• lived in a different country?
• came from another religious, racial, economic, or class background?
• was twenty years older/younger?
• was a different gender?

3. You can also talk with other people about your beliefs and see how their perspectives differ. It’s always great to learn from those around you and get different points of view if you can!

And remember, it’s not necessarily a bad thing if some of your opinions don’t have a fact basis or change if your circumstances change. All of us have unique backgrounds and experiences, and as admirable as it is, it’s nearly impossible to have all of your beliefs grounded in fact or reason because even the most objective of us can be influenced by emotion. Either way, it’s a good exercise to stay humble and stop to examine some of our more deeply-held beliefs from time to time. Rather than become rooted in one way of thinking, it’s nice to explore some other perspectives!

That’s all that I have for today, but I hope it went well for you guys! Have a nice Tuesday, and I’ll see you again on Thursday.

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Week 2 Overview

Hey everyone! Hope your Monday is going well. This week we’re moving on to another da Vincian principle: Dimostrazione. Demonstration.

From Michael J. Gelb’s books, dimostrazione represents “a commitment to test knowledge through experience, persistence, and a willingness to learn from mistakes.”

Leonardo famously referred to himself as discepolo della esperienza, a disciple of experience. He believed that experience (specifically, your own experience) was the source of wisdom, so he questioned much of the accepted theories of his time and preferred to learn and discover things by himself. Leonardo was also remarkably practical — it was his independent spirit combined with his practicality and curiosity that led him to champion originality and think for himself by rejecting imitation and questioning authority. He considered the work of others as “experience by proxy” that should be carefully studied and ultimately tested through his own experience.

Leonardo states, “No one should imitate the manner of another, for he would then deserve to be called a grandson of nature, not her son. Given the abundance of natural forms, it is important to go straight to nature…” This idea mainly applied to artwork — one should draw straight from nature rather than drawing from the works of another. However, it can be applied to nearly every other subject as well. This type of thinking was especially remarkable in Leonardo’s time period, where most assumed that “all knowledge was already known.”

Even so, Leonardo maintained a library and knew that it was also important to study the classics of any subject he was interested in. And, learning from experience also means learning from mistakes. Not all of your experiments and attempts to learn subjects throughout life will be successful, so it’s important to stay humble and determined throughout failures and continue to learn and explore.

Tomorrow we’ll start strengthening our sense of dimostrazione by examining our own opinions and beliefs! Until then, have a good one.

Challenge 4: Perspectives

Thanks for all of the comments on the last challenge! I really appreciate them, and I’m planning on responding to them all but haven’t gotten around to it yet because of how busy this week has been. But let’s get on to the challenge for today!

Curiosity is all about asking questions. Yesterday, we learned how to ask effective questions, but most of them were from your own perspective because they were about things that mattered specifically to you. While this approach works fine for some situations, successful problem solving often requires us to reframe the initial question to look at things from different points of view. One psychologist, Mark Brown, used this example:

“How do we get to water?” vs. “How do we get the water to come to us?”

This was a shift in questioning as a result of a major transformation in human societies — from nomadic humans concerning themselves with finding sources of water and agrarian humans wanting to figure out how to direct nearby water to their fields.

For today’s challenge, I’d like you to either look back at your questions from yesterday or come up with a whole new question and then try to reframe that question to look at things from another perspective by focusing on different things.

This can be pretty tricky to do, so I think it’d be best if you either tried this out as a class or broke up into small groups for this. To give you some ideas, you could try reframing the question to what you think a child would care about vs. what a teenager would care about vs. an adult vs. an older person. You could also take a broader questions like, “What is the meaning of life?” and change it to, “How can I make my life meaningful?” Those two questions are going to have vastly different answers.

The ultimate goal of this challenge is to improve your ability to ask questions without just limiting yourself to your own point of view. It’s impossible to be completely objective, and often when we ask questions, we’re biased to asking about the parts of the topic that we care about. It’s important to look at things from the perspectives of other people to come up with the best answers and, if you’re doing this for a paper or something, to be able to connect with as much of your audience as possible.

Good luck!

And, there are a lot of other cool activities that improve you curiosity that I wanted to include but didn’t think would fit in 5-10 minutes for a classroom environment. I’ll edit this post a bit later to add a list of them here! For now, just focus on the challenge above.

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Challenge 3: Curiosità and How to Ask Questions

This week we’ll be focusing on one of da Vinci’s seven principles, curiosità. Curiosity. Humans are naturally curious — more so as children, of course. However, I think that retaining that sense of curiosity throughout your time as a student and as an adult is extremely important. You need to be willing to ask a lot of questions about the world in order to learn as much as possible. So, let’s get started with some activities to bolster curiosity!

First off, I’ve created a kind of “Curiosity Self-Assessment” for everyone to take. I’ll have you take this survey today, at the start of the challenges, and again on Friday, at the end of the challenges, to see just how much your ability to be curious changed as a result.

Here’s the link to the survey!

*Hey everyone, I couldn’t find any free survey websites that let me add more than 10 questions, so you still won’t be able to take this. I’m going to see if I can get this website unblocked sometime so that I can use it in future posts.

Now that that’s out of the way, we can get into some more interesting things.

Asking Questions

Ideally for this challenge, I’d have everyone make a list of 100 or so questions that they have about life or the world around them, but there’s definitely not enough time for that in ten or so minutes. Instead, I’d like you to come up with 5-10 questions about anything you’d like. They can be about your life, your goals, your passions, current events, social issues — anything that you’d like to learn more about or explore.

From this list, pick the one that interests you most. Now, try to come up with follow-up questions. No answers yet, just questions that expand upon that initial question. Here’s an example from one of Michael J. Gelb’s books when he did this activity:

Topic question: How does a bird fly?

Follow-up questions:

• Why does it have two wings?
• Why does it have feathers?
• How does it “take off”?
• How does it slow down?
• How does it accelerate?
• How high can it fly?
• When does it sleep?
• How good is its eyesight?
• What does it eat?

I think you can get the picture from there. Don’t be afraid to ask simple or naive questions — da Vinci’s questioning was extremely simplistic at times when he was trying to get to the root of a problem. So, try it out now! See how it goes, and if you’d like, post your questions in the comments below when you’re finished.

I think that in school, we’re often taught that answers (specifically, the correct answers) are more important than questions. It’s easy to see, then, how most of us lose our childlike sense of curiosity, and it’s sad that a place that’s supposed to be all about learning and fostering a love for learning can have such an adverse effect on it. Of course, the right teachers can make up for that, but one bad experience has the potential to ruin things for a student. Regardless, that’s what this first challenge is all about — focusing on the questions rather than the answers. You need to be able to develop good, essential questions with anything you do before you can come up with meaningful answers.

Stream of Consciousness Writing

Now that you have a better sense of what your topic question is all about, we can take a moment to write about it more in-depth. I’d like you to try something known as stream of consciousness writing — it’s about what you’d expect from the name. Using the topic question from the previous activity, take a minute to really contemplate what it’s asking, and then write your thoughts and associations as they occur without stopping to edit anything.

This can be hard to do if you’re prone to taking the time to carefully craft each sentence and edit as you go (I’m guilty of this with everything that I write), but it can be extremely rewarding. The trick to effective stream of consciousness writing is to keep your pencil moving. Roll with the mistakes and let your thoughts flow freely to the paper — don’t stop to erase or think about what to say next, just write. You can type this out as well, of course, as long as you type without stopping.

Now it’s time for you to try it out — take five or ten minutes (depending on how much time you have available) and write continuously about the topic question from earlier. You can write more questions, why the topic interested you, what you think would be most important to research about it, why other people should care, literally anything that comes to your mind. Don’t worry if your writing goes a bit off-topic or seems nonsensical and redundant! Gelb states in his book that this is actually a sign that you’re “overriding the habitual, superficial aspects of your thought process.” He states that through stream of consciousness writing, “you’ll eventually open a window through which your intuitive intelligence will shine.” You might not get that feeling from just one session of trying this, but I’m sure that with enough practice you could tap into some part of your mind that helps you with both problem solving and thinking more creatively.

Best of luck to everyone! See you again on Thursday.

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Overview post

Hey everyone,

I forgot to schedule the Monday post for this morning, so it likely won’t be up until after school today. I’m really sorry for the inconvenience, and I’ll be doing my best from now on to double-check these things so that this doesn’t happen again. If you’d like, you can have your students check in tonight to read the post, but it’ll probably be best to just glance over it tomorrow before you start the challenge.

Hope your Monday goes well regardless! I’ll make sure the challenges go up on time for Tuesday and Thursday, no worries.