Tag Archives: quotes

Map of Mathematics

I came across this Map of Mathematics in a TikTok where people working in the field of Mathematics were all sharing how their fields intersected different parts of the map. Here is the video:

I love how the concepts and fields of study connect and interconnect.

The the video starts with a ‘stitch’ of a Tiktok user asking, “Did everyone know that Mathematicians are, like, discovering new Math?”

This plays into a recent post in which I state that Math is ‘Discovered more than invented‘. There is so much more to discover, and I believe, thanks to my conversations with Joe Truss, that geometry is the foundation of Math. But math is a hard conceptual language with which to understand the geometry… and if we study the geometry we can understand the universe without having to do the hard math. Oh, and if Mathematicians better understood the geometry they could discover new Math a little faster.

In the Map of Mathematics, Geometry is the key.

Discovered more than invented

Is Math invented or is it discovered? Is Math a human, or at least biological construct that helps mammals understand the world we live in? Or does it exist inherently in the universe and is it revealed to us through curiosity and scientific discovery?

I’ve shared my fascination in playing, learning, and discovering secrets held in Geometry (here and here) with Joe Truss.

Recently I watched a video that quoted Galileo Galilei:

“Mathematics is the language with which God has written the universe.”

With everything Joe and I have been playing with, I thought of an adaptation of this quote:

The universe is written in the language of geometry, and Mathematics allows us to measure it.

When I shared this with Joe, he tweaked it:

The universe is written in the language of geometry, and Mathematics allows us to take its measure.

I like this because it speaks to the idea of Math being discovered, of it being inherent because it is present in the geometry. It is Geometry that is the underlying language. Math is the alphabet, the universe is written in geometry. This is why Pi pops up where you don’t expect it; why the Fibonacci sequence is prevalent in nature; why we can land a ship on the moon and Mars; and even why our religious symbols come out of geometry.

The challenge we have is that we don’t fully understand the geometry, sometimes rather than discovering the true essence of the mathematics, we have to invent approximations that help us make sense of universe. Understand the geometry and maybe we can remove infinities and irrational numbers in our calculations… Understand the geometry, and the math becomes more accurate. Understand the geometry and maybe we can unify our theories that currently seem to contradict themselves.

Discover the geometry and we discover the math behind it, no longer needing to invent approximations of the math to translate the geometry into a world of calculations and numbers that don’t quite fit with they universe we are trying to describe. When we discover the geometry, we no longer needs to invent Math, the geometry allows us to take its measure… And in fact we can explain the universe with the geometry, and then we don’t have to be a physicist or mathematician to understand it.

A Quote on Judgement

“We judge others by their actions, but we judge ourselves by our intentions.”

I saw this quote and wondered who said it? I was lead by my search to Stephen Covey, “We judge ourselves by our intentions and others by their behavior.”

This made me think about all the things I have the good intention to say and to do, but I don’t follow through. Looking at this from the outside, there is no action, just unrealized intention. For example, I wanted to show my appreciation or write a thank you card, but never got around to it; good intentions, but to anyone else, no action. In fact, lack of action could actually be judged as lack of appreciation. My intentions were good but…

We very often don’t know another person’s intentions. We judge their behaviours and actions (or lack there of) and assume their intentions. And we know our intentions and don’t always see that our actions don’t represent what those intentions are.

This quote is a reminder not just to think about what another person’s intentions are, but also for us to think about how our actions truly represent our behaviours and actions to others. Are we living a congruent life where are actions demonstrate our intentions? Because good intentions are not enough if we aren’t expressing them.

A quick life lesson

“If I couldn’t handle not being good at something, then how can I consider myself a successful person?” ~ Gerald Hodges

Watch this story about a young man who picked a sport that was the most challenging one he could choose, to prove to himself that he can find success when challenged.

https://fb.watch/bROEBEZ6cB/

Even if he didn’t get his team to qualify for the state championships, which he did, this is the kind of attitude I want to see in my kids and the kids in my school.

No vs Know

Sharing some wisdom from George Couros and his mom, who always told him ‘it never hurts to ask, because the dreams you have are sometimes just a question away’. Here is the quote, and I really love it:

“It’s better to hear ‘no’ than to never know.”

When people meet me, they don’t often know that I’m an introvert. I used to spend hours living in my own head, and I still go there too often. Solitude is my friend, and I’d rather hang out with one friend, maybe 2, but I tune out crowds and would rather be alone than be in a group.

As a kid, and early into adulthood, I would build scenarios in my head about what could happen, but I wouldn’t speak up. I’d turn down opportunities that would have been great. And I’d not ask a simple question that could have opened doors for me, or provided my with opportunities. I’m still learning how to ask for help rather than doing a lot of work myself.

It’s not even that I fear the ‘no’, it’s the idea of asking that holds me back. So, maybe that’s why I love this so much… because I can think of many times in my life that hearing ‘no’ would have been better than not knowing.

Question my answers

Here is a wonderful quote from Derek Sivers, in a podcast interview on ‘Far Out‘.

“I like to ask myself questions, and then most importantly I like to question my answers. I like to doubt myself, and I assume that I am accidentally lying to myself. I assume that the person speaking is a liar, meaning me. So I like to dissect my beliefs and habits and actions, and see if they might be hollow.”

Later he talks about wanting to do something for a really long time and says that if that’s the situation you are in, then you really don’t want to do it. That is to say, if you really wanted to do something, then you’d do it. If you keep saying you want to do it but you don’t, you aren’t being truthful to yourself.

What do you really want to do? Whatever your answer… question it!

—–

I’m a huge fan of Derek, you can find his books, blog, and podcast all here: https://sive.rs.

Read Fiction

It was probably the January semester, 1989 that I took a Rural Extension course on Leadership, at the University of Guelph, when I met Professor Al Laozon. He was my first prof to have us call him by his first name. The first prof to have us sit in a circle, despite there being about 24-26 of us in the class. He listened as much as he talked. And he quickly became a friend.

Al had us read The Tao of Leadership, which to this day is still one of my favourite books, and one that I call my ‘Leadership Bible’.

And while his class was one of my more memorable courses at university, it was his office hours chats that I most enjoy and remember. They were filled with insights and wisdom, but also with the things friends talk about, like our childhoods and stories of family members.

Yesterday I wrote a post about my struggles with going through the motions of my healthy living routines with low energy and effort. It helps me to share these things ‘out loud’ and I was able to push my workout harder than I have in weeks as a result. But another benefit of sharing is getting insights from readers, and Al was kind enough to share a comment. With respect to mediation I said,

“I’ve missed more meditations in the last 6 weeks than I’ve missed for the rest of the year. When I do meditate, it’s more like I am am having a quiet moment to think about random things. I can’t seem to focus on my breath any more than I could when I started my daily meditation routine almost 3 years ago.”

And to this Al said,

“Our routines, like life in general, ebbs and flows of its own accord. Be patient. I have had a meditation practise since 1991 and some days are good and other days, well the monkeys are running amok in the “store” despite my desire for them to quiet themselves. Somedays you just go with it.“

I also said, about listening to audiobooks,

“I’m an avid audio book listener, and I usually get through almost a book a week unless I am reading something that’s really long, then it could be two weeks. But I just took three weeks to listen to a 5-hour long book, and didn’t feel I got as much out of it as I had hoped.” And later added, “I’ll start a fictional novel even though I usually wait for the holidays to choose a book that I’m not learning from.”

To which Al commented,

“As for reading fiction, there is much to be learned from fiction. As I have often said, novelists often have more insight into humans and their behaviour than do the best of social scientists. Do not deprive yourself of that which can offer insight, nor dismiss it as simple entertainment or distraction. The arts offer much in terms of insights into our collective journey. After all, there is no greater means of learning than a good story, be it true or fabrication. I recently wrote elsewhere that science offers us knowledge, but the arts offer us truth. I will take truth any day over knowledge.”

All these years later, and miles apart, but Al is still my teacher, advisor, and wise friend, sharing insights I need to hear.

Usually I only ‘let myself’ read fiction on holiday breaks. But I’ve been drawn a lot more to fiction in the last couple years. It started a couple Christmas breaks ago when I received some free ebooks from Audible and I listened to a science fiction novel and got hooked into an epic series. Then I listened to a couple books that I never would have selected for myself, just because they were free… and I loved them. But reading fiction outside the holidays always came with a little self-imposed guilt.

Not anymore. Al’s words have given me permission to indulge guilt free. I will choose more fiction. Let me know if you have a favourite you’d like to share.

“Science offers us knowledge, but the arts offer us truth. I will take truth any day over knowledge.” ~ Al Lauzon

20 years experience

I heard a question yesterday that really made me think. The question was, “Does he have 20 years experience, or one year of experience repeated 20 times?”

Years of experience is different from years of growth. Many students finish grade 12 and graduate. Some did the bare minimum, some got really good at ‘doing school’ year after year, some come out lifelong learners ready for anything that comes their way, and will actually seek out new learning experiences.

The same can be said for teachers, doctors, lawyers, and tax accountants. Some get good at doing the same thing over and over, some are constantly learning and becoming better… many are a mix between the two.

What are you really good at? How long have you been doing it? What do you suck at, despite putting years into it? And for the latter, what are you going to do differently, so that you are adding to your experience, and not just your years of doing it.

I’ll never look at expertise the same again… ‘years of experience’ comes in many different forms.

In times of change

I recently shared this quote with a few teachers when I gifted them a book.

“In times of change learners inherit the earth; while the learned find themselves beautifully equipped to deal with a world that no longer exists.” ~ Eric Hoffer

In a conversation with another educator this weekend we talked about the fact that we both knew some people who were terribly upset about technology upgrades because it took them out of their comfort zones. This isn’t just a fear of change, it’s also a frustration about not having everything where it ‘should be’. It can be hard to lose your favourites on your browser, if you never signed in and saved them. It can be frustrating to sign into all your accounts again, or to re-setup all your quick shortcuts (again).

But maybe this becomes the time that this person can learn to sign into their browser and take their favourites with them wherever they go. Maybe they can begin to use the cloud to save their documents rather than their hard drive. But they won’t do this without help.

We can share fancy quotes about the importance of lifelong learning, but if we aren’t helping to foster adult learners on their journey, then are we fostering a learning culture ourselves? Everyone is on their own journey with their own comfort levels. When we push people out of their comfort zones, we need to provide the scaffolding and support so that they can learn and adapt. That doesn’t mean that we keep people in their comfort zone, that we don’t make the need to change… But it does mean that too much frustration without support leads to people shutting down rather than being willing to change.

That unlearning thing ain’t easy

“The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn.” ~ Alvin Toffler

I love this quote, it speaks to the need to embrace change, and to understand that best practice is still just practice. However as easy as it is to understand this idea, it’s much harder to acclimate to. Especially the unlearning part.

I’ve been back into archery since the winter break, got a personal best score of 280 recently, and have been able to duplicate that score a second time. (Scoring is 10 rounds of 3 arrows, with a max score of 10 points per arrow, totalling 300 for a perfect score.) However, I was using a very bad technique with my thumb squeezing the trigger rather than using backward tension on my hand and arm to trigger the release. Since trying to do this properly, I’ve been struggling more and scoring between 267 and 274.

Today I scored a 267, but I was also able to score an X-X-10 three times while practicing. I had been unable to score a perfect 30 in a round for weeks. (An ‘X’ is 10 points but also signifies that I was able to get the arrow in or on the line of the center ‘X’ ring that is the size of a penny, shooting from 18m or 20 yards away.)

While trying to work on my release these past couple weeks, my scores have been lower, and my ability to hit the ‘X’ has been infrequent. But I know that if I continue to punch the trigger with my thumb, I will not shoot nearly as high of a personal best score in the future. My trigger pulling could show some short term gains, but those gains will limit me later on. The problem is, as I unlearn doing this, my scores have gone down.

Unlearning something is hard. Right now there are many things I need to focus on, and when I’m trying to change my muscle memory, my other muscles do funny things. For instance, my bow hand has been gripping the bow tighter, rather than being relaxed, while I think about my back-tension release. And when I relax my hand after drawing, I find it hard to not relax my arm, causing me to have less tension holding my bow ‘hard against the wall’, meaning keeping pressure on the bow’s cams at the back of a full draw.

Without talking about archery technique specifically: while I focus on unlearning a bad habit, my body, accustomed to doing things wrong, doesn’t know how to put all the good moves together. Unlearning one technique means not just learning something new, but also relearning other things as they related to the old vs new learning.

This dip in my scores is part of the unlearning process, and it’s not easy to go through. When we practice new skills, we want to see a quick payoff. But sometimes we need to recognize that unlearning isn’t nearly as easy as learning, and the payoff comes from the practice itself, and not immediate progress. I can focus on my technique, and unlearning a bad habit, or I can worry about my score right now… what I can’t do is both at the same time.