## 👓 Limits and Colimits, Part 1 (Introduction) | Math3ma

I'd like to embark on yet another mini-series here on the blog. The topic this time? Limits and colimits in category theory! But even if you're not familiar with category theory, I do hope you'll keep reading. Today's post is just an informal, non-technical introduction. And regardless of your categorical background, you've certainly come across many examples of limits and colimits, perhaps without knowing it! They appear everywhere - in topology, set theory, group theory, ring theory, linear algebra, differential geometry, number theory, algebraic geometry. The list goes on. But before diving in, I'd like to start off by answering a few basic questions.
A great little introduction to category theory! Can’t wait to see what the future installments bring.

Interestingly I came across this on Instagram. It may be one of the first times I’ve seen math at this level explained in pictorial form via Instagram.

https://www.instagram.com/p/Bdd8vmfBQvG/

I want to read 42 books in 2018.

I sometimes feel guilty about failing miserably at these based on the way GoodReads counts their books vis-a-vis finishing complete books, particularly when I’m often reading such dense technical books in which reading a page a day is a near Herculean task.

Thus, because I can have finer control of things on my own website, I’ll try to break things out on a more granular level.

I want to read (aka work my way through) 2-3 technical textbooks in 2018.
I want to read 10 non-fiction books in 2018.
I want to read 20 fiction books in 2018.
I want to read 10 juvenal fiction/literature books in 2018.

## 📗 Read pages i-14 of The Theoretical Minimum: What You Need to Know to Start Doing Physics by Leonard Susskind and George Hrabovsky

📖 Read pages i-14 of The Theoretical Minimum: What You Need to Know to Start Doing Physics by Leonard Susskind and George Hrabovsky (Basic Books, , ISBN: 978-0465028115)

I’d read a portion of this in the past, but thought I’d circle back to it when I saw it sitting on the shelf at the library before the holidays. It naturally helps to have had lots of physics in the past, but this has a phenomenally clear and crisp presentation of just the basics in a way that is seldom if ever seen in actual physics textbooks.

### Highlights, Quotes, & Marginalia

Lecture One: The Nature of Classical Physics

There is a very simple rule to tell when a diagram represents a deterministic reversible law. If every state has a single unique arrow leading into it, and a single arrow leading out of it, then it is a legal deterministic reversible law.

Highlight (yellow) – 1. The Nature of Classical Physics > Page 9

There’s naturally a much more sophisticated and subtle mathematical way of saying this. I feel like I’ve been constantly tempted to go back and look at more category theory, and this may be yet another motivator.
Added on Wednesday, January 4, 2018 late evening

The rule that dynamical laws must be deterministic and reversible is so central to classical physics that we sometimes forget to mention it when teaching the subject. […] minus-first law [: …] undoubtedly the most fundamental of all physics laws–the conservation of information. The conservation of information is simply the rule that every state has one arrow in and one arrow out. It ensures that you never lose track of where you started.

Highlight (yellow) – 1. The Nature of Classical Physics > Page 9-10

This is very simply and naturally stated, but holds a lot of complexity. Again I’d like to come back and do some serious formalization of this and reframe it in a category theory frameork.
Added on Wednesday, January 4, 2018 late evening

There is evan a zeroth law […]

Highlight (gray) – 1. The Nature of Classical Physics > Page 9

spelling should be even; I’m also noticing a lot of subtle typesetting issues within the physical production of the book that are driving me a bit crazy. Spaces where they don’t belong or text not having clear margins at the tops/bottoms of pages. I suspect the math and layout of diagrams and boxes in the text caused a lot of problems in their usual production flow.
Added on Wednesday, January 4, 2018 late evening

##### Guide to highlight colors

Yellow–general highlights and highlights which don’t fit under another category below
Orange–Vocabulary word; interesting and/or rare word
Blue–Interesting Quote
Gray–Typography Problem
Red–Example to work through

## Reply to Why Trump? by George Lakoff

Replied to Why Trump? by George Lakoff (George Lakoff)
Donald Trump is winning Republican presidential primaries at such a great rate that he seems likely to become the next Republican presidential nominee and perhaps the next president. Democrats have little understanding of why he is winning — and winning handily, and even...
I appreciate the logic you’ve laid out on multiple levels here. I wish it were more widely viewed and shared. There’s an additional linguistic trick which Trump seems to take heavy advantage of as well: doublespeak. I’ve laid out some of the details here: http://boffosocko.com/2016/09/30/complexity-isnt-a-vice-10-word-answers-and-doubletalk-in-election-2016/ though I’ve got a slightly more nuanced approach now a year on and with additional data.

I enjoy your take on Direct vs. Systemic Causation which I bundle a bit more simply under the concept of “complexity”. The example I provide certainly fits well into your argument. It also seems to explain the political divide, which also follows the same party lines, in the ways the country views science in general, but the ideas of climate change and evolution specifically. While the evolution portion may be in direct conflict with the religious right, it doesn’t explain why so many don’t believe in the sciences generally or why they would be climate change deniers. Direct causation would seem to supersede the simple religion argument and explain the backlash against the sciences in general.

## Reply to a Comment on Supporting Digital Identities in School

Replied to Comment on Supporting Digital Identities in School by Christina Smith (Read Write Respond)
Your post reminded me of a challenge I see every time Couros posts about students having those three aspects of a digital identity: no matter how much we as educators may encourage this, ultimately it is up to the students to make it part of their lives. I have been blogging with my students for some years now, and when it is not a class requirement, they stop posting. I think part of this digital presence that we want students to establish – the \”residency,\” as Robert Schuetz said in the recent blog post that led me here (http://www.rtschuetz.net/2016/02/mapping-our-pangea.html) – is not always happening where we suggest. I know my students have an online presence – but it\’s on Instagram and Snapchat, not the blogsphere. Perhaps instead of dragging kids on vacation to where we think they should set up shop, we need to start following them to their preferred residences and help them turn those into sturdy, worthy places from which to venture out into the world.
This is certainly an intriguing way to look at it, but there’s another way to frame it as well. Students are on sites like Instagram and Snapchat because they’re connecting with their friends there. I doubt many (any?) are using those platforms for learning or engagement purposes, so attempting to engage with them there may not translate for educators. It may have the colloquial effect of “I’m on Snapchat because my parents aren’t; if my parents join I’m either going to block them or move to another platform they’re not on.” Something similar to this was seen in cultural teen use of Facebook as parents swarmed to the platform over the past decade. To slightly reframe it, how many high school teachers in the past have seen students in the hallways between classes socializing and thought to themselves, “I should go out and teach in the hallway, because that’s where the students are and they seem alert?”

It might also shed some light on our perspectives to look at what happens at the end of a quarter or semester in most colleges. I always remember book sellback time and a large proportion of my friends and colleagues rushed to the bookstore to sell their textbooks back. (I’ll stipulate the book market has changed drastically in the past two decades since I was in University, but I think the cultural effect is still roughly equivalent.) As a bibliophile I could never bring myself to sell books back because I felt the books were a significant part of what I learned and I always kept them in my personal collection to refer back to later. Some friends I knew would keep occasional textbooks for their particular area of concentration knowing that they might refer back to them in later parts of their study. But generalizing to the whole, most students dumped their notes, notebooks, and even textbooks that they felt no longer had value to them. I highly suspect that something similar is happening to students who are “forced” to keep online presences for coursework. They look at it as a temporary online notebook which is disposable when the class is over and probably even more so if it’s a course they didn’t feel will greatly impact their future coursework.

I personally find a huge amount of value in using my personal website as an ongoing commonplace book and refer back to it regularly as I collect more information and reshape my thoughts and perspectives on what I’ve read and learned over the years. Importantly, I have a lot of content that isn’t shared publicly on it as well. For me it’s become a daily tool for thinking and collecting as well as for searching. I suspect that this is also how Aaron is using his site as well. My use of it has also reached a fever pitch with my discovery of IndieWeb philosophies and technologies which greatly modify and extend how I’m now able to use my site compared to the thousands of others. I can do almost all of the things I could do on Facebook, Twitter, etc. including interacting with them directly and this makes it hugely more valuable to me.

The other difference is that I use my personal site for almost everything including a wide variety of topics I’m working on. Most students are introduced to having (read: forced to maintain) a site for a single class. This means they can throw it all overboard once that single class is over. What happens if or when they’re induced to use such a thing in all of their classes? Perhaps this may be when the proverbial quarter drops? Eventually by using such a tool(s) they’ll figure out a way to make it actively add the value they’re seeking. This kernel may be part of the value of having a site as a living portfolio upon graduation.

Another issue I often see, because I follow the space, is that many educational technologists see some value in these systems, but more often than not, they’re not self-dogfooding them the same way they expect their students to. While there are a few shining examples, generally many teachers and professors aren’t using their personal sites as personal learning networks, communications platforms, or even as social networks. Why should students be making the leap if their mentors and teachers aren’t? I can only name a small handful of active academic researchers who are heavily active in writing and very effectively sharing material online (and who aren’t directly in the edtech space). Many of them are succeeding in spite of the poor quality of their tools. Rarely does a day go by that I don’t think about one or more interesting thought leaders who I wish had even a modicum of online space much less a website that goes beyond the basic functionality of a broken business card. I’ve even offered to build for free some incredibly rich functional websites for researchers I’d love to follow more closely, but they just don’t see the value themselves.

I won’t presume to speak for Aaron, but he’s certainly become part of my PLN in part because he posts such a rich panoply of content on a topic in which I’m interested, but also in larger part because his website supports webmentions which allows us a much easier and richer method of communicating back and forth on nearly opposite sides of the Earth. I suspect that I may be one of the very few who extracts even a fraction of the true value of what he publishes through a panoply of means. I might liken it to the value of a highly hand-crafted trade journal from a decade or more ago as he’s actively following, reading, and interacting with a variety of people in a space in which I’m very interested. I find I don’t have to work nearly as hard at it all because he’s actively filtering through and uncovering the best of the best already. Who is the equivalent beacon for our students? Where are those people?

So the real question is how can we help direct students to similar types of resources for topics they’re personally interested in discovering more about? It may not be in their introduction to poetry class that they feel like it’s a pain doing daily posts about on a blog in which they’re not invested. (In fact it sounds to me just like the the online equivalent of a student being forced to write a 500 word essay in their lined composition book from the 1950’s.) But it’ll be on some topic, somewhere, and this is where the spark meets the fuel and the oxygen. But the missing part of the equation is often a panoply of missing technological features that impact the culture of learning. I personally think the webmention protocol is a major linkage that could help ease some of the burden, but then there’s also issues like identity, privacy, and all the other cultural baggage that needs to make the jump to online as seamlessly (or not) as it happens in the real world.

…perhaps we’re all looking for the online equivalent of being able to meld something like Maslow’s Hierarchy of Needs with Bloom’s Taxonomy?

I’ll have to expand upon it later, but perhaps we’re all looking for the online equivalent of being able to meld something like Maslow’s Hierarchy of Needs with Bloom’s Taxonomy? It’s certainly a major simplification, but it feels like the current state of the art is allowing us to put the lower levels of Bloom’s Taxonomy in an online setting (and we’re not even able to sell that part well to students), but we’re missing both its upper echelons as well as almost all of Maslow’s piece of the picture.

With all this said, I’ll leave you all with a stunningly beautiful example of synthesis and creation from a Ph.D. student in mathematics I came across the other day on Instagram and the associated version she wrote about on her personal website. How could we bottle this to have our students analyzing, synthesizing, and then creating this way?

## 🎞 Doctor Strange (2016)

Watched Doctor Strange from Walt Disney Pictures
Directed by Scott Derrickson. With Benedict Cumberbatch, Chiwetel Ejiofor, Rachel McAdams, Benedict Wong. While on a journey of physical and spiritual healing, a brilliant neurosurgeon is drawn into the world of the mystic arts.
I watched this over the past three nights in chunks.

Entertaining, but the narrative was a bit too on-the-nose with large chunks of explanation moving the plot along. The characters were a bit annoying and inconsistent. Dr. Strange was reasonably well developed but didn’t have a serious arc to speak of. His sharp wit would have been more entertaining if I wasn’t constantly comparing the character to Deadpool the entire time. I’m not sure Cumberbatch was the right chose for this type of “comedy”. I didn’t get any chemistry at all between the two supposed romantic leads.

I feel like I watched more Benedict Cumberbatch movies in the last two weeks than I saw movies during the entire last year…

Watched on Netflix on Kindle Fire 7″.

Rating:

Reposted “My ten hour white noise video now has five copyright claims! :)” by Sebastian Tomczak (Twitter)

Information Theory and signal processing FTW!

(Aside: This is a great example of how people really don’t understand our copyright system or science in general.)

According to Pocket, I’m still in their top 5% of their readers/users despite the fact that I cut way back on using it this past year in strong deference to using other feed readers including one built into my website.

Apparently I read 678, 617 words in their app this year which according to them is the equivalent of reading 14 books. To ballpark things I think I read 5 times as much in other apps. Now I don’t feel quite as bad about my poor Goodreads numbers.