# The Heart of the Mandelbrot

In recent posts I’ve presented the complex numbers and the complex plane. Those were just stepping stones to this post, which involves a basic fact about the Mandelbrot set. It’s something that I stumbled over recently (after tip-toeing around it many times, because math).

This is one of those places where something that seems complicated turns out to have a fairly simple (and kinda cool) way to see it when approached the right way. In this case, it’s the way multiplication rotates points on the complex plane. This allow us to actually visualize certain equations.

With that, we’re ready to move on to the “heart” of the matter…

To begin with, here’s what inspired these posts:

Don’t worry, it’s not as bad as it looks (although I admit I tip-toed around it myself). It turns out there’s a way of thinking about it visually that makes it a lot less mysterious.

What the formula describes is a cardioid curve drawn on the complex plane. When graphed, it looks like this:

Cardioid curve (red), unit circle (blue), and half-sized circle (gray).

That red curve happens to also be the boundary of the main cardioid of the Mandelbrot. All points inside the curve are guaranteed to be in the Mandelbrot set. (Which is why I was interested in all this. Normally these points have to be calculated to the max iteration limit to show they’re in the set. That takes time.)

In the equation above, the two variables, c and u, each represent an infinite set of complex numbers. The result, c, is all the points on the cardioid curve. The input, u, is all the points of the unit circle.

[The unit circle is just a circle with a radius of one centered on the origin. It is related to the unit square mentioned last time in that points inside operate differently from points outside.]

We can’t compute with infinite sets, so how this actually works is that, as explained in the last post, we generate a bunch of points for u — the more we generate, the finer the resolution (the smoother the curve) of the cardioid we’ll create.

We might, for example, generate a point for every degree around the circle. That gives us 360 points (complex numbers). Then we execute the formula above with each point, which gives us 360 results — 360 points that are in the cardioid.

We can do this with more or fewer points, depending on how smooth we want the cardioid curve to be. (The graph above was done with 360 points along each curve.)

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None of which involves the simple way to see what’s happening.

It describes the algorithmic process of generating a cardioid curve, but it doesn’t provide much sense of how or why the curve emerges.

To see that we need to think visually about what the formula means.

§ §

We start with the set of infinite points represented by u — the unit circle.

When we see u in the equation, we visualize a circle with a radius of one centered on the origin. Then we ask what the equation does to that circle.

The first thing that happens is that u, in both cases, is divided by 2. Conceptually, what might a circle-divided-by-two be? Invert the idea; what might it mean to multiply a circle by some number?

One logical result is to make the circle bigger or smaller. Dividing is inverse multiplying, so it would likewise affect the circle’s size.

Therefore, u/2 in the equation means a half-sized circle. Now when we see u/2 in the equation, we think of a circle with a radius of one-half (still centered on the origin).

The graph above shows the half-size circle in gray.

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Now we can consider the part inside the parentheses. What does one-minus-a-half-circle mean?

There’s a fine point in the section above I skipped past. Previously I said that multiplying points on the complex plane rotates them, but here I said multiplying the point of the unit circle changes the size.

Recall that, in addition to rotating, multiplying also changes the distance from the center (“magnitude”) unless one (or both) of the points has a magnitude of 1.0. By definition, all points in the unit circle do have a magnitude of 1.0 — that’s what the unit circle is.

When we divide by 2, what we’re really dividing by is the complex number (+2, 0i), which lies on the positive x-axis — therefore its angle is zero. So the multiplication preserves the angle of the points in the circle while the real value shrinks or expands the size.

Likewise, when we add one, we’re really adding the complex number (+1, 0i). Addition is member-wise, so this just adds 1.0 to the real parts of all the points in the unit circle. That shifts each point to the right by 1.0 — the whole circle shifts right.

Subtracting the circle from (+1.0, 0i) has a slightly different effect. Think about what we get with four key points (the four cardinal points):

1. “12 o’clock”: (+1.0, 0.0i) – (0.0, +0.5i) = (+1.0, -0.5i)
2. “3 o’clock”: (+1.0, 0.0i) – (+0.5, 0.0i) = (+0.5, 0.0i)
3. “6 o’clock”: (+1.0, 0.0i) – (0.0, -0.5i) = (+1.0, +0.5i)
4. “9 o’clock”: (+1.0, 0.0i) – (-0.5, 0,0i) = ( +1.5, 0.0i)

The right edge of the circle stays where it is, the center moves right to 1.0, and the left edge moves from -0.5 all the way right to +1.5. Also, the top is flipped to the bottom and vice versa.

The circle has again moved one unit to the right, and it has been reversed both horizontally and vertically.

On the gray half-size circle (also on the light blue unit circle), the point at “3 o’clock” is the start of the circle, the point with the angle zero. The angle of the circle increases moving counter-clockwise, so “12 o’clock” is 90°, “9 o’clock” is 180°, and “6 o’clock” is 270°.

The red circle is reversed, so its zero angle is at its “9 o’clock”. The angle still increases in the counter-clockwise direction, so “6 o’clock” is 90° and so on.

Remember that the zero-angle point of both circles is the same — it’s where the two circles touch.

So our equation amounts to a half-size circle multiplied by another half-size circle that’s been reflected to the right.

All we have to do now is figure out what it means to multiply one circle by another.

§

Previously we modified the circle with a fixed quantity — dividing by two or adding one. Now we’re multiplying two circles. What does that even mean?

It means we multiply points in one by the matching points in the other. How do we match up points to multiply? By their angle. We multiply together points with the same angle.

What makes it a little interesting is that, while the points on the centered half-size circle (gray) have the angles just described, since the reflected circle (red) is no longer centered, the angle to its points is different:

The diagram above shows the angle to eight points around the reflected circle. Angle is always from the origin. (So is magnitude.)

Remember that the red circle “starts” at the “9 o’clock” position and goes counter-clockwise from there. So the point angle slowly increases in the negative direction and then returns to zero at the “3 o’clock” position.

The angle to the points on the upper half of the circle is positive, again slowly increasing and then returning to zero.

Note that when determining which points match, we use the original angles as first described above. But when multiplying points, we consider their actual angles as described here.

Note also the lengths (magnitudes) of the red lines. Roughly half of them have a magnitude less than 1.0 and half of them are greater. The ones that are less will shrink the magnitudes of points we multiply, and the ones that are greater will increase the magnitude. This is part of where the shape of the cardioid comes from.

The idea is the same as described for generating points to draw the cardioid. Conceptually infinite points, but we pick as many actual points as makes sense for our need.

It turns out that when we multiply these points, the resulting set of points describe a cardioid curve.

§ §

Remember that multiplying one point by another creates a new point that sums the angles and multiplies the magnitudes.

On the centered half-size circle (gray) the magnitude is always 0.5, so one part of that multiplication is one-half times something. The other part, the reflected circle (red), as we saw above, offers magnitudes that change from 0.5 to 1.5 and back.

This immediately gives us some sense that the resulting curve will be lopsided, starting with a smaller magnitude that grows to maximum at the 180° point and then gets smaller. Exactly like a cardioid.

We can also see that the angle of the cardioid points is retarded in the first half (by the negative angle to the red circle) and advanced (by the positive angle) in the second half. These effects on magnitude and angle give us the cardioid curve.

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Some specific cases to illustrate how we do this:

The first points are where the two half-sized circles touch, the (original) zero angle. The point is: [+0.5, 0i].

Both points have zero angle, both have magnitudes of 0.5. Multiplying them rotates by zero degrees. Multiplying the magnitudes gives us 0.25, so the new point is [+0.25, 0i]. And, sure enough, that’s the “widow’s peak” of the cardioid.

To keep things easy, if we jump to the opposite side of both circles, the first point is [-0.5, 0i] (with an angle of 180°) and the second point is [+1.5, 0i], with an angle of zero, so there is no rotation, and the resulting point has the same 180° angle as the first point.

We’re multiplying a magnitude of -0.5 times +1.5, which gives us -0.75, so the resulting point, halfway around the cardioid, is at [-0.75, 0i] (which turns out to be a special point in the Mandelbrot; more on that another time).

Now a slightly harder one, the “12 o’clock” point on the first circle matches the “6 o’clock” point on the second. The first point has an angle of 90° and the other (from the origin to the bottom of the red circle) has an angle of just over -26° and a magnitude just under 1.12.

So the new point is rotated backwards (clockwise) by -26° and has a magnitude of  about 0.56. Here’s what that looks like:

The purple point is the point on the cardioid curve. Its angle is the the 90° of the blue point plus the negative angle of the red point.

The magnitude of the red point is a bit greater than 1.0, so the purple point has a larger magnitude than the blue point. You can see it’s just beyond the half-size circle boundary.

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This turned out to be harder to explain than I’d anticipated, so I made an animation to show the process:

Note how the purple point is always between the blue and red points (because it combines their angles).

All-in-all, I thought it was an interesting illustration of the geometric nature of the complex plane. It’s also a good example of how, at least sometimes, we can think about math visually.

BTW: If you look at the Wiki page for cardioid, you’ll find there are many ways to generate this curve. It is, in some regards, a fundamental emergent structure.

Stay heartful, my friends!

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

#### 18 responses to “The Heart of the Mandelbrot”

• Wyrd Smythe

Minnesota’s Governor has issued a travel ban that starts 3/27 at midnight and runs for two weeks. Only essential travel allowed (groceries, required work, caring for others, etc).

It’s occurred to me that a lot of us have been waiting since 2016 for some sort of return to “normal” and now… will we ever see normal again?

• SelfAwarePatterns

Louisiana went into full lockdown Monday, although we were in near lockdown for the previous week. I haven’t left my house (other than going outside to pick up mail, etc) since Monday of last week.

In personal terms, although I remain pretty anxious about what’s happening in the country and I’ve been working from home, it’s felt a lot like a staycation. Eventually I’ll have to go out for groceries like milk or frozen dinners, although I’m getting a lot delivered from Amazon.

This is definitely the strangest situation I’ve seen in my lifetime. (And I say that as someone who’s been through numerous hurricanes and flood events, including Katrina.)

• Wyrd Smythe

It’s kinda scary given all the SF novels I’ve read about pandemics. Will we eventually look back on this as we do Ebola or Y2K — something we got through okay — or… I find myself wondering if I’ll see the election in November. (I kinda wonder if it’ll happen or if this will be the perfect excuse to not have one.)

A friend of mine just found out today she’s getting a 25% pay cut. She works for a concert theatre management firm, and no shows for now. Others are getting laid off or getting hours reduced severely. Two friends still working have been told to go home (with pay) and wait it out.

Streets have little traffic, only grocery store parking lots are full. (And a local liquor warehouse, Total Wine, is doing big business. I just stocked up on groceries and beer, so I should be good for a few weeks.)

We seem to be accelerating well beyond normal here. Hard to know what to think. (So I mostly try not to.)

So,… how about that Mandelbrot cardioid curve, eh? 😉

Funny true story: My ex-wife (before she was my ex-) never, never let me live down thinking the big arteries in our neck (the ones assassins slit) were called the “cardioid” arteries. (She’d done some medical transcribing work long ago and learned all the abbreviations and terminology.) Made sense to me… blood, heart, cardioid. I ran into “cardioid” long before I ever ran into “carotid” and obviously didn’t look too closely at the word. Starts with “car” and ends with “id” so… there ya go.

• SelfAwarePatterns

Yeah, from what I’ve read, the unemployment claims soared to 3.3 million last week, and that’s probably only the beginning. This is not going to be pretty.

I’m trying to keep in mind that, although it’s been a century, the world has lived through other pandemics before. It doesn’t mean the next year or two is going to be pleasant, but by 2024 we’re likely to have moved on. I think back to the devastation in Louisiana after hurricane Katrina. It didn’t seem like we would ever recover. Yet a year later life was mostly back to normal.

That said, I would definitely stay home. And wash your hands after going out or touching anything new that comes into the house. If I were retired, I think I’d stay isolated until there’s a vaccine. (I’m actually eligible to retire in June, although I don’t know if the relevant offices are functional enough for me to do the paperwork if I wanted to.)

Sorry. Wish I had something intelligent to say about the Mandelbrot cardioid curve, except that I can definitely see conflating “cardioid” with “carotid.”

• Wyrd Smythe

It comes in part from never having heard the word. The other one I got really wrong was “paradigm” which was a really hot word (along with “paradigm shift”) around the time C++ became hot (the paradigm shift in question being a move to OOP).

I sounded it out from the spelling as “pair-rad-a-gym”… fortunately I managed to hear someone use it before I embarrassed myself. Paradigm. 20 cents. (“pair of dimes” 😀 )

What’s weird about the staying home is that it is business as usual for me, but now that I’m required to stay home, it feels different, weird, and confining. And the vibes you get from people in the store… oh, dear, so many SF novels with horrific goings on spring to mind…

The world, and humans, will certainly continue. But in what form I can’t help but wonder. Many have been aching for the normality of pre-2016. Now even pre-2020 is starting to sound good.

• SelfAwarePatterns

There was a tweet recently urging people not to make fun of anyone for mispronouncing a word. It means they learned it by reading. It reminds me of when I didn’t know how to pronounce “Descartes.”

On feeling confined, I know what you mean. Despite being pretty comfortable, I have this nagging worry that I’ll need something that’s not currently available. I hope nothing major breaks during this period.

On 2016 normality, my life has had many jolts since then, and 2016 itself was a pretty bad year. I’m not sure what normalcy looks like anymore.

• Wyrd Smythe

I know a number of people for whom the 21st century hasn’t been all that great. I hope you and we all get some stability and comfort soon.

Certainly I haven’t been a happy camper in this millennium. I miss the 20th century. I was born in NYC, and the 2000s started with 9/11. My marriage was obviously a mistake by that time; divorce followed shortly thereafter. Then they closed my department at work and I had to find another job in The Company. Then my beloved dog suddenly died of cancer. A few years later they eliminated my position (due to changes in IT) and I had to again find another position. And that one sucked so badly I retired early. And my mom and dad died.

I will say that since retirement in 2013 things have been okay (just okay), but age and health and the 2016 election have all been big weights. (And now we’re all gonna die, maybe, so there’s that. 😮 )

As far as people not knowing things, I try to live by this very wise take on it. I was just hanging out with a friend of mine (Bentley’s mom) who mentioned that, although my more technical posts go over her head and she doesn’t really see them as being for her, when she has time sometimes she’ll read them anyway and sometimes, to her surprise, she learns maybe one little something cool… Oh, man; music to my ears. That’s exactly why I do it. The light in someone’s eyes when you teach them something and they get it… best high I know.

“Psssst! Here’s some cool knowledge. Pass it on.”

• SelfAwarePatterns

The 21st century overall has been a mixed bag for me, but then the 20th was as well. Of course, I’m like anyone, and often miss the halycon days of youth, but I also try to remember how limited many things were in the old days, such as not having easy access to pen pals across the world!

Since 2016, I’ve lost my father and a number of other relatives, had career jolts (not all bad, but all stressful) and lately been wrestling with whether I’m ready to retire, with an wary eye on everything going on in the world.

That’s a good xkcd! And it’s right. The joy of showing something new to someone definitely outweighs whatever minor satisfaction from scoring points against them.

• Wyrd Smythe

Somewhere I read the idea that ‘life is a process of eliminating possibilities (pruning branches) and what remains is you.’ Which is to say we’re the sum of our experiences, but I was caught by seeing it as eliminating parts of life as opposed to seeking or gathering them. Which we do, of course, but it was interesting to think about it in terms of things lost or pruned.

Giving up both dreams of being a musician or filmmaker are two biggies for me. Those branches pruned I ended up a software designer. (Ironically, the scientist branch got pruned long ago when I discovered my artist side. Up to then I was probably headed for a career in science. The reason I took German in high school was to be able to read German papers by scientists, which at the time seemed there was a lot of, or maybe it was all echoes of Einstein.)

And then there are the people and beloved pets one loses, which is a whole other kind of pruning. I’ve always been very taken with McDonald’s sandbar metaphor — another view of pruning and loss. (Condolences for your dad. Sons and fathers, daughters and mothers, is always a tough one (sometimes even in life).)

The thing about the 21st for me is the lack of balance. Lots of big bads without compensation. My 20th was far more balanced in that regard. Some of it is just age and weariness. Some of it is the nature of the world. Some of it is just my strange luck. So it goes.

I have a lot of of teachers and preachers in my family tree (grandpa preached, dad preached, mom teached, sister teaches, other relatives teach, uncle taught religion), and I’ve done some teaching myself. My blog definitely reflects a desire to teach, to pass on some of the cool stuff I’ve been taught along the way. (There is even a certain amount of preaching in the stuff I write about life and spirituality.)

So I kinda come at all the pedantry naturally is what I’m saying. 😀

• SelfAwarePatterns

I’ve been thinking a lot lately about the challenges of growing older as an introvert. One of the things about being an introvert, is that we don’t make friendly easily. (I’m assuming you’re an introvert. If I remember correctly, you’re a fellow INTJ.) That means if we’re not careful, our social connections gradually diminish as the years pass, and an increasing sense of loss sets in.

It means we have to make an effort to cultivate new connections, which isn’t always easy, particularly in today’s world (and obviously impossible in the immediate circumstances), and I’m not particularly successful at this myself. But I’m increasingly thinking the effort is necessary.

I’m not sure what my motivations are for blogging. Teaching does seem like a component. Also testing ideas. But possibly also for having conversations that rarely happen in real life. Most people in my real life want to talk about sports, music, or video games, not science, philosophy, and usually not science fiction.

• Wyrd Smythe

“If I remember correctly, you’re a fellow INTJ.”

Wow, it’s been a while since I’ve even thought of Myers-Briggs, so that’s a good call (or good memory). I do usually test as INTJ, but only the “I” and “T” are really stable — I have definite “S” and “P” traits that balance the “N” and “”J”. But INTJ is fairly dominant.

Good point about social circles closing. When one retires one finds how just much of one’s social input came from interaction with co-workers. Even the circle of friends that I’ve hung out with for 30+ years — that’s gotten smaller as some have moved on to other things (and a few have died). Even the “everyone invited” parties are much less than half the size they used to be. (Used to be a lot of fun. Now they’re old folks being mellow. 😀 )

But meeting new people, yeah, is very hard. Taking a class or volunteering is one way. I met someone who turned into a good friend in a night class. The trick is there being some other reason to be hanging out with folks to make things more comfortable. Also to find a situation with as many different folks as possible.

My problem is finding people who I can stand to be around plus, more importantly, who can stand to be around me. I know I’m strong medicine. You’ve commented at my passion in debate. It’s rarely being rabid about the topic (which I can often take or leave); it’s just that I’m passionate, period. In person it amounts to a kind of performance art (I coulda been Lewis Black — I totally get that guy).

But,… I can’t count how many people have confessed they find me “intimidating” — even people who ought to know me better (as all bark, no bite) are sometimes put off. So for me, social interaction, even online, often amounts to suppressing myself. Trying to act in ways people won’t find so threatening. And that has really put me off people.

“But I’m increasingly thinking the effort is necessary.”

As you say, right now all bets are off, except online. For people like us, maybe a book club or astronomy club can be a good fit. If I ever really craved online social interaction, I think I’d start really participating in the comment section of Tor dot com.

I’ve always kind of meant to. It’s a pretty well-behaved place with tons of experienced SF lovers. I even recognized a few old names from my FidoNet and USENET days. In most groups I qualify as an SF expert, but in that crowd not so much. It’s refreshing. And educational.

Church (along with school and work) was always a traditional place to meet people, both romantically and socially, but I don’t suppose that’s an option for you. Taking (or teaching) a class, or volunteering for some cause (animal shelter, homeless shelter, political, etc.) are good ones. You meet people with the same interests.

“But possibly also for having conversations that rarely happen in real life.”

Ah, yes, very good point. I’ve been doing this so long (since the 1980s) I take that for granted. One great blessing of the internet (also a curse): it brings together folks of like mind (for good or ill).

Since those early days there were topic-specific groups. USENET has thousands of them. For me it was the Star Trek and computing groups. I spent a lot of time in the comp.lang.c group.

It set a standard for what things can be in my eyes, but those days are mostly gone. These long comments we indulge ourselves in are remnants of that time. It was all kind of based on email, or email-like protocol, so we wrote long comments (with quoting to make things clear and a little conversational) — debate essays, really.

I was lucky that the guy I hung out with for 30 years was as into SF as I was. He was also into physics, electronics, and cosmology, so we had many good discussions over the years. We kind of parted ways when his interests collapsed to hunting and fishing and smoking meat. All of which he does very well, but it ended those discussions. We used to hang weekly; now just occasionally.

I’ve found I no longer crave the human contact I once did. Too many disappointments, especially romantically. Now I almost dread going out because I know I’m going to end up dealing with stupid humans one way or another (just driving some place makes me shake my head). Hanging out with Bentley’s mom, the occasional party or gathering with the old crowd, an occasional dinner out, those were enough for me. Now most of those are on hold, so we’ll see. The change isn’t huge, but I do feel it.

• SelfAwarePatterns

On INTJ, you, Tina, and I had a conversation several years ago about it. At the time, it seemed striking that we all were INTJs, and I wondered if that type was disproportionately attracted to blogging.

I occasionally got the intimidating remark myself when I was younger. As I’ve gotten older, I’ve learned to reign it in. Being intimidating as a manager may sound like an asset, but it’s actually seriously counter-productive.

I’ve been checking out Meetup groups lately. There are a couple I’ve been meaning to check out. One I did briefly, but it was about writing and everyone was knee deep into their novel, and I’m not really writing anything but blog posts right now, so a group to circle back to when I finally start fiction writing again.

I did once, several years ago now, try church out as a way to meet people. The issue is that they want you to buy the doctrine. That attempt triggered an exploration of what I really believed and the discovery that I didn’t buy any of it anymore. It felt duplicitous to stay under those conditions. One of the Meetups I’m looking at is a freethinkers group, although I’ll lose interest quick if they’re at all political about it.

On old friends’ interests collapsing into a few subjects, I know what that’s like. One of my college buddies, who used to have all kinds of interests, became a born again Christian and only wants to talk about his church and their goings on. (It was actually his church I discussed above.) Another friend who I used to have really good science fiction conversations with, changed jobs, and suddenly was only interested in gaming and music.

On human contact, I actually don’t know that I need that much of it myself, but I know I need at least some. I often dread the specific events, although many turn out to be better than expected, and having them somehow makes life feel better.

• Wyrd Smythe

Ha, I can relate to so much of that. I know what you mean, both about dreading going to some social thing, and about how good it usually turns out to be during and after. People really do need people, even the hermits and misanthropes and introverts.

(In truth, a lot of people get introverts wrong. It’s just about what generally energizes you and what generally requires your effort — spends your energy. And, yin-yang, everything has a bit of the other. Interacting with people drains me, but it also has some energizing effect. Introverts are energized by their inner life (which is usually rich), but being alone does have a cost. We find interacting challenging, but there is reward there, too. Nothing is just one thing.)

I learned I was a social creature when I first started working from home. After a few days totally on my own, once back at work I found myself indulging in longer than normal chat sessions with co-workers. For about a half-day, and then things went back to normal, but it was interesting to discover how much I craved conversation after being alone.

(I’ve had friends who’ve done day care, and they get to craving adult conversation. 😀 )

“I wondered if that type was disproportionately attracted to blogging.”

It would make sense, I think. Introverts have that rich inner life, and it’s human to want to share, to have some kind of community. Blogging invites conversation and community without face-to-face or real-time challenges. Kind of perfect for us, really.

It’s definitely a thought behind my blog, the idea of finding the like-minded. My net hasn’t turned up much in almost a decade, but I’ve definitely met some interesting fish, and fellow swimmers like you and Tina kinda put the account in the black.

“Being intimidating as a manager […is] actually seriously counter-productive.”

Speaking as the mostly managed, absolutely. The managers who got the best work out of me were those that respected what I brought to the table (a hell of a lot) and worked with me. Those that tried to control me caused me to change positions. (One guy was more interested in my butt being in my chair by a certain time than whether I produced good work. I transferred to another department.)

Honestly, one reason I stayed as far away from the management track as possible was wanting nothing to do with gaining the emotional intelligence to handle people. For most of my life I figured my abilities bought me the freedom to be irascible and difficult. Temperamental artist type. I’ve mellowed with age. A little.

So many managers found me a challenge. The key to me was simple, though. Give me a good problem to tackle and then get the hell out of my way.

A while back Eric compared you favorably with Gandhi, and that is a definite difference between us. I just don’t have the patience with people you obviously do. On some level I never wanted it, although I really respect those that have it. For me it can be a filter so I just don’t have to deal with people who make my head hurt. But I wish I was more Gandhi-like sometimes. It’s not like raging misanthropy is a fun choice.

There was a House, M.D. episode which involved a disease that removed this guy’s social filters. He said exactly what he thought from moment to moment. It nearly destroyed his marriage and relationship with his daughter before House cured him. Things were strained to the breaking point.

What struck me was the idea espoused by the spouse that not everyone even thinks those things. Not everyone makes those judgements that we usually keep to ourselves. As someone who absolutely makes those judgements, but has known people who seem not to, I’ve always wondered if it’s repression or they really don’t see things that way, because I can’t fathom not at least thinking it.

But people, I’ve come to believe, really do see the world in ways I can’t comprehend.

Re church: I knew you had previous experience and were an “escapee” of sorts. I’ll just say that, from my experience, many are rejecting the church, which I get and even agree with, but I think a spirituality is a separate matter. It’s the human implementation of something versus the putative something that might exist. I’ve found there is a certain comfort in thinking there might be a purpose of some kind. It gives me a moral foundation, for one thing, and having some sense of the absolute can be an anchor. Pascal’s Wager, perhaps, but one has to “surrender to faith” for it really to work. Many can’t make that surrender. I don’t reject any aspect of science. I just think there might be a Yang to its Yin.

• SelfAwarePatterns

On craving conversation, it’s interesting you mention that. Right now I’m having daily check ins with my managers at work. We do it with video calls. Initially the calls were fairly brief, but as things have gone on, I’ve noticed they’ve become longer. Apparently people are craving conversation with others outside of their household. It’s caused me to allocate a full hour in the morning to those calls. (I have four managers who report to me and the calls are now averaging 10-15 minutes.)

The patience with people is actually a skill, one that gets easier with practice. I acquired it through necessity, but now it’s like an old vest I put on whenever necessary. Although I’m far from perfect at it, as some of the conversations on my blog show. I sometimes wonder if I would retain it if I retired.

On the spouse saying not everyone even thinks those things, I personally don’t buy it. I think people do think all kinds of unkind and selfish thoughts. And I’ve read enough biographies, where historians were able to dig up things the subject probably never thought anyone would find, to know that just about all of us at times behave in ways we’re not proud of. To me, the filters matter.

I will say that there’s something to being mindful on which thoughts you dwell on. Repeatedly dwelling on the failings of others, or on perceived slights, makes it much more likely those thoughts will burst through the filter. Recognizing you’re brooding on those thoughts, and making an effort to replace them with more productive ones, makes a difference.

But both filters require strong frontal lobe activity. If there was a pathology, they might both be caught up in it.

I don’t begrudge anyone the comfort and meaning they get from their spirituality. I have no interest in convincing them out of it, at least unless they try to force it on me. But aside from when I was very young, it never worked for me, although I couldn’t admit it to myself until that attempt at going to church. (And even then, I didn’t admit it to others for a long time. Even now, although I don’t keep it a secret, I don’t wear it on my sleeve in real life.)

• Wyrd Smythe

“Apparently people are craving conversation with others outside of their household.”

Makes sense. People crave the novelty. People you live with know you too well! 😀

“On the spouse saying not everyone even thinks those things, I personally don’t buy it.”

I definitely lean that way, but I have met a few individuals who made me wonder. I think some of it is how one takes certain things about people. I have a low tolerance for certain behaviors whereas others hardly seem to notice or take it more in stride.

Very true what you said about dwelling on things. A phrase I heard long ago and try to apply touches on that: “Your mind is like your house. You can’t control who (what thoughts) knock on the door, but you can control who you let in.” By extension, not only who you let in, but who you entertain as your guest at length.

AIUI, clinical depression, in part, comes from dwelling on negative thoughts to the point your mind adjusts to that as the new normal, just as it does with many drugs. Once that’s your normal, you’re kinda screwed. Anti-depressants push you to a new state that ultimately resets your normal and you can stop taking them.

The mind is such a complex system with all sorts of odd modes. It breaks in fascinating ways.

• SelfAwarePatterns

On tolerance toward behaviors, I think we all have innate responses to those things, but also learned habitual ones. Overriding our current responses doesn’t come easily, but in time they become habitual, and then they seem natural.

I like the “you can’t control who knocks on the door” metaphor. It emphasizes that we are the filter, not the initial impulsive reaction.

• Wyrd Smythe

Yes, that’s what grabs me about it, too. Our thoughts are free; our actions are (self) constrained.