The Universe at walking speed

There’s a certain familiarity we all have with how long it takes to get somewhere on foot.  Taking something well known to us like walking, I thought I’d attempt to use this as a measuring stick for the stars. The preferred walking speed for most people is around five kilometers for one hour spent walking (5 km/hr).  I know some fast walkers get up to 9 km/hr or more, but I’m going to use a comfortable gait that we’d want to stick to for long periods of time since walking takes time especially when you have a long way to go.

This week NASA announced that it has found 7 new planets around a small star that is 39 light years away from us. This star and its planets are named the Trappist-1 system.

A friend asked me this week, So, how many years in a light year again?Of course, there is one year in a light year, but what he was inferring was, “How bloody far away is that if we wanted to get there?”

The speed of light is 299,792,458 m / s

For argument’s sake, let’s say light travels at ~300,000 km/s.
* Please note that I’m going to cheat by rounding up or down here and there and if you notice that I’ve made a significant error somewhere, please feel free to point it out and I’ll update this post for future readers, but for the most part, I think we’re in the ball park on these numbers. *

At the speed of light, light can travel the distance of 9,460,800,000,000 kms in 1 year  (9.46 trillion kms)  (or 9.461 x 1012 kms)

The fastest man made object ever created [on record by NASA] was the Juno spacecraft that was sent to Jupiter.  It got up to the incredible speed of 265,000 km/h.  That’s like Mach 214, but in outer space no one can hear you scream as you go by that fast.

For our fastest spacecraft Juno, it would take ~35,701,132 hours or 1,487,547 days or about 4075 years to travel 1 light year and to span the distance of 39 light years, it would be 39 x 4075 years = 158,925 years for our fastest spacecraft to reach these newly discovered planets!

That’s a long wait to get there.

If we were to drive to Trappist-1 in a car at an average speed of 100 km/hr it would take 10.8 million years per light year x 39 light years  =
that’s 421.2 million years now that’s a long drive.

If you had to walk to the Trappist-1 system (at a constant rate of 5 km/hr without stopping once), it would take over 8.4 billion years for you to get there!

The estimated age of the earth is 4.5 billion years. The estimated age of the universe is 13.8 billion years.

Fortunately red dwarfs like the star in the Trappist-1 system live a long time (estimates are 10 trillion years, although I’m not sure how reliable those estimates really are), but chances are that the star will still be there by the time you get there in 8.4 billions years from now.  Well, that’s assuming it’s moving in the same relative direction as our sun.

Our solar system, and probably most of our neighbouring star systems, are spinning around our galaxy.  It is estimated to take 225-250 million years to do a full turn.  So over a period of 8.4 billion years, our solar system would have gone around our entire galaxy somewhere between 33 to 37 times.

The Juno spacecraft is always traveling at a the same speed after its initial acceleration by rocket or when it gets a speed boost from a ‘gravity slingshot’ around a planet or moon.  However, if the spacecraft we send were to accelerate throughout the first half of the trip, always gaining speed and then it were to flip around and decelerate for the second half to slow down enough by the time it gets there, we could probably get there much much quicker.  This sort of thing might be possible with the ‘impossible EM drive’, if it works.  A continuously powered engine similar to that might be used to get to our closest stellar neighbours in a couple of centuries rather than 160 millennia.  I’m not sure how fast this ship would get, perhaps at the halfway mark it could be as much as 20% the speed of light?  I’m speculating, I think it depends on how quickly it’s accelerating, but if it’s continuous acceleration then it doesn’t have to be that much.  Of course, some people argue that faster than light travel is possible (even though Einstein thought otherwise).

For us to send a message to the Trappist-1 system, it would take 39 years and then we’d have to wait another 39 years for the answer to come back to us assuming they receive the message and respond back right away.

In comparison, when light leaves the sun and travels roughly 150 million kms to hit earth, it only takes 8 minutes to cover that distance.  So for us to talk back and forth with an astronaut near the sun, it’d take 8 minutes each way.

Venus is only 6 minutes away from the sun at light speed and Mercury is only 3.2 minutes!  Mars 12.6 minutes, Jupiter 43.2 minutes, Uranus 159.6 minutes, Neptune 4.1 hours, Pluto 5.5 hours!

Imagine if we turned on a laser beam to signal to the Trappist-1 system.  After turning on the beam of light, it would shine past Pluto within five and a half hours on the first day of the trip but we then would have to wait 39 years before it is seen by someone on one of those planets.  That is, assuming they were looking for it and that there were such an incredibly bright laser beam like that.

If there ever were such a thing as a laser beam that curved in such a way that it followed the curve of the earth’s surface, we could shine a beam around the world.  You know how long it would take for that light to go around the planet and hit you in the back of the head after turning it on?  Roughly 1/10th of a second which is actually quicker than the average blink of an eye (which is typically 300 to 400 milliseconds).

In comparison to walking to a nearby star, how long would it take to walk around the world?  Well, Jean Béliveau left Montreal and visited 64 countries and hiked over 75,500km in 11 years.  That’s like walking around the earth twice (the earth’s circumference is 40,075 kms).

Walking to California from Ottawa (~4,687 kms) would take you just over a month of continuous walking without a single break (about 39 days). If you ran all the way without stopping once, you could do it in about 13 days.  Most likely you could only run at that speed for about 8 hours a day. If you’re a super human runner, it would take about 39 days at the same speed (15 km/hr) for a full 8 hours every day. That would be like running 3 marathons every day.  There would be 111 marathons (42 kms each) between California and Ottawa. I can’t imagine anyone doing such a thing ever.

Surprisingly, Katie Visco ran just over 5,040 kms from Boston to San Diego in 276 days.  That’s the equivalent of 120 marathons in 276 days.  Wow!

You would have to run 8.7 trillion marathons to reach Trappist-1 and to think that Trappist-1 is pretty close to us!  A mere 39 light years (that’s only about 12 parsecs).

The center of our galaxy is estimated to be ~26,666 light years from here (about 8 kpc). A parsec is 3.26 light years, a kiloparsec (kpc) is 1,000 parsecs.

The center of our galaxy is 252,281,692,800,000,000 kms (or 252 quadrillion kms) from us. That’s just to get to the middle from where we are on one of the arms.  The whole galaxy is about 100K light years across, but our galaxy isn’t even that big compared to the biggest known galaxy.

The “IC 1101” galaxy is about 6 million light years wide (about 60 times bigger and 20,000 times more massive than our milky way galaxy).

There are 100 to 200 billion galaxies in the observable universe. The observable universe is estimated to be about 93 billion light years across (about 28.5 gigaparsecs).

The actual size of the universe is assumed to be bigger and might be infinite depending on who you talk to but that’s for another post.  How long would it take to walk across the part of the universe that we can currently see with our radio telescopes?  I won’t go into the fact that what we see expands over time or that the universe itself is believed by many astronomers to be expanding at an accelerating rate which would make it difficult to ever reach your end point especially if you’re walking.  Of course, you can’t actually walk in space without anything to walk on so we could substitute walking with ‘slow floating at a constant rate of 5 km/hr‘ assuming you never get pulled into a nearby star or such.

Distance of a light year times the number of light years in the observable universe:

9,460,800,000,000 km x 93,000,000,000 light years =

8.7985 x 1023 =

879,854,400,000,000,000,000,000 kms / 5 km/hr =

1.7597088 x 1023 hrs / 24 hrs / 365 days =

2 x 1019 (20,000,000,000,000,000,000) years

It would take 20 quintillion years to walk across the observable universe!

As they say, if you walk a mile in my shoes you’ll end up at the bar. 😉

Free Money!

I find it funny how much money there is supposed to be in the world and yet there never seems to be enough of it to do certain things.  It makes you wonder how there can be so much of something that can actually do so little for so many.  It’s not to say that money doesn’t do some great things for a lot of people.  It certainly does.  Very nice things have come from kind monetary investments from very generous people.  Money makes the world go round, or so I’ve heard.

mb_m1_and_m2_aggregates_from_1981_to_2012

As we all know, ‘money does not grow on trees’.  If it did, I hope we’d be kind enough to pass around some money tree seeds to share with our neighbours.  Unless of course, money trees turn out to be only good for making money and nothing else.  On the other hand, if money trees produced units of ‘work’ which consisted of a magic mix of raw energy, skill, and efficient application; we could all use one of these trees growing in our front yards.  We could use these trees to accomplish wonderful things.  As it turns out, we are the money trees, after all, if we do the right things, at the right time, we can make money.  If we’re lucky, we even make enough money to pay ourselves for the effort (this is usually called financial savings).  I know, this is a rather odd concept for me too, and as I understand, something like 63% of Americans don’t have any substantial financial savings.  The cost of living takes up most of the made money if not more.  Who knows, maybe some of us even ‘waste’ their money on booze and cheap entertainment.  That could be, or it could also be that we’re all being duped by the existing financial system.

As we all know, we need to buy low and sell high!  We need to reduce our costs and maximize our profits!  Sure, sure, whatever, that’s all well and good, but it’s within our power to tweak a few parameters to make the financial system work for us again (rather than against us).  President Donald Trump, if you’re reading this, you can make America great again!  Please read on to find out how.

As you probably know, the Federal Reserve in the US has a role in how much ‘money’ is created.  You may also be quite aware that the Federal Reserve did some ‘Quantitative Easing’ for a while which is another term for ‘increase the money supply’.  If this sounds all hocus pocus, that’s probably because it is.  This created money consists mostly of digits on computer spreadsheets.  In theory, QE is supposed to stimulate the economy by encouraging banks to make more loans.  Loans to who and for what?  Well, chances are these loans will be for real estate more than for new or existing business (you know, businesses are the place where money trees are productive, not where they sleep).  Whether the economy is actually changed really  depends on how the ‘stimulus’ is spent not on how much of it there is.  Did QE increase inflation as it was designed to do?  Who the hell knows?  Not me, that’s for sure.  Maybe I did benefit from the QE program in some way, for instance, the whole banking system didn’t collapse and that should be a good thing, right?  But who knows if this newly created money was actually beneficial to anyone?  How do we measure this?  I’m sure a few people have more ‘on paper’ but does that really matter?

The funny thing is that it’s possible to create money which would be completely beneficial to everyone.  What?  No way, you say!  I say way!  What is this magical thing that can do such things?  Well, it’s called basic income and it goes like this:  Everyone and I mean everyone is given some money.  How much money?  Well, it depends on how much we decide on, the thinking though is that it’s enough to get by on for food and basic shelter and maybe some bus money, maybe that amount differs a little based on where you live.  You know, it’s something, not a lot money, but something to keep you from robbing  or begging for food.  Isn’t this a form of welfare?  Well no, it’s not like welfare because everyone would get a basic income no matter what, no conditions need to be met.  Is there a catch?  Sure, let’s say that you owe money on a credit card, well perhaps this money needs to pay off the debt before you can just get the cash.  Fair enough, at least you’re getting some free money eh?

Now, at this point you might be thinking, “Well this is nice but inflation is going to happen!”  Well, duh, inflation is already happening, whether more people are given some money doesn’t mean that will necessarily change.  Some things are still going to be expensive while other things are still going to be cheap.  The difference is that a lot of people would have a safety net.  A means to get by when all else fails.  It’s an investment in the money tree when the money tree can’t produce fruit that year.  Not only that, but this ‘basic income’ idea has already been tried and tested.  Turns out that if you have this basic income for everyone, some people slack off and take advantage of the free money!  What?  Yup.  Stay at home moms spend more time with their kids when they have that option!  (It’s like a few months extra, not the end of the world, these moms still go back to work eventually).  You know what else?  Turns out that a lot of these slackers take the money to learn new skills to be more productive money trees.  Insane!  I know, you’d think there must be a problem with basic income, that it can’t be as good as they say it is!  Well, let’s give it a shot and see how much damage we can do!

The funny thing is that we’re probably all ok with giving more money to people that already have money, but poor people?  When you give money to poor people, they often spend the money!  What?  Yup, poor people spend!  And what is all that spending good for?  Growing the real economy!  More participation, more consumed goods.  If you’re at all like me, and I trust that you’re not, but for the sake of argument, you might begin to wonder if poor people spending money means that poor people will be eating more, and consuming more products such as kitchen appliances and automobiles?  After all, it’s the horrid middle class that eat so much meat and drive their stupid cars!  Well, yes and no.  Having more money doesn’t mean you’ll eat more, in fact, you might have the freedom to eat better, to have more choice in what you eat.  Whether we decide to build a transportation system that uses clean energy and that costs less to run is another discussion entirely.  Poor people drive cars too, with some extra cash they might buy more gas and drive around more, but really?  Who cares?  That will probably happen whether we like it or not.  Don’t like cars and all that nasty pollution?  Well, let’s tackle that problem on its own.

An ounce of prevention is worth a pound of cure.

Up here in Canada at least, a homeless person will cost society more living on the street and interacting with police and the hospital system than they would if they were given free housing.  What?  Yeah, it’s way cheaper to spend money making sure that people have food and shelter than it is to pay their medical bills.  I know, you’re thinking, well, let’s stop paying for their medical bills!  No, let’s make sure we always invest in money trees whether they make fruit or not so that the whole orchard can benefit.

Free Won’t

From what I understand about artificial intelligence (AI), in particular, today’s known software programs like Google’s DeepMind. The software can learn from the experience of repeating a task, such as playing a game, driving a car, or reading lips.

sentinel

The more the AI program practices the better it gets and practice it can! By playing against itself over and over very quickly, always learning and improving as it goes. Before you know it, the AI is better at certain tasks than humans are. Not only that, let’s say that one AI program learns something new after repeating these tasks millions of times over, this program can then pass this new learning to all the copies out there playing games, driving your car, or reading lips (or whatever else it might be tasked to do).

It seems clear to me, that the AI program that drives a car must have certain ethical ‘rules’ programmed into it. For instance, a rule such as: “Don’t go crazy and run over every person that you see.” Most of these rules are pretty obvious, and are probably not something the AI would not follow even by accident.

However, what about the more subtle rules? Have these been written yet? Imagine rules for a scenario such as, “When traveling at full speed down a highway and suddenly a crowd of people run in front of the car.” Of course, the default action is to stop.  But what if this distance is less than the breaking distance, and the only other option is to swerve off the road and potentially kill the passengers in the car?  What decision will be made, if any? Is it simply a matter of counting how many will be killed and picking the best option? Is the AI program always going to make the same choice? Are car passengers entitled to override these settings? Can you make these choices in the admin settings or do you have to hack the software? Unfortunately, it seems like the ethics have to be ‘hardwired’ and practically unhackable. For instance, if the ethics routine isn’t verified as ‘secure and working’ the program can’t run.

Of course, this might all be moot. If these AI software programs can be used to drive cars, I’m sure they can just as easily drive war machines. They’re just automatons following instructions. They aren’t ‘driven or motivated’ they’re simply repeating a learning process to perform tasks the best they can.  You still need to define what’s ‘ok’ and what isn’t in the parameters of the program.

Currently, the ethics parameters with rules such as ‘don’t drive into people’ isn’t something that changes as the AI program learns how to master the task of driving.   The parameters of what is ‘ok’ to do or not do cannot be changed by the AI learning software, it is only controlled by the program’s design.  The AI program follows the rules but can’t change them.  However, I could imagine a world where the AI software would be designed to have the ability to learn and improve upon its own ethics routines.  Perhaps these ‘improvements’ would be small incremental changes, but over time, after millions of interactions and experiences, could these routines become something completely different than what it started with?

It’s funny how we expect these AI programs to have better ethics than the average person has but these programs will only be learning based on what we teach them to start with.  If we even bother to teach them anything.  It’s nice to imagine that a self-learning AI program would come across some pictures of cute kittens on the internet and then suddenly ‘learn’ some ultimate truth that ‘love conquers all’ and somehow it ‘knows’ all about right from wrong, but the reality is that the software might not measure these morals the way humans do at all.  For instance, the machines might think organic beings are irrelevant or that some micro-organism in the ocean must be the dominant life form on earth (at the cost of everything else).  It sounds like a crap shoot to let machines figure it out for themselves, not that I wouldn’t want to listen to what insights they might have, but I don’t want my automated car telling me that I shouldn’t be driving my car at all, that I should walk even though it is raining.

Even if we taught these programs to have perfect ethical sub-routines (whatever that might mean).  Will these programs ever have ‘free won’t’?  Can AI really make choices if it isn’t ever given an option to choose?  Sure, a developer might allow a software program to ‘randomly’ do or not do something, but that’s not what I’m talking about. I’m talking about actual choice. The choice to do nothing. If you don’t have ‘free won’t’ you clearly do not have free will. Of course, if the software just does nothing all the time, it’s probably not very good software or it’s conflicted about something and one of the routines will need to be reset or something.

I guess, what I’m implying is that you choose not to do something when part of your spirit says, ‘No wait, despite what I’d like to do, and perhaps am very good at doing, let me reconsider and instead do nothing.’ You can probably visualize a similar situation, for instance, your first reaction after being physically assaulted might be to respond in kind and sometimes well we just react the way we do and hope for the best. We’re only human after all, I know I am.

The thing is though that, just like a learning software program, whether or not I choose to do something, is most likely due to all my previous experiences. You can imagine that an ‘aggressive’ version of who I am might quickly develop if I were always under some physical threat. I might be more prone to swearing or yelling at people for instance.  Even if I started off as a nice peaceful dude, under the wrong circumstances my attitude might change.  Hopefully my ethics would not change no matter what the circumstances, but that sounds more idealistic than realistic.

I imagine it can be argued that AI software programs have no ‘real feelings’ even if programmed to emulate ‘real feelings’.  That’s why machines are so much better than us ‘mere humans’.  Well, that and because computers are so much faster and never make mistakes (unless they’re programmed to make mistakes or simply have mistakes in their code which also sometimes happens).

Just for the record, I’m against any sort of automated killing machines, even the ones that are made ‘by accident’.  Of course, most of the ‘bad machines’ are usually controlled by people.  In fact, to my knowledge all machines are still under the control of people even the ones that run intelligent programs that can read your lips.

I will babysit your Clash of Clans game 4 U

Finally I’ve found a job that is better than ‘Price checker at the dollar store’. The job title is Game Babysitter. In particular, I babysit ‘Clash of Clans’ the ever so addictive game filled with lots of clicking. Well, since it’s played on a tablet, that’s just touching, not clicking, you get the idea. Things happen, you touch the screen and then more things happen eventually. You have to wait for it.

clash

But… if you don’t touch the screen then all sorts of evils await you. Everyone attacks you over and over again and you can’t keep up. You start to lose! Oh no! How retched a game that never lets you end the game.
No worries, I know how awful you must feel to let your little army of  clan men and women die of neglect. That’s why for a small fee I will take care of your digital village for you.  Keep in mind you must hand over your iPad or android device for me to look after.  Also remember that you have to eventually take your game of clans back from me.  I’ll only look after it for so long after that my service fee goes up.

Am I Turning Geek?

According to the google, this is the typical definition for geek:

geek-definition

However, I would much prefer this definition on urban dictionary.  It’s pretty close.  I’m not big on video games.  However, I have spent far too much time on the interweb, but that alone does not make me a geek.  Geek is more about attitude and how much time you can spend on the same task.  I also don’t think you have to ‘be a computer programmer’ to be a geek.  To “geek out” is to obsess over something, it could be a movie, a book, a groovy dance tune or a few lines of code.

man-standing-at-corner

Are you socially awkward?

Most likely, sometimes it’s unnoticeable.  Other times it’s a glaring obvious panic induced situation that I would rather avoid.  I’m not entirely an introvert but I’d much sooner avoid social occasions where there are more than 3 people gathering unless we’re all dancing or at least listening to music, then small crowds are ok.  Never more than about 100 people though if possible.

Things like Canada day gatherings on Parliament, forget about it, you’ll never see me in a crowd like that, not on purpose.

Also, you need not be a geek to enjoy listening to ‘Background Noise 4 Geeks’.  It’s not just for geeks, although I’m hoping a few will enjoy it.

Background Noise 4 Geeks now on Spotify!

Woo hoo!  You can now find me on Spotify!

I’m a somebody!

This means real people are actually listening to me right now, ok, so there’s only the 3 of us so far, but wow!

background-noise-4-geeks-small

I’m listening right now on my iPad.  Spotify is an app for your smartphone.

What does this mean?

It means you’ll be able to listen to the whole album for free!  Err, I’m not sure how that works out for me, exactly.  To read more about how artists like me could potentially make money on Spotify.

How do I find the album?

In the Spotify app there should be a magnifying glass icon that will open a search box.

Typing ‘Background Noise 4 Geeks‘ should work.  Please let me know if you can’t find it.  It might depend on which country you’re listening from.

 

What is the best background noise for work?

About 15 years ago I worked in an office with a white noise generator.  It kept an otherwise loud environment filled with many lively coversations to a dull roar.  It worked rather well, to a point.  Pretty quickly your brain tunes out the white noise, it just becomes part of the environment and makes it easier to concentrate on your work. I’m sure some noise generators are better than others.

Noise Generation

However, a white noise generator can also be very irritating for some people.  I’ve read that it can possibly even increase your stress level rather than do what it is supposed to do which is to provide a peaceful and seemingly quiet work space.

My current office has a rather loud ventilation system that blocks out quite a bit of the distracting conversations in the adjacent cubicles.  When the fans turn off, there’s a sudden deafening silence.  It feels strange without the white noise of the ventilation system.  It turns off so rarely, otherwise it runs continuously all day, every day, winter or summer.  Without the vents on, everything and everyone seems so much louder, so much more noticeable.

If I had to block out the surrounding office noise by wearing headphones, I would not choose to listen to most of the ‘ambient’ noise generator apps that I’ve tried.  There are some exceptions of course, but typically for me,  10 to 15 minutes is all I can take of ambient music, after that my skin starts to crawl. I find that listening to music with vocals can be equally distracting.  If I’m reading or otherwise trying to concentrate, Jazz or Classical music would be a good choice.  I tested my album to see if I can actually work while listening to it.  I have to say it really depends on what I’m working on.  If it’s a mostly visual task like working with Photoshop then it passes the test quite nicely.  Ultimately, not having to wear headphones to block out the noise at work would be best.

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In my opinion, the best background noise for work would be the natural sounds you hear sitting in the woods among the trees, the birds and the insects.   Far away from the fax machine, the paper shredder and the sound of the ventilation system. Somehow, I don’t think listening to a recording of ‘sounds of the woods’ will help my work environment.  If only we could open a window in our office.  Oh imagine the nuisance of that! There would be no end to it, some of us would want the window to always be open, others for it to always be shut.

So it goes.

Deep Ambient Agitation

Looking for something to keep you awake at night?

Want to relax?

Wind down from a busy day with a quick listen to this ambient track that might make you feel slightly agitated.  No sense being completely at ease!

I’m experimenting with SoundCloud.  So far, I’ve really enjoyed the fabulous selection of music on this site.

This track is made in part with the ever magical ‘Trope’ app made by Brian Eno and Peter Chilvers (and with some additional synthesizers for good measure).

Can’t Stop Yourself from Singing?

If words suddenly pop into your head while you’re listening to this album, and you feel the urge to sing.  That’s super cool!

Be Courageous!

I hope that you can find the courage to record your voice and share it with others.  Please share it with me!  If you can, please send me a link and I’ll give it a listen.

Do you like one of the tracks but think it could be so much better?  Think that it should have a lot more _______________ or  without so much  ______________?  [please fill in the blanks].  Let me know in the comments.  Good or bad, but please don’t be too nasty, I’m just a kid [at heart].

microphone

This is a screenshot of the microphone I ordered from eBay.  That was weeks ago and it’s still not here!  How frustrating, but that’s ok, because it’ll just make it that much better when it finally arrives!

Then watch out!  Lyrics here I come!  Good grief.

You Silly Wabbit!

Why is track 12  named “:(){ :|:& };:”?

That line of special characters consisting of some colons, a semi-colon, parentheses, brackets, braces and an ampersand is what is known as a fork bomb or wabbit.  This tiny bit of code will replicate itself like a couple of rabbits until it uses up all of your computer resources and your machine crashes.  You would need to type this into a terminal window for it to execute (not a good idea).  To read more details on how it works check out this Wiki article.

When I was creating track 12, the sound from the ‘retro space lead’ synthesizer I was using made me think of a recursive loop.  That is when the fork bomb name came to mind.

Interestingly, when this title was uploaded to the iTunes store, certain characters were stripped out and you end up with only this line: [::&];:  Typing this into a terminal window will give you the following response: ‘-bash: [::: command not found. In other words, it’s completely harmless.

There are some variations between music stores, the Google Play store shows the title as () [:|:&];:  I’m guessing the programmers added a rule that you can’t start the name of your song with a colon (:) because that might be confused with the same character that is  sometimes used in the path name to denote a directory.

At Amazon you end up with :() [:|:&];:  Different software with different rules on how to handle special characters but they all do pretty much the same thing, protect their data from getting messed up.  It seems for whatever reason that all stores swapped the squiggly braces ‘{}’ for brackets ‘[]’.

Where can I find out more information about punctuation marks?

Please try the punctuationguide.com