Black holes and light cones

I’ve been furthering my investigations into whether an event horizon collapses on you as you approach it.  One of the main sticking points now seems to be the concept of the light cone.  In short, the light cone shows you in which way space and time warp as your inertial frame changes in a relativistic fashion (significantly large relative to light speed).

This is about as accurate a picture as I could find:

A proper light cone.  The diagonals represent the speed of light, or c.

A proper light cone. The diagonals represent the speed of light, or c.

Obeying the absolute nature of light speed, or c, the diagonals always stay at 45 degrees.  It’s space (x axis) and time (y axis) which shift on us.  Things moving away are stretched out, things approaching us are smushed in.  Both time-wise and space-wise.

Here’s a nice top view of the above light cone.

Light Cone Top View

Top-down view of the above light cone.

Now I don’t know why, but for some reason, established journals are throwing this light cone out the window when using them to illustrate the approach of a black hole.  Here’s one:

blackhole lightcone

Keep in mind this is the same light cone as what we rigorously explained above.  Not sure what’s so special about the area outside a black hole that it would rewrite the very nature of how those light cone diagonals would point?  Call it hubris but it seems quite sloppy to me.

Of course, the very idea of those light cones inside the black hole, with both diagonals pointing inward, is like having an axis with two negative sides.

Here’s another one:

Rotating light cones?

Rotating light cones?  Where are we getting rotation from?

I could show more but they’re equally eyebrow raising.  Again, I’m fully committed to admitting I’m wrong.  But if I am, we have some simpler issues to straighten out first.

More later.

 

Alt Right Manifesto

A spectre is haunting the Internet – the spectre of Alt Right.  All the powers of the Internet have entered into a holy alliance to exorcise thie spectre: Government and Facebook, Buzzfeed and the clickbait mob, Democrats and Republicans.

Where is the outspoken Tweeter that has not been decried as Alt Right by a verified Twitter account?  Where is both the college radical and the government official that has not hurled back  the branding reproach of “Alt Right”?

Two things result from this fact:

  1. Alt Right is already acknlowledged by all Internet powers to be itself a power.
  2. It is high time that the Alt Right should openly, in the face of the whole internet, publish their view, their aims, their tendencies, and meet this nursery tale of the Spectre of Alt Right with a manifesto of the internet tendency itself.

Bourgeois and Internet

Commoners continuously have fought for their own voice in our society, only to have their opinions coopted by established voices who quickly sold them out as they became valuable enough to do so.

And this history of the last twenty years has manifested itself in the history of the Internet.  Ever since the 60s, the baby boomer generation has held the mantle of “anti-society” and has taken their attitudes all the way to the major parties and the corporate boardrooms.  With this creep into established society, they have also crept into Silicon Valley and the helm of the Internet.

Thus Silicon Valley, which is now said to rival Wall Street itself in pure capital power, also has the heritage of the 60s.  But it is a heritage that keeps sticking to staler and staler ghosts of its rebel past.  The fact that the anti-vaccine craze has its center in Marin county should come as a surprise to nobody.  All the wealthiest benefactors of internet wealth live up there, a living contradiction of both being The Man and being Against The Man.

One need not look very far to see this tendency in all sorts of stale politics: transgender/LGBT politics, the GMO and anti-Vaccine craze, blaming a fictional past on all our woes, white guilt and the weird way it warps racial politics.

Now the Internet billionaires also ushered in an entirely new era – the era of decentralized communications.  But while they hailed this as a new era of equality, where anyone can talk to anyone, they also ingratiated themselves to all that was stale and old in our society:  Hollywood, the recording industry, governments seeking to promote globalist agendas.

This is why companies like Facebook and Twitter, despite their claims to democratize the national conversation, are becoming more egregiously partisan, blocking any conversation they deem against the globalist agenda.

The Proletarian Internet

While Silicon Valley has done everything it could to centralize the internet and bring people under its fold, voices have emerged and exploited the internet for their own dissident opinions.  It started as a sort of a crack in the dam.  When a proper liberal was supposed to champion things like “women are always right feminism” or pop psychology or liking any music that the radio stations threw your way, these people said NO.

I’ve seen such voices ever since the early 2000s.  Maddox was a good proto-champion of the Alt Right from the early days.  Not only did he have a dissident voice, his very platform was dissident.  To this day he still uses Xmission, some obscure, libertarian webhost in Utah.

Nor was this Alt Right confined to the Internet.  Jim Goad wrote the Redneck Manifesto, a good anthropology of working class America that stays clear of stale racial categories and in fact rebels against them.  It is from this seed of truth that the Buzzfeed article above builds its mountain of bullshit that Alt Right is about White Nationalism.

And if I may interject my own personal experience, it was in dealing with the GMO debate that I, a hitherto good liberal, decided to jump the train and speak out against what I saw was people just sticking with what would later become virtue signaling: speaking up about an issue they know nothing about, just to look cool to their peers.

Kony 2012 was a watershed moment in virtue signalling – when the slogan-based politics of the established left became so removed from reality that it was an Emperor’s New Clothes moment.

Gavin McInness and Rebel Media have also risen to internet fame as a member of the Alt Right.  He gives a good understanding of the 14 different types of conservatives.  While he has a rather narrow understanding of Alt Right himself, this is a good starting point for the understanding of who falls under this rather large, colorful umbrella of Alt Right.

Because, over the last couple years, such virtue signaling has come to a head.  Events like the 2014 Israel-Gaza war, Bruce Jenner becoming Catelyn Jenner, Ahmed Clockboy, Black Lives Matter.  And probably most of all, the unfettered Muslim immigration coming into Europe and all the devastating consequences it’s had for European Society.

And it is this last issue most of all where the battle lines are so clearly drawn.  The old 60s liberals that have become established are policing the Internet for people in power.  And the Alt Right seem to be the only ones that are opposing established views.

Milo Yiannopoulous, a gay conservative, has seen himself catapulted to the eye of this storm.  He’s considered a modern day champion of the Alt Right, taking such basic stances like Muslim immigration is dangerous to gays, and questioning the statistics of college rapes and female wage gaps.  As he’s put it, he’s welcome to debat things, but he wants to debate facts, not just being called a racist.

The 2016 Election

And with this election of Hilary v. Trump, we may see as many Democrats become Trump Democrats as there were Reagan Democrats.  The Alt Right is largely responsible for this movement.  It is not because the country has shifted to the right.  It is because the left has moved into irrelevance.  Indeed all the political forces of the past 16 years have drifted into irrelevance.

All the powers of the media and the internet have placed themselves solidly in the camp of Bernie/Hilary.  To the point where they smear Trump and anyone who supports him.  The Democrats literally treat Trump as The Devil.  The only argument they have left is “vote for Hilary or the Devil.”  They even threaten violence against his supporters.  I wonder how many more people would have Trump signs and stickers if they didn’t fear vandalism.

And the Alt Right is getting smeared right along with Trump.  The same lies they put up about Trump are being used against this shadowy movement of nebulous neo-Nazis which happen to include Jews and Gays.  So it leads us to ask, just what does Alt Right believe?

What the Alt Right believes

The Alt Right is ultimately not defined by its own goals – our goals are myriad and contradictory – but our refusal to associate with championed issues of the established left.  Catelyn Jenner is still a man, and men should not be involved in women’s sports.  This issue has put someone as innocent as Rhonda Rousey as a hated conservative, for saying transgender men should not be allowed to compete against female fighters.

Being pro-science is also a major bone of contention of the Alt-Right.  We have no problem with GMOs or vaccines.  I’ll admit I may be in the minority of the Alt Right for believing Global Warming is an issue.  But I fall right back in when I say governments aren’t doing anything about it other than as an excuse for subsidies to their friends.

We value education, we don’t think it’s a tool of rich white males to mold your mind.  We’re not afraid to bring up that rap is corrupting and that being a thug will land you in jail.  We like cops, we like that they keep civilization.  Maybe they have problems but the problem would become much greater if they go away.  So yeah, we think a cop’s life is more worth protecting than a civilian’s, and even more so than someone of questionable conduct.

We think being black or female does not excuse you from being an asshole.  We think there’s an issue with Islam.  We believe in borders, letting through those we accept, and keeping the rest out with deadly force if necessary.  And with that, we are opposed to “safe spaces”.  If you want to be relevant, you’re going to be insulted, you’re going to be attacked.  Only toddlers need safe spaces.  Children should be exposed to increasing levels of reality and danger.

And that brings me to the final disclaimer of what we believe: we disagree on a lot.  Anyone calling themselves Alt Right can disagree with any one of these precepts.  The difference is we are able to disagree without branding each other and casting each other off into the hell of moral condemnation.  Which, yes, is as ridiculous as it sounds.

What the Alt Right wants

If you could sum it all up in one catchphrase, it’s “we’re tired of being PC.”

Although, as the virtue signaling leftist media spins it, that means if you’re not PC you’re an asshole that rapes and beats women, wants to lynch black people, and send Muslims and Jews to the concentration camps.

It sounds ridiculous when you put it that way.  And it is.  Even among those who are outspoken racial advocates, they tend to not let themselves get baited into leftist politics.  But when you look at the picture the media have painted of Trump, that’s exactly it.  He’s never talked about rounding up anyone, just closing and enforcing the borders.  And nevermind that more deportations have happened under Obama than anyone else.

The point here is, it would be nice to have conversations about immigration, or Islam, or cops, or any of these issues, without being branded as a racist homophobe Islamophobe animal killer.  And not just being branded, but being ostracized.  Because at some point the ostracizers become the ostracized.  The way things are going worldwide, the far right are the only ones who are echoing these sentiments.  This is giving them more and more power, while more and more mainstream parties are losing power.

It is possible to see the Democrats completely disappear as a party in November.  This is not healthy.  But it is absolutely the fault of those who think they have some moral cudgel to bash people around any time they disagree with something.

At this point I’d like to pat the back of fellow Gen X’ers.  They seem to be the ones spearheading the Alt Right movement, and I think it’s because we’re the last generation to be raised without mandatory seatbelts.  I honestly think the two are related.  If you live your life thinking you’re immune from danger, you live your life thinking you’re immune from strife and discord.

But life is all about strife and discord.  It’s what makes life dynamic.  It’s why I both agree with a Warren Buffett, who thinks America has plenty of dynamism left, and a Donald Trump, who for all his quirks, has a point when he says we can Make America Great Again.

And that’s why he’s the dark horse Republican Nominee.

Pokemon Go Strategy Guide

Tips for beginner players

In the beginning, the whole Pokemon Go world may seem a bit daunting.  At L5 you have your prize 100CP pokemon, and you make your first foray into the gyms, and all these ultra-intimidating 1000+CP Pokemon that you don’t think you’ll ever find in your life are guarding all the gyms.  It makes you want to throw your hands up in despair.

Well, don’t.

The key to surviving Pokemon is patience.  Patience and experimentation.  The game has enough randomness and handicaps factored in where you will have advantages over experienced players.  But, if you’ve just hit L5, don’t expect to be taking over any gyms.  In fact until you hit L10, you should only be focused on capturing Pokemon and tagging Pokestops.

But that sounds boring!

Don’t worry, there’s plenty to explore and learn until level 10.  Effectively capturing Pokemon is a skill in itself that you need to learn.  Not just how to effectively flip that pokeball, but what spots to hang out at, what bonus items to exploit.

So, go to your favorite neighborhoods, see what Pokestops are around.  Check out a park or a body of water somewhere and go “fishing” – just waiting around and seeing what pops up.  If you can make something out of your “Pokemon Near Me” screen, go for it.  It’s been spotty for me.

IMG_6698

That white ring you see represents your “discovery” limit. Any Pokemon, Pokestop, or gym in this ring will become interactable.

You can try to use the Pokemon Near Me screen to find those Pokemon you covet.  But you don’t know which direction they are, and if you’re like me, you can no longer even see how far away they are – just relative to each other (they read like a book – nearest is top left, farthest is bottom right).  So if you want to sweep for them, keep an eye on your white ring.  Run it through a neighborhood like a vacuum cleaner – up and down, back and forth, not missing any spots.

EDIT: I used to think you compete with other players for Pokemon.  You don’t.  What shows up for you shows up for others, but you all have the capacity to catch it yourself.  Even the rare ones.

What does happen is they “blink”: a Pokemon will appear in a specific location, but it will only hang out there 15-20 minutes before disappearing.  So if you chase a Pokemon that seems close and all of a sudden it’s no longer even on your radar, it’s because time’s up.  It does make the radar look like it’s messing with you.

The good news is it also means Pokemon tend to “blink” in the same spot – at least the more common ones.  So if you (or a friend) caught a Pokemon in a specific spot before, feel free to go hang out there some other time and see if it will pop up again.  Also, if you’re near that area and you see it registering nearby, go to that same spot.

You’ll also notice different types of Pokemon gather in different spots or streets.  So don’t waste too much time in your quiet cul de sac hoping a couple will show up.  Go to popular hangouts, and, well, hangout.  See what pops up.  Talk to other people and see where they caught good Pokemon.  A classic one is water Pokemon hanging around bodies of water.

This is where those lures and incense come in handy.  I think the jury is still out on how they operate, but I think they increase the chance of a Pokemon “blinking” into existence.  That is, if it is already known to blink there.

Catch them all – don’t worry if you have a bunch.  Did you know you can transfer unwanted Pokemon to the professor for a piece of candy?  So you’ll get that, you’ll get XP, and you’ll get precious stardust.

Don’t get me wrong, lures are nice.  If you combine them with a Lucky Egg and incense, you can have a wonderful time harvesting and leveling up with it.  Just try to find ones that haven’t lured everyone in sight.  I’ve seen some lured Pokestops that are virtual ghost towns.

At some point you’ll have enough basic Pokemon where you can experiment with powering up and evolving them.  But you should be cautious with spending your stardust and candy until you have some better choices on what to do with it.  Which leads us to

To Evolve or to Powerup?

It took me a lot of trial and error to figure out just how I wanted to budget my candy and stardust.  Which is part of the fun of the game.  But if you want to fine-tune it, there’s one basic rule to start: Don’t evolve weak pokemon.

Pidgey

Note the position of the dial. Don’t let this Pidgey fool you … it’s a butt kicker.

If you haven’t figured it out yet, above every Pokemon’s picture is a rainbow-shaped dial which corresponds to their CP (Combat Power).  Far-left is the weakest, far-right is the strongest.

At lower levels, you’ll have access to predominantly weak Pokemon.  But as you level-up you’ll see stronger and stronger ones.  One reason you wait till L10 is by then you’ll have some halfway-decent Pokemon worth powering up.  As well as a good idea of what Pokemon in your area are plentiful and which ones you should keep a tight budget with.

This Pidgey to the right is a classic example.  It’s powerful in its own right – certainly more powerful than some Pidgeots I’ve caught in the wild.  Also, if you were to take this to a gym, defeating an enemy could win you a powerful bonus.  Pokemon has a built in handicap system where if a low-CP Pokemon beats a high-CP Pokemon, you win much greater prestige.  But we’ll get to that later.

IMG_6701

This Pidgeotto was evolved from the Pidgey above. Note the position on the dial is exactly the same – though the “XL/XS” tags can change.

The thing to remember about evolving is, any Pokemon you evolve maintains the same position on the dial after it evolves as before.

If you’ve already “wasted” your stardust on your weaker Pokemon, don’t fret.  Powering up weak pokemon is a relatively cheap affair.  But once they get near their limit, we’re talking 2000+ stardust per upgrade.  And I imagine this Pidgeotto has about half a dozen upgrades left before it’s maxed out.

So, Stardust or Candy?  At some point, you will want to pull the trigger and evolve that kinda-powerful Pokemon.  Never regret that decision.  But the bottom line is this – if a Pokemon is plentiful (like this Pidgey) you will get plenty of candy to evolve it.  So don’t waste stardust on it – find that ultra-powerful Pidgey and evolve it away.  Save stardust for those rare finds that you will want to power up.

One other note – evolving a Pokemon will automatically run a full heal.  So waiting to evolve a Pokemon until after it’s been beaten up is a good way to go.  Also, if you wait to chain a bunch of evolutions at the same time, you can get a Lucky egg in there and get that XP bonus.  Especially if you’re evolving it into an undiscovered Pokemon type.

Gym Strategy

Okay, so you’re L10, you’ve got some Pokemon ready, and you’re raring to hit the gyms.  But before you go charging in, remember – potions are limited, and they’re the only way to heal your Pokemon (aside from evolving, we’ll get to that later).  You can easily spend all your potions to take over a gym, only to have someone else knock you out in a few minutes.  So this guide will help you figure out how to save those potions for maximum benefit.

First thing to do is copy this to your phone and memorize it.

IMG_6678

Got it?  Okay, we’re ready to move on.  Here’s where you should learn the secret: don’t let high CP Pokemon intimidate you.  I’ve gone in and wasted them with Pokemon of less than half their CP.  The key is in studying this chart, studying the Pokemon you’re attacking, and finding the right Pokemon to beat it for maximum prestige change and minimum HP loss.

A Pokemon’s type reflects their defense.  A Pokemon’s attack reflects their attack.  The two are rarely the same, and are relatively randomized.  For example, I have two Pidgeots – both are normal/flying.  But one has a Steel attack and one has a Flying attack.

When going up against an enemy Pokemon, the strategy is to find what attacks they’re vulnerable to, and what resists their attacks.  Then choose the Pokemon with the minimum CP that you think could defeat them.  Note there’s some randomness here.  You’re not really sure what their attack is, you just have a couple choices to choose from.

One way to find out is in combat.  If someone wanted to figure out my Pidgeot, he would put a Rock Pokemon to fight it, and then see if the Pidgeot’s attack is “Super effective”, which would mean a Steel attack, or “Not so effective”, which would mean a Flying attack.

As for dual nature Pokemon, I’m not quite sure how their defense works.  Do they get the strengths and vulnerabilities of both?  Are they averaged out?

Why take over a gym?

I’ll start this off with an anecdote.  I have a gym just out of reach of my house, and I have a couple neighbors in the Red team (I’m in Blue).  They told me how they need to stay in control of that gym, so any time someone took it over they took it right back.

I haven’t seen that gym go Red in a couple days now.

I imagine they kept trying to take it over until they ran out of potions.  Now, they’re powerless to do much of anything.  The point is, don’t let pride get in the way.  You don’t need all the gyms all the time.  What you do need is to have the gyms at the right time.

Well, what time is that?  Once you take over your first gym, immediately go to your Shop.  You’ll notice a shield icon in the top right corner.  Click on that to start the timer, which runs for 21 hours.

Now, during those 21 hours, you don’t actually need to control any gyms.  In fact, if you wanna really piss people off, put a weak Pokemon in there, a Pokemon you’re ready to evolve or transfer to the Professor anyway.  Start the timer, let people beat it up, then do what you will with it.  No potions wasted.

Once that 21 hour timer expires, now it’s time to take over some gyms.  You can let it expire without having any gyms, it doesn’t matter.  Just see how many gyms you can control simultaneously when you finally go to the shop to collect your bonus.  I’ve had up to four gyms at a time when I went to collect.  2000 XP and 40 Pokecoins is nothing to sneeze at.

But HOW do I take over a gym?

Oh, that’s right, it’s still all confusing.  The way they set up gym combat was built for high turnover.  If you go up against an enemy gym, you get to use six Pokemon.  If you go up against your own color gym, you only get to use one.

To ease your way into gym combat, you probably want to find a gym with a free spot.  Then put a Pokemon in there and see what happens.  If there are no free spots, you can make one.  You do this by battling the gym.  Put up a Pokemon that you think will beat the first one (what I call the Doorman) for maximum prestige and minimum HP loss.  After that fight is over, you’ll have option to keep fighting the rest until you run out of HP, but I tend to run away after that.

That gives the gym added prestige.  Once it hits a certain threshhold, another slot opens up.  Put your Pokemon in there, and it will file in according to CP.  Lowest CP is first to fight and first to get kicked out.  The top CP (champion) goes down with the gym.

Which leads to the next topic – how to take down an enemy gym.  You get six Pokemon to do it, and you get to choose (on the fly) which Pokemon goes up against which defender.  So chances are good you can defeat the whole gym.  It doesn’t mean you take it over, but defeating all a gym’s Pokemon will deliver a huge prestige blow.  And as its prestige goes down, its bottom Pokemon get kicked out, and it becomes easier to beat.

The basic rule is – the fewer and lower CP Pokemon you use, the more gym Pokemon you take out, the more prestige damage you deliver.

And while a friendly gym will only send your Pokemon to 1HP, an enemy gym will make your Pokemon faint (0HP).  Which requires a Revive crystal.  This is a good thing.  While potions are pretty scarce, I tend to have a lot of revive crystals.  So if you can find a way to attack a gym when all your six Pokemon are at 1/2 health, you won’t need any potions to defeat it.  Just Revive crystals, and patience.  They’re also good to use on high-powered Pokemon, since they restore more HP.

Ronnybiggs is an LA based player who won’t be selling his account for $100.

Brexit happened because of immigration

I feel like the discussion about Brexit has been disingenuous at best. And if we are going to stop Brexit from becoming a total rout of the EU and the world economy, we need to bring it back home.

The Brexit vote was about immigration. Pure and simple. Not about Polish immigration or Sikh immigration, it’s about the unfettered Muslim immigration from countries that have slipped into anarchy. More so, it seems the EU has found an ingenious way to circumvent all immigration law by using the “refugee” loophole. I.E.: If you can let Muslims pour into Greece, Italy and Spain, they are welcome anywhere in the EU. Including England.  This is what is making people flinch and tip in favor of Brexit, in what would have otherwise been a much more tepid discussion.

Now, I get the population increase argument. Economics is a dismal science, and part of that means that if your population isn’t growing, the economy crashes. But where did people think they could get away with this “refugee” scheme? Did they think people would fall for it and NOT have some massive backlash? And did they remember that immigration is one thing, assimilation is another?

No, apparently not.

Officials need to at least own the situation we’re in. Own the consequences of the last few years of unfettered immigration and the dismantling of existing law. First of all, we know that a 90% male influx isn’t refugees, it’s taking advantage of the loophole they’re so proud of.

Second, Muslims in the EU need to be assimilated – we can’t just ignore this massive clash of values.  If a Muslim commits terrorism, call it Muslim terrorism.  Really, Orlando is a gun control issue?  That’s just … autistic.

And yes, assimilation happens violently, with draconian laws, machine guns and billy clubs (back to that dismal science). No-go zones need to be acknlowledged, and put under siege. Mosques need to be tightly monitored for terrorist ties (as has been done quite successfully in France). Any Muslim that doesn’t like it is free to find another country.

And if the EU isn’t to be completely torn asunder by a right-wing resurgence, it needs to QUICKLY revamp its “freedom of movement” policy. This “refugee” loophole needs to be closed.

Keep in mind, I dislike the extreme right as much as anyone. Whenever they come into the government, things get messy. I would have liked someone other than Nigel Farage or Boris Johnson to have the day in Parliament. But if they’re the only ones to address the Muslim elephant in the European room, they will continue to surge in the polls. They will continue to fill all sorts of crazy agendas along with a sloppy resolution the the immigration issue.

But if the mainstream continues to ignore this debate, the extreme right will seize the next few years, all over Europe. England is only the first domino.

Arya Stark and the Iron Bank of Braavos

Note: this post is a work in progress.  I am adding more as I go along.  

“The Iron Bank is the Iron Bank.  There is no ‘someone’… [like] a temple is comprised of stones.  One crumbles, and another takes its place.  And the temple holds its form, for a thousand years or more.  And that’s what the Iron Bank is, a temple.  We all live in its shadow, and almost none of us know it.  You can’t run from them, you can’t cheat them, you can’t sway them with excuses.  If you owe them money and you don’t want to crumble yourself, you pay it back.” – Tywen Lannister, S4E5

Looks like GoT is preparing next season to be a clash of the seven major kingdoms.  The Free City of Braavos exists as a completely sovereign kingdom of its own.  It is most known among the kingdoms as the home of the Iron Bank.  How does an Iron Bank like that exist, in a city with no visible army, and continue to prosper and accumulate wealth?  How is it not a pile of gold waiting to be looted by any passing marauder or unscrupulous monarch?

The answer is the Faceless Men and the House of Black and White.  This is their enforcement wing.  It operates as a totally clandestine army, operating exactly as Tywen describes.  My hunch is that they have been very much aware of Arya Stark’s potential since the beginning, and are ready to use her to great benefit in season 7.  They’ve been preparing her ever since season 1.  Let’s unfold the timeline.

In Kings Landing, Arya gets swordsmanship training (water dance) from Syrio Forel, the First Sword of Braavos.  Pretty sure if the First Sword of any country sacrifices himself so you can run away, he’s got plans for you.  Of course the fact that we don’t actually SEE him dead, which in GoT is always suspect.  Especially when associated with a Faceless Clan.

She runs away from Kings Landing with the help of Eddard’s friend (brother?).  Quite shortly into her journey, she runs into Jaqen H’ghar, trapped in a cage with two other prisoners.  First, it means he and Syrio were in King’s Landing at the same time.  But he immediately knows her name and tells her his origins – but not the right one (free city of Lorell?).  She saves him and the others from burning up in their cage during a melee.

Once in Harrenhall, he finds her in a quiet spot and immediately talks to her in third person language.  “A man”, “a girl”, etc.  And he schools her in the justice he knows.  “A man pays his debts.  A man owes three.  Only death may pay for life.  You stole three deaths from the Red God, we have to give them back.”  Whether he truly follows a credo or wants to build a relationship with her is irrelevant.  It’s one and the same thing.

His second target is by poison dart.  “Wolfsbane.  A rare substance.  This is no common assassin.” – Tywen Lannister.  And the funny thing is he doesn’t suspect a thing.  He thinks it’s some Brotherhood nonsense.  BTW notice the name Wolfsbane, is the namesake of the Stark sigil?

Okay, so at this point we know something’s up.  How does a skilled assassin get caught in some cage with two rogues, unless he intends to?

After he helps Arya escape, he continues to stalk her.  In a really creepy fashion.  “If you would learn you must come with me to Braavos.”  “My dancing master was from Braavos.”  Here he introduces her to the Faceless Men and knows all the names she wants dead, says she can offer them to the Red God.  He gives her a coin “of great value” but “not meant for the buying of horses.”

So, at this point, Arya has learned his exacting bookkeeping credo, how to avoid being noticed, and the esoteric value of a coin.

Meanwhile, we are introduced to some Iron Bank executives when Stanis asks them for a loan.  They too are faceless, in their own way.  Expressionless, characterless, no discerning characteristics.  They only repeat the mantra of the bank.  The fact that we think bankers are dry and boring actually works against us.  It is the credo they thrive on.

And we’re also introduced to the dread the Lannisters (who always pay their debts) have to the Iron Bank.  Tywen’s quote above comes from a very informative conversation he has with Cersei, divulging the debt they owe to the Iron Bank.   “We all live in its shadow, and almost none of us know it.”  A number of ironies here, namely that Jaqen had been training Arya literally under Tywens nose at Harrenhall, and he never suspected a thing.  Tryion shares a similar dread of the vengeance of the Iron Bank.

This drops us off in season 5 and drops off Arya in Braavos.  It’s worth pointing out his description of the statue guarding the city.  A shield and broken sword – implying a city that does not attack, but has a supernatural ability to defend itself.  And when Arya thanks the sailor for dropping her off at the House of Black and White, he says “any man of Braavos would have done the same.”  See what he did there?  The whole city has a certain faceless heritage.

Jaqen H’ghar answers the door in disguise, and gives her the cold shoulder.  And yet he watches her every move – from dropping the coin in the sea to intercepting her encounter with the three rogues.  He probably knew she didn’t drop Needle.

It’s all part of a complicated training program he puts Arya through.  Not going to get into all of it here, but there was one telling conversation: explaining the insurance agent’s corruption to Arya, and how the Faceless Men provide justice to those who’ve been cheated.  “Perhaps the gambler loses his bet and decides he does not have to pay after all.  A destitute woman and her small child, what can they do to such a man if he keeps their money for himself?  To whom can they turn for recourse?”

Ah.

So, if the Many Faced God will bring retribution to such a destitute woman, what kind of retribution does he provide to, say, the Iron Bank, if a powerful family like the Lannisters decide they don’t want to pay their debts?

There’s other lessons we could talk about here.  Like Arya learning what it means to be noone.  And that while faces change, credos, institutions, loyalties, house names remain.  “A girl is Arya Stark of Winterfell.”  She isn’t denying she’s noone, she’s saying the Stark name isn’t just faces.  It’s a valuable lesson the Iron Bank brings to the story as a whole.  Especially to those who just see characters like Arya as Arya, i.e. individual faces with individual stories.  Alone, apart from this grand waltz, they make no sense.  “The faces are as good as poison.

The real story is, the House That Always Pays Its Debts owes a huge amount of money to the Iron Bank That Always Collects Its Debts.  It’s too glaring a plot twist to ignore, especially at a time when the Lannisters seem to be militarily dominant and the Starks so weak.

 

Why America needs a Trump candidacy

Most of my coworkers are Latinos – most of those are El Salvadoran.  So when we went out for lunch one day, it was only a matter of time before they found out I was leaning towards Trump.

Needless to say, it got awkward at first.  First came the comments about his disparaging attacks on Latinos.  Then his comments about Muslims.  But after I wasn’t knuckling other to either one, since I honestly think both charges are bullshit, the silence led one of them to make an illuminating comment:

“Of course we need to have laws.”

We need to have laws.  Indeed.  That’s the crux of the Trump candidacy, and it’s the crux of the European electoral tumult.

I’ve been in politics a long time – since my naive days of Jerry Brown’s 1992 presidential campaign.  I can say that the primaries are a brainstorming session for both parties – they let any comers shoot off any strange and unformed ideas they have, and see what sticks with the voters.  It’s only towards the end of the primaries, heading into the convention, that they decide it’s time to close down the session and rally around a candidate they feel represents them.

Only sometimes it doesn’t quite work as planned.  Like this year.  This year has been a real popular backlash against ruling class policy – that of abolishing all immigration law, and allowing anybody on earth to move anywhere they want.   We may have our “illegal immigrant” problem here at home (I’ll get to that in a bit).  But it’s nothing compared to the brilliant EU loophole of allowing “refugee” status to people in any one country and then letting them in through that back door into any other country in Europe.

As Douglas Murray puts it “‘imagine there’s no countries’?  We don’t have to imagine it, we’re seeing the real consequences of getting rid of borders, and that’s people blowing themselves up in the heart of Paris.”

It’s no stretch to say this is deliberate policy.  And part of that policy is to smear anyone who criticises the scrapping of immigration law and borders as a bigot.  This is happening both in European and American governments, both Democrat and Republican parties.

And that’s why when Trump comes in and says things like “build that wall” or “seal the borders” it’s a signal that he supports something THEY CANNOT ALLOW TO HAPPEN.

The remarks themselves aren’t even worth scrutinizing that much.  In a brainstorming session, one wants provocative remarks like this, because they spur thought, reaction, debate.  Nevermind if they’re unworkable or offensive, we have plenty of time to take those comments, see the direction they’re going in, and hammer them out into workable policy.

Like the “ban all Muslims” remark.  Nevermind that they twisted what he said.  Nevermind that there’s no way to ban based on religion.  But there are bans based on country of origin.  It’s not that hard to go from one to the other, and we did it to Iran after their hijackings.

But back to the American issue of immigration.  If I make one point, it’s this.  It’s okay to demand immigration be made legal.  It’s okay to make sure those immigrating here legally can do so more easily than those who don’t.  It’s okay to demand that those who pose a terrorism risk aren’t allowed in.  The more voters who make these demands are made to feel like bigots, the more they will rally and solidify behind a man like Trump.

It’s in everyone’s interests that everyone in this country is here legally.  The fact is, someone who is here working illegally is someone who is working with no rights.  Are there issues with this?  Of course.  That’s a whole separate article.

But nobody’s saying “kick out all the Mexicans” or “Mexicans are criminals”.  Those are just slanders.  Trump’s main remark, time and again, is that we can’t just ignore our own laws and let people pour over without any record.

That’s a great starting point.  If we’re short on workers, nobody has a problem with liberalizing immigration law.  As my coworkers told me, and I suspected, poor Latin Americans can’t immigrate legally to USA.  Only the rich can.  Well, that’s a problem.  And we can change that.  With laws.  Not by ignoring laws and ridiculing those that have a problem with it.

It’s no secret that America’s a nation of immigrants.  My coworkers relay to me their parents’ stories of escaping violence and poverty to seek a better life in America, and honestly, it doesn’t sound too different from anybody else’s story.  That’s why nobody’s doing themselves any favors by claiming the Trump campaign anti-immigrant.  Because those who’ve been paying attention to Trump’s remarks realize it’s a “pro-law” campaign.

Because America is a nation of immigrants, but it’s also a nation of laws.  And one doesn’t trump the other.

You can travel faster than light speed

“And I think it’s gonna be a long, long time
‘Til touchdown brings me ’round again to find
I’m not the man they think I am at home” – Rocket Man by Elton John

A misconception exists in Einstein’s famous equations – that there’s some absolute speed limit where we couldn’t possibly travel to the stars any faster than light speed.  It’s actually false. Well, to everyone we knew out on Earth, they’ll be long gone by the time we come back to regale them with our tales.  But to us and our crew on the SS Enterprise, well we could explore half the galaxy in one lifetime, with the right warp drive (which is entirely another issue).

First, the Twins Paradox – and the hidden paradox within.  The focus of the twins paradox is how one twin flying to a distant star and back will barely age, while their counterpart back here on Earth has aged several decades.

Okay, do you see what I’m talking about yet?  Here’s another hint.  Do you think they were hanging out on their spaceship all those years enjoying some fountain of youth?  No – they literally took that amount of time to travel back and forth.  While years and years passed on Earth, only a few days or months passed on the spaceship.

And that, to me, is the far more interesting paradox.  Let’s take our favorite star, Alpha Centauri, hanging out four light years away.  I’ll leave my brother off at home, and take off on my high speed rocket at near the speed of light, so it takes nine earth years to go there and back.  But my brother and I, being rather perceptive people, don’t just notice that he aged and I didn’t.  When we compare clocks, literally only a year passed for me, while nine years passed for my brother.

Wait.  How can that happen?  How could I have travelled to Alpha Centauri and back, something light would do in nine years, in only a year?  Did I mysteriously break the speed of light?  And if so, how did I do that?

Well, yes and no.  What the absolute speed of light says is that no object can reach the speed of light relative to another object.  That’s why it appears to my brother to take me this long.

But what happens to me?  The answer is another twin – time dilation’s lesser known twin, space dilation.  As my ship accelerates past Earth into sublight speed, it’s not just time that shrinks to nothing, space also shrinks to nothing.  The distance I have to travel to get to Alpha Centauri now shrinks from four light years to only half a light year.

lorentz

The Lorentz transformation – how spacetime dilates with relative velocity.

And yes, the shrinkage is exactly the same.  It’s called the Lorentz transformation and is why Einstein called it spacetime and not just time or space.  Both time and space dilate equally according to gamma.  This is what allows a photon (ray of light) to appear to travel the same speed relative to everyone looking at it.

Here’s another fun way of looking at it.  As we said above, accelerating a spaceship to that speed is well out of our technology, and that’s the real issue of space travel.  But we regularly accelerate particles to quite near light speed in our accelerators.  So let’s pretend this particle is a spaceship and see how long it would take for it to get to, say, the center of our galaxy (25k light years away).

Fortunately my favorite website has a great example – just as it throws up its hands in at the implication that we’re permanently Earthbound.

Difficulty of acceleration

The fun part is, right below it they talk about the problems with variable mass – implying problems in general.

Saves just a second for you landlubbing Earth dwellers, maybe.  But let’s see how the world looks from the perspective of that electron.  By the Lorentz transformation, space and time dilate by a factor of about 60 for the first electron, and about 11,000 for the second one.  A good way to understand gamma is you’re going gamma times the distance in one gammath (1/gamma) the time.

Essentially, that first electron is going 60 times the distance in 1/60th the time.  So spacetime has dilated to 3600 times what it was used to back at rest – particle 1 is going 3600 times the speed of light of its old frame of reference.  Particle 2?  It’s going 121 MILLION times the speed of light of its old frame of reference.

Translation?  Particle 1 could get to the center of the Milky Way galaxy in about seven years.  Particle 2 could get there in a little under two weeks.

Of course we’ll never see the news of either of these guys travels.  We would have to wait here at rest for 50,000 years for them to return.  Entire civilizations, entire species will have come and gone by then.  But that’s not for rocketmen to ponder.

When you think about it, fiction portrays it rather accurately. The stars imploding on the ship are a good portrayal of how space would dilate.

When you think about it, fiction portrays it rather accurately. The stars imploding on the ship are a good portrayal of how space would dilate.

 

The event horizon – a cosmic mirage

Black holes – or more specifically, their event horizon – are a cosmic mirage.  Not much different from a rainbow.  Oh, they’re real alright, I’m not talking about leprechauns with the pot of gold at the end, but the way we experience them is totally different from the thing itself.  There is no such thing as “falling though the event horizon” because the “event horizon” is precisely only our experience of it.

Contradictions in last episode

The interesting thing about scientific inquiry is you’re never satisfied with your answers.  Answers always lead to contradictions, things that don’t make sense, new questions.  I had answered how something can accelerate to light speed in a black hole’s pull.  But what if it doesn’t?  What if some daring astronomer constantly decelerates himself as he comes closer and closer to the event horizon, constantly making sure he’s both aiming for dead center, and making a nice slow descent?

Now you could counter by saying that if you didn’t let yourself freefall, the G forces would tear you to shreds.  But here comes the complicating factor.  Supermassive black holes exist which have relatively weak gravitational force at the event horizon.  A black hole with a radius of about one light year, for example, would have a gravitation at its event horizon equivalent to here on Earth’s surface (aka 1G).

Not so coincidentally, if you were to accelerate for about a year at 1G, you would reach what I call nominal light speed – which is your actual speed if you accelerated to light speed in a simplified Newtonian universe  That just happens to be 0.618c (0.618 the speed of light) – which is exactly the proportion of the golden rectangle (?) – but we’ll save this tidbit for later.  The question right now is how is such weak gravity at an event horizon even possible?  Aren’t black holes supposed to spaghettify us and tear us into subatomic shreds and stuff?

What’s an event horizon doing with such, well, EARTHLY gravity?

Wait, what?

Yes, that’s right.  radius accelSupermassive black holes have very low gravity at their event horizon.  It’s a simple formula, really.  The radius of the event horizon is the inverse of its acceleration – i.e. gravity.  r*a is the same for each and every black hole.

I could do some extra wizardry to show you the math, but you have the internet for that.  Small black holes pull really hard on that photon to whip it in a circle.  Large black holes can take their sweet time.  And here’s the fun part – if you were to free-fall into a black hole radius accel integral– ANY black hole – from somewhere outside its influence, you’d accelerate to the speed of light.  Ve = velocity at event horizon = c (speed of light).

But the twisted logic that happens at that event horizon remains the same.

A lesson on geodesics

Well, how do we wrap our minds around that?

black hole geometry

The non-euclidean geometry (geodesics) of a black hole, as discussed in our previous post

For that we have to delve into the world of geodesics.  And first in that, a beef.  I don’t like the term “geodesics.” It conjures up hippy domes in the middle of the desert.  I prefer the term “non-Euclidean geometry”.  It easily tells us we’ve left the familiar world of ancient geometers with their simple circles and triangles on a flat surface, and are falling down the rabbit-hole (so to speak) of curved spaces and planes.

And that’s what we need to know to understand a blackhole.  It’s how we can picture Einstein’s theory of relativity.  If you’ll recall from my last post, this 3D well describes the spacetime around a black hole – how it curves down into an infinite well.

There’s a few things going on in that diagram, so we’ll try to take it a bit at a time.

The thing to remember about this well is, it’s not like gravity is pulling everything down it.  It mainly describes how light, a massless particle that always travels in a perfectly straight line, can still seem to bend.

Now there’s difference in the specifics of how light and massive entities  fall towards a gravitational center.  But what’s the same is the acceleration.  Here on Earth, we are constantly accelerating towards it at 9.8m/s2.  And light is no different.

Even though it travels in a straight line.

And that’s my second beef with “geodesics”  – the definition of a straight line as the closest distance between two “local” (i.e. “close”) points.  That’s a bit of a copout, like saying “well we’re reducing this to a map”.  I prefer the term “no sideways pull”.

plane aileron

The (air)plane rotates, twisting the (geometric)plane it’s on, and then lifts into a turn. Get it?

But let’s go back to our analogy of the plane from last chapter.  There’s rudderless planes out there.  By just rotating the plane with ailerons, and using the elevators in back, you can turn every which way without ever having sideways pull.  Just rotate the plane, and go up or down.

So if you look at what makes the plane “turn without turning”, the factor here is “which way is up”.  As it rotates, it changes that “upwards” direction, and then goes up or down in that upwards direction.

And BTW, this works equally for spaceships in zero gravity.  So gravity has nothing to do with which way is up.  In more complicated math, it’s called “orthogonal” which is defined as the perpendicular to the plane.  This allows us to pile on more dimensions.

But we’re here to discuss black holes, not study math.  So let’s translate this “upness” into black holes.  earth v supermassiveCompare Earth’s gravitation of a beam of light – a1 – and compare it with a REALLY massive black hole, whose acceleration near the event horizon is less than at Earth’s surface.

As a light beam approaches earth, it enters Earth’s gravity, changing its “upness” and starts to “curve” around Earth.  What causes the curve is the “upness changing”.

Now, compare that to a supermassive black hole.  By the time you’re near the event horizon (as seen by this incredibly drawn cut-out) you’re practically vertical.  But there’s not much “upness” left to change.  You’re just being whipped around in what seems like a flat surface, in a very large cylinder, “upness” pointing directly into the middle.

Any way you look at it, it’s the speed of light

The problem though, with such small scale cutouts, is they conveniently leave out just how far we’ve come to get to this “vertical space” in the supermassive black hole.  As I hinted earlier, before we get to this spot in a supermassive black hole, we’d have been freefalling literally for years and years.

But what if we decided not to freefall?  What if we got some theoretical rocket thrusters and slowed down our descent, so we avoided being anywhere near the speed of light at the event horizon?

Einstein’s Theory of Gravitation

The answer is it doesn’t matter.  Because how would you do that?  You would manually accelerate yourself in this gravitational field.  If you did the same manual acceleration outside a gravitational field (i.e. deep space), you would go from 0 to light speed.  So no matter what your behavior is around the event horizon – hovering, freefalling, or some combination of the two (i.e. orbiting) – you’d be at near light speed.

This is what Einstein is talking about, that we experience a spacetime dilation in a gravitational field, even if we’re hovering/standing/using rocket thrusters.  The spacetime dilation is basically equal to the sum of acceleration from deep space to whatever surface you’re at.

Back to where we started

Which takes us back to the incredible shrinking black hole, except this time we take it a step further.  In the last post, we talked about the fact that a black hole shrinks away from any object approaching it.  But just how?  We don’t want to just WATCH something fall into a black hole, we want to KNOW what it’s like.  We want to BE whatever it is that falls in.

Well, considering we nixed any realistic possibility of crossing the event horizon with strange tricks, let’s pretend  we’re freefalling directly to a black hole’s heart.  And orbits are boring.  We want to go straight in.  So we have this craft that doesn’t try to resist gravity, and doesn’t let us slip to the right or left.  And we’ll start well outside a nice supermassive black hole, about 1 light year diameter.

The best way to picture this is pretend we’re falling in a Newtonian universe, and at periodic intervals, we’ll recalibrate to allow for how spacetime changed around us.  Don’t worry, if someone gives us flak for this, just tell them delta apporoaches zero.  If it doesn’t shut them up, send them my way.

If you were to freefall to what you think is the event horizon, you’d hit what you’d think was light speed in a Newtonian universe – i.e. “nominal light speed”, or to put it another way, Newtonian velocity = momentum divided by mass = light speed (v=p/m=c).  So let’s take our new bearings.

Distance to center is still r.

Actual relativistic speed is now ?c (~.618c).

At ?c, distances shrink to ??.  So the radius of the new black hole is r*??.

Time also dilates to ?(1+?) for those outside of you, but we don’t care about them, so that’s kind of irrelevant.

Recalibrate your instruments for your new reality, and freefall AGAIN to “nominal light speed” – the speed you’d reach at the new event horizon at r*??.

Distance to center is now r*??.

Except now you’re at ?c compared to where you were before, or basically, your momentum doubled from your starting point.  You’re at  ?c compared to your last point.  Or, to put It another way, Newtonian velocity is twice the speed of light (p/m=2c).

New event horizon is now r*?.

freefall graph

While “light speed” is maximum, momentum is infinite. Here’s how momentum compares to the relative size of an event horizon. You would even out where the event horizon was ?? times the distance from the singularity as you are.

And so on, in the grand progression of the golden rectangle.  The ultimate equation is that y=r*a/ ?0.5(x-1) . Where y is your Newtonian velocity (momentum/mass) and x is the radius of the black hole.

Here, you know what?  Let’s draw a graph.

Notice there’s no time here.  Acceleration is whatever it is to get you to the light speed you’d reach at event horizon.

How far down do you want to go?  How much can your imaginary ship take?  How infinitely fast do you want to go?  How far do you want to escape those boring confines of flat spacetime and see the universe from the perspective of the infinite?

That is what it’s like to fall down that well.

 

 

 

 

The Incredible Shrinking Black Hole

Couple interesting stories in the news lately.  One was about the discovery of gravitational waves.  The other was about directly witnessing a star get swallowed by a black hole.

star getting swallowedExcept it seemed the writers of these stories were so abuzz about the actual event, they didn’t point out the curious aspect of HOW a star gets sucked in by a black hole.  Observe the artist’s illustration:

Wait, what?

Did you see that?

Here, let’s take the REALLY interesting part of this diagram.

gravity pulling away notes

Shouldn’t the star be getting sucked directly into the black hole?  If the black hole has such all-powerful gravity, shouldn’t the star’s mass be getting pulled right along the blue line, right into the center of the black hole?  What’s it doing curving AWAY from it, like with the red line?  When was the last time you saw an object fall and turn AWAY like this?

For this, we need to get into the deeper workings of Einstein’s theory of general relativity – the idea that space is curved, and all we can ever see as observers is a flattened version of it.  Not far behind is the mystery of black holes, those unknowable holes of nothingness, those Bermuda Triangles of the universe, and ultimate examples of relativity in action.

To better understand the relativity of black holes, we must understand the concept of curvature of space.  flight mapThis is the branch of mathematics known as non-Euclidean geometry, and we’ve all seen it at one point or another.  Take, for example, an intercontinental flight.  Watch your flight take place on a map, and your plane seems to curve along its way to the target, rather than going in a straight line.  That seems a bit … inefficient.

flight globeUntil you recall that we’re not travelling on a map, we’re travelling on the surface of a sphere.  We and the pilot are very nicely travelling along a straight line, never veering to the left or right as the map would have us believe.

Likewise, light always travels straight, unperturbed by gravity since it has no mass.  So why does it bend in a gravitational field?  This is where Einstein’s theory comes in.  He said that gravity is more accurately understood as a warping of space and time (spacetime), and that a massless beam is still travelling straight through the field.  flight whirlpoolMuch like if, instead of traversing a globe, our plane were to fly through a depression or whirlpool without turning.  It would also bend its path even though we were flying perfectly straight.

So here’s the issue, mathematically speaking.  If a straight line goes through any whirlpool, no matter how steep, it will spiral in, level out, and eventually spiral its way out.  If a black hole simply has really, really steep walls, light will be able to escape.  There would be no such thing as an event horizon, through which light can never escape.

flight steep whirlpoolFrom a mathematical perspective, the only shape that can hold a straight line is a cylinder. flight cylinder

And that’s how we would need to understand the topology of a black hole – not that it is just really really steep, but that it’s more like a well – with walls asymptoting (limiting themselves) at the event horizon.

Which brings us to an interesting concept.  “Light can’t escape a black hole” is actually a misnomer.  Fact is, light can never ENTER a black hole.  By our idea of the asymptotic well, light will always spiral in ad infinitum. black hole well

We can see evidence of this in the picture below of a black hole crossing over a galaxy.  That corona around it?  That’s light from the galaxy hitting the black hole, spiraling into its well, before spiraling back out in that ring formation.

And let’s take that the actual mass of a black hole is a infinitesimal speck right in the middle of the event horizon.  What we’re seeing already is a black hole is literally a RUPTURE in spacetime.  By this model, there is no spacetime between the black hole and the event horizon.

black hole galaxy

The “corona” around this black hole is light from the nearby galaxy that gets trapped in its pull. It then spirals in, flattens out at a certain depth, and spirals back out at us.

This is where things start to get weird.  To better understand this weirdness, we need to understand just HOW spacetime warps around a black hole.

There is no speed limit

First of all, the “speed of light” is a misnomer.  There is no universal “maximum speed” per se.  It may take four years for light to reach here from Alpha Centauri.  But that’s from the perspective of us sitting here on Earth.  If you were somehow to hitch a ride on a beam of light, you’d arrive at Alpha Centauri in an instant.  It’s only to all your friends back home that it seemed to take you four years (eight years, really, since it would take four more years for news of your arrival to hit home).

So what’s going on?

If you were to somehow speed up that quickly, and slow down again, what you’d see is the whole universe collapsing all around you, Alpha Centauri would only seem a step away, you’d make a quick jump, and then the universe would expand again as you slowed down, finding yourself at your new star in just a moment.  Meanwhile, everything around you just aged four years.

Cool, huh?  Of course we haven’t even gotten to the fact that you’d have to accelerate far faster than the speed of light to get anywhere near it – meaning, if you had some gyroscopic speedometer that was based purely on acceleration, it would say you’re going far far faster than light speed.  But let’s save that for another time.

Here’s a more realistic application – the Cern supercollider, which accelerates particles to near the speed of light.  It runs them along a magnetic circular track, accelerating them to near the speed of light.  What happens from an observer’s perspective is far different from the particle’s perspective.

cern observerFor simplicity’s sake, let’s say the track has a radius of 1 mile.  It accelerates to near the speed of light, running round it at 100 times/second.

But let’s say we could shrink down to that particle level and hitch a ride.  What would we experience?  As we approached the speed of light, time would slow down for us, AND distances would shrink.  Other things would happen too, like we’d become more massive.  But the distance and the time are the interesting part.  cern particleOur track would shrink to only 1 meter radius, and now while we were at around the same near-light speed the observer sees us at, we’re now doing the track at 160 THOUSAND times/second.  In that second, we’d see the outside world age 25 minutes.

Okay, now back to black holes.  One fascinating phenomenon about matter entering black holes is, for a while it seems to turn AWAY from the black hole.  As if the black hole wants matter to orbit around it rather than sucking it right in.  How can that even happen?

Once again, this is an illusion brought by travel along non-Euclidean spacetime.  Let’s go back to our diagram of a black hole as a well.

Better yet, let’s look down an actual well.well

Now, imagine this well is really deep.  I mean, really REALLY deep.  See that disk at the bottom?  How small can you imagine it?  And remember, it’s the exact same diameter at the bottom as it is at the top.

Now, try shining a laser pointer at  the bottom of this really deep well.  Not too easy, is it?  You’ll inevitably end up hitting the surrounding wall.

And that’s what happens when matter or light hits a black hole.  Let’s take what we learned from our Cern particle and see what happens as matter hits a black hole.  From an observer’s perspective, it approaches, then mysteriously turns away as it accelerates and starts orbiting the black hole.enter observer

The incredible shrinking black hole

But what happens from the particle’s perspective, as it hurtles towards that black hole at breakneck speed, powerful gravitational forces accelerating it near the speed of light?  We go back to our Cern illustration.  As it accelerates, its universe collapses around it.  Rather than curving away from the hole, the very black hole it seems to be hurtling into shys away from it. enter particle It continues ever towards it, missing this now shrunken black hole.  Since it can never aim for absolute dead center, the black hole will always shy away just enough to have it “miss” and gett pulled into orbit instead.  Keep in mind it’s the same black hole, it’s still travelling a similar near-light speed, but it orbits this shrunken black hole 1000 times in the time it takes the observer to see it orbit the black hole once.
That infinitesimal dot at the bottom of our well is starting to make a lot more sense now, doesn’t it?  Also, it’s a nice location for the Restaurant at the End of the Universe.  But we digress.

So, here’s where things get REALLY interesting.  If the event horizon is the circumference at which light can no longer escape – it means from the perspective of anything on the event horizon, that black hole is now infinitesimal in size.  Which just happens to be the perfect distance for quantum mechanics.

Now, I’m not much of a quantum mechanist.  I know enough about the subject to separate science from new age bunk, but that’s about it.  But as a mathematician and armchair philosopher, I also know about Zeno’s paradox: That nothing can ever get from point A to point B.  That’s because it has to travel half that distance first, and half that distance before that, and so on ad infinitum.

The solution to that paradox is also the prediction of the atom – that ultimately the universe is composed of indivisible quanta.

plasma globeAnd that’s what I think is happening between the event horizon and the point of singularity.  The concept of spacetime in here is bunk.  It’s a hole in spacetime.  An infinitesimal hole, a quantum leap between the event horizon and the point of singularity.  And particles snap to singularity.  Kinda something like this plasma globe.

 

Some fun observations

So let’s go back to our black hole eating the star.  What’s happening?  As the star’s matter approaches the black hole, it’s getting accelerated to speeds approaching light.  To them, they’re going straight into it.  But the black hole is shrinking.  While we’re watching them slowly orbit around it, they’re orbiting it at fractions of an instant.  As friction eats away at their orbit and they get nearer and nearer the “event horizon” it keeps shrinking farther and farther away from them until they get shredded into the light show you see above.

People are fascinated with the event horizon.  More so, they’re obsessed with CROSSING it.  What’s on the other side?  We now see that simply APPROACHING the event horizon gives us plenty of questions to answer before we throw a probe into a black hole and hope it doesn’t fall apart.

The fun thing about black holes is they’re such a drastic warp of spacetime that they render our very flattened perception of them meaningless.  For example, the more massive a black hole is, the smaller its apparent gravity at the event horizon.  There are some black holes so massive that, as far as we can tell, gravity at the event horizon is less than gravity at the earth’s surface.

That doesn’t make any sense, does it?  If you could hang out like this at the event horizon with some rocket thrusters, it would be very easy to throw a depth charge through the horizon, watch it explode, and witness the event via the light that crosses through the horizon.

Except you just contradicted the whole concept of an event horizon.  Something’s wrong about our calculations.  Ah yes – we forgot we’re not in flat space-time.

It’s not just the faster you travel that the smaller everything gets.  The more warped the spacetime you’re in, the smaller everything gets.  It’s all the same phenomenon really.  So even if you somehow managed to temper your descent into a black hole so you got to what you thought was the event horizon, instead you’d be seeing a smaller black hole.

Animated black hole

It’s not just an accurate portrayal of falling down a black hole … the downward spiral is a great literary device.

Matter will always be accelerated towards a shrinking black hole until it reaches light speed, and the whole universe collapses around it to a timeless point.

These are certainly things worth thinking about.  We have to remember, when we think about these things, that an event horizon is such a profound warp of space-time, we can’t just “hang out around the horizon” like sci-fi illustrations would have us believe.  As we can see from the 3D diagrams, before we think of crossing the event horizon, we have to understand the profound differences of anything approaching it.  Any matter we interact with it would either have to accelerate an orbit to nearly the speed of light, or experience gravitational force that would rip any matter to subatomic shreds.

All this, within a space of millimeters by our outside perspective, that was somehow stretched to astronomical lengths invisible to our naïve eyes.