Roger Penrose Nails it Again

The James Webb Space Telescope

There's recently been a lot of excitement about the images coming in from the so-called JWST, the latest telescope sent out by NASA and the JPL, and commentators and geeky influencers are getting themselves excited with the possibility that the Big Bang Theory might be wrong!!  "Please, please, let it not be so!"  Don't panic; all future cosmological theories will (probably) incorporate some version of the Big Bang.

As I was watching, at long last, Roger Penrose on YouTube, I was startled for one big reason.  In grad school, where I studied all sorts of things (in contrast to a lot of my fellow-students, who were already focused on getting to the research stage ASAP,) my research group---OK, it was just me and my advisor---but he loosely belonged to the group that had collaborated with Roger Penrose and Ezra (Ted) Newman, Paul Todd, John Porter and co, to develop a technique based on complexification of Einstein's theory.

I never could see the point of complexification of spacetime.  I loved and was quite at home with Complex Analysis, the mathematics of complex numbers; they are an elegant and unifying approach to various aspects of math, but I had learned physics from a completely non-complex point of view, and I merely endured the idea of complexification, because I did not want to be rude, and I did not want to spend an age before I graduated.

A central idea with complex analysis is that of conformal transformation.  This term refers to transforming graphs (bear in mind that a lot of mathematics is about graphs) in such a way that lengths and distances may be distorted, but angles are preserved.  Einstein's equations can be transformed conformally as well.  (If you transform the geometry of a problem, you can transform the equations as well.  Sometimes the equations don't look anything like they used to; sometimes they are hardly changed at all.  In this case, the equations were the same except for a non-zero formula that could be divided out from both sides of each equation; what a stroke of luck.)

There is sure to be a print explanation of Penrose's idea on the Web somewhere, but here is the gist of it.

The Boundary of Spacetime

A favorite thing for Penrose and Newman---principally the latter---to do, was to reduce the infinite part of space into a surface.  This sort of thing has been done in many cases.  For instance, the Number Line (or the Real Line, as it is known to its friends) can be reduced to just a line segment with two endpoints.  The whole infinite part of the number line is collapsed---very carefully, obviously---to the two dots at the end of the line segment: minus infinity and plus infinity.

In the case of Spacetime, every point (or event) has to lie on a set of what are called null geodesics, that is, paths of light rays.  Now, in principle, light rays will leave every point in every direction.  We say that there is a sphere's worth of light rays emanating from each point.  Each of these, like the number line, can be reduced to a line segment, with two endpoints.  The clever part of the method is that all these endpoints can be formed into a surface.  Two surfaces, actually; one in the (infinite) past, and one in the infinite future.  The shrinking of spacetime is done conformally, so that the equations are transformed nicely.  So this was the basis of my dissertation, and for obvious reasons, I tried to keep it under wraps, because I was vaguely embarrassed by the whole thing.

Heat and Cold under Conformal Transformation

This is where matters stood, until I happened to watch Penrose explain his theory on YT.  The first point to note is that if a portion of space is compressed conformally, it becomes hot.  Secondly, if a portion of space is expanded, or stretched, it becomes cold.  Thirdly, Penrose pointed out, that if the physics of the so-called Big Bang Singularity is stretched out, it becomes quite smooth, and not a singularity at all.  (All this has to be proved, but Penrose has apparently demonstrated all this to the satisfaction of those who are interested.) 

Now here's the punchline.  Penrose says, if you take some sort of catastrophic event, like a supernova for instance, and follow its matter and its light rays all the way out to infinity---in our model, that means chasing it down until it hits the future boundary---we will see how it will appear from the distant future of the entire universe.  In fact, Penrose says, it will look very much like the images observed by the JWST as emanating from inside the Big Bang!  These sorts of phenomena, the reverse of a Big Bang, have been called a Big Slurp!

To join the dots, it's beginning to look like we're just one of a sequence of spacetimes, and the end of each spacetime is in fact the Big Bang of the next one in the sequence.

This is not a new idea; the model of a cyclic cosmology was one of those shown us in college, in baby relativity class.  I never dreamed that that theoretical concept would turn out to be something that astronomical observations would someday nudge us towards!

Apparently Some People Hate Education

The picture some analysts paint of those who have followed Trump ardently for the last decade or so, is of hardworking, conservative people, mostly rural, who do not like the educated elite.  They point out that college-educated people are everywhere, taking all the jobs, including the army and the police, everything. 

Well, this is true.  Businesses tend to hire college graduates, just to filter down their applications.  Then again, everything is getting more digital: even talking to your doctor goes through a computer, so having a college man or woman dealing with phone calls sort of makes a tiny bit of sense. 

Non college citizens are naturally resentful that they can hardly do anything easily, unlike in years gone by, and it looks like a plot just to make life harder for Trump followers. 

What's going to happen?  Are businesses going to stop investing in computer solutions to everything, just to make Trumpies happy?  I don't think so.  Many business owners are Trump conservatives, but they're not going to give up on the advantages of advanced technology.  And they're going to need techies to work the systems for them.  They might not be college - educated techies, though; they may have gone to 2- year colleges, where they can pick up the basics of what they need, to run the software and the hardware.  (Unfortunately, half- baked techies can really screw up big time.)

The population of anti- tech luddites has sort of leveled, but for some obscure reason, some immigrants and Latinos are joining their ranks, and we can only guess why.  (Perhaps they feel that the little education they have can go a long way with those who have no education at all.)

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Indiana Jones and The Dial

Yeah, we watched it.  We thought it was good, but we're not mainstream types, and we tend to like oddball things.  We both like Harrison Ford, after all, he invented the motor car.  We both like Phoebe Walls and Bridges, just because.  So we had fun.  As I have mentioned elsewhere, the endless chases are boring, and the caves and booby traps are all getting to look the same.  But in spite of all that, it was a fun movie!

The Greatest Composer of All Time!!!

There's no such person.  Let me explain.

Suppose we have a collection of points on a line, and we had a direction on that line that corresponded to "better", and the opposite direction corresponded to "worse".  Then it's possible that one of the points might be The Best point of all. 

But composers can't be put on a line that way.  It is impossible to compare two composers and say, this composer is better than that composer.  It is just not possible.  We say that the set of composers is not linearly ordered.  The subject that we're getting into is topology.  Given two points on the XY plane, can we say which point is more?  Given two books, can we say which book is better?  There is usually a matter of judgement involved; any comparison involving a matter of judgement cannot yield a 'best' that cannot be questioned.

I don't mind confessing that, in my personal view, Bach is the best musician.  But there are really great pieces that Haydn wrote, pieces that Mozart wrote, Beethoven wrote, Mendelssohn wrote, Brahms wrote, Schumann wrote, Wagner wrote, and so on, which Bach may not have been capable of writing!

Even beauty pageants, in which they compare the beauty of women, really make no sense; women can't be ordered linearly either.  Deciding a "greatest" in these sorts of cases is always arbitrary.  There is a lot of 'celebrating the best' in American society, but in my humble opinion, it is not the best feature of it. 

There's always some joker who wants to establish that Paul McCartney was the greatest bass player in history, or that the Beatles were the greatest group, or that Barack Obama was the greatest president.  We must just smile, and think to ourselves that the fellows who set up these rankings are idiots. 

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A Mystery Post that Ended Up in Archie's Archives!!!

Yes, that's right; the post I intended to put here went into Archie's Archives.  Please pop over there and get it.  I should move it over, but it's 8:32 at night, and it has been a long day. 

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Methodist Church Troubles

I'm reading in the news, and seeing on YouTube, etc, that the United Methodist Church (UMC for short) is undergoing great organizational disruption.

It's been decades since I left the church, so the present problems the UMC organization is facing does not affect me personally.

What is happening, to oversimplify, is that the UMC is tearing itself apart over how various clergy, and various parishes, handle the problems of same-sex marriage: officiating them, and tolerating same-sex couples in their congregations.

Every denomination has to have rules that govern the behavior of the members, the leaders, and how the property of the church is to be managed; after all, every Sunday a certain amount of money is collected in each church, and the members contribute financially to the church, and there are rules as to how much is sent to the central state or regional church office from each of its churches.

The members of the UMC are, like Americans generally, a diverse lot.  They vary from extremely liberal members---and clergy---who are impelled to welcome all descriptions of members; and members---and clergy---who are very strict in their attitudes towards LGBT++ folks; how much time must be given to congregations that vote to leave the denomination, and so on.

It is impossible to imagine that the members of any congregation could be united in their attitudes towards anything, let alone their attitudes towards people of alternate preference.  There could be extremely religious individuals seeking to continue their church membership, surrounded by quite intolerant members regarding them with hostility.  This is a tragic situation, because church is so often regarded as a spiritual refuge from an intolerant society.

In certain states, the central organization of the UMC (of that state) has been extremely impatient towards congregations that have become unable to make their payments to the mother ship.  This is unsurprising, especially if the majority of members are senior citizens, or poor people, and they have been closed down, which means that the church is shuttered, and the members have no place to meet on a Sunday.

To some extent, church real estate is becoming a major stumbling-block to the denomination holding together.  In situations like this, legal minds within the church leadership have to take control, to enforce church rules, and they are often draconian in how they do this.  Cruelty is inevitable, because legal action must proceed according to a schedule, which is difficult for a congregation that might be accustomed to only meeting on Sundays, and most of whom are elderly, and unaccustomed to fraught situations where quick decisions are expected.

So, despite my disinterest in the denomination from a philosophical point of view, thinking of Methodists in the abstract, it really appears that they are sheep without a shepherd.  The same goes for all the protestant denominations.  The exception is these mega-churches, each of which is a single congregation, where I expect that the çhurch is not at all run in a democratic way, which of course makes it easier on the leadership!  It is a sad time for Christians.

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Major Repair

I just noticed today that the post on 'Kim's Game' had been left incomplete, and terminated abruptly in the middle of a sentence.  I fixed this.