terça-feira, maio 22, 2018

Plebiscitum: “Disco Sour” by Giuseppe Porcaro



Disclaimer: I received an advance reader's copy (ARC - Uncorrected Manuscript Proof) of this book from the Author in exchange for my honest review. All opinions expressed are my own, and no monetary compensation was received for this review.

"My new app, Plebiscitum (®), will allow anyone to express their opinions anytime, anywhere, and will include geolocalisation systems"

In “Disco Sour” by Giuseppe Porcaro


This novel at first sight provokes in me worry of "assessing someone's democratic ability" and if people don't match to certain criteria, what, no right to vote? I agree Democracy should be a "very important school subject"; moreover, education in general should be about creating inquisitive minds in the young, only then can there be any hope of people becoming able to see through the shortcomings of politicians and the shortcomings of representative democracy. However education at present is exclusively directed (with some notable exceptions) at formatting young people to fit in to a wholly capitalistic society, in other words to become the little soldiers of capital for the benefit of the few. Alas, the 'born to rule' class still exists, this is the caste that needs breaking up, this poison which has insidiously infiltrated the minds of so many. To a point where the electorate will continue shooting themselves in the foot in a sort of perverse admiration saying 'if they can, so can I!' And even if they don't think in this way, others get caught up in a viscous circle of simply surviving. An important aspect of this education should be that policies are more important than personalities, that the choice of a policy is the political will of the electorate; who is, or are, employed to execute this policy is a separate issue. Higher education in Democracy should be freely available. It should be compulsory for everyone who wants to be a councillor or MP, complete with official exams. The general public should be encouraged to do these courses, too. The need for online democracy arrived about 15 years ago. All the referendum results of the last 15 years would have been different, with voting online, and there would be no Brexit either. The problem is political corruption, politicians persuading people that their physical presence is an essential part of representative democracy. If they did not attend once a week (safe seat people sometimes only go a couple of times a year) and it were obvious that they did not, then their pay would be more seriously in doubt than it is already. If referendums, direct democracy procedures are to be used more frequently, somebody will have to decided precisely what kind of decisions are suitable for it. At the moment it is complete chaos. The main purpose of the General Election is to re-establish the authority of representative democracy over direct democracy, which only reinforces the perception that online democracy is a bad thing, that physical presence is essential, and that representative democracy is the only way. Where it exists, Democracy is our most important human progress. It means we all count in the process of deciding who will form our government. However, there are many things wrong with existing democracies. Here I will make suggestions about solving just one problem, the general ill-preparedness of the average voter. Democracy should be a very important school subject, taught from as early as possible and, in time, put into practice within the school context. The history and development of Democracy should be taught, along with descriptions of different democratic systems. Before reaching the age of 18, minors should take exams, the passing of which qualifies them for voting in local, national and, where possible, international elections.

That's why online voting is not a good idea.

Similarly, it's incredibly difficult to hack pieces of paper with pencil marks on them. Unlike electronic voting machines. Self-preservation is the only reason I can see they persist with it when it is so obviously bad for the country and the economy whilst leaving the majority disenfranchised. Nowhere it its inadequacy more apparent than Brexit, where large numbers of pro-votes were drawn from both retired Conservative supporters, and just about managing Labour supporters, neither of which had benefited from EU membership, whilst both parties had signed up to various treaties on their behalf. For some it worked, for others it didn't. Now there is no-one to blame but that which we should have been blaming all along, but which has been as steadfast in refusing to evolve into a genuine democracy as North Korea. Hopefully when Brexit unravels, people will wake up to that which caused it, not because Brexit was impossible, but because FPTP ("First-Past-the-Post") couldn't deliver it, any more than it could deliver our successful position at the forefront of European integration. Due to being incapable of long-term planning, backed by the majority, it's just not up to the job. The majority of people don’t like thinking they’ve been suckers. Even conspiracy theories are maintained because the people promoting them don’t want to accept that they’ve been suckered in. People don’t like admitting to being wrong. Which is not really surprising particularly as there may well not be a right and wrong. Things do just happen. Without any real plan. Facebook started out as a college revenge project and grew into a sort of weird new form of socialising and eventually into a media company. By the time they had to move on from “hot or not” they’d given the game away for free. In those early days could Facebook had simply charged people to access the survey? If they had then they wouldn’t need to harvest as much data. But by the time the IPOs came round the subscription horse had bolted and all they had left was their data. Of course the flip side is that users were only too happy to share their data instead of their money. And so it’s hard to put too much of the blame on Facebook. The issue is not the big revelatory LIE. It’s what we need to do about it if there are more people in the world who are concerned about their data than the number who are not. If people continue to not give a shit then there won’t be much of a change but if we people do then, what are we going to do about it?

Could Facebook move away from data harvesting and make money through a paid for subscription service? Would people pay to do whatever it is they do on Facebook? If not, then seems to be the bigger problem. Facebook is counting on its millions of members who are completely oblivious to the manner in which Facebook uses its members as products and have no real interest in finding out. In other words, most of its members don't care and don't want to know about its indiscretions, and just want to be able to communicate with their friends. Such is the rather shallow life of an average Facebooker.

There's only one slight problem:

People not understanding that individuals are not important, have never been important. People get a kick out of this "society doesn't exist" meme. In truth, it's the individual that doesn't. Society is very real and a single entity is so much easier to control than sixty five million or three hundred and forty million people. A copy of "The Unfinished Game" and Snowden's slides should be delivered to all registered voters. Do you think there have been any deaths by keyboards? So we should get rid of keyboards too, the one I’m typing on? Is Facebook merely a space? What data goes into that supposed space? Is it up to the software companies and the personal preference of its online users? Like my brain is space, I can fill it with nonsense arguments or critical means of thinking. Making Facebook the enemy just shows how out of touch politics is with the digital world we live in, and it’s lazy. No, Facebook is an API to a graph of data items. The code behind that API does quite a bit. It is not just a space. You don't need development teams or a company for a space.

USENET was a space.
WAIS was a space.

Facebook collected your phone messages and call logs off your phone without authorization and on some phones you couldn't deinstall. It did this even if you never created an account. I'd hardly call that a space.

Porcaro's attempt at getting to the real root of the problem is quite interesting; he wants to explore the relationship between human psychology and mass media. We are hardwired for selfishness and tribalism. From the first moments of consciousness within the womb, we as individuals are inevitably more real and more important to us than anything or anyone else. Later we extend this beyond 'me' to 'mine': my people, my group. Some of us really take this to heart, really understand that others have the same rights as we do, and really live this way — many, many others do not. Most historical strife comes from the latter group, call them the intolerants, who aggress against and war with either other intolerant groups or with more tolerant ones (the current American situation is both). Many societies have never resolved this and live in perpetual intolerance, with peace only deriving from the temporary domination of one intolerant side over another. More fortunate societies have, over time, gradually and often painfully, built a fragile system based on tolerance, which is always accompanied by certain limitations on what intolerants can say and do, and has always benefited from the limited ability of the many, many intolerants to unite and work together. Good fences, as they say, make good neighbours, i.e., hindrances to mass communication are in some ways beneficial. Consider how the rise of mass media assisted and went hand in hand with the rise of both outright fascism and, later, once the art of more subtle manipulation through TV had been mastered, corporate control. The internet throws off almost all control, enabling not only the union, education, brainwashing and rise of intolerants, but a vast enhancement of corporate fascism — as we are now realising. The internet itself is the problem. It does allow massive interconnection, as Zuckerberg says. What he knows but does not say is that is also massively enhances the reach and effectiveness of corporate — and other — fascism. By its very nature, it feeds the selfish, aggressive, intolerant side of humanity, undoes centuries of social evolution and smashes the painfully achieved and highly fragile model of a workable tolerant society.

Bottom-line: This novel proves that one should pay attention to what is being published outside the familiar trodden paths publishing-wise.

domingo, maio 20, 2018

Over-the-top World-Building: "The Hammer" by K. J. Parker




When I was attending The British Council back in the day in Lisbon, in the summer, the best students usually went to the Linguistic Mother Land to brush up on their English. On our first visit I stayed in a posh hotel. Imagine my surprise and chagrin when we I found out no bidet in the loo! Good God! Had I returned to the middle ages? I went down to the reception and politely tried asking the concierge whether there was another room with that particular feature. Can you imagine the dialog? Cutting the story short, I couldn't make the concierge understand what a bidet was!!! I went there two years ago (to another hotel), and I found out the same thing: no bidet! Good grief. Now I understand why the Brexit. The Natives don't want to install bidets in hotels. I heard from some Londoners that the bidet is also absent from the common home...I can't understand this aversion to the bidet. For starters, we're not sitting on the nozzle... it doesn't make contact. It sprays from several inches below the action area and at an angle. On top of that, we wash away the stuff that gets lifted off your bits without thinking. With a bidet, the bog roll is bought maybe twice a year in small batches... for guests from abroad. My arsehole smells clean after a shit. Yours? Sorry to be blunt but this is a disease... Some Europeans have known the truth for over a century.

The idea that being cleaner is something to be worried about is... weird. This is a case of pure stubbornness on the part of some Lands. I'm of the opinion that the invention of the bidet was a great service to humanity. I feel really dirty if I haven't had a good rinse post bowel movement. Also it doesn't negate the need for paper. I use just as much as I would when using a non-bidet toilet. It sometimes amazes me how little some folk know about something so fundamental. I'm all for cleanliness. Same can't be said for some my local boozer's bogs and some of the men who use them. I have a particular loathing for those who 'shake and stuff' whilst texting. But maybe that's just me. I might also add that the absence of the bidet also happens in Europe (so that my Anglo-Saxon readers don't think I'm targeting them...lmao). A central country in Europe which I won’t name, has also got an even stranger thing. Anyone who's been there will know that bidets are not in fact widespread, and that there is a distressing trend for that country’s hotel rooms to include a complete transparent bathroom cubicle, which means that should you be sharing a room with someone, you can look each other in the eye when one of you is going... There are also numerous hotels in resorts popular with folk coming from that central European country that have also adopted this horrifying approach to bathroom construction. Why the strange fascination with the bidet when reviewing “The Hammer”? It's all about stubbornness, and the Gignomai character has plenty of it.

The main character, Gignomai met'Oc, is as memorable as was Bassianus Severus. Gignomai is the youngest member of a sentenced family of exiles on account of the political betrayal of an aristocratic family and he's clearly different from his relatives - he does not enjoy the birth privileges due to his birth, and he willingly spends time with the colonists, and with the passage of years he foments a revolt against hypocrisy and the game of appearances. From here on it is only a few steps away from initiating a political revolution and industrial revolution, and the reader is fortunate to be a witness to the whole process, described in the smallest details. It is worth paying special attention to the image of the world presented; K.J. Parker avoids the mistake of many other fantasy writers, i.e., not boring the reader with the history of past ages, dozens of geographical names, and complex genealogy. Parker is much smarter than that. He goes in a completely different direction, smuggling further information in dialogues or skimping data in descriptions, thanks to which he constantly keeps the reader's attention. We construct the subtle details in our minds.

Parker’s very unusual prose is also present. Minimalist for lack of a better word. Very sparingly administered information. I like the way Parker sets up the characters of his novels as pawns on the chessboard and then plays the narrative game. Thanks to this, his prose is so intimate, theatrical. It has its undoubted charm. Reading "The Hammer" I had the impression that this book is asking for filming in the style of "Dogville" by Lars von Trier. The plot is a simple story about revenge and stubbornness, but Parker is good at outlining different types of character streaks, playing with the fantasy world along the way.

The downside lies on the fact that Parker does not really engage the characters in moral dilemmas; on top of that, Parker indulges in an over-the-top plot and we also need some suspension-of-disbelief to apply (e.g., could a land like the one depicted be left virtually untouched?). Despite all that, the book will make you ponder stuff. It’s not perfect by a long shot, but with so much SF crap being published nowadays...  

Bottom-Line: A tale of obsession, stubbornness and technological revolution. While reading it I had ambivalent feelings for most of the time, but when everything was clear, it turned out to be good and engaging.


sábado, maio 19, 2018

Triteness and Boringness: "Cover Her Face” by P. D. James





“The cultured cop! I thought they were peculiar to detective novels.”

In “Cover Her Face” by P. D. James


Sometimes people just like to talk about the books they're reading. Not boast. Just talk. I realise such plebeian behaviour may not be acceptable in the rarefied circles some people move in, but for the rest of us mere mortals it happens quite a lot. Given that reading is becoming less and less common, one would think you'd be happy people are reading at all, without feeling the need to bitch about the fact that they happened to have enjoyed something so much they might want to read it again. Unless you think reading should just be restricted to the real intelligentsia, among whom some people obviously count themselves. So, unless those people have evidence that re-reading causes cancer or blows up the WC, why not back off and let the rest of us do what we like. Or better, why not direct that scathing anger at something that really matters? "Oh, I'm re-reading ‘Cover Her Face’.” Yes, there are people who like to brag about re-reading the Shakespeare plays, but most of us are just trying to be accurate. If you say, "I'm reading such-and-such," people assume you mean "reading for the first time." I'm not sure why this applies to books and not movies, but it doesn't seem like that hard a thing to accept. As for our being too stupid to understand books the first time around -- sure! Fine! I admit it! I didn't even begin to understand “The Moon is a Harsh Mistress” when I read it at fifteen or sixteen. But strangely enough, I wasn't too ashamed of my terminal idiocy to read it again in college and loving it. Plenty of books need a second or third reading, not because we're stupid, but because they're complex. But as almost everyone has said, this is all so painfully obvious that I can't believe I'm actually bothering to point it out.  “Cover Her Face” was one of the first books I discovered at the British Council’s library. Fond memories. Some of them I’m not allowed to state here…But I loved re-reading it although it’s not that good. It's so trite and boring how family and witnesses ALWAYS complain when asked questions... And always having the same depressed, desperate, selfish and despondent characters and family members ... And every character always deciding not to tell what they know...like life really.  And then getting killed just when they decide to tell (this part I’m not particularly fond of.) I, for one, think Katherine is pitiful; the character is so clingy to that man-child doctor it’s a cause for the vomit police. And Doctor Stephen needs a kick up the arse as well! It did surprise me upon this re-reading what a nasty piece of work Dalgliesh can be denying lawyers and bullying witnesses. I always knew Dalgliesh had a mean streak...

Bottom-line: It’s all about Memories after all.

quinta-feira, maio 17, 2018

dAction/dx = d/dt(dLagrangean/dv)-dLagrangean/dx = 0: “The Theoretical Minimum - What You Need to Know to Start Doing Physics” by Leonard Susskind, George Hrabovsky




Math is just a skill, like any other and not everyone can do it. What gets my goat is the "anyone can do anything if only they try hard enough "attitude. No, they can't. Some people are good at certain skills and not other, and others have different skills. I happen to be good at math. I get annoyed when people say "Ooh, you must be so clever!" when I tell them. No - I just have that particular skill - I can no doubt be as dumb as the next person at something else. As Courtney Barnett puts it: "The ambulance driver thinks I'm clever 'cos I play guitar /I think she's clever 'cos she stops people dying." Laughing at general illiteracy isn't so funny, because that is a relatively simple skill that most of us can learn, and it hurts people not to have it; but Quantum Mechanics? Come on, no one groks it, and it really doesn't matter for most of us.

The innumeracy and scientific illiteracy that is being normalised is part of the social environment which enables a powerful minority to continue to dominate and exploit a majority by ensuring that as few people as possible have the necessary logical skills and knowledge to seriously question the stories they are told about the world. Accepting this kind of thing as "humour" is accepting a narrative which says that math and science are things that only a tiny number of geeky people care about or understand on account of its alleged "difficulty" and irrelevance. It's all part and parcel of the maintenance of power. In truth, math and science are not that hard until they get to work on us school to persuade us that they are. They also get to work on suppressing our creativity. There's nothing funny about this at all. Mass literacy has been accepted as a necessary evil and it's no longer acceptable to be proud of illiteracy.

Why aren’t more kids learning Physics? It has to be a combination of teaching methods and the way physics is stereotyped in the media. Physics is an absolutely fascinating subject. It's about understanding the very fabric of reality. What could be more interesting than that? It depresses me that most people seem to see the subject as being dry and dull. It really isn't. On top of that, people who study physics have to do it because they love physics, and many people do love it. However, there is virtually no prospect of future employment in the field in Portugal.

A lot of physics at degree level can be downright dull IF NOT TAUGHT RIGHT. You really have to be interested in why things are the way they are from an early age to circumvent that, and I find it hard to believe that gawking at Carl Sagan (the one I grew up with) on the telly is going to make that happen. I can't remember having role models as such - I just loved taking things like hifi, toasters, phones and bikes to bits to see what made them tick (or to see if they'd worked when I'd put them back together...), and finding math equations extraordinarily beautiful. Yes, there's the sexy stuff like astrophysics (relatively easy as much of it was qualitative when I studied it), but to have even the barest of a good all-round grasp of physics as a whole, you have to have done the fairly sophisticated mathematical groundwork, get your head around such utterly scintillating concepts like statistical mechanics, thermodynamics and Fourier optics, before you can set the world alight with your re-jigged theory of quantum gravity (which I did study after I finished my Computer Science college degree).

Moving in a little closer to the book’s content. His explanation of the Lagrangean is something I've never seen done this way before. We have determined experimentally that we can represent very generally the laws of physics by deriving them from a condition which states that a certain quantity (called the Action) must be kept minimum. The action is differently defined for each system, but always represented as the integral between two points in time of another quantity (Called the "Lagrangean Quantity") that is a function of position and velocity at any point in time. Since the action must be kept minimum, the derivative of it (with respect to position) must be kept 0. Both position and velocity are considered to change with respect to time. As such, we can write:

dAction/dx = d/dt(dLagrangean/dv)-dLagrangean/dx = 0  (Euler-Lagrange Equation)

By selecting the Lagrangean function to equal KE-PE, the above equation derives Newton's 2nd law of motion. Brilliant. Moreover, the lagrangean's form can be changed in order to change coordinate system. By doing so first and then solving the Euler-Lagrange equation, the laws of motion for even Non-Inertial Reference Frames can be readily computed (as long as they are non-relativistic), such as in a circularly moving Reference frame. Like so, fictitious forces (those observed in NIRFs but not in IRFs) can be calculated, such as the Coriolis force.

[Paraphrased] "There are some things you only want to experience once, like a book. You don't want to read the same thing over and over again. But there are other things, like music, that you'll want to listen to continually because it just feels good. I hope my lectures are like that... (Paraphrased)." Why yes, Professor Susskind, the lectures in your book are a treasure to read.

I have never seen some of these topics explained with so much clarity. He is one of the greatest teacher in physics, and I admire his effort to go through all of physics for the benefit of beginning students. It is a great contribution to the field as a whole, and hopefully some of his readers will become future physics stars thanks to this, just like the Feynman lectures. Incidentally, I had a Professor in college, José Maria Quadros e Costa, who approached Physics in just the same manner Prof. Susskind does, i.e., from first principles. One can never over emphasize the basics. This is what separates great teachers from ordinary ones. I find that a lot of the students brush through the basics and find later that they do not have a deep understanding. The concepts of state/phase space is a good example of this; they’re actually not as simple and are so critical in understanding a lot of the world, and they’re worth spending some time on.

Bottom-line: Everyone knows leptons live in Alentejo and spend their lives looking for crocks of gold at the end of rainbows. However, I concede that without scientific discoveries, mathematics, physics and books like these, we'd be explaining the universe in myth and legend.

quarta-feira, maio 16, 2018

Shut the Fuck Up and Calculate (Or Not): "The Nature of Space and Time" by Stephen Hawking and Roger Penrose




"I have emphasized what I consider the two most remarkable features that I have learned in my research on space and time: (1) that gravity curls up space-time so that it has a beginning and an end; (2) that there is a deep connection between gravity and thermodynamics that arises because gravity itself determines the topology of the manifold on which it acts".

In “The Nature of Space and Time" by Stephen Hawking and Roger Penrose by Stephen Hawking in the lecture "Quantum Cosmology"


"We should think of twistor space as the space in terms of which we should describe physics."

In “The Nature of Space and Time" by Stephen Hawking and Roger Penrose by Roger Penrose in the lecture "The Twistor View of Spacetime"


"These lectures have shown very clearly the difference between Roger and me. He's a Platonist and a positivist. He's worried that Schrödinger's cat is in a quantum state, where it is held alive and held dead. He feels that can't correspond to reality. But that doesn't bother me. I don't demand that a theory correspond to reality because I don't know what it is. Reality is not a quality you can test with litmus pap. All I'm concerned with is that the theory should predict the results of measurements. Quantum theory does this very successfully. It predicts that the result of an observation is either that the cat is alive or that it is dead. It is like you can't be slightly pregnant: you either are or you aren't."

In “The Nature of Space and Time" by Stephen Hawking and Roger Penrose by Stephen Hawking in the lecture "The Debate"


Can I write a review on such a book? Hawking and Penrose... It's staggering...I don't even know what day the mailman comes...After having re-read this oldie after Hawking's passing, I'd say it depends on where you are in the universe, whether you're on/near some sizeable object (of mass), its rotation, distance from other masses, or whether you live in my neck of the woods...When in doubt I always follow "the flat earth" rule (Medieval behaviour is so "in" now). The world is the centre of (my own)) universe that you/I live in and it's getting flatter every day. Which hopefully means you can see further and observe when others perform the same behaviour. Or ask them. Preferably in a suit of armour while riding a horse. Possibly a lance too. (Until you understand the society you live in). I'm all for a flat and cubist planet! Our time is here! And it'd be easier to fence. And we could launch spaceships off the corners. Uncannily, the mailman knows when I'm on the phone, asleep or having a quiet moment on the throne...I sniff a time conspiracy here (*It'll End in Tears theme music*)

When it comes to Quantum Theory, the math in the book includes every possible outcome, and the predictions it makes are simply probabilities - e.g. there's a 1% chance X will happen, 90% chance Y will happen and 9% chance Z will happen. How you choose to interpret this is still up for grabs, if you go with Everett's "Many Worlds Interpretation" idea then all possibilities are equally real and actually happen in different universes; if you go with the Copenhagen Interpretation then the wave-function of "possibilities" collapses down to one single result. On a fundamental level, whichever way you choose to interpret it (there's about 8 main contenders for interpretation) the math remains unchanged, and the possibility remains that the math itself is the "truth" and there is no further interpretation, usually called the "shut the fuck up and calculate" interpretation (my favourite).

Bottom-line: This is not a book à la Smolin, i.e., it's not for laymen. I still remember some of the reviews I read in 2010 when the second edition of the book came out. Hilarious! E.g., "Clearly the work of two great minds" (possible Translation - "I didn’t understand the bits I speed read, but they looked dead clever and I have to say summat"...).

terça-feira, maio 15, 2018

Non-Distinctive Narrative Voice: "All Systems Red" by Martha Wells


“I remember every word ever said to me." That was a lie. Who would want that? Most of it I delete from permanent memory.

In "All Systems Red" by Martha Wells




"I'm six-foot five inches tall, black wavy hair, turquoise eyes, and with a cat under my arm." In a first-person narration how can I describe this? Should I use an admiration take or just be factual? For starters, admiration has nothing to do with sexual attraction. You can admire someone for what they do or say, but when it comes to sexual attraction the first and foremost things on your mind are… But then I am a full bodied male and I suppose my sexuality is more "aggressive" because of that, not that I'm unable to appreciate the higher components of an individual of course. Because of this "nuances", first-person narration is always rather difficult to engineer with complete success. They do involve a lot of tinkering to make sure you do indeed avoid the tiresome repetition of "I" in favour of more interesting ways of presenting the character's perspective. The question is always the same: How is it possible to have an absolutely distinctive voice from the first page onwards? How can I build a story around the other characters by using "the eyes" of the first-person narrator? Could my hypothetical first-person narrator say something like "I'm choked with admiration for you!"? Narrative-wise is it a perfectly feasible emotion? I think so. A bit creepy to say otherwise, I would think, unless you walk around with porn goggles on. It’s very difficult to shift point-of-view in first person. With so many characters, should Martha Wells have written alternating chapters all in first-person narrative, one for each of the crew members (along with the chapters for the murderbot)? Yes, but then we'd have a longer novel and maybe Wells didn't want to go down that path. Who knows? This is only SF right? As it is, all the characters seem basically identical in voice and all are clearly just riffs on the author's voice. Not good enough. But 3 stars for the attempt just the same.


SF = Speculative Fiction.

sábado, maio 12, 2018

Lagrangean Systems: "Levels of Infinity - Selected Writings on Mathematics and Philosophy" by Hermann Weyl, Peter Pesic




“It is a well-known anecdote that Hilbert supported her [Emmy Noether] application by declaring at the faculty meeting, ‘I do not see that the sex of the candidate is an argument against her admission as Privatdozent. After all, we are a university and not a bathing establishment.´”


In the memorial address “Emmy Noether (1935)” delivered in Goodheart Hall, Bryn Mawr College, 26 April 1935, and included in “Levels of Infinity - Selected Writings on Mathematics and Philosophy” by Hermann Weyl, Peter Pesic

Mathematics is, in a sense, profoundly anarchistic - you can't use authority to change or control its progress, and nothing is ruled in our out without proof agreed by the collective of practitioners, and Weyl was one of our most distinguished practitioners of the art of doing beautiful mathematics and physics. Sometimes practitioners have a brave and frankly generous stab at letting the layman get a feel for some of the broader concepts, but ultimately this is an intellectual edifice that's been built by thousands of people over the last five centuries or so and there's no reason whatsoever that we should be able to understand it at all without putting in the hard yards - the problem is not with math, it's with us and our arrogance in assuming that's possible. Weyl, as this homage book testifies, was able to put math into language people could understand and it's absolutely essential for a general audience. Language needs to be a vehicle of understanding and not an obstacle to it.

What amused me as an engineer is how engineers are taught many mathematically valid shortcuts that they use to solve many problems, while mathematicians are not taught them. Then again, how engineers and mathematicians interpret the ideas expressed in the mathematics that they use is obviously different, so perhaps although I find it amusing it is not particularly important in the greater scheme of things, (if there is a scheme). Of course, we do get taught be shortcuts, but only in the context of understanding exactly where they break down. We engineers get to live in a world of 'nice' functions where we can do things like differentiate under the integral or assume sin theta equals theta without getting too antsy about it...

I'm glad both Hilbert, Einstein and Weyl made a top shout out to Emmy Noether! She proved one of the most important and foundational results in modern physics - in a just world she'd be as well-known as Einstein, but (a) she was a woman and (b) there's no easy way to explain what she did with a glib pop science metaphor...but after having read Weyl's kind of mathematical eulogy for her, and because today is woman's day (8th March), I'll just have to give my two cents... 

Noether proved it as a theorem specifically about physical systems. It only works because the physics is fully determined by a Lagrangean which is minimised. And if that Lagrangean is covariant under a continuous symmetry (e.g. spatial translation) it leads to a conserved quantity (e.g. momentum). If the system cannot be described by a Lagrangean whose action is minimised then Noether's Theorem does not necessarily hold. Noether showed that physics being the same whatever time it is leads to Conservation of Energy. Being the same regardless of your position leads to Conservation of Momentum and being the same no matter what direction you look at leads to Conservation of Angular Momentum. All of which are examples of a symmetry which results in a conserved quantity. I'm not sure it really requires the usual glib metaphors to explain, most people have heard of Conservation of Energy and Momentum. You can explain Conservation of Angular Momentum by the usual example of a skater rotating faster as they pull their arms in. And the idea that physics is the same at all times and places and whatever direction you look at should be straightforward to understand with a small amount of thought. The extraordinary thing is that it isn't a particularly complicated proof and isn't really about physics particularly. What is surprising is no one discovered it earlier. Even Newton had the mathematical tools to do so. That he and none of the succeeding two centuries of mathematicians did suggests she had a special talent. Maybe because she was really a mathematician where she is famous for solving much more difficult problems. But it is strange nevertheless that Noether's Theorem isn't more famous. Certainly up there with Einstein's Special Theory of Relativity. And of course is widely used in theoretical physics today.

It is still important today because the basis for any theory of physics such as particle physics is also a Lagrangean whose action is minimised. If that Lagrangean is covariant under a continuous group then there is an associated conserved quantity called the Noetherian current. Another conserved quantity which can be explained by Noether's theorem is conservation of electric current as a result of phase symmetry in the wave function of quantum mechanics.

As always the ghost of Emmy Noether, one of the greatest mathematical physicist of the 20th century for her work on symmetry and conservation of quantities (energy, momentum, angular momentum), presides over all. It is a pity she was never awarded a Nobel Prize of her own. I would describe Noether's work as (a) mathematical physics for her work on symmetry and conservation and (b) pure mathematics, for everything else. For her work on symmetry alone she deserves to stand in the pantheon of great mathematical physicists. Both for its insight and subsequent centrality to modern particle physics and quantum mechanics.

Thanks Hermann Weyl for doing what you did at the time.



NB: The essay on Noether, along with the essays “The Mathematical Way of Thinking” (1940), and “Why is the World Four-Dimensional?” (1955, the year Weyl died), on their own, are worth the price of admission.