Monday, February 07, 2011

Book review: “The Shape of Inner Space” by Yau and Nadis

The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions
Shing-Tung Yau and Steve Nadis


Yes, I said I have no intentions reading the book. But then I was offered a copy for free. And, since I had it anyway, I could as well read it, no?

“The Shape of Inner Space” is a curious mixture of Yau’s autobiography, a crash-course in differential geometry, and physics-themed popular science, sandwiched between an introduction to the history of geometry and philosophical considerations about the beauty of mathematical truth. The string that runs through the book and weaves it together are Calabi-Yau manifolds. Shing-Tung Yau, the “Yau” in “Calabi-Yau,” has spent pretty much his whole life on these manifolds and won the Fields Medal in 1982, among other achievements, for his proof of the Calabi conjecture. So the reader learns first hand from the world expert. Steve Nadis is a popular science writer, and the two have joined forces to produce the book.

The result is interesting and also courageous.

After the introduction, it follows a brief history of geometry. From Pythagoras and Plato over Euclid, Descartes, Gauss and Euler to Minkowski, Riemann, Einstein, Kaluza, Klein and, of course, Calabi. As we come closer to the 21st century, we learn about the geometrization of physics and its successes. To move on beyond Platonic solids, the reader is introduced to mathematical lingo in a rapid fire treatment. It starts with the innocent concept of derivative and integrals. From there it goes on to partial derivatives, curve integrals, non-linear partial differential equations, manifolds (differentiable, compact, orientable, product of), complex numbers, metric (in n dimensions, hermitian), parallel transport, geodesics, curvature and Ricci curvature, groups, tangent spaces, fibre bundles, exotic spheres, homeomorphic diffeomorphisms, harmonic equations, Betti numbers, Chern classes, holonomy and cohomology, Ricci flow, Riemann surfaces, Kähler manifolds and of course Calabi-Yau spaces. Just to mention a few. If you're afraid of math, this book is not for you.

In the later chapters follow the contemporary topics, and the connection to string theory is established. The reader learns about the Dirac equation, Yang-Mills theory, mirror symmetry and the Seiberg-Witten equations. We come across Yukawa-couplings, correlation functions, black hole information loss, moduli and the landscape problem. We meet familiar names like Hawking, Penrose, Guth, Strominger, Kachru, Witten, Greene, Gross, Susskind, Vafa, Giddings and more. Nadis has interviewed many researchers in the field and the text is frequently supplemented by quotations from these interviews (and other sources). One might find it an expression of laziness (or maybe cowardice) to export explanations and opinions into quotations from other people. But I found it very readable and interesting to hear the researchers’ comments and explanations of their work, and that of others, in their own words. I liked that a lot.

The mathematical and physical explanations are accomplished basically without equations (though there are a few examples) and without formal definitions. Sometimes the text is accompanied by figures that I found very helpful and well done, but figures only get you so far to understanding six dimensional spaces. Now all the used concepts are explained somewhere, and I was familiar with most of the terminology before reading the book anyway. But I suspect if you don’t know anything about field theory, differential geometry, and topology, “The Shape of Inner Space” is a very heavy read.

With use of the introduced mathematical concepts the reader then learns what Yau proved, what his colleagues proved and how the field has evolved within the last some decades. Then the authors explain how the connection to string theory came about and how this intersection of physics and math has been fruitful for both sides. That I found indeed the most interesting aspect of the book: The interrelation between mathematics and physics and the mutual benefit for both sides. Yau writes:
“[I] like to position myself at the interface between these two fields, math and physics, where a lot of interesting cross-pollination occurs. I’ve hovered around that fertile zone since the 1970s and have managed to get wind of many intriguing developments as a result.”

However, the book is very focused specifically on the cross-pollination between differential and algebraic geometry and string theory that has sprung from Calabi-Yau spaces. It is a pity there was not more about the recent and not-so-recent history of the math-physics exchange in a broader sense.

Towards the end of the book, after a somewhat bizarre interlude about the way you would die through false vacuum decay, we then find a chapter on experimental tests of string theory. Yau is a mathematician and takes the point of view of an interested outsider. His main interest is mathematical truth, and if physicists with their methods can help mathematicians discover previously unknown relationships, then what does it matter if the physics eventually turns out to be a description of reality? But one or the other reader might care.
“At the end of Dorothy’s adventures in the Land of Oz, she learned that she had the powers to get back home all along. After some decades of exploring the Land of Calabi-Yau, string theorists and their math colleagues (even those equipped with the penetrating powers of geometric analysis) are finding it hard to get back home – to the realm of everyday physics (aka the Standard Model) – and, from there, to the physics that we know must lie beyond. If only it were as easy as closing our eyes, tapping our heels together, and saying “There’s no place like home.” But then we’d miss out on all the fun.”

Thus, in the chapter “Back to the real world” we learn about possibilities to test string theory in the early universe, by bubble collisions and their relics, by cosmic strings or – in the case of large extra dimensions – at the LHC. (I guess this is pretty much the last time a popular science book will talk about the latter possibility.)

Unfortunately, it is not very clearly pointed out that all these tests are tests not of string theory itself but of string theory inspired phenomenological models. Finding such evidence would certainly be a boost for string theorists, but not finding it doesn’t need to bother them either. A quotation by McAllister states it very carefully correct: “It’s possible that string theory will predict a finite class of models, none of which are consistent with the observed properties of the early universe, in which case we could say the theory is excluded by observation.” Yes, it is possible. But at the moment it seems like there’s a string theory motivated model to explain whatever the data will be.

Yau and Nadis avoid commenting on the controversy about the usefulness of string theory as a description of reality. On the landscape problem Yau writes “It’s fair to say that things have gotten a little heated. I haven’t really participated in this debate, which may be one of the luxuries of being a mathematician. I don’t have to get torn up about the stuff that threatens to tear up the physics community.”

“Critical treatments of [string theory], such as The Trouble with Physics and Not Even Wrong are mentioned in the passing, decorated with quotations from Henry Tye saying “string theory is too beautiful, rich, creative, and subtle not to be used by nature,” and Michael Atiyah letting us know that “even if we can’t measure it experimentally, [string theory] appears to have a very rich… mathematical structure. [String theorists] are onto something, obviously. Whether that something is what God’s created for the universe remains to be seen. But if He didn’t do it for the universe, it must have been for something.” (Like, maybe the multiverse?)

It then follows some elaboration on beauty and mathematical truth, and its relevance for physics:
“Of course, if beauty is going to guide us in any way […] that leaves the problem of trying to define it […] There’s no doubt that a blind adherence to mathematical beauty could lead us astray, and even when it does point us in the right direction, beauty alone can never carry us all the way to the goal line. Eventually, it has to be backed up by something […] more substantial, or our theories will never go beyond the level of informed speculation, no matter how well motivated and plausible that speculation may be.”

But Yau and Nadis remove themselves from the debate about physical relevance by focusing on the mathematics:
“Whereas the final proof in physics is in experiment, that is not the case in math… If the mathematics associated with string theory is solid and has been rigorously proven, then it will stand regardless of whether we live in a ten-dimensional universe made of strings or branes.”

And that is what the book is about – it’s a book about the mathematics of Calabi-Yau spaces, not more and not less. Just so you know what to expect should you consider buying “The Shape of Inner Space:” It’s not, in the first line, a book about string theory and certainly not about quantum gravity*. It is a book about a special kind of manifold and the interaction between physicists and mathematicians it has brought.

The book is generally well written, though I found the writing style over long stretches somewhat uninspired. Many pages it goes along the lines that soandso wrote this paper on this, and then soandso wrote a paper on that, and then a student of soandso wrote a paper on this and that, and so on. Also, I found it somewhat disturbing that in several places technical terms are used that are only introduced in later chapters, sometimes with, sometimes without, mentioning of the later explanation (metric and entropy for example). The book has a glossary, but if hadn’t known anyway what they were talking about I’d have found it a quite annoying break in the reading flow.

The book is also discontinuous in the level of explanation. Over many pages it reads almost like a review paper on Calabi-Yau spaces, summarizing who proved what when by which method. And then there comes the occasional pop-sci explanation. Just to give you an impression, here’s a quotation from a randomly chosen page (133):
“The presence of those [covariantly constant] spinors helps ensure the supersymmetry of the manifolds in question, and the demand for supersymmetry of the right sort is what pointed Strominger and Candelas to SU(3) holonomy in the first place. SU(3), in turn, is the holonomy group associated with compact, Kähler manifolds with a vanishing first Chern class and zero Ricci curvature.”

(That supersymmetry partners bosons and fermions is btw explained only some pages later.) The level of the pop sci explanations are for example that of an exchange particle mediating an interaction by the common analogy to a ball being thrown, or for quantum foam by analogy to the British railway. (“The geometry, in other words, would be undergoing shifts so violently it hardly makes sense to call it geometry. It would be like a rail system where the tracks shrink, lengthen, and curve at will –a system that would never deliver you to the right destination and, even worse, would get you there at the wrong time.”).

The impression I had was that Yau wrote a draft, and Nadis then sprinkled pop sci explanations and quotations on it.

Taken together, I enjoyed reading the book more than expected. It is a very comprehensive summary of research I have a peripheral interest in, and Yau and Nadis have presented it very nicely, so I learned some relations that previously hadn't been clear to me. I was surprised though that the AdS/CFT correspondence is only briefly mentioned and its recent applications are not discussed at all. I'd have found it relevant to the question of what string theory is a theory of. And, there's no explanation of what is actually plotted in the omnipresent pictures of Calabi-Yau spaces you find for illustration all over the place.

Reading the book I couldn't help wondering what audience it is aimed at.
Readers should at the very least have read a fair share of popular physics books because they will not get an introduction to general relativity and quantum mechanics, not to mention quantum field theory, though these are essential to understanding big parts of the book. Black holes, entropy, the standard model, dark matter, inflation etc are explained with only a few sentences each. This, I will admit, was a great relieve to me because I’ve read more than enough stories about quantum pets and suicidal astronauts plunging into black holes. I’m just saying you better bring that knowledge along because otherwise you’ll miss big parts of the story. And, given the mathematical rapid fire treatment, the reader should at the very least have a high school exam, preferably a few semesters math in addition.

In summary, the book might be interesting for you if you have some, though not necessarily expert knowledge in math and physics. “The Shape of Inner Space” will give you a good impression about the state of the art, the history, and a glimpse on the possible future of research on Calabi-Yau spaces. You will learn about the interaction between math and physics it has inspired, and it will give you opportunity to ponder eternal truth and beauty in mathematics, and its relevance for Nature.


* In the introduction it is made clear that “Because of our focus on so-called Calabi-Yau manifolds and their potential role in providing the geometry for the universe’s hidden dimensions – assuming such dimensions exist – this book will not explore loop quantum gravity, an alternative to string theory that does not involve extra dimensions […]” And that's the first and last time alternative approaches to quantum gravity are mentioned.

88 comments:

Christine said...

Hi Bee,

I still have to understand why most readers rate this book so highly. I was so much annoyed throughout the book with the immodesty and also false modesty of Yau, like it never happened prrviously in any other book that I have read. I marked my copy several exclamation marks. I think it was a good idea to expose the maths behind Calabi-Yau manifolds. But I was distracted throughout and really annoyed by the auto-biographical parts (or whatever those were intended to be). I don't know what makes most people enjoy this book. Well... Never mind.

Best

Christine

Phil Warnell said...

Hi Bee,

Thanks for spending the time to write this nice synopsis and critic of a book that’s garnered some attention lately. I’m happy to hear it’s a book primarily about the mathematics in respect to its relation to physics and not simply a guised recommendation for string theory, which has me to think I might just give it a look. I’m also pleased that it doesn’t drag one through the preambles of physics as so many books seem compelled to do, as I think there is a demographic of readers out there that this type of book better serves; some of them being even professional scientists.

I particularly like that they have given a voice to people other than themselves in respect to presented topics by including statements that they’ve made, with the only thing to wonder about is if they’ve done it honestly, as in the proper context. Anyway one thing for certain as the focus being on Calabi-Yau manifolds I would agree as you pointed out we can’t do much better than to hear what it’s all about straight from the horse’s mouth. So I guess I'll put this book on my list although the list seems to be getting longer every day.

Best,

Phil

Phil Warnell said...

Hi Christine,

I would ask if you’ve ever read Susskind’s “Black Hole Wars” as if the self back patting is on a scale close to this one it might alter my decision to read it. If not then perhaps Bee could make an assessment as I think if I recall she has or like me at least made the attempt.

Best,

Phil

Christine said...

Hi Phil,

No, I didn't read that book, nor do I intend to. I have a large list of books to read as well, and life is limited in time, so I have to be very selective. I was interested in Yau's book, but as I read it, I was more and more disapointed. I think the style should have been different. Maybe I was expecting something like Penrose's expositions... And Yau's book does not reach that standard, IMO. I would edit out all immodesty-related mentions throughout. If the reader can do that mentally, then maybe he/she can avoid the annoyance; I couldn't.

Best
Christine

Steven Colyer said...

Thank you for this frank and honest review, Bee. I'm not surprised he doesn't go into alternate theories of quantum gravity, as very few (that I know of) make the assumption of alternate dimensions other than the 3S and 1T we're sure exists.

I enjoyed this book immensely. Few reviewers mention Yau's background as a street tough and gang leader in the streets of Hong Kong.

A gangbanger in Math Phys ?! What the ... ?

Then he gets accepted at Berkeley and pretty much lives in the Math Library so much so that ... and I hope this doesn't shock anyone ... he didn't have a social life! :-)

He also writes quite a bit about how he helped/worked with Richard Hamilton (now at Columbia Math) develop Ricci flow in its early stages which Hamilton took 95% of the way toward proving Poincare's Conjecture, and that Grigori Perelman finished. It also shows how mathematicians work together far more than scientists, i.e., less weenies like that guy Phil mentioned.

Best of all is how Bee stated he doesn't commit to SuperString Theory being true or not, the Physics is not his field. That kind of honesty is greatly appreciated.

I found the book extremely helpful in defining what Super Strings are and are not, and would recommend it to String Theory critics to help them ease their pain to plow through the "hard math" of String theory, which isn't as tough as some SSTers would have you believe.

Yan & Nadis also clearly point out there is much work still to be done and what that is (Kahler vs non-Kahler mostly). I enjoyed it.

Thomas Larsson said...

I was under the impression that CY manifolds became popular because string compactifications on them lead to low-energy susy. What would it mean for the physical relevance of CY if low-energy susy is disproved at the LHC?

Steven Colyer said...

Thomas asks a good question. From reading Woit's weblog I get the feeling the SSTers will say SUSY exists just at larger masses than they predicted, larger than the LHC is capable of revealing even at full rated power, and with a little hocus pocus they'll rework the maths to explain that, and if its not too much trouble CERN could you please build a bigger machine and in 50 years we'll know more?

Bee said...

Hi Thomas,

I think Steven says it well. With some creativity the energy scale will shift and voila, the LHC would have missed them. Best,

B.

Bee said...

Hi Christine,

I didn't find the autobiographical stuff particularly interesting or inspiring, but I didn't find it too repulsive either. Best,

B.

Arun said...

Betty numbers

Betti?

Bee said...

Hi Phil,

No, it's clearly not a recommendation, but it's also not as critical as one would expect a scientific book to be. As I wrote, Yau and Nadis pretty much avoid to discuss controversial topics by stating they only care about the math. I personally find it somewhat unsatisfactory. But then that's probably because it's what I'd have been more interested in than who wrote what paper when with whom. Best,

B.

Bee said...

Oops :-) Thanks, fixed that typo.

Uncle Al said...

Uncle Al respectfully submits that Calabi-Yau manifolds are mirror symmetric while the universe is chiral at all scales. Socks - plus manually inserted symmetry breakings - are being used to describe shoes.

Super-Kamiokande is 50 kilotonnes of water. Protons did not decay, SUSY recalculated a few more decimal places, and all was saved. IceCube is a cubic kilometer of ice. That is

[(1000 m)(100 cm/m)]^3(0.9 g/cm^3)(1 kilotonne/10^9 g) = 900,000 kilotonnes or 18,000 Super-Ks.

http://www.mazepath.com/uncleal/horse.htm
SUSY is already dead.

Christine said...

Hi Bee,

I didn't say repulsive, but annoying. There are several passages of immodesty of the kind: "This was the most difficult problem ever in the history of Math , no one could solve it even after years and years, then I thought about it and came with a solution." It is easy to find several of these! And other examples involving false modesty. Embarrassing. But I will not waste time quoting them. I got annoyed with the style of the book, it could have been much, much better.

Best,

Christine

Steven Colyer said...

False modesty (FM), Christine? Yeah, there's more than a little of that, but THAT is not a good enough reason to not read the book. Btw, have you read the whole book, or was the FM enough of a turnoff to have you stop reading? I have read the whole book, and what FM there was was concentrated in the beginning.

Also, are you aware of the man's accomplishments other than proving Eugenio Calabi's conjecture? There's a thin line between Ego and Egomaniac in my view, and yah he crosses it from time to time which annoys me as well, but given the extent of how he has helped (and his grad students as well) Mathematics, I have to cut him a bit of slack. He could have been worse. He could have been Susskind.

(But I see no reason to bring in what it takes to survive being raised in the South Bronx so I move on)

Uncle Al, if I ever have the pleasure of meeting you I will present you with a pair of socks, one green and one red.

I hear and agree with you on the Super K results so far, but Ice Cube in Antarctica was just completed and I would advise being patient and waiting for results to pour in, prolly in 2 years at minimum and no more than 3 I expect.

We shall see said the blind man to the deaf man, who was looking away.

It's all good, it's all ongoing, it's always controversial.

What a ride, hmm?

Bee said...

Hi Christine,

I suppose it's difficult to be winner of the Fields Medal and write a book that's supposed to spark interest in a very abstract topic and neither appear falsely modest, nor immodest, nor outright boring. Best,

B.

Bee said...

Hi Steven,

Yes, of course, other approaches towards qg don't need Calabi-Yau. But on the topic of interaction between math and physics there's more to say. Take the whole network/graph stuff for example. I'd have been interested to hear how the exchange has been going there. But that would have been a different book. Best,

B.

Christine said...

Hi Steven,

I said I read the book. Yes, when I read a book is from beginning to end.

Also, I did not say that people should not read the book because of the "FM issue". I said the book could have been much better with an appropriate edition. Otherwise, the sensitive reader should try to mentally do so or will get annoyed or distracted. At least, IMO. But as I said, most people appreciate the book. I didn't. A pity. Could have been much better.

But you are right, most of the problem lies in the first half of the book. But towards the end, it became somewhat speculative, which could have been another source of annoyance but at least one is warned.

Best,
Christine

Christine said...

Hi Bee,

I don't want to make comparisons, but here it goes a simple note. By reading the -- also Field Medalist -- Terrece Tao's blog, I think one can find a counter-example to your thesis.

Best,
Christine

Steven Colyer said...

I said the book could have been much better with an appropriate edition. Otherwise, the sensitive reader should try to mentally do so or will get annoyed or distracted. At least, IMO. But as I said, most people appreciate the book. I didn't. A pity. Could have been much better.

I agree, but IMO every book published so far for John Q. Taxpayer Intelligent Laymen could have been much better written.

I cut all of them much slack (Roger Penrose, doubly so), however, because just as I don't expect any English or Language teacher to be anything other than totally ignorant about Math or Physics, I don't expect any Mathematician or Physicist to write like Chaucer, Shakespeare, or Tolkien.

By hook or by crook, we WILL get to the promised land. Not as fast as we'd like given our genetic impatience, but ... eventually.

Regarding THIS book for example, English is definitely a second language for Yau, and I think given the circumstances, Steve Nadis did a fantastic job of making it accessible for an English-reading audience.

For his next trick, and since all three live in the Boston area, I hope Steve Nadis tries to translate Seth Lloyd's work to the English language, Lloyd being, while brilliant, the very LAST author that any editor wishes to receive in his in-box, and it's not like Quantum Computing isn't important, because it is.

Eric said...

I remember reading ten year old encyclopedias as a child in the late 1950s that still referenced that the universe contained an aether. It wasn't at all unusual to see these references to something that was pressumed to exist four decades after they were scientifically proved not to.

Someone important, don't know who, said that science moves ahead when all the people who were trained on the outdated views finally die. That is more true than we like to believe. We look back on Einstein's revolution as if it behaved as a revolution. It didn't. The idea was revolutionary but the world just kept plodding along until all the people trained in the aether finally died.

That is how string theory and it's required calabi yau manifolds to hide the extra energy is. It may be a mathematically beautiful thing but it doesn't 't model nature in the way they are presuming. It may model something but we don't yet know if it does or what it would be.

We actually know now that the vacuum does not hold a plenum of near infinite energy that includes frequencies up to the Planck length. If it did the universe wouldn't cool as it expanded. Yet physics continues to go on their merry way acting as if it doesn't cool and there is this secret store of energy in waves up to the Planck length wavelength. Everybody knows it cools but physics persists in performing the kabuki dance that it really does not. And there lies all the complication that requires Supersymmetry, string theory etc.

Decades from now after all the people promoting those concepts have died people will look back and say the new revolution happened when we discovered the CC in today's universe is tiny but positive. And they will wonder why there are still so many books promoting string theory when there was no longer any need to hide the vacuum energy anymore in extra dimensions.

It will be because even the most intelligent human beings are far more susceptible to brainwashing than they would like to believe. Only when those brainwashed people die will the new books reflect it.

Christine said...

Steven,

Please don't extrapolate what I wrote. I was not asking for a litetary piece. Not a question of English.

BTW a typo in my previous comment: Terrence.

Best

Christine

Steven Colyer said...

Please don't extrapolate what I wrote.

No dice. I extrapolate everything. So do you, so does everyone if they wish to take that which is known and ask questions.

So when I comment on your comments, that's what I'm doing: I'm extrapolating.

You don't get get a free pass, sorry, especially at a website whose two young hosts are all aBOUT advancing science based on that which is known, specifically: extrapolating.

I guess the thing is to not extrapolate TOO much, hmm? If so and if you think I've done so, I may be wrong, but if so, pls be more specific in your criticism.

Eric said...

Steven, You shouldn't always drag Bee and Stefan into your arguments with other posters. I'm not saying you are doing this, but the outward appearance comes across as sucking up to them to drag them in on your side. It is not at all an intellectually honest way to argue even if it might accomplish what you would like to happen.

Steven Colyer said...

Steven, You shouldn't always drag Bee and Stefan into your arguments with other posters. I'm not saying you are doing this, ...

Except you just did, and I wouldn't be replying here if I didn't admire them, so stop it.

Christine said...

I extrapolate everything. So do you, so does everyone if they wish to take that which is known and ask questions.

Well, the point that I was making is, I believe, clear from what I wrote, as Bee understood, as well as yourself, seemed to understand initially. But somehow you brought the question that I was criticising the English level of that work, which I didn't at all. That was what I meant by extrapolation.

It may be true that extrapolations are a tool in Science, but what we are doing here are just commenting in a blog. No need to react as if there was more to it.

Best

Christine

Phil Warnell said...

Hi Steven,

There is a distinction to be made between extrapolation and speculation; with the latter being what I feel Christine was actually concerned with in respect to your assumptions as to what she would have understood.


“People who jump to conclusions rarely alight on them.”

-Philip Guedalla


Best,

Phil

Eric said...
This comment has been removed by the author.
Christine said...

Hey, no need for that. Bee is busy taking care of newborn twins and have no time for this; so let us all clean the mess here in this comment section and get back to the topic, ok? Peace to all.

Christine

Steven Colyer said...

let us all clean the mess here in this comment section and get back to the topic, ok? Peace to all.

Best advice I've heard in a good long while, so agreed, let's get back.

I contacted Steve Nadis and asked him to respond here. He declined, but he's read everything at this post and comments. Liked Bee's original review, thought she backed up a bit in the comments section.

Steve Nadis contacted me out of the blue once upon a yesterday offering to send me a copy of his book that I would review it at my blog. Huh what, me? Who am I? I'm nobody, at least not yet. I'm a learnin' guy I am, and loving every minute of it.

So I declined, because I'd already bought the book (and also had done a pre-review). A very nice e-mail relationship ensued. Nadis is cool.

The POINT is there aren't THAT many books on the shelves at the local bookstore that go THIS deep into what this "string theory" (Mathematics) stuff is all about. In fact there is no other, other than reading the actual papers that go into the details, and that's a complement given the next closest are Not Even Wrong and Road to Reality.

Christine said...

Well, I've also received books freely in the past, from editors, without asking for them, and have written reviews in my old blog. And I am certainly not an "important" person. Even so, I have received those books. Blogs seem to offer an interesting space for discussions on new books, giving additional visibility to potential readers who share similiar interests. So I think that is the main criterion. If the blog is serious enough, it is interesting enough to have reviews there.

Now, back to Yau/Nadis book, I have pinpointed previously what I regarded to be an annoying issue that could have been easily corrected with edition. This could have made the book much more readable, at least in my view. But concerning the math exposition purely, the material is no doubt interesting for the lay reader. I would however like it better if told in a different style. If the reader is not bothered with the issues I have mentioned, or regard them not as bad as my reading of them, then...

Steven Colyer said...

But concerning the math exposition purely, the material is no doubt interesting for the lay reader.

Agreed yet again with you! And there you have it folks, as Bee emphasized in her review, this is a book about MATHEMATICS moreso than Physics.

If SuperString Theorists like Calabi-Yau with N=6, which is the small part of C-Y that SSTers lock onto to embrace their theory, fine, it matters not what one thinks of SST.

But C-Y as pure mathematical truth is in the bag, pure math being what it is: True. So if anyone wonders if buying this book they'll be led astray as Warnell cautions re Susskind's works, fret not!

Calabi-Yau is real, real Math, and the field is far from finished. Much work to be done. I have to give the book a huge thumb up, definitely one of the ten books I'd like to have if I was stranded on a desert island with. Thanks, Christine.

Bee said...

Hi All,

Thanks for sorting this out among yourselves - very adult ;-)

Eric, while I can understand that you preferably comment if you disagree and keep quiet when you agree, the extrapolation to the case when everybody did this is that the poor blogger (ie. me) would be left with the impression that nobody agrees with anything they write. Very depressing!

Christine, it's a matter of taste, so nothing worth arguing about. As I said, I didn't find the style remarkable neither in the positive nor in the negative sense.

Steven, I was trying to disentangle my personal interests with what there is to say about the book. See, I'm just not that interested in Calabi-Yau spaces, I'm more interested in quantum gravity as you know. But I can't blame Yau for not writing a book serving exactly my interests. So what is there to say? They state very clearly what the book is about and that's what it is about, and it's well done. That I'd rather have read more about something else isn't really a fair criticism.

Best,

B.

Phil Warnell said...
This comment has been removed by the author.
Christine said...

Hi Bee, Steven,

I am not particularly interested in Calabi-Yau manifolds, at least not at this point of my personal studies, but the book was so highly rated and so much talked about that I thought I should give it a try.

Maybe I raised my expectations too much, and then for the issues that I have mentioned, I end up disliking a book that I know that otherwise I would have liked very much. I see from reviews that most people liked the book, so my personal annoyance is maybe, well... just my personal annoyance.

Yes, the subject is clearly stated and I knew what I was into, so no problem with that. From the point of view of exposing the maths, I have no particular objections, and the book makes a reasonable good job at that.

I do love maths, so just for that any book on maths for me already starts with 2 "amazon stars". But I subtract 2 amazon stars for being so much annoyed with the style, the "issue of modesty" in particular. (My husband asked two or three times what I was mad at when reading that book, just from my face and grumbles. That is unusual.)

So I would give it maybe 3 amazon stars.

Best,
Christine

Phil Warnell said...

Hi Christine,

It seems between Bee’s description, yours and Steven’s, considering taking the bad with the good this book still might be something I would benefit from reading. I would agree that self promotion doesn’t have much of a place when one is attempting to have something understood, yet if it is mainly to do with the history of the some concept this also can be helpful at times. However if taken to the levels such as Susskind has, it comes off as little more than gossip or innuendo, rather than serving to strengthen and or clarify the author’s argument(s).

To be honest the whole idea of compacted dimensions for me has always been a stumbling block when considering string theory, as if it having any connection with reality, so perhaps Yau and Nadis can have me to think otherwise. In a similar vein I read a book by Leanard M. Wapner as few years ago called “The Pea and the Sun; a Mathematical Paradox” which is a explanation of the Banach-Tarski Theorem, which demonstrates that at least from a purely mathematical perspective one can get something for nothing. This had me come away with a better understanding as to how if the world in the end truly is not much more than a mathematical construct, then scenarios such as the big bang can be given a footing of reason going beyond having such being more than simply a starting point still begging a miracle.

“Let’s be clear. There are no knives sharp enough to perform the dissections required for Banach-Tarski phenomena. Given the fact that infinitesimally minute detail is required, with no means (mathematical or physical) of constructing the pieces, we can safely rule out all hope of performing the duplications and magnifications ourselves. Neither you, I, nor Arlo Lipof will ever succeed in such regard. But Banach-Tarski duplication may occur naturally, if we choose to believe so. To accept such phenomena, we must accept The Axiom of Choice, adopt a permissive Go-Go philosophy with respect to physics, and be willing to define physical reality in such a way Banach-Tarski processes are being executed. This is not science fiction; it’s just one way of making sense of the physical world.”

- Leanard M. Wapner, “The Pea and the Sun; a Mathematical Paradox”, (page 190)

Best,

Phil

Phil Warnell said...

Just as a correction and to not further mess up this comment section the author of the “The Pea and The Sun; a Mathematical Paradox”, should have read Leonard M. Wapner not Leanard. One thing I can tell you about this author is his love for mathematics has all such considerations for self as to be all but nonexistent. Although being a professor of mathematics at El Camino College in Torrance California he has not even so much as Wikipedia page. Further he doesn’t have a web page at the college, with the best I could do was to discover his office hours and schedule, as to be certain he actually exists. Perhaps there is something to be said for carrying modesty a bit too far.

That remind me there is one other assistant professor whom which we are all familiar that also refuses to have Jimmy Wales give her the nod;-)

Christine said...

Hi Phil,

Thank you for your notes.

Best
Christine

Kay zum Felde said...

Hi Bee,

I have been red yet til page 54 of this book. Now it appears for me a little difficult. I don't know, when I will read it further. For now, my Ph.D. thesis has priority.

Best, Kay

Eric said...

Hi Bee,
Yes I can see how only negative feedback when people disagree with you would be depressing. But I did say that when you go out on a limb with an unpopular idea, but in my view correct idea, I will go out of my way to support you. Remember when everyone climbed all over you when you supported the idea of cosmic "strings" because you used the word "string". I knew you needed support there and that what you were saying was really very little different from "axions" used to model dark matter. I'm there when you actually need me.

On the other hand I often feel like I'm talking into an echo chamber here. I don't really know how I'm being viewed. I can tend to be bombastic just to get a reaction and thus find out. And you are right, it can be depressing waiting for a non-existent reaction.

Steven Colyer said...

Kay zum, in which field of Physics are you specializing, and also good luck on your thesis.

A "bit" off topic. The Drake Equation has been criticized as being worse than useless. Well, our knowledge is mighty but our ignorance is mightier yet. My question is how much "less useless" is Frank Drake's equation now given the latest results of Kepler?

My gut feeling is we've gone from certainty in a 1% to 99% range, to a 2% to 98% range, but that would be progress! Or am I being too critical?

Plato said...

On a wider class of complex manifolds - the so-called Calabi-Yau manifolds - there is also a natural notion of special Lagrangian geometry. Since the late 1980s these Calabi-Yau manifolds have played a prominent role in developments in High Energy Physics and String Theory. In the late 1990s it was realized that calibrated geometries play a fundamental role in the physical theory, and calibrated geometries have become synonymous with "Branes" and "Supersymmetry". Dr. Mark Haskins

Pulled this from blog entry of 2005

Plato said...

Some important work of Andrew Strominger has shown that Calabi-Yau manifolds can be continuously connected to one another through conifold transitions and that we can move between different Calabi-Yau manifolds by varying parameters in the theory. This suggests the possibility that the various 4-dimensional theories arising from different Calabi-Yau manifolds might actually be different phases of an single underlying theory.SUPERSTRINGS! Extra Dimensions

So your resistant to the research and you have your opinions about, don't let this stop you from investigating more about the subject in relation too, so that you do not miss the information that has been there all the while you had been going through life oblivious. :)

Best,

Plato said...

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall

That logic mathematically induced is explained in all that came before it, and leads too, the outer edges of, in regard to the physics of? So you are there in a front row seat, waiting in expectancy, as along as the logic that has been introduced leads to theoretical implications for experiential purposes.

If no plan, how would ever expect "to see" anything at all?

Bold added for emphasis

Bee said...

Hi Eric,

Yes, I appreciate your support. Best,

B.

Phil Warnell said...

Hi Plato,

“If no plan, how would ever expect "to see" anything at all?”

In case I hadn’t made it clear before I am neither a physicist nor a philosopher, yet merely a wonderer. As for seating accommodations anyone with access to a computer or a library card can be afforded the same ;-)

”I am not ashamed to confess that I am ignorant of what I do not know.”

"There is nothing proper about what you are doing, soldier, but do try to kill me properly."


- Marcus Tullius Cicero

Best,

Phil

Bee said...

Hi Kay,

Good luck with the thesis :-) Reg the maths in Yau & Nadis' book, you might find this book helpful, maybe you can find it in the library. Best,

B.

Kay zum Felde said...

Hi Steven,

my first name is Kay. Zum is only a prefix like "van" in van Beethoven. Zum is only very seldom. I work on gauge theories and on spontaneous symmetry breaking.

Best, Kay

Steven Colyer said...

I thought it was "von" not "van". And he wasn't as good as Mozart or Bach whatever you call him. :-)

Well good for you. Gauge theories are cool. Wouldn't "Phase" theory have been a better term? Well, it's too late now. Einstein didn't like "Relativity" to describe his theory either. "Gauge" reminds me of the thicknesses of wire, and junior high Electric Shop. Good times.

"Spontaneous" reminds me that an "unseen" hand needn't exist for Physics to be the way it is. But some "body" or "thing" had to set this crazy Universe up. Or not.

But it's all about symmetry, regardless. For example, about Paul Dirac:

Dirac was also noted for his personal modesty. He called the equation for the time evolution of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak of Fermi-Dirac statistics for half-integer-spin particles and Bose-Einstein statistics for integer-spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Einstein statistics" for reasons, he explained, of "symmetry"

What do you think of Randall-Sundrum models? That's where I first heard of the term, in Lisa's book.

Topology books, there's so many of them. Has that German book you recommend been translated into English, Bee? What's the best topology book in English, anyone? I think of Simon Donaldson alot, his interests parallel my own, with the important difference he's successful. :-)

Kay zum Felde said...

Hi Steven,

the German term for "gauge theory" is called "Eichtheorie". "Eichen" means in German to calibrate. So this is in my opinion quit a good term for what is going to be done with the fields.

Best, Kay

Plato said...

As for seating accommodations anyone with access to a computer or a library card can be afforded the same ;-)

Yes, it is that easy.

An overseer of sorts on all information that is out there....so you tend to want to encourage scientist to be open and up to date so they are on the pulse of scientific changes taking place on what we currently know.

Communications clear and non constrained, is to keep society and their knowledge current, and available.

This the basis of helping society be realistic and not monetarily challenged, because this affects the corners of society that middle income have in advantage that those really lean cannot afford.

When does culture suffer or require a revolution as much a science requires there's in break breakthrough's?

Best,

Plato said...

Of course history of topology is important.

Topology as "a label" reveals efforts to understand while those mathematical bent were off doing other things and missed it in their evolution?:)

Einstein would, I think, have been both surprised and gratified
by the extent to which his geometrization of physics has
progressed. The mathematical by-products would have
surprised him even further. But the fact that his ideas
were so fruitful would only encourage him in his fundamental
beliefs. In particular he would still be encouraging us to
dig beneath the mysteries of quantum mechanics. In another
century we might find what Einstein was looking for.
Einstein and geometry by Michael Atiyah

His take on topology is interesting from a Global perspective?

Steven Colyer said...

Beautiful words from Atiyah, thank you for that, Plato. Michael Atiyah, one of the best minds of our age, yet totally under appreciated.

A shame that huh? In place of Atiyah or Is Singer, Americans focus on the latest screw-up of the week ... either Lindsay Lohan or Charlie Sheen, they take turns. Or in a slow week, Brett Favre or Tiger Woods fills in the blanks. So sad. :-(

Zephir said...

/*..debate about physical relevance by focusing on the mathematics..*/

From AWT perspective the algebra is the physics of colliding countable units, i.e. natural numbers aka particles. Even the abstract theories are formed with physical processes inside of human brain and they're even intersubjectivelly accepted with another brains. They can be indeed distant from physical reality, which they're trying to describe, but they cannot be distant from reality so much. Actually the biggest problem of string theorists isn't, they're developing too abstract models, but the fact, they cannot see their application in neighbouring reality. It's not so surprising, because some applications would violate some postulates of their own theory, but many concepts, which string theorists trying to reveal are still surprisingly common and widespread (extradimensions and multiverses are all around us).

Kay zum Felde said...

Hi Bee,

thanks for the recommendation of Klaus Jaenich's book. I will buy it soon.

Thank you also for your best wishes on my thesis.

Best, Kay

GW said...

Christine: I am just starting the book, but I have already been put off Yau somewhat by a scathing account of the Perelman/Yau flap about the Poincare conjecture proof. See the essay by Sylvia Nasar in the New Yorker. It is fascinating:
http://www.newyorker.com/archive/2006/08/28/060828fa_fact2?currentPage=all

Steven Colyer said...

That was a slander piece by Nasar. Every genius makes their share of enemies, and Yau is no different. Any fool investigating the piece itself discovers Nasar didn't do her homework, which yeah, I know is surprising for a journalist. Who knew?

Perelman and Hamilton both admitted Yau's contributions at the start of the long road to turn Poincare's Conjecture into Poincare's Theorem, so, feh.

Christine said...

@SW, Steven,

Yeah, I know all that story, and I don't believe in what journalists write, in general.

Again, I have nothing absolutely against the person of Yau. I don't know him personally and all I know is that he is a top mathematician. I'd be happy if I knew 10% of what he knows.

I just think he could have done better in that book if he omitted certain embarrassing and unnecessary passages.

Best,
Christine

Steven Colyer said...

I just think he could have done better in that book if he omitted certain embarrassing and unnecessary passages.

Could you be more specific? What embarrassing or unnecessary passages? He didn't mention Nasar's hatchet job at all, her attack on his reputation.

Growing up in the Hong Kong (i.e., English) system, such a slander would be illegal and give grounds to sue. But America isn't England. Yau did look into suing, and it was explained to him that being a celebrity (published and notable) in the USA given our laws, that he had no case.

I like the way Lee Smolin responds to Lubos, for example. Lee just ignores him. The best way to deal with a bully is to do just that. They go away and pick on someone else after a while.

Agreed on not believing stuff you read in print, especially if it's negative or controversial. It makes one wonder if being famous is worth the effort. It's much easier to tear down than it is to build up.

Christine said...

Could you be more specific?

I thought I was clear enough in my previous posts. I never mentioned Nasar in my previous remarks, it was GW, so why to you bring that up?

But since you need some specifics, here are some excerpts/passages/samples that I would edit. All that can be true, all that could have indeed happened, but it's not the way one writes about. I wouldn't write that way.

===========


page 33: "It was a surprising question for me to ask..." etc

page 36: regarding that he did like Confucius.

page 38, last paragraph, depending on how interpret from that.

page 39, second paragraph: while the rest of the mob read popular books, he read Milne.

page 40: "Having no office..." etc.

page 42: "I was pleased to have finally contributed to the great body of mathematics, but I didn't feel as if what I'd done was specially noteworthy. I was still searching for a way to truly make my mark."

page 47: "At the risk of sounding immodest..."

page 53: "We had thus settled a major question in geometry that had been debated for decades. But that was not the end of the story."

page 57: "...most physicists thought it was true (as they kept bringing it up at their conferences, year after year)." And then:

page 58: "Relying on our geometric intuition in turn, Schoen and I then managed to succeed where physicists had previously failed."

page 63: "This was a purely mathematical discovery about objects whose existence would soon be confirmed by observation."

page 63: "... what we believe to be the first rigorous mathematical proof of a long-standing black-hole problem."

page 77: "I consider myself fortunate..." until end of paragraph.

page 80: "From this sprang the work I've become most famous for."

page 80: "For me the conjecture was almost inescapable: Just about every road I pursued in my early investigations of curvature led to it."

page 105: "... it's rare for a single conference to change the course of your career. Twice."

page 105:" I was told that by virtue of this work, I'd made a big contribution do the conference, and afterward I felt quite proud of myself".

page 109: "... the sort of equation that had never been solved before. Even though no one had previously managed to solve a problem of this exact type..." etc

page 112: paragraph beginning in "So in the end..." ... "It was still incredibly difficult", etc, then page 115 last paragraph.

page 119: paragraph on "Turned out to be pretty magical".

page 120:, last phrase.


Etc.

Steven Colyer said...

I wouldn't write that way.

Ah, so I see said the blind man to the deaf man who was looking away.

I think the issue here then is one of "ego" which I'll guess offends you, because yup, he has a strong one.

To be frank, a strong "ego" offends me too somewhat, to the point that my own personal bullshit detectors go to Code Red when people start complementing themselves, because we all know the difference between "ego" and "egomaniac" is a thin line.

So I did go to Code Red, but I didn't see really where he actually crossed it. There's such a thing as "pushing the edge of the envelope" so to speak however, and thanks to that wonderful list you just provided, I shall re-read and reconsider.

But look at it this way and as Phil Warnell pointed out:

He ain't Susskind!

Then again, I cut Lenny much slack because he's from New York, and they ... DO have a way about them in that regard, but when you get to know them, they're really nice people.

GW said...

Christine and Steve: While the Nasar article was certainly anti-Yau, I wouldn't call it slanderous. Perelman, who is by all accounts modest, not overly ambitious, and certainly not materialistic, was so put off by what he regarded as intellectual shenanigans in the math community that he rejected prizes and withdrew from math (even resigning from Steklov institute). It was not so much Yau as some of his students who seemed to ignore Perelman's contribution, minimized it, denied his proof, said they fixed it etc.
Yau is a great mathematician, but as Christine says, seems that his ego is pretty big, and I think it is undeniable that he and others could have been more generous to Perelman.

GW said...

Steve: Hamilton didn't know how to finish it; neither did Yau.
Also, why are you bringing up Lubos and Lee Smolin. Lubos is a hell of a physicist (particularly if you love string theory) who takes what one says completely literally and is pretty quick to insult on blogs, but is quite nice off them. IMO I wouldn't criticize his physics. Lee to me seems all over the map with his speculations. But why bring them up as it just fuels trollishness.

GW said...

Perelman refused to accept the Millennium prize in July 2010. He considered the decision of Clay Institute unfair for not sharing the prize with Richard Hamilton,[4] and stated that "the main reason is my disagreement with the organized mathematical community. I don't like their decisions, I consider them unjust."[5] from wikipedia on Perelman

Steven Colyer said...

Geez, GW, have you ever actually READ the Wikipedia article on the YES slanderous hatchet job that was the article Manifold Destiny? I just linked it, so don't believe me, read that and the links and form your own opinion, brah.

Also, you're not going to make many friends mentioning good things about Lubos HERE, considering how CLOSED-minded the guy is. Intelligent? Yes. Knowledgeable about proven physics? Absolutely. OPEN-MINDED about quantum gravity theories? Absolutely NOT! A true scientist should be open-minded and willing to switch gears should better experimental results prove them wrong.

IS Lubos that guy? Well I don't know, let's see WHERE are the experimental results one way or the other of String Theory? Answer: nowhere. So, the rational scientist should be at least open-minded and willing to respect others' (like Smolin's) opinions until such time as experimental results that prove or disprove one way or the other come in. Lubos is NOT that guy.

Kepler, Gamow, and Hoyle were all wrong in some of their theories. To their credit, they admitted they were wrong when the evidence proved them otherwise. Outstanding. Honest.

GW: read this, then consider before responding, just a tip.

GW said...

Steve Colyer: Interesting. Then why are you over posting on Lubos' blog on Feb 11? I suggest reading this before responding. Just a tip:
http://en.wikipedia.org/wiki/Hypocrisy

I am aware of what you posted but do not want to get drawn in so stop now. BTW, string theory has not been proven wrong or not even wrong. In fact, it is the best bet going right now. You know that direct experimental evidence is going to be difficult because of energy limitations...once again see
http://en.wikipedia.org/wiki/Hypocrisy

GW said...

I did read the wikipedia article on Manifold Destiny as you suggested. We must not be reading the same article.
The whole thing is still murky and Yao does not come off too well there either, with his students basically being forced to change the title of their paper claiming priority and barely mentioning Perelman. Also Anderson and Strook fail to confirm their supoosed letters or comments on Yao's blog. I don't want to diss Yao, but no one really comes out of this unscathed except perhaps Perelman.
About the other link, well yes, its outrageous and I seem to remember an attack on Christine as well, but I like Lubos. I have also liked Christine's blogs.

stefan said...

Guys,

can you please get back to the topic of the post? It was about the book and its content.

Thanks, Stefan

Steven Colyer said...

I can, and I will, and I thank you Stefan as I've said all I have to say on the unpleasant subject and have better things to do than debate Kantians. In any event, your house, your rules, and I for one totally respect that.

Btw so good to hear from again Stefan, world's newest daddy. How go the pampers wars? :-)

back on topic regarding what is IN the book rather than not, I found the following 3-star review of the book by George Musser at Goodreads refreshingly honest in George's usual refreshingly honest way:

"It's very hard to assign a rating to this book. For people with a math or physics background, it should get five stars: it explains the math underlying string theory (and much besides) at a more intuitive level than textbooks or research papers typically do. But for the general reader, it deserves maybe two stars: it assumes a great deal of background and motivation to work through the topic. " ... George Musser

Since I DO have a Math and Physics background, I do give it a 5.

Bee said...

Hi Steven,

Stefan is fighting bravely, though Gloria scored recently with peeing 3 times on the changing table before I managed to open a new pack of diapers (that Stefan had stored on the uppermost shelf that, unfortunately, I couldn't reach without help of a chair, the nearest of which was in the kitchen). He's about to qualify for the contest in changing-diapers-eyes-closed-right-hand-on-the-back. The babies were recently promoted from size 1 to size 2.

But I'm off topic ;-) Back to the book, it's worse than needing two ratings for readers with different levels of knowledge, one would need different ratings for different chapters. If you only read the first and last few and skip the middle, the book would score much higher in my opinion. Not so much because there's a lot of math in the remaining chapters but because I found the writing quite uninspired. Best,

B.

Steven Colyer said...

Yes, lol and thanks about the 3-pee story! I have a similar one with a sadder ending, maybe.

What happened was, when my firstborn was 2 months old I was changing his diaper when my visiting sister and her husband walked it. So I picked our naked pride-and-joy up with one hand on his back and one under his fanny, and our young man chose that very moment of introduction to his kin to defecate into my palm! And it wasn't one of those nice solid ones, either. Suffice it to say that left quite the impression on that first of my sister's husbands, such that he never had kids. So here's to my boy for "doing his bit" on controlling the world's overpopulation! :-)

Yes, about the book, true enough. It does read like a series of essays. Nadis and Yau are careful to point out in the Intro that they will not reveal which chapters were written by whom or the proportions therof, but upon re-reading I am sure it will become more obvious. We will note your knowledge of Math Phys far exceeds mine, so I was perhaps more excited reading it as most of this was new to me. I also grow weary of bashing string theory, and strongly feel that to do so one should at least understand the math in question, and this book helped me loads in that regard.

damigiana said...

"figures only get you so far to understanding six dimensional spaces"

My favorite space has dimension minus six. As in, six less than zero. Harder to draw.

And many thanks to you, as a physicist, writing such a positive report about a math book. It's hard to write such a book because while high school makes you acquainted with at least the keywords from twentieth century physics (think neutrino, boson, quark) mathematics stops at 1900 or earlier. Manifolds, varieties, cohomology are on a par with the terms I mentioned before in importance and age, but no nonprofessional would have heard of them.

Bee said...

Hi damigiana,

Yes, it's true, one doesn't learn a lot of math in school. Worse, the little one learns is uninspiring and leaves people wondering what it's good for. It's a shame, really, especially some topology wouldn't be hard to teach. Best,

B.

Steven Colyer said...

Good point Bee, and if I may continue in this vein because believe it or not, it will be a very, very short time before your girls enter the educational "system", i.e., bureaucracy (spits).

Looking back, I liked all of my high school and university teachers in Math and Science, with one exception each. 97% good is good enough sigma for me. ;-p

No, the problem I think is in the elementary schools, the primary education. The problem I experienced, and realize now that I've contemplated it, is that most elementary TEACHERS aren't all that good at Math, and the public schools, at least here in America, cowtow to the teachers.

Topology is in many ways easier than Algebra, and like you say if Math is taught without practical applications, the student's passion is quickly lost.

I'm not sure what to do about that. Well, um, actually I am but no need to go into it now. My point is: Education begins at home. If we do it right, I see no reason why a 6th grader with an IQ of 100 can't grasp Differential Calculus. I really don't. Slope of a line. What's hard about that?

Briefly, I would adjust as follows:

Currently:
1st grade - Counting
2nd grade - Addition and subtraction
3rd grade - "clock arithmetic", Money counting
4th grade - Multiplication, Division, Times tables and god-awful "word problems"

to

Pre school - Counting
Kindergarten - Addition and Subtraction, Clock arithmetic, Money counting, Euler's characteristic and elementary Topology
1st Grade - Multiplication and Division, Times tables
2nd Grade - Elementary algebra, elementary exponential function and sines and cosines, polynominals, squares and square roots
3rd grade - Euler's trigonometric formula, powers and roots, Infinite series and elementary Fourier analysis
4rd grade - Matrix mechanics

I think the kids could handle it. But if the teachers don't know that stuff, then, feh.

Bee said...

Hi Steven,

You forgot formal logic. In any case, the teachers don't make the schedule, I think you know that, so they're not the ones to blame. I frankly think the whole school system with age-separated classes and fixed schedules sucks. I'd prefer a point system where classes are offered on different topics and the kids can put together their schedule as they want and can. The advantage wouldn't only be that children can learn at their own pace, but also that they can combine topics as they wish. I for example seriously hated it that each day you had 5 different topics. I'd have much preferred to have 2 weeks German, then 2 weeks math, etc. Best,

B.

Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...

Hi Steven & Bee,

I think that’s why it’s referred to as a formal education, which I think can’t be avoided as to not have things ending in chaos; that is at least for most. When my kids were growing up they experimented with a more open system and the overall result for that generation turned out to be by in large an abysmal failure. The hall mark of it was to have the teachers given more freedom with the curriculum and expect them to create their own lesson plans. The end result being most didn’t learn much at school, leaving the only hope for the children is if the parents themselves took a more active role in their studies and teaching. Now as it turns out I now work with and supervise many from this generation and I can tell you for certain it was an experiment that should have never have been conducted.

Now don’t take me wrong, as I don’t think the end all and be all is a formal education. However from my own experience people have a tendency to follow what interests them and there is more to it than simply having them exposed to things earlier on or creating a system which is less rigidly structured. I think the main problem being more one of attitude, where education is presented the same as work in our society, in it being projected as an obligation, rather than an challenge presenting an opportunity, whose main purpose is to serve and benefit society first and then perhaps the individual if successful, instead of the other way around. So for me the focus of education should rest with how to maintain and cultivate a child’s natural sense of curiosity, rather than having us decide what they should be curious about or a simple abandonment of structure.

” Whereas our argument shows that the power and capacity of learning exists in the soul already; and that just as the eye was unable to turn from darkness to light without the whole body, so too the instrument of knowledge can only by the movement of the whole soul be turned from the world of becoming into that of being, and learn by degrees to endure the sight of being and of the brightest and best of being, or in other words, of the good.”

-Plato, Allegory of the Cave, Book VII of the Republic


Best,

Phil

Christine said...

I agree with Phil. I know of a few "experimental" schools that allow children to "choose their interests" and to "learn at their own pace". These schools don't work for most children and are generally a big failure; I know this from colleagues who ended up very unsatisfied with the results.

The question is not the "formal" issue. I'm almost certain, Bee, that when your babies grow, you'll be all pro formal education.

Here is an excerpt that you may find interesting to look for in a school:

"we want children to feel happy, safe and valued so they develop an enthusiasm for learning, the ability to be self-motivated and the confidence to persevere; to approach life flexibly and creatively; to respect themselves and others and grow into responsible members of the community."

"Aims for Pupils

Pupils will:

Achieve their full potential through the curriculum. 
Develop their individual talents and positively work on improving identified areas for development. 
Become independent "Life Long Learners". 
Celebrate and learn from difference. 
Use the school as a training ground to be caring and committed to the needs of others who may have different.
Life experiences and apply that knowledge to life outside the school. 
Be committed to equality of opportunity.

Aims for School

The school will provide:

A broad and balanced challenging curriculum. 
An enriching programme of extra-curricular activities.
A stimulating learning environment. 
A rich and varied and up to date range of learning resources. 
Innovative teaching and opportunities for independent learning.
An ethos of support, challenge and encouragement to succeed.
Opportunities to maximise individual talent. 
Opportunities to take responsibility for decisions which add value to the school and the wider community. 
An all inclusive strategy that takes into account the different needs of individuals. "

Look for schools associated with Unesco, for instance.

Best

Christine

Steven Colyer said...

Hi Bee, you wrote:
You forgot formal logic.

Really? But if you did that the powers-that-be would be disappointed your kids don't fall for their programmed sheeple-herding fear-mongering.

It's tough to say when formal logic should be taught. Also bear in mind I was speaking of only Math and Science (well, Math). I would include Logic with Science. Both Math and Science grew out of Logic (Philosophy, if its good Philosophy), in different directions, only to be reunited thanks to Computer Science in our own time.

So it's tough to decide when to introduce it. What about fantasy? What about "Where the Wild Things Are" and the Brothers Grimm and Stephen King and the troll that hid under the bridge in The Three Billy Goats Gruff? How can they appreciate those if they're logical? Will they be fun at parties if so?

Actually I still get nightmares about that troll, so I guess you're right. ;-)

I took Introduction to Logic as an elective in my second semester of my freshman year. Best. Elective. Ever. It was taught by the Philosophy department. My chief regret is it's not required for ALL college freshman.

the teachers don't make the schedule, I think you know that, so they're not the ones to blame.

Yes and no. Once they become part of the system, and 2 years after they're in the system (because you need 2 seasons to note the patterns), they become part of the system, and therefore have an implied responsibility to change the system, or take the easy way out and maintain the system.

Steven Colyer said...

Fastest Declining Academic Fields at 4-year Colleges

Ain't looking good for Math. Or Germanic languages/literatures.

Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...

Hi Christine,

I thought we might see things similarly in such regard as I remember your comments about your experience with your son’s classmates and you noticing how delightfully curious many were. I also remember how you lamented that by the time children reach the latter grades they display a marked decline in their curiosity. What I find interesting is this way of looking at education is no longer simply an unsubstantiated theory, yet rather one demonstrated to be correct by people such as John Mighton, with his participation and development of the JUMP (Junior Undiscovered Math Prodigies) program.

I don’t know if you take notice of the PI public lectures that are available Online, yet the one John Mighton gave called “The Ubiquitous Bell Curve: What it does and doesn't tell us” you might find interesting. The thing is such a change of thinking is still in its infancy, yet gives reason to hope that more children in the future may find education as something they enjoy and then remain an important part of their lives, instead of something they are thankful to have simply survived.

Best,

Phil

Plato said...

Taken from my entry

The scientist does not study nature because it is useful. He studies it because he delights in it, and he delights in it because it is beautiful.Jules Henri Poincare (1854-1912)



HENRI POINCARE

Mathematics and Science:Last Essays

8 Last Essays

But it is exactly because all things tend toward death that life is an exception which it is necessary to explain.

Let rolling pebbles be left subject to chance on the side of a
mountain, and they will all end by falling into the valley. If we
find one of them at the foot, it will be a commonplace effect which
will teach us nothing about the previous history of the pebble;
we will not be able to know its original position on the mountain.
But if, by accident, we find a stone near the summit, we can assert that it has always been there, since, if it had been on the slope, it would have rolled to the very bottom. And we will make this assertion with the greater certainty, the more exceptional the event is and the greater the chances were that the situation would not have occurred.


Do correspondences linked in rhetorical comments of Poincare allow us to see better abstractly in today's landscape of ideas?

This correlation was an important step for me, maybe it will be for you?

Best,

Plato said...

Ach! Have to do some re- research:(

Last 8 Esays

Sorry.

Plato said...

Also see William Thurston

Best,

Christine said...

Hi Phil,

Thanks for the link to John Mighton's lecture. I'll take a look opportunely.

Best,

Christine

Phil Warnell said...

Hi Steven,

A thought came to mind as a result of this side discussion about the general state of education and that was perhaps that you could do something to make an impact in such regard. Now I realize your main focus as of late is along the lines of you yourself making some meaningful contribution to physics or math, yet with all things considered wouldn’t you think that enhancing the changes of future generations might stand as more likely to provide better value and even perhaps a greater degree of personal fulfilment.

That is my thought runs along the lines of you contacting someone like John Mighton, who I mentioned to Christine that heads up the JUMP program to explore the possibly of you getting involved in such a program, as to how you could be instrumental in having it introduced into your area. That is from my way of looking at things, with your deep love of Math that with a little training providing the right tools, direction and focus you could accomplish wonderful things for many. That’s to say perhaps being a mentor rather than a sage might be just what you are looking for and at the same time make available what so many desperately need.

Best,

Phil

P.S. I apologize for running of topic

Steven Colyer said...

Thank you, Phil, I'll look into it. Click here to see what we're up against.