text:
You are here
Textbook on linear algebra
Linear algebra is significant to many aspects of mechanics. For some years I have been using the book by Shilov. But this book may or may not be a good one to recommend to a student, depending on his or her prior experience. On StackExchange Mathematics, there are several excellent threads discussing textbooks of linear algebra. A particular recommendation was made for textbooks of linear algebra at three levels. Do you have any recommendations?
- Zhigang Suo's blog
- Log in or register to post comments
- 217159 reads
Re: Textbook on linear algebra
Dear Zhigang:
A classic on this subject is:
P. R. Halmos, Finite-Dimensional Vector Spaces, Springer, 1987.
I use parts of the following book in the applied math course I teach at Georgia Tech.
A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering and Science,
Springer, 2000.
Jim Knowles wrote a more applied book that may be more appropriate for beginners.
Re: Vector spaces and tensors
Dear Zhigang:
Yes, I like this book. I actually read it when I was a graduate student at Caltech.
I think that definition is fine and general enough even for stress. 1) If you consider Cauchy stress it is a tensor. It is a linear map that given a unit vector (normal to an area element) gives you the force acting on that area. Force is a convector, which can be identified with vectors using the trivial Euclidean metric (or even in more general spaces). 2) If you consider the first Piola-Kirchhoff stress it is a two-point tensor. It is a linear map that given a unit vector in the reference configuration (normal to an undeformed area element) gives you the force on the deformed area (a convector in the ambient space). This is a two-point tensor and obviously conjugate to the deformation gradient.
Again the "domain" and "range" need not be the same.
Linear algebra done right
Dear Zhigang, I have followed the linear algebra discussion on iMechanica with quite a bit of interest. Although I don't have anything meaningful to contribute beyond what has already been said, I would like to make a book recommendation.
When I joined the University of Houston as a young assistant professor, Lewis Wheeler used to teach our required graduate math course sequence (--which I later taught as well). He is a big believer in teaching linear algebra in depth and also successfully convinced me of its importance for mechanicians. He refers to several books in the math course however, when I had asked him for an elementary text, he recommended the following; which he used heavily: "Linear Algebra Done Right":
I was amused to see on your post that there is also a book with precisely the opposite title! I had read the Linear Algebra Done many moons ago and liked it quite a bit. If I recall correctly, it does not quite get into tensors but lays out all the foundational material both rigorously and an easy to understand manner
Re: linear map and tensor
Dear Zhigang:
I haven't read this book but tensors are multilinear maps. You can certainly have more than one vector space. An example in continuum mechanics is "deformation gradient", which is a linear map from a vector space in the reference configuration (tangent space at a given point X in the reference configuration) to another vector space in the ambient space (tangent space at the image of X in the ambient space). This is an example of a two-point tensor.
Re: tensors as shorthand for linear maps between vector spaces
Yes, this is correct.
Tensors etc.
Zhigang - What you say above is correct except I would add that the spaces in question are finite dimensional. Bounded linear operators on infinite dimensional spaces come close to tensors on finite dimensional spaces, but even then it is a bit of a different ball-game.
I uploaded a couple of set of notes by Don Carlson - I had to use optimized pdf as the file sizes were too large otherwise. If you take a look at Chapter A.4, the connection betweeen the multilinear approach and viewing tensors as a linear transformation between a f-d vector space and spaces of higher-order tensors on the same space are all spelled out.
If there is interest, I can upload the rest of the notes too. It is absolutely beautiful stuff for the beginner and has changed the course of at least one life....
Re: A more general definition of tensor?
Zhigang: The definition of (higher-order) tensors that I find useful and have used extensively in mechanics is A 4.1.1. out of Carlson, not the multilinear function mapping to R. One feature of that use of tensors is that the domain and co-domain are not the same vector spaces....
What goes by the name of a linear transformation (e.g. Carlson A 2.4) has the generality you seek; in fact even more as no notion of dimension need be associated with domain and co-domain - and this is useful in mechanics too as with linear differential operators.Tensors use a little more structure, thus in my opinion a different name is OK.
Anyway, in the end, these are all definitions and the important thing is to understand them well enough to do something reasonable with them without too much fuss......
Re: this definition does not even allow stress to be a tensor
Zhigang: May be I misunderstand the point you are trying to make and, then again, may be not. As you know, the tensors of most common usage in classical continuum mechanics is the tensor of order 2 that takes vectors from V_3 to V_3, this being the space in which we think the stress tensor belongs. In what you say above, do you want distinct vector spaces for domain and co-domain? Then, even the tensor of order 1 allows these to be different. If you are thinking of the domain to be a Cartesian product, that can also be handled as a fancy V_n.
Agreed that if one gets very picky, one could say why and how is it valid to write (when one chooses to do so) position vectors, velocities, tractions etc. all in some common basis for (the translation space of) a 3-d Euclidean space by thinking of them as members of the same vector space; it is with this identification that the classical definition of stress as a second-order tensor makes sense. But as we all know, this works out just fine, and I admit I have not thought about this seriously. I believe that to do this precisely, one implicitly utilizes the isomorphism that necessarily exists between the 3-d vector spaces for each of these quantities. If I understand you correctly, you would prefer to think of say position vectors and velocities also as members of separate vector spaces?
Btw, I have uploaded the rest of Carlson's notes as you requested. Naturally, Balance of linear momentum with stress as a 2nd order tensor between V_3 to V_3 is worked out there in gory detail.
Also, the few pages of introductory Continuum Mechanics in Hill's "Aspects of Invariance in Solid Mechanics" article are fantastic and complementary to say Carlson's treatment. In particular, it does a great job of explaining convected derivatives for people without background in differential geometry on manifolds. Again, Hill utilizes the identification that you would probably not like (with things like 'common background frames' in play).
Re: displacement, work, force
Hi Zhigang: For me, the work, force, displacement example at least provides a way of seeing why the conventional mechanics interpretation works out because the underlying vector space has an inner-product and it is easy to see why the force can be associated with a vector in the same space as u. (And even physically, I for one can feel the direction and magnitude of a shove more immediately than something from an abstract dual space to displacements contacting me :).
However, the other question of why conventional mechanics gets away with treating position vectors, displacements, velocities, area vectors, tractions etc. as all belonging to the same vector space (when physically we cannot really add displacements and velocites, e.g.), does not seem to get addressed by representation theorem duality.... This is even before we get to linear transformations......It would be good to know if someone has sat down and worked out the logic carefully.....It must have to do with dimensional analysis too, I guess....
Re: why conventional mechanics gets away with it?
Zhigang: Under 'Velocity' you mentioned "We can choose the basis of this space to coincide with the basis of U." Since there is no unique basis to choose, and in any case velocities are still velocities and positions, positions, in the context of this discussion in my opinion this case is also best left as the general M case that you discuss afterwards.
The linear map A that you try to describe is an isomorphism that I mentioned in an earlier comment between two finite dimensional vector spaces of equal dimension. For me, first such a physically meaningful mapping would have to be discovered for each pair of spaces. Otherwise, there are infinitely many that can be constructed, and since physics does not care for convention, i.e. physical results have to be invariant w.r.t. choice of convention, it needs to be shown that your choice of a map A between say the space of velocities and position vectors (A is independent of bases in either space), and my choice of another map A between the same spaces keep all the mechanics we want to do invariant...Alternatively, I cannot see a physically meaningful linear map that associates each possible position vector to a corresponding velocity vector....and even if I did, I am not sure to what extent you or a third person would accept that is the only choice to work with. So it seems like proving the invariance with respect to different choices of the mapping A might be the way to go, and this needs some careful reasoning, which I am probably not doing typing on imechanica, so this tells me that if I should talk about this any further, I should better get my act together and do some serious thinking in solitude and then get back to say something if I have anything meaningful further to say...
Until then, with my best regards,
- Amit
Re: Some thoughts on tensors
Dear Zhigang and Amit:
Thanks for this interesting discussion. Just some thoughts:
Let us consider a very simple example. A particle moving in the Euclidean three space. Position vector x(t) at any instant of time t can be written with respect to the canonical Cartesian basis vectors {i,j,k}. If you now differentiate x(t) with respect to time you get the velocity v(t) that has components with respect to the same basis {i,j,k}. We think of both the position vector and velocity as vectors living in the same linear space. But with the understanding that we cannot add a position vector and a velocity vector as they have different physical dimensions.
Note also that when curvilinear coordinates are used the natural bases would have different physical dimensions and consequently components of a vector may not have the right physical dimensions, e.g. in spherical coordinates. Here, one would have to use the so-called physical components.
If this particle moves in a curved space then position vector is not even defined. However, velocity is defined and at any given time t it lies in the tangent space to the ambient space at the point x(t). So, in this case one cannot even pose the question of adding "position" and velocity vectors.
Let us call the linear space of velocities at a point x, V. Using rate of change of energy or power, velocity and force are dual to each other (similarly force and displacement are dual to each other as Zhigang mentioned). Forces live in the dual space of V, i.e. V*. This is the space of one-forms or covectors. Choosing a basis for V, one has a natural dual basis for V*. These, in general, have different physical dimensions. There is a natural pairing between elements of V and V* and this natural pairing does not require an inner product (or metric). An inner product (metric) induces an isomorphism between V and V*, i.e. one can identify the two linear spaces. Note that, in general, this isometry changes from point to point.
Given two linear spaces V and W an isomorphism is a one-to-one and onto linear map. If you specify the map on a basis for V then the map is uniquely defined. The two vector spaces being isomorphic doesn't mean you can add a vector in V to a vector in W. In this sense, identifying the linear space of forces with that of velocities doesn't mean you can add the two.
I think Cauchy stress is a tensor in the sense of tensors in the notes of Prof. Carlson using the isomorphy between vectors and covectors. One doesn't even need to worry about identifying the linear spaces of forces and velocities. Cauchy stress can be simply represented using a basis of covectors (and is obviously symmetric). However, again, I agree with Zhigang that for mechanics applications one should work with multilinear maps on a collection of linear spaces that are not necessarily identical. The obvious examples are deformation gradient and the first Piola-Kirchhoff stress.
Re: Some thoughts on tensors
Hi Arash: A few remarks on your comments:
1. "We think of both the position vector and velocity as vectors living in
the same linear space. But with the understanding that we cannot add a
position vector and a velocity vector as they have different physical
This is the crux of the problem, as it sounds like a contradiction in terms. Ideally, we would like to be able to say that if two objects live in the same linear space then they absolutely should be'addable' and if not, then they do not belong to the same linear space.
2. "If this particle moves in a curved space then position vector is not even defined."
I get the point you are making and the context, but just to play devil's advocate, as long there is a good, physical embedding space, it all works out just fine. E.g a 2-d shell in 3-d space - of course, we do very good mechanics using position vectors on the shell.
3. "Given two linear spaces V and W an isomorphism is a one-to-one and onto
linear map. If you specify the map on a basis for V then the map is
uniquely defined. The two vector spaces being isomorphic doesn't mean
you can add a vector in V to a vector in W. In this sense, identifying
the linear space of forces with that of velocities doesn't mean you can
add the two."
For any linear transformation (on a finite dimensional space at least), whether an isomorphism or not, knowing its action on a basis completely determines it, obviously. However, this property of all linear transformations (on fd spaces) obviously does not uniquely pick any one of them.
The goal in utilizing an isomorphism would not be to add vectors from the different spaces. The goal would be to work with only one space and hopefully be able to do mechanics relevant to the other through this space, utilizing the identification afforded by the isomorphism.
4. "However, again, I agree with Zhigang that for mechanics applications one
should work with multilinear maps on a collection of linear spaces that
are not necessarily identical. The obvious examples are deformation
gradient and the first Piola-Kirchhoff stress."
Since this is just an opinion, let me share mine from practical experience. I have followed beautiful, nonlinear shell theory (of the Antman, Fox-Simo, etc. variety), done some of that theory, and also numerically implemented some without ever thinking of multilinear maps. Anyone who as done shell theory will immediately realize that you have to deal with the deformation gradient on a shell by considering the tangent spaces at corresponding points on reference and target shell as fundamentally different, but I do not see this as any reason for making the multilinear map point of view as essential for mechanics application......It is what it is - just a point of view.
Re: Re: Some thoughts on tensors
Dear Amit:
Thanks for your remarks. I think the main one I'd like to understand is the first remark (I pretty much agree with your other comments). I'm not sure if this is the solution but one may be able to think of two copies of the same linear space. In other words, position vector and velocity vector live on two copies of the same linear space. This would mean that you can't even mathematically add vectors from the two copies.
This idea of different copies of the same linear space you clearly see in differential geometry. Given an n-manifold, tangent space at any point is an n-dimensional linear space. You have different copies of the same linear space at different points. These linear spaces are all isomorphic but you cannot add vectors from different copies of the same linear space. The extra structure that would allow you to do so is "connection". Just some thoughts of course.
Re: Re: Re: Some thoughts on tensors
Hi Arash,
I of course agree with what you say about a linear connection, but that takes us into calculus on manifolds while in this discussion everything is in some sense in 'one tangent space.'
In fact, in my opinion that is where the fuss with different linear spaces really starts to matter, and one has to take a stance. For instance, suppose we fuss a lot in the linear algebra and then when we have to do calculus we adopt balance of linear momentum and start adding traction vectors from different tangent spaces (the latter I am perfectly happy to do and have bought into, and I would not fuss with the linear algebra either), then what was the initial fuss while doing algebra about? I know of your work on covariantization of elasticity, so you seem to 'fuss consistently,' which I like - (this is a joke, take it lightly) .
A non-dimensional linear space as a canonical choice?
Hi Zhigang and Arash:
Here is a thought that I have not completely checked through for logical consistency:
One takes a linear space, of say, dimension 3, that contains objects that have no physical dimensions.
Suppose we now take a fundamental set of physical units. Then we nondimensionalize each of the elements of each of the dimension 3 physical vector spaces of interest - space of position vectors, velocities, area vectors, tractions, etc. - appropriately. For each of these physical vector spaces, this act of nondimensionalization induces a mapping between them and the non-dimensional vector space (say, DND mapping).
We then do linear algebra and mechanics on the non-dimensional space, defining tensors etc. based on it. For interpretation of results, we go back, using the inverse of the appropriate DND mapping to the relevant vector space.
The DND mappings may be isomprhisms - I have not checked carefully. But even if they are not, it seems like this is the right physical choice. Moreover, there should be an invariance of implied mechanics over all possible choice of fundamental sets of physical units chosen to induce the DND mappings, simply by the invariance of the laws of mechanics over choices of fundamental units.
May be this is what is implied in mechanics when we lump position vectors, velocities, tractions etc. in the same vector space.
Re: A non-dimensional linear space as a canonical choice?
Hi Amit,
If I understand you correctly, pretty much you're saying let's look at different copies of the same linear space (using your DND mappings) and each quantity of interest lives in one copy. What do you think?
Re: Re: A non-dimensional linear space as a canonical choice?
Hi Arash,
Yes, that's what I am saying. Of course, the main issue in this discussion that took a bit of thinking was the manner in which the copies should be constructed as there are infinitely many ways of doing so and one wants to find the way that is consistent with what we routinely do in continuum mechanics, the latter of course being sensible, given the weight of its results.
I find the the DND mappings interesting in that by dimensional consistency they link the various copies - they cannot be generated from completely arbitrary isomorphisms, say.
why map?
Dear Zhigang,
Map is an action. Nobody has to to define tensor as an action. It can be defined as an object - analogously to vector. No maps no problems :)
maps and tensors
Not exactly. You define maps by their actions. Objects are defined by their properties. You do not need to map vector to vector in order to define tensor. You may define tensor by the transformation properties of its components (as Levi-Civita did). Or you may define tensor as a linear combination of dyads, tryads etc. They can be used for maps but they do not need maps for their definition.
why stress is a tensor
Zhigang, Cauchy stress is defined as a sum of three dyadic products of vectors - see Eq. (3.21) of my lecture notes on Mechanics of Soft Active Materials.Thus, it is a tensor by construction.
good memories
Dear Zhigang,
Thank you for refreshing good memories :)
Happy New Year to you too!
Let us map old discussions into new year.
I am a big fan of iMechanica - I learn from it (not only your students do that). I have a feeling that you are becoming a mathematician. This is a dangerous process and I will try to slow it down in May :)
Linear algebra
Zhigang: I have found the book by Strang (one of the books listed in your link) to be an excellent introduction to linear (matrix) algebra. It is readily accessible by any undergraduate/graduate in engineering. Even though you might be looking for a more advanced textbook (links to tensor algebra and mechanics), I thought of putting in a plug for Strang's book. Besides the necessary math, the distinguishing feature of the book is a clear presentation, with geometry as an aid, of the main concepts (role of row- and column-spaces) in linear algebra. Armed with the know-how from this book, a student will be better-prepared to grasp more advanced topics in linear algebra.
I would like to second Suku's endorsement of Strang. It's a very clearly written text written in a style that can be accessed by both engineers and mathematicians, I believe. As an aside, Strang was one of the forerunners in doing mathematical analysis of the finite element method, so those researchers interested in that subject can become familiar with Strang's style via his linear algebra textbook.
Horn and Johnson, Lax, Gurtin
I have read the books by Naylor & Sell and Jim Knowles mentioned above. I liked both of them. In addition, I find Horn and Johnson's book very useful. However, it is not an introductory book. Peter Lax has a Linear Algebra text that I have not read, but will be good if one can generalize from the clear style of his Functional Analysis text.
Of those that I have listed above, only Knowles' book discusses tensors. Mort Gurtin's continuum mechanics books have much of what is required in continuum mechanics for tensor algebra and calculus.
Kaushik Dayal
Strang Strang Strang
Strang is the eye-opener. He gives intuitive geometric view of the subject. Mathematicians do not like him but I strongly recommend Strang for any physicist or engineer.
More linear algebra
Definitely. For a mechanician, I think a solid foundation in linear algebra and (convex) optimization is invaluable. With a clear understanding of the concepts in matrix algebra that Strang lists, understanding finite-dimensional function spaces is eased. From Strang's book, I found that thinking of Ax as a linear combination of the columns (row-picture is the norm) is the main take-home message. His online lectures are very clear. Variational methods in mechanics are often solved in a finite-dimensional setting (e.g., Galerkin methods) with a set of linearly independent basis functions. The end result is a linear system of equations Ax = b that has to be solved; since A is formed via a suitable `inner product' of basis functions, tools from linear algebra can be used to provide a mathematically sound means to construct A. The recently proposed virtual element method adopts this viewpoint.
more math
Alternatives to Strang:
Brown - A second Course in Linear Algebra
Hoffman & Kunze - Linear Algebra
Book by Tadmor et al
I usually recommend my Ph.D. students to take Arash's course on Applied Math. I also developed a self-contained class on Fundamentals of Solid Mechanics aiming to expose first year graduate students to a broad range of topics in the area within a unified and modern framework. Necessarily, I have to cover some basic tensor algebra at the beginning of the course. I found that the book by Tadmor et al on Continuum Mechanics (Chapter 2) does an excellent job at introducing the topic in a way that is accessible for engineers without sacrificing much rigor.
Julian J. Rimoli
Undergraduate course on continuum mechanics
Dear Zhigang,
Thanks for bringing up an important topic. I teach two continuum mechanics courses at the undergraduate level (sophomore and junior) and need to balance between the rigor of linear algebra, tensor calculus and the applied aspects of continuum mechanics. J.N.Reddy's book "Principles of Continuum Mechanics" is written from the viewpoint of undergraduate students.
I agree with Julian's comment above on the book by Tadmor, Miller and Elliott; it has the necessary basics on tensors written in a lucid manner. Over the past couple of years, I have been working on customized class-notes for these courses that rely on several sources.
Some references that I have found extremely useful are:
1. Lecture notes by Rohan Abeyaratne: http://web.mit.edu/abeyaratne/lecture_notes.html
2. Introduction to the Mechanics of a Continuous Medium (Malvern)
3. The Mechanics and Thermodynamics of Continua (Gurtin, Fried and Anand)
Ray Bowen's elaborate notes on Linear Algebra and Continuum Mechanics are also available online at http://rbowen.tamu.edu/.
Books for linear algebra
Dear Prof Suo,
As an math major undergraduate, I used the text book <Matrix Analysis> by Roger A. Horn and Charles R. Johnson. I want to just briefly mention this book to complement the great set of books people have already suggested. This book is a little bit heavy on math, but it is an excellent second book on linear algebra. The definitions are clear, discussions are succinct, and proofs are complete, making this book very good for reference.
It has detailed discussion on the exact conditions on diagonalization, co-diagonalization, triagularization, and various matrix factorizations - making it very useful for deriving general theories in mechanics, and physics in general.
Linear Algebra Done Right-Sheldon Axler, Springer
Dear Prof. Suo,
As the best of my knowledge, this book has a wide audience for beginners from math and physics departments in our university.
Most linear algebra textbook written for engineering students may neglect the mathematical aspects of linear space. Although the book "Linear Algebra Done Right" is only an introductory book, it covers and describes all the basic knowledge of finite vector space completely with abract formulation and concrete examples.
The elegant arrangement of the book, namely, abract formulation, proof in conjunction with concrete examples make it accessible even to students with only knowledge of basic caculus. The electronic copy could be downloaded by the following link.
Higher order tensors, equivalent definitions
Hi Zhigang: I haven't had the time to take a look at the book you mention, but here is a guess as to why it makes a lot of sense to define whatever one needs (e.g. 2nd order tensors, higher order tensors), especially when doing mechanics - it is to ultimately to do the mechanics one wants to do. If 2nd order tensors are all one needs, one does that. If higher order tensors are needed (as from the time of the Brothers Cosserat, at least, in continuum mechanics, through Green-Rivlin, Noll, Truesdell etc.; of course linear elasticity came even before that), one uses a logically satisfactory definition for that, and then gets on with life. And, based on these examples, I wouldn't say mechanicians stop at order 2.
As for "routinely "creating"/"discovering" new tensors" - I feel it is important to add to your statement that while any mechanician with an iota of basic training and good sense appreciates equivalences between disparate definitions as a deeper understanding of his/her subject, none in this class think that coming up with such definitions is an achievement in its own right or that one particular definition among equivalent definitions is somehow better. Moreover, they are also completely agnostic and mercenary in their approach to such definitions - they learn all of them as well as they can to deploy (all of) them effectively as particular situations demand.
And, a final note - let's not forget the purely component-transformation-rule based approach for introducing tensors that we have not discussed at all. Again, that is an equivalent definition, and Einstein would be very mad with us - or think we were really ignorant - if we were to tell him that the multilinear approach of introducing tensors is really the way to think about tensors and their applications to mechanics.
Re: Re: Higher order tensors, equivalent definitions
Dear Zhigang:
I haven't looked at this book but I don't think we're restricted to work with linear spaces of the same dimension the way we define tensors. For example, deformation gradient for a shell is a linear map from a two-dimensional vector space to a three-dimensional vector space. So, it is a two-point tensor and its matrix representation is not a square matrix.
I agree with Amit that one shouldn't worry too much about what definition is better and/or more general. I would say one should use what is appropriate for the application of interest.
Re: I have a dream--about tensors
Dear Zhigang:
The book by R.W. Ogden (Non-Linear Elastic Deformations) defines tensors very similarly to what has been done in Carlson's notes (page 43). Let me also say that this is an excellent book that focuses on finding exact solutions in nonlinear elasticity.
Marsden and Hughes (Mathematical Foundations of Elasticity) differentiate between tensors (page 65) and two-point tensors (page 70). I think they did not define anything more general as they didn't find much use for it in the context of elasticity.
Green and Zerna (Theoretical Elasticity) define tensors in terms of coordinate transformations and how tensor components change under such transformations (Amit already mentioned this).
Re: Re: Higher order tensors, equivalent definitions
Hi Arash,
Here's how I see it:
The tangent map for either the reference or the deformed shell goes from 2-d to a 3-d space; thus the matrix representation is rectangular as you say.
The deformation gradient goes from a 2-d tangent space to a different 2-d tangent space (vectors in one in general do not lie within the linear span of a basis for the other). Thus its matrix is square 2x2, the 'canonical' representation in convected coordinates being the 2x2 identity matrix.
Did I miss anything?
rectangular matrices for tensor representation
Zhigang: This is in response to a statement you made.
A third-order tensor on a 3-d vector space V_3 in the direct formulation of continuum mechanics (a la Carlson, say) is a linear transformation from 3-d space to the 3x3 = 9 dimensional space of second order tensors on V_3. Thus its representation on bases yields a rectangular 9 by 3 matrix. Similarly the transpose of this tensor is a linear transformation from the 9 dimensional space of second order tensors to the 3-d space - that yields a 3 x 9 matrix.
So what we do in continuum mechanics very much results in rectangular matrices when required and quite naturally (unlike what you claimed to be the case), but obviously these are trivial details not to be fussed over.
For some serious actual use of 3rd order tensors in continuum mechanics with the direct formulation definition:
Online lecture notes on linear algebra
All, thanks for a fruitful cascade of discussion, which I follow with great interest. I've updated the Lecture Notes page of iMechanica to include downloadable lecture notes on linear algebra alluded in the discussions under the "Mathematics for Mechanics" section.


text:
-Discretion when it comes to accepting gifts or freebies.
-Advice to new bloggers. (Which mostly came to: write about what is interesting to you. What works for one blogger doesn't always work for another, and writing about the exact same stuff that a popular blogger writes about will go unnoticed since someone else is already doing the same thing.)
-A blogger's place at Fashion Week.
-Hey, remember when we all decided we were the greatest people ever and that blogs were the new everything? Me neither! The media likes the story but it ain't no big thang.
-We can't predict the future of fashion blogging. The same way no one saw it coming, no one knows where it will go.
The big difference between bloggers and journalists isn't the fact that we're using computers. I mean, Cathy Horyn and Lynn Yaeger have blogs, lots of critics write for style.com, and a number of editors, including Hamish Bowles and Andre Leon Talley, write blog posts; but it's not the same as my having a blog - the difference is experience. It's not remarkable that we're using the internet!!! but what most people are pointing out - with me, mostly, since this doesn't apply to the other bloggers that were on the panel - is lack of experience. I haven't gone to journalism school, I haven't had any internships, etc. And I'm 13, which, oh my God, I can't tell you how excited I am to outgrow that number. This, honestly, is what I think is the future of fashion blogging, or at least part of it. The same way teenagers can start a Flickr account and be noticed by a magazine, or a band can start a MySpace and be picked up by a label, blogs will act as jumping-off platforms for people that want to work in the industry.
When I started Style Rookie in March of 2008, only ElleGirl and teenvogue.com would write about blogs. It wasn't a big media thing and having one wasn't an affiliation for Fashion Week, it was a nice circle of ladies and occasional dudes who supported each other and often found themselves saying "Thank you for this post! None of my friends get my feelings about ______." Then some of us started taking opportunities that had arisen, and I spent some money on a Hussein Chalayan dress, and then all of a sudden it was like, JUDAAAAAAAAAAS.
Which is, you know, bizarre. Allow me to direct you to this epic Dave Eggers essay.
So now my inbox and comment section are full of "Can you critique my blog? Can you tell me what to do to get invited to shows? How do I get my blog recognized in the industry?" which isn't a bad thing, I guess (other than the critiquing thing, which like..it's about you and your thoughts. No one is able to tell you what to think or how to explain your thinking to others.) Now blogging is a full-time job for some people and in some cases a segway into the industry but I guess that's the way it goes. And it's sort of a bummer, especially because now I'm far more aware of the number of people that read my blog, and when I take this into consideration when writing a post I feel pressured to sound smarter or fancier when mostly I just enjoy writing journal-like streams of thought (my blog has always been a virtual diary) even though I'm supposed to be writing grand reviews because a newspaper or magazine told whoever to expect that. That's a problem with my own outlook, though, and I still enjoy blogging. A lot. And, thankfully, it doesn't have to be a job for me. When it starts to feel like one, I'll stop.
But I don't think anyone is saying blogs are the equivalent to magazines, or inexperienced bloggers like myself are the equivalent to journalists, anyway. Still, there is nothing wrong with having a range of perspectives. I think fashion is important to discuss.
Which brings me to this recent Isabel Marant quotation:
"For me, fashion shows are not for the public, they are trade shows for the press. It's time for the press to understand the collection and then spread the information. That's more interesting than just the image. Everyone wants to be first. It's too too much. There should be privacy and mystery. There is no excitement about anything anymore as everything is available immediately and all the time – you don't have to wait for anything. I don't like the idea of being flooded with image and information. I don't belong to the generation of spending time on the internet. I think it's too fast and too fake. It's like going to a museum on the internet – where is the pleasure? It's sad because everyone is running after everything, but after what? Everything is too quick. There is no room in your heads for all this information. No one retains anything."I think that when it comes to fashion shows being online, it's exposure for a brand. I think that a customer deserves to see the show and get to know the world of that label. I like privacy and mystery too, but there's a fine line between that and exclusivity.
And-TWIST!-I also hate the fastness of the Internet! And the fakeness! I like buying my magazines and zines and having special stuff I can hold in my hand! And this Internet, it makes the already fast fashion very very fast! And it's scary and a lot of it feels very unauthentic and sad. And fast.
But, in five years, the iPhone will be Oldy McOldster from Oldsville, Oldesota. And tumblr then will be like xanga now. Who knows where fashion blogging will be. Point is, things are changing.

subset: commoncrawl


text:
Early EMV Compliance Benefits U.S. Merchants
Earlier this week Revel Systems, a Point-of-Sale solutions provider, became the first company to offer EMV-enabled hardware through an iPad-based POS solution. The company is offering EMV compliance to the merchants that it works with well ahead of the deadlines set by the major credit card companies requiring merchants to accept EMV. But many businesses would do well to make the switch to EMV as soon as possible since making the switch now - even before the card companies' deadlines - can save money for businesses, says Chris Ciabarra, Revel's CTO and co-founder.
Those savings are the reason many clients have been pushing Revel Systems to release EMV compliance hardware early, Ciabarra explains. Revel works with some rather large businesses, some of whom pay thousands of dollars annually to meet traditional PCI compliance standards for card security that card companies have long required of merchants, he says. But Visa and other card companies have said that they will not require merchants to stay PCI-compliant if they are EMV-compliant. And merchants can take advantage of those savings if they make the switch now even though Visa's deadline for merchants to accept EMV isn't until 2016, Ciabarra explains.
[See Related: Why More Banks Are Moving Toward EMV Adoption]
And businesses who switch to EMV early will also be able to take advantage of the greater security that the technology provides, Ciabarra points out, giving businesses another reason to add EMV as soon as possible. "The clients who have been hacked the most want to jump at it," Ciabarra says.
Ciabarra says that right now the biggest barrier to widespread EMV adoption among merchants is simply awareness. "Big retailers know about it, but smaller businesses aren' as aware," he explains. He predicts that EMV compliance will start with the bigger retailers and then trickle down to smaller businesses over the next few years - just as happened with PCI compliance - as the deadlines for EMV compliance approach.
From Revel's perspective it also made sense to push out EMV hardware just to get it done and out of the way, Ciabarra adds. With so many developments taking place out the Point-of-Sale such as mobile POS, EMV integration and digital wallets, those working in this space have a lot to tackle in the next few years. And who knows what the next point-of-sale technology right around the corner may be. In this environment it's bet to move quickly, Ciabarra explains. "The more things we can put out early the better," he says.
Jonathan Camhi has been an associate editor with Bank Systems & Technology since 2012. He previously worked as a freelance journalist in New York City covering politics, health and immigration, and has a master's degree from the City University of New York's Graduate School ... View Full Bio


text:
Do you know what "Dimensional Weight" is? It's a rule the shipping companies use to charge you for the size of your package—and not just the weight. If you don't use the correct box size, you may be paying (a lot) more than you need to. The Postal Route has a box to fit almost anything — we'll make sure you get the right one!
Are you moving and need lots of stuff? We offer bundle pricing on large orders. Don't like to pack? Bring it to us, and we'll pack it for you! The packing experts at The Postal Route are trained professionals. If we pack your items, they're guaranteed for insurability.
Call 803-548-6755 if you have any questions about our packaging and moving supplies selection. Not in a hurry? Click on the button below to send us a message.


text:
Related Topics
May 8, 2012
Guest: Maurice Sendak
TERRY GROSS, HOST: This is FRESH AIR. I'm Terry Gross. Today we devote our entire show to honoring Maurice Sendak and his work. The great children's book author and illustrator died today at the age of 83, after a recent stroke. We're going to listen to four of the interviews he recorded on our show, dating from 1986 to 2011, in which he talked about his work, his own childhood, growing old and facing death.
Let me read you some of his New York Times obituary by Margalit Fox. Quote: Sendak was widely considered the most important children's book artist of the 20th century, who wrenched the picture book out of the safe, sanitized world of the nursery and plunged it into the dark, terrifying and hauntingly beautiful recesses of the human psyche.
His books were essential ingredients of childhood for the generation born after 1960 or thereabouts, and in turn for their children. Unquote.
Sendak's most famous books are "Where The Wild Things Are," "In The Night Kitchen" and "Outside Over There." We'll begin our tribute to Maurice Sendak with an excerpt of our 1986 interview, in which he told me that when he was a child, adults looked big and grotesque to him, and he couldn't imagine ever becoming one.
MAURICE SENDAK: It was inconceivable to me as a child that I would be an adult. I mean, one assumed that it would happen, but obviously it didn't happen, or if it did, it happened when your back was turned, and then suddenly you were there. So I couldn't have thought about it much.
GROSS: Because adults seemed really big and different, you couldn't imagine becoming one?
SENDAK: And awful. Yeah. I mean they were mostly dreadful, and if the option were to become an adult was to become another dreadful creature, then best not, although I think there had to be a kind of normal anticipation of that moment happening because being a child was even worse.
I mean, being a child was being a child - was being a creature without power, without pocket money, without escape routes of any kind. So I didn't want to be a child.
I remember how much - when I was a small boy I was taken to see a version of "Peter Pan." I detested it. I mean the sentimental idea that anybody would want to remain a boy, I don't - I couldn't have thought it out then, but I did later, certainly, that this was a conceit that could only occur in the mind of a very sentimental writer, that any child would want to remain in childhood. It's not possible. The wish is to get out.
GROSS: Are there any memories that typify your childhood to you now, looking back?
SENDAK: Well, it's typically '30s in many ways in that I had a series of long illnesses, but then there were no drugs, and there was no penicillin, so kids all ended up having diphtheria, scarlet fever, pneumonia, blah, blah, and I spent a lot of time being sick, as I recollect, and there is the happy memory, actually, of being indoors and watching - the window became my movie camera, my television set.
One of the happiest memories I have is when my grandmother would come to stay with us on those occasions and she would put me on her lap, and then she used the window shade like a magic lantern. She'd pull it down, then I'd hold my breath, and she'd pull it up, and the same thing would be there: a car, or my brother and sister making a snowman or whatever.
So happy memories of being indoors looking out of windows, and I think it's no accident that windows, or children looking out of windows or going through windows or whatever, becomes an obsession in most of the books I've written.
GROSS: A lot of your books deal with the children trying to overcome certain fears, trying to get control of them. What were the things that frightened you when you were a child yourself?
SENDAK: Well, odd things. I don't know if my books are about that, by the way. I mean they are probably partly that, but I don't set out to write a book that's going to conquer a fear or do anything but amuse or entertain or distract a child. But my own fears were very peculiar. I was terrified of the vacuum cleaner, you know, all - untraditionally.
I mean, people sit around saying, well, don't let kids do that, and don't let kids do that, it'll be too frightening, but who would have ever imagined anybody saying don't let a kid in the room with a vacuum cleaner.
But when my mother plugged the vacuum cleaner in, and it was those old-fashioned Hoovers, you know, the thing blew up visibly, and the sight of that bag swelling used to just drive me right up the wall, literally. I had to get out of the house, and I was sent to the neighbors until she was all done.
"The Invisible Man" was one of the most terrifying of my nightmares and I think definitely led me to being an insomniac for the rest of my life.
GROSS: The movie "The Invisible Man"?
SENDAK: The movie with Claude Rains. We were taken to see it, and I remember coming home and being in shock, and it was from that moment on that my sister had to stay with me until I fell asleep, because he could be anywhere in the room.
SENDAK: I mean, there was no way you could say, well, you see, he's not there, you see, he's not there. My answer was: Well, you can't see him, so what's the big deal? So he was - I mean, even when it's repeated now on Channel 13 in New York, I have trouble watching that movie. I try to, and the scene where he unravels his head, the bandages, and there's nothing underneath, you know, it's extra Valium that night for me.
GROSS: In "Where the Wild Things Are," a young boy is sent up to his room without supper, and he's really angry at his mother. So he decides to leave home and go to where the wild things are, and he becomes king of the wild things, and the wild things are these wonderful monsters or beasts that you've created. What inspired the shape and the faces, the bodies of the monsters?
SENDAK: Well, there was a lot of work on that, and I didn't want them to be traditional monsters, like griffins and gorillas and suchlike. I wanted them to be very, very personal, and they had to come out of my own particular life. And I remember it took a very long time until that gestation occurred and where they began to appear on drawing paper and they began to be what I liked, and it was only when I had them all that I realized they were all my Jewish relatives.
SENDAK: They were all the adults who treated us in such silly fashions when we were kids, and these were the real monsters of my childhood. You know, people come on Sunday and wait to get fed, uncles and aunts, and you used to get all dressed up, and you have to sit and listen to their tedious conversation when you want to be with your brother and sister and listening to the radio or whatever.
And they all say the same dumb thing while you're beating time until food gets put on the table - how big you are and how fat you got, and you look so good we can eat you up. In fact, we knew they would because my mother was the slowest cooker in Brooklyn, so if she didn't hurry up, they would eat us up.
So the only entertainment was watching how - watching their bloodshot eyes and how bad their teeth were. You know, children are monstrously cruel about physical defects.
So my entertainment was to examine them closely, you know, the huge nose, and the hair curling out of the nose and the weird mole on the side of the head, and so you would glue in on that, and then you'd talk about it with your brother or sister later, and they became the wild things.
GROSS: One of the things I love about the monsters in the book is that they're really goofy. I mean to me they're not really frightening. Okay, granted, I'm an adult, but still, there's something really kind of goofy and playful and big and floppy about them.
SENDAK: Yes, there is, but at the same time they are threatening. I mean, if Max were not in control of them, they could indeed be in control of him, and when they say, oh, please don't go, we'll eat you up, we love you so, they mean just that.
And he knows that, and I think children know that too, that the fun of that book is a perilous tightrope between him being a little boy and very vulnerable to these huge creatures and the absurdity of his having control over them by staring into their yellow eyes. It's what every child would like, to have control over such things.
Kids are not afraid of them because Max is not afraid of them.
GROSS: "In the Night Kitchen," which is the second book of your trilogy, when the book came out, Mickey, who is the main character in it, is nude during part of it, and I understand that there were librarians who actually blocked up the little infant penis so that children wouldn't be exposed to it.
SENDAK: Yeah, he had to wear little diteys or diapers or shorts before they'd let the book into the library.
GROSS: Now, I was really surprised because I thought that all - you know, as much fear as people have in our society of nakedness, that I thought infant nakedness was okay.
SENDAK: Well, we live in a very strange society. I mean, I was outraged when that book came out and there was a such a hullabaloo over his genitals.
I mean, I assumed everybody knew little boys had that and that this wasn't a breakthrough. The fact that people considered that outrageous: incredible. I mean, you go to the Metropolitan Museum of Art, you go to the Frick, you go to the Philadelphia Museum of Art, and there's a Christ child with his penis. It's accepted in fine art, but somehow in books for children there's a taboo.
Well, the hell with that. I mean, I didn't set out to cause a scandal. I set out to do a very particular work where he had to be naked in order to confront a particular dream he was in. You don't go into a dream wearing Fruit of the Loom underwear or PJs. You go tutto. You go yourself, your being, and that's why he was naked, and it was idiocy. It was incredible idiocy what went on over that book for many, many years about Mickey being naked.
GROSS: Maurice Sendak, recorded in 1986. He died today at the age of 83. We'll hear an excerpt of our 1993 interview after a break. This is FRESH AIR.
GROSS: Today we're devoting our show to the life and work of Maurice Sendak, the children's book author and illustrator. He died today at the age of 83. We're listening to excerpts of the interviews I recorded with him. This next one was recorded in 1993, after the publication of his book "We're All in the Dumps with Jack and Guy."
Inspired by two English nursery rhymes, it tells the story of children dealing with homelessness, sickness and hunger.
Your new book deals with some real world fears, like homelessness and being scared by what could happen to you as a kid now. What were the real big events in your life that you found really frightening when you were young?
SENDAK: When I was young, the big events were being sick and being expected to die, and knowing that at a very early age I might. This was spoken. My parents were very indiscreet. My parents came from a foreign country. They were immigrants. They didn't know about Freud. They didn't know about what to say or not to say in front of children.
So it was the awareness at a very early age of mortality which pervaded my soul, apparently, and I think provided me with the basic ingredients of being an artist. And I remember a game my father played with me, which you would not exactly call a death game but did move in that direction, which was that if I lay in bed, which I spent a lot of time doing, and I remember in one particular place we lived in Brooklyn - we moved quite frequently because of financial problems - and just opposite the foot of my bed was a window looking out in the backyard facing a just very boring brick wall. And he said if you - to me - if you looked and didn't blink, if you saw an angel, you'd be a very, very lucky child. And so I did that frequently.
Of course, I would always blink because it hurt not to blink. And then you didn't see it, and he'd say, well, you blinked, didn't you? And I'd say yes. And I remember once I didn't blink, and I saw it - or I imagined I saw it. But the memory of it is so vivid I could even describe it to you.
GROSS: Would you?
SENDAK: Well, I was lying in the bed, obviously, staring out the window, my eyes aching, staring, staring, staring. And something very large like - almost like a dirigible, but it wasn't a dirigible because it was right past my window, it was a slow-moving angel.
She - he - whatever, moved very gracefully and slowly coming from left, going across to right, not turning to observe me at all. I don't have a memory of the face but I remember a memory of the hair, the body and the wings. It took my breath away. It just moved so slowly that I could examine it quite minutely.
And then I shrieked and hollered, and my father came in, and I said I saw it. And he said I was a very lucky kid.
GROSS: Did you see your parents as being really capable parents who could help fend off death or fend off what other problems that you had?
SENDAK: No, no because they were so vulnerable to problems. They caved in on problems all the time. So I did not see them - and this is not a criticism of them. Their lives were extremely hard. But no, no. I did not see them that way.
GROSS: Now, they were from Poland?
SENDAK: They were from Poland, yeah.
GROSS: And they fled before World War I?
SENDAK: Yes they did. Just before World War I. They didn't flee. My father left on a lark.
GROSS: Oh. Well, what was that?
SENDAK: He had no cause to come here. My grandfather was a rabbi, and he was the youngest son, and he was obviously the spoiled younger son of my grandmother. And he actually fell in love with a young woman, and it became a little bit scandalous, and she was put on a boat and shipped off to America.
And he sulked and pouted and got money out of his siblings and got on another boat to follow her here. And his family was appalled at his behavior. Because of that trivial behavior, he was the only survivor of his entire family.
I mean all of my uncles and aunts and all of the children were destroyed in concentration camps. My father's grief his entire life was that his survival was based on such a trivial impulse.
GROSS: You grew up before the Holocaust. Did - was he still really regretful about...
SENDAK: Oh, he was terribly regretful and guilty, and he was - he had survivor guilt, as did my mother, who had much less cause because she was shipped off when she was about 17 to come to America. She was uneducated, untrained in anything. She was a girl.
My grandfather on her side, also a rabbi, had died at a very early age of a coronary, and there was no money to take care of everybody. So she was sent here to do it, to work hard, earn money and then bring them over. Which was typical.
She met my father, they married, and all the first income was spent on bringing one aunt, then an uncle, then another uncle, then another aunt, then my grandmother, until finally all but one brother on her side were all here.
And then they were going to turn to my father's side, and then it was too late. That was in the '30s. There was no getting Jews out of Europe at that point. And so growing up during the war, that was tough, having to live through that in all its complexity. It colors your life forever.
We didn't get much of my mother's life. My mother was silent about that period of her life.
GROSS: I think as a lot of people from Eastern Europe who came to America were. Did they seem like aliens to you? Because, I don't know, they probably - did they speak more Yiddish than English around the house?
SENDAK: Yes, they spoke more Yiddish. I spoke Yiddish as a child. My parents spoke English very, very late and very poorly. And we lived in a part of Brooklyn which was teeming with immigrants, either other people from Eastern Europe, Jews - or Sicilians, and I couldn't tell the difference.
I mean, we lived next to the Sicilians and I had a real - it sounds like coy conceit, but it's a fact. I had a real confusion because right across the hall from us was my best friend at one place we lived, Carmine, and his sisters and brothers and his huge mother and huge father. And I used to run across the hall because they had un-Kosher food, which was much better, much better than Kosher food because it was - it was pasta. It was great Italian cooking. And they laughed, and they drank wine, and they grabbed me, and I sat on their laps, and they had a hell of a good time. And then you come back to my house and you have this sober cuisine and not so rambunctious family life. And I really did have a confusion that Italians were happy Jews, that they were a sect.
GROSS: Oh, that's really interesting.
SENDAK: And that I would have a choice - that I would have a choice after my bar mitzvah to belong to either the sober sect or the happy sect.
GROSS: And they went to a different synagogue where they had pasta.
SENDAK: Yeah. I was a dumb kid, let me tell you.
I mean, all the parents were - looked alike. They all wore the same dull black dresses and you couldn't tell the difference, not to me.
GROSS: I remember I interviewed you - I don't know, eight years ago or something. Something that you said really stuck with me. You were talking about the monsters in "Where The Wild Things Are," and you were saying that when you were young, the monsters were just adults. They were people with like moles on their faces and hairs growing out of their noses and...
SENDAK: Yeah, old relatives, actually.
GROSS: Yeah, old relatives, exactly, exactly, and that, that - that really struck a chord.
GROSS: And then I started thinking, well, I'm one of those people now. I mean, I don't know if I actually have hair growing out of my nose but, you know, I have some of those things that I'm sure kind of like scare kids.
SENDAK: Oh sure.
GROSS: And do you have a sense of yourself as that too...
SENDAK: Of course.
GROSS: ...of like, you know, a monster to some kids?
SENDAK: Of course I have. I see it in their eyes. When I'm autographing books, which I don't like to do much anymore, and children are shoved at me...
GROSS: Yeah.
SENDAK: ...they have no idea why they're on the line. They'd much rather be in the bathroom.
SENDAK: And they're standing on line, and they're being told something which is so frightening and confusing, which is being told by mom or dad: This is the man you like so much, honey. This is the man who did your favorite book. And they clutch their book even closer because that really means he's going to take it away, because if this is the man's favorite book, then he's going to take your book...
SENDAK: And the look of alarm and the tears, and they stare at me like pure hatred. Who is this elderly short man sitting behind a desk who's going to take their book away? Then on top of that, the parent says, now give him your book, honey. He wants to write something in it. Well, there, they've been told: don't write in a book. Okay. Why then is it all right for a perfect stranger to write in their book? It's horrible for them. And I become horrible unwittingly. I make children cry.
GROSS: They cry when...
SENDAK: They cry when they meet me because they don't know what I'm doing. It's quicker with girls because girls are smarter than boys. We all know that. They grow up faster. And girls, by the time they're seven or eight, already know the business of autographing and what it means. Boys don't till they're about 40, I think.
And so they'll pull it away. There's only one child who ever had the courage, and his father was urging him forward, urging him forward. I can see the hesitation. I just felt so bad for the kid, and I put my hand on the book to help draw it away from him. And he literally screamed and said: Don't crap up my book.
SENDAK: It was the bravest, the bravest cry I've ever heard. I nearly wept.
GROSS: So what did you do?
SENDAK: Well, I took the father aside because I think, I think the father was going to kill the kid because he'd embarrassed him and made everybody laugh. And I had to sit down and say how great I thought his kid was and not to be angry with him because the child just didn't understand what this whole nonsense, this social nonsense of autographing was all about. And it would be criminal to punish him for this.
GROSS: This is great. Every time you do a book signing it's kind of like dysfunctional family America.
SENDAK: That's right - becomes into psychiatric sessions.
GROSS: You must feel awful, though, you know, because you're being misunderstood by the kids who love your book.
SENDAK: Well, frankly that's why I do not visit children in classrooms. That's why I've stopped autographing, for the most part, for that very, very reason. It's such a paradox that I, who adore them, and I'm interested in their welfare, should become their enemy. It's only because it's set up that way. If I'm to visit a school, they're all warned, threatened and browbeaten for three days before I get there. Now I want all of you to be nice...
SENDAK: ...and you must raise your hand and I want everyone to go to the bathroom before Mr. Sendak comes.
SENDAK: I mean, their lives are ruined. So why should I be the person who does that to them?
GROSS: Maurice Sendak recorded in 1993. We have two more interviews with him in the second half of the show as we continue our tribute to the great children's book author and illustrator who died today at the age of 83. I'm Terry Gross, and this is FRESH AIR.
GROSS: This is FRESH AIR. I'm Terry Gross. Today we're remembering Maurice Sendak, the great children's book author and illustrator, and listening back to our interviews with him. He died today at the age of 83 after a recent stroke.
Several generations of children have grown up with his books, such as "Where the Wild Things" and "In The Night Kitchen." His work for children always had a dark edge, but nothing quite as dark as his 2003 collaboration with Tony Kushner, who's best known for his play "Angels in America." They adapted a children's opera that was originally performed by children in the Nazi concentration camp Terezin. The opera, "Brundibar," is a parable about evil that was written in 1938 by a composer who was killed in the gas chambers. An English adaptation with Kushner's libretto and Sendak's sets was performed in Chicago and New York in 2003. That same year, their book adaptation of "Brundibar" was published, featuring Kushner's text and Sendak's illustrations.
In 2003, I asked Maurice Sendak why the children in the Nazi concentration camp Terezin performed the opera "Brundibar."
SENDAK: This opera was written by Hans Krasa, a very young Czech composer, and it was written for children, Jewish children, in an orphan asylum in Prague, to amuse them. It was a contest, who could write the prettiest opera for the children. And Krasa wrote this and everybody loved it. And at that very same point the Nazis entered the country and the orphanage was emptied and the children put into Terezin, the camp. And he was too, as was the librettist, and it became a show camp, became known as Hitler's favorite camp. He set it up in such a way, and made a film of how well the Jews were being treated and the Gypsies and the homosexuals. And this was to - because rumors were getting out that were frightful - and so he set this up to prove to the Red Cross and diplomats who were traveling the world to come by, see a show, and see how happy everybody was.
And it's in the film. You see the children singing in the last portion of the opera. It is impossible for me to doubt that the children knew what their fate was. Imagine standing up on the stage and singing about brotherhood and if we all hang together we're going to succeed and the bully will not - and knowing that as soon as this audience left, kaput, their lives are finished. I can't even grasp that now. But it ended the same way for all of them.
GROSS: So the performances were for visiting diplomats to show off the camp?
SENDAK: Yeah. Yeah. Yeah.
GROSS: Do you know if they fell for it?
SENDAK: Oh, yeah. Oh, absolutely, they fell for it. The streets were cleaned, trees were planted, all the children were given clean clothes, all the inmates were given clean clothes, everything was swept up, and they went and you had a pass, quite an attractive pass, which I'd love to have an original of, but I've used as an image in the book, to get in to see "Brundibar."
GROSS: How do you think the paintings and drawings that you did for the new book, which is a kind of Holocaust fairytale...
SENDAK: Mm-hmm.
GROSS: ...how do those compare with the classic books that you did like "Where the Wild Things Are" and "Outside Over There"?
SENDAK: This is, strange to say, more personal. "Where the Wild Things Are" and "Outside Over There" and...
GROSS: "In The Night Kitchen."
SENDAK: Yeah, "In The Night Kitchen," are all books that came from my original creative soul, self, whatever, that have no conscious connection to events in my life. And I just think of them as terrific inventions that came upon me and dominated my life until I finished them. This, which takes the form almost of a Grimm fairy tale, actually - it's a little Hansel and Gretel story over and over and over again. All those stories work for children. But this had such personal import. I've been carrying this around since childhood and frankly wanting to rid myself of it - the Holocaust and memories of childhood and my parents suffering, and no childhood. There was no such thing as childhood, you know. I was born early. The Wall Street crash, my father always blamed me for the Wall Street crash.
SENDAK: Thought he was endowing me with great strength for a one-year-old. But he was a very reasonable man so he probably believed it. And then right after that, well, he lost all his money in his little tailor shop and then the war began. And I think mostly the point of the marriage of my mother and father was that you had to have a partnership. When you're a young immigrant who spoke no English, who'd just come over on the boat, you got together as two partners, whether love was involved in it, maybe, if you were lucky - maybe not. But the point was to pool your money and bring everybody over as fast as you can, because most of them knew what was going on and what was about to happen.
GROSS: If you don't mind my asking, you know, we've talked about how the Holocaust affected you and how, you know, being Jewish, you know, branded you in a way. And do you think of yourself - I know you feel very defined in some way by being Jewish.
SENDAK: Yes.
GROSS: Are you secular Jewish or are you observant?
SENDAK: Total secular.
GROSS: Total secular.
SENDAK: I love being Jewish.
GROSS: Uh-huh.
SENDAK: I love the bits of it that - I love the candles. I especially love the memory of the dead, the little yahrzeit that you put out.
GROSS: The candles, the 24-hour candle. Yeah.
SENDAK: The candles that burn for 24 hours, yeah. But other than that, nothing. I'm not a religious person, nor do I have any regrets. The war took care that for me. You know, I was brought up strictly kosher but it made no sense to me. It made no sense to me what was happening. So nothing of it means anything to me. Nothing, except these few little trivial things that are related to being Jewish.
GROSS: Do you ever wish that you had faith?
SENDAK: No.
GROSS: Why not?
SENDAK: Because I don't need it. I don't believe in that. Faith is - you know who my gods are, who I believe in fervently?
GROSS: Who?
SENDAK: Herman Melville, Emily Dickinson - she's probably the top. Mozart, Shakespeare, Keats. These are wonderful gods who have - who've gotten me through the narrow straits of life.
GROSS: Maurice Sendak, recorded in 2003. Sendak died today at the age of 83. We'll hear the final interview I recorded with him last September after a break. This is FRESH AIR.
GROSS: Today we're listening back to interviews with Maurice Sendak, the beloved children's book author and illustrator whose books include "Where the Wild Things" and "In The Night Kitchen." He died today at the age of 83.
Last year, Sendak published a new book called "Bumble-ardy." It was the first book in 30 years to feature his original text and illustrations. We thought it was the perfect time to catch up with him again, but he was too frail to get to a studio, so last September we just called him on his home phone.
GROSS: Maurice Sendak, congratulations on your new book. And it gives me this opportunity to call you up and see how you're doing and say hello and talk with you about your work. So how have you been?
SENDAK: Well, it's been a rough time. I've gotten quite old, Terry, since you've seen me last, which is not very unusual. And I'm working very hard but I feel that I'm working for myself at this point, because everything I'm doing is, if it's publishable, fine. If not, it makes not too much difference because I claim that this time is for me and me alone.
GROSS: Well, in your new book, "Bumble-ardy," the main character is a pig who is orphaned and lives with his aunt.
SENDAK: Yeah.
GROSS: And when his parents were alive, he never had a birthday party because his immediate family frowned on fun. Then he turns nine. His aunt buys him some gifts to throw him a quiet party for two. But then he decides to throw a costume party for himself and he invites some grubby swine.
The party begins after his aunt leaves for work and then mayhem ensues. And when his aunt returns, she throws everyone out and says, OK, smarty, you've had your party, but never again. And then Bumble-ardy says in tears, I promise, I swear, I won't ever turn 10.
SENDAK: Right.
GROSS: So when the aunt says never again, which people say about the Holocaust, when she says that in reference to never having a party again, that's really, really loaded.
SENDAK: I don't know what to answer to that. You've just picked the two lines of the book that are my favorite lines. There's something so poignant and extremely funny, if you could say that's funny about his answer, I'll never turn 10. In fact, it sums up my life, it sums up my work. What is mad and ludicrous and funny and odd is true.
What you just said is extremely insightful. Nobody has said anything like that. But I always expect that from you. Those two lines are essential. But I won't pretend that I know exactly what it means. I only know it touches me deeply, and when I thought of it, I was so happy I thought of it. It came to me, which is what the creative act is all about.
GROSS: You know, let me ask you, those two lines where she says, OK, smarty, you've had your party but never again. And he says, I promise, I swear, I won't ever turn 10. What a bargain that is, you know?
GROSS: He has to promise to never have boisterous fun again, to not get older, to just like stay in that moment, the nice little boy.
SENDAK: That is correct. I will do as you say.
GROSS: Yeah, did you have to make that bargain with your parents to get love?
SENDAK: I had somewhat the same problem. I had a brother who was my savior, made my childhood bearable. He was older by five years, Jack Sendak. He wrote a number of books. He was very, very, very gifted. More importantly to my life, he saved my life. He drew me away from the lack of comprehension that existed between me and my parents. And he took his time with me to draw pictures and read stories and live a kind of fantastical life.
And my sister occasionally joined in, but mostly - after all, she was a girl. All that was expected of her was that she should grow up and be very pretty and marry a decent man. So she had to concentrate on what my parents expected of her. And she didn't have the creative insanity that existed between me and my brother to go further with that. I wish she had. I loved her very much.
But that life with him contradicted the prosaic life that I was expected to be a decent child. I was expected to be with my brother and help him and to shut up and just be a quiet kid. I hated them for a long time. But I don't anymore because God knows, it's a blessing to have a quiet kid.
SENDAK: I don't have kids at all and I thank God that I never did.
GROSS: Yeah, but isn't there a part of you that wishes like you had a son or a daughter to come help take care of you and shop for you and bring you things and...
SENDAK: Yes. I would infinitely prefer a daughter. If I had a son, I'd leave him at the A&P...
SENDAK: ...or some other big advertising place that, you know, and somebody who needs a kid would find him and he would be all right.
GROSS: Isn't that stereotyping what a son would be?
SENDAK: I suppose it is, but I'm just an ordinary human being. A daughter would be drawn to me. A daughter would want to help me. I mean girls are infinitely more complicated than boys and women more than men. And there's no doubt about that, we all know it, we just don't like to think about it, and certainly the men don't like to think about it. But a daughter would - oh, God. I've fantasied(ph) a daughter. I have lived my whole life with a dream daughter.
GROSS: Well, let me ask you this: You came out a few years ago.
SENDAK: Correct.
GROSS: If you were able to be out in a period like we live in today, where it's socially acceptable in lots of circles to be gay and have children, it's so much easier to be gay and have children now, would you have had a child?
SENDAK: No. No.
GROSS: You just said that you fantasized all your life about having a daughter.
SENDAK: Fantasized.
SENDAK: There's too much hard work involved.
GROSS: Uh-huh.
SENDAK: And I am devoted to being an artist and a person who reads books for the rest of my life, however long I have.
GROSS: And that takes a certain amount of self-absorption to be able to do that.
SENDAK: Well, I think so, and I think it has to do with time spent trying to understand what it means to be an artist, to get under the skin of what is happening as best you can. And to have a real child, a real daughter, would mean hard work, work I would not want to do.
GROSS: Mm-hmm.
SENDAK: Changing clothes, fixing, taking her to school, putting up with her anger, putting up with her indifference, and praying all the time that she grew up to be a good woman and take care of her poor old dad. Yes...
SENDAK: ...it is typical of a male and it doesn't make any difference what kind of male you are, you are a selfish pig in very, very complicated ways.
And, yes, I would fantasize a daughter full-grown. She would have to be in her late 30s or early 40s and be all over me and taking care of poor old dad.
GROSS: Do you have someone to help you?
SENDAK: Yes. Yes. And she is a youngish lady who puts up with my oldness, that is I'm fighting and struggling against. She puts up with my bad behavior and she loves me and I love her.
GROSS: Is she a friend? Is she a nurse?
SENDAK: She's a friend.
GROSS: That's great.
SENDAK: And I've known her since she was a little girl.
GROSS: Oh, wow. So it's kind of almost like a daughter.
SENDAK: Yes. And she belonged down the road and her mother was a saint in the best sense of that word, the best sense of what I imagine Christianity is all about. I adored her mother and I adore her. Her name is Lynn and I adore her brother; his name is Peter. And they both have grown up and are attached to me, and I might as well have had them for my kids. They put up with everything.
GROSS: Oh, that's beautiful. Plus, you didn't have to do the work, so...
GROSS: We've talked before how you've been in therapy. And your late partner, who died in 2007, you were together for about 50 years? Do I have that right?
SENDAK: Oh, about 50 years. Yeah.
GROSS: Yeah. And he was a psychoanalyst, right?
SENDAK: He was a psychoanalyst.
GROSS: OK. So here's the thing: like, when you're in therapy, you have to decide if you're going to tell your spouse, your friends, your family about things that happen in those sessions, things you learned about yourself, things you said about other people or not. You know, whether you're going to confide in people about that or not. So since your partner was a psychoanalyst, did you talk to him about your therapy sessions?
SENDAK: No. No. It just seemed like - it just seemed inauthentic and incorrect to burden him with that. My therapies went on forever. My being gay was something of not great interest to me - you just have to believe that. And the person I lived with, we lived together for all of those years so that we could make trips to our favorite places in Europe, so that we could read our favorite books, so that we could - and this is most important - we could listen to music.
Now, I couldn't deal with 9/11 the other day. I just couldn't bear it. I...
GROSS: The 10th anniversary of 9/11?
SENDAK: Yes.
GROSS: Mm-hmm.
SENDAK: Yes. But that evening of 9/11, they conducted Mahler's 2nd Symphony, the Resurrection Symphony, which has never been a great favorite of mine, but Mahler is a great favorite of mine. And I sat there and cried like a baby listening to the music. It got through where the whole day had not gotten through to me.
I just couldn't deal with the whole situation. But sitting there and listening to music that was written almost now a hundred years ago, it had nothing to do with 9/11, except that it had to do with the life and death of human beings, which takes me back, for some reason, to Bumble-ardy's "I won't turn 10."
The fragility of life, the irrationality of life, the comedy of life. My tears flow because two great, great friends died close together - a husband and a wife - who meant everything to me and I am having to deal with that, and it's very, very hard.
GROSS: Did they die very recently?
SENDAK: Yes. She died two months ago, and he died the day before yesterday. And I was, except for his son, the last person to speak with him. He was my publisher and I loved him and I loved her.
GROSS: Are you at the point where you feel like you've outlived a lot of people who you've loved?
SENDAK: Yes. Of course. And since I don't believe in another world, in another life, then this is it. And when they die they are out of my life. They're gone forever. Blank. Blank. Blank. And I am not afraid of death. And I begin to - as maybe a good many elderly people do. Who knows? When I did "Bumble-ardy" I was so intensely aware of death.
Eugene, my friend and my partner, was dying here in the house while I did "Bumble-ardy." And I did "Bumble-ardy" to save myself. I did not want to die with him. I wanted to live, as any human being does. But there's no question that the book was affected by what was going on here in the house.
GROSS: We're listening back to the interview I recorded with Maurice Sendak last September. Sendak died this morning. We'll hear more of the interview after a break. This is FRESH AIR.
GROSS: Today we've been listening back to four interviews I recorded with Maurice Sendak, the beloved children's book author and illustrator. He died this morning at the age of 83. Let's get back to the interview we recorded last September.
We've talked before about how, you know, you're Jewish but you're very secular. You don't believe in God. You don't...
SENDAK: No, I don't.
GROSS: Yeah. And I think having friends who die, getting older, getting closer toward the end of life tests people's faith and it also tests people's atheism. It sounds like your atheism is staying strong.
SENDAK: Is what?
GROSS: Staying strong.
SENDAK: Yes. I'm not unhappy about becoming old. I'm not unhappy about what must be. It makes me cry only when I see my friends go before me, and life gets emptied. I don't believe in an afterlife, but I still fully expect to see my brother again. And it's like a dream life.
I am reading a biography of Samuel Palmer, which was written by a woman in England. I can't remember her name. And it's sort of how I feel now, when he was just beginning to gain his strength as a creative man and beginning to see nature. But he believed in God, you see, and he believed in heaven, and he believed in hell. Goodness gracious, that must have made life much easier. It's harder for us nonbelievers.
But, you know, there's something I'm finding out as I'm aging - that I am in love with the world. And I look right now, as we speak together, out my window in my studio and I see my trees, my beautiful, beautiful maples that are hundreds of years old, they're beautiful. And you see, I can see how beautiful they are. I can take time to see how beautiful they are.
It is a blessing to get old. It is a blessing to find the time to do the things, to read the books, to listen to the music. You know, I don't think I'm rationalizing anything. I really don't, since this is all inevitable and I have no control over it. "Bumble-ardy" was a combination of the deepest pain and the wondrous feeling of coming into my own, and it took a long time.
It took a very long time, but it's genuine. Unless I'm crazy. I could be crazy and you could be talking to a crazy person.
GROSS: I don't think so.
SENDAK: I don't know anymore and I don't care.
GROSS: What are your physical restrictions like? Can you walk OK? Can you get around at all?
SENDAK: No, I can't walk OK. I'd love to walk. That's why I've been doing that since the '70s when I had my first coronary. I have heart trouble and I've had a very bad time after Eugene died and I was very sick and they thought I would die, and I came back to do "Bumble-ardy." And I have nothing but praise now, really, for my life. I mean I'm not unhappy.
GROSS: Mm-hmm.
SENDAK: I cry a lot because I miss people. I cry a lot because they die and I can't stop them. They leave me and I love them more. But I have my young people here, four of them who are studying and they look at me as somebody who knows everything, those poor kids.
SENDAK: If they only knew how little I know. But obviously I give off something that they trust, because they're all intelligent. Oh God, there are so many beautiful things in the world which I will have to leave when I die but I'm ready, I'm ready, I'm ready.
GROSS: Well, listen - yeah.
SENDAK: You know, I have to tell you something.
GROSS: Go ahead.
SENDAK: You are the only person I have ever dealt with in terms of being interviewed or talking to who brings this out in me. There's something very unique and special in you, which I so trust. When I heard that you were going to interview me or that you wanted to, I was really, really pleased.
GROSS: Well, I'm really glad we got the chance to speak because when I heard you had a book coming out, I thought, what a good excuse...
SENDAK: Well...
GROSS: ...to call up Maurice Sendak and have a chat.
SENDAK: Yes, that's what we always do, isn't it?
GROSS: Yeah. It is.
SENDAK: That's what we've always done.
GROSS: It is.
SENDAK: Thank God we're still around to do it.
GROSS: Yes.
SENDAK: And almost certainly, I'll go before you go, so I won't have to miss you.
GROSS: Oh, God what a...
SENDAK: And I don't know whether I'll do another book or not. I might. It doesn't matter. I'm a happy old man. But I will cry my way all the way to the grave.
GROSS: Well, I'm so glad you have a new book. I'm really glad we had a chance to talk.
SENDAK: I am too.
GROSS: And I wish you all good things.
SENDAK: I wish you all good things. Live your life, live your life, live your life.
GROSS: Maurice Sendak, recorded last September. Listening to the four interviews that we featured today, you can hear that he spent a lot of time thinking about death and the loss of friends and loved ones. He's always been kind of obsessed with death. It arrived for him today after a recent stroke.
I wish I knew what he'd been thinking recently, but I'm grateful that he shared so many of his thoughts with us and left behind such wonderful books. Good-bye, Maurice.
GROSS: You can listen to longer versions of the interviews we featured with Maurice Sendak on our website, freshair.npr.org, where you can also download podcasts of our show.
Transcripts are created on a rush deadline, and accuracy and availability may vary. This text may not be in its final form and may be updated or revised in the future. Please be aware that the authoritative record of Fresh Air interviews and reviews are the audio recordings of each segment.


text:
One can be sure there is no empathy in Heaven. That would involve some amount of personal discomfort that a human being would feel when observing the pain of another. Instead, the believer will be in complete bliss while watching the spectacle unfold (as well as those being tortured in Hell).
"The happiness of the elect will consist in part of witnessing the torments of the damned in hell, among whom may be their own children, parents, husbands, wives and friends; ... but instead of taking the part of their miserable being, they will say 'Amen!', 'Hallelujah!', 'Praise the Lord!'." (Rev. Nathaniel Emmons / 1745-1840)Twentieth-century apologist C. S. Lewis likened the experience of Heaven to "transsex." He made the analogy of an adult understanding the pleasures of heaven as like explaining the pleasures of sex to a child. The greatest pleasure the child knows is his love for chocolate, but he simply can't imagine the pleasure of sex. By analogy, if sex is the greatest pleasure an adult knows, heaven would have something so great as to make sex seem like the passing taste of a chocolate bar. Surely, C. S. Lewis's concept of heaven would make the would-be Muslim suicide bomber yearning for his 72 regenerating virgins seem rather quaint. (See Atheist Experience episode #413 for more.)
So imagine watching the destruction of all humanity while having a "transsex" orgy simultaneously with all the dead people who ever believed in Jesus. Even without the sex angle, the thought of this being a person's ultimate desire takes sociopathology to the extreme.
I've been at a serious loss for words to describe how I feel about this. I had previously use the term "Christian snuff porn" to describe my disgust, but on Sunday's show, I likened this rapturous desire to jacking off at a car wreck.
I expect there will be some fallout for that comment. I find it interesting that one of our producers decided to censor the comment on the version of the show that is to air here in Austin. (I do admit that I didn't take the opportunity to explain why I made it and it may have seemed out of place.) This two second silence got me thinking though: What does it say about our society that we are so shocked by an admittedly twisted sexual analogy, but that millions of Americans yearning for complete human destruction fails to even raise an eyebrow? Why do we give tax breaks to "charities" that promote these ideas, while the atheists who point out the treason to humanity are the least trusted group in the United States? Why is everyone so concerned about Ted Haggard's sexual proclivities, but the fact that he may have had a hand in influencing Bush to go to war in the Middle East is not newsworthy? Haggard, who was then head of the National Evangelical Association, was meeting with the White House weekly on Bible Prophecies related to the end times. Bush apparently was concerned enough about Gog and Magog to try to get then France's Prime Minister Chirac involved. Why is this not shocking to everyone? Why aren't we locking Bush and all of his fellow sociopaths up in padded cell? Keep them where they can't hurt themselves or anyone else.
I suspect we're all still too influenced by this sick little religion of Christianity, its torture device logo, glorification of suffering, and its wide path of inhuman destruction. I make no apologies for my comment, however. It's time our silence stops.


text:
Become a Seller
Fasheen Back Cover for Micromax Canvas Xpress 4G Q413 (Multicolor, Silicon)
Price: Not Available
Currently Unavailable
Suitable For: Mobile
Material: Silicon
Theme: Animals/Birds/Nature
Type: Back Cover
Read all details
Now you can stylishly & easily protect your smartphone with this modern case protection. This case covers the back and corners of your smartphone with an impact resistant, flexible Soft shell, while still providing access to all ports and buttons. Designed for your phone this sleek and lightweight case is the perfect way to show off your style. This case acts as the perfect weapon you require to guard your phone from everything unwanted. It covers the entire front of the case with the artwork. It has permanent embedded designs with high print quality which are long lasting , Hence your design won't peel off. This case fully covers the back side of your mobile and hence you do not have to replace the original back cover. Once you decide to purchase, Request you to place order once afer You are fully decided about your designs, As these Cases are specifically Manufactured against your Order Hence, Do Not Cancel after Placing the order. Kindly Note that there can be slght difference in image colors as we can only Match 85% -90% Of Image Colors because the maximum Printer Ink Transfer Rate is 90%.
Read More
Sales Package
1 Premium Designer Back Cover
Model Number
Model Name
Micromax Canvas Xpress 4G Q413
Designed For
Micromax Canvas Xpress 4G Q413
Brand Color
Have doubts regarding this product?
Post your question
Safe and Secure Payments.Easy returns.100% Authentic products.
Back to top