edit log meta REVIEWED

Meta Edit Log PhL 1.15.16 I made massive changes to wedge doc in Sept 2015 to Jan 2016 and here is a review. It is just unbelievable how much complexity and confusion is involved, no wonder this took so long. But I think my end result has clean threadings of all the confusions. // 5.116.16 I am unable to control all the edit phases because I forget all the earlier phases. So will try a meta edit log to fix that problem. 9.1.15 (before edit log started) Am looking at general wedge stuff and Spivak book. 9.10.15 (still before edit log started). Have started writing the doc by this time. 9.20.15 (still before edit log started). Am working on Chapter 1 stuff. 9.22.15 (still before edit log started). Am working on Kronecker Delta section. 9.24.15 Have already worked multiple weeks without an edit log. Looking at various PDF's. I think most of Ch2 is already written at this time, my tensor doc review. Have idea of Chapters 5,6,7,8 being parallel structure, as it is now. 9.27.15. And Ch 1 also seems to be written. Discovery of the paradox that need (ei)r = δi,r for any basis. Should I use covariant notation or not? 9.28.15 Doing outer products section. Chapter 2 is in place at this time, converted it to covariant. 10.1.15. State matrix of components like (em)(u)n = Rmn , but this is confusing notation. 10.2.15 Kronecker made covariant. Edit pass through current 4.1,4.2,4.3 k=2 stuff 10.3.15 Edit pass through current 4.4,4.5 but halted before 4.6 and wrote up my "math theory wedge product" thing which was meant to be Ch 5 but now is targeted to Ch 9. This is similar to Ch 1 stuff. 10.3.15 Resume Ch 4 editing with 4.6 and 4.7. I ask how T(v1,v2....vk) "transforms", perhaps for the first time 10.4.15 Am wondering how λi "transforms". Still hazy on 1.15.16 ! Lots of inline notes on this. Realize that I have omitted a section of dual space of V, so wrote that as 2.11, which is still there. Do edit pass on most of Ch 4 at this time. Confusion about scale of Aii...i. Early notes on T^S comparing to that mysterious Spivak claim with ω and η . 10.5.15 - 10.15.15 Cape Cod trip, no work done ( 11 lost work days) 10.16.15 Decide to put 1/2 in wedge definition, and 1/k! later for general wedge of vectors. Am now working in tensor-wedge v2 doc. Putting this change into Ch 4. Looking at Spivak and Benn-Tucker and many other PDF sources. Dealing with Aii...i = (1/k!) ΣP (-1)S(P) TP(i)P(i)...P(i). Pondering wedge of multiple vectors. This is now in 7.5. 10.18.15-10.27.15 Hawaii trip, no work done. ( 10 lost work days) 10.28.15 In line work on what is now an Appendix A item "Ordered Sum theorem". On 1.15.16 this item is not installed anywhere. 10.29.15 Working on Ch 5 (k, tensor product) and Ch 6 (k, tensor product, dual). I notice to my surprise that Tii...i = ai bi ... qi is not totally antisymmetric but claim to have "fixed that up". Early notes again on T^S stuff. At this point I still have T = Σii....i Tii....i (ei^ ei .....^ ei), so have done neither italics on coeffs nor T^ idea on the left. But did write up first cut of T^S and T^S^R stuff which now lives in 7.9. 10.30.15 Am using both alt and Alt operators. 10.31.15 Clean up "A normalization". At this point to a full proof of 2.1-2.11. I then confuse λi with ei. This caused a full rewrite of 2.11. Now working at tensor-wedge v4 doc. 11.1.15 Edits in 2.10 and 2.11. Then work on Chapter 3. Then start into Ch 4 edits. 11.2.15 Review 4.3. Review Ch 5 and Ch 6. 11.3.15 Here I make the change from Tii....i to Tii....i in symmetric sums. Now working in tensor-wedge v5 doc. But later I will undo this italic notation. 11.4.15. Doing T = S + A + X decomposition stuff. Wrote up theorem that Yii...i = ΣP (-1)S(P) RP(i)P(i)....P(i) is totally antisymmetric. I think this has since left. This now lives in App A v4 as (A.2.11) generic. Rearrangement theorem is being used, but it has no home yet. I created App A at this time. 11.5.15 First cut at Ch 7. Trouble with εjj...j. 11.6.15. Another Appendix A is written. Worrying about "tensor functions". At this time there are sections 6.11 and 7.11, but now (1.15.16) Ch 6 ends with 6.7, not sure what happened. 11.6.15. Working on 6.5 through 6.10. 11.7.15. Deal with associativity of the wedge product, made it an axiom. 11.8.15. Full proofing of 6.11 through 6.11. Added associativity of in Ch 2. Reproof Ch 5. 11.9.15 On this day I removed duplication of "tensor algebra" T(V) graded stuff between 3.1 and 5.6, although now 1.15.16 it seems to be in 5.4. The direct sum stuff is still in line at this point. More on λi not being a vector so don't bold it. Yet another review of 4.1 thru 4.4. Decision to have a parallel world with Chapters 5,6,7,8. 11.10.15 Edits on 6.1 thru 6.3. But here I move direct sums to Appendix B and that is where it still is. Put symbols into t = Σij Tij eiej Σijk Tijk eiejek since you are direct summing elements. Read through 6.1 thru 6.6. Contents of Ch 6 are as they are now. 11.11.15. Pause to look at Benn Tucker. Review of Ch 7 through 7.11. Realize that Ch 8 will be a lot of work. I keep mentioning "functions" but not doing much about it. The functions issue arises in Chapter 8 which is k, wedge, and dual. I seem to have a Ch 8 at this time with sections 8.1 thru 8.11, tons of editing it says. I must be writing this in separate file Ch 8 doc which is now not the most recent. 11.12.15 I am still using script (T^S )ii....i stuff at this time. Worrying about associativity of ^. And I have italic and non-italic script stuff, not very nice. Talk about Alt for function. At this point I suddenly start using notation T and T^ , not sure how these are defined. Then I suddenly I start in to Appendix C, and have lots of inline stuff, concerned about ordering of perm operators. I think this is all cleared up now on 1.15.16. A Tiny Theorem is stated, now appears implied around current (C.2.13). I have the Spivak theorem as a goal but not there yet. 11.13.15 Working on 8.12 which no longer exists, related to (TS) and (T^^S^). These and ^ subscripted tensors are now everywhere! I think I defined them maybe in an earlier App C version being written at this time. Talking about multiplying tensor functions. I suspect later I decided just to drop the subscript on a "regular" tensor, but not yet, it is still here. Starting now into my three theorems I think, but still have subscript. More rewriting of Appendix C. 11.14.15 Am puzzled about the meaning of (T^S^)^ , 11.15.15 Added special rules for when S or T is a scalar. Still doing 7.12. 11.16.15 Trying to clean up Appendix C, using Q and Q' . Seeing need for something "generic". 11.17.15 I am ecstatic about App C v 4 which has generic followed by applications. 11.18.15 I finally ask this question: "Should I start using T^ notation earlier in my doc, as in "everywhere there is a wedge product? For vectors there is no difference, but for any expansion there is. By having no T^ I was forced to use coefficients T. " I made this change tentatively in scratch 4.3 and 4.4. This trial change is still sitting only in that scratch doc on 1.15.16 and has not yet been installed! Why did I not install it? Probably because I wanted to stabilize the k=k cases in the later chapters first. I then started doing this change in Ch 7 but then got sidetracked on doing yet another Appendix A with the rearrangement theorem. 11.19.15 Doing in-situ editing of Ch 7. Today on 1.15.16 all the italics are gone and T^ is in place. Got the new idea that vj^ vj^ .....^ vj = Alt(vj vj ..... vj) . I finished an edit of 7.4 and install it. Then continue on with 7.5, 7.6, 7.7, 7.8. Then I start into Section 7.9 in temp5 doc. Still unable to show the Spivak theorems. (temp5 was installed as 7.9 (a) thru (e)) . 11.20.15 Rewrite 5.6 then return to 7.9. I comment that at this point Ch 6 and Ch 8 are completely out of date. I finally can prove the Spivak theorems. Talk of the Three Theorems (in App C). I did a C pass and now we have Appendix C v5 which is the current one on 1.15.16. Thinking about "translation rules" I guess for how you create Ch 8 from Ch 7. 11.21.15 Wrote A.8 which is the application of the generic to "tensor functions". I replace confusing A by A in the non-dual analysis. I then make a pass through Ch 8 Nov 20.doc, sections 8.1 through 8.8. But the headings still seem wrong in that doc! I think I never to past section 8.8 and that is why. There is an ok to here mark before 8.9 to confirm that guess. I pause there and go back an update Ch 6 notation. Then I ask about this T'(vi, vj) = RiaRjb T(va, vb) business and I am off on that whole subject! I talk about creating a certain C.5 but today I see not such C.5. I am quoting PDF's and wondering about Spivak's normalization factor. I am then on to some new PDF author. I claim to have added a "transformation section" to C.5. But later this gets moved to be App D I think. This was a busy day. 11.22.15 I have now written Appendix D, taking away C.5. The two senses of transformation for a vector function. I liked it then, but feel uncomfortable today 1.15.16. 11.23.15 Doing edits back in Ch 2. Noted that 2.10 (b) is identical to 5.2. What should I do about that? Decided to keep both and to make them identical. Major edit on 2.11 on dual space stuff. I discover today that (λi λi ..... λi)(vj, vj ....vj) = (vj vj.... vj)ii...i so maybe this gives more insight into how to deal with "tensor functions", but I don't pursue it. Instead, I am back to the question of what is a scalar. Thinking about rotating apparatus with and without rotating basis vectors. I now have to rethink App D. I write that "vector transformation" business for the v's. I write a short essay about this confusion. 11.24.15 Resolve the issue that there are not "two kinds of component indices". 11.25.15 Add Picture E to 2.6. Cleaning up after realization of previous day. Barrage of questions and experiments. 11.26.15 Suddenly switched over to bowl doc because Robert Maier sent me an email and I realized bowl doc was in a sorry state of update. This took rest of November, all of December and first quarter of January!! The bowl doc release was 1.5.16. Then did a week of maintenance work, did colo, got a cold, and am now suffering on 1.15.16 (39 days lost doing bowl doc upgrade) 1.13.16 Tried to get back into tensor wedge after this huge gap. Read Ch 1 and Ch 2. 1.14.16 Try cleaning up the rats nest of docs. Read Appendices A,B,C which seem good. 1.15.16 Decided to write this meta edit log to try and reconstruct the status of my tensor wedge doc which right now sits in about 8 different docs all with vague names. Also put away all docs I felt were no longer relevant for the future of wedge tensor doc. [ 5.16.16: I may continue this meta log...]