summer now ....

??? "algebraic closure as analog of universal unwrapping", so to speak ... ???.... ????vs .... ?????? "algebraic closure with particular subfield nailed down as analog of partial unwrapping" .... ??????

...piglet .... ?????...... ??? fiber ... decoration .... ??? algebra vs geometry ... ???? "algebra fiber-wise, geometry base-wise" ... ????.....

"discriminant" .... ?????? ...... symmetric rational functions of x,y vs general rational functions of x,y ... ???? spectrum pictures here .... ?????..... ?????? ?? permutation vs braid ... ????? .....

????? mysteriousness of "clock multiplication" ..... ????? ..... piglet and clock addition .... decoration .... monotony ... ???? ...... periodicity .... ????? ....


????? for thursday ....

galois's principle and 20th cyclotomic field .... ??? also and field of rational functions in n variables ... ??????

???? maybe start with gaussian integers example .... ????? ......

??? can you define _the_ twentieth root of 1 in terms of _the_ square root of -5 and _the_ 5th root of 1 ....?? ... ????? ..... hmmmm ... ????

??? mass hyperboloid picture of binary quadratic forms .... ???? ......