Naq jura Uneel bcrarq uvf rlrf, ur fnj whfg jung ur’q orra ubcvat gb frr, n sbyqrq cvrpr bs cncre yrsg ba gur sybbe, gur tvsg bs uvf shgher frys.
Pnyy gung cvrpr bs cncre “Cncre-2”.
Uneel gber n cvrpr bs cncre bss uvf cnq.
Pnyy gung “Cncre-1”. Vg jnf, bs pbhefr, gur fnzr cvrpr bs cncre. Lbh pbhyq rira frr, vs lbh ybbxrq pybfryl, gung gur enttrq rqtrf zngpurq.
Uneel erivrjrq va uvf zvaq gur nytbevguz gung ur jbhyq sbyybj.
Vs Uneel bcrarq hc Cncre-2 naq vg jnf oynax, gura ur jbhyq jevgr “101 k 101” qbja ba Cncre-1, sbyq vg hc, fghql sbe na ubhe, tb onpx va gvzr, qebc bss Cncre-1 (juvpu jbhyq gurerol orpbzr Cncre-2), naq urnq ba hc bhg bs gur pnirea yriry gb wbva uvf qbez zngrf sbe oernxsnfg.
Vs Uneel bcrarq hc Cncre-2 naq vg unq gjb ahzoref jevggra ba vg, Uneel jbhyq zhygvcyl gubfr ahzoref gbtrgure.
Vs gurve cebqhpg rdhnyrq 181,429, Uneel jbhyq jevgr qbja gubfr gjb ahzoref ba Cncre-1 naq fraq Cncre-1 onpx va gvzr.
Bgurejvfr Uneel jbhyq nqq 2 gb gur ahzore ba gur evtug naq jevgr qbja gur arj cnve bs ahzoref ba Cncre-1. Hayrff gung znqr gur ahzore ba gur evtug terngre guna 997, va juvpu pnfr Uneel jbhyq nqq 2 gb gur ahzore ba gur yrsg naq jevgr qbja 101 ba gur evtug.
Naq vs Cncre-2 fnvq 997 k 997, Uneel jbhyq yrnir Cncre-1 oynax.
Juvpu zrnag gung gur bayl cbffvoyr fgnoyr gvzr ybbc jnf gur bar va juvpu Cncre-2 pbagnvarq gur gjb cevzr snpgbef bs 181,429.
Vs guvf jbexrq, Uneel pbhyq hfr vg gb erpbire nal fbeg bs nafjre gung jnf rnfl gb purpx ohg uneq gb svaq. Ur jbhyqa’g unir whfg fubja gung C=AC bapr lbh unq n Gvzr-Gheare, guvf gevpx jnf zber trareny guna gung. Uneel pbhyq hfr vg gb svaq gur pbzovangvbaf ba pbzovangvba ybpxf, be cnffjbeqf bs rirel fbeg. Znlor rira svaq gur ragenapr gb Fylgureva’f Punzore bs Frpergf, vs Uneel pbhyq svther bhg fbzr flfgrzngvp jnl bs qrfpevovat nyy gur ybpngvbaf va Ubtjnegf. Vg jbhyq or na njrfbzr purng rira ol Uneel’f fgnaqneqf bs purngvat.
Uneel gbbx Cncre-2 va uvf gerzoyvat unaq, naq hasbyqrq vg.
Cncre-2 fnvq va fyvtugyl funxl unaqjevgvat:
QB ABG ZRFF JVGU GVZR
Uneel jebgr qbja “QB ABG ZRFF JVGU GVZR” ba Cncre-1 va fyvtugyl funxl unaqjevgvat, sbyqrq vg arngyl, naq erfbyirq abg gb qb nal zber gehyl oevyyvnag rkcrevzragf ba Gvzr hagvy ur jnf ng yrnfg svsgrra lrnef byq.
Gb gur orfg bs Uneel’f xabjyrqtr, gung unq orra gur fpnevrfg rkcrevzragny erfhyg va gur ragver uvfgbel bs fpvrapr.
Vg frrzf gung guvf Aneengvir Pbafgehpgvba sbepr (Ryvrmre, va ernyvgl, jura ur jnf pbzvat hc jvgu gur fgbel) bayl fgrref gvzr geniry riragf gbjneq ybbcf gung ner fgnoyr nsgre bar vgrengvba. Lrf, n tenaqsngure cnenqbk jbhyq abeznyyl pnhfr n gjb-vgrengvba ybbc, ohg vs gung jrer cbffvoyr va guvf svpgvbany havirefr, gura Uneel’f rkcrevzrag jbhyq unir fgnovyvmrq ba “457 k 397” engure guna “QB ABG ZRFF JVGU GVZR”. Vg frrzf gung gur Aneengbe fgrrerq Uneel gbjneq jevgvat gung zrffntr engure guna pbagvahvat uvf rkcrevzrag nf cynaarq.
(V pbhyq vzntvat guvf pbfzvp ragvgl vffhvat Uneel n qverpg jneavat (Ybirpensg-fglyr) nsgre gur svefg gvzryvar gung ur punatrq uvf cerivbhf shgher frys’f zrffntr, yrnqvat Uneel gb fraq uvf bja jneavat gb uvf arkg cnfg frys, jvgu gur zrffntr naq unaqjevgvat fgnovyvmvat npebff gvzryvarf fubegyl gurernsgre.)
For the same reason, I would expect any time traveler attempting a grandfather paradox would find themselves thwarted in surprising ways, resulting in no grandfathers getting killed (or realizing that the man they thought was their grandfather actually wasn’t). Even if the time traveler succeeded in the first few iterations, creating a two-iteration loop, I think Narrative forces would cause this to destabilize until a one-iteration loop was achieved.
In other words, no convergent series need be assumed. Convergent series are enforced.
To quote a future chapter in ROT13:
Vg frrzf gung guvf Aneengvir Pbafgehpgvba sbepr (Ryvrmre, va ernyvgl, jura ur jnf pbzvat hc jvgu gur fgbel) bayl fgrref gvzr geniry riragf gbjneq ybbcf gung ner fgnoyr nsgre bar vgrengvba. Lrf, n tenaqsngure cnenqbk jbhyq abeznyyl pnhfr n gjb-vgrengvba ybbc, ohg vs gung jrer cbffvoyr va guvf svpgvbany havirefr, gura Uneel’f rkcrevzrag jbhyq unir fgnovyvmrq ba “457 k 397” engure guna “QB ABG ZRFF JVGU GVZR”. Vg frrzf gung gur Aneengbe fgrrerq Uneel gbjneq jevgvat gung zrffntr engure guna pbagvahvat uvf rkcrevzrag nf cynaarq.
(V pbhyq vzntvat guvf pbfzvp ragvgl vffhvat Uneel n qverpg jneavat (Ybirpensg-fglyr) nsgre gur svefg gvzryvar gung ur punatrq uvf cerivbhf shgher frys’f zrffntr, yrnqvat Uneel gb fraq uvf bja jneavat gb uvf arkg cnfg frys, jvgu gur zrffntr naq unaqjevgvat fgnovyvmvat npebff gvzryvarf fubegyl gurernsgre.)
For the same reason, I would expect any time traveler attempting a grandfather paradox would find themselves thwarted in surprising ways, resulting in no grandfathers getting killed (or realizing that the man they thought was their grandfather actually wasn’t). Even if the time traveler succeeded in the first few iterations, creating a two-iteration loop, I think Narrative forces would cause this to destabilize until a one-iteration loop was achieved.
In other words, no convergent series need be assumed. Convergent series are enforced.