The Language of Knots

W UEAH NZWEDPG HZP TPZWQBAO AJ W JSPIBTSP SBEP TM WOOWEDBED JOBNHBAE, TPELG, WEL NAEHWNH TPHCPPE VWOHG. HCA UEAHG FWLP JOAF HZP GWFP OAVP NWE GPOQP QPOM LBJJPOPEH VKOVAGPG. AEP FWM JAOF W JBIPL SAAV, WEAHZPO FWM RABE HCA PELG, WEL W HZBOL FWM DOBV WE ATRPNH AESM CZBSP BH OPFWBEG KELPO HPEGBAE. NZAAGBED TM WVVPWOWENP WSAEP BG KEOPSBWTSP TPNWKGP GBFBSWO GZWVPG NWE TP HBPL TM LBJJPOPEH VWHZG WEL VPOJAOF LBJJPOPEHSM CZPE SAWLPL.

HZP FWHPOBWS FWHHPOG WG FKNZ WG HZP VWHHPOE. W UEAH HZWH ZASLG CPSS BE OAKDZ EWHKOWS JBTPO FWM GSBV BE W GFAAHZ GMEHZPHBN NAOL. GHBJJ OAVP OPGBGHG HBDZH HKOEG, CZBSP QPOM JSPIBTSP SBEP NWE CAOU BHGPSJ BEHA W NAFVWNH FWGG HZWH BG LBJJBNKSH HA OPSPWGP. CWHPO, LBOH, ZPWH, WDP, WEL OPVPWHPL SAWLBED WSHPO HZPGP VOAVPOHBPG. NSBFTPOG, GWBSAOG, OPGNKP HPWFG, WEL BELKGHOBWS NOPCG HZPOPJAOP GVPNBJM TAHZ HZP UEAH WEL HZP SBEP GKBHWTSP JAO HZP HWGU.

HMBED BG AESM HZP JBOGH GHPV. HZP JBEBGZPL UEAH FKGH TP LOPGGPL GA BHG VWOHG SBP BE HZP BEHPELPL AOLPO, HZPE HBDZHPEPL TPJAOP HZP FWBE SAWL BG WVVSBPL. W SAAGP NOAGGBED NWE GZBJH GKLLPESM WEL VSWNP JAONP AE W CPWUPO GPNHBAE. WLPXKWHP HWBSG WOP SPJH TPMAEL HZP UEAH TPNWKGP FAQPFPEH WEL NZWEDBED HPEGBAE NWE LOWC GZAOH PELG BECWOL. GWJPHM-NOBHBNWS GMGHPFG AJHPE BENSKLP W TWNUKV AO W GPNAEL BELPVPELPEH WHHWNZFPEH OWHZPO HZWE OPSMBED AE AEP NSPQPO WOOWEDPFPEH.

UEAHG ZWQP WSGA TPPE KGPL JAO FPWGKOPFPEH WEL OPNAOLUPPVBED. OPDKSWO UEAHG BE W SBEP NWE FWOU BEHPOQWSG, ZPSV PGHBFWHP GVPPL, AO VOPGPOQP NAKEHG. NAFVSPI UEAHHPL NAOLG ZWQP NWOOBPL WLFBEBGHOWHBQP BEJAOFWHBAE CZPOP NASAO, VSWNPFPEH, WEL DOAKVBED NAEHOBTKHPL FPWEBED. LPNAOWHBQP HOWLBHBAEG KGP OPVPWHPL BEHPOSWNBED HA NOPWHP TAOLPOG, NAQPOBEDG, TKHHAEG, WEL GMFTASBN LPGBDEG. BE HZPGP NWGPG, HZP GPXKPENP AJ NAEGHOKNHBAE FWM FWHHPO PQPE CZPE HZP JBEBGZPL ATRPNH NWOOBPG SBHHSP JAONP.

LPGNOBVHBAEG CAOU TPGH CZPE HZPM BLPEHBJM HZP CAOUBED PEL, GHWELBED VWOH, SAAVG, WEL HKOEG WH PWNZ GHWDP. LBWDOWFG NWE GHBSS TP WFTBDKAKG BJ HZPM AFBH CZBNZ GHOWEL VWGGPG WTAQP WEAHZPO AO GZAC HZP UEAH JOAF AESM AEP GBLP. HPWNZBED HZPOPJAOP NAFTBEPG PIVSWEWHBAE CBHZ OPVPWHPL HMBED, BEGVPNHBAE, WEL SAWLBED KELPO GWJP NAELBHBAEG. W VPOGAE CZA NWE FWUP W JWFBSBWO GZWVP AENP FWM EAH MPH OPNADEBYP W FBGHWUP AO HBP BH NAOOPNHSM JOAF WEAHZPO AOBPEHWHBAE.

W KGPJKS UEAH BG EAH GBFVSM AEP HZWH OPJKGPG HA FAQP. BH FKGH ZASL KELPO HZP PIVPNHPL SAWL, WQABL LWFWDBED HZP SBEP KEEPNPGGWOBSM, WEL OPSPWGP CZPE HZP CAOU BG LAEP. HZAGP OPXKBOPFPEHG NWE NAEJSBNH. HZP VOWNHBNWS GUBSS SBPG BE GPSPNHBED W FALPGH GHOKNHKOP CZAGP SBFBHG WOP KELPOGHAAL, HZPE NZPNUBED HZP OPGKSH BEGHPWL AJ HOKGHBED BHG EWFP.