diff --git a/docs/assets/js/mathjax.js b/docs/assets/js/mathjax.js index 0c7803cf..561944cd 100644 --- a/docs/assets/js/mathjax.js +++ b/docs/assets/js/mathjax.js @@ -1,9 +1,11 @@ window.MathJax = { + loader: {load: ['[tex]/colortbl']}, tex: { inlineMath: [["\\(", "\\)"]], displayMath: [["\\[", "\\]"]], processEscapes: true, - processEnvironments: true + processEnvironments: true, + packages: {'[+]': ['colortbl']}, }, options: { ignoreHtmlClass: ".*|", diff --git a/docs/fundamentals/ideas/congeneric_decomposition.md b/docs/fundamentals/ideas/congeneric_decomposition.md index bedc9037..6ce33b9a 100644 --- a/docs/fundamentals/ideas/congeneric_decomposition.md +++ b/docs/fundamentals/ideas/congeneric_decomposition.md @@ -11,35 +11,191 @@ This reversible process preserves the order of the sequence and allows the origi The concept of Cogeneric decomposition can be demonstrated using an example: -Let's assume there is a symbolic sequence `INTELLIGENCE IS THE ABILITY TO ADAPT TO CHANGE` congeneric decomposition +Let's assume there is a symbolic sequence `INTELLIGENCE IS THE ABILITY TO ADAPT` congeneric decomposition could be presented by the following table, where each row is a congeneric sequence and `-` is an empty position in a congeneric sequence. -| I | N | T | E | L | L | I | G | E | N | C | E |    | I | S |    | T | H | E |    | A | B | I | L | I | T | Y |    | T | O |    | A | D | A | P | T |    | T | O |    | C | H | A | N | G | E | -|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| -| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | -| I | - | - | - | - | - | I | - | - | - | - | - | - | I | - | - | - | - | - | - | - | - | I | - | I | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | -| - | N | - | - | - | - | - | - | - | N | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | N | - | - | -| - | - | T | - | - | - | - | - | - | - | - | - | - | - | - | - | T | - | - | - | - | - | - | - | - | T | - | - | T | - | - | - | - | - | - | T | - | T | - | - | - | - | - | - | - | - | -| - | - | - | E | - | - | - | - | E | - | - | E | - | - | - | - | - | - | E | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | E | -| - | - | - | - | L | L | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | L | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | -| - | - | - | - | - | - | - | G | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | G | - | -| - | - | - | - | - | - | - | - | - | - | C | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | C | - | - | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - |    | - | - |    | - | - | - |    | - | - | - | - | - | - | - |    | - | - |    | - | - | - | - | - |    | - | - |    | - | - | - | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - | - | - | S | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | H | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | H | - | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | A | - | - | - | - | - | - | - | - | - | - | A | - | A | - | - | - | - | - | - | - | - | A | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | B | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | Y | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | O | - | - | - | - | - | - | - | - | O | - | - | - | - | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | D | - | - | - | - | - | - | - | - | - | - | - | - | - | -| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | P | - | - | - | - | - | - | - | - | - | - | - | - - -Congeneric sequence for `I` + + + + + +``` mermaid +block-beta + columns 36 + seq1["I"] seq2["N"] seq3["T"] seq4["E"] seq5["L"] seq6["L"] seq7["I"] seq8["G"] seq9["E"] seq10["N"] + seq11["C"] seq12["E"] seq13[" "] seq14["I"] seq15["S"] seq16[" "] seq17["T"] seq18["H"] seq19["E"] seq20[" "] + seq21["A"] seq22["B"] seq23["I"] seq24["L"] seq25["I"] seq26["T"] seq27["Y"] seq28[" "] seq29["T"] seq30["O"] + seq31[" "] seq32["A"] seq33["D"] seq34["A"] seq35["P"] seq36["T"] + + space:36 + + i1["I"] i2["-"] i3["-"] i4["-"] i5["-"] i6["-"] i7["I"] i8["-"] i9["-"] i10["-"] + i11["-"] i12["-"] i13["-"] i14["I"] i15["-"] i16["-"] i17["-"] i18["-"] i19["-"] i20["-"] + i21["-"] i22["-"] i23["I"] i24["-"] i25["I"] i26["-"] i27["-"] i28["-"] i29["-"] i30["-"] + i31["-"] i32["-"] i33["-"] i34["-"] i35["-"] i36["-"] + + n1["-"] n2["N"] n3["-"] n4["-"] n5["-"] n6["-"] n7["-"] n8["-"] n9["-"] n10["N"] + n11["-"] n12["-"] n13["-"] n14["-"] n15["-"] n16["-"] n17["-"] n18["-"] n19["-"] n20["-"] + n21["-"] n22["-"] n23["-"] n24["-"] n25["-"] n26["-"] n27["-"] n28["-"] n29["-"] n30["-"] + n31["-"] n32["-"] n33["-"] n34["-"] n35["-"] n36["-"] + + t1["-"] t2["-"] t3["T"] t4["-"] t5["-"] t6["-"] t7["-"] t8["-"] t9["-"] t10["-"] + t11["-"] t12["-"] t13["-"] t14["-"] t15["-"] t16["-"] t17["T"] t18["-"] t19["-"] t20["-"] + t21["-"] t22["-"] t23["-"] t24["-"] t25["-"] t26["T"] t27["-"] t28["-"] t29["T"] t30["-"] + t31["-"] t32["-"] t33["-"] t34["-"] t35["-"] t36["T"] + + e1["-"] e2["-"] e3["-"] e4["E"] e5["-"] e6["-"] e7["-"] e8["-"] e9["E"] e10["-"] + e11["-"] e12["E"] e13["-"] e14["-"] e15["-"] e16["-"] e17["-"] e18["-"] e19["E"] e20["-"] + e21["-"] e22["-"] e23["-"] e24["-"] e25["-"] e26["-"] e27["-"] e28["-"] e29["-"] e30["-"] + e31["-"] e32["-"] e33["-"] e34["-"] e35["-"] e36["-"] + + l1["-"] l2["-"] l3["-"] l4["-"] l5["L"] l6["L"] l7["-"] l8["-"] l9["-"] l10["-"] + l11["-"] l12["-"] l13["-"] l14["-"] l15["-"] l16["-"] l17["-"] l18["-"] l19["-"] l20["-"] + l21["-"] l22["-"] l23["-"] l24["L"] l25["-"] l26["-"] l27["-"] l28["-"] l29["-"] l30["-"] + l31["-"] l32["-"] l33["-"] l34["-"] l35["-"] l36["-"] + + g1["-"] g2["-"] g3["-"] g4["-"] g5["-"] g6["-"] g7["-"] g8["G"] g9["-"] g10["-"] + g11["-"] g12["-"] g13["-"] g14["-"] g15["-"] g16["-"] g17["-"] g18["-"] g19["-"] g20["-"] + g21["-"] g22["-"] g23["-"] g24["-"] g25["-"] g26["-"] g27["-"] g28["-"] g29["-"] g30["-"] + g31["-"] g32["-"] g33["-"] g34["-"] g35["-"] g36["-"] + + c1["-"] c2["-"] c3["-"] c4["-"] c5["-"] c6["-"] c7["-"] c8["-"] c9["-"] c10["-"] + c11["C"] c12["-"] c13["-"] c14["-"] c15["-"] c16["-"] c17["-"] c18["-"] c19["-"] c20["-"] + c21["-"] c22["-"] c23["-"] c24["-"] c25["-"] c26["-"] c27["-"] c28["-"] c29["-"] c30["-"] + c31["-"] c32["-"] c33["-"] c34["-"] c35["-"] c36["-"] + + sp1["-"] sp2["-"] sp3["-"] sp4["-"] sp5["-"] sp6["-"] sp7["-"] sp8["-"] sp9["-"] sp10["-"] + sp11["-"] sp12["-"] sp13[" "] sp14["-"] sp15["-"] sp16[" "] sp17["-"] sp18["-"] sp19["-"] sp20[" "] + sp21["-"] sp22["-"] sp23["-"] sp24["-"] sp25["-"] sp26["-"] sp27["-"] sp28[" "] sp29["-"] sp30["-"] + sp31[" "] sp32["-"] sp33["-"] sp34["-"] sp35["-"] sp36["-"] + + s1["-"] s2["-"] s3["-"] s4["-"] s5["-"] s6["-"] s7["-"] s8["-"] s9["-"] s10["-"] + s11["-"] s12["-"] s13["-"] s14["-"] s15["S"] s16["-"] s17["-"] s18["-"] s19["-"] s20["-"] + s21["-"] s22["-"] s23["-"] s24["-"] s25["-"] s26["-"] s27["-"] s28["-"] s29["-"] s30["-"] + s31["-"] s32["-"] s33["-"] s34["-"] s35["-"] s36["-"] + + h1["-"] h2["-"] h3["-"] h4["-"] h5["-"] h6["-"] h7["-"] h8["-"] h9["-"] h10["-"] + h11["-"] h12["-"] h13["-"] h14["-"] h15["-"] h16["-"] h17["-"] h18["H"] h19["-"] h20["-"] + h21["-"] h22["-"] h23["-"] h24["-"] h25["-"] h26["-"] h27["-"] h28["-"] h29["-"] h30["-"] + h31["-"] h32["-"] h33["-"] h34["-"] h35["-"] h36["-"] + + a1["-"] a2["-"] a3["-"] a4["-"] a5["-"] a6["-"] a7["-"] a8["-"] a9["-"] a10["-"] + a11["-"] a12["-"] a13["-"] a14["-"] a15["-"] a16["-"] a17["-"] a18["-"] a19["-"] a20["-"] + a21["A"] a22["-"] a23["-"] a24["-"] a25["-"] a26["-"] a27["-"] a28["-"] a29["-"] a30["-"] + a31["-"] a32["A"] a33["-"] a34["A"] a35["-"] a36["-"] + + b1["-"] b2["-"] b3["-"] b4["-"] b5["-"] b6["-"] b7["-"] b8["-"] b9["-"] b10["-"] + b11["-"] b12["-"] b13["-"] b14["-"] b15["-"] b16["-"] b17["-"] b18["-"] b19["-"] b20["-"] + b21["-"] b22["B"] b23["-"] b24["-"] b25["-"] b26["-"] b27["-"] b28["-"] b29["-"] b30["-"] + b31["-"] b32["-"] b33["-"] b34["-"] b35["-"] b36["-"] + + y1["-"] y2["-"] y3["-"] y4["-"] y5["-"] y6["-"] y7["-"] y8["-"] y9["-"] y10["-"] + y11["-"] y12["-"] y13["-"] y14["-"] y15["-"] y16["-"] y17["-"] y18["-"] y19["-"] y20["-"] + y21["-"] y22["-"] y23["-"] y24["-"] y25["-"] y26["-"] y27["Y"] y28["-"] y29["-"] y30["-"] + y31["-"] y32["-"] y33["-"] y34["-"] y35["-"] y36["-"] + + o1["-"] o2["-"] o3["-"] o4["-"] o5["-"] o6["-"] o7["-"] o8["-"] o9["-"] o10["-"] + o11["-"] o12["-"] o13["-"] o14["-"] o15["-"] o16["-"] o17["-"] o18["-"] o19["-"] o20["-"] + o21["-"] o22["-"] o23["-"] o24["-"] o25["-"] o26["-"] o27["-"] o28["-"] o29["-"] o30["O"] + o31["-"] o32["-"] o33["-"] o34["-"] o35["-"] o36["-"] + + d1["-"] d2["-"] d3["-"] d4["-"] d5["-"] d6["-"] d7["-"] d8["-"] d9["-"] d10["-"] + d11["-"] d12["-"] d13["-"] d14["-"] d15["-"] d16["-"] d17["-"] d18["-"] d19["-"] d20["-"] + d21["-"] d22["-"] d23["-"] d24["-"] d25["-"] d26["-"] d27["-"] d28["-"] d29["-"] d30["-"] + d31["-"] d32["-"] d33["D"] d34["-"] d35["-"] d36["-"] + + p1["-"] p2["-"] p3["-"] p4["-"] p5["-"] p6["-"] p7["-"] p8["-"] p9["-"] p10["-"] + p11["-"] p12["-"] p13["-"] p14["-"] p15["-"] p16["-"] p17["-"] p18["-"] p19["-"] p20["-"] + p21["-"] p22["-"] p23["-"] p24["-"] p25["-"] p26["-"] p27["-"] p28["-"] p29["-"] p30["-"] + p31["-"] p32["-"] p33["-"] p34["-"] p35["P"] p36["-"] + + classDef c1 fill:#ff7f0e,color:#fff; + classDef c2 fill:#ffbb78,color:#000; + classDef c3 fill:#2ca02c,color:#fff; + classDef c4 fill:#98df8a,color:#000; + classDef c5 fill:#d62728,color:#fff; + classDef c6 fill:#ff9896,color:#000; + classDef c7 fill:#9467bd,color:#fff; + classDef c8 fill:#c5b0d5,color:#000; + classDef c9 fill:#8c564b,color:#fff; + classDef c10 fill:#c49c94,color:#000; + classDef c11 fill:#e377c2,color:#fff; + classDef c12 fill:#f7b6d2,color:#000; + classDef c13 fill:#bcbd22,color:#fff; + classDef c14 fill:#dbdb8d,color:#000; + classDef c15 fill:#17becf,color:#fff; + classDef c16 fill:#9edae5,color:#000; + + class seq1,seq7,seq14,seq23,seq25,i1,i7,i14,i23,i25 c1 + class seq2,seq10,n2,n10 c2 + class seq3,seq17,seq26,seq29,seq36,t3,t17,t26,t29,t36 c3 + class seq4,seq9,seq12,seq19,e4,e9,e12,e19 c4 + class seq5,seq6,seq24,l5,l6,l24 c5 + class seq8,g8 c6 + class seq11,c11 c7 + class seq13,seq16,seq20,seq28,seq31,sp13,sp16,sp20,sp28,sp31 c8 + class seq15,s15 c9 + class seq18,h18 c10 + class seq21,seq32,seq34,a21,a32,a34 c11 + class seq22,b22 c12 + class seq27,y27 c13 + class seq30,o30 c14 + class seq33,d33 c15 + class seq35,p35 c16 ``` -I - - - - - I - - - - - - I - - - - - - - - I - I - - - - - - - - - - - - - - - - - - - - - + +Congeneric sequence for `E` +``` mermaid +block-beta + columns 36 + e1["-"] e2["-"] e3["-"] e4["E"] e5["-"] e6["-"] e7["-"] e8["-"] e9["E"] e10["-"] + e11["-"] e12["E"] e13["-"] e14["-"] e15["-"] e16["-"] e17["-"] e18["-"] e19["E"] e20["-"] + e21["-"] e22["-"] e23["-"] e24["-"] e25["-"] e26["-"] e27["-"] e28["-"] e29["-"] e30["-"] + e31["-"] e32["-"] e33["-"] e34["-"] e35["-"] e36["-"] ``` -could be a part of multiple symbol sequences that have the same order of `I` element. + + +could be a part of multiple symbol sequences that have the same order of `E` element. While keeping the main idea, the congeneric decomposition could be applied, with a flavor, to any type of special case symbolic sequences, such as Order. diff --git a/docs/fundamentals/ideas/interval_as_a_basic_information_unit.md b/docs/fundamentals/ideas/interval_as_a_basic_information_unit.md index 5e8b547f..634e1606 100644 --- a/docs/fundamentals/ideas/interval_as_a_basic_information_unit.md +++ b/docs/fundamentals/ideas/interval_as_a_basic_information_unit.md @@ -13,6 +13,11 @@ block-beta columns 12 s1["A"] s2["C"] s3["T"] s4["A"] s5["C"] s6["G"] s7["A"] s8["A"] s9["A"] s10["T"] s11["A"] s12["A"] i1["3"]:3 i2["3"]:3 i3["1"]:1 i4["1"]:1 i5["2"]:2 i6["1"]:1 i7["1"]:1 + + classDef c3 fill:#2ca02c,color:#fff; + classDef c4 fill:#98df8a,color:#000; + class s1,s4,s7,s8,s9,s11,s12 c3 + class i1,i2,i3,i4,i5,i6,i7 c4 ``` In general, a sequence does not necessarily end with the same symbol it begins with. @@ -26,6 +31,11 @@ block-beta s1["A"] s2["C"] s3["T"] s4["A"] s5["C"] s6["G"] s7["A"] s8["A"] s9["A"] s10["T"] s11["A"] s12["A"] space s13["T"] s14["C"] space i1["3"]:3 i2["9"]:10 s12 --> s13 + + classDef c3 fill:#2ca02c,color:#fff; + classDef c4 fill:#98df8a,color:#000; + class s2,s5,s14 c3 + class i1,i2 c4 ``` The circular pattern preserves both the statistical properties and the order of elements. diff --git a/docs/fundamentals/ideas/order_as_a_property.md b/docs/fundamentals/ideas/order_as_a_property.md index 32b2851f..401d2928 100644 --- a/docs/fundamentals/ideas/order_as_a_property.md +++ b/docs/fundamentals/ideas/order_as_a_property.md @@ -12,35 +12,291 @@ sorted by the appearance of the elements in the original sequence [1, 2, 3]. The concept of an Order can be conveniently demonstrated using an example: -Let's assume there is a symbolic sequence `INTELLIGENCE IS THE ABILITY TO ADAPT TO CHANGE` +Let's assume there is a symbolic sequence + +``` mermaid +block-beta + columns 36 + s1["I"] s2["N"] s3["T"] s4["E"] s5["L"] s6["L"] s7["I"] s8["G"] s9["E"] s10["N"] + s11["C"] s12["E"] s13[" "] s14["I"] s15["S"] s16[" "] s17["T"] s18["H"] s19["E"] s20[" "] + s21["A"] s22["B"] s23["I"] s24["L"] s25["I"] s26["T"] s27["Y"] s28[" "] s29["T"] s30["O"] + s31[" "] s32["A"] s33["D"] s34["A"] s35["P"] s36["T"] +``` + Find and enumirate the first appearance of each element -| I | N | T | E | L | L | I | G | E | N | C | E |    | I | S |    | T | H | E |    | A | B | I | L | I | T | Y |    | T | O |    | A | D | A | P | T |    | T | O |    | C | H | A | N | G | E | -|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| -| 1 | 2 | 3 | 4 | 5 | | | 6 | | | 7 | | 8 | | 9 | | | 10 | | | 11 | 12 | | | | | 13 | | | 14 | | | 15 | | 16 | | | | | | | | | | | | +``` mermaid +block-beta + columns 36 + s1["I"] s2["N"] s3["T"] s4["E"] s5["L"] s6["L"] s7["I"] s8["G"] s9["E"] s10["N"] + s11["C"] s12["E"] s13[" "] s14["I"] s15["S"] s16[" "] s17["T"] s18["H"] s19["E"] s20[" "] + s21["A"] s22["B"] s23["I"] s24["L"] s25["I"] s26["T"] s27["Y"] s28[" "] s29["T"] s30["O"] + s31[" "] s32["A"] s33["D"] s34["A"] s35["P"] s36["T"] + + space:36 + + i1_1["1"] i2_1["2"] i3_1["3"] i4_1["4"] i5_1["5"] space:2 i6_1["6"] space:2 i7_1["7"] space + i8_1["8"] space i9_1["9"] space:2 i10_1["10"] space:2 + i11_1["11"] i12_1["12"] space:4 i13_1["13"] + space:2 i14_1["14"] space:2 + i15_1["15"] space i16_1["16"] + + classDef c1 fill:#ff7f0e,color:#fff; + classDef c2 fill:#ffbb78,color:#000; + classDef c3 fill:#2ca02c,color:#fff; + classDef c4 fill:#98df8a,color:#000; + classDef c5 fill:#d62728,color:#fff; + classDef c6 fill:#ff9896,color:#000; + classDef c7 fill:#9467bd,color:#fff; + classDef c8 fill:#c5b0d5,color:#000; + classDef c9 fill:#8c564b,color:#fff; + classDef c10 fill:#c49c94,color:#000; + classDef c11 fill:#e377c2,color:#fff; + classDef c12 fill:#f7b6d2,color:#000; + classDef c13 fill:#bcbd22,color:#fff; + classDef c14 fill:#dbdb8d,color:#000; + classDef c15 fill:#17becf,color:#fff; + classDef c16 fill:#9edae5,color:#000; + + class s1,i1_1 c1 + class s2,i2_1 c2 + class s3,i3_1 c3 + class s4,i4_1 c4 + class s5,i5_1 c5 + class s8,i6_1 c6 + class s11,i7_1 c7 + class s13,i8_1 c8 + class s15,i9_1 c9 + class s18,i10_1 c10 + class s21,i11_1 c11 + class s22,i12_1 c12 + class s27,i13_1 c13 + class s30,i14_1 c14 + class s33,i15_1 c15 + class s35,i16_1 c16 + + s1 --> i1_1 + s2 --> i2_1 + s3 --> i3_1 + s4 --> i4_1 + s5 --> i5_1 + s8 --> i6_1 + s11 --> i7_1 + s13 --> i8_1 + s15 --> i9_1 + s18 --> i10_1 + s21 --> i11_1 + s22 --> i12_1 + s27 --> i13_1 + s30 --> i14_1 + s33 --> i15_1 + s35 --> i16_1 +``` -The alphabet for the sequence would be sequence of unique elements: +The alphabet (with indexes) for the sequence would be sequence of unique elements: -| I | N | T | E | L | G | C | | S | H | A | B | Y | O | D | P | -|---|---|---|---|---|---|---|---|---|----|----|----|----|----|----|----| -| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | + +``` mermaid +block-beta + columns 16 + s1["I"] s2["N"] s3["T"] s4["E"] s5["L"] s8["G"] + s11["C"] s13[" "] s15["S"] s18["H"] + s21["A"] s22["B"] s27["Y"] s30["O"] + s33["D"] s35["P"] + + space:16 + + i1_1["1"] i2_1["2"] i3_1["3"] i4_1["4"] i5_1["5"] i6_1["6"] i7_1["7"] + i8_1["8"] i9_1["9"] i10_1["10"] + i11_1["11"] i12_1["12"] i13_1["13"] + i14_1["14"] + i15_1["15"] i16_1["16"] + + classDef c1 fill:#ff7f0e,color:#fff; + classDef c2 fill:#ffbb78,color:#000; + classDef c3 fill:#2ca02c,color:#fff; + classDef c4 fill:#98df8a,color:#000; + classDef c5 fill:#d62728,color:#fff; + classDef c6 fill:#ff9896,color:#000; + classDef c7 fill:#9467bd,color:#fff; + classDef c8 fill:#c5b0d5,color:#000; + classDef c9 fill:#8c564b,color:#fff; + classDef c10 fill:#c49c94,color:#000; + classDef c11 fill:#e377c2,color:#fff; + classDef c12 fill:#f7b6d2,color:#000; + classDef c13 fill:#bcbd22,color:#fff; + classDef c14 fill:#dbdb8d,color:#000; + classDef c15 fill:#17becf,color:#fff; + classDef c16 fill:#9edae5,color:#000; + + class s1,i1_1 c1 + class s2,i2_1 c2 + class s3,i3_1 c3 + class s4,i4_1 c4 + class s5,i5_1 c5 + class s8,i6_1 c6 + class s11,i7_1 c7 + class s13,i8_1 c8 + class s15,i9_1 c9 + class s18,i10_1 c10 + class s21,i11_1 c11 + class s22,i12_1 c12 + class s27,i13_1 c13 + class s30,i14_1 c14 + class s33,i15_1 c15 + class s35,i16_1 c16 + + s1 --> i1_1 + s2 --> i2_1 + s3 --> i3_1 + s4 --> i4_1 + s5 --> i5_1 + s8 --> i6_1 + s11 --> i7_1 + s13 --> i8_1 + s15 --> i9_1 + s18 --> i10_1 + s21 --> i11_1 + s22 --> i12_1 + s27 --> i13_1 + s30 --> i14_1 + s33 --> i15_1 + s35 --> i16_1 + + i1_1 --> s1 + i2_1 --> s2 + i3_1 --> s3 + i4_1 --> s4 + i5_1 --> s5 + i6_1 --> s8 + i7_1 --> s11 + i8_1 --> s13 + i9_1 --> s15 + i10_1 --> s18 + i11_1 --> s21 + i12_1 --> s22 + i13_1 --> s27 + i14_1 --> s30 + i15_1 --> s33 + i16_1 --> s35 +``` Determine the order of the sequence by replacing each element of the sequence with its corresponding alphabet index +``` mermaid +block-beta + columns 36 + s1["I"] s2["N"] s3["T"] s4["E"] s5["L"] s6["L"] s7["I"] s8["G"] s9["E"] s10["N"] + s11["C"] s12["E"] s13[" "] s14["I"] s15["S"] s16[" "] s17["T"] s18["H"] s19["E"] s20[" "] + s21["A"] s22["B"] s23["I"] s24["L"] s25["I"] s26["T"] s27["Y"] s28[" "] s29["T"] s30["O"] + s31[" "] s32["A"] s33["D"] s34["A"] s35["P"] s36["T"] -| I | N | T | E | L | L | I | G | E | N | C | E |    | I | S |    | T | H | E |    | A | B | I | L | I | T | Y |    | T | O |    | A | D | A | P | T |    | T | O |    | C | H | A | N | G | E | -|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| -| 1 | 2 | 3 | 4 | 5 | 5 | 1 | 6 | 4 | 2 | 7 | 4 | 8 | 1 | 9 | 8 | 3 | 10 | 4 | 8 | 11 | 12 | 1 | 5 | 1 | 3 | 13 | 8 | 3 | 14 | 8 | 11 | 15 | 11 | 16 | 3 | 8 | 3 | 14 | 8 | 7 | 10 | 11 | 2 | 6 | 4 | + space:36 -The order of symbolic sequence `INTELLIGENCE IS THE ABILITY TO ADAPT TO CHANGE` is + i1_1["1"] i2_1["2"] i3_1["3"] i4_1["4"] i5_1["5"] i5_2["5"] i1_2["1"] i6_1["6"] i4_2["4"] i2_2["2"] i7_1["7"] i4_3["4"] + i8_1["8"] i1_3["1"] i9_1["9"] i8_2["8"] i3_2["3"] i10_1["10"] i4_4["4"] i8_3["8"] + i11_1["11"] i12_1["12"] i1_4["1"] i5_3["5"] i1_5["1"] i3_3["3"] i13_1["13"] + i8_4["8"] i3_4["3"] i14_1["14"] i8_5["8"] i11_2["11"] + i15_1["15"] i11_3["11"] i16_1["16"] i3_5["3"] -| 1 | 2 | 3 | 4 | 5 | 5 | 1 | 6 | 4 | 2 | 7 | 4 | 8 | 1 | 9 | 8 | 3 | 10 | 4 | 8 | 11 | 12 | 1 | 5 | 1 | 3 | 13 | 8 | 3 | 14 | 8 | 11 | 15 | 11 | 16 | 3 | 8 | 3 | 14 | 8 | 7 | 10 | 11 | 2 | 6 | 4 | -|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| + classDef c1 fill:#ff7f0e,color:#fff; + classDef c2 fill:#ffbb78,color:#000; + classDef c3 fill:#2ca02c,color:#fff; + classDef c4 fill:#98df8a,color:#000; + classDef c5 fill:#d62728,color:#fff; + classDef c6 fill:#ff9896,color:#000; + classDef c7 fill:#9467bd,color:#fff; + classDef c8 fill:#c5b0d5,color:#000; + classDef c9 fill:#8c564b,color:#fff; + classDef c10 fill:#c49c94,color:#000; + classDef c11 fill:#e377c2,color:#fff; + classDef c12 fill:#f7b6d2,color:#000; + classDef c13 fill:#bcbd22,color:#fff; + classDef c14 fill:#dbdb8d,color:#000; + classDef c15 fill:#17becf,color:#fff; + classDef c16 fill:#9edae5,color:#000; + class s1,s7,s14,s23,s25,i1_1,i1_2,i1_3,i1_4,i1_5 c1 + class s2,s10,i2_1,i2_2 c2 + class s3,s17,s26,s29,s36,i3_1,i3_2,i3_3,i3_4,i3_5 c3 + class s4,s9,s12,s19,i4_1,i4_2,i4_3,i4_4 c4 + class s5,s6,s24,i5_1,i5_2,i5_3 c5 + class s8,i6_1 c6 + class s11,i7_1 c7 + class s13,s16,s20,s28,s31,i8_1,i8_2,i8_3,i8_4,i8_5 c8 + class s15,i9_1 c9 + class s18,i10_1 c10 + class s21,s32,s34,i11_1,i11_2,i11_3 c11 + class s22,i12_1 c12 + class s27,i13_1 c13 + class s30,i14_1 c14 + class s33,i15_1 c15 + class s35,i16_1 c16 + s1 --> i1_1 + s7 --> i1_2 + s14 --> i1_3 + s23 --> i1_4 + s25 --> i1_5 + + s2 --> i2_1 + s10 --> i2_2 + + s3 --> i3_1 + s17 --> i3_2 + s26 --> i3_3 + s29 --> i3_4 + s36 --> i3_5 + + s4 --> i4_1 + s9 --> i4_2 + s12 --> i4_3 + s19--> i4_4 + + s5 --> i5_1 + s6 --> i5_2 + s24 --> i5_3 + + s8 --> i6_1 + + s11 --> i7_1 + + s13 --> i8_1 + s16 --> i8_2 + s20 --> i8_3 + s28 --> i8_4 + s31 --> i8_5 + + s15 --> i9_1 + s18 --> i10_1 + + s21 --> i11_1 + s32 --> i11_2 + s34 --> i11_3 + + s22 --> i12_1 + s27 --> i13_1 + s30 --> i14_1 + s33 --> i15_1 + s35 --> i16_1 +``` + + +The order of symbolic sequence `INTELLIGENCE IS THE ABILITY TO ADAPT` is + +``` mermaid +block-beta + columns 36 + i1_1["1"] i2_1["2"] i3_1["3"] i4_1["4"] i5_1["5"] i5_2["5"] i1_2["1"] i6_1["6"] i4_2["4"] i2_2["2"] i7_1["7"] i4_3["4"] + i8_1["8"] i1_3["1"] i9_1["9"] i8_2["8"] i3_2["3"] i10_1["10"] i4_4["4"] i8_3["8"] + i11_1["11"] i12_1["12"] i1_4["1"] i5_3["5"] i1_5["1"] i3_3["3"] i13_1["13"] + i8_4["8"] i3_4["3"] i14_1["14"] i8_5["8"] i11_2["11"] + i15_1["15"] i11_3["11"] i16_1["16"] i3_5["3"] +``` + Despite the triviality of the concept Order, it allows us to separate the elements and composition of a sequence and to define the compositional equivalence of different sequences. Example of sequences with equals orders: