Previously in [12], it has been shown that DNAs of men and women have two different packings and their radiated waves are different. Thus, there should be two types of structures for water to store information of these two types of structures. However, we couldn’t see any differences between structures of waters in four dimension. In this section, we will show that in extra dimensions, the structures of two types of water become different and these waters radiate some toposiomerase-like waves that interact with two types of DNAs, open them and read their information. In biology,

We can rewrite the action of triangle which is formed by one atom of DNA with two near atoms as [14, 15, 16]:

$$\begin{array}{}{\displaystyle {S}_{3,DNA}=-{T}_{tri}\int {d}^{3}\sigma}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}\sqrt{{\eta}^{ab}{g}_{MN}{\mathrm{\partial}}_{a}{X}^{M}{\mathrm{\partial}}_{b}{X}^{N}+2\pi {l}_{s}^{2}U(F)++2\pi {l}_{s}^{2}\overline{U}(\overline{F}))}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}U=(\sum _{n=1}^{2}\frac{1}{n!}\left(-\frac{{F}_{atom1-atom2}{F}_{atom1-atom3}}{{\beta}^{2}}\right)+{F}_{atom2-atom3})}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\overline{U}=(\sum _{n=1}^{2}\frac{1}{n!}\left(-\frac{{\overline{F}}_{atom1-atom2}{\overline{F}}_{atom1-atom3}}{{\beta}^{2}}\right)+{\overline{F}}_{atom2-atom3})}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}F={F}_{\mu \nu}{F}^{\mu \nu}\phantom{\rule{1em}{0ex}}{F}_{\mu \nu}={\mathrm{\partial}}_{\mu}{A}_{\nu}-{\mathrm{\partial}}_{\nu}{A}_{\mu}}\end{array}$$(16)

where *g*_{MN} is the background metric, *X*^{M}(*σ*^{a})’s are scalar fields which are constructed from paring two electrons with opposite spins, *σ*^{a}’s are the manifold coordinates, *a*, *b* = 0, 1, …, 3 are world-volume indices of the manifold and *M*, *N* = 0, 1, …, 11 are eleven dimensional spacetime indices. Also, *U* is the nonlinear field [15] and *A* is the photon which exchanges between atoms. Also, *U* is the nonlinear field which is created by packings of DNA [15] and *A* is the photon which exchanges between atoms.

Following method in previous sections and substituting *X* → *ψ*^{↑}*ψ*_{↓}, we can rewrite the trigonal Hamiltonian as:

$$\begin{array}{}{\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{H}_{3,DNA}=4\pi {T}_{tri}\int d{\sigma}_{11}..d{\sigma}_{1}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}{Q}_{3,un-packed}{\overline{Q}}_{3,acked}{E}_{3,un-packed}{\overline{E}}_{3,packed}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{E}_{3,un-packed}=(1+{\eta}^{ab}{g}_{MN}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}{\cdot \phantom{\rule{thinmathspace}{0ex}}{g}_{MN}{\psi}_{O}^{M,\uparrow}{\mathrm{\partial}}_{a}{\psi}_{H}^{M,\downarrow}{\psi}_{H}^{N,\uparrow}{\mathrm{\partial}}_{b}{\psi}_{O}^{N,\downarrow})}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{Q}_{3,un-packed}={Q}_{atom2-atom3}+{Q}_{atom1-atom2-atom3}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{Q}_{atom2-atom3}={\left(1+\frac{{k}_{1}^{2}}{{\sigma}_{1,atom2-atom3}^{4}}\right)}^{1/2}}\\ {\displaystyle {Q}_{atom1-atom2-atom3}={Q}_{atom1-atom2}(1}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}+\phantom{\rule{thinmathspace}{0ex}}\frac{{k}_{2}^{2}}{{Q}_{atom1-atom2}{\sigma}_{atom2-atom3}^{4}}{)}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{Q}_{atom1-atom2}=(1+\frac{{k}_{1}^{2}}{{\sigma}_{atom1-atom2}^{4}}{)}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\overline{E}}_{3,packed}=(1+{\eta}^{ab}{g}_{MN}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}{g}_{MN}{\overline{\psi}}_{O}^{M,\uparrow}{\mathrm{\partial}}_{a}{\overline{\psi}}_{H}^{M,\downarrow}{\overline{\psi}}_{H}^{N,\uparrow}{\mathrm{\partial}}_{b}{\overline{\psi}}_{O}^{N,\downarrow}{)}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\overline{Q}}_{3,packed}={\overline{Q}}_{atom2-atom3}+{\overline{Q}}_{atom1-atom2-atom3}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\overline{Q}}_{atom2-atom3}=(1+\frac{{k}_{1}^{2}}{{\sigma}_{1,atom2-atom3}^{2}{\theta}_{1,atom2-atom3}^{2}}{)}^{1/2}}\\ {\displaystyle {\overline{Q}}_{atom1-atom2-atom3}={\overline{Q}}_{atom1-atom2}(1}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}+\phantom{\rule{thinmathspace}{0ex}}\frac{{k}_{2}^{2}}{{\overline{Q}}_{atom1-atom2}{\sigma}_{atom2-atom3}^{2}{\theta}_{atom2-atom3}^{2}}{)}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{Q}_{atom1-atom2}={\left(1+\frac{{k}_{1}^{2}}{{\sigma}_{atom1-atom2}^{2}{\theta}_{atom1-atom2}^{2}}\right)}^{1/2}}\end{array}$$(17)

We can extend these calculations to hexagonal and pentagonal manifolds:

$$\begin{array}{}{\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{H}_{6/5,DNA}=4\pi {T}_{tri}\int d{\sigma}_{11}..d{\sigma}_{1}{Q}_{6/5,un-packed}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\cdot \phantom{\rule{thinmathspace}{0ex}}{\overline{Q}}_{6/5,acked}{E}_{6/5,un-packed}{\overline{E}}_{6/5,packed}}\\ {\displaystyle \phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{E}_{6/5,un-packed}=(1+{\eta}^{ab}{g}_{MN}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\phantom{\rule{thinmathspace}{0ex}}\cdot {g}_{MN}{\psi}_{O}^{M,\uparrow}{\mathrm{\partial}}_{a}{\psi}_{H}^{M,\downarrow}{\psi}_{H}^{N,\uparrow}{\mathrm{\partial}}_{b}{\psi}_{O}^{N,\downarrow})}^{1/2}}\\ {\displaystyle \phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{Q}_{6/5,un-packed}={\mathit{\Sigma}}_{ij}{Q}_{atom,i-atom,j}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}+\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Sigma}}_{ijk}{Q}_{atom,i-atom,j-atom,k}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{Q}_{atom,i-atom,j}={\left(1+\frac{{k}_{1}^{2}}{{\sigma}_{1,atom,i-atom,j}^{4}}\right)}^{1/2}}\\ {\displaystyle {Q}_{atom,i-atom,j-atom,k}={Q}_{atom,i-atom,j}(1}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}+\phantom{\rule{thinmathspace}{0ex}}\frac{{k}_{2}^{2}}{{Q}_{atom,i-atom,j}{\sigma}_{atom,i-atom,j}^{4}}{)}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{Q}_{atom,i-atom,j}={\left(1+\frac{{k}_{1}^{2}}{{\sigma}_{atom,i-atom,j}^{4}}\right)}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\overline{E}}_{6,packed}=(1+{\eta}^{ab}{g}_{MN}{g}_{MN}{\overline{\psi}}_{O}^{M,\uparrow}{\mathrm{\partial}}_{a}{\overline{\psi}}_{H}^{M,\downarrow}{\overline{\psi}}_{H}^{N,\uparrow}{\mathrm{\partial}}_{b}{\overline{\psi}}_{O}^{N,\downarrow}{)}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\overline{Q}}_{6/5,packed}={\mathit{\Sigma}}_{ij}{\overline{Q}}_{atom,i-atom,j}+{\mathit{\Sigma}}_{ijk}{\overline{Q}}_{atom,i-atom,j-atom,k}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\overline{Q}}_{atom,i-atom,j}={\left(1+\frac{{k}_{1}^{2}}{{\sigma}_{1,atom,i-atom,j}^{2}{\theta}_{1,atom,i-atom,j}^{2}}\right)}^{1/2}}\\ {\displaystyle {\overline{Q}}_{atom,i-atom,j-atom,k}={\overline{Q}}_{atom,i-atom,j}(1}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}+\phantom{\rule{thinmathspace}{0ex}}\frac{{k}_{2}^{2}}{{\overline{Q}}_{atom,i-atom,j}{\sigma}_{atom,j-atom,k}^{2}{\theta}_{atom,j-atom,k}^{2}}{)}^{1/2}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{Q}_{atom,i-atom,j}={\left(1+\frac{{k}_{1}^{2}}{{\sigma}_{atom,i-atom,j}^{2}{\theta}_{atom,i-atom,j}^{2}}\right)}^{1/2}}\end{array}$$(18)

Each DNA has various pentagonal, hexagonal and in some packings, trigonal manifolds (See Figure 5). Thus, we can write Hamiltonian of a DNA summing over Hamiltonians of all manifolds in equations (17,18):

$$\begin{array}{}{\displaystyle {H}_{DNA}=4\pi {T}_{tri}\int d{\sigma}_{11}..d{\sigma}_{1}{\mathit{\Sigma}}_{n.m,X,Y}^{w}}\\ {\displaystyle {\mathit{\Pi}}_{a,b,c=1}^{N}{P}^{DNA}(a,b,c,n,m,X,Y)}\\ {\displaystyle {\mathit{\Pi}}_{i=1}^{n}{Q}_{6,un-packed,i}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{6,packed,j}}\\ {\displaystyle {\mathit{\Pi}}_{k=1}^{X}{E}_{6,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{6,packed,l}\times}\\ {\displaystyle {\mathit{\Pi}}_{i=1}^{n}{Q}_{5,un-packed,i}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{5,packed,j}}\\ {\displaystyle {\mathit{\Pi}}_{k=1}^{X}{E}_{5,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{5,packed,l}\times}\\ {\displaystyle {\mathit{\Pi}}_{i=1}^{n}{Q}_{3,un-packed,i}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{3,packed,j}}\\ {\displaystyle {\mathit{\Pi}}_{k=1}^{X}{E}_{3,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{3,packed,l}}\end{array}$$(19)

Figure 5 Pentagonal and hexagonal manifolds of a DNA

where *P*(*a*,*b*,*c*,*n*,*m*,*X*,*Y*) is the probability for producing a hexagonal, *b* pentagonal and c trigonal manifolds with n un-packed photons, *m* packed photons, *X* un-packed fermions and Y packed fermions. To open this complicated system, we needs to some waves which play the role of topoisomerase in biology. These waves should open the structure of DNA, read it’s information and transmit it to water. When, topoisomerase-like waves achieve to DNA, excite it and total topology and Hamiltonian tends to a constant number (See Figure 6). We can write:

$$\begin{array}{}{\displaystyle {H}_{DNA}+{H}_{wave}=1\to}\\ {\displaystyle \phantom{\rule{2em}{0ex}}{H}_{wave,extra}=4\pi {T}_{tri}\int d{\sigma}_{11}..d{\sigma}_{1}{\mathit{\Sigma}}_{n.m,X,Y}^{w}{\mathit{\Pi}}_{a,b,c=1}^{N}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times [({P}^{wave,4-dimension}(a,b,c,n,m,X,Y)}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{H}^{wave,4-dimension}(a,b,c,n,m,X,Y){)}^{-1}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times {\mathit{\Pi}}_{i=1}^{n}{\mathit{\Pi}}_{j=1}^{m}{\mathit{\Pi}}_{k=1}^{X}{\mathit{\Pi}}_{l=1}^{Y}\delta ({\sigma}_{nX}^{2}-{\theta}_{mY}^{2})}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}-{P}^{DNA}(a,b,c,n,m,X,Y){\mathit{\Pi}}_{i=1}^{n}{Q}_{6,un-packed,i}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{6,packed,j}{\mathit{\Pi}}_{k=1}^{X}{E}_{6,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{6,packed,l}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times {\mathit{\Pi}}_{i=1}^{n}{Q}_{5,un-packed,i}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{5,packed,j}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{5,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{5,packed,l}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times {\mathit{\Pi}}_{i=1}^{n}{Q}_{3,un-packed,i}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{3,packed,j}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{3,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{3,packed,l}]}\end{array}$$(20)

Figure 6 Topoisomerase-like waves join to DNA and topology of system becomes simple

where *H*^{wave,4−dimension}(*a*, *b*, *c*, *n*, *m*, *X*, *Y*) is the Hamiltonian of structures of wave that can be seen in four dimensions. Also, *H*_{wave,extra} is the Hamiltonian of structures of waves in extra dimensions. These waves act like topoisomers in biology. When these waves achieve to DNA, excited it and the Hamiltonian and topology of system tends to one. In these conditions, all information of DNA can be recovered and stored in waves. This wave can exchange information with water so. Thus, we can obtain the structure of water in extra dimension as:

$$\begin{array}{}{\displaystyle {H}_{water}={H}_{wave}\to}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{H}_{water,extra}=4\pi {T}_{tri}\int d{\sigma}_{11}..d{\sigma}_{1}{\mathit{\Sigma}}_{n.m,X,Y}^{w}{\mathit{\Pi}}_{a,b,c=1}^{N}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}[({P}^{water,4-dimension}(a,b,c,n,m,X,Y)}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{H}^{water,4-dimension}(a,b,c,n,m,X,Y){)}^{-1}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{\mathit{\Pi}}_{j=1}^{m}{\mathit{\Pi}}_{k=1}^{X}{\mathit{\Pi}}_{l=1}^{Y}\delta ({\sigma}_{nX}^{2}-{\theta}_{mY}^{2})}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}-\phantom{\rule{thinmathspace}{0ex}}{P}^{DNA}(a,b,c,n,m,X,Y){\mathit{\Pi}}_{i=1}^{n}{Q}_{6,un-packed,i}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{6,packed,j}{\mathit{\Pi}}_{k=1}^{X}{E}_{6,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{6,packed,l}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{Q}_{5,un-packed,i}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{5,packed,j}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{5,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{5,packed,l}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{Q}_{3,un-packed,i}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{3,packed,j}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{3,un-packed,k}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{3,packed,l}]}\end{array}$$(21)

where *H*^{water,4−dimension}(*a*, *b*, *c*, *n*, *m*, *X*, *Y*) is the Hamiltonian of structures of water that can be seen in four dimensions. Also, *H*_{water,extra} is the Hamiltonian of structures of water in extra dimensions. Types of packings of DNAs in women is different from types of packings of DNAs in men. Thus, we can write:

$$\begin{array}{}{\displaystyle \phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{H}_{water,women}={H}_{wave,women}\to}\\ {H}_{water,extra,women}=4\pi {T}_{tri}\int d{\sigma}_{11}..d{\sigma}_{1}{\mathit{\Sigma}}_{n.m,X,Y}^{w}{\mathit{\Pi}}_{a,b,c=1}^{N}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}[({P}^{water,4-dimension}(a,b,c,n,m,X,Y)}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}{H}^{water,4-dimension}(a,b,c,n,m,X,Y){)}^{-1}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{\mathit{\Pi}}_{j=1}^{m}{\mathit{\Pi}}_{k=1}^{X}{\mathit{\Pi}}_{l=1}^{Y}\delta ({\sigma}_{nX}^{2}-{\theta}_{mY}^{2})}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}-\phantom{\rule{thinmathspace}{0ex}}{P}^{DNA,women}(a,b,c,n,m,X,Y)}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{Q}_{6,un-packed,i,women}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{6,packed,j,women}{\mathit{\Pi}}_{k=1}^{X}{E}_{6,un-packed,k,women}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{6,packed,l,women}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{Q}_{5,un-packed,i,women}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{5,packed,j}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{5,un-packed,k,women}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{5,packed,l,women}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{Q}_{3,un-packed,i,women}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{3,packed,j,women}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{3,un-packed,k,women}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{3,packed,l,women}]}\end{array}$$(22)

$$\begin{array}{}{\displaystyle \phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{H}_{water,Men}={H}_{wave,Men}\to}\\ {\displaystyle {H}_{water,extra,Men}=4\pi {T}_{tri}\int d{\sigma}_{11}..d{\sigma}_{1}{\mathit{\Sigma}}_{n.m,X,Y}^{w}{\mathit{\Pi}}_{a,b,c=1}^{N}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}[({P}^{water,4-dimension}(a,b,c,n,m,X,Y)}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{H}^{water,4-dimension}(a,b,c,n,m,X,Y){)}^{-1}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{\mathit{\Pi}}_{j=1}^{m}{\mathit{\Pi}}_{k=1}^{X}{\mathit{\Pi}}_{l=1}^{Y}\delta ({\sigma}_{nX}^{2}-{\theta}_{mY}^{2})}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}-\phantom{\rule{thinmathspace}{0ex}}{P}^{DNA,Men}(a,b,c,n,m,X,Y)}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{Q}_{6,un-packed,i,Men}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{6,packed,j,Men}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{6,un-packed,k,Men}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{6,packed,l,Men}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{Q}_{5,un-packed,i,Men}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{5,packed,j,Men}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{5,un-packed,k,Men}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{5,packed,l,Men}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\times \phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{i=1}^{n}{Q}_{3,un-packed,i,Men}{\mathit{\Pi}}_{j=1}^{m}{\overline{Q}}_{3,packed,j,Men}}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}{\mathit{\Pi}}_{k=1}^{X}{E}_{3,un-packed,k,Men}{\mathit{\Pi}}_{l=1}^{Y}{\overline{E}}_{3,packed,l,Men}]}\end{array}$$(23)

Above results show that there are two types of structures for water (See Figure 7). However, these structures are the same in four dimensions and different in extra dimensions. For this reason, an observer on four dimensional manifold can only observe the same structure for all waters.

Figure 7 The structure of two waters in extra dimensions

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