Unity shader normal vector confuse

There is code about Shader in a book sample. My confuse is that the v.normal is object space.
v.normal wants to convert to world space. Should not v.normal multiple with unity_ObjectToWorld as below?
fixed3 worldNormal = normalize(mul( (float3x3)unity_ObjectToWorld,v.normal,));

But the book is wroten as below:
fixed3 worldNormal = normalize(mul(v.normal, (float3x3)unity_WorldToObject));

Does somebody know the meaing of converting normal vector to world space?

Code (CSharp):

1.             struct a2v {
2.                 float4 vertex : POSITION;
3.                 float3 normal : NORMAL;
4.             };
5.            
6.             struct v2f {
7.                 float4 pos : SV_POSITION;
8.                 fixed3 color : COLOR;
9.             };
10.            
11.             v2f vert(a2v v) {
12.                 v2f o;
13.                 // Transform the vertex from object space to projection space
14.                 o.pos = mul(UNITY_MATRIX_MVP, v.vertex);
15.                
16.                 // Get ambient term
17.                 fixed3 ambient = UNITY_LIGHTMODEL_AMBIENT.xyz;
18.                
19.                 // Transform the normal from object space to world space
20.                 fixed3 worldNormal = normalize(mul(v.normal, (float3x3)unity_WorldToObject));