Why do we apply Vibuthi ( 3 horizontal lines) and What does it signify?
Does it deal with more than religious beliefs?
The significance of Bhasma is well explained by Lord Shiva himself in the Linga Purana as follows:
Significance of Bhasma: Bhagavan Shiva further analysed the significance of Bhasma which was product of Agni Karyaas like daily homas and Yagnas; the burning of ‘Sthavara Jangamaas’ by Fire would result in Ash:
Bhasmattadvihitam Sarvam Pavitramidamuttamam,
Bhasmaanaa Veeryamaasyaaya Bhutaani parishanchati/
Agnikaaryam cha yah krutwaa karishyati triyaayusham,
Bhasmanaa mama veeryena muchyatey Sarva kilbishey/
Bhaasatey –tyeva yadbhasma shubham bhaavayatey cha yat,
Bhakshanaat Sarva ;paapaanaam bhasmeyti parikeertitam/
Ushmapaah Pitaro Jneyaa Devaa vai Somasambhavaah,
Agnishomaatmakam Sarvam Jagarsthaavara jangamam/
Ahamagnirmahaa tejaah Somaschaishaa Mahaambikaa,
Ahamagnischa Somascha Praktrutyaa Purushah Swayam/
Tasmaadbhasmam Mahaa Bhaagaa madveeryamiti chochyatey,
Swarveeryam vapushaa chaiva dhaarameeti vai sthitaya/
Tadaaprabhruti lokeshu rakshaarthamashubheshyucha/
Bhasmaanaa kriyatey raksha sutikaanaam gruheshucha/
Bhasmasnaana vishuddhaatmaa Jita Krodho Jitendriyah,
Matsameepam Samaagamya na bhuyo vinivartatey/
Vratam Pashupata yogam kapilam chaiva nirmitam,
Purvam Pashupatim hyetannirmitam tadanuttamam/
(Uttama Bhasma is produced by the scorching of the wood of trees and other materials of Nature. Shiva stated that by way of Bhasma, he carried his virility to human beings. Bhasma generated by Agni Karyaas while reciting the Mantras like ‘Triyaamshu’ is basically is the bye-product of Shiva’s ‘veerya’ and demolishes all kinds of Sins. This ‘bhasita’ or the radiant product emerges from Shiva’s Body and is responsible for the Bhakshana of Mahaa Paapaas and hence it is called Bhasma. Mahadeva futher explained that the word ‘Ushmapa’ or hot and burnt material is ‘Pitreeshwar’ or the material consumed by the Lord of Pitraas, while Devataas consume Amrita or Soma Rasa; Agni is of Soma Swarupa; Shiva is Agni and Soma rupi is Devi Ambika; Shiva is Purusha and Ambika is Prakruti. This is the reason why Bhasma is called Shiva’s veerya as his Veerya is generated from Shiva’s body. Thus Bhasma destroys Evil and Inauspiciousness / ‘Ashubha’ anywhere especially in households; any person taking a bath and applies Bhasma is stated to be eligible for performing the Sacred Paashupata Vrata Kapila Yoga and is assured of Bandha vimochana or the shackles of Samsara to Shiva Loka.
BTw,it should be noted that vibhuti is sacred to Shaivites,sandal paste is likewise to Vaishnabas and kumkumam to the Shaktas.
Significance of Bhasma & how to properly wear it is also described in the Devi Bhagavata Purana ;
Use of Bhasma ( ash), preferably by the Fire oblation performed by Brahmanas themselves or atleast by burnt remains of cow dung, is to be smeared on forehead , shoulders and chest is as important as wearing Rudrakshas. Soon after bath, the use of Bhasma mixed with water drops as three curved lines be applied first as two top lines by the middle finger and ring finger from left to right and then the lowest line by the thumb from right to left. The applications of bhasma is to be done thrice a day, before the Tri-Sandhya Gayatri Japas.
Then apply Bhasma as prescribed above. If Bhasma is not applied, Brahmanas are not entitled to perform ‘Sandhavandana’or Gayatri Japam. Contrarily, no sin could enter the body once Bhasma is applied as prescribed. This is why Brahmanas take care to apply the Tripundra by the use of the three fingers as the ring finger represents as A, the middle finger represents U and the fore finger represents M from the Pranava Mantra OAM. At the same time however, any person irrespective of caste could use ‘Vibhuti’ ( not the Bhasma as disinguished above ie. from Yajna fire or from dried cow dung burnt) and the application of vibhuti has far reaching beneficial impact
Devotees of Shiva hence apply three horizontal lines of Vibhutis and when conjoined with a red kumkumam dot at the centre it represnts the union of Shiva & Shakti which is the cause of everything in the manifested and unmanifested creation.
Shiva grants bhasmasur a wish that if he keeps his palm on anyone's head then they will be destroyed and turned into ashes. Once he keeps his palm on his head himself and turns into ashes. This is the reason of using vibhuti.
This is the story of bhasmasur. He was granted a wish by Shiva i.e; if he touches his palm on others head they are drawn into ashes. Once he touches his own head by his palm he turn into ashes.
If Bhasma is not applied, Brahmanas are not entitled to perform Gayatri Japam. Contrarily, no sin could enter the body once Bhasma is applied as prescribed.
The connotation of Vibhuti is that it is used as a symbol for remembrance of death, the final destiny of the body. So, that is its significance:
Shiva’s temple is the consciousness.
Shiva is not in the stones or in temples, he is in the consciousness of the human beings.
Our body all becomes ashes, so ash signifies the last, the ultimate.
Vibhuti does not mean the ashes one puts on the head.
Excerpts from a talk by Sri Sri Ravi Shankar: https://xa.yimg.com/kq/groups/17184919/.../understandingshiva.pdf
Vibhuti is a purifying ash. If you notice how it makes your nervous system feel when you apply it, it is felt to be calming and uplifting. A major reason for wearing holy ash, vibhuti, is that when we have it on we can be seen by the devas in the inner worlds. It also identifies us as a devotee of Siva.
Look at the portion of where you apply the Vibuthi. It is just around the space between eyebrows. The space between eyebrows is very significant in spirituality. There's a lock in the space between eyebrows.
This is referred by VALLALAR RAMALINGASWAMY in his writing THIRUVARTUPA as "KAN PURUVA PUTTU". PURVAM meaning is = eyebrows. KAN Here refers to Spiritual eye. The lock of spiritual eye.
In Tantra/Yoga path, to break the lock of between eyebrows, they stop the Pranan in space between eyebrows to open the lock. Agastya gives symbolically on how to stop this Pranan in between eyebrows. "One who knows 8 & 2, he is half Guru". You can refer this on Agastya 12000, and also on Antharinga Diksha Nool of Agastya where he speaks to his disciple Pulastya.
So for ordinary householders life, the Vibuthi which is made of cows, sanam, we believe if we apply it regularly in space between eyebrows we can open the lock. So basically the practice is to open the lock so that our inner spiritual nature reveals itself and we leave the body via the path of Brahmandhara so one attains Moksha. Also for this worldly life, we get proper Wisdom in leading our life here.
I cant find specific quote from sites on Agastya songs. So I have given reference on book which is even now available in shops.