If we see, each of the god in Hinduism has some quality. For example, we say that lord Ganesha is a god of Wisdom, lord Shiva is for destruction, Hanuman for strength and so on.. They signify these traits in some or the other way...
Hence the question arises that why each of the god has some special quality about them and why they can't be one?
If lord Brahma is the creator then why he cannot destruct or maintain instead of Shiva and Vishnu doing those tasks? So the question is why not a single god but various gods with particular significance (quality) about them?
To give more examples :-
Lord Shiva - Destroyer
Lord Brahma - Creator
Lord Vishnu - Maintainer
Lord Hanuman - Strength
Lord Ganesha - Wisdom / Wealth(Riddhi Siddhi) / Knowledge
Goddess Saraswati - Knowledge
Goddess Laxmi - Wealth
Kubera - Wealth
Yama - Death
Kamadeva - Human Love
So as we see, each of the god is specific to one work, no common trait, they are unique in their own ways and they are not recognized for any other thing.
For example, no one will say that lord Shiva is a god of Wisdom / Wealth. Also am sure if lord Brahma can create then he can certainly destroy but no, we have a separate god for that task so why is that so?
Ramakrishna Parmahamsa gave the example of a man who is a judge. When he goes into the courtroom he is seen by the people present as a judge. When he comes home his wife sees a husband. His children sees him as a father.
It is all the same person, the different perceptions are in the eye of the beholder. God is one. "Ekarh jyotir bahudha bibhati - The one Light appears in diverse forms" (Atharva Veda).
Many people actually believe that all of these Devas simply represent various forms or aspects of a single central God. This single God is commonly interpreted as Brahman, Trimurti, or MahaVishnu depending on who you ask.
The other common interpretation is that these Devas are not truly immortal dieties, but rather posts which may be occupied by jivatmas with extremely high karma. In other words, the work of running the universe has been smoothly delegated amongst all of these Devas. The reason that they don't double up on the work is simply because it's not their job. Brahma does not destroy anything because even though its within his ability, its his job to create and destruction on his part would interfere with Shiva's work.
That being said, to some degree there actually is a bit of overlap in qualities (i.e. not all of these traits are unique to the Deva that describes them). For instance, both Saraswati and Hayagriva are worshiped as deities of knowledge.
Finally, it's worth considering the fact that many of the more frequently worshiped Devas actually do take on many forms, to represent several qualities. For example, as @Kedarnath pointed out, Rudra and Natarajan both represent very different traits, but they are both forms of Shiva.
Let us first check what Hindu scriptures say about the Divine.
Mahabharata Santi Parva Section CCLXXX says, "Know that this entire
universe is under the control of one divine Being. The Veda that is in
the soul.......regards the unity of various creatures. When a living
creature realizes this unity in consequence of true knowledge, he is
then said to attain to Brahman".
What is the status of Brahma, Vishnu and Rudra/Shiva?
Mahabharata Vana Parva Section CCLXX says," The Supreme Spirit hath
three condition, In the form of Brahma, he is the Creator, and in the
form of Vishnu he is the Preserver, and in his form as Rudra, he is
the Destroyer of the Universe".
Brahma, Vishnu and Rudra/Shiva are simply three names and forms of Brahman.
One can extend this even further and say that all the other Devatas are simply different names and forms of Brahman, i.e., different aspects of Brahman.
In all the answers above, although there is stress on God as One philosophy, there is a lack of appreciation of critical differences among different forms of God, as asked in the Question. I'd try to address that.
We must understand that primary role of Major Gods like Brahma-Saraswati, Vishnu-Lakshmi, Shiv-Shakti (along with others) is to run this universe in a grand sense. These forms, therefore, are genesis of this requirement (otherwise supreme God is happy being as One only!). Having appreciated that, Can Brahma destroy this world? Perhaps No. When the Time will come to destroy this world, Brahma won't be able to do it because He is too attached to its own progeny. Therefore, the very trait of Brahma being creator inhibits the development of destroyer in Himself. I think this is very important to realise that one trait can be incompatible with other.
Vishnu, not Brahma, is the taskmaster who runs this universe according to dharma. I think the analogy could be that of Guru and Parents. Why can't parents become teachers of their own children, even if they are learned? Upholding dharma requires Danda, manipulations, avatars and many more which neither the creator Brahma nor the destroyer Shiva appreciates much. Shiva, on one hand is happy to let things go on their own ways while Brahma is too lost in the beauty of its own creation. Only Vishnu can hold the destroyers of Dharma by neck and establish it again and again. Without Vishnu, creation and destruction of world will become every yuga's affair. Think about that!
Shiva is neither concerned about how this world came into picture nor how it is being run or should be run. His only concern is people should not cross their limits so as to disturb the equilibrium of this universe else he will stamp his presence and destroy the root of the problem. He is happy to go back to his Samadhi again after the job is done. Can world be run like this? As I said before, if Vishnu is not there such destructions by Shiva will become inevitable at the end of every Yuga, when Dharma starts sharply losing its value. Can Vishnu be destroyer of this Universe? No. Perhaps Vishnu will always be involved into how to run it, and that no matter what he can always run it. Besides, Being involved with its people so much, he is also in the same situation as Brahma : too much attached to its own subjects. Therefore, only a Sanyasi Shiva is fit to become destroyer of this world, neither Vishnu nor Brahma.
Therefore, we see that creation of Brahma, Vishnu and Mahesh by Supreme God is not by chance but by design. It is only by appreciating these different aspects of Supreme God that we will be able to understand the Supreme God as much as possible. That's why Gods like Vishnu and Shiva have sahastranaam, which describes the same God in so many different ways, each being unique and essential. Whereas God is one, it is by learning its different aspects that we get closer to Him.
The one fact that is common through the ages of Hinduism and our Holy Books, is that God resides in everything that is perceivable in three dimensions for humans, but if you dive deep with the mantras and stotras the people who acquired knowledge say that anything perceptible and imperceptible in Three and higher dimensions, are nothing but an instance of God.
If you give it a thought, all the religions worship a common belief of God as a light or energy. In Islam and other religions they have generalized that there's only one God and I respect these beliefs.Whereas, in Hinduism every aspect of the human life either good or bad is considered as an instance of God.Hence every God has a personality or a vibe associated with it.
Every Hindu God has a distinctive set of features and each of them isn't limited to a human form and values, say for example, you visit a rare place in the wilderness and you find immense peace and a sense of liberation there, what you are experiencing there is Lord Shiva's calm state or Maa Saraswati's calm and serenity.Also, when you are in deep sleep or 'Yog Nidra' you don't perceive anything, you experience Lord Shiv's 'Chitta' state, where you are exposed to the realm that the 'Yogis' and 'Buddhas' were stating through the ages, that "nothing is real", "everything is a perfectly simulated experience", "all we have to do is seek the truth and beware that we don't wander off into the circus that the human society and the mind creates, how much ever they force us to".God comes in all forms and mediums, if you watch a picture, a video, meet a person, visit a serene place, introspect and gain wisdom then you've experienced the wisdom of Lord Ganesh,Maa Saraswati,Maa Gayatri.
The reason us Hindus bow before entering a Temple, or in that case any positive place is to acknowledge and worship the presence of Maa Saraswati and Maa Gayatri's positivity and purity.So if you come across any place, person,object,thought that imparts knowledge or positivity or any other Godly element do bow or at least acknowledge its presence and be glad that you had a chance and the level of awareness, to experience it.
One thing that is constant through the tides and ebbs of the Time and Religion, is that people have grown less conscious,intellect and aware, actually to state the truth people have just grown dumb.It sometimes saddens me to see how religion is used to do the things that it strongly condemned.
Just to summarize, God is everywhere and certainly in the vibes and experiences.
Just to teach you something from Hinduism, "Be Humble". Be humble to family,people,animals and their lives,be humble to nature,to environment,to the whole universe and be humble to yourself.Realize the essence of God around you and thank him for giving you the marvel of this universe called "Life".
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