How may the aid of modern science, logic, and personal observation help in discovering God?

Both science, logic, and personal experience will help in the discovery of God.

In Bhagavad Gita God has give a process by which He can be understood as He is. It is a scientific process called bhakti, or devotion to God. It is scientific because it can be tried and tested and verified like any other science.

By executing devotional service to Krishna, one will get personal experience of God.

Some people will object, so to know God we first have to surrender to His service. I’m not willing to do that. I want that God manifests Himself to me, before I will serve Him.

But that’s like telling one’s professor at the university - I don’t want to follow your directions in mathematics, I want to have a clear understanding of mathematics, before I surrender to the process of learning mathematics.

To learn anything in this world, one must learn from an authorized teacher. Similarly, to understand God, one must surrender to the process of bhakti, as directed by the spiritual master, which will reveal God to a person.

Krishna says:

My dear Arjuna, only by undivided devotional service can I be understood as I am, standing before you, and can thus be seen directly. Only in this way can you enter into the mysteries of My understanding. —Bg 11.54

Srila Prabhupada explains:

Krishna can be understood only by the process of undivided devotional service. He explicitly explains this in this verse so that unauthorized commentators, who try to understand Bhagavad-gita by the speculative process, will know that they are simply wasting their time.

No one can understand Krishna or how He came from parents in a four-handed form and at once changed Himself into a two-handed form. These things are very difficult to understand by study of the Vedas or by philosophical speculation. Therefore it is clearly stated here that no one can see Him or enter into understanding of these matters.

Those who, however, are very experienced students of Vedic literature can learn about Him from the Vedic literature in so many ways. There are so many rules and regulations, and if one at all wants to understand Krishna, he must follow the regulative principles described in the authoritative literature. One can perform penance in accordance with those principles.

For example, to undergo serious penances one may observe fasting on Janmastami, the day on which Krishna appeared, and on the two days of Ekadasi (the eleventh day after the new moon and the eleventh day after the full moon). As far as charity is concerned, it is plain that charity should be given to the devotees of Krishna who are engaged in His devotional service to spread the Krishna philosophy, or Krishna consciousness, throughout the world. Krishna consciousness is a benediction to humanity.

Lord Chaitanya was appreciated by Rupa Gosvami as the most munificent man of charity because love of Krishna, which is very difficult to achieve, was distributed freely by Him. So if one gives some amount of his money to persons involved in distributing Krishna consciousness, that charity, given to spread Krishna consciousness, is the greatest charity in the world.

And if one worships as prescribed in the temple (in the temples in India there is always some statue, usually of Vishnu or Krishna), that is a chance to progress by offering worship and respect to the Supreme Personality of Godhead. For the beginners in devotional service to the Lord, temple worship is essential, and this is confirmed in the Vedic literature (Svetasvatara Upanisad 6.23):

“One who has unflinching devotion for the Supreme Lord and is directed by the spiritual master, in whom he has similar unflinching faith, can see the Supreme Personality of Godhead by revelation.”

One cannot understand Krishna by mental speculation. For one who does not take personal training under the guidance of a bona fide spiritual master, it is impossible to even begin to understand Krishna. The word tu is specifically used here to indicate that no other process can be used, can be recommended, or can be successful in understanding Krishna.

The personal forms of Krishna, the two-handed form and the four-handed, are described as su-durdarsam, very difficult to see. They are completely different from the temporary universal form shown to Arjuna. The four-handed form of Narayana and the two-handed form of Krishna are eternal and transcendental, whereas the universal form exhibited to Arjuna is temporary.

The words tvad anyena na drsta-purvam (Text 47) state that before Arjuna no one had seen that universal form. Also, they suggest that amongst the devotees there was no necessity of showing it. That form was exhibited by Krishna at the request of Arjuna so that in the future, when one represents himself as an incarnation of God, people can ask to see his universal form.

The word na, used repeatedly in the previous verse, indicates that one should not be very much proud of such credentials as an academic education in Vedic literature. One must take to the devotional service of Krishna. Only then can one attempt to write commentaries on Bhagavad-gita.

Krishna changes from the universal form to the four-handed form of Narayana and then to His own natural form of two hands. This indicates that the four-handed forms and other forms mentioned in Vedic literature are all emanations of the original two-handed Krishna. He is the origin of all emanations.

Krishna is distinct even from these forms, what to speak of the impersonal conception. As far as the four-handed forms of Krishna are concerned, it is stated clearly that even the most identical four-handed form of Krishna (which is known as Maha-Vishnu, who is lying on the cosmic ocean and from whose breathing so many innumerable universes are passing out and entering) is also an expansion of the Supreme Lord. As stated in the Brahma-samhita (5.48),

"The Maha-Vishnu, into whom all the innumerable universes enter and from whom they come forth again simply by His breathing process, is a plenary expansion of Krishna. Therefore I worship Govinda, Krishna, the cause of all causes."

Therefore one should conclusively worship the personal form of Krishna as the Supreme Personality of Godhead who has eternal bliss and knowledge. He is the source of all forms of Vishnu, He is the source of all forms of incarnation, and He is the original Supreme Personality, as confirmed in Bhagavad-gita.

In the Vedic literature (Gopala-tapani Upanisad 1.1) the following statement appears:

"I offer my respectful obeisances unto Krishna, who has a transcendental form of bliss, eternity and knowledge. I offer my respect to Him, because understanding Him means understanding the Vedas and He is therefore the supreme spiritual master."

Then it is said, krsno vai paramam daivatam: "Krishna is the Supreme Personality of Godhead." (Gopala-tapani Upanisad 1.3)

Eko vasi sarva-gah Krishna idyah / eko 'pi san bahudha yo 'vabhati: "That one Krishna is the Supreme Personality of Godhead, and He is worshipable. Although He is one, He is manifested in unlimited forms and expanded incarnations." (Gopala-tapani Upanisad 1.21)

"The Supreme Personality of Godhead is Krishna, who has a body of eternity, knowledge and bliss. He has no beginning, for He is the beginning of everything. He is the cause of all causes."

In the Vishnu Purana (4.11.4) it is said, yatravatirnam Krishnakhyam param brahma narakrti: "The Supreme Absolute Truth is a person, His name is Krishna, and He sometimes descends on this earth." Similarly, in the Srimad-Bhagavatam we find a description of all kinds of incarnations of the Supreme Personality of Godhead, and in this list the name of Krishna also appears. But then it is said that this Krishna is not an incarnation of God but is the original Supreme Personality of Godhead Himself (ete camsa-kalah pumsah Krishnas tu bhagavan svayam).

Similarly, in Bhagavad-gita the Lord says, mattah parataram nanyat: "There is nothing superior to My form as the Personality of Godhead Krishna."

He also says elsewhere in Bhagavad-gita, aham adir hi devanam: "I am the origin of all the demigods."

And after understanding Bhagavad-gita from Krishna, Arjuna also confirms this in the following words: param brahma param dhama pavitram-paramam bhavan,

"I now fully understand that You are the Supreme Personality of Godhead, the Absolute Truth, and that You are the refuge of everything."

Therefore the universal form which Krishna showed to Arjuna is not the original form of God. The original is the Krishna form. The universal form, with its thousands and thousands of heads and hands, is manifest just to draw the attention of those who have no love for God. It is not God's original form.

The universal form is not attractive for pure devotees, who are in love with the Lord in different transcendental relationships. The Supreme Godhead exchanges transcendental love in His original form of Krishna.

Therefore to Arjuna, who was so intimately related with Krishna in friendship, this form of the universal manifestation was not pleasing; rather, it was fearful. Arjuna, who was a constant companion of Krishna's, must have had transcendental eyes; he was not an ordinary man.

Therefore he was not captivated by the universal form. This form may seem wonderful to persons who are involved in elevating themselves by fruitive activities, but to persons who are engaged in devotional service the two-handed form of Krishna is the most dear.