"The one who looks at me is seeing the One who sent me." (John 12:45)

What does Jesus mean by 'the one who looks at me'?

Here Jesus is describing someone who trusts in Jesus and understands who Jesus is. The phrase, 'one who looks at me' is describing someone having some understanding of Jesus.

This verse continues from Jesus' previous statement:
"Whoever believes in me does not believe in me only, but in the One who sent me." (John 12:44)
As mentioned with that verse, the word "believe" does not mean to believe in Jesus' existence. He was standing in front of those he was speaking to, so they certainly knew he existed. Rather, "believe" is translated from the Greek word πιστεύω (pisteuō), which means "to think to be true, to be persuaded of, to credit, place confidence in" according to the lexicon. 

So Jesus is speaking of trust here. He is talking about someone trusting in what he was teaching.

What does 'seeing' mean here?

Jesus is not talking about seeing with the eyes here. He is standing in front of those he was speaking to, and certainly, they could all see him with their eyes. "Seeing" is being translated from the Greek word θεωρέω (theōreō), which can mean to see physically with the eyes, but also to 'perceive, 'consider' or 'ascertain' (understand) according to the lexicon.

Jesus is speaking of the ability to see a little deeper here.

We could compare this to how a government official from one country might see an ambassador from another country. The government official doesn't just see the person standing in front of them when they meet. The official understands that the ambassador is an emissary of his government. The ambassador represents his government, and he was sent by his government.

The government official understands this as they meet. If the government official were to abuse or embarrass such an ambassador, the government who sent the ambassador would become upset. This could disturb the relationship between the two governments. Thus the government official treats the ambassador with the kind of respect deserving of the government the ambassador represents.

Jesus is in the same role as the ambassador, with respect to the Supreme Being. Jesus is not to be seen as the Supreme Being, or as the Supreme Being turned man - as taught by some. Jesus, as he clarifies here, was sent by the Supreme Being. He is representing the Supreme Being. He is speaking for the Supreme Being.

This means that while we should give Jesus due respect as God's representative, it would be improper to think of Jesus as God. Just as it would be rude for the government official in the example above to greet the ambassador as the president of his country. Doing so would insult that country's real president, as well as insult the ambassador and his country.

This was made clear by Jesus when he said:
"Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but only he who does the will of my Father who is in heaven. Many will say to me on that day, 'Lord, Lord, did we not prophesy in your name, and in your name drive out demons and perform many miracles?' Then I will tell them plainly, 'I never knew you. Away from me, you evildoers!'" (Matt. 7:21-23)
So Jesus is more than a little upset with those who confuse Jesus with God. He wants them to get away from him. He is calling them "evildoers."

Why are they 'evildoers'?

Aren't they going to church every Sunday, giving alms, spreading their version of the "gospel" and "healing" people in Jesus' name? Isn't that okay?

Jesus is clarifying the criteria: Only those who do the "will of my Father who is in heaven." are pleasing to Jesus.

This means that Jesus is not pleased with the teachers who virtually ignore God while they ask their followers to sentimentally cry out "I am saved" and other such monikers.

Meanwhile, they ignore Jesus' instruction to do God's will and virtually ignore God. Many consider "God the Father" as some vague force that became a man. That is ridiculous. God never has to become a man. God is always the Supreme Being. He never has to come under the confines of the physical dimension. He created the physical dimension.

Is God an old man with a long white beard?

Others think of the Supreme Being as this old man with flowing gray hair and a long white beard. As if God is so old that he must have wrinkled skin and gray hair. God created time and designed the aging process. Why would He - their controller - be subject to them?

Both of these speculative perceptions of the Supreme Being are incorrect. God is beyond the confines of the physical world, yet He is a Person. Consider again Jesus' statement above:
"Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but only he who does the will of my Father who is in heaven."
This clearly indicates that God is a Person "who" resides in the "kingdom of heaven" and "heaven" is located outside the physical world. If the "kingdom of heaven" were on the earth now or in the future, why would Jesus refer to God being in the "kingdom of heaven" in the present tense; and why would some people be able to go there while others cannot? 

This also relates to seeing the Supreme Being. If God's "kingdom of heaven" were here, why does Jesus speak of going there?

This can also be seen within the question many ask:

Why can't I see God?

We want to see the Supreme Being with our physical eyes but we can't. Some of us even challenge God's existence, proclaiming that if we can't see God, He must not exist. This exhibits our perceived self-importance and our assumption that our senses can perceive everything in existence.

Have we ever considered that maybe God doesn't want us to see Him?

God doesn't want us to see Him because we don't really want to see Him. This is why we are here in this physical world, operating these temporary physical bodies. Our physical bodies were designed not to perceive God because we wanted to get away from God. We wanted to do our will, not His. We wanted to enjoy life without God. So He simply granted our wish.

This also means that we also cannot accurately speculate about God. Because we are currently separated from God, we cannot see Him with these physical eyes or physical mind. Because our mind is a recording device of the senses, the mind also cannot perceive God. We, therefore, cannot use our minds and the experiences of our senses to imagine Him. He resides personally in the spiritual world - a place not governed by time and physical space, and thus outside the range of our physical senses.

Still, we know from Jesus' statements that God is an individual Person. Anyone who has a separate will is an individual, and anyone who wills is a person because a will requires a personality.

Also, we know that God's will is different from our will because some people do God's will and others won't. This means that His will is distinct from ours. We can choose to do His will or not.

Can the mind imagine God?

Conjuring up an imaginative speculative vision of God within the mind is not seeing God. It is seeing what we want to see. The best way to reliably "see" (perceive) God with our physical senses is by hearing from God's representative. We can know God through His messenger, as He is introduced and described by those who love Him.

For example, we can know from God's messengers that God enjoys relationships and enjoys exchanging love. God wants our love. We can see that by simply hearing the teachings and observing the activities of God's messenger. This is illustrated by Jesus' most important instruction:
“‘Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment." (Matt. 22:37-38)
This instruction communicates that love for God is not just a sentimental feeling. Many will even say whimsically, "Oh, I love God." But do they even know who God is? Loving God as defined by Moses, Jesus and other representatives of God means dedicating our lives to Him. It means doing what pleases the Supreme Being on a practical basis. 

This is why it was important to Jesus to do God's will - as mentioned in the verse above. Pleasing God was Jesus' highest priority, because Jesus loves the Supreme Being and wants to please Him.

Because loving God requires knowing God, we will see the Supreme Being when we too want to please Him.