This is a great short article - from Hugh Ross and Reasons.org - pondering the so-called "hiddenness" of God. I've talked about this before - that why would a God who WANTS us to know Him obscure Himself - at least directly so. Why doesn't He just part the clouds and say, "Here I am!" Or an occasional, "Peekaboo!" Of course, Believers all know of Him have a strong sense of His presence (even if it wanes from time to time), if indirectly from their experiences and the powerful evidences He has left all over His creation. Believer can cite where they seem Him and the ways they've experienced Him - and sometimes, thought rarely, miraculously so.
I actually think there are two aspects of God's hiding, that are very different. God has always been mysterious - and it wasn't until He took on humanity in the form of Jesus that man first truly saw Him close up and talked to Him as one would talk to another man.
"Truly, you are a God who hides himself, O God of Israel, the Savior." (Isaiah 45:15)
Remember the childhood game of hide and seek - with the object of the game is to find the one hiding by SEEKING them. And I think that's got a lot to do with why unbelievers can see or experience Him - as they fail to seriously open their hearts and minds to actually seeking him - typically doing the opposite, either avoiding or denying Him (either denying His existence or WHO exactly He is). So, I think there are several reasons for God remaining "hidden" from unbelievers. One is, He has ALREADY redundantly revealed His existence to us through things He's made, beginning with the Creation of the Universe.
"For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse." (Romans 1:20)
God tells us in multiple places in Scripture He CAN be found if we'll only seek Him - just as the Roman Centurion Cornelius did, as God sent Peter to witness to Him. Why? Because he earnestly sought and desired to know God. So, God has ALREADY provided ample evidences of Himself AND many powerful evidences of Himself - but people want Him to reveal Himself per THEIR desired methods. But the first thing that is necessary to find and perceive God is to not close off one's heart and mind to Him. God will not FORCE Himself upon a person. So, the means to find Him are available, but people fail to want to seek Him. And seeking God is as easy as exercising our own breath to addressing Him.
"And without faith it is impossible to please him, for whoever would draw near to God must believe that he exists and that he rewards those who seek him." (Hebrews 11:6)
Lastly, people assume that if God directly showed Himself and His power that they would desire and love Him, follow Him - if only ... But when God showed up in the flesh, doing wondrous and unbelievable miracles, many still would not open their hearts to Him - with the religious leaders cooking up schemes to kill him, and with claims His miracles were done via demonic power. They saw God in the flesh, but remained hardened in their hearts and minds (of their OWN doing - and thus they remained blind to the truth of WHO He was!). Mighty miracles humiliated the demonic host and "false" gods of the Egyptians, freeing Israel after four centuries of brutal slavery and backbreaking labors - how long was Moses out of camp before the Israelites began grumbling and making a golden calf idol to worship. So, many assume, "If only God did this or that, THEN we would believe." But God knows better - that physically or miraculously showing Himself won't necessary change people's hearts - least not the ones determined to resist Him. He also knows mere belief is not a salvation-seeking desire to know Him. So, God has provided other pathways to know of His existence and to seek relationship with Him - as He says, "MY ways are not YOUR ways!"
Others feel free to share your thoughts on this "invisibleness / hiddenness" of God.
