Yes, "simulation theory" has been around since the time of Plato, though Plato didn't think of it in digital terms.

Scientists of all stripes believe we live in a simulation. Elon Musk, for instance, thinks there's a one-in- billions chance we're living in "base reality," or actual reality. Neil deGrasse Tyson puts our odds at living in a simulation at "better than 50/50."  

Various clues point us to the fact that we are. For instance, the double-slit experiment shows that particles behave differently when observed vs. when they're left unobserved. Almost as if they're changing behaviors based on whether or not they're being watched... as if these particles know. This change of behavior during observation suggests something similar to what happens during video games, a rendering of reality happens when we look at something and only when we look at something in order to save processing power. 

You'll find a lot of physicists seem to believe we're living in a simulation. Physicist and cosmologist Max Tegmark has written quite a bit on the mathematical nature and precision of the universe, suggesting its structure is mathematical, much like a game program would be. Nobel laureate Eugene Wigner called this the “unreasonable effectiveness of mathematics in the natural sciences.”

Nobel Prize-winning astrophysicist George Smoot believes we live in a programmed universe, and even delivered a TED Talk titled “You Are a Simulation & Physics Can Prove It.” Physicist Martin Savage notes that anomalies found in particle physics such as limitations in high-energy cosmic rays could indicate a "resolution" to our universe not unlike pixels on a screen. 

The precision of the strength of gravity or the speed of light, and the ratio of matter to antimatter is so precise that physicist Paul Davies said, “The impression of design is overwhelming.”

I'm with Musk, all things considered. The chances that we're living in a base reality are low, but I don't need science to tell me that... although it helps. 

The idea that we're living in a simulation is already something discussed in the Bible. In fact, if you change up Christian lingo a bit so it looks more like we're talking about a digital programmer, you'll find we talk about living in a simulation a lot. 

Paul already spilled the beans in 1 Corinthians 13:12 when he said, “For now we see only a reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known.”

In Hebrews 8:5, you'll see more talk of a "shadow" with “They serve at a sanctuary that is a copy and shadow of what is in heaven.”

C.S. Lewis picked upon this as well, referring to our world as a "Shadowland." He writes about it in "The Weight of Glory": 

“At present we are on the outside of the world, the wrong side of the door. We discern the freshness and purity of morning, but they do not make us fresh and pure. We cannot mingle with the splendors we see. But all the leaves of the New Testament are rustling with the rumor that it will not always be so. Someday, God willing, we shall get in.”

We often hear about the temporary nature of this world and the completeness of the word resided in by God. In 2 Corinthians 4:18, it says “So we fix our eyes not on what is seen, but on what is unseen, since what is seen is temporary, but what is unseen is eternal.” 

God is often seen as a father figure, which He absolutely is, but what's not often talked about is his abilities from a scientific point of view. We use the term "creator" as a catch-all descriptor and then picture Him as an old bearded man sitting in the clouds like Zeus. Strip away all that human dressing and what we have is what amounts to a cosmic mathematician whose talent and skill is such that he can order the function of an entire universe, from its massive black holes down to its tiniest molecule, and on a universal scale. 

He has written the code of the universe, and he can interact with that code, alter and improve it at any point in the spacetime of the simulation. He even brought himself into his simulation at one point in time to use Himself as a corrective code to fix a massive error in the system. Before He did that, He would rewrite code from within the simulation at will, producing what we refer to as "miracles." 

For instance, when Christ fed 5,000 people near Bethsaida with five  loaves of bread and two fish, Christ just rewrote the code, so the value of the given food was enough to feed everyone present. One can imagine Christ simply entering commands through mere word, and the code of the universe altering itself to His will in order to accomplish the task.

Physics suggest we're living in a program, and the Bible seems to agree and points to the programmer. 

I'm not suggesting that God is working with mere ones and zeroes. Something on this scale is more complicated than binary digital programming, and God is far more powerful and capable than what you see on a computer screen, but I do believe that what we're living in is His creation, and we're told it's something that mirrors His world but not in a complete way. 

I find this idea entirely fascinating, but as a Christian, not that surprising. This world we're living in is hardly the most astounding thing we'll ever see according to the Scriptures, and that's because this is merely something akin to a simulation. It has rules that govern its movements, limitations, and even a glitch or two here and there. I'm sure you have your own stories of seeing something odd happening that you know wasn't normal. 

So logically, yes, we do live in a simulation... but we've known that for ages. 

Here's an interesting thought to drive this further. God told us He made us in His image, but it's hard to think that He simply meant that in a physical capacity. Did He mean to say that He made us to be little programmers like Him? If so... we're certainly a chip off the ol' block. We are, as a species, habitual programmers, and on various levels. We program animals through behavioral conditioning, we program each other through raising children, ads, and storytelling. Yes, we also program actual programs, and we seem to have an insatiable urge to create programmable intelligence in AI. 

Could we, one day, access the code of the universe from within it as Christ did? Psalm 82:6 says,  " I have said, Ye are gods; and all of you are children of the most High," and this was repeated by Christ in John 10:34 who said “Is it not written in your Law, ‘I have said you are “gods.”

I think if we were to look at the universe as a program and God the programmer, who used fixed mathematical formulas to dictate the goings-on of our simulation, we "little gods," as Lewis called us, may find the base code of the universe. We could understand the very program we live in, and as little programmers who take after our Father, begin working within the program to achieve great works.