How big would the brain of an omnipresent being be?

Question

There is a being who has been alive for as long as there has been life on earth. It has the ability to anomalously produce matter from its body out of nothing. Through the production of microfine strands of flesh dotted with tiny eyes, it has the ability to see and be cognizant of everything happening on every square micrometer of planet earth, all at once.

It needs a brain large enough to store all of this information, since it wants to remember everything that has ever happened on earth.

Presuming it uses storage space with the same efficiency as a human brain, approximately what volume/size would a brain have to be to remember everything that has ever happened on earth from the dawn of life to present day, and that brain was only used for storing memories? Would it be planetary or celestial in size, or relatively small enough to be kept on earth?

Answer 1

Storing the Earth using optimized storage methods.

Since the OP says the eyes can only see the "surface" of the Earth, we can assume that we do not need to capture the complex inner workings of the oceans or clouds, just the surface level. It's hard to estimate what the actually complexity of Earth's average surface is but, let's be REALLY generous and say that you will have an average of 100 surfaces you need to capture per unit area of the Earth's surface. If you want to assume a top-down projection of the Earth, then you can just remove 2 orders of magnitude from all of my following results.

This puts your total pixel data at ~5e26... and when you add in things like wire-frames, normal maps, etc. that 3-d models would need as additional overhead, you are looking at something closer to 1.1e27 bytes of data per frame... but we are not done here.

Most of the Earth's surface is either organic or mineral. Both of these things form highly repetitive patterns that are very easy to resample in other parts of your image. Your average exterior cell for plants and animals for example is 10-100 micrometers. Meaning if you find one type of cell, you can store a library of a few dozen to a few million samples of that kind of cell depending on how much fidelity you need and be able to generate a nearly lossless image all the way down to the micrometer scale.

Since a single plant can have a surface area of trillions of micrometers, but often has less than 10 kinds of surface cells, it means that a single plant can have enough repeating textures to make a 1 million sample library of each cell type increasing texture compression by 5 orders of magnitude, but if you then reuse that library across all of the trillions of instances of that plant before it evolves enough to need to resample, you could be looking at a total savings of 17 orders of magnitude on the texture mapping of that plant species... at least in pixel data... you would still need to call each cell that needs to be generated; so, while the pixel data has become immaterially small, actual compression would only be down to the cellular level of about 100-10000 times compression. As for the overhead of your pointers on such a large scene, through careful indexing, you can get away with relatively small pointers. So, your plant as a whole could have a meta-data set that builds your lookup tables for each library it needs, and from there each cell could use very short pointers, maybe 3 bytes per cell for the texture pointer, plus maybe 6 bytes for rotational and offset data. More general position data could be inhered from its position in your data stream. Since a single pixel is normally 6 bytes, this means you can achieve about 67 to 6667 time compression on most organisms.

Minerals are just as easy to generate libraries for because they form predictable crystalline structures. With less than 5000 common minerals here on Earth, and minerals not evolving, your library for these can be quite small, and your shapes very predictable. It's hard to say how compressible minerals are, but it is probably more so than plants.

So, overall I would estimate that you could get at-least 3000:1 compression on the Earth's land mass.

The Oceans are way easier to texture since there is only really 1 layer over most of the Ocean, and the whole thing only needs a single library... So we can drop two orders of magnitude right off the top to eliminate that 100 layer thing I added in to account for the complexity of minerals and organics. So Ocean compression is more like 300,000:1 from my total pixel data estimate.

Then there is the re-usability of data from one frame to the next. In a 3d video file, you do not save the whole state of each object for each frame, instead you only update them when at key-frames using tweening to approximate the in-between states. While plants, animals, and liquid water may change a lot from one frame to the next, minerals and ice do not. Minerals will often be able to go millions if not billions of frames before needing a new keyframe; so, mineral textures over time will take up a relatively negligible amount of space.

So, to estimate data usage, we know that the Earth's historical averages are that ~20% of the surface has been covered by dense life, ~70% by liquid oceans, ~10% by deserts and/or glaciers.

So the oceans need about 2.5e21 bytes per frame (1.1e27 * .7 / 300000) Life needs about 7.3e22 bytes per frame (1.1e27 * .2 / 3000) Deserts and glaciers need several orders of magnitude less per frame; so, I will just drop them as statistically insignificant.

This means you need ~7.55e22 bytes per frame in total.

Also, although life evolved ~3,770 million years ago, it only moved onto land about 430 million years ago. This means that we can completely throw out the Earth's landmass as "deserts and glaciers" for 3340 million years.

Before 430 million years ago, you only needed ~2.5e21 bytes per frame.

While humans can technically perceive "quality" differences up to 120 frames per second, you can generally sample speeds as low as 12 frames per second and most people will not notice an issue in the quality of the video. Especially if you use tweening tricks to simulate the intermediate frames. So if we assume 12 frames per second this means that you have ~1.0e17 frames before life moved to land and ~1.4e16 frames thereafter.

So your total dataset using compression is about (7.55e22 * 1.4e16) + (2.5e21 * 1.0e17) = 1.3e39 bytes.

Human memory is believed to be associated with pyramidal neurons which have an average of just over 5000 synapses, and there are ~57 billion pyramidal neurons in the human brain taking up about 2/3 of your brain's real-estate.

This means that the human brain can store ~4.5e16 bytes/m^3; so, you need 2.9e22 m^3 of pyramidal neurons to store the record using the compression methods as described above. If this brain were then organized into a sphere, it would have a radius of ~19,000km putting it somewhere between the size of Earth and Neptune.

Answer 2

Sensor Input Calculation

The Earth is 6,371 kilometers in radius, and has another 100 kilometers of atmosphere (6,471 km total). Converted into pixels of information every micrometer $1 \times 10^{-6}$ meters, that is 6,471 km = 6.471 million ($10^6$) meters = 6.471 trillion ($10^{12}$) micrometers.

The volume of a sphere is ${4 \over 3} \pi r^3$. For the whole Earth, then, each "frame" of information is $8.64 \times 10^{38}$ pixels of information.

If just the surface area of Earth : $4 \pi r^2 d$ = $4.32 \times 10^{28}$ pixels.

Brain Size

Presuming it uses storage space with the same efficiency as a human brain

A small frame challenge here. Human brains aren't designed to store raw information. The human brain composes raw input into symbols (leaving a lot of detail on the cutting room floor), and further composes those symbols into context, and so on. Memorizing a specific sequence of details (think of the seven digits in your phone number) requires a great deal of effort.

Let's say, then, that this is not a human brain; but rather some design better suited for the job of recording exact details, like a holographic media. The media can handle 8.5 TB ($1 \times 10^{12}$) bytes of information per 4 inch x 4 inch x 1 millimeter (guess on depth) layer = 10 cm x 10 cm x 0.01 cm $\rightarrow$ 0.1 m x 0.1 m x 0.0001 m ... or 8.5 $\times 10^{18}$ "pixels" per cubic meter.

This is assuming a “pixel” is merely on/off (the simplest expression of visual data). More information could be recorded about what each micrometer eye “sees”.

All of History

The rest comes down to recording rate and history. The Earth is 4.5 billion years old, and most folks seem to agree that life started 4.4 billion years ago. There are 31 million seconds in a year. So, total number of seconds being recorded is between $139 \times 10^{15}$ (everything) to $136 \times 10^{12}$ (just life). If you use a semi-awake human's alpha wave frequency of 4 hertz (4 samples per second), you will need around $400 \times 10^{15}$ "frames" of information for your whole data record. Each frame will contain $4.32 \times 10^{28}$ bits of information. So, the size of the entire record is $1,600 \times 10^{43}$.

Taking the "brain" data density, your brain would need to be $1,600 \times 10^{25}$ cubic meters. Or $11 \times 10^8$ meters (or a cube 1.1 million kilometers on a side) to hold the data. Compare to the Earth's radius of 6,000 kilometers; it would be 183 Earths.

it has the ability to see and be cognizant of everything happening on every square micrometer of planet earth

Another small frame challenge : if you were to switch the scale from micrometer to millimeter (still very small), you would trim 9 zeros off the final answer, above. This would give you a less-than-Earth size final brain size ($1,600 \times 10^{16}$ cubic meters or about 1,100 kilometers on a side)

Answer 3

It's omnipresent. It's right there in the name. The only way to store all the information in the history of the Universe is with a storage device the size of the Universe itself. The Universe essentially is the omnipresent being's brain. We're living in a giant storage device. It used to be highly compressed, but through the process known as "time", it is in the process of decompressing all of that data. Of course whoever is observing all of that data must exist outside of time, and thus outside of the Universe, undetectable to all of us inside it. A better (but of course unanswerable) question would be "How big is the rest of this being?"

Answer 4

Unable to tell

We do not have a real way to measure how much storage you need for a certain bit of information, or a group of information. That makes it impossible to quantify.

To further complicate the problem, we see that increased brain tissue suggest an exponential growth in capabilities. At the same time, many incredibly smart people have shown to not have remarkably more or less brain tissue than the average.

To even further complicate things, there are signs that having more and more brain tissue can eventually be detrimental. The sheer amount of neurons can start interfering with each others electric fields, leading to noise on the neural pathways. If that trend is left unchecked, a much larger and compact brain would eventually stop to work. Separation would be needed, which would probably counteract (part of) the exponential growth of information that can be stored.

Besides all that, you want a specific kind of memory. Lots of brain doesn't need to be used for mobility or processing, but simply storing what happened. As it is impossible to tell how much of the brain is used for just that purpose, we can't extrapolate further how much we would need.

With no way to quantify the data, the brain area or even how we actually store it, it is impossible to tell how big it would need to be. Not to mention all the ways it can interfere with itself.

Answer 5

Sorry to be pedantic, but an OMNI-PRESENT being wouldn't require any additional brain size / "storage". They are not all intelligent, they do not necessarily need to KNOW anything more than you or I do. Omnipresent means "Everywhere at once" or "in all places at once". Unless you are postulating that it would take "brain power" to be in all locations at one time, the answer to the question is likely to be "No larger or smaller than what's capable of keeping the being alive and functioning."

I believe the word you're looking for is Omniscient or "all knowing", in which case I do not believe there is a good answer. Humans or other creatures as we define and understand them are not capable of "all knowing" due to a multitude of limitations, therefore no measurement based upon our existing understanding of "memory storage" would be sufficient to answer the question. Until we understand what an Omniscient creature would "look like" (in the architectural sense of its makeup and capabilities, not its physical appearance), there is no answer to the question you postulate.

Further, any being capable of knowing all would also likely be capable of storing that information in any way they so choose...perhaps like a Google search an omniscient creature need not "remember" everything about everything but simply have a means by which to instantly access that information...requiring a "brain" no larger than that which sustains the creature.

Answer 6

Storing everything is impossible, for so many reasons. One is that we have to define "everything," which turns out to be easy to do in causal speak and frustratingly impossible when talking about things that have "omni-" prefixes in them. The demands are just too high. Does it remember that at Julan Date -8482293.4848282832729328, hydrogen atom #73738283754928375923838238527293923723783225728332 underwent a hyperfine transition? Didn't think so.

The other reason is that it, itself, is on Earth. And there's a strange loop that forms when it tries to remember what the parts of its brain did. At some point you run into issues with descending infinite sets, and admit that it can't be done. If I may quote:

"The world, marm," said I, anxious to display my acquired knowledge, "is not exactly round, but resembles in shape a flattened orange; and it turns on its axis once in twenty-four hours."

"Well, I don't know anything about its axes," replied she, "but I know it don't turn round, for if it did we'd be all tumbled off; and as to its being round, any one can see it's a square piece of ground, standing on a rock!"

"Standing on a rock! but upon what does that stand?"

"Why, on another, to be sure!"

"But what supports the last?"

"Lud! child, how stupid you are! There's rocks all the way down!"

So what can be done about this?

Well, you say this entity is omnipresent. Can it affect our reality at a subtle level? If it acts to make our reality a mirror of our own, in some tiny detailed way, then it doesn't have to remember what happens and when in some big table. It can remember it procedurally, remembering at what times it allows what events to happen. This would lead to us observing fractaline geometry in our world... strangely enough, the kind of thing Paul Bourke cataloged on this website.

Now if I'm wrong about your assumptions, and this entity is outside of the Earth, this may be enough. Everything at a low enough level just has to be done in ways that are algorithmically provable for the omnipresent entity. Then we just have to ask "what is a brain," in the context of such an entity. Does it have to use neurons? This would assuredly say something about its size... but this fractaline pattern points out that you have a tradeoff. The less freewill the world has (and the more "apparent" freewill that's actually procedural fractaline algorithms), the smaller the brain could be.

If the entity is part of the Earth, we still have the issue of it knowing itself, which is a pesky concept that still eludes humans. Sun Tsu said that to know yourself and not your enemy, you will win half your battles -- and most people can't claim that win record! And indeed such a problem is insurmountable in First Order Logic, which ends up being where most people actually end up resting when they try to define what it means to "know" everything about the history of the earth (whether they intend to go that way or not).

If I may offer a fascinating math tidbit that I love to share, there's a fascinating concept that's been nicknamed a Willard World, after Dan Willard. Instead of starting with 0 and 1, and working with addition and multiplication to get 2, 3, and so on, he starts with infinity, and uses subtraction and division to construct everything in his world. It turns out that, when he does this, he can create something that is exactly like the rules of arithmetic except that you can't prove multiplication is total. But, fascinatingly, his systems can prove their own consistency -- which is as close as math ever gets to "know thyself." So the mathematics he describe could be a powerful piece of the puzzle for understanding this omnipresent beast.

I geek out over math, it's true. But sometimes there's fun tidbits. One of the fun consequences of Willard's systems is that you can start with a set that is "countably infinite" from an outside observer's perspective, and construct a Willard system around that can prove such a number is "uncountably infinite" from within the system, a much larger category of number. It always felt like there was a worldbuilding opportunity there, for a world ruled by a "god" which, from the inside, appears to be uncountable in its infinite reach... but all the gods know it's actually just countable.

So brain size? I didn't answer that. It could be arbitrarily small depending on how you shape your world. Or it could have to be much larger than the planet itself. It all depends on how you define "everything" - a pesky word that is so easy to throw around until you have to actually define it. Then it just looks at you, smiles, and says, "give it your best shot."

"The Tao that can be named is not the eternal Tao." - Lao Tzu

Answer 7

It is all brain.

Because that and its senses are all it needs. It perceives and remembers but does not act. Every fiber stores memories, and there is a lot of redundancy because disasters have wiped out large swaths of this creature in the earth's past. The various memory versions are not all the same. The creature mourns the ones it has lost - it can remember how the first flowers in the Cretaceous smelled and tasted, but some of these memories are dark because the catalcysm wiped out the memory of color and shape.

The creature is all on earth. But not all on the surface; not after the Permian. It goes down, and down. And down there there are also wonders to perceive.

Answer 8

Focus on density One of the key properties of brains we know about, is density. You need very interconnected processes to develop complex capacities, as an increasing amount of parameters have to be processed concurrently. For an omnipresent brain, the challenge would be to increase the cardinality of synapses.

Thus, maybe density would be a more defining property than size. In other words, going towards an infinitely dense brain (black-whole kind of thing), instead of an infinitely large brain. In the end, the result is the same (infinite capacity) although implemented more efficiently.

Answer 9

The being clearly is the Earth (and God clearly is the universe).

The reason is that you cannot store all the information on Earth in anything smaller than the Earth, and you cannot store the information in the universe in anything smaller than the universe.

Answer 10

...to remember everything that has ever happened on earth...

A frame challenge - if the assumption is that this 'brain' is on the Earth, you have an infinite regression.

In order to 'remember' something, there must be a change in the brain.

It has the ability to anomalously produce matter from its body out of nothing.

This brain is on Earth, that change in the brain would have to be recorded in the brain. But this would cause a change in the brain, which must be recorded. But this would create a change in the brain, so this must be recorded. Ad infinitum.