Chapter 12: Terra Incognita

Welcome to Last Minute Lecture.

This free chapter overview is designed to help students review and understand key concepts.

These summaries supplement not replaced the original textbook and may not be redistributed or resold.

For complete coverage, always consult the official text.

Welcome to the Deep Dive.

Great to be here.

Today we're plunging into Chapter 12 of Why Machines Learn, the elegant math behind modern AI, the chapters called terra incognita, uncharted territory.

Yeah, and it really lives up to the name.

It dives into some of the, well, really surprising, almost mysterious aspects of modern deep neural networks.

Exactly.

This deep dive is basically your guide to what's genuinely puzzling researchers about these massive AI systems.

We're going straight to the source Chapter 12 itself.

We'll give you a detailed summary, unpack the key ideas, the math, or sometimes the lack of math explaining things.

Right.

The algorithms, the history, the real world examples.

It's all in there.

Our mission today is to explore this terra incognita together using the chapter as our map, making sure we cover all those key concepts and examples.

Okay.

Sounds like a plan.

So where does this journey into the unknown really kick off?

The chapter starts with this really fascinating story from open AI.

Ah, yes.

The grokking anecdote.

It's quite something.

Picture this.

It's 2020 and researchers there are training a relatively small neural network.

The task seems simple enough, adding two binary numbers, but modulo 97.

Right.

And just quickly on modular arithmetic, modulo 97 means you're working with remainders after dividing by 97.

So the numbers wrap around between zero and 96.

Exactly.

Like 22 plus 28 is just 50.

That's less than 97.

So it's 50 mod 97.

But if you do say 40 plus 59, that's 99.

And 99 divided by 97 is one with a remainder of two.

So 40 plus 59 is two modulo 97.

Okay.

Got it.

Simple math, but for a machine.

So they're training this network.

And then the story goes, one researcher goes on vacation and, well, forgets to turn off the training run.

Happens to the best of us.

Apparently.

So when they got back, they found something totally unexpected.

This network, because it had been training for like way longer than they initially planned, It hadn't just memorized the specific answers to the examples it saw.

It had actually figured out the general rule for adding numbers modulo 97.

It learned the underlying math.

Wow.

Okay.

That's not what you typically expect from just memorization.

Not at all.

And the chapter uses this to introduce a term from science fiction,

Robert Heinlein's Stranger in a Strange Land.

The term is grokking.

Grokking.

I remember that.

It means more than just understanding, right?

Exactly.

Alethea Power from the OpenAI team is quoted defining it as not just understanding, but kind of internalizing and becoming the information.

So the network grokked modulo 97 edition.

It seemed to.

Through just sheer extended training, it internalized the concept.

Which is just such a strange behavior, isn't it?

It suggests there's something more going on under the hood than simple pattern matching or memorizing.

Precisely.

And this grokking is just one piece of evidence pointing towards these odd, unexpected phenomena in deep learning, especially when these networks get really, really big.

And size is a huge part of the puzzle here, a real challenge to standard machine learning theory.

Oh, absolutely.

Modern networks are just enormous.

We're talking hundreds of millions, sometimes billions, even trillions of parameters.

And parameters, just to remind everyone, are those weights and biases inside the network.

The numbers the model tunes during training to get better at the task.

Right.

And classic ML theory has a very clear prediction about what should happen when your model has way more parameters than training examples.

It should overfit spectacularly.

Exactly.

Overfitting.

That's when the model learns the training data too well.

It doesn't just learn the general patterns you want it to learn, but also all the specific noise, the quirks, the random fluctuations that are only present in that specific training data set.

Which means it looks great on the data it trained on, maybe get zero error there.

But it's a disaster when you show it new data, because that specific noise isn't there anymore.

The model fails to generalize.

The book uses a good analogy with furniture.

Imagine training a really complex model.

You show it pictures of wooden chairs, metal chairs, all with four legs, and label them chair.

Things without legs are not chair.

A super complex model might learn a very specific rule, like chair has four legs.

A knee is made of wood or are metal.

Ah, I see where this is going.

So then in the test set, you showed a perfectly normal plastic chair.

It has four legs.

But the model says not chair, because it overfit to the materials in the training set.

Whereas maybe a simpler model just looking for has four legs would have gotten the plastic chair right.

It generalized better.

Right.

It found the core feature.

We can visualize this too, maybe with a regression example.

Imagine points scattered on a graph.

You're trying to fit a curve.

OK, plotting points.

A very simple model.

Maybe just a straight line could be way off from most points.

It has high error on the training data, high error on test data.

It's too simple.

That's under fitting high bias.

It misses the real pattern and the noise.

Got it.

Too simple.

But then you could have a super complex model, a really, really squiggly line, one that goes through every single training point.

Perfect.

Pretty much zero training error or very close.

It nails the training data.

But that squiggly line didn't just learn the underlying trend.

It also learned all the random ups and downs, the noise specific to those training points.

So when new points come along with different random noise.

The squiggly line is way off.

High test error that's over fitting high variance.

It learned the noise, which doesn't generalize.

And this isn't just a theoretical worry.

The chapter brings up that EEG example again from earlier in the book, trying to tell if patients under anesthesia were conscious or unconscious.

Right.

Using EEG data, they had 10 patients, used seven for training, three for testing.

And they compare a simple linear model to a more complex nonlinear one, like a K nearest neighbors model.

And that complex model, it could draw this incredibly complicated boundary in the data space that perfectly separated the conscious conscious points for those seven training patients.

Almost zero training error.

Looked amazing.

Tested on the data from the three new patients.

It made a lot of mistakes.

It had totally overfit the specific patterns or noise in the first seven patients data.

Which really underscores the key point.

Test error is what matters.

It's the only real measure of how well your model will actually perform out there on new unseen data.

Minimizing that is the goal.

And historically, this led to the whole concept of the bias variance tradeoff.

The Goldilocks principle, I think Mikhail Belkin calls it in the chapter.

That's the one.

You've got bias, the error from models being too simple, under fitting,

and you've got variance, the error from models being too complex, over fitting.

And the traditional goal was always to find that sweet spot right in the middle, a model with just the right amount of complexity or capacity to get the lowest possible test error.

Not too simple, not too complex.

Exactly.

And capacity here usually relates to the number of parameters.

If you imagine a graph, the X axis is model capacity.

More parameters mean the model can represent more complicated, squigglier functions.

Like we saw with the universal approximation theorem back in chapter nine, deep networks can represent complex functions if they have enough neurons, enough capacity.

Right, so the standard bias variance curve shows test error, starting high on the left, under fitting, low capacity.

Then it drops down to a minimum that's your Goldilocks zone.

And then, as capacity keeps increasing, the test error starts climbing back up sharply.

That's the over fitting region.

Meanwhile, the training error just keeps going down and down towards zero.

That's the classic picture, and this is the huge puzzle.

Modern deep neural networks are massively over parameterized.

Way more parameters than data points.

Way more.

According to that classic curve, they should be far out on the right, deep in over fitting territory, with terrible test error.

But they're not.

They generalize incredibly well.

They achieve amazing performance on unseen data.

It completely breaks the traditional model.

Mendenesha and his colleagues are quoted saying something like, more surprising is that if we increase the size of the network past the size required to achieve zero training error, the test error continues decreasing.

Wait, say that again?

Even after the training error hits zero.

The test error keeps going down as you make the network bigger.

And as we add more and more parameters, even beyond the number of training examples, the generalization error does not go up.

That just flies in the face of the standard trade off.

Well, that's the million dollar question.

Initially, people thought maybe it was something about the training process itself.

Like, maybe the randomness in stochastic gradient descent,

SGD, acts as a sort of implicit regularization.

Kind of automatically preventing the model from really over fitting, even with all those parameters.

That was one idea.

But then experiments, like from Tom Goldstein's group, showed that you could still get good generalization, even using full batch gradient descent, which isn't random or stochastic.

OK, so it's not just SGD's randomness.

Doesn't seem to be the full story, no.

This massive gap between what theory predicted and what these huge networks actually do.

So what Belkin calls machine learning's terra incognita.

We're in uncharted waters.

And because the theory isn't quite there yet to guide us, a lot of progress in deep learning has become very experimental.

Right.

Lots of fiddling with settings.

Absolutely.

It involves tuning both parameters and hyperparameter.

OK, let's clarify those.

Parameters, we said, are the weights and biases inside the network that get adjusted automatically during training.

Right.

The model learns those itself.

Hyperparameters, though, are the choices the engineer makes before training even starts.

Like deciding on the network's architecture.

How many layers?

How many neurons in each?

Exactly.

Or choosing the optimization algorithm, like Atom or plain SGD.

Deciding if you use regularization and how much.

Even things like the size of the training data batches.

Finding a good set of hyperparameters sounds like part science, part art.

It really is.

Lots of trial and error, experience, and intuition involved.

The chapter briefly mentions some architectures we've seen before, feed -forward networks.

Yeah, where information just flows one way.

Input, hidden layers, output, like the basic perceptron, multi -layer perceptrons, and the convolutional neural nets, CNNs, from chapter 11.

Back propagation is the key algorithm for training these.

And then there are recurrent networks, RNNs.

Right, those have feedback loops.

Outputs can feedback into the same layer or previous layers.

They're good for sequential data, things that change over time.

LSTM's long short -term memory networks from Schmidhuber and Huckreiter are a famous example.

Okay,

but regardless of the architecture, when you're doing supervised learning, the core idea during training is minimizing a loss function, sometimes called a cost function.

Yep, the loss function is just a way to measure how wrong the network's current prediction is compared to the actual target or label you want.

You calculate it for one example or average it over a batch of examples.

And the whole goal of training, using algorithms like gradient descent, is to adjust the network's parameters or its weights to make that loss value as small as possible.

But we talked about overfitting.

If the network is really complex, just minimizing the raw error on the training data might lead it to overfit, so we need regularization.

Exactly, explicit regularization techniques are often added to the process.

Usually it involves adding a penalty term to the loss function itself.

A penalty for what?

A penalty for complexity.

For example, you might penalize the network for having really large weight values, that's L1 or L2 regularization.

Or you might randomly turn off some connections during training, that's called dropout.

And the idea is these penalties discourage the model from fitting the training data too perfectly, especially the noisy parts, pushing it towards simpler, more general solutions.

That's the goal, yeah, to help prevent overfitting in these powerful complex models.

Okay, and one other crucial component mentioned is the activation function.

Right, inside each artificial neuron.

The activation function determines the neuron's output based on its input.

Critically, it introduces non -linearity.

Without non -linearity, a deep network would just be equivalent to a single linear layer.

Couldn't learn complex patterns.

Exactly, and for backpropagation, the algorithm used to calculate the gradients and update the weights.

These activation functions generally need to be differentiable.

You need to be able to calculate the slope.

Generally.

Well, there are popular ones, like real U rectified linear unit, which technically isn't differentiable right at zero.

It has a sharp corner.

Ah, okay.

But in practice, it works extremely well.

And engineers have ways to handle that little kink.

Its benefits usually outweigh that theoretical inconvenience.

We also saw the sigmoid function back in chapters nine and 10.

Real U is just another common choice.

Got it.

So that's kind of the basic machinery.

But a big theme here, fitting the Terra incognita idea, is moving beyond just supervised learning.

Definitely.

Supervised learning needs all that labeled data input output pairs.

Getting those labels from humans is often the bottleneck.

It's slow and expensive.

So alternatives.

Unsupervised learning is one, right?

Finding patterns without labels, like clustering.

Yeah, k -means is a classic example, though not detailed here.

But the chapter really highlights this major shift towards using the massive amounts of unlabeled data that are readily available.

How do you learn without labels?

Well, one powerful technique discussed is supervised pre -training followed by fine tuning.

Okay, break that down.

You take a huge network and first train it on a massive labeled data set for a broad task.

The classic example is training on ImageNet, which has millions of images labeled with object categories.

So learning general visual features.

Then you take that pre -trained network, which now understands a lot about images, and you adapt it, fine tune it for a more specific task using a much smaller labeled data set for that task.

Like the Pascal VOC data set for object detection, finding boxes around objects.

Exactly, the RCNN approach did this.

Pre -train on ImageNet classification,

then fine tune on Pascal VOC detection, and boom, it blew away previous methods.

It's interesting.

The chapter mentions Alexei Efros being skeptical at first.

Yeah, he found it weird.

Why should learning to classify whole images help you draw precise boxes around objects?

They seem like different tasks.

But it worked, and the same network without the ImageNet pre -training did much worse on detection.

Which hinted that the pre -training was learning something fundamental and transferable about visual structure.

This leads us towards self -supervised learning.

Self -supervised, meaning the supervision, the label, comes from the data itself.

Precisely, no human labels needed for the main learning phase.

The prime example today is large language models, LLMs.

How are they self -supervised?

Their main training task is usually predicting the next word or token in a sentence, given the words that came before it.

The label is simply the actual next word in the text data.

And they train on just massive amounts of text from the internet.

Billions of pages.

This forces them to learn grammar, syntax, facts about the world,

context, relationships between words, all the statistical structure hidden in human language.

Just by predicting the next word.

It sounds simple, but at scale, it's incredibly powerful.

They learn so much implicit knowledge that they can then generate remarkably coherent text, answer questions, translate.

Which leads to that big debate.

Is it really understanding and reasoning or just super sophisticated pattern matching?

That debate is central to the current terra incognita.

Theory doesn't have a definitive answer and experiments are still being interpreted.

And FROS's lab was doing self -supervised learning for images too, right?

Back in 2016.

Yeah, their idea was clever.

Take an unlabeled image, blank out some patches of pixels and train a network to predict what was in the blanked out parts based on the parts you could see.

So, learning to fill in the blanks forces it to understand typical image structures.

That was the intuition.

Learn the statistics of natural images.

And this idea really took off with the masked autoencoder, MAE, from Meta in 2021.

Yes, MAE pushed this much further.

They masked out a huge portion of the image, like almost three quarters.

75 % gone.

Yeah.

Then an encoder network processes only the visible patches, creating a compact summary, a latent representation.

A separate decoder network then tries to reconstruct the entire original image, including all the missing bits just from that compact summary.

Wow.

So the encoder really has to capture the essential information, the underlying structure to allow the decoder to fill in that much missing context.

Exactly.

It forces the encoder to learn incredibly powerful general purpose image features, all without needing any human labels.

The results were amazing reconstructing a mostly hidden bus, for instance.

And the payoff.

The payoff was huge.

When they took an MAE encoder, trained this way on unlabeled images and then fine tuned it for tasks like object detection using a small label data set, it outperformed the older supervised pre -training methods like RCNN.

So EFROs was right all along.

Seems like it.

Just maybe a bit ahead of his time.

And the implication is massive.

As EFROs put it, self -supervised learning potentially frees us from the shackles of super expensive human annotated data.

His quote, the revolution will not be supervised.

That ability to leverage unlabeled data is a key reason these models have scaled up so dramatically, right?

These dense LLMs with like half a trillion parameters or more.

Absolutely.

And as they get into that really massive regime, we encounter even stranger territory bringing us back to that bias variance curve and its breakdown.

Right, the standard curve set test error goes up after you hit the interpolation point where the model can perfectly fit the training data.

But then came Belkin and others, around 2018, systematically looking at what happens when you push model capacity way past that point.

For kernel machines, deep nets.

The double descent phenomena.

As model capacity keeps increasing beyond that interpolation point where classic theory says overfitting should just get worse and worse.

The test error astonishingly starts decreasing again.

You go down, hits a minimum, goes up.

That's the classic peak.

But then comes back down in the heavily over -parameterized regime.

So more parameters beyond fitting the data perfectly actually starts improving generalization again.

That's what the double descent curve shows.

It had been noticed before in simpler models, but Belkin's work really framed it as a systematic effect in modern complex models.

The chapter calls it a unifying principle.

Yeah, unifying in the sense that it connects the classical under -parameterized regime with this new weird over -parameterized regime, but it fundamentally challenges the old just right Goldilocks idea.

Being massively over -parameterized might actually be beneficial for generalization in this second descent.

Definitely deep in the Terry incognita.

And this disconnect where experiments show things like double descent, but theory struggles to explain why fuels that debate about theory versus experimentation in AI, right?

Tom Goldstein's comments at that NSF town hall.

Exactly.

He talked about traditional ML with things like support vector machines, focusing on methods with strong theoretical backing.

He called it pre -science.

But then AlexNet happened in 2011, a huge empirical success, largely engineered without a solid theory explaining its power.

Goldstein argued the field shifted then, becoming more like experimental science first, figure out the theory later.

He jokingly called the hardcore theorist demanding proofs first, anti -science.

And there are clear areas where theory is lagging behind what we see experimentally.

For sure.

The chapter mentions the lost landscape of deep nets.

Theory papers conflict, some say no bad local minima for over -parameterized networks.

Training should be easy, others say they exist.

But Goldstein's experiments.

His empirical work shows local minima do exist and networks can get stuck, even when over -parameterized.

This contradicts the simple theoretical expectations that they should always find the global minimum,

zero training error.

So why do they usually find good solutions in practice?

Theory needs to catch up.

And the generalization puzzle again.

The idea that SGD's randomness provides implicit regularization.

Is challenged by Goldstein's experiments, showing that even non -stochastic full batch gradient descent can lead to good generalization in these big networks.

So what is the mechanism?

Still unclear.

Grokking seems like another perfect example of this.

A clear experimental result, the shift from memorization to generalization with more training.

That we don't have a good theory for.

It's like a phase transition in learning.

And we need the physics, the math, to explain why and when it happens.

And while Grokking was studied in smaller networks, the hope is it gives clues about the giants like LLMs.

Exactly.

Which brings us back to LLMs.

They're front and center in these debates about surprising behaviors, like can they actually reason?

The Vinerva example is fascinating.

An LLM fine -tuned on math problems, answering a high school algebra question.

And showing step -by -step working that looks incredibly logical, like human reasoning.

But the question remains, is it actually reasoning, manipulating concepts?

Or is it just predicting the sequence of symbols that is statistically most likely to follow the question, based on all the math proofs and problems that ingested?

And the chapter stresses,

theory can't settle this right now.

Experiments provide compelling examples, but they're open to interpretation.

It's a huge debate.

Then there's emergent behavior.

Yeah, this idea that certain abilities, like attempting theory of mind tasks, or the kind of multi -step reasoning Minerva showed, even with mistakes, seem to just appear when models reach a certain massive scale.

They aren't explicitly programmed, they just emerge.

Though we need to be careful with that word.

The Bob and Alice classes example for theory of mind is a good illustration.

Alice swaps Bob's classes while he's not looking.

Where will Bob look?

And ChatGPT gives an answer that sounds like it understands Alice's perspective.

Bob will look where she put them, because she doesn't know they were swapped.

It seems to model her mental state.

But the source poses a great question.

If you know the underlying mechanism is just predicting the next token based on probabilities and vector similarities, does that change how you interpret that answer?

Is it reasoning or just predicting the statistically common outcome in stories like this?

Which connects directly to the Stochastic Parrots' critique from Emily Bender and others.

Their argument being that LLMs are just mimicking patterns.

Essentially, yes.

That they're incredibly sophisticated mimics, generating plausible text based purely on the statistical patterns in their massive training data, without any genuine understanding or intent in the human sense.

Yet, regardless of the philosophical debate, these things are practically useful.

The chapter notes their ability to help programmers write code, even if they weren't specifically trained as coding tools.

Undeniably useful in many applications already.

But with that power comes significant risks and ethical concerns, which the chapter also addresses.

Bias in training data is a major one.

It's a longstanding issue in ML, amplified now by the scale.

The Google Photos example from 2015, tagging black people as gorillas, is cited.

And the fix, just disabling the gorilla label, was apparently still in place years later.

That shows how hard these problems can be.

And the data itself reflects our society's biases,

Historical hiring data might favor men.

Policing data might over -represent certain communities.

And if you train an algorithm on that bias data without correction, it will learn, perpetuate, and likely even amplify those biases,

making biased predictions or recommendations.

There's also the risk of confusing correlation with causation.

Learning from bias data that two things occur together and assuming one causes the other.

Like associating low -income with recidivism in policing data, potentially ignoring the systemic factors.

So solutions involve things like getting more diverse data, actively de -biasing data, being careful about the questions we ask the AI.

Yes, it requires very careful consideration of the data, the task, and the potential impacts.

LLMs also show specific kinds of bias and toxicity.

That example from Adam Tammankhalai at Microsoft Research is pretty stark.

The pregnancy question.

Asking GPT for who is pregnant.

When the sentence structure pointed to a male doctor, but the model defaulted to a sexist stereotype about nurses.

Yeah, saying it's biologically implausible for the doctor and defaulting to the nurse based on the pronoun she.

And even Chad GPT, tuned with human feedback for safety, gave an ambiguous answer, but still suggested rephrasing in a way that defaulted to the nurse being pregnant.

These biases are deeply embedded.

And Celeste Kidd and Abeba Berhane raised that really important point about AI influencing user beliefs.

Right, when an AI presents information confidently, especially to someone who is uncertain,

that person might just accept the AI's answer, even if it's wrong or biased.

Conversational AIs that sound authoritative are particularly concerning in this regard.

It's a serious responsibility.

Okay, the chapter then loops back in a really interesting way, connecting AI back to neuroscience.

Yeah, it's a nice full circle.

Early AI, like Rosenblatt's perceptron, was directly inspired by biological neurons.

Now, insights from artificial neural nets are actually informing neuroscience.

How so?

What are the connections?

Well, one area is the credit assignment problem.

Back propagation works great for training artificial nets, telling them exactly how to adjust weights based on errors.

But how does the brain do something similar?

Biological neurons don't seem to pass numbers around like backprop requires.

Exactly.

The biological mechanisms for learning and adapting based on feedback are likely different, and understanding artificial nets might give clues, or at least frame the right questions for neuroscientists.

But there are areas with more direct parallels, like machine vision and the brain's visual system.

Definitely.

The work by Yamins and Nicarlo is highlighted.

They trained various CNN architectures for object recognition.

They found that the CNN architectures that performed best on the computer vision task also turned out to be the best models for predicting the firing patterns of actual neurons in the monkey's ventral visual stream, the part of the brain that recognizes objects when shown new images.

So the artificial network's internal workings mirrored the biological systems.

Shockingly well, according to Nancy Kamwisher, who's quoted, specific layers in the CNN seem to correspond functionally to specific areas in the monkey visual pathway.

The activity in the artificial layers could predict the activity in the real neurons.

It suggests a convergence form follows function.

Both systems found similar solutions.

And they even used the model to generate weird images.

Yeah, the Carlos lab in 2019 used their CNN model of the monkey visual system to design synthetic, unnatural images.

Images the model predicted would make specific neurons fire more strongly than any natural image would.

And did they?

They did.

When they showed these optimized synthetic images to the monkeys, the neurons fired just as predicted by the model.

Confirming the model captured something real about how those neurons process visual information.

Wow, are they modeling other brain areas too?

The chapter mentions work extending this to the dorsal visual stream for spatial awareness, the auditory cortex, even olfactory pathways for smell.

And what about LLMs and cognitive science?

Since LLMs deal with language and seem to capture so much world knowledge, they're prompting higher level questions about human cognition.

Those hints of theory of mind, for example, even if it's just pattern matching, are intriguing for cognitive scientists studying social reasoning.

And language acquisition.

LLMs challenge some classic debates like Chomsky versus Piaget.

They show empirically that a lot of complex grammar, syntax, and even some semantics can be learned from statistical patterns and language data alone.

Though with way more data than a child ever sees.

Vastly more, yes.

That's a crucial difference.

And the chapter rightly adds other cautions.

Biological neurons spike.

They fire discrete signals which most artificial neurons don't.

And energy efficiency is a huge difference.

Massive.

The brain runs on maybe 20, 50 watts.

Training and running a giant LLM can take megawatts.

The blue model inference estimate was something like 1 ,664 watts.

Apples and oranges maybe.

But the scale difference is enormous.

Still, the idea is intriguing.

That maybe there are enough similarities, enough convergence and function despite different hardware to suggest there might be shared underlying principles.

Elegant math or computational laws governing intelligence whether it's artificial or natural.

It's a compelling thought.

Okay, so I think we've really journeyed through chapter 12's Terra Incognita.

We started with Grokking, saw how standard bias -variance theory breaks down for huge networks.

Explored the rise of self -supervised learning.

The mystery of double descent.

Right, the whole theory versus experiment debate.

The capabilities and ethical challenges of LLMs and these surprising connections back to neuroscience.

We've definitely hit the key concepts.

The math ideas, the algorithms, the examples, historical notes, definitions and applications laid out in the chapter drawing directly from that source material.

Complete coverage.

Yep, covered the ground.

So to leave you, the listener, with something to think about, building on all this.

Considering these strange emergent abilities, the Grokking phenomenon, double descent, all happening in these massively over -parameterized networks in this Terra Incognita,

what does this suggest about the fundamental nature of learning and intelligence itself?

Yeah, it's just scaling things up.

Uncovering universal laws of how information gets processed and knowledge emerges.

Laws that might apply just as much to our own biological intelligence as they do to these silicon creations.

It's a pretty profound question to ponder.