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Recently I’ve been listening to some amazing music with absolutely incredible lyricism, discussing a variety of topics with beautifully-written phrases. These lyrics often include ambiguous language, allowing the listener to interpret their meaning, but still direct enough to challenge the issue the artist initially intended. To me, this shows music as a beautiful art form, able to communicate ideas in this wonderful thing we call language.

Kezia

In particular, I recently (re-)listened to Protest The Hero’s album Kezia, which discusses a fictional scenario of a girl, Kezia, set to be executed by firing squad, possibly due to being a heretical prostitute. The album can be interpreted as a critique of modern society and its patriarchal roots, with minor themes of questioning authority and morality. In the following paragraphs, I’ll mention a few of my favourite passages.

The opening track No Stars Over Bethlehem follows the point of view of a priest in the prison Kezia is contained within. He has lost his faith, possibly due to the corruption of humanity as a whole. One passage reads

Someone plunged a dagger deep into God’s chest
And when he groaned it laid our entire civilization to rest
When he pulled out that dagger
And marveled in the pain he could create
We stuck another in his back and sealed Creation’s fate

To me, this reads as if humanity has been given this beautiful thing we call life, but became corrupt, throwing morality away in favour of greed. In this metaphor, God gave us another chance to make things right, but we backstabbed him and tried again to get everything with no regard for what’s right.

Probably my favourite track of the album, Blindfolds Aside, discusses the story from the point of view of one of the soldiers tasked with carrying out Kezia’s execution. The soldier tries to justify his task as simply taking orders, but begins to question his own morality: Is it right and just to take a life simply because someone has decided so? The track opens with a simple but hard-hitting

We woke up as men, but tonight
Tonight we’ll sleep as killers

Once this decision is made, it cannot be undone. If Kezia is executed, these soldiers will have blood on their hands for the rest of their lives. The soldier tries to justify the incoming execution with

To atone for a sin I didn’t care for
But a sin that paid my debts
A sin that fed my children
That burned my smiles and cigarettes

He recognises this is wrong, but how else will he feed his family? He questions if he really has a choice in this matter; does morality die in the hands of a failed justice? Can he justify the killing as duty?

Five soldiers forever sedated
With the “No one’s responsible”
Pathological drama of our
Social justice dribble, dribble, dribble

If he pulls the trigger, is he responsible? If he is simply following orders, does that absolve him of responsibility? This directly relates to the officers of Nazi Germany: Many of them said they were simply following orders, but does that relieve them of their horrible crimes? How is this different than what the soldier is being ordered to do?

The penultimate track, The Divine Suicide Of K, is written from the perspective of Kezia herself as she walks to the execution. Throughout this story, she has become at peace with being killed, with the hope that she can become a martyr and catalyse a change in the system. In particular, she describes herself

Like an ulcer in the stomach of the beast

She believes even if she could not fix a broken system, she may have some influence and cause some change. Even if she cannot directly cause the change, she may be the beginning of it:

Resurrected to be killed then maybe born again
I’ll always be Kezia as long as any hope remains

She hopes that after her death, others may follow to fix this system. While the body of Kezia may cease to exist, her influence can remain in the hearts of the rebels to authority. She may die and others too, but her spirit will be regularly resurrected, and Kezia will continue to exist as long as any hope remains.

Architects

Some of my favourite lyrics come from the group Architects. While I’m not particularly fond of their recent music, some of their earlier work contains extremely profound concepts. At the time, their main lyricist was sadly losing a fight with skin cancer. The album All Our Gods Have Abandoned Us discusses acceptance of impending death and making peace with one’s own demise. My favourite track, Memento Mori, directly faces this idea, with excerpts from the late philosopher Alan Watts speaking about embracing death. Specifically, it states death is inevitable, so let it happen. But if death must occur, what then is life but a chance to make a difference? Possibly the most impactful lyric I’ve ever heard is

Was your life worth dying for?

Why live if you have no impact on the world? Did you make the most of your life while you had it to make death worth it? It’s a strong message; live while you can. Don’t let life pass you by. Once it’s gone, it’s gone forever.

A loss of finesse

With the rise of artificial intelligence, I worry society will lose some of its language finesse. We’ve seen already that ChatGPT overuses certain words and phrases, reducing the linguistic diversity we’ve seen in the past. I’m concerned that with overreliance on these tools, we’ll forget what makes language special. AI has little-to-no metaphorical understanding, but metaphors are the backbone of poetry and storytelling. Likewise with other language tools; AI is far too literal to understand, let alone, execute these wonderful uses of language.

I hope the world remembers its relationship with language and the diversity of words. We cannot allow ourselves to sink into the same words and phrases, and must keep language evolving and everchanging. We don’t want every person to sound exactly the same; that would signal the loss of what makes us human.

I find public key cryptography fascinating. It’s stunningly simple but incredibly secure against current compute technology.

Basic idea

The fundamental concept of public key cryptography is based on a few (usually very large) numbers. A public key is simply one of these numbers; a private key is another. However, the main difference is that the private key is kept secret, whereas the public key is distributed to anyone.

The public key can be used to encrypt data, which can then be securely transmitted to someone. In my eyes, the interesting part is that once encrypted, most of the encrypted data is discarded before being transmitted; this is why reversing the encryption algorithm isn’t possible. Even if an eavesdropper captures the transmitted data, it’s not feasible to decrypt. Upon receipt of the encrypted data, the intended recipient can use the private key to decrypt and read the data.

A simple example

While computers use extremely large numbers for encryption, a basic example can be shown with small (human-understandable) numbers. This will use RSA encryption with a public key of 11 and a private key of 7 under modulo/base 10. These numbers have certain relations to one another and are computed in a certain way, but we won’t go over that here. Note again that the private key is known only to the recipient of the data.

Encryption

Let’s say you want to transmit a single number (0-9) to me. You choose a number, say, 8, and encrypt it using the following equation.

While that looks a little complicated, it’s rather simple. We take the plaintext data (8), raise it to the power of the public key (11), then take the modulo with the base (10). The module operation simply means we divide by the base, then take the remainder. Therefore,

Therefore, the encrypted data is simply the number 2. Again, what makes this interesting is that we have discarded 8,589,934,590, meaning the exponentiation is not feasible to reverse.

Decryption

Once I received your message of 2, I can decrypt it with the private key. All I need to do is run the same operation you did, but with the private key instead:

We can see we’ve obtained the original data. One thing that makes this algorithm even better is that the mathematical operations are computationally cheap and very simple to implement. The difficulty comes with finding pairs of public and private keys, but the actual encryption and decryption are very easy to compute. Additionally, for many applications, the keys only need to be computed once and can be used many times.

Eavesdropping

A bad actor could fairly easily intercept your message of 2. However, they are unable to work out what the original data was without trial-and-erroring a bunch of options. This example is just using the digits 0-9, so this brute force approach is pretty simple: The eavesdropper can simply run the (public) encryption algorithm on every digit and find out which one results in 2.

That being said, modern encryption algorithms use ridiculously large numbers (for human brains), and trial-and-error is basically impossible. With modern algorithms, it’s generally thought that brute forcing a decryption would take billions of years or more, and therefore they are considered safe.

I will note here that with the early signs of quantum computing, it is possible these algorithms may be brute forced more easily in the future, but many smart people are working on this and finding solutions. Additionally, quantum computers are very much not ready for any task, so most people need not worry about it right now.

Cryptographic signing

Another application of this idea is digital signing to cryptographically “prove” someone has signed a document. Put simply, I could come up with a pair of keys and distribute the public key while keeping the private key secret. To digitally sign something, I could encrypt a message of something like “I am the real James and the 2026 rental contract was signed on Jan 3, 2026”. Once encrypted, I could attach the encrypted message to the document.

The document with the encrypted message could be distributed along with the public key (which is known to come from me). Any recipient could easily run the encryption algorithm with the public key on the encrypted message, and would obtain the original message stating “I am the real James…”, indicating I have cryptographically signed it.

Of course, there is more to this algorithm to increase its security, but the basic idea is nice and simple. A bad actor (without access to the private key) cannot come up with encrypted data that would lead to the same message, so it’s secure and reliable.

Conclusion

Public key cryptography has been around for decades and will likely be around for many more due to its combination of security and simplicity. There have been updates to the algorithms over the years, but they are usually related to the length of the keys; the process remains the same. Public key cryptography is a wonderful mathematical tool giving robust security and allowing the modern internet to exist.