DEV Community: Satvik gupta

How Language Shapes Your Thoughts

Satvik gupta — Sat, 05 Jul 2025 09:32:50 +0000

We speak, we write, we connect. But what if the very words we use are subtly dictating our reality? Language, often seen as a mere tool for communication, possesses a hidden power — a power so immense it shapes our thoughts, beliefs, and even our understanding of the world. And its true complexity is almost always ignored.

The Hidden Burden of Words

What are words? They’re a bunch of syllables that are attached to an object or idea. Words have complicated meanings and carry the burden of context and historical usage. Anyone who engages in any kind of discussions must have realized the amount of semantic gap there is between people and the idea you are trying to convey. This leads to subjectivity.

Language is almost never interpreted as you actually mean it, and you don’t even know how the person you are debating with is actually interpreting your words.

Some people say you must follow the Oxford dictionary to avoid semantic misunderstandings. This has use and is helpful, but with words like “society,” “religion,” “god,” “evil,” “woman,” “man,” “intelligence,” and “consciousness,” the contextual burden these words carry is so great, it is only a brutal simplification to reduce them to two-liner definitions. So being ignorant of this fact is a crime.

I think that when we hear a word, we form an image in our minds, from our own lens which is made of our emotions, past experiences, and personal values.

The Subjectivity of Words

To understand this phenomenon better, let’s take the word Palestine for example. If you look at the Wikipedia definition for this word, you would get something pretty simple referring to it as a geographic location in the Middle East or something. But when you hear that word, even though it just refers to a fixed objective geographic entity, different people — let’s say a guy who knows nothing about Palestine, a Jew, a Muslim, a person who just read Palestinian history, someone who knows the culture of the place — each person would have a different idea of Palestine in their head, and this is the subjective burden is ignored in conversations.

So to an extent, there are 1000s of different versions of the word Palestine, but in conversation, they are clubbed into one word. I have seen this happening countless times in debates related to complicated topics such as “What is gender?” and religious debates related to scripture. This simple phenomenon causes so much confusion and gaps in communication.

Language Forms the Boundary of Your Thought

Building on this understanding of how words carry subjective meaning, I believe the impact goes even deeper. In my opinion, the language you speak can ultimately influence even how you think about the world.

To highlight how much language you speak dictates how you think about the world, let’s explore an example. When I first heard about the 9/11 attacks, along with the deep shock and grief, one thing I couldn’t understand was how is it even possible for a human being to do such a thing? What possibly could motivate them to not only take the lives of 1000s of innocent people, but that too while committing suicide?

So I think I now have an answer to that question: let’s explore how ISIS brainwashes children and how language plays a big role in it.

But first, let me explain the foundation that led me to this understanding. Ask yourselves, where do all your beliefs come from? Where does all your knowledge come from? Where do the skills that you have acquired come from? Either you discover them yourself, though this is quite rare — only a few people are creative or skilled enough to create knowledge from nothing — but the bulk of our knowledge comes from society, other people, books or resources created by others, your parents, etc. Right?

This is what separates humans from animals fundamentally, not only our ability to reason about information and gain insights from it but also pass it down to the next generation. This is what drives civilization’s progress ultimately; without this, we wouldn’t have been able to advance at all.

And what tool do we use to pass down this knowledge? Well, language. So essentially, everything you know, you have somehow acquired from the external world.

Doubting My Rationalism

This realization led me to question everything I thought I knew about myself. I used to always think I am a rationalist, that all beliefs have a rational and logical basis. But this line of thinking now made me question everything about what I know — an existential crisis of sorts, lmao.

For example, religion. I thought, what if human civilization started from scratch again and no one was taught about Islam or Christianity? Would they emerge exactly in the same manner? Probably not. The things that would be true in the real sense.

I thought if humans started from scratch, people would again, through the process of hit and trial, discovering things, passing that knowledge to the next generations, things like mathematics, concepts like numbers would probably still be invented, and they would look exactly the same. But religion also probably will be formed (this is a whole discussion on its own, so let’s leave it for later), but they would for sure look entirely different. Islam would not be formed exactly in the same way, same for Christianity or Judaism or any religion for that matter.

This is because it was formed as a complex byproduct of a lot of human interaction throughout the course of history, which for sure wouldn’t play out exactly the same.

An Interesting Thought Experiment

This insight crystallized into my go-to thought experiment to distinguish truth from falsehood. If something would look entirely the same if humanity restarted from scratch, it’s towards the truth; if it looks different, it’s made up.

Objective truths: mathematics, logic, physical laws — which would likely re-emerge.
Constructed truths: religions, social norms, ideologies — which would look totally different.

Armed with this axe, I started cutting down all trees of my understanding of the world: the concept of countries and their existence, the concept of family, power structures that exist in society, the role of government, police, basically everything that fails the litmus test of that thought experiment.

In our society, these things have become so deeply ingrained in our psyche that most people wouldn’t ever question them or just can’t even imagine a world without them. Well, voila! There it is. This was the answer to my original question.

This is what makes you vulnerable; this is when I realized how vulnerable each one of us is. And in a sense, how brainwashed each one of us is, actually very similar to how ISIS fighters are brainwashed.

I realized it wasn’t my rationality or logic stopping me from becoming a soldier of the caliphate; it was sheer luck. I was luckily brainwashed with Western ideals of freedom, democracy, liberty, individualism, mixed with Indian nationalism, Hinduism. Now, if that is objectively better or not is a topic of debate for some other time.

ISIS and the Power of Language

Now let me show you, with this background, how ISIS indoctrinates people.

I would urge you now to put yourself in the mind of a young Muslim. You have to consider all the stuff that he has learned from his childhood; that is what will form the core unchanging basis of their understanding of the world.

Ludwig Wittgenstein said,

“The child learns to believe a host of things. I.e., it learns to act according to these beliefs. Bit by bit there forms a system of what is believed, and in that system some things stand unshakeable fast and some are more or less liable to shift. What stands fast does so, not because it is intrinsically obvious or convincing; it is rather held fast by what lies around it.”

I know it’s hard to do, but let me help you. Put yourself in the shoes of a young Muslim. Forget, for a moment, your own background — whether you’re Hindu, Christian, secular, liberal, or anything else. Try to see the world through the mental model of a Muslim raised in a conservative, religious environment, one where belief in God is not a question — it’s the starting axiom.

If you are born as a child in Raqqa at the heart of Syria, you aren’t even allowed to look at any other language except Arabic. This is some vocabulary used by ISIS:

As you may notice, some of these concepts don’t have specific words for them in English directly; nothing directly translates exactly into English. Bay’ah, for example, which means allegiance to one’s leader, or Istishhad, which means seeking martyrdom, shows the society this language belongs to must value these concepts or they have some higher significance, either positive or negative, than Western or Indian counterparts.

So a child living in such an environment doesn’t even have the words to think about certain things; this clearly shows how your language limits your capability to reason. Your language is the literal boundary of your thoughts. Again quoting Wittgenstein,

“The limits of my language means the limits of my world.”

A Multilinguist Perspective

This understanding becomes even clearer when you examine multiple languages, as I’ve experienced personally. I am bilingual; I can speak English and Hindi, and these languages have been developed in such different environments with rich histories of their own. I can myself notice that the concept of untranslatables is very real. I have seen a lot of Western people who read Sanskrit texts be completely ignorant of this fact, and they end up not actually grasping the contents of the texts by assuming stuff like Atman = soul, Brahman = god, Moksha = liberation, etc.

And same goes for me trying to read and understand the Quran.

I see the amount of untranslatables as a good measure of isolation of certain cultures. As India was colonized by the Britishers, I see a sort of Abrahamization of India’s perception of whatever we call religion (note religion is an English word), and I would argue we didn’t have a concept directly mapping to it ever in India.

So when you examine Sanskrit texts, the amount of untranslatables to English is insane; this shows it was a culture coming up with original and unique ideas of its own. Post-colonization, you can clearly observe as Indians grow up to be bilingual in English and Hindi, without any touch from Sanskrit while still following the Vedic religion.

Due to lack of untranslatables, many Indians have started mapping ancient Indian concepts in Sanskrit to Hindi and English, but due to lack of those concepts in English society, they are losing the capacity to understand their own culture, causing Abrahamization of the Indian tradition, unlike Sanskrit and English.

This would be pretty hard for a monolingual person to understand. I would love to know what a polyglot thinks about this especially if they know languages from vastly different cultures, like ancient Egypt, ancient India etc.

Conclusion

Language is not just a tool for communication — it’s the scaffold of our thoughts, beliefs, and identities. From the subjective meanings we attach to words like “Palestine” to the way ISIS uses vocabulary to brainwash children, language shapes how we see the world. Understanding this power — and our vulnerability to it — might be the first step toward genuine intellectual freedom.

Make Beautiful Art for Your Game even If you suck at It!

Satvik gupta — Mon, 14 Apr 2025 15:00:02 +0000

Are you A Solo dev drowning in art,code,marketing and music
or maybe someone from a programming background with art that looks like a 5 year old went wild on MS paint !

Today I am going to give you some actionable steps , beyond the usual just practise more bro bullshit.

Lets be Honest ,games that look like that dont get much unfortunately but
dont worry you dont need to an artist to make your game look good ,I was in the same boat when I started development for my game Acord and managed to create something that looks like this , not AAA but stylish and decent!

Here are some simple tricks I discovered which can help you out

THE MINDSET

You need to be what I call CREATIVELY LAZY

so , the truth of the matter is you cant draw shit ,so you need to constantly think of ways to make up for this .
When in doubt say to yourself whats the laziest way i can make this look good ?

I didn’t pick the sketchy art style in Acord because I loved it.
I picked it because it was:
1.Easier to draw
2.Easier to animate
3.Didn’t require crazy painting skills

It saved me hours of effort — and it actually looked cohesive once applied to everything.
So here’s the key:
Don’t aim for beauty — aim for consistency and ease.
Pick a style that works with your skill level, not against it.
it can be as simple as stick figures , it can still look good if you make it cohesive and consistent

2.RELY ON THE GAME ENGINES

make up for your shitty artskills with some game engine magic
Modern game engines like unity and unreal have features to add beautiful lighting , post processing effects and other crazy stuff like shaders, normal maps , particle effects ! and these arent that difficult to do
I would urge you to look into these techniques and design around them , instead of relying on ur ability to draw let the engines do the heavy lifting please
like here are some of my games with and without any game engine magic

THE ILLUSION OF DETAIL

What makes a game from looking average to amazing , its the details each little thing matters . Now a solo dev or a small team cant out detail a Studio so you need to create an illusion of detail
How you do that is using textures
got a boring looking wall , just slap on a texture , combined with normal maps and lighting you got urself something that looks awesome!

Now with chat GPT image generation this got so much easier !

each element in this is just simple shapes with a texture slapped onto it ,the ground is just a rectangle with a floor texture , the wall is just a rectangle with a wallpaper and crack texture and so on

4.COLOR THEORY

now this is the one thing you cant escape from ,choosing the right colors is arguably the most important thing to make ur art look good .
now following the first principle i managed to escape this lmao , but i would recommend these youtube videos to learn about color theory
after these practise , simple shapes + some color theory can go a long way

https://uxplanet.org/free-resources-to-learn-color-theory-3deeadc22336

Here you go spilled all my secrets ! now make some epic looking stuff and
you can share it with me at
satvik730gupta@gmail.com

Does Certainity Exist ?

Satvik gupta — Sun, 30 Mar 2025 12:43:55 +0000

Why We Know Less Than We Think

I see people arguing about whether free will exists or not, whether God exists or not, what gender is, and various political issues, but it all seems kind of skewed. I have come to the conclusion that everyone should be humble enough to accept that we have no idea what's going on with these topics

There are various ways of searching for the truth. I am a big fan of the scientific method; it's mind-boggling how this simple approach has created so many wonders and extended our understanding of the world like no other. I have studied high school level science. I know my knowledge of science is pretty limited, but I have made some interesting observations.

So what's the tool that we use to engage in scientific communication? It's mostly math and very precise definitions, thus leading to rather accurate and helpful results. The more a science deviates from these principles, the more inaccurate its results are.

Math relies on pure reasoning and is always absolutely correct because the object of discussion is very simple (say a line, circle, vector, slope, etc.). We define every single thing about the object, we lay out our assumptions at the start, then through logic, we derive more facts about that object and its behavior, and we are very strict with our logical rigor.

It always fascinates me how the repetition of this simple process yields amazing results. The most unobvious theorems, even artificial intelligence, and counter-intuitive yet true results are just a result of this process, continuous abstraction of simple results in an innovative and creative way.

Through stepwise deduction, and basing each step on a set of well-defined axioms which are obviously true, we can reach truths which were previously hidden from us.

Any crazy math theorem is just a result of this seemingly simple process

And this is what makes Math beautiful.

You can realize how simple things lead to profound and complicated insights by deductive reasoning and thousands of layers of abstraction.

Physics is a bit less accurate and includes more assumptions rather than relying on extremely obvious axioms like mathematics, as we are dealing with more complicated things. Already, the need for logical rigor becomes a second priority. But we still build precise models and then use those to make predictions which are mostly accurate.

But again, in physics, from the little knowledge I have, there's this huge problem that the models we create for how the universe works seem to break down depending on what scale we are talking about. If it's electrons and atoms, things behave according to a different model (quantum mechanics), and if they are as huge as a supernova, they behave under a different model (relativity and such, I think).

We often use things like approximations that would make any mathematician frown over the lack of rigor.

Actually, Einstein put this perfectly:

"As far as the laws of mathematics refer to reality (physics), they are not certain; and as far as they are certain, they do not refer to reality (math)."

It's definitely interesting.

And chemistry discusses even more complicated systems, hence it's even more abstract and less rigorous in its approach. From the little organic chemistry I have studied, we don't actually have any precise models or rules in chemistry. What we have are trends we observe that we generalize over certain cases. Like in coordination chemistry, I remember studying the EAN rule, and it doesn't always apply. That's fine, but it's not like we have created a precise model of how atoms work and now we can just predict what would happen in a reaction based on that. The approach is more like first you observe the reaction and try to fit it into some logical trend or order so you can make sense of it and at least try to predict something with a similar system. You aren’t creating a generalised model of how reactions work based on a set of fixed axioms instead you create multiple models for multiple situations , which rules out certainty

I bet if you ask a math student a question and keep grilling them again and again on "why this, why that", like in the earlier example about the prime number theorem, for each step in the process you could keep making the flow chart bigger and bigger by asking questions and in the end you will ultimately reach the very fundamental axioms of mathematics.

So you see how as the things to analyze get more complex, our scientific models become less and less accurate. My point is basically that science as a method of inquiry into truth works because it relies on mathematical deduction, so we can be sure of things only in a mathematical world.

But the problem is there are questions which science can never answer, and it has its limitations (maybe because the problems can't be solved). We turn to other fields like philosophy, political science, and psychology to look for answers to such questions.

But here our logical rigor seems to fade away entirely. We completely start discussing topics in terms of analogies, stories, and emotions, which introduces a whole bunch of complexity and confusion to something which is already extremely complex. It seems like the more complicated the topics get, the more humans dumb them down for themselves (i.e., focus less on the precise mathematical rigor because at this level of abstraction it becomes almost impossible).

When I was a kid and heard there was this math question called the Poincare Conjecture with a million dollar prize on it enough to spark a child's interest , I thought stuff like this was the peak of human intelligence, the hardest thing the human brain could ever do. When I looked up the proof, I saw this 140-page article filled with scary Math, all of inferential deduction just to demonstrate this simple fact, but now that I look at it I realize actually simple average political discussions are way more complex and maybe require even more analysis than this proof, but we, for our own convenience, don't actually think about every single variable of the puzzle. We create a model in our heads based on the fragments of information that we have picked up along the way and then form an opinion out of it.

THE PROBLEM WITH LANGUAGE

The tool we use for philosophical communication is language. I think it's often ignored how complicated language is. What are words? They're a bunch of syllables that are attached to an object or idea. Words have complicated meanings and carry the burden of context and historical usage. Anyone who engages in any kind of discussions must have realized the amount of semantic gap there is between people and the idea you are trying to convey. This leads to subjectivity.Language is almost never interpreted as you actually mean it,and you don't even know how the person you are debating with is actually interpreting your words. Some people say you must follow the Oxford dictionary to avoid semantic misunderstandings. This has use and is helpful, but with words like "society," "religion," "god," "evil," "woman," "man," "intelligence," and "consciousness," the contextual burden these words carry is so great, it is only a brutal simplification to reduce them to two-liner definitions. So being ignorant of this fact is a crime

I think that when we hear a word, we form an image in our minds , from our own lens which is made of our emotions, past experiences and personal values.

Let's take the word Palestine for example

Of you look at the wikipedia definition for this word , you would get something pretty simple referring to it as a geographic location in middle east or something But when you hear that word, even though it just refers to a fixed objective geographic entity .different people let's say a guy who knows nothing about Palestine, a Jew, a Muslim, a person who just read palestinian history, someone who knows the culture of the place , each person would have a different idea of Palestine in their head , and this is the subjective burden is ignored in conversation s.So to an extent there are 1000s of different version of the word palestine but in conversation they are clubbed into one word.

I have seen this happening countless times in debates related to complicated topics such as "What is gender?" and religious debates related to scripture.

This simple phenomenon causes so much confusion and gap in communication.

The second pillar of which we form any opinion is our morality. I think it is simply a function of emotions and generationally passed on learnings of our ancestors, again at the root of which was again human emotion, and human emotion is subjective thus leading to morality being subjective. For example, people argue endlessly on whether abortion is "moral" or not, eating meat is moral or not. Now as I have been explaining, something like this has 1000s of variables attached to it, religion, etc.

PERCEIVED VALUE

Another thing we often ignore in our discussions is the subjective value attached by every individual to an object. What I mean by this is, let's say I have two exact copies of the same football, but one of them is the football Ronaldo played his last match with. Now this football has a higher perceived value than the other football. So let's say we are talking about these footballs; I think it's a crucial factor to consider. This becomes specially important in discussions involving objects of historical, religious or artistic importance like the ram mandir issue or the israel palestine conflict .But again, whenever we talk about politics or history, we fail to do an accurate analysis of the perceived value of the objects in discussion or any other issue. To each human, each thing has a different value. Again, this laziness and ignorance is understandable as it would be another impossible thing to account for, but I think it's an important variable to account for .

Now try to get your head around this during any said political discussions: 1000s of words are being used which all have a deep-rooted context and the subjective image created in everyone's mind for each one of them is different. There are 100s of variables they play into that discussion and each variable has subjective perceived value based on history, culture which is again 1000s of years old.

Isn't it impossible to wrap your head around?

we dumb all of this down and look at the world through a lens or a perspective of our own making, and every experience we have slightly alters our emotional consciousness, what we feel empathetic towards, what we feel disgusted by etc., and these tiny nudges make everyone a different person.

And we all know how much of our thoughts are bound by the chains of emotions. Another thing we love is to lie to ourselves and perpetuate the collective lies we believe, hiding that under the veil of positivity! In other words, we like to believe in things which we wish were true rather than the truth. There may be many more such impossible variables for the human brain to account for which I am not able to think of right now, which are very much needed in our analysis of the world but it's just not in our capabilities to account for them correctly.

Just think about it: there have been thousands of political scientists and philosophers from Adi Shankaracharya and Aristotle to Nietzsche and Buddha, who spent their entire lives contemplating about the world. Why then, even after so much effort in the search for truth, are their truths just completely different? No matter how much they try, they make subjective judgments, based on their own life experiences and morality and all that other jazz I discussed above.

I think this is because we haven't developed (I don't know if something like this can even be developed) a proper logical tool for engaging in good philosophy.

See, I am not saying all these discussions are pointless or useless . This article is basically just an urge for humbleness in the fact that we can't really be opinionated on these things and we are forced to live on the edge of "Yes" and "No," which is sometimes hard for people. This could actually be a really healthy mindset in this modern world, where people have become so opinionated politically as if they think they are some sort of moral superheroes who care about the world and on the other side everyone is a vicious demon who is evil, instead of recognizing the subjectivity of it all.

This makes me think we humans only possess a certain level of cognitive abilities. Are we even capable of logically discussing these extremely complicated ideas? We should really question our capabilities and at least be a little humble about how little we know!

This perspective just makes you way less arrogant about your views. In short, I think humans are too limited for philosophy or political science; hence, it's just a fun little mental exercise you can do for fun, but don't take yourself that seriously.

4d Fractals using the Chaos game Algorithm

Satvik gupta — Tue, 18 Mar 2025 15:23:31 +0000

EXPLORING THE 4th DIMENSION THROUGH FRACTALS

What I really find beautiful about mathematics , is just how simplicity leads to beautiful results

so lets explore the world of 4 dimensions through the lens of fractals .

So I was just looking for some programming projects , that is when I came across this algorithm

The Chaos Game

Its deceptively simple

You mark Three 2D points say A,B,C to form an equilateral triangle using x,y coordinates then choose any random point on the plane .

A certain set of points which satisfies these properties is for example ,

ND CHAOS

We can verify this using the distance formula for 2d spaces.

Then proceed to mark a third point on the midpoint of the chosen random point and Any of the Points again randomly chosen from the A B or C , using the midpoint formula for 2 dimensional space

And infinitely repeat this process , By placing a point again on the resultant point and randomly chosen point from the three vertices of the triangle

https://www.youtube.com/watch?v=kbKtFN71Lfs&t=458s check out this video for a complete explanation

Now let's apply this to our triangle

at first it looks like well CHAOS but slowly you see a pattern starts to emerge

What if we arrange the points co linearly ?

What if we start with a square ?

For those of you who are curious ,I leave those questions for you to answer as an programming exercise

Tweaking these sets of initial points and adding more restrictions gives rise to even more interesting fractals, go ahead and try experimenting

Here are some examples

Notice the element of randomness in this algorithm , yet it produces a beautiful deterministic patterns , tbh I found it very strange at first and you know what's crazy

it forms these fractals in infinite dimensions , but before getting too ahead of ourselves

First lets extend this simple algorithm to Three dimensions

That's right

Instead of a triangle we take a regular tetrahedron which is basically just a triangular pyramid with equal sides and repeat the same process

And again from chaos emerges a sierpinski tetrahedron , These infinitely repeating self similar patterns that you see forming are called fractals.

You see them emerge everywhere in nature from tiny snowflakes to entire galaxies

Crazy stuff !

But now begins the fun part ,

The cool thing with math is you aren't bound by the laws of reality or the limits of human perception , lets dig deeper

So we are going to step it up a notch and extend this same pattern to 4 dimensions

For that we need to first examine a few things

We experience the world within our senses , we experience a 3d world which is then projected on the 2d retina ,

Slowly through evolution our brain has figured out certain tricks .

Like shadows , foreshortening and perspective through which it makes sense of the 3d world and its depth even though we are limited to a 2d retina ,

Artists since millennia have figured out techniques to fool the brain ,the 2d picture they are looking is actually 3d

But sadly our brain has no frame of reference to perceive the fourth dimension

It understands a 3 dimensional world through a 2d retina after all .

First of all let's start with finding the 4 dimensional equivalent of an tetrahedron ,

So let's analyse what did we just do earlier

In 2 dimensions, we defined an equilateral triangle using two coordinates: x,y.
By applying the euclidean distance formula, we ensure that the lengths of all three sides are the same. Where x1,y1 and x2,y2 are the corresponding points on the triangle

Moving to 3 dimensions, we use three coordinates: x,y,z
Again, applying the distance formula ensures the sides are equal, giving us a tetrahedron.

But here’s the exciting part:
We’re not limited to these dimensions

Similarly for finding the Midpoint we can use

Both of these formulas have been derived by extending the patterns from 2d and 3d spaces to an abstract world of n - dimensional Euclidean space .

Similarly ,

In 4 dimensions, we can define a shape with four coordinates: x,y,z,w
.

With the following coordinates

(1,1,1,−1 )

(1,−1,−1,−1)

(−1,1,−1,−1)

(−1,−1,1,−1)

(0,0,0,2)

We can apply the same distance formula to verify if it verifies the property of a equilateral sides , and voilà

It’s the 4-dimensional equivalent of a tetrahedron.

Some of you may be more comfortable with this strange idea of extending the euclidean formula to any n dimensional space

To all of those who are skeptical , with math ,the thing is you just follow the patterns and see where it takes you , so for now i would recommend you all to just follow the patterns and follow beauty and see where it guides you

We can take this abstract 4D figure and apply the same Chaos Game algorithm to it.

Pick a random point in 4D space.

Mark the 5 points of a 4d tetrahedron in 4d coordinates

Choose a random vertex of the 4-simplex.

Mark the midpoint

"Now, I know what you're thinking:

That midpoint that we just found its in 4 dimensions too , now how the heck do we visualise it
How can we see something that's 4-dimensional if we're stuck in 3D?

This is where the beauty of math and art intersect.
think about shadows.

Imagine yourself as a 2-dimensional being, living on a flat plane and you cast light on a 2d object
What would you see ?

A point shadow

Why?

Because a 2-dimensional object, like a line, casts a 1-dimensional shadow. To you, that shadow looks like just a point.

Now, again let's extend this idea to 3d

As 3-dimensional beings, what do we see when we look at an image of a cube on a 2D screen?

We’re looking at its 2D shadow, not the cube itself.

As we discussed earlier
Your brain uses tricks—perspective, foreshortening, shading—to interpret this 2D projection of the 3D object

By now You might have started seeing an idea here , we try to find patterns in 2nd and 3rd dimensions and just blindly trust the math and extend it to 4d

So ,

What would shadow of a 4 d object look like , if we follow the pattern it should create a 3d shadow which could be projected on a 3d space

And there it is , a way for us to visualise the 4 dimensional fractal we just generated

Now the question is How do we cast its shadow , or in other worlds project it onto the 3d plane

Every time we project an object from n-dimensions onto a lower dimension, we lose some information.what I mean by that is that you can not infer every property of an n dimensional object while looking at its n-1 dimensional projection

Like when you look at a cube projected on a 2d screen you can not see all of its edges at once for example as they get hidden by the faces in front of them

This is why There are tons of ways of projection

But each projection system is designed to preserve different aspects of the image.

One case where we encounter a similar problem is maps where we need to project an entire 3d spherical earth onto a 2d map

Different projection techniques lead to different results , each giving us some unique insight about the 3d object .

Like the one to left is a stereographic projection , it preserves the circular shape of the globe

And one to the right is a mercator projection which preserves the actual shapes of the countries

now the math involved in these is out of scope of this article , for now just think of it as an formula which takes 3 dimensional inputs and spits an 2 dimensional input

While wrapping our minds around the 4th dimensions , we need to take a similar approach
And that’s the beauty of it.

With math, we can step beyond our sensory limitations, moving through dimensions that our brains simply can’t directly perceive.

We can use projections to reveal parts of the 4-dimensional world, even if we can’t fully understand .

Each projection will reveal something more about our 4d fractal , similar to how each type of projection of a 3d earth reveals different details about it .

Let's start with a stereographic projection , generally it preserves angles at which curves meet and thus approximately preserves shapes.

So obtained 4d points earlier , we can use the following stereographic projection formula which converts our points into 3 dimensional points .

Now that we have tamed the 4-d figure to something we can visualise

Lets repeat the chaos game steps

I got these results

Please feel free to experiment with different shapes , rules and projections methods and explore the world of fractals infinite dimensions

What you are looking at is two 3 dimensional views of a 4 dimensional Sierpinski 5-cell rotated relative to each other , further projected onto your 2d screen

When you look at this fractal, remember: you're not just looking at a shape, but at the hidden beauty extending in theoretically infinite dimensions which we can peek into by seeing the ripples of their majesty in their 3d and 2d projections