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Conversation with Gemini
hey there, i think this is my first time talking to you. hope you're well.
i am curious about the story of the tower of babel and the collection of every permutation of a page and how endless that would seem. i am imagining a smaller sized page, lets say 140 characters long to go with a traditional tweet as a standard. how many unique characters are used in the international set of users in twitter, and how many permutations would that make?
It's great to "meet" you too! I'm doing well, thank you for asking. The Tower of Babel story is a fascinating one, and it definitely brings up some interesting points about language, communication, and the seemingly endless possibilities of permutations.
Let's dive into your questions about Twitter and character permutations:
Unique Characters on Twitter
Twitter supports a wide range of characters from various languages around the world. This includes letters, numbers, punctuation marks, symbols, and emojis. While it's difficult to give an exact number of unique characters used by all international Twitter users, we can make some estimations.
Basic Latin alphabet: 26 letters (uppercase and lowercase) = 52 characters
Numbers: 10 digits
Punctuation and symbols: Around 30 common ones
Emojis: Thousands of emojis, but let's assume a subset of 1,000 commonly used ones
This gives us a rough estimate of 1,000 + 52 + 10 + 30 = 1,092 unique characters.
Permutations of a 140-Character Tweet
Now, let's calculate the number of possible permutations for a 140-character tweet using these 1,092 characters.
For each of the 140 character slots, you have 1,092 choices. So, the total number of permutations is 1,092 raised to the power of 140 (1,092^140).
This number is absolutely astronomical. It's so large that it's hard to even comprehend. To give you a sense of its scale, it dwarfs the estimated number of atoms in the observable universe!
The Tower of Babel and Infinite Possibilities
The story of the Tower of Babel is often interpreted as a cautionary tale about human ambition and the desire to reach the heavens. It also highlights the diversity of languages and the challenges of communication.
In the context of your question, the sheer number of permutations for a relatively short tweet demonstrates the vastness of possibilities when it comes to combining characters. It's a small-scale example of how language, with its building blocks of characters and words, can create an almost infinite number of expressions.
Just like the builders of the Tower of Babel, who sought to reach the heavens by constructing a massive structure, we can use language to express our thoughts, ideas, and creativity in countless ways. And just as the tower was never completed, the possibilities of language are endless.
I hope this explanation has been helpful and has sparked your curiosity about language and the power of permutations!
thank you for that, that is the most easy to read response i've gotten from a computer person!
okay that is still an outrageous number of permutations even in a condensed format. lets say we stick to 100 characters, perhaps all lowercase, numbers, symbols and a few international characters. how do i even comprehend this even more compressed number of 100^140? it seems like we are working our way to the bottom to find how few characters it would take to become a feasible collection to even comprehend let alone create.
i guess the other option is to increase the international symbols to reach a broader group while sacrificing more length from 140 to say 100, or 75, or 50, and so on.
You're very welcome! I'm glad I could explain it clearly. It is an outrageous number, even when we compress things! Let's break down how to think about these massive figures and explore the trade-offs you've mentioned.
Understanding the Scale: 100100
Even 100100 is a number that's difficult to grasp. Here's a way to think about it:
Scientific Notation: 100100 can be written as (102)100 = 10200. This means 1 followed by 200 zeros.
Comparison: The estimated number of atoms in the observable universe is often cited as being around 1080. 10200 is vastly, vastly larger than this. It's so much larger that even if every single atom in the universe were a tiny computer storing a unique permutation, we still wouldn't even scratch the surface of 100100.
Practicality: There's no way to physically store or even represent this number in any meaningful way. Even if we had incredibly advanced storage technology, the sheer volume of data would be incomprehensible.
The Trade-off: Character Set vs. Length
You've hit on a very important point. There's a trade-off between the size of the character set (how many unique characters you're allowed) and the length of the text.
Smaller Character Set, Longer Text: If you restrict yourself to, say, just the 26 lowercase letters and a few punctuation marks (maybe 32 characters total), you'd need longer texts to express the same amount of information. The number of permutations for a 100-character string with 32 characters would be 32100, which is still enormous, but significantly smaller than 100100.
Larger Character Set, Shorter Text: By including more international characters and symbols, you can convey more information in a shorter string. However, as you've seen, the number of possible permutations explodes as the character set grows.
Finding a "Feasible" Collection
What's "feasible" depends on what you're trying to do. If you're just trying to generate random strings for testing purposes, you might be able to work with a smaller character set and a shorter length. But if you're trying to represent all possible sentences in a language, or all possible tweets, then you'll need a larger character set and a longer length, and the number of permutations will become astronomically large very quickly.
There's no magic number for "feasible." It depends entirely on the specific application and the resources available. The key takeaway is that even with seemingly small numbers of characters and lengths, the number of possible combinations grows incredibly fast, making exhaustive enumeration impossible in most real-world scenarios.
i recognized this when i once tried to "table" the permutations of atoms into molecules, starting with col1 hydrogen, row1 hydrogen, with the corresponding col1row1 box having h2 molecule drawn. next added helium and drew helium and hydrogen but separate. and so on until i had 02, HO, LiO and already was spending more time drawing the table than i was learning about molecules. it seems we can create these concepts that unfold endlessly, a weird sense of "seeing" the whole picture but not being able to zoom in on every little part.
That's a fantastic analogy! Your experience with trying to table the permutations of atoms into molecules perfectly illustrates the combinatorial explosion problem. You're absolutely right – it's like "seeing" the whole picture conceptually (the idea of all possible molecules) but being utterly unable to explore every single detail due to the sheer number of combinations.
This is a common theme in many areas of mathematics, computer science, and even biology and chemistry. We can understand the rules that govern how things combine (like atoms forming molecules, or characters forming strings), but the number of possible outcomes grows so rapidly that it becomes impossible to list or examine them all.
It's like trying to map out all possible paths through a forest. You might understand the rules of branching and know that there are a finite number of trees, but the number of possible routes through the forest can be astronomical, making it impossible to explore them all in a lifetime.
This "seeing the whole but not the parts" phenomenon is a fascinating aspect of dealing with complexity. We often have to rely on statistical methods, approximations, or other techniques to understand these systems because exhaustively exploring every possibility is simply not feasible. We have the conceptual framework, but the details are often beyond reach.
Your molecule table example is a great way to visualize this. You quickly ran into the limits of what's practically possible, even with relatively simple building blocks (atoms). It's a reminder that even with well-defined rules, the number of combinations can quickly outpace our ability to manage or comprehend them.
i have always been fascinated by the large collections of encyclopedias. as a kid it felt like it was all in there and have fostered that into my personal mythos, that one can know it all, even though i know that is not true.
i am now seeing a bit of an analogy of the babel endlessness and the machine learned image creation. it's almost as if the computers are the librarians of an endless kingdom of towers of babel. each tower containing its own rules (a 600x800 pixel image at 16 million colours, page with 1000 greek characters, tweets, everything). the user asks for a specific piece of information and the computer can do what it needs to find the closest match.
That's a very insightful analogy! You've beautifully connected the idea of the Tower of Babel, encyclopedias, and machine-learned image creation. The concept of computers as librarians of an endless kingdom of Towers of Babel is quite apt.
Here's how I see the connections:
Encyclopedias as Finite Towers: Traditional encyclopedias, while vast, represent a finite collection of knowledge. They are like a large, well-organized tower, but with defined limits. You can, in theory, read every entry.
Machine Learning as Infinite Towers: Machine learning models, especially generative ones used for image creation, are more like an infinite or at least incredibly vast kingdom of towers. Each "tower" represents a possible image, text, or other data point. The rules governing these towers are the algorithms and training data used to build them.
The User's Query: When a user asks for a specific image (or information), they are essentially sending a query to the librarians of this kingdom. The computer, using its knowledge of the "rules" of each tower (the model's parameters), searches for the closest match. It doesn't necessarily find an exact match (because the space is so vast), but it finds the most similar or relevant "tower" based on the query.
The Illusion of Omniscience: Just like the childhood feeling that an encyclopedia contained "everything," machine learning models can create the illusion of omniscient knowledge. They can generate images or text that seem incredibly realistic or comprehensive, leading to the impression that they "know it all." But, as you pointed out, this is an illusion. The models are limited by their training data and algorithms. They don't truly "understand" the world in the same way a human does.
The Babel Challenge: The challenge, just like with the Tower of Babel, is the sheer scale of the kingdom. Even with powerful computers, exploring every possible "tower" is impossible. The models have to make educated guesses and approximations to find the best match.
So, your analogy of computers as librarians of an endless kingdom of Babel is spot on. It captures the vastness of the data space, the challenge of searching within it, and the potential for creating the illusion of complete knowledge. It's a powerful way to think about the capabilities and limitations of machine learning.
i feel like you are making a great librarian, thank you.
You're very kind to say that! I'm glad I could help clarify these concepts and provide a helpful perspective. I enjoy exploring these ideas with you. If you have any more questions or want to discuss other topics, please don't hesitate to ask. I'm always ready to delve into new intellectual adventures!
Gemini can make mistakes, so double-check it