There are 2¹⁰²⁴ things you can do with a kilobit
twitter.com
twitter.com
1 KiB or a kilobyte has 256^1024 different states, not 2^1024. Can be written also as 2^(1024 * 8).
This fact is also mentioned in author's own reply, just submitting this comment to avoid other people scratching their heads.
The idea of an ideal communication channel rivals most ideas ever had. The original paper is surprisingly accessible. Highly recommended if anyone hasn’t had a chance to give it a tour.
And here’s the book, just to not be a tease: https://pure.mpg.de/rest/items/item_2383164/component/file_2...
Once you refresh your knowledge of the greek alphabet, it’s not that scary. Math just needs a lot of symbols.
A good starting point would be infinite series, as this is the basis on which we imagine things bigger than a human lifetime. And it reminds us why we had to define a “limit” as a summation that strangely looks like ∑
It took me years to see the significance of arithmetic series, but as with any ∑, you have to start somewhere! (Often at -∞ and +∞)
The trick to all of it is that there are patterns declared by the underlying structures. There is not really a way to understand them without playing around with equalities and diagrams until you reach a certain zenlike moksha. Trust me, it is quite fulfilling!
I digress. Assume a bit for every “if” statement (branch) that is taken within a function (less those that are deeply nested and don’t affect each other). That’s the Kolomogrov complexity.
I'm not even sure you can accurately tell me all the uses for a 1 bit value let alone a kilobyte. The number of uses is independent of the number of combinations. If your answer is two you're way off.
Since when does knowing how many combination of states determine what you can do with something? Just because something has 256 states doesn't mean there are 256 different uses for it. There might be 124 uses for binary 00000000. But you won't know that by calculating 2^8.
There might be only three uses for 10100111. One of them makes the world feel pleasant, another melts your face off and another releases three male rabbits into the same cage. But I doubt there's only three. There's likely millions of potential uses for just that pattern alone. How exactly would you calculate how many? Accurately? I'm unconvinced.
The real issue here is lack of imagination. Placing limits where none need exist as well as failing to see possibilities without considering the vastness already present. 2^8 doesn't even begin to cover the number of uses for a single byte.
Rephrased differently: how many uses for a hammer? Can you know only by analysing its orientation? I doubt it.
Rephrased differently (again): feeding a particular combination into different machines will generate a different result. Can you predict the number of results from a given combination without knowing how many machines could process it? I doubt it. The question itself has too many unknowns in it.
I was going to write something very similar, now I can use that time better.
Yes, if an atom was compressible to a bit, you could represent this many universes. It’s analogous to a perfect compression dictionary.
But that’s the rub: an atom isn’t compressible to a bit, at least in this universe. So you have these massive scales competing against each other. The more you say about the atom, the fewer multiverses you have (on an exponential scale!)
It’s an okay way of expressing how many states a kilobyte can take, but what that state means (is it a universe per state or an arrangement of about 1024 ascii characters?) is what’s important.
(Ninja edit: That would imply you can arrange 1024 ascii characters in that-many-universes ways! That’s also fun!)
To best guess, there are about 10^24 stars in the sky. That’s about 2^80.
That means you could simply, on Earth-prime, give an id to all the stars in 2^944 universes. Way way less than the multi-multiverse in question, let alone anything atomic.
Even if you had a perfect 3D coordinate system and atoms worked on float64 boundaries, you’d still have 64 bits to represent one atom. So you could fit, at best, 128 atoms. These are the competing scales.
Unless you knew ahead of time the exact state of an entire universe, then the kilobyte would be your key into that value, as it were.
(Ninja edit again: you’d need 3 float64s! So 128/3 atoms in a kilobyte. Not much. Point stands)
Isn't it when an atom is compressible to a kilobyte? If a kilobyte were the data, not the alphabet, it would only contain... 8096 atoms.
As my comment below, it’s maybe a couple dozen atoms, in perfect conditions (the conditions are again absurd) so this is some definite jiggery-pokery and let’s focus on what they got right? (Ie, how many states a kilobyte can take)
What you’re saying is true— if you replace an abstract state with an atom — but the problem here is people are thinking about individual atoms, and not static arrangements of atoms in a in a universe.
Edit: Or, put another way, you changed the game. Of course there are more states in a kilobyte than the sheer number of atoms. But when you start claiming multiverses… no, it doesn’t work. Which the tweet did, and it confuses things.
What many people have done is interpret that to mean that somehow complexity theory is broken or that the tweet author was arguing for multiverses. It appears that not everyone actually read the tweet.
> What you’re saying is true— if you replace an abstract state with an atom
That is not at all what was written in my comment. There is no replacement being mentioned anywhere.
Sorry, it was totally in the tweet. Literally used the word replaced
That would be 2^(2^hundreds). That's not the representation that's interesting here.
The interesting comparison is 2^1024 versus the number of things that exist or ever will exist.
If a piece of information has ever been written down, or will ever be written down, you can point to the exact place and exact time in much less than a thousand bits.
For example, let's say my wedding is serving salmon or steak, I decide to allocate a single bit to storing those. Now let's say Caesar's thumb gets tired from deciding who lives or dies, so he decides to use a single bit to light up his verdict.
We've now thought of 2*(2^2) "things you can do" with 2 bits.
Also, just from the title: why 2 ^ 1024 and not 2 ^ 8000?
How long would the document be to explain that many state flags, even if we did it in ascii and gzipped it?
There are 2^8 things you can do with a byte. But you can't do them all at once with a single byte.
Fuck, we forgot food.
[0]Programming the Universe, by Seth Lloyd, a great read about physics and computation: https://www.amazon.com/Programming-Universe-Quantum-Computer...
[1]The book is accessible with free account at archive.org: https://archive.org/details/programmingunive00lloy/page/n13/...
[1]Interview with Lloyd where he also mentions this calculation (search for "hamlet"): https://www.technologyreview.com/2006/07/01/39028/qa-seth-ll...
A kilobyte is 8192 bits long (2^13), so there are 2^8192 distinct values you can store in a kilobyte.
Without a data structure, this would take GigaBytes (1M times the space).
That's pretty incredible to me.
Do the combinatorics of every possible combination of 4B distinct 64-bit integers that that 1.5kb can represent.
Mind blowing.
20 Exabytes is probably close to all the information stored in Google...
So it's more like 2^2^13.
Technically a kilobyte is 1000 bytes exactly, so I'm not sure why the title says 2^1024 rather than 2^8000, which is the actual number of states in a kilobyte.
Working on things like the busy beaver problem helps us understand how "fancy" you can make a program of a given size.
For 1024 bytes, even with an inefficient instruction encoding, the answer is "pretty fancy".
After all, you can fit a LISP into 512 bytes of x86 code-- https://github.com/jart/sectorlisp . About 64 bytes of that is strings!
In addition to all those programs-- about anything you can write in any language on a page or so fits compressed. So every short poem, etc, small essay, newspaper column, etc.
But if you needed to store even one bit of information per atom (e.g. whether it is hydrogen or not), then don't you need 2^240 bits uncompressed?
(And yes, I am familiar with who John Baez is and his work).
https://leanchess.github.io/#editions
This really blows my mind, as this comment (including the link) is already up to 124 bytes. I’ll include some extra text so that this comment is 288 bytes, just for a clear visual of how little space that actually is :)