The Infinity Machine
The Infinity Machine, by Simon Tatham, explores a hypothetical computing environment with infinite speed, featuring an infinitely long memory line and minimal instruction set, raising questions about computation and memory limits.
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The Infinity Machine, conceived by Simon Tatham, is a speculative exploration of a hypothetical computing environment where computers operate at infinite speed. This work does not follow a traditional narrative structure but instead delves into the technical implications of such a machine, appealing primarily to computer programmers and mathematicians. The concept originated from a remark in Ian Stewart's book, which suggested a light switch that could be toggled infinitely within a finite time, prompting thoughts on a computer capable of executing infinite computations in a similar manner.
The proposed architecture features an infinitely long memory line of bits, allowing for the separation of data into infinite substreams. This structure enables efficient memory management and supports various data types, including arrays of infinite size. The Infinity Machine operates on a clock system that can execute either a single instruction or an infinite sequence of instructions within one clock cycle, depending on the use of an "infinity" instruction.
The instruction set is minimal yet powerful, incorporating basic operations and the ability to perform complex computations through infinite sequences. Tatham's exploration raises intriguing questions about the nature of computation and memory in a world where infinite processing is possible, while also highlighting the challenges and paradoxes that arise from such a concept. Overall, The Infinity Machine serves as a thought experiment that invites readers to consider the boundaries of computing and mathematics.
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11 commentsI find it so fascinating that fundamental properties about the laws of physics integrate so tightly with what is computable. The standard definition of compatibility involving Turing machines sounds kind of arbitrary, but those machines are representative a truly fundamental concept in our universe: that which is physically knowable, since you can build Turing machines out of the stuff in the universe.
Almost. Turing machines have unbounded tape. But the universe does not contain an unbounded amount of information or space with which to work. Sufficiently large Turing computations, though theoretically finite, are not realizable in our universe. Should such computations be considered decidable or undecidable?
https://en.m.wikipedia.org/wiki/Thomson%27s_lamp
I used it as an interview question many years ago. I wasn't very rigorous about it, basically any plausible answer was good enough for me. Answers fell into two categories, the theorists (it's an infinite series that doesn't converge) and the pragmatists (you couldn't physically do it).
1. Simon Tatham is the author of PuTTY
2. In the early days of the web, many people's personal sites were hosted on shared computers (e.g. my first was on my university's DEC Ultrix system). The URLs started with a reference to the user's home directory. This page is hosted on a machine that has a page to lists all the user's home pages: https://www.chiark.greenend.org.uk/users.html
3. The home page has this awesome spam detector:
If you want not to be able to send mail here in future, please send mail to tabasco@chiark.greenend.org.uk.I would make a programming language where you couldn't write code, only detailed specifications and tests. In a VM Every possible permutation of bytes/opcodes/instructions/whatevers would be tests to produce the smallest and fastest (presuming the code is to run on other machines) possible binaries that pass your tests. Ideally this would produce a Pareto front of possible outputs and you could choose from among them.
Another idea solving old problems the hard way. Since fermat's last theorom is countably infinitely problem and this computer is uncountably infinite in performance it should be able to knock it instantly by simply enumerating all integers and trying them.
Could we write algorithms that search all the digits of pi for patterns? Or mayb messages on speculation of creators or others who might be able to tamper with it?
Could other math things be searched? Have we proven there is no upper limit to prime numbers? I know the largest known mersenne prime fills a novel sized book with just one number, but when does a number get too big to be prime if ever?
It's different from how we modeled things like Turing machines, where if we needed more memory, we would append more tape, as opposed to subdivide the existing tape further.
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