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The correct answer is: the largest number representable in 1 bit is any number (including +infinity and beyond). This article describing various Rube Goldber

The correct answer is: the largest number representable in 1 bit is any number (including +infinity and beyond). This article describing various Rube Goldberg machines, there is no need to agree on different ways of representing numbers when one can set a single bit to 1 to represent any desired pre-defined number, or 0 to represent its absence (or the number 0).

pseudohadamard 8mo ago
Came here to say the same thing. In my encoding there are close to 2^64 standard numbers and a few values just below the top end reserved for encoding of hyperoperations. That should cover most requirements, including silly ones.
- nivertech 8mo ago
  That's similar to how kdb+/q represent nulls and infinities This is certainly pragmatic, although it breaks the math q type size q literal forms underlying integer value (encoding) ---------------------------------------------------------------------------------------------------------- short (h) 16-bit 0Nh / -0Wh / 0Wh null = -32768; -inf = -32767; +inf = 32767 int (i) 32-bit 0Ni / -0Wi / 0Wi null = -2147483648; -inf = -2147483647; +inf = 2147483647 long (j) 64-bit 0N (or 0Nj) / -0W (or -0Wj) / 0W (or 0Wj) null = -9223372036854775808; -inf = -9223372036854775807; +inf = 9223372036854775807 -- https://code.kx.com/q/basics/datatypes/ https://code.kx.com/q/basics/datatypes/ https://code.kx.com/q/basics/datatypes/#infinities https://code.kx.com/q/basics/datatypes/#infinities
tromp 8mo ago
A Rube Goldberg machine is one intentionally designed to perform a simple task in a comically overcomplicated way, usually consisting of a series of simple unrelated devices. Programs like Melo and w128 are the opposite, performing a hard task with the simplest means, using only a few highly inter-related parts. Your proposed representation is exactly the kind of cheating, to get the results you want, that the article purposely avoids.
- nivertech 8mo ago
  1. s/The largest number representable in 64 bits/The widest set of numbers representable in 64 bits/ 2. Using a Turing machine to model a von Neumann machine looks exactly like a Rube Goldberg machine. It even resembles it [1]. 3. There is no point in talking about a 64-bit limit when the underlying model requires an infinite amount of RAM (tape). 4. > A Rube Goldberg machine is one intentionally designed to perform a simple task in a comically overcomplicated way People usually don't realize they've built a Rube Goldberg machine... 5. > Programs like Melo and w128 My point is that just as you pre-defined the program you're going to use, you can pre-define the largest integer. That's 1 bit of entropy. I was working on a project with custom 5-bit floating-point numbers implemented in hardware, and they had pre-defined parts of the mantissa. So the actual bits are just part of the information. --- 1. https://en.wikipedia.org/wiki/Turing_machine#/media/File:Turing_Machine_Model_Davey_2012.jpg https://en.wikipedia.org/wiki/Turing_machine#/media/File:Tur...

pseudohadamard 8mo ago

Came here to say the same thing. In my encoding there are close to 2^64 standard numbers and a few values just below the top end reserved for encoding of hyperoperations. That should cover most requirements, including silly ones.

nivertech 8mo ago
That's similar to how kdb+/q represent nulls and infinities This is certainly pragmatic, although it breaks the math q type size q literal forms underlying integer value (encoding) ---------------------------------------------------------------------------------------------------------- short (h) 16-bit 0Nh / -0Wh / 0Wh null = -32768; -inf = -32767; +inf = 32767 int (i) 32-bit 0Ni / -0Wi / 0Wi null = -2147483648; -inf = -2147483647; +inf = 2147483647 long (j) 64-bit 0N (or 0Nj) / -0W (or -0Wj) / 0W (or 0Wj) null = -9223372036854775808; -inf = -9223372036854775807; +inf = 9223372036854775807 -- https://code.kx.com/q/basics/datatypes/ https://code.kx.com/q/basics/datatypes/ https://code.kx.com/q/basics/datatypes/#infinities https://code.kx.com/q/basics/datatypes/#infinities

tromp 8mo ago

A Rube Goldberg machine is one intentionally designed to perform a simple task in a comically overcomplicated way, usually consisting of a series of simple unrelated devices. Programs like Melo and w128 are the opposite, performing a hard task with the simplest means, using only a few highly inter-related parts. Your proposed representation is exactly the kind of cheating, to get the results you want, that the article purposely avoids.

nivertech 8mo ago
1. s/The largest number representable in 64 bits/The widest set of numbers representable in 64 bits/ 2. Using a Turing machine to model a von Neumann machine looks exactly like a Rube Goldberg machine. It even resembles it [1]. 3. There is no point in talking about a 64-bit limit when the underlying model requires an infinite amount of RAM (tape). 4. > A Rube Goldberg machine is one intentionally designed to perform a simple task in a comically overcomplicated way People usually don't realize they've built a Rube Goldberg machine... 5. > Programs like Melo and w128 My point is that just as you pre-defined the program you're going to use, you can pre-define the largest integer. That's 1 bit of entropy. I was working on a project with custom 5-bit floating-point numbers implemented in hardware, and they had pre-defined parts of the mantissa. So the actual bits are just part of the information. --- 1. https://en.wikipedia.org/wiki/Turing_machine#/media/File:Turing_Machine_Model_Davey_2012.jpg https://en.wikipedia.org/wiki/Turing_machine#/media/File:Tur...