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March 13th, 2014, 01:00 PM   #1
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New number type that has quantum-like weirdness

First, what is mutable vs immutable?
In software we have an idea called mutable vs immutable. An immutable object can be widely shared without thread sync or needing to handle the many interactions with it as they related to eachother, because immutable means the data is constant. Subtypes of java.lang.Number, like Byte and BigInteger, are immutable. My open source software Immutable Sparse Wave Trees lets you store wave data in memory fast enough to play on the speakers, as each piece of the wave is constant data, has a constant length and amplitude of the wave at each position in time. This allows the extreme optimization of being able to copy/paste any time range into any other time range, any number of times, back to back or in any combinations, copy paste any range of that, and keep going, and after you have generated more (highly redundant from the copy/pastes) wave data than could fit in all the computers on Earth if stored the normal way, it will cost you only log_base_2 number of cpu cycles and memory to get average amplitude of any range you ask about even if that range is precise to a microsecond and covers years of data until another precise microsecond. You can do this calculation millions of times per second on an average computer because its an immutable number, not the literal data.

The new number type thats both immutable and mutable simultaneously...

Imagine a data space that goes from 0 to some number of bits, like an integer of that many digits. This is an immutable/constant integer even before we observe any of its bits, because immutable means it is always the same every time its observed. But we havent observed it yet.

We can define the integer so that the first place we observe in it, whichever of its bit locations that is, will always be a 1, and the rest will be 0. It could be 10000 or 01000 depending on how we observe it, and every observation after that will give the same bits.

The quantum-like weirdness is this number type is in superposition until observed, and that despite it having mostly 0 bits and being immutable, it is impossible to first observe any of those 0 bits.

This is a way of thinking about why quantum does the strange things it does, when you consider that many of these kinds of numbers can represent a variety of parts of physics from different perspectives. This is also a research path of all the possible ways we can design lazy-evaluated (thats the technical term for it) immutable numbers.

A thing is immutable because it can only choose once per each part of itself, not choose again to be something different. Lazy-evaluated means to defer that one choice to the observer like quantum weirdness.
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