Comments by "kazedcat" (@kazedcat) on "Something Strange Happens When You Keep Squaring" video.

@leif1075 It is very necessary to keep the property neg(0)=0. In compliment operation you have comp(b0000)=b1111. The fix is to add b0001 and ignoring the carry overflow. So comp(b0000)+b0001=b0000 now you have an operation that is exactly the same as negation.
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@leif1075 What you suggested is possible but not hardware efficient. You will have trouble doing mix operations because negative numbers needed to be handled by a different hardware circuit and the positive numbers by a different hardware then you have too add a lot of hardware circuits to handle doing mix operations. Basically you need hardware for (-x)+(-y), (-x)+y, x+(-y), x+y. Then you also need hardware for (-x)-(-y), (-x)-y, x-(-y), x-y. Using 2's compliment all this hardware requirement is reduce to x+y, and the compliment(x) hardware.
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It was briefly mentioned in the video. P-adic was invented because of the definition of absolute value. There are only three definitions where the required relations of absolute value works and P -adic number system is one of them.
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@leif1075 basically it is an operation that swaps 1 into 0 and 0 into 1. This is a very cheap operation in terms of logic circuits and the operation preserves the order of negative number so for example the compliment of 4 which is b0100 becomes b1011 if you add 1 (b0001) then the result is b1100 which is the compliment of 3 (b0011). This correspond to (-4)+1=(-3). The compliment operation is an analog to negation with the problem of having two zeroes that is fix by adding one when doing proper negation.
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Sorry to break it to you but we already know that the pieces will never be complete. That is the whole point of Gödels incompleteness theorem. There will always be questions that cannot be answered.
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2's compliment is truncated 2-adic.
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Do you even understand what 0.99repeating represent. For example if you have a cake what does a 0.999... cake look like? What about a 0.999... cow? Many people think that numbers are absolute truth but in reality numbers are just a bunch of nothings.
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@Gábor There is even a term for it lazy evaluation. You only compute what you needed and forget about the rest. This is even formalized in lamda calculus where lazy evaluation is required.
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We deliberately and forcibly made infinity work. Mathematicians forcibly declared that infinity exist as one of the fundamental axiom and the reason is because the concept of infinity is useful even if working with it is problematic.
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It's called Two's compliment and this how computers represent negative numbers internally.
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For mathematicians mathematics is about exploration. Visiting unknown lands and delving on unexplored dungeon. Their motivation is trying new things and seeing where it gets them.
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I just tested it. It is not possible. The second digit must be a2b1+a1b2=1 and a2=b2 also a1b1=1. There is no binary value that can satisfy all three equation.
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Not yet. But p-adic might solve the format problem of AI. Floating point is sadly not powerful enough to represent weight values but a number system with natural encodings of fractions might do the trick.
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@leif1075 The problem with just using a sign bit is you end up with both positive zero and negative zero represented in your number format and this really really screw up many calculations. The +1 in 2's complement fixes this two zero problem.
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@jojijoestar4762 Yes It does not stop mathematicians from exploring but it is useful to know the limits before you explore the Pacific with a rubber boat and only 3 days of supply.
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