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Negative Base

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Re: Negative Base

#11

Post by roywiggins »

vinceguidry wrote: post #7
empath75 wrote: post #4

Earlier quoted context omitted.

I can’t imagine there ever would be.

I don't think anyone ever imagined a use for imaginary numbers either, but those turned out to be quite useful for reducing dimensionality. Towards the bottom of the article it states that Donald Knuth proposed imaginary base numerical systems. So this may eventually find a use, likely with higher-dimensional math.

Imaginary numbers were useful as soon as they were invented. They are algebraically closed, unlike the real numbers, and are required for the fundamental theorem of algebra.

https://en.m.wikipedia.org/wiki/Fundamental_theorem_of_algeb...

The first use of negative roots was to find the (real) roots of certain polynomials. They were considered a mathemathical hack: useful, but specious on their own. And then it turned out that if you take them on their own terms, they're fantastically useful.

Re: Negative Base

#12

Post by [deleted] »

ainar-g wrote: post #8
vinceguidry wrote: post #7

Earlier quoted context omitted.

I don't think anyone ever imagined a use for imaginary numbers either, but those turned out to be quite useful for reducing dimensionality. Towards the bottom of the article it states that Donald Knuth proposed imaginary base numerical systems. So this may eventually find a use, likely with higher-dimensional math.

It will be really funny if there is some bit of new, undiscovered physics, that went undiscovered for so long just because it's best described using some esoteric maths like complex base numbers. Highly unlikely, but fun to think about.

[deleted]

Re: Negative Base

#13

Post by jerf »

vinceguidry wrote: post #7
empath75 wrote: post #4

Earlier quoted context omitted.

I can’t imagine there ever would be.

I don't think anyone ever imagined a use for imaginary numbers either, but those turned out to be quite useful for reducing dimensionality. Towards the bottom of the article it states that Donald Knuth proposed imaginary base numerical systems. So this may eventually find a use, likely with higher-dimensional math.

In addition to the other points, imaginary numbers immediately added to the representation of things we could represent. Simply rewriting existing numbers in other ways isn't all that interesting; it doesn't add anything. We already knew there's an infinite number of ways to serialize numbers to symbols. Negative base numbers don't behave differently than positive base numbers, because "negative base numbers" and "positive base numbers" are artifacts of English and don't actually exist mathematically. There are numbers, which are written in different representations, but are not actually different entities.

So there's no possible way this could be useful for "higher dimensional math" or anything, because there's no entity being added here. Higher dimensional math already uses numbers. At most there might be one or two concepts that might in some manner if you squint hard enough could be better represented by negative base numbers, but even then the positive base representation would probably still be how people actually understood it.

Re: Negative Base

#15

Post by msoucy »

When I was part of an organization in college, part of the onboarding process was that each applicant had to have a conversation and (possibly) do a "quest" for each member. My standing quest was that I would write the first 12 or so numbers in negabinary on my whiteboard, and have them determine the next few numbers and explain what they meant. I had people sitting outside my room for hours trying to figure it out. A few did do it, and normally had some expletives for me afterward.

Re: Negative Base

#16

Post by empath75 »

fwdpropaganda wrote: post #14
empath75 wrote: post #4

Earlier quoted context omitted.

I can’t imagine there ever would be.

So in your mind people are just coming up with these things for no reason, is that it?

It’s fun and interesting to figure out. There are lots of ways to represent numbers but they don’t change the thing they represent.

Re: Negative Base

#17

Post by wawhal »

dvfjsdhgfv wrote: post #3

Can anyone provide some examples of practical applications of this?

Science need not necessarily have any practical use. That’s why it is called Science. Science, the way I define it is: Study for the sake of it.

Re: Negative Base

#18

Post by philbarr »

Sharlin wrote: post #10

See also balanced ternary [1]. [1] https://en.wikipedia.org/wiki/Balanced_ternary

Which you can use to solve the puzzle:

"You have 12 coins that all look exactly the same. One is counterfeit and is either heavier or lighter than the other 11. With a balance beam scale, isolate the counterfeit coin in three moves."

Any uses for Negative-base systems?

Re: Negative Base

#20

Post by misja111 »

gota wrote: post #5
empath75 wrote: post #4

Earlier quoted context omitted.

I can’t imagine there ever would be.

Well, the number of digits tell you the sign of the number, right? It could save a sign bit I think the ideal wikipedia page for this kind of thing has a 'Properties' section from which to start thinking about this

The bit saved for the sign is lost because you need more bits to represent a number.
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