If we did not use integers as a basis, what would we be using?

[Kyriakos]

The progression of integers (eg the natural series, 1,1+1,1+1+1, etc, to infinity) is the basis of our examinations of progression and alterations in volume. But the notion of an integer is at the same time a limiting one, cause to be "one" means concurrently to be an absolute integer and to be a closed sum in such a group deemed again as an integer (for example in one building there are many apartments, but in one apartment there are many rooms, in one room many smaller objects, etc, and "one" is not tied to any set object but to a sense of completeness in a context).

I want to ask what kind of progression or sum we would be using if we did not intuitively have the sense of an integer.

My intuition is that the math built from this notion (and leading to other things, eg limits or partial numbers, or irrationals, or even unreal and complex) may be seen as a special case of some hypothetical generalisation where the notion of an integer itself is only peripheral.

 

[Kennigit]

gestalt? that's the generalization as far as I know

 

[Kyriakos]

gestalt? that's the generalization as far as I know

Ok, but how would you present a progression of such an indistinct and taken all together, event? Ie how would you tie one group gestalted (sic ) to any other there?

(reminds me a bit of Borges' story about Founes, who tried to have a numbering system where each number was not tied arithmetically to any other).

 

[Gigaz]

You can use "True" and "False" as possible content of a single bit of information and construct anything else from bits. Integers, sets or buildings.

 

[Timsup2nothin]

There is a reason the natural numbers are called natural. Assessing things as whole things, then as a count of whole things, is the first obvious intrusion of numbers on physical reality. If we didn't start from the natural numbers we would have to have bypassed mathematics all together, as far as I would guess. The old "where would we be if we had started out with base six, or base eight, or whatever else?" conversations, while interesting themselves, just don't lend themselves to expansion beyond integers.

Without reaching the descriptive limits of natural numbers first we have no need for the rest of the integers. Without reaching the descriptive limits of integers we have no need for rational numbers. Until we have explored those and found that there are things that still cannot be described we have no need for the rest of the real numbers. I could say the same for imaginary numbers, and should since it is too late for et cetera.

 

[Borachio]

Integers are plainly derived from counting on one's fingers.

So any alternative method probably involves taking one's shoes and socks off.

(Which, incidentally, is the reason the Mayans operated to base twenty. Now, I don't suppose you'd thought of that, had you?)

 

[Leifmk]

Integers are plainly derived from counting on one's fingers.

So any alternative method probably involves taking one's shoes and socks off.

(Which, incidentally, is the reason the Mayans operated to base twenty. Now, I don't suppose you'd thought of that, had you?)

That's, um... still integers.

 

[Lohrenswald]

Fractions, I guess

 

[Kyriakos]

^Fractions are also tied (and following) from the notion of an integer. So are other kinds of numbers (mentioned in the OP already)

The question is if humans can (and might in the future) use some basis for progressions or groups or sums, not centered or following from integers.

(and what such a basis might be, as well).

Something which again is partly based on integers, but is somewhat different, could be some progression where there is no single bit on any of its positions, cause those are indistinct or even include every other position. But this again is similar to probability theory, if you can form a set by any item or any collections of items on the same position, including all positions covered by just one super-collection of one item, etc.

Anyway, those won't actually negate the central position an integer has. Cause we seem to be stuck with 0, 1 and 2 at any rate. (and maybe also 3).
Examples: In Anaxagorean model all objects are argued to potentially include all other objects, but in some different manner from any other object, and so they appear to be distinct after a level. In eleatic models any object is likely theorised to be only a pseudo-distinct fragment of a whole, the whole being not evidently sensed as one.

 

[Borachio]

That's, um... still integers.

Oh? Silly me! Why didn't I think of that?

I know what I was thinking of: digits.

 

[cybrxkhan]

I remember coming across a hypothetical situation where a hypothetical alien species used colors or sounds to make sense of its world, rather than the more vision-dependent integer numbers. But this is all 3deep5me so I dunno how it works out exactly.

 

[warpus]

You can use the fibonacci sequence as a way to create a different base, I think, but those will still be integers.

Is this for a story you're writing, about an alien race or something similar? We use integers, because they correspond quite nicely to reality. Any alternative is probably going to be unnecessarily complex.

 

[Kyriakos]

You can use the fibonacci sequence as a way to create a different base, I think, but those will still be integers.

Is this for a story you're writing, about an alien race or something similar? We use integers, because they correspond quite nicely to reality. Any alternative is probably going to be unnecessarily complex.

You know that it would be way too unrealistic for a story. So i am using it in math

(and yes, any series still is integer based, even the steps are integers in the series- its positions).

I don't have any suggestion for something serving as basis, which would be at the same time non-integer based and actually leading somewhere (ie not being a one-off, like the 'numbers' in that Borges story i alluded to and i think you would like )

Here is an english translation of that work, in the public domain: http://www.srs-pr.com/literature/borges-funes.pdf

 

[Hygro]

love

 

[Perfection]

Using discrete morphemes to express quantity lends naturally to integer basis. That is human grammer treats words digitally and so we express quantities digitally.

But an alien grammar could be different. Quantities could be expressed in an analog manner. Here's a toy grammar: all words have an analog component represented by pitch that indicate some relevant quantity. So a low-pitched "hill" may represent a very tall mountain whereas a high-pictched "hill" might represent small knoll. Verbs like "go" might have pitch indicate distance.

An example sentence might be...

(25.4 pound) Dog (136.3 yards) walked to (1235 square foot) house.

 

[Kyriakos]

^ In another Borges story, titled "The library of Babel", there is the claim (or rather hypothesis, not proven) that maybe some books containing loads of lines with the same letter more of less (eg hundreds of rows of HHHHH etc), might mean something intelligible as long as each H there gets a different meaning tied to position, or other parameters not known which may not be limited to the book itself.

But that still seems integer-based. I mean it is viewed as rows of H.

(naturally a human cannot just forget/erase the ability of sensing things in integers/wholes/distinct, or thinking likewise).

 

[Formaldehyde]

(reminds me a bit of Borges' story about Founes, who tried to have a numbering system where each number was not tied arithmetically to any other).

If a man had many cows and sold some of them, how many would he have left?

 

[Kyriakos]

If a man had many cows and sold some of them, how many would he have left?

Without integers there is only a collective cow (which likely is tied to other stuff and not just cowness so to speak...) so selling it would not factor from that point of view- i suppose.

Think of it as being a cow merchant, but being exiled to India And moreover being turned into a 2d being. That should do it, i think.

 

[Antilogic]

Integers are too deeply ingrained in how we are programmed to think about math for me to figure out an alternative that doesn't involve counting. You'd have to rebuild math from scratch to answer that.

 

[Kyriakos]

Integers are too deeply ingrained in how we are programmed to think about math for me to figure out an alternative that doesn't involve counting. You'd have to rebuild math from scratch to answer that.

And *probably* not just math or other orders (eg language). Although *maybe* preschool children don't tend to think (at least only) in integers. Iirc before an age the child is not even having a sense of his/her body as 'one' with emotions/thoughts he/she has. And i doubt anyone identifies instantly with the image on the mirror the first time they see it as an infant.