How many things is a blob? [closed]

Question

Imagine you have two types of play-do. You mix them up till you can't tell the difference between them but you have a machine that can split them up. How many types of play-do do you have in your hand?

Answer 1

It's inherently unclear. Almost any question of the kind, "How many types of X are there?" is unclear, because the answer depends entirely on how you choose to assign instances of X into categories. There are generally many possible ways to do this, often infinite possible ways.

One answer to your play-doh question, the one most would expect, is that there is one type of play-doh in your mix. It appears uniform, so you could count it as uniform.

If you have a machine that can un-mix them, like unshuffling a deck of cards, then you could reasonably say there are two types. One type would be defined as the type that could be un-mixed into red play-doh, the other type would be defined as the type that could be un-mixed into blue play-doh.

You could also say that there are more than two types - infinite types, if you wish. Because there will always be minor variations in color and density and chemical composition between different parts of the seemingly-uniform play-doh. You could divide the parts of the play-doh into types in any manner you wish; you could say there are ten types, according to certain specific gradations of density you specify. Or you could say there are fifty types. Or a million.

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However, we should refer to what is pragmatically useful. Sometimes it is pragmatically useful to say, "there is one type of play-doh." If we can't un-mix them, and can think of no immediately useful application for which the minor differences between the different parts of the blob matter, then it is most useful to say there is one type of play-doh.

If we can un-mix them using our machine, and if we are doing something involving the machine, then it would be pragmatic to say there are two types. If the machine is simply in the room with us but we are making play-doh art without bothering with it, then it might be pragmatic to say there is one type despite the presence of the machine.

And similar things can be said for ten types, or fifty types. It all depends on what we want to do, and whether it is useful to our purpose to make such fine distinctions or not.

Much of language is like that: utterances may be useful to some purpose in a particular context, even if they can't necessarily be interpreted as some ultimate truth.

Answer 2

This problem of identity applies to all objects in our world. They all are “heaps” with no rigid boundaries. Essentialism, “thisness” does not seem to apply to any macro object. All our labels of thingness are pragmatic, not essential.

Answer 3

There is a mathematical answer. Play-Do is modelled by manifolds if we avoid situations where we tear the play-do, or develop holes. This is because at any point we can erect a system of axes and although they warp when the play-do is played with, the axes will not coincide. Further, we require avoiding infinitely long or wide play do. The mathematical term corresponding to this is compact. Finally, notice we can always measure length and amgle in a piece of play do. The mathematical term corresponding to this is Riemannian.

Thus the classification of such 3d compact Riemannian manifolds solves the question. I think there os such a classification. Ask on Math.SE or Math.OF for fuller details.

Answer 4

I think you are punning

on two different senses of 'blob'

a drop of a thick liquid or viscous substance. "blobs of paint"

and

an indeterminate roundish mass or shape. "a big pink blob of a face was at the window"

That something has vague boundaries does not mean that it is substance similar to water, and I don't see what the playdough example is meant to show or illustrate.

If you're asking what counts as one thing, you could look into 'identity', but only for so long as you aren't equivocating on those two senses.

https://plato.stanford.edu/entries/identity/

I don't see how liquid raises any interesting dilemmas about the subject, though vagueness might

Like the impossibility of contingent identity, the impossibility of vague identity appears to be a straightforward consequence of the classical concept of identity (Evans 1978, see also Salmon 1982).

etc..

In general, not only blobs (of anything) or liquids can be combined with and split into similar things; indeed, heaps can be combined, same as many sorts of collections (my marbles and yours).