# 'volume is a conservative dimension'?

What does volume is a conservative dimension mean in the context? Does conservative have to do with the verb conserve in meaning?

During their second year, children learn to use the words old and young, which indicate that they have appropriated the age dimension. They can use this dimension to classify people. However, an understanding of an abstract time domain develops much later. Spatial metaphors for time are ubiquitous: it is difficult to talk about time without using words that originate from the visuospatial domain. Jean Piaget emphasizes that “time and space form an inseparable whole” in children’s minds. In other words, young children cannot treat space and time as separate domains. This situation parallels the dimensions of height and volume, which are inseparable for preschool children but become separable when children learn that volume is a conservative dimension. Similarly, space and time start as a single metric that becomes gradually differentiated into two separable domains.

The Geometry of Meaning: Semantics Based on Conceptual Spaces By Peter Gärdenfors

Looking into the Cambridge Dictionary, the most suitable definition for conservative is:

conservative (adj.) (AGAINST CHANGE) = not usually liking or trusting change, especially sudden change

• Older people tend to be more conservative and a bit suspicious of anything new.

Applied to the text, it should mean that volume does not change. However, that is not entirely true.

1. The text mentions height and volume. From here we may conclude that the authors have in mind solids. And regarding solids, that principle is (almost) true. It does not matter how you cut or re-shape a solid, its volume will remain unchanged. In some cases, that logic appears to be broken: wood will get bigger when wet, a squeezed sponge will get smaller... (actually, there will be the volume of water added, or the air removed, respectively).

2. The same is true for liquids, if we do not take evaporation / condensation into discussion.

3. HOWEVER! If we talk about gases, the statement that "volume is a conservative dimension" is totally untrue: gases occupy the volume of the space where they are stored.

So the statement "volume is a conservative dimension" might be true only in a very restricted case.

What I strongly disagree with is the idea that volume is a dimension. From my point of view, volume is a property, or the result of the composition of dimensions, but not a dimension in itself.

Also, according to the Cambridge Dictionary:

volume (n.) (AMOUNT) = the amount of space that is contained within an object or solid shape:

• Which of these bottles do you think has the greater volume?

The same remains true if we look into the Merriam-Webster Dictionary for the word dimension:

dimension (mathematics) = measure in one direction (the dimensions of the room); specifically: one of three coordinates determining a position in space or four coordinates determining a position in space and time

This idea, expressed in that way, seems to be fairly unique to this book. It seems likely that it actually means that volume is a conserved quantity, which it is if you're dealing with liquids or solids and not loosing any.

A conserved quantity, in strict terms, is something the total amount of which doesn't change in a closed system. Momentum is conserved, energy is conserved, mass is conserved (though the last two become a combined conserved quantity under certain circumstances), and we call those conservation laws in physics.

The trick here, to understand why volume being conserved makes any sense, is the context - childhood development. Through observation and play, a child will realise that a metre-tall column of water in a narrow vessel becomes a much 'shorter' amount of water when decanted into a wider vessel. They might think some has been lost, but you can then put it back into the narrow vessel and the child will see the amount is still the same, and realise that while the height of a substance can change, its volume does not unless some is removed.

I'm fairly sure this is what the author means, but the use of non-standard terminology makes it difficult. However, they can be forgiven that unusual terminology, including the odd use of 'dimension', because they appear to be a social scientist.