Looking at truth, one grain at a time

Imagine 1,000 grains of sand in your hand. Whatever that may look like, I want you to now remove one grain. Would you call your 999 grains of sand a pile? Yes? Now remove one more. How about 998, is that still a pile? Yes? Continue removing grains of sand until there is only one grain left, is that still a pile? At what point, did your pile of sand become something else? And what is that something else?

A pile (?) of sand. Via Wikimedia commons

Sorites paradox – the continuum fallacy

When does green become red?

Often in life there is a mismatch between small changes and big consequences. When stepping along the colour wheel, most of us (unless you are a Pantone employee) don’t notice a change in colour. Until you realise you started in “green”, and are now in “red”. How can this happen? And how, if all steps are indistinguishable, can you know when to draw the line and separate green from red? The philosopher Eubilides first thought of this mismatch in 400 BC, and used the example of a pile of sand to illustrate it. He questioned the idea of what it is to “know” something – be it a pile, or the colour red.

Where does green end, and red begin? Via Wikimedia Commons

What is a rose?

The idea of definitions, that red, green, or “a pile” are definite, knowable things that we can categorise is a part of philosophy that is under debate. The continuum fallacy says, that both 1000 grains of sand and one grain of sand is a pile and that both sides of this colour strip are the same.  Instinctively, we know this to be wrong. Hence it is a paradox – or a blip in logic. A competing idea suggests that humans are good at prototyping – knowing what something is, say a pile, processing new information and then mapping it back to old definitions. So when we see one grain of sand in front of us, the old idea of a “pile” we have in our mind is not linked to the one grain of sand we see. Hence we can distinguish these previously indistinguishable things.

So does anything exist?

How is anything definite then? Take the idea of one kilogram of mass. It is defined as “being equal to the International Prototype of the Kilogram (IPK)”. The IPK has always been man-made, a physical object.

The mass of this IPK is a kilogram, or is it? Via Wikimedia Commons

The gram (1/1000 of a kilogram) was first defined in 1795 as one cubic centimetre of water at the melting point of ice. Indefinite, right? What temperature of water? Where do you get the water from? How do you measure the temperature? Obviously the definition was too indefinite, and so it evolved and evolved. But the kilogram is still defined by an object, the IPK cylinder, and not a fundamental property, like say the speed of light. Meaning every time it was measured, it had a different mass. Which doesn’t make it a very good definition. Although they are working on it, there still is no fundamental definition of a kilogram. But how do we all know what 1kg is, and how do our kitchen scales know? And if the definition of the standard mass changes (say with surface marks) does that mean the entire worlds scales are suddenly wrong?

Ultimately, it is a discussion of certainty and definition, and some things like colour and piles of sand will always be open to interpretation. As long as you don’t get into trouble giving someone one grain of sand when they ask for a pile, for now I think we will be OK.


6 Responses to “Looking at truth, one grain at a time”

  1. Nastasia Bartlett says:

    You are quite right, Robin, the CSIRO was working in collaboration with the National Measurements Institute from about 2007 to create a perfect silicon sphere, in order to define the kilogram by the atomic mass of high purity silicon and Avogadro’s number. Although they were able to make what is arguably the world’s roundest object the average amount the diameter of the sphere was off (called “out-of-roundness”) was determined to be too large as of last effort.
    In 2016, when the Consultive Committee for Units met to decide the new SI units, they instead chose to define the kilogram in terms of the speed of light and Planck’s constant.

  2. Robin Sanchez Arlt says:

    Hi Nastasia, I remember that the CSIRO was all trying to make a new definition of the kg, based on a sphere of silicon-28. i.e. based on Avogadro’s number. Do you know what happened with that?

  3. Nastasia Bartlett says:

    The project is actually how they are redefining the kilogram. As mass is a fundamental unit, they are aiming to define all SI units by constants of nature such as Plancks constant, the speed of light, the charge of one electron and so on. How it will impact the scientific community will be interesting. I wonder what we could study with these new levels of fundamental certainty…

  4. Tomas Haddad says:

    This reminds me of a really cool project beyond redefining the kilogram that scientists are working on, which redefines *all* SI units (time, length, temperature …): https://en.wikipedia.org/wiki/Proposed_redefinition_of_SI_base_units

    While it won’t solve the problem of when blue ends and green begins on the colour spectrum (too much philosophising hurts my brain), at least these definitions will no longer be relative to a variable that is always changing and needs to be maintained as a constant, rather than a fundamental, physical constant.

    Cool stuff.

  5. Nastasia Bartlett says:

    Thanks Tharaka! Wikipedia has a list of logical fallacies, it’s a mind bending page!

  6. Tharaka Kaluarachchi says:

    Great article! Love learning about the different paradoxes and fallacies out there.