## Monday, October 10, 2011

### Why I Don't "Believe" In Science... (Part I)

Over at Wired Magazine there is an article about the "Kilogram."  As most hopefully know this is a unit of weight measurement.

So reading the article you will find that here in the USA there is, in a secret, locked storage facility a "kilogram" standard.  This is a cylinder made of platinum and iridium to the precise specifications of a whatever a true "kilogram" is supposed to be.

It turns out that in the world today there are several of these standards.

But there is also a problem...

Every so often these standards are taken out of storage, sent to France, and compared by weighing them on a very precise scale.

The US version of the kilogram is losing weight - albeit not more than a few hundredths of a milligram - but losing weight non-the-less.  Since the 1940's the weight of our kilogram standard as diminished.

No one really knows exactly why.  Perhaps ours has been "handled" more than the other - wearing away a small amount of the surface with each touch.  Or perhaps the materials making it up were forged slightly differently and are out-gassing some trapped gases from within its metal structure.

So let's think about this.  "Science" is about making observations, making a hypothesis, comparing the hypothesis to the observations, constructing theories, and so on.  Things like chemical reactions depend on ratios of materials - so much oxygen, so much hydrogen, so much water.  Observing this process we know that water is dihydrogen monoxide.

But how can we be sure of what we are measuring and doing in chemistry if we do not really know or understand how much things weigh?

Now let's compare this to mathematics.

Take the value of Pi as an example (3.14159...).  This is something which can be calculated (and has been) calculated to a trillion digits.  If we were to convert this to a "weight" problem we would be able to calculate the weight of someone to an accuracy less than the weight of an electron.

The only problem is that it would not be possible to weigh a person with such precision because of many factors: a person absorbs oxygen from their surroundings, a person out-gasses CO2, water evaporates from with skin, and so on.  All things which would, at any given point in time, make the specific weight of the person very far, far more than the accuracy with which we could measure their weight.

Pi is calculated mathematically by using a Taylor series - an infinite number of terms which can be combined to calculate, in this case, a very precise value of Pi (see this of how its done).

When measuring physical things we do not have the precision of mathematics because real things, like the platinum-iridium kilogram "standard", are not "infinitely divisible".

If I were to chop up the kilogram standard into ever smaller and smaller parts eventually I would reach the level of atoms - beyond which I would be chopping up atoms and not the kilogram standard.  So as I chop up the standard eventually I reach a point where I have a single atom of platinum or iridium.  Either this atom is part of the standard or its not.  But the weight of this single atom is only represented by about 23 digits.  So eventually we would know the weight of the standard to value 23 digits to the right of the decimal point.  But beyond that the standard's weight cannot be subdivided because only complete atoms can participate in the standard - free electrons or protons would zoom off into the surround environment.

We know the value of Pi to a trillion digits and if we cut it off at 23 or 24 digits its easy to write equations that will be wrong using this truncated value of Pi.

So in the world of mathematics truncating something to a lower resolution creates an error.

In the physical world a thing like the kilogram standard cannot be made up of anything but atoms and beyond a certain point we are simply counting up the number of atoms that make it up - but that number is not infinite for anything but, say, the universe.  That number is always about 23 or 24 digits because that's what atoms weight and all things are made up of atoms.

Pi, on the other hand, is the result of an algorithm - repeatedly applying terms to a Taylor series.

In fact, we don't even need to keep around the value of Pi to a trillion digits, just the algorithm that creates it.

The Kilogram standard, on the other hand, relies on mathematics for its construction and existence: "the absolute weight of a volume of water equal to the cube of the hundredth part of the meter, at the temperature of melting ice" according to Wikipedia.  None of this can be done without mathematics - temperature calculations, divisions of a meter, and so on.

So science, in order to impose order on the universe, requires a tools like mathematics.

Mathematics is arbitrarily precise with representations to a trillion digits or more.  The physical universe is not so - eventually mathematics exceeds the details of the physical reality - and what does it measure beyond that?

Another problem is this.  We know the weight of the iridium and platinum atoms that should make up a kilogram - but these weights are defined in terms of the very standard they are trying to measure.  Sort of like trying to find the definition of a word in the dictionary that itself does not use a word from the dictionary.  You cannot really do it - certainly not for common everyday words.

So, like the dictionary, science is defined in terms of itself: kilograms, atoms and all the rest linked by a self-defining circular pattern - just like the dictionary.

And just like a dictionary science "works" for its intended purpose - I can make calculations, observations, and so on - and within the context of what these things are I can rely on the result.  Just like a dictionary - I can reliably look up virtually any word and find a useful definition.

But science, like the dictionary, is only made up of its own terms and is defined in terms of itself.

So from my perspective I am happy to make use of science - and this is what engineering is - taking some knowledge and multiplying it by mathematics or other knowledge to "do more" with a basic understanding.

But I cannot have science, like chemistry, without a concept of weight.  And while I can create an artificial, self-defined notion of weight such as the kilogram to perform more science I must understand that science does not tell me what weight is and that in the universe at large weight is only something we humans have invented.

Like Newton's Laws.  Like Einstein's formulas.

Because we cannot build things like a kilogram standard from individual atoms we must use a completely different tool, mathematics, to create a self defining description of weight to use instead.  Because we do not have perfect control over out environment things like the "shrinking US kilogram standard" are going to challenge this self-definition.

Yet many people believe in science as fervently as any religion.

Like believing all of human knowledge is contained somehow in a dictionary...