The Metaphysics of Philosophy, Knowledge and Morality Chapter 5

Chapter 5

The limitations of science

Aristotle correctly stated that the starting rules of science cannot be proved in themselves. It follows from this that any scientific knowledge we glean is guesswork, as opposed to exactly proved step-by-step data.

Physics, for example, shows several gaps. There is no particular reason why particle physics should have different rules than macrophysics. Yet physicists assert that small objects behave quite differently from large objects. Electrons move differently from nano particles, which move differently from human-sized objects, which move differently from planets and galaxies... It's as though they inhabited different worlds.

The gravity model is flawed. According to Newton's laws, planets could not stay in orbit, they should fly off into space. The dodgy excuse that some misterious dark matter keeps them in position is nothing but a wild card in the absence of plausible knowledge. We know nothing about this imperceptible dark matter, so chances are that dark matter doesn't exist. Physicists made it up to fill a gap in their model.

The Big Bang model is flawed too. If all matter started to drift away from an exploding singularity, its expansion should slow down, come to a halt and then start drifting back toward that singularity. This is not what we see happening. Galaxies are drifting apart at an increasing pace, which contradicts the Big Bang theory. So physicists came up with another wild card, dark energy. Dark matter supposedly pulls stuff together, while dark energy causes it to expand ever faster... These two contradictory wild cards represent the biggest yarn in the history of science. Physicists should come out and simply admit that there are more holes in their model than in a ton of Swiss cheese.

For those not well-versed in the history of science, wild cards are sometimes used to fill gaps in our knowledge, but only one at a time. Flogiston, for instance, was supposed to explain the phenomenon of burning, until it turned out that burning is oxidisation. There is no such thing as Flogiston. Ether was used for a while to explain how waves propage in space. Space was supposed to be full of Ether. Needless to say, there is no such substance as Ether either. But Flogiston and Ether were not used at the same time in the same model, because two wild cards just don't work. When you have more than one in your model, you no longer have a model. So it is remarkable that there are two wild cards in our model of the Universe, and no-one complains about that. To me it shows that humanity has developed a blind faith in science and will take any yarn from established scientists without batting an eyelid. My guess is it won't be long before dark matter and dark energy turn out to be bogus, and the current physical model collapses.

This is not to suggest that science is wrong and we should explain the world using the Bible. I'm merely saying that while science is the best way to find out as much as we can about the world, we should think reasonably and check every model carefully. Science is one of the new powers, so we need checks and balances to harness it for our benefit.

Mathematics is also full of holes. We know that numbers don't exist in the outside world, as they are in our head. Yet maths books talk about prime numbers, real numbers, irrational numbers, etc. as existing multitudes, like trees in a huge forest that you can go out and explore. This is still based on Plato's flawed concept of ideas. If ideas are the products of our mind, then numbers are nothing like trees in a forest. They are possible outcomes of computations that have yet to be performed. Numbers exist only as outcomes of operations and should not be described as though they had a life of their own.

The ancient Greeks divided numbers till the result was an integer and then stopped with the remainder. For example, 5 horses divided among 3 people yields 1 horse each plus a remainder to 2 horses. Unless you want to slice up those two horses, further division makes no sense. Some things, like pizza, can be carved up, so it makes sense to subdivide them. That depends on the context, and the ancient Greeks understood this well. While it seems an advancement to divide 5 horses by 3 and get a result of 1+2/3 horses, the user should be warned that 2/3 of a horse does not have a specific meaning. Worse, when you express 1+2/3 horses as 1.666 horses (an infinite decimal fraction), you ignore that there is no such thing as 0.666 horse and also that 2/3 into 0.666 is an ill-advised conversion. Since 10 is indivisible by 3, you should not convert thirds into tenths, unless you have a very good reason for doing so.

If you think about it, a 1/3 is not so much a number as an operation in progress. You are merely describing the process of taking 1 and trying to divide it into 3 parts, which you can't, of course. 1/3 is a process description and not a number. It can be used as a ratio, when you have 999 cans of beer and you can actually divide that by 3. So 1/3 is a process description for ratios within larger quantities where division is possible.

Most "infitite" decimal fractions can be expressed as finite natural fractions: 1.1666... looks much simpler as 7/6 or 1+1/6. There are notable exceptions when a proportion cannot be expressed either as a decimal or as a natural fraction, such as the ratio between the  hypotenuse of a right-angled triangle and the two other sides. There is no such fraction. Or the ratio between the diameter and the perimeter of a circle (pi). There is no such fraction either. The reason is that geometric calculations work seamlessly only with straight lines and right angles. The hypotenuse is not at a right angle, and a circle is not a straight line. If you check the method for calculating pi, you will find that it is about squaring the circle. No wonder that you get an infinite result: you can't square a circle after all, but you knew that, didn't you? To call the result a "number" is a stretch. These hypothetical proportions can only be approximated, and they are, for practical purposes.

Another loophole is division by zero. It is not done. There is no other number that you can only multiply with but can't divide with. There doesn't seem to be a good reason for not dividing by zero, other than that you don't get a sensible result. So what? If you don't like the result of division by 2, you won't divide by 2? That's nonsense. It is more reasonable, perhaps, to say that zero is not a genuine number, which is why it behaves asymmetrically. Zero is more like the concept of nothingness, which is just as odd as this "number".

For centuries, mathematicians believed that numbers were real-world objects and that the world could be expressed as a series of mathematical formulas. That nature somehow spoke a language, that of mathematics. They no longer have a reason to think so, yet the idea persists. If you want a simple example to demonstrate that "nature" does not speak mathematics, take the calendar. There are about 29.53 days in a moon month (from full moon to full moon). Try and divide 29.53 days into weeks. You can't. Not even into days, as there is no such thing as 0.53 days. A year is about 365.25 days, which you can't divide into days, weeks or months. Our Gregorian calendar is a good (though complicated) approximation, but it still is off a day every 3000+ years. If you consider that a day is defined by Earth's rotation around its axis, a week is an arbitrary number of days from Mesopothamian culture and the Bible, a moon month is defined by Earth's shadow on the Moon, and a year is based on Earth's orbit around the Sun, you may ask why the proportions of the movement of Earth, Moon and Sun should be integers. Why, indeed? If the Universe spoke mathematics, these proportions should be expressible in nice soothing integers. There should be so many days and weeks in a moon month, and so many moon months, weeks and days in a year. Appearently, there aren't. It is my intuition that if there is a higher order in the Universe, it's not as simple as Earthly mathematics.

These are just a handful of examples to show that science is limited in ways we don't like to think about. It appears that science is for practical purposes, for building roads that don't was away, bridges that don't topple, houses that don't collapse - not two often anyway. But to look to science for an ultimate understanding of reality is way too tall an order.