Galileo - A famous quote… in full

Galileo Galilei is famously quoted as stating that...

    ‘Nature is written in numbers.’

Another version, almost as often quoted, states that...

    ‘The book of nature is written in the language of mathematics.’

The fuller, more accurate version is found in Galileo’s 'Il Saggiatore' (The Assayer), published in 1623. That reads:

‘Philosophy [nature] is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.’

So, while the shorter versions capture something of its essence, the more complete quotation provides a richer understanding of Galileo's belief in the fundamental role of mathematics in comprehending the natural world.

But we should ask, while the book of nature may be written in numbers, is it only to be understood in numerical terms? I do not deny that there is much that numbers tell us. Yet, do numbers on their own always tell the whole story? Or, do they need to be translated into another language so that the book may be read more easily?

Data is nothing but a set of digits until interpreted, and that interpretation is in terms of conceptual language. The interpretation of data is a conceptualisation. Two sets of data might contain exactly the same numbers but relate to quite different phenomena. One set may be a record of the heights of a group of men; the other might be a record of the heights of a group of sunflowers. Using numbers alone, there is nothing that inherently differentiates between them—they are just numbers.

One common failing I found in students I used to teach was their assumption that by simply including pages of tabulated data, all would be obvious to the reader. Quite the opposite was the case. Data needs to be described and turned into something meaningful. And meaning resides inside concepts.

My group of men and my group of sunflowers may have reached the same height, but I need to know more. I need context. It may have taken the men three decades to reach this height and the sunflowers three months. With that simple bit of added information, the whole picture changes instantly.

Ptosis (and ptoses)

There is a range of medical conditions to which the term ‘ptosis’ is applied. The term comes from the Greek πτῶσις, meaning 'dropped, a fall, or a falling'. Typically the term is applied where there is a droopiness or abnormal downward displacement of a body part or organ. On the surface of the body, structures that can be clearly seen to be affected include the eyelid, the breasts and the chin.

The condition may also occur internally. If affecting the stomach, the condition is called gastroptosis; if affecting the kidneys, it is called nephroptosis. The general term for organs that are found lower than expected is ‘visceroptosis’ (although the terms ‘splanchnoptosis’ or ‘abdominal ptosis’ may also be used.) Originally it was called Glénard's disease (after French physician Frantz Glénard (1848–1920)). However, eponymous terminology is now considered somewhat outdated.

However, with regard to the internal organs, whether this constitutes a ‘disease’ is uncertain. Internal organs cannot be seen directly, and when they can be visualised, they can demonstrate considerable variability in their vertical placement. This has led some to doubt the veracity of conditions such as Glénard's disease and even to speak somewhat disparagingly of it. There has been some suggestion by sceptics that visceroptosis was a product of the discovery of X-rays by Wilhelm Röntgen in 1895.

The story has been told of how, in the early days after the discovery of X-rays (a period during which Frantz Glénard was active), patients would present to their doctor with abdominal discomfort for which no obvious cause could be found. Now with the invention of X-ray machines, one could peer inside the body, and so the patients were sent to a hospital so that that could be done. At that time, the patient would typically stand between an X-ray source and a fluorescent screen that would show a shadow of their insides to an examining doctor. Finding their organs lower than described in the textbooks, the cause of their discomfort became immediately obvious: fallen organs. To which the more scientifically sounding names 'ptosis' and 'Glénard's disease' were applied.

It was later pointed out that the descriptions and drawings in textbooks were based on cadavers as seen at autopsy or in the anatomical dissecting room. These were invariably laid out horizontally, whereas the patients being examined by X-ray stood up. The effects of gravity on the organs were not taken into account. They move up when we lie down and move down when we stand up.

 

From - ‘Reveries of the Solitary Walker’ by Jean-Jacques Rousseau

I thought these snippets clipped from Jean-Jacques Rousseau’s ‘Reveries of the Solitary Walker’ posted without additional comment would be worthy of your consideration.

What am I? This must now be the object of my inquiry.

If an old man has something to learn, it is the art of dying.

I decided to devote my walk of the following day to a self-examination on the subject of falsehood, and I embarked on it in the firm conviction that the 'Know Thyself' of the temple at Delphi was not such an easy precept to observe as I had thought in my Confessions.

Botany is the ideal study for the idle, unoccupied solitary; a blade and a magnifying glass are all the equipment he needs for his observations. He wanders about, passing freely from one object to another, he considers each plant in turn with interest and curiosity, and as soon as he begins to grasp the laws of their structure he receives from his observations an effortless pleasure as intense as if it had cost him a great deal of labour. This ideal occupation has a charm which can only be felt when the passions are entirely at rest, but which is then enough to make our lives pleasant and happy; but as soon as our self-interest or vanity are brought into play and we are concerned to obtain positions or write books, as soon as we learn only in order to teach, and devote ourselves to botany merely for the sake of becoming authors or professors, all this sweet charm vanishes, we see plants simply as the instruments of our passions, we take no real pleasure in studying them, we do not want to know, but to show that we know, and the woods become for us merely a public stage where we seek applause—or else, confining our attention to the study or at best the botanical garden, rather than observing plants in their natural setting, we concern ourselves solely with systems and methods, a subject for endless argument, but which does not discover a single unknown plant or throw any real light on natural history or the vegetable kingdom. Thence come all the hate and jealousy that the struggle for fame arouses in authors of botanical works just as much as in other scholars—perhaps even more so. They distort this delightful study, robbing it of its true nature and transplanting it to towns and academies, where it degenerates no less than exotic plants in the gardens of collectors.

How much do you know?

Reading The Intellectual Life by Antonin Sertillanges (1863-1948), I came across various quotes that linked together. The common theme was the amount that we know, think we know or can know.

Sertillange suggests that:

‘The half-informed man is not the man who knows only the half of things, but the man who only half knows things.'

Furthermore, he cites Blaise Pascal (1623-1662) as pointing out that ‘We do not know all of anything’ and Claude Bernard (1813-1878) as suggesting that ‘To understand a single thing thoroughly, we should understand all things.’

There is a certain tension between these quotes. Perhaps they are not entirely consistent with each other. However, I think that this tension is potentially productive. Dwelling upon these three quotes raises a number of questions. Try it.

If we do not know all of anything, and to understand a single thing thoroughly requires that we understand all things, then it must follow that we cannot understand a single thing thoroughly—which does not seem unreasonable.

Ralph W. Gerard and ‘Body Functions’ (2)

I am particularly interested in how the older-style books treated anatomy and physiology—human and animal. So Gerard’s ‘Body Functions’—to which I have made reference in a previous post—was attractive in that respect.

Three things struck me about this book.

1. The book’s contents
2. The illustrations (three in particular)
3. The Index

The book does not have the textbook layout prevailing today. (See the Contents page at the end.) Interestingly, it begins with muscles and other ‘effectors’—that is, cells that make a change/difference. (Today textbooks typically start with some sort of ‘orientation’. This is followed by something on atoms—typically using the Bohr model—molecules and basic chemistry, i.e., the matter from which everything is formed. Then something about cells and tissues—as the building blocks of the body—usually follows.)

I always find the way in which older textbooks were illustrated intriguing. They are often a mix of anatomical accuracy and conceptual explanation. Three illustrations I found particularly interesting.

On p. 76 the autonomic nervous system is presented face-on with the two subdivisions on one side of the body. How successful, I’m not sure. (Read the legend.)

On p. 86, there is an interesting way of depicting glands. (Read the legend.)

On p. 177, another interesting way of depicting glands. (Read the legend.)

I also found the index to be somewhat innovative. I wish the approach it used was more common—even standard. It was, in effect, an index cum glossary. Each term in the index had a brief explanation. What this means in practice is that I can find two things at once. I can have a term defined and see where it is mentioned in the text. I include the first page as an illustration.

Ralph W. Gerard and ‘Body Functions’ (1)

In a previous post, I referred to a quotation from Ralph W. Gerard (1900-1974). This prompted me to look at his other writing. The title of one book that particularly caught my eye was Body Functions (1941). (It was subtitled simply ‘Physiology’ as if body functions and physiology were in some way synonymous.) I am rather sensitive to the use of the word ‘function’. I once had to teach a course entitled ‘Human Function’. That was not a phrase of my own devising. It was meant to be a course on human anatomy.

I was once invited to a planning meeting in Heidelberg by a German philosopher friend. The aim was to put together a funding application for the study of the philosophical understanding of function from a biological perspective. The late American philosopher Karen Neander who did much work in this area was invited as a speaker. At that meeting I became acutely aware of the implications and problems that surround the word ‘function’—especially for philosophers. Frequently, the word implies something deliberate and purposive. In nature, there are no such things. There is no guiding or directing force; what happens does not happen for a specific purpose or with a particular aim. Whatever the personal religious beliefs of the scientist, any role for a deity offering a guiding hand is excluded. The scientific approach holds that everything can be explained by what there is; no external factors or entities are necessary. (As such science is inherently materialistic—although the conceptual framework offered by physicalism is preferred nowadays.)

The language we use to convey science must adhere carefully to the ethos of being unguided and undirected. Using words like ‘function’, with its purposeful connotations, can be misleading and must be avoided. To talk of the function of the heart is wrong. It does pump blood but it was never designed or meant for that specific purpose. It simply does something that contributes to the organism’s survival.

Lizard walking

One of the realisations one makes when continuing to study a subject beyond one’s initial formal education is that things you were once told in all honesty are sometimes not quite right. There are many reasons for this although one thing is sure. No teacher or lecturer ever deliberately provides their students with false information. (Or if they do, it is to make a point that is immediately made clear.)

When it comes to models of the atom, the situation is perhaps a little greyer. I was taught the Bohr model of the atom at school—although it was not given that name. It was ‘the atom’. When I went to university we were taught something quite different. The flaw in what I was taught at school was not some much the inaccuracies as the fact that we were not told that it was only a model. We thought that it was what the atom was really like.

As a model, the Bohr model serves many useful purposes—but not as a description of what the structure atom is really like. What we were taught at university was also a model—albeit a better one—but a model nonetheless.

As undergraduates, when studying the nervous control of movement, we were told by an old professor that reptile movement was slower and deliberate because they had to ‘think’ about each movement. That is because their cerebella are much simpler than that in higher animals. The input the reptile cerebellum makes to locomotion is limited. The missing input had to come from elsewhere. That was from the brain, which had to divert what it was doing to ‘thinking’ about locomotion.

This description is not wrong but not a complete description.

Firstly, it overlooks the fact that reptiles are ectothermic animals and have a particular way of life. Indeed, when sufficiently warm, ectotherms can move quite quickly. They demonstrate a ‘sprint-and-pause’ style of movement which is, in fact, a highly efficient way for them to conserve energy. Furthermore, that plays a key part of their survival and hunting strategies.

Secondly, and very easily overlooked, is how in animals with side-to-side movement, walking and breathing at the same time is difficult. There is a need to stop every so often in order to breath. This is now known as Carrier's constraint after the American biologist David R. Carrier.

And about which a limerick has been penned by the English paleontologist Richard Cowen.

The reptilian idea of fun
Is to bask all day in the sun.
A physiological barrier,
Discovered by Carrier,
Says they can't breathe, if they run.

The realisation that walking and breathing at the same time was difficult for animals with side-to-side movement, only came to prominence in the late 1980s, after my old professor has retired. So he could not have known about it. However, when discussing organisms, it must be remembered that many different factors are in play at the same time. To do otherwise is, in a quite literal sense, not organismal thinking.

And there is always the caveat that something we haven’t thought of (yet) might apply too.