Today via twitter my attention was drawn to “10 Astronomical Discoveries Made Without a Telescope” posted by a Shanna Freeman at Curiosity.com from Discovery, of itself a worthy endeavour. However upon closer examination the post proved to be rather less than perfect.

On the opening page we are presented with the image of an instrument, with the information, “The astrolabe was an important astronomical tool, used since at least 150 B.C.” Now I haven’t been able to identify the instrument displayed but of one thing I’m certain, it isn’t an astrolabe. The statement made is also repeated in the text and in the interest of accuracy I should point out that the oldest extant astrolabe is from the ninth century CE and although tradition attributes the invention of the astrolabe to Hipparchus, who lived in the second century BCE the earliest extant description of an astrolabe is from the sixth century CE.

Moving on to the 10 discoveries we find that the list includes solar eclipses, auroras, constellations and comets. Now you can call me pedantic but these are not what I understand under the word discovery. In fact if you were in the right place at the right time you would have to be literally blind not to notice a solar eclipse, an aurora or a comet. They were never discovered they occurred. Constellations is something completely different not only are they not discoveries they are not even natural. Constellations are artificial human constructs to help astronomer/astrologers find their way around the heavens.

In the text on solar eclipses we have the following wonderful statement:

However, exactly when the first solar eclipse occurred is a matter of dispute — aligning sometimes vague historical records with the exact date of an eclipse based on what we know of their cycle can be difficult.

The emphasised phrase should of course read, “exactly when the first solar eclipse observation was recorded…” Reading things like this explains why proofreaders and editors exist.

In the text on constellations we find the following:

However, the original 40 constellations described by Ptolemy in A.D. 150 were based on star lists on Babylonian cuneiform dating back to 687 B.C. In turn, this system was likely based on even earlier Sumerian concepts. Another 44 constellations were added over the years to create the system recognized by the IAU today.

Ptolemaeus lists 48 constellations and the IAU officially recognises 88 and in case you can’t do the arithmetic that’s another 40 that were added over the years.

Most of the text on heliocentricity is acceptable, with gritted teeth, but this half sentence is definitely not:

…but it took hundreds of years after Galileo for acceptance of heliocentrism to become widespread.

Within the scientific community heliocentrism had become generally accepted by about 1660, i.e. about twenty years after Galileo’s death.

Again the text on comets is OK with the exception of the last sentence:

Now that we can predict the orbit of Halley’s Comet (and other short-period comets), astronomers can use computer models to retrodict the comet’s orbit and match it to reported sightings.

You don’t need a computer to predict the orbit or periodicity of a comet. Comet Halley is called Comet Halley because Edmund Halley calculated its orbit and periodicity with a pencil and a piece of paper (he might have used a quill pen!) and the orbits and periodicities of several other comets were calculated over the two centuries between Halley’s work and the invention of the computer.

In general the text on sunspots is also OK except for an unfortunate typo, “Sunspots were not mentioned in Western literature in A.D. 807” should of course read “until A.D. 807.” However we have again one unacceptable sentence:

However, prior to Galileo, most of these observers believed they were seeing transits of planets in front of the sun.

A small number of historical pre-telescopic planet transits reports are now considered to be sunspot observations. There are however reports of disfigurements to the surface of the sun that are not recorded as planet transits.

Next up we have the subject of planetary movement and here our author gets into serious difficulties. First up we have the following:

Although it took thousands of years for astronomers to accept the theory of heliocentrism, ancient stargazers did become aware that the planets were rotating as well as orbiting around a central location.

Between Aristarchus (310 BCE – ca.230 BCE) and the acceptance of heliocentrism in about 1660 there are not quite two thousand years. Now one might again accuse me of pedantry but if somebody uses the expression “thousands of years” one usually understands significant more than two. Also the awareness of planetary rotation is a product of telescopic observation in the seventeenth century. It however gets worse:

The Greek astronomer Hipparchus accurately created geometric models of both lunar and solar motion in about 150 B.C. He measured angles using instruments that preceded the astrolabe and used trigonometry to make calculations. About 150 years later, Ptolemy, a Roman citizen living in Egypt, expanded upon the work of Hipparchus and others to create models of planetary movement. He also understood the retrograde motion — and that planetary orbits varied.

Not only did Hipparchus create models of planetary motion for all of the seven known planets, Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn but he was fully cognisant that those models need to explain retrograde motion. Even worse the same is true of the geometrical models of planetary motion created by Eudoxus, Callipus and Aristotle in the fourth century BCE.

Moving on we now have Neptune! A reminder the title of this post is “10 Astronomical Discoveries Made Without a Telescope”. Here the author produces the following strange paragraph:

Astronomers had been able to accurately predict the orbits of other planets like Jupiter and Saturn, but the orbit of Uranus had unexplained variations. Three days after astronomer Alexis Bouvard’s death in August 1846, another French cosmologist named Urbain Le Verrier announced that he had discovered the cause of Uranus’s perturbation: the gravitational pull of a previously unknown planet nearby. Le Verrier had spent nearly six months performing complex calculations before coming to this conclusion. Neptune’s existence was confirmed by telescope in September 1846.

Something is definitely missing from this paragraph! It reality Bouvard calculated the exact orbit of Uranus and from the irregularities in its orbit hypothesised the existence of another, not yet observed, planet. Both the English astronomer John Couch Adams and the French astronomer Urbain le Verrier calculated the theoretical orbit of the hypothesised planet from Duvard’s figures. Using le Verrier’s calculations Johann Gottfried Galle discovered Neptune with a telescope!

Moving on to the speed of light we hit a low point in this post. Ole Rømer determined the speed of light at the end of the seventeenth century using the determinations of the orbits of Galilean moons of Jupiter made by Cassini with a telescope!

The author’s final example is to put it mildly bizarre, radio astronomy. She describes the discovery of interstellar radio waves by Karl Jansky but somehow neglects to mention that radio astronomy is conducted using radio telescopes!

The post that I have ridiculed above appeared on a major commercial website that almost certainly attracts a lot of traffic. The post is supposed to be both informative and educational but what we have is full of errors, badly written and badly edited. It’s posts like this that give the Internet a bad reputation amongst professional educators. “Don’t use the Internet its only full of false information”. Those of us who care about the Internet as an educational medium should make it our duty to pillory such posts and their authors and force them either to correct their rubbish or delete it.

A person can only submit posts when they know they exist.

The first person to know about the existence of a post is the author.

When you write a blog post about histsci, submit it right away right here.

The first person to know about the existence of a post is the author.

A person can only submit posts when they know they exist.

Giants’ Shoulders only works if people submit posts.

We can see Venus pass in front of the sun once every one hundred and twenty years.

Actually it’s twice in one hundred and thirty years. In intervals of approximately one hundred and twenty and then eight years

Ever since it’s been observed, a strange thing has been happening.

Horrocks the first to observe a Venus transit in 1639 did not record the black drop effect.

Instead of appearing as a dark circle moving across the sun, Venus formed a tear drop shape that slowly oozed onto the solar disc. It took three hundred years for scientists to understand the Black Drop Effect.

It’s actually still contested as to whether we can explain it or not.

In 1769, James Cook was in Tahiti, trying his best to set up telescopes.

No mention of Charles Green the actual astronomer of the expedition or Joseph Banks who also took part in the observations.

His trip over was partially sponsored by the Royal Academy, for no lesser purpose than laying out the solar system itself.

They got the expedition organised real quick considering that the Royal Academy was only founded in 1768. Maybe she meant the Royal Academy of Music but they were first established in 1822. Perhaps she meant the French Royal Academy of Science? Oops Cook was English wasn’t he. The expedition to Tahiti to observe the transit of Venus was organised by the Royal Society and paid for by the British Government.

People knew, roughly, the order of the known planets, but they had no way to know the actual mileage involved. How far were the planets from the sun?

People knew the order of the known planets exactly. They also knew the size of the planetary obits relative to the size of the Earth’s orbit around the Sun. If one could determine the latter then one could automatically determine the size of all the other orbits.

One way of finding out was taking a look at how fast a planet crossed a known distance, like how fast Venus moved from on side of the sun to the other.

You actually need to determine the transit duration from two different points on the Earth in order to then, using parallax and trigonometry, determine the distance not of the planet, as half implied here, but of the Sun.

The problem was, a ‘transit of Venus,’ when Venus passes between the sun and the earth, happened rarely. An eight year period saw two of them, and then there were no more for another 120 years. The astronomers needed to make the most of their chances.

Didn’t she just tell us that there is only one transit in one hundred and twenty years?

Cook observed the transit, and made a drawing of it in his journal. Oddly, the journal showed not a black circle passing in front of a bright one, but a transit that looked like a drop of water falling from a surface. The black spot had a wide base for too long a time, as if it were water coalescing into a drop. Then it tapered off into a tail, and broke free, moving as a circle across the sun.

The black drop effect was well known to Cook, Banks and Green before they made their observations as it had been observed and recorded by many astronomers during the 1761 Venus transit.

This has been observed regularly since then. The Black Drop Effect has puzzled astronomers for centuries, and only recently have two astronomers figured it out.

Actually many observers in 2004 saw no black drop and as already stated the explanation reported by Inglis-Arkell is still not accepted by all astronomers.

I’m curious what subject Ms Inglis-Arkell will choose next to display her extensive ignorance.

Sunday past Ms Jardine chose to muse for her ten minutes on the subject of gardening and politics and started of with the phrase, “Francis Bacon Lord Chancellor to James I and the father of modern science…” thereby, in my opinion committing a serious historical sin as well as perpetuating a seriously misleading historical myth.

I think the phrase ‘father of’ should be permanently banned from the vocabulary of all historians of science and technology. In fact I think that writers on the history of science and technology should have a special programme installed in their computers that as soon as they type the phrase ‘father of’ slowly and irrevocably dissolves their hard disk whilst uttering ear splitting screams of despair interspersed with gales of fiendish laughter. You might well ask why I cultivate such a negative attitude to what seems like a relatively harmless expression? The answer is quite simple, there is no such person as a father of any discipline or sub-discipline they do not exist and to claim that they do is a serious perversion of the history of science and technology.

There are at least five scholars to whom the phrase father of modern science has been and still is regularly applied and I could add at least three or four more who are equally deserving. For those who might be led to thinking that the problem is confined to the origins of modern science, it is not. I could name at least seven fathers of physical optic and five of modern physical optics, five fathers of physics, five of chemistry, four or five of geology and eleven of the computer. Even if one were to concede that a discipline does not possess one single father but is rather the prodigy of a collective of fathers one would be ignoring the fact that each of them is very much dependent on a whole group of not so significant figures who supplied the building blocks out of which he created his ideas. Science is a collective co-operative enterprise that progresses gradually through the contributions of whole legions of workers some more significant than others but none standing alone as ‘the father’. Let us never again have to read this ridiculous epithet.

Having dealt with Lisa’s sin what is the myth she was guilty of perpetuating? Even if the phrase father of modern science were valid, and I repeat it is not, then it is not applicable to and should not be applied to Francis Bacon.  I know that it is very common usage to describe Francis Bacon as the father, founder, originator etc., etc. of modern science but this attribution is simply false. In his philosophical work bacon developed and described a methodology for the investigation of the natural world but his methodology actually contradicts the methodology developed and practiced by people such as Galileo, Huygens and Newton who are usually credited with being the founders or progenitors of modern science. This is exactly the conflict on which I have written more than once between, as Rutherford put it so pithily, the scientists and the stamp collectors. Bacon is the original stamp collector and although his methodology has a great deal of validity in astronomy, the earth sciences and the various braches of natural history it is not the methodology, which people (falsely, there’s more than one) think of as the methodology of modern science, which is a variant of that outlined by Newton in the footnotes and appendices of his great works.

Giants’ Shoulders #44 will be hosted by yours truly here at the Renaissance Mathematicus on 16^th February 2012. Submissions as always by 15^th February either direct to your genial host, that’s me of course, or to the blog carnival website.

As always we are desperately searching for hosts for the rest of 2012 so if you have a blog and want to host the best blog carnival in the blogosphere the contact either Dr SkySkull at Skulls in the Stars or Thony C at The Renaissance Mathematicus.

Giants’ Shoulders #42 appeared punctually and in full glory edited by Darin Hayton at the PACHS blog on 16^th December 2011 and if by chance you still haven’t read it you should get on over there now and enjoy a months worth of first class history of science blogging.

Giants’ Shoulders #43 will be hosted by our own very favourite bull doggie, Michael Barton Darwin’s Bulldog, at that wonderful repository of all things Darwinian The Dispersal of Darwin on 16^th January 2012. Submission as usual either direct to the host or to the blog carnival’s website by 15^th January 2012.

As always Giants’ Shoulders is desperately seeking hosts for the next months so if you are seeking fame and glory this is your chance. You just need to contact either Dr SkySkull at Skulls in the Stars or myself that’s Thony C at The Renaissance Mathematicus.

Strangely my major objection from yesterday has mysteriously disappeared from her post (did somebody tip her off that she was making a fool of herself?) but there remains enough ignorance and stupidity to amuse those with some knowledge of Cantorian set theory and transfinite arithmetic, knowledge, which Ms Inglis-Arkell apparently totally lacks.

Ms Inglis-Arkell’s dive into the depths of advance mathematics starts so:

Imagine a thin line, almost a thread, stretching to infinity in both directions. It runs to the end of the universe. It is, in essence, infinite. Now look at the space all around it. That also runs to the end of the universe. It’s also infinite. Both are infinite, yes, but are they the same? Isn’t one infinity bigger than the other?

 The answer to the second question is actually no! Cantor demonstrated, counter-intuitively, that the number of points on a straight, the number of points in a square and the number of points in a cube are all infinite, all equal and all equal to ‘c’ the cardinality of the real numbers and the power set of aleph-nought.

After defining the infinite number of natural numbers as aleph-nought Ms Inglis-Arkell then writes the following:

But then what about real numbers? Real numbers include rational numbers, and irrational numbers (like the square root of five), and integers. This has to be a greater infinite number than all the other infinite numbers.

 These three sentences contain three serious errors, one implied and two explicit. The rational numbers includes the integers so to state them separately when describing the real numbers is either wrong or at best tautologous. Secondly, and this is the implicit mistake, a set consisting of the rational numbers and those irrational numbers, which are also algebraic numbers i.e. describable with an algebraic equation for example X² = 2, is also a countable infinite set that is equal to aleph-nought. Only when one includes the so called transcendental irrational numbers, those that cannot be described with an algebraic equation for example the circle constant π, that the infinite set become larger than aleph-nought. This result is again extremely counter-intuitive, as very few transcendental numbers have ever been identified. The final error is very serious because the cardinal number of the real numbers ‘c’ (for continuum) is by no means “a greater infinite number than all the other infinite numbers.”

Cantor could demonstrate that the so-called power set of an infinite set, i.e. the set of all the subsets of the set, has a larger cardinality than the set itself. This newer set also has a larger power set and so on ad infinitum. As stated above c is equal to the power set of aleph-nought. There is in fact an infinite hierarchy of infinite sets each one larger than its predecessor. On of the great mysteries of Cantorian set theory is where exactly c fits into this hierarchy. Cantor asked the question whether c is equal to aleph-one where aleph-one is defined as the the cardinality of the set of all countable ordinal numbers (1)? He himself was not able to answer this question. It later turned out that it is in fact an undecidable question. In the axiomatic version of Cantorian set theory, the theory is consistent, i.e. free of contradictions, both when c is assumed to be equal to aleph-one and when they are assumed to be not equal. This produces two distinct set theories, the first with c equal to aleph-one is called Cantorian the other non-Cantorian.

Although my sketch of Cantorian set theory and transfinite arithmetic is only very basic I hope I have said enough to show that it is really not a subject about which one should write if, as appears to be the case with Ms Inglis-Arkell, one doesn’t have the necessary knowledge.

(1) Going beyond this and explaining exactly what this means goes futher than is healthy in normal life. For those who are curious I recommend Rudy Rucker’s Infinity and the Mind, Birkhäuser, 1982

Later additions: I have corrected the mistakes kindly pointed out by Sniffnoy in the comments. Note to self: Turn brain on before skating on the thin ice of transfinite arithmetic.

Imagine a thin line, almost a thread, stretching to infinity in both directions. It runs to the end of the universe. It is, in essence, infinite. Now look at the space all around it. That also runs to the end of the universe. It’s also infinite. Both are infinite, yes, but are they the same? Isn’t one infinity bigger than the other?

That’s the question that Georg Cantor, a German mathematician who died shortly before World War I ended, grappled with throughout his life. Infinity was supposed to be an absolute number, especially in mathematics, where dividing infinity by a billion or multiplying it by a billion results, invariably and always, in infinity. Cantor thought about it and came up with aleph-nought, a ‘number’ that counts all the integers — whole numbers without fractions — that there are in existence. Aleph-nought has to be infinity, since there are an infinite quantity of whole numbers. But what about all the ‘real numbers’? Rational numbers include whole numbers, but they also include fractions of whole numbers. And since a whole number can be divided into an infinite number of fractions in and of itself, the set of rational numbers had to be larger than aleph-nought. But then what about real numbers? Real numbers include rational numbers, and irrational numbers (like the square root of five), and integers. This has to be a greater infinite number than all the other infinite numbers.

 This was when mathematicians started, metaphorically, booing and hissing when Cantor went by. The idea simply didn’t make sense to them. Infinity was infinity. That was the end of it. Cantor called his various sets of different quantities of infinity ‘transfinite’ numbers — they are also known as cardinal numbers — and designated aleph-nought as the smallest transfinite number in existence. The controversy his views stirred up cost him an appointment at the University of Berlin. It also cost him his sanity on many different occasions. Throughout his later life he stayed in mental hospitals regularly.

 Ms Inglis-Arkell’s first major error is in the first emphasised section above. The set of rational numbers is not larger than aleph-nought! One of the counter intuitive results that Cantor demonstrated in his investigations into the infinite is that although the set of the natural numbers is a subset of the set of rational numbers, the two set actually have the same cardinality i.e. they are the same size. This is not a trivial mistake on the part of Ms Inglis-Arkell but display a fundamental ignorance of Cantorian theory.

Her second error is on a human level historically possibly even worse and one of the most persistent and ignorant myths in the history of maths. Georg Cantor suffered from bi-polar disorder and whilst the stress caused by the serious objections to his work by a number of his colleagues probably aggravated his illness it was almost certainly not its cause.

In the second paragraph above Ms Inglis-Arkell propagates an unfortunate deception that has crept into the history of maths. It is implied that those such as Kronecker, Poincaré or Brouwer who raised objections to Cantors work did so out of ignorance or spite, whereas the objections raised by the constructivists and intuitionalists are based on solid mathematical and philosophical grounds. Objections, I would point out that have not been adequately dealt with till this day. It should be pointed out that the opening paragraph posted above supposedly outlining Cantor’s motivation is historically false but the true grounds for his work are much to complex to deal with here.

 Human anatomy, by Leonardo Da Vinci (1509-1510)
At a time in history when few people had methodically attempted to document human anatomy both inside and outside the body, Renaissance artist Leonardo Da Vinci did both. He produced over 200 drawings, based on dissections he observed, of human musculature and skeletal structure. Not only were these images beautiful, but they were among the most accurate medical diagrams created in Europe up to that point. By combining scientific observation with his art, Da Vinci helped to invent modern anatomy studies.

 Of itself the paragraph quoted above is, at least up to the last sentence, almost correct. The only thing that I would criticise is the implication that Leonardo was somehow unique in his anatomical studies. In fact he was doing nothing that almost all of his contemporary artistic colleagues were also doing. Anatomical studies of this type were part and parcel of the apprenticeship of a Renaissance artist. In fact Leonardo was introduced to the practice by his master Andrea del Verrocchio. The only thing one can say is that Leonardo did it better than his colleagues with the possible exception of Michelangelo. My problem is with the final sentence:

By combining scientific observation with his art, Da Vinci helped to invent modern anatomy studies.

Leonardo did not help to invent modern anatomical studies because his anatomical sketches remained largely unpublished and unknown. A very small amount of the material saw the light of day in his Treatise on painting, which was edited by his heir Francesco Melzi but first published in 1632. Of course by this time the study of anatomy had been truly revolutionised by the medically far superior illustration in Vesalius’ De fabrica, which was published in 1543. If anybody should be credited with producing anatomical images that changed the course of science then it is Vesalius’ artist who was probably Jan Steven van Calcar.

Image as usual stolen borrowed from Wikipedia

You might ask why I have included this, albeit short, new post under the rubric ‘Monday blast from the past’. One could regard the above as a footnote to my post from last year criticising people who include Leonardo in the history of Renaissance science, Pissing on a Holy Cow.