When describing Leonardo da Vinci's scientific achievements, it's hard to avoid using the phrase "ahead of his time". His careful observations and logical analysis in fields from astronomy to physiology seem a world apart from anything his contemporaries were doing, and it took centuries for mainstream science to catch up with his insights. It's as if someone took a modern scientist and teleported them into the Renaissance.

But it turns out that the driving force for many of da Vinci's studies was very distant from anything that today's researchers would recognise; in fact it was decidedly mystical. So can we still call him a scientist?

I've just written a feature for New Scientist about the discovery that da Vinci made spectacular advances in a previously unnoticed area - the study of trace fossils, or ichnology. Da Vinci studied fossilised sea creatures found in the mountaintops near Milan, where he worked for many years, and his progress in interpreting their origin is well known. He realised that the ground there once formed the bed of an ancient sea, and that the fossils were the remains of animals preserved when the sediment they lived in turned to rock.

This was at a time when everyone else was hotly debating whether the creatures had been carried into the mountains during the great flood described in the Bible, or were inorganic structures that had spontaneously grown within the stone.

Now a new analysis of one of da Vinci's secret notebooks shows that as well as studying body fossils (the direct remains of an organism), the scholar was interested in trace fossils - the marks and trails left behind by ancient creatures. These abstract traces are tough to interpret, in fact their origin was not accepted by mainstream science until the early 20th century. But da Vinci had it all worked out 400 years earlier.

The notebook shows that da Vinci knew certain trace fossils were the remains of creatures crawling between layers of sediment before they turned to rock, and that this interpretation was crucial for his arguments against the Biblical and Inorganic theories of fossil formation. Palaeontologist Andrea Baucon, who made the discovery, hails da Vinci as the "father of ichnology".

You can read more about all this, including possible representations of trace fossils in da Vinci's art, in my feature. But one question I was fascinated by when digging into all this was: why was da Vinci so obsessed by fossils? What made him study them in such detail when no one else was paying much attention?

It turns out that the answer is in a brilliant essay by the late Stephen Jay Gould in his 1998 book "Leonardo's mountain of clams and the diet of worms", which by a lovely coincidence was sitting on the bookshelf right next to me when I sat down to write my article. (I've been a fan of Gould ever since I read Wonderful Life at school, in fact he was a big influence on my decision to study biology at university. By another coincidence Gould was the guest speaker when I later graduated from Leicester University in 1995. Except that the organisers arranged for him to speak to the arts graduates, who graduated in the morning, whereas those of us receiving science degrees in the afternoon got to listen instead to an actress, I think she was from The Bill. I have never forgiven them.)

In his essay Gould attacks the image of da Vinci as a "scientist ahead of his time". He points out that da Vinci's fossil studies were driven by his desire to prove a theory that now sounds bonkers from a scientific point of view - that the human body (the "microcosm") and the Earth (the "macrocosm") are connected in some metaphysical way and therefore mirror each other in form and function. In other words, the Earth is a living organism: its soil is like our flesh, its rocks are like our bones, and the water flowing in its rivers is like the blood in our veins.

In studying fossils, da Vinci was looking for evidence to support his macrocosm-microcosm theory. According to Gould: "He featured fossils in order to validate the cherished centrepiece of his premodern worldview - the venerable argument, urged throughout classical and medieval times, for interpreting the earth as a living, self-sustaining 'organism', a macrocosm working by the same principles and mechanisms as the microcosm of the human body. Leonardo required, above all, a general device to make the heavy elements, earth and water, move upward against their natural inclination - so that the earth could sustain itself, like a living body, by constantly cycling all its elements, rather than reaching inert stability with heavy elements in permanent layers below lighter elements."

Da Vinci never managed to do this for water - a source of great frustration to him. But in marine fossils found at the tops of mountains, he had found evidence that rocks could move from the bottom of the earth to the top.

So although da Vinci's observations were undoubtedly brilliant, Gould argues, the fact that he was driven by such an "unscientific" theory means it is misguided to think of him as a modern scientist somehow transported into the past. "Leonardo, the truly brilliant observer, was no spaceman, but a citizen of his own instructive and fascinating time."

However the Leonardo biographer Michael White responded in his 2000 book "Leonardo: the first scientist" that (you've guessed it from the title) we should recognise him as a true scientist after all.

White says: "Professor Gould claims Leonardo's motivation must surely rob him of the mantle of the genuine scientist, but the fact that Leonardo never succeeded in making irrefutable observations to support his vague idea that water circulated within the Earth and that he never once attempted to fudge the matter, merely adds strength to my conviction that he was a true scientist. Many of Leonardo's peers would have failed to understand that facts must fit and support theory or else that theory is invalidated, whereas Leonardo never contemplated forcing the facts to suit his pet hypothesis."

Much as I admire Gould, I think I agree with White on this. I'm sure there are plenty of theories in science today that will come across as laughable in a few hundred years' time, and who knows, perhaps our whole view of the universe will look simplistic and childish. But as long as we're doing our best to carry out robust experiments and observations and to be guided by the results, I hope future boffins won't judge our efforts too harshly. 

The "absent-minded genius" is one of the most powerful stereotypes in science. But where did it come from? Perhaps its earliest appearance is in descriptions of the death of Archimedes. The great mathematician and inventor was supposedly killed during the Roman conquest of his home city Syracuse - despite orders to keep him alive - when he refused to break away from some geometry that he was studying.

Now an Italian historian, Cettina Voza, is suggesting that this image of Archimedes was invented by the Romans to hide the fact that they targeted him deliberately. In doing so, they created a stereotype that still colours how we see scientists today.

It's hard to know what really lies behind ancient historical accounts - most of them were written long after the episodes concerned by authors who did not witness events firsthand. Interpreting them is always going to involve a fair bit of speculation and personal opinion. But I think Voza's arguments are fascinating (and would love to hear what others make of them) so I'll summarise them here.

A Roman army led by General Marcellus attacked the city of Syracuse (in today's Sicily) in 214 BC, after the city's king switched allegiance from Rome to its rival Carthage. It should have been a quick victory but the Romans weren't prepared for Archimedes' fearsome war machines. His inventions, such as catapults, siege towers and a giant claw for attacking ships (and who knows, maybe even a flaming cannon) kept the Romans at bay and turned their attack into a long and exhausting siege.

Finally, in 212 BC, Marcellus's men found a weak spot in the Syracusans' defences and swarmed into the city. According to ancient accounts, Marcellus was so impressed by Archimedes' abilities that he had ordered him to be kept alive. Yet the mathematician was killed that day by one of Marcellus's soldiers.

Cicero says that Archimedes was so focused on tracing signs in the dust that he did not notice the Roman attack. Likewise, Silius Italicus says Archimedes "was intent on studying geometrical figures traced in the sand, not at all disturbed by the terrible ruin of the city". Valerius Maximus says he was killed because he carried on tracing figures on the ground instead of obeying the soldier's order to give his name.

These authors also say that when Marcellus found out that Archimedes had been killed, he was "supermoleste tulisset" (he bore it with the greatest difficulty), helped out the grieving relatives, and arranged a suitably grand funeral.

At a conference on Archimedes held in Syracuse last June (the proceedings of which have now been published by Springer), Voza suggested that these stories have more to do with propaganda than reality. She believes Archimedes' killing was absolutely intentional, and describes it as a "state-sponsored assassination".

She has a couple of reasons for doubting the above versions of events. First, she points out that Archimedes was famous in the ancient world and presumably very recognisable. So she questions whether a Roman soldier would have been so quick to disobey the orders to spare him. Such a transgression would have resulted in serious punishment (indeed, in one version of the story, the soldier was killed for it).

Second, she questions whether Archimedes would really have been so oblivious to reality. The scientist was supposedly at the heart of Syracuse's defence, having created the advanced weapons that kept the Romans at bay for so long. Shouldn't he have been slightly quicker to catch on that the city was being conquered?

Voza argues that because of his role in the siege, Archimedes would have been one of the Romans' main targets when they took Syracuse. She believes that in an early example of political spin, pro-Roman sources later embellished the story of his death, to justify the fact that the Romans had killed the greatest scientist of the ancient world, and to portray Marcellus as an honourable and cultured man.

But in creating this new version of events, she says, the Romans also invented and exploited the image of a genius divorced from reality - an image that has persisted as long as the memory of Archimedes himself. Their story, she says, "creates and establishes for the future expectations of what science should be: pure speculation and theory, divorced from any practical application".

Intriguingly, Voza mentions an alternative source of information about Archimedes' death: Dio Cassius (c. 155-235 AD). Tracing his version of events illustrates something of the difficulty of relying on ancient historical accounts. We don't have his description of the siege directly, but it was paraphrased by the 12th-century authors John Zonaras and John Tzetzes. In turn, Dio's source was Coelius Antipater, who lived very close to the time of the siege of Syracuse, and based his account on writers who supported the Carthaginians.

These accounts are similar to the more popular ones described above but with a few subtle differences. For example, when surprised by the soldier in his house, Archimedes apparently said in anger "my head, but not my drawing!" The advancing soldier told him to move away from the drawing, then killed him. Tzetzes's account adds that Archimedes shouted, "somebody give me one of my machines", presumably to defend himself.

Stubborn, perhaps, but hardly absent-minded. Voza reckons this is a more plausible description of the man who was solely responsible for the strenuous defence of his city. "This offers us a different vision of Archimedes," she says. "This time angry, still immersed in defence projects, and ready to take material action against the enemy."

We'll never know what really happened. But I rather like this new image of a forceful, battle-ready Archimedes. Wouldn't it be nice if he could finally conquer the stereotype of the absent-minded professor.

I've just written an article for New Scientist about a suggestion that researchers should consider issues such as consent and privacy when working on ancient mummies. I started off thinking this was a pretty strange idea. How can the concept of consent have any meaning for someone who has been dead for thousands of years?

But after researching the story I reckon it is at least a question worth thinking about. Strict ethical guidelines quite rightly cover research on the recently dead. So when exactly do human remains become fair game for scientists, and why?

My news story was sparked by a discussion paper in the Journal of Medical Ethics by anatomist (and mummy researcher) Frank Rühli and ethicist Ina Kaufmann of the University of Zurich, Switzerland. They argue that human remains retain their moral value no matter how old they are. While they don't give any advice on what research should or should not be done, Rühli and Kaufmann want scientists planning to study mummies to consider whether the person who has died would have been likely to consent to the research, and weigh that up against the work they want to carry out.

For example, perhaps Tutankhamun would have been happy with the long-lasting fame that research on his mummified body has brought him. Then again maybe he would be aghast at the endless speculation about the various diseases that he might have suffered from.

I ran this idea past a few researchers who work on ancient human remains. They weren't too impressed by the idea of second-guessing the wishes of someone who has been dead for hundreds or thousands of years. Their concerns are more practical, focused on how their research is likely to affect people who are still living, rather than the dead themselves.

Franco Rollo of the University of Camerino, Italy, has carried out research on Ötzi the iceman, who died in 3300 BC and whose mummified remains were found in the Alps. Rollo argues that as long as a body comes from a distant or ancient society, the ethical concerns are minimal. For example, he says he has "no problem at all" studying important figures from the Italian Renaissance, such as the Duchess of Urbino, or members of the Medici family. On the other hand, he was once involved in a project that aimed to study the bodies of two Austrian soldiers who died on the Alps at the end of World War I. It was stopped by the Black Cross, an Austrian organisation that honours dead soldiers, so the men could be buried in a war cemetery.

Likewise Helen Donoghue of University College London, who has analysed human remains from around the world for signs of infectious disease, says she has no qualms about research on mummies as long as it is carried out for valid scientific reasons, and the work is not opposed by any living descendants. She is carrying out research on the naturally mummified remains of some Hungarian people who died as recently as the 18th century, and says she has no problem doing this because the descendants are happy for the work to be carried out.

I got a different perspective, however, from an ethicist I interviewed. Soren Holm is a philosopher and bioethicist based at the University of Manchester, UK, and editor-in-chief of the Journal of Medical Ethics. He says that there are situations where the rights of the dead themselves should be taken into account. For him the important factor is whether a person is identifiable, and therefore still has a reputation that can be damaged.

The more famous the person, the more careful researchers should be. As an example he cites Queen Christina, who ruled Sweden in the early 1600s. Because she never married and often dressed in men's clothes, there have been calls to test her DNA for signs of a gender disorder, something that Holm suspects may be politically, rather than scientifically, motivated. "Even if we end up saying that we should allow the research, there is still a question to be discussed," says Holm. "We can't say that her reputation is irrelevant."

Holm says that such arguments must apply to identifiable individuals no matter how old they are. "If we still have a narrative about someone, it can't really matter whether they are hundreds of years old, or thousands of years old," he says. "We can still tell something about them that can detract from their reputation." He's not trying to stop valid research, but wants scientists to think about whether their research is really motivated by scientific questions, or simply by gossip or curiosity: "Do we really need to sort out the intricate details of Tutankhamun's family history?" (See the bottom of my New Scientist article for some interesting comments about whether curiosity is a sufficient justification for research.)

I don't know if Holm would agree with this but maybe it's a case of being thoughtful and respectful about the research that is carried out, rather than saying what can and can't be done. If we are going to treat dead people's remains with respect, then perhaps we should extend that courtesy to their reputations too.

In 467/6 BC, Greece was hit - literally - by an historic celestial event. According to ancient accounts, a meteorite the size of a "wagon-load" fell near Aegospotami in northern Greece. Plutarch later wrote that for 75 days before the stone fell, a huge fiery body was visible in the sky, "like an inflamed cloud, not still but moving with complex and branching motions, so that fiery fragments from its shaking and errant course flew in every direction, flashing like shooting stars".

Once the stone had fallen, the local inhabitants got over their fright and gathered around the crater. Peering in, "they saw no activity of fire, not even a trace, but a rock lying there, large indeed, but representing no appreciable fraction of that fiery mass above." The meteorite became a tourist attraction for the next 500 years.

This is exactly the kind of event that might normally have been subject to some mythological or religious explanation. But surprisingly, the impact was subsequently described in purely scientific terms. This seems to have been due to a young astronomer called Anaxagoras, who had supposedly used his theories to predict the meteorite's fall.

There are a few strange things about this story. First, what was the fiery body? The meteor itself would not have been visible in the sky for 75 days. And second, meteorite impacts are essentially random events, so how could Anaxagoras have predicted it?

Both issues are cleared up in a recent paper by philosopher Dan Graham and astronomer Eric Hintz of Brigham Young University in Provo, Utah (Journal of Cosmology, vol 9, p 3030).

It has been suggested before that the account of the fiery body is a perfect description of a comet. But Graham and Hintz go further than this, identifying this observation as the earliest documented sighting of Halley's comet.

Halley is unique among bright comets for making frequent returns to Earth's neighbourhood - roughly every 75 years or so. Many of its ancient visits are known from the detailed records of Babylonian and Chinese astronomers, with the earliest documented sighting having been made by the Chinese in 240 BC.

Graham and Hintz knew that 467/6 BC corresponded roughly with an expected pass of Halley's comet so they modelled the exact path that the comet would have taken, and compared it to all of the details they could find in ancient accounts, for example that the object was in the western sky when the meteorite fell, and was surrounded by shooting stars.

As I've written in a news story in this week's New Scientist, they showed that the ancient descriptions are indeed compatible with a sighting of Halley. The comet would have been visible for a maximum of 82 days between 4 June and 25 August 466 BC. It was in the western sky from 18 July onwards. Around this time, the Earth was moving under the comet's tail, so its debris field would have generated shooting stars.

 Unlike the detailed Babylonian and Chinese records, the Greek stories don't give an exact date or any precise information about the location of the comet in the sky. So it isn't possible to say for sure that the fiery object that accompanied the meteorite's fall was Halley. But Graham says it must be a "strong contender". Such bright comets are rare, so it would have been quite a coincidence if there was another one in the sky at around the same time (though not impossible - a brilliant daylight comet appeared just three months before the long-awaited return of Halley's comet in 1910).

On to the second part of the mystery - how did Anaxagoras predict the meteorite's fall? Graham says that despite suggestions that the astronomer predicted this particular meteorite, it's much more likely that he predicted the general possibility that a rock might fall from the sky. According to Plutarch: "it is said that Anaxagoras predicted that one of the bodies entangled in the heaven might, if there were some slip or agitation, break off and fall or be cast down."

Although that sounds rather less impressive, Graham says it was actually a revolutionary idea. He is writing a book about Anaxagoras, and says that he deserves to be recognised as "the star of early Greek astronomy".

Before Anaxagoras's time, celestial bodies such as the Moon and planets were thought to be fiery, lighter-than-air objects. But Anaxagoras, after observing a solar eclipse in 478 BC, worked out that they were actually heavy, rocky objects, held aloft by a centrifugal force. He warned that such rocks might one day fall to Earth, and when the Aegospotami meteorite crashed into the ground, he was dramatically proved right. "From then on, all of the other theories disappeared," says Graham.

That leaves just one question - was there any causal connection between the comet and the meteorite? Graham says it's impossible to know for sure; the appearance of both at the same time could have been a coincidence. On the other hand, the comet might have nudged a near-Earth asteroid from its course and sent it hurtling towards northern Greece. Either way, the Greeks' view of the cosmos was changed forever.

I've just reviewed Boffinology: The real stories behind our greatest scientific discoveries by Justin Pollard. It's a collection of short, snappy tales from the history of science, from the invention of Velcro to Einstein turning down the position of President of Israel.

It's an enjoyable read that emphasises the human side of science and technology through the ages (my review is here). Most of the stories have been told before, however. From the ancient world, for example, Archimedes, Hero of Alexandria and Thales of Miletus are all rather predictably featured.

But jumping ahead a millennium and a half, I was happy to see a short description of one of my favourite historical inventions, Agostino Ramelli's 16th-century revolving bookcase.

I came across this intriguing contraption when I was researching Decoding the Heavens, because like the Antikythera mechanism, the bookcase makes use of epicyclic gearing. This type of gearing is quite hard to get your head around without a diagram but basically it involves gear trains riding around on other wheels, so you get one set of circles imposed on another.

The Antikythera mechanism, which dates from the 1st or 2nd century BC, is by far the oldest known example of epicyclic gearing. Its creator used the technique to model the varying motion of the Moon, and perhaps also the Sun and the planets. The same principle was used in astronomical clocks in Europe from the 14th century onwards.

Ramelli used the gearing for a quite different purpose, however. His invention carries books.

An Italian military engineer, Ramelli worked for rich and powerful patrons in France, including King Henry III. His major surviving work, called "The Various and Ingenious Machines of Agostino Ramelli", was published in 1588. His machines include water pumps, bolt cutters, siege engines and portable bridges. But there are also several household gadgets, including the revolving bookcase.

Such bookcases did already exist but they rotated about a vertical axis, like a merry-go-round or "lazy susan". Ramelli's rotated about a horizontal axis, like a water wheel. Of course such a device would normally tip all of the books onto the floor as it turned, which is where the epicyclic gearing came in. Epicyclic gear trains caused each shelf to make one counter-rotation for each full turn of the bookcase, keeping them at the same angle - about 45 degrees - with respect to the floor, and ensuring that the books stayed safely in position. (The top image, taken from Ramelli's 1588 publication, shows a cross-section of this gearing.)

Ramelli wrote about his device: "This is a beautiful and ingenious machine, very useful and convenient for anyone who takes pleasure in study, especially those who are indisposed and tormented by gout. For with this machine a man can see and turn through a large number of books without moving from one spot."

Ramelli's invention took up a lot less floor space than a conventional revolving bookcase. But the complex gearing involved was hardly practical. As later scholars pointed out, it would have been much easier to hang the shelves independently of the main wheel, so gravity would keep them at the proper angle.

Historian Bert Hall, now at the University of Toronto in Canada, published an analysis of the bookcase back in 1970 (Technology and Culture, vol 11, pp 389-400). He says that Ramelli often used complex gearing to perform tasks that could have been achieved more easily using other means. The inventor didn't really expect such devices to be used, says Hall. He was simply showing off his virtuosity, "just as we today would expect an artist to demonstrate a particular personal ‘style' in his paintings". Hall suggests that Ramelli may even have conceived the whole bookcase simply to demonstrate his knowledge of epicyclic gearing.

But besides showing off the potential of this gearing technique, Ramelli's device also has a peculiarly modern significance that Hall, writing in 1970, could not have realised.

The bookwheel allowed a scholar to work on several open texts simultaneously, flipping quickly from one to another without losing his or her place (see second image, taken from an 18th century publication). So Ramelli's invention foreshadowed the concept of cycling through various texts or windows of information. Of course this principle pretty much defines the way we now access and work with information, from the ability to flip between different tabs on our computer screens to the hypertext links between pages on the world wide web.

In Boffinology, Pollard even describes the bookcase as a "wooden world wide web". He says: "The ability to read many texts at once and jump between them was a novelty and Ramelli's machine might be claimed an even more distant predecessor of hypertext than Vannevar Bush's Memex machine."

Actually, scholars were reading several texts at once for a long time before Ramelli. But he may well have been the first to develop a piece of technology specifically to enable such parallel study.

What Pollard doesn't mention is that (like the Memex machine) Ramelli's device was never built. Indeed as the Dead Media Archive puts it, the bookwheel is a fascinating example of a medium that was dead even when it was alive: "It was influential without ever actually existing."