First conceived as a technological aid to astronomers by Napier, the logarithmic tables were a kind of printable analog computer. The logarithms are now 400 years old, and this is a good time to ponder about their role in the history of science.
It was not until 1614 that Napier’s first…
[Image: Torricelli with barometer, 19th C engraving]
I’ve never read any of Frederick Engel’s writings, but due to my interest in the history of science I was oddly pleased to see these words in his correspondence:
If, as you say, technique largely depends on the state of science, science depends far more still on the state and the requirements of technique. If society has a technical need, that helps science forward more than ten universities. The whole of hydrostatics (Torricelli, etc.) was called forth by the necessity for regulating the mountain streams of Italy in the sixteenth and seventeenth centuries. We have only known anything reasonable about electricity since its technical applicability was discovered. But unfortunately it has become the custom in Germany to write the history of the sciences as if they had fallen from the skies.
This is curious on many levels.
Firstly, what could be this technical need of a society that catapults its science forward?
Secondly, I think the following statement about Torricelli is very careless in its attempt to link the emergence of science with its natural context ( necessity is the mother of invention, etc ). Historians of science who know more than me would be quick to point that out.
Thirdly, Engels is very often applying metaphors and terms from physics as if they naturally apply to society. Here is an example from the same letter:
Under economic conditions are further included the geographical basis on which they operate and those remnants of earlier stages of economic development which have actually been transmitted and have survived – often only through tradition or the force of inertia; also of course the external milieu which surrounds this form of society.
I have observed elsewhere that the science of ‘statistical mechanics’ may have been the prime metaphor behind Marxism/communism itself. It is defined as:
the description of physical phenomena in terms of a statistical treatment of the behaviour of large numbers of atoms or molecules, especially as regards the distribution of energy among them.
Replace energy with money and that sounds a lot like economic theory. Society as an ideal gas, subject to the laws of thermodynamics as it were…whose status could be measured by some kind of barometer.
The metaphors of physics are worth delving into further because we are told elsewhere (pdf):
Marx wanted to develop a theory that explained the motor of history, i.e., the laws behind processes of historical change. It seems appropriate, then, that he should incorporate ideas of physical motion. The most common such idea in Marx’s work is found in Newton’s third law of motion, the Law of Conservation of Momentum, which says that for every action there is an equal and opposite reaction. This idea is most apparent in Marx’s overarching idea that capitalism brings about its own demise as the pushing down of the proletariat must lead eventually to its springing back up. The idea is expressed, though, in many details as well.
This relationship between political ideology and scientific worldview is very close:
The emphasis upon a specific field and a particular direction depends upon the needs, structure and superstructure of a particular society. There was, in the sixteenth and seventeenth centuries, an obvious connection between the concentration on astronomy and the development of world trade. There is an obvious connection between the present emphasis on atomic physics and the current imperialist military struggles.
So the question is merely whether we are approaching a point in history where scientific worldview and political ideology will completely merge into each other.
Will the laws of the universe then dictate the blueprint for laws of society? How?
"Prime Vérité" is a short film about the ZetaTrek expedition (est. 2011) where science and math hobbyists all over the world are trying to solve the Riemann Hypothesis. This video discusses some of the current research around this problem.
The film features the project founder Rohit Gupta ( @fadesingh on twitter) and was directed by Aiman Ali of Asylum Films. The production crew consisted of Vidya Muralidharan, Surbhit Saxena, Divya Sharma, Nikita Mhatre, Ram (sound) and Amit Kumar Manikpuri.
A lot of the stuff I spoke about did not make the cut, and what did might require further explanation. So here it is.
The film essentially explores connections between prime numbers and physical reality. Because the primes are indivisible, they are like building blocks or atoms. But this metaphor is taken much further…
After starting off with the famous meeting between Dyson & Montgomery at Princeton, I mention the occurrence of prime numbers in the biological world. And this has been known for some time in the context of periodical cicadas.
So how do the cicadas know how to calculate prime numbers? They don’t. They’re cicadas. The pattern probably emerged as a result of Darwinian natural selection: cicadas that naturally matured in easily divisible years were gobbled up by predators, and simply didn’t live long enough to produce as many offspring. Those who, by chance, had long, prime-numbered life spans fared best, survived longest, and left the most offspring, becoming the dominant variation of the species. (There are now at least fifteen distinct populations of periodical cicadas.) As things stand now, cicada emergences are so tightly timed, with the bulk of the insects emerging within a span of a few weeks, that any cicada that tries to break the pattern is simply taking her offspring’s life into her own hands.
And then I go on to mention the departure patterns of Mexican bus drivers. This is a more recent idea and the whole article is worth reading.
The men handed over their used papers. When the researchers plotted thousands of bus departure times on a computer, their suspicions were confirmed: The interaction between drivers caused the spacing between departures to exhibit a distinctive pattern previously observed in quantum physics experiments.
Towards the end I talk about an atom bouncing around for infinity inside a circle, which is essentially an allusion to the circular billiards model. I also briefly talk about the prime numbers as a gas, or the “primon gas" system. So now, you have to think of a box of gas as a 3-dimensional billiards table with a very large number of particles. From prime numbers as atoms, we have arrived at the idea that an infinity of such numbers could behave like a gas.
This stuff is a little hard to grasp unless you’re familiar with statistical mechanics and something called a “partition function”, but here is the source of this idea.
And a very stunning explanation by Matthew Watkins from an interview:
"Imagine a fluctuating integer, where prime factors are coming and going all the time, joining and leaving, so the energy of that integer is going up and down, the more prime factors there are the higher the energy, and the less prime factors the lower the energy. The zeta function naturally becomes the partition function of such a system."
The solo exhibition “Thinking Matters” — which represents another step in Nikolaus Gansterer’s visual research — explores in detail the relationship between drawing, thought and action. His work is a true example of interdisciplinary studies; it is the result of a close confrontation between socio-humanistic, scientific and artistic disciplines from which the artist takes single methodologies and applies to these his unique, higly personal artistic language. The result of this work is an installation which occupies the entire space: the work is composed of autonomous elements which, contemporaneously, are tiles of a vaster mosaic which the artist has developed specially for the gallery space.
This manuscript page from 1665 shows a 23-year old Isaac Newton calculating the area under a hyperbola ( the curve drawn on the top left of the page).
He calculates no less than 55 decimal places, meticulously adding values from each term of an infinite series. The series emerges…
“I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the ‘Law of Frequency of Error.’ The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete…