The Egyptian Pharaoh Akhenathen invented the first historic monotheism, according to Freud’s Moses and Monotheismus (1939). Sensibly, the sun was the God, worshipped as the true generator of life in this planet. Everything we have depends on the constant flow of solar energy. Animal life (human life being a subset thereof) is but a parasite of plant life, which in turn derives its energy from the Sun. The old pharaoh was ultimately correct, if prescientific.
Now, at University of California in Berkeley, it appears that they have managed to artificially reproduce the process of photosynthesis. Or, in other words, to make Diesel fuel out of and sunlight, see here.
Princeton physicist Freeman Dyson, in The Sun, the Genome, the Internet mused over the demographic problem of overcrowded cities and its possible solutions. Gentrification for rural areas, if cheap fuel is available, would be an easy answer.
Historically the transition to big cities happened as the economics of large concentrations of people drove ever more people into large agglomerates: btw, the steady loss of economic function on the part of smaller towns was also the reason why they retreated into themselves, thus becoming “provincial” and ultimately parochial (see Eric Hobsbawm, “The Age of Revolution”).
The availability of cheap fuel (because of artificial photosynthesis) and the possibility of locally engineering the components of production (via 3D printing and Internet) could reverse the historical process of big concentration of people in cities thus making most of the planet suitable for advanced life-conditions.
When in Brazil they produce ethanol out of crops, they are ultimately using plants as a (non-linear) black-box to store the flow of energy coming from the sun. The net efficiency is very low. What if we could engineer processes to make that efficiency higher (via artificial photosynthesis f.e.) and thus have plants that produce diesel fuel, say, just out of thin air and (free) sunlight?
Ipython as a prototyping tool for scientific computation is very neat and useful indeed.
After the Win 8 minimal installation reviewed in a previous post, now we are going for some simple Crank Nicolson of a parabolic PDE. We are going to have non-degenerate diffusions, as we don’t want the problem to become hyperbolic and to lose parabolic smoothing.
To run the notebook, one simply needs some more libraries, “numpy” and “matplotlib”.
They can be obtained as precompiled “wheel” files courtesy of Christoph Gohlke
After the relevant wheel files have been downloaded, simply run cmd (as administrator) and issue
from the directory where they have been saved:
pip install "numpy_my_version.whl"
pip install "matplotlib_my_version.whl"
(where of course the suffix “my_version” has to be changed into whatever the version is).
This zip contains a modified version of some buggy notebook found over the internet. It is now fully working in Python >= 3.x.
After uploading in the usual way, run it. The Finite Difference stencil is easily computed, and the heatmap is nicely displayed. Latex is there as well to document the mathematical steps.
Literate Programming at its best.
This post documents the installation of Ipython in Windows 8.
As an example of Don Knuth’s Literate Programming, Ipython is simply great.
One can devise the mathematical equations of a model, code the numerics and run the program against data.The full lifecycle of science, in a single sheet.
1) Install the “Python” runtime. Version 3.x is recommended, from this link.
2) Suppose that the version has been installed in: “C:\Python3.4”. Add this directory as well as “C:\Python3.4\Scripts” to the system path
3) Save this file in the same directory “C:\Python3.4”, and running cmd as administrator, from a shell issue
4) A C compiler is needed to compile extensions. Among various choices this is the simplest:
5 ) Create a vcvars64.bat file in C:\Program Files (x86)\Microsoft Visual Studio 10.0\VC\bin\amd64 that contains :
CALL "C:\Program Files\Microsoft SDKs\Windows\v7.1\Bin\SetEnv.cmd" /x64
6) Issue as admin
pip install markupsafe
Finally, run it
After that, the page
will open in the browser and under the heading Files->Upload
unzip this minimal ipython notebook and load it. The first ipython program is up: it can be executed and modified intereactively.
Ἐν ἀρχῇ ἦν ὁ λόγος, καὶ ὁ λόγος ἦν πρὸς τὸν θεόν, καὶ θεός ἦν ὁ λόγος (John 1:1)
The standard translation of the incipit of St. John Evangelion is: “In the beginning was the Word, and the Word was with God, and the Word was God”. A better translation of the Greek word ὁ λόγος would be the Latin “ratio”. In English the best bet is probably to keep the word “Logos”.
If as Bertand Russell says in “History of Western Philosophy” (HWP, pg. 56) Pythagorism is behind Plato’s philosophy (“Let no one untrained in geometry enter”) and much of Western “intellectualized theology”, then the Evangelical phrase has a different interpretation, the following.
The mathematical structure of the universe (the “Logos”) was there at the beginning, in some Platonic realm. But this mathematical structure of the universe (think to Spinoza’s “deus sive natura”) had to descend upon our species of primates in order for us to make sense of the world.
And so it did. “Καὶ ὁ λόγος σὰρξ ἐγένετο” (John 1:14: “and the Word became flesh”) which translates in this interpretation into “the mathematical structure of the universe became embedded in our mind”.
The unreasonable effectiveness of mathematics is not that unreasonable, if contemplated from such a vantage point.
The whole structure of Western science rests on this unstated assumption, that our finitude is capable of touching upon the infinite in its very essence of what’s beyond time and space (the mathematical structure of the universe). This was Pythagoras then Plato, S. Thomas, Descartes, Spinoza, Leibnitz, Kant. See again Russell, HWP.
Others gave a simpler interpretation, more palatable to the (average) cultural level of the first century A.D. But the meaning does not change.
Fact: “Nobel Prizes have been awarded to over 850 individuals, of whom at least 22% (without peace prize over 24%) were Jews, although Jews comprise less than 0.2% of the world’s population.” (from this Wikipedia page)
Explanation (Norbert Wiener):
“He had an interesting theory to account for Jewish devotion to learning. It was in fact the case that a young man who was a good Talmudic scholar, no matter how poverty stricken or unworldly, was considered a good match for the daughter of even the wealthiest family.
Adhering to Orthodox tradition the couple would raise a large family supported by the wife’s father or by the wife herself. At the same time over the centuries the learned Christian young man entered the Church and was barred from marriage. This process repeated over tens of generations could have added a genetic bias to the existing cultural bias for learning that prevailed among the Jews.”
(N. Levinson, Wiener’s life).
This is a marvellous paper by former colleague of Norbert Wiener, N. Levinson.
The bibliography of his papers is here.
“It is no coincidence that my first childish essay into philosophy,written when I was in high school and not yet eleven years old, was called The theory of ignorance. Even at that time I was struck with
the impossibility of originating a perfectly tight theory with the aid of so loose a mechanism as the human mind. And when I studied with Bertrand Russell, I could not bring myself to believe in the existence of a closed set of postulates for all logic, leaving no room for any arbitrariness in the system defined by them. Here, without the justification of their superb technique, I foresaw something of the critique of Russell which was later to be carried out by Gödel and his followers, who have given real grounds for the denial of the existence of any single closed logic following in a closed and rigid way from a body of stated rules.
“To me, logic and learning and all mental activity have always been incomprehensible as a complete and closed picture and have been understandable only as a process by which man puts himself en rapport with his environment. It is the battle for learning which is significant, and not the victory. Every victory that is absolute is followed at once by the Twilight of the gods, in which the very concept of victory is dissolved in the moment of its attainment.
“We are swimming upstream against a great torrent of disorganization, which tends to reduce everything to the heat-death of equilibrium and sameness described in the second law of thermodynamics.
What Maxwell, Boltzmann, and Gibbs meant by this heat-death in physics has a counterpart in the ethics of Kierkegaard, who pointed out that we live in a chaotic moral universe. In this, our main obligation
is to establish arbitrary enclaves of order and system. These enclaves will not remain there indefinitely by any momentum of their own after we have once established them. Like the Red Queen, we cannot stay where we are without running as fast as we can.
“We are not fighting for a definitive victory in the indefinite future.
It is the greatest possible victory to be, to continue to be, and to have been. No defeat can deprive us of the success of having existed for some moment of time in a universe that seems indifferent to us.
“This is no defeatism, it is rather a sense of tragedy in a world in which necessity is represented by an inevitable disappearance of differentiation. The declaration of our own nature and the attempt to
build up an enclave of organization in the face of nature’s overwhelming tendency to disorder is an insolence against the gods and the iron necessity that they impose. Here lies tragedy, but here lies glory too. These were the ideas I wished to synthesize in my book on cybernetics»
[“I am a mathematician”, pp. 323-325].