Posts from 2010-07
I have received a number of questions and remarks about my keynote talk at EuroSciPy 2010, ranging from questions about technical details to an inquiry about the release date of Python 4.0! Rather than writing lengthy replies to everyone, I try to address all these issues here.
First of all, my intentions behind the keynote were
- Encourage scientists to look at new tools and developments that I believe to be important in the near future (Python 3, Cython) and at others that might become important to scientific applications (JIT compilers, alternative implementations).
- Make computational scientists think about future commodity hardware (which is what we use most of the time) and its implications for programming, in particular the generalization of massively parallel computing.
- Show that easy-to-use parallel programming paradigms, in particular deterministic ones, exist today. Computational scientists need to realize that MPI and OpenMP are not the last word on parallel programming.
- Make my ideas concrete by showing how they could be implemented in Python.
My "Python 4.0" is completely fictitious and will probably never exist in exactly that form. However, it is important to realize that it could be implemented right now. With the GIL-free Python implementations (Jython, IronPython), it would even be rather straightforward to implement. For CPython, any implementation not removing the GIL would probably be too inefficient to be of practical interest.
Most of the ingredients for implementing my "Python 4.0" are well-known and have already been used in other languages or libraries:
- The "declarative concurrency" programming paradigm has been used in Oz and FlowJava, but to the best of my knowledge not in any mainstream programming language. It is explained very well in the book Concepts, Techniques, and Models of Computer Programming, by Peter van Roy and Seif Haridi, and also in the freely downloadable essay Programming paradigms for dummies. Basically, it is the functional paradigm extended with annotations that identify computations to be done in parallel. Remove those annotations, and you get plain functional programs that yield the same results. Declarative concurrency is free of deadlocks and race conditions, which I think is a critical property for any parallel programming paradigm to be considered for a high-level language such as Python. Another nice feature of declarative concurrency is that data parallelism, including nested data parallelism, is a special case that can be implemented on top of it. Data parallelism is a useful paradigm for many scientific applications.
- Futures are asynchronous tasks provided as library functions for various languages. A Python library for futures is the subject of PEP 3148; an implementation is already available.
- The importance of effect-free functions for all kinds of code transformations (automatic or not) is widely recognized. It is equally recognized that a useful program needs to have effects. The two basic approaches to dealing with this contradiction are (a) allow effects, but make it as easy as possible not to use them to encourage a mostly effect-free style and (b) design a language without effects (pure functional language) and provide a mechanism to put in effects with special annotation or syntax but clearly as an exceptional feature. The best-known language in the second category is Haskell with its use of monads for controlling effects. Most functional languages are in the first category.
- Efficient data structures for functional programs have been a subject of research for quite a while and quite a few good ones are known. It would be straightforward to replace Python's tuple implementation by something more efficient in typical functional settings, or to add an efficient immutable dictionary implementation. The standard reference is Chris Osaki's book Purely Functional Data Structures.
Futures may seem to provide most of what declarative concurrency promises, but this is not quite true. Futures are objects representing computations. They have a method that client code must call to wait for the result and retrieve it. Since waiting is an explicit operation on a standard object, it is easy to create a situation in which two futures wait for each other: a deadlock. This can only be avoided by not having futures accessible as standard objects. The language implementation must recognize futures as special and insert a wait call before any access to the value of the result. For this reason, declarative concurrency cannot be implemented as a library.
Another important condition for implementing declarative concurrency with futures is that code inside a future must be effect-free. Otherwise multiple concurrently running futures can modify the same object and create a race condition.
Probably the only truly original contribution in my "Python 4.0" scenario is the dynamically verified effect-free subset of the Python language. Most languages, even functional ones, provide no way for a compiler or a run-time system to verify that a given function is effect-free. Haskell is perhaps the only exception in having a static type system that can identify effect-free code. In Python, that is not a viable approach because everything is dynamic. But why not provide at least a run-time check for effect-free code where useful? It's still better to have a program crash with an exception saying "you did I/O in what should have been an effect-free function" than get wrong results silently.
Here is an outline of how such an approach could be implemented. Each function and method would have a flag saying "I am supposed to be effect-free." In my examples, this flag is set by the decorator @noeffects, but other ways are possible. Built-in functions would of course have that flag set correctly as well. As soon as the interpreter enters a function marked as effect-free, it goes into "functional mode" until it returns from that function again. In functional mode, it raises an exception whenever an unflagged function or method is called.
Some details to consider:
- Effect-free functions may not contain global or nonlocal statements. Probably the only way to enforce this is to have special syntax for defining effect-free functions and methods (rather than a decorator) and make those statements syntactically illegal inside.
- It would be much more useful to have a "referentially transparent" subset rather than an "effect-free" subset, but this is also much harder to implement. A referentially transparent function guarantees to return the same result for the same input arguments, but may modify mutable objects that it has created internally. For example, a typical matrix inversion function allocates an array for its result and then uses an imperative algorithm that modifies the elements of that array repeatedly before returning it. Such a function can be used as an asynchronous task without risk, but its building blocks cannot be safely run concurrently.
Finally, a comment on a minor issue. I have been asked if the "async" keyword is strictly necessary. The answer is no, but it makes the code much more readable. The main role of async is to write a function call without having it executed immediately. The same problem occurs in callbacks in GUI programming: you have to specify a function call to be executed at a later time. The usual solution is a parameter-free lambda expression, and that same trick could be used to make async a function rather than a keyword. But readability suffers a lot.
This weekend I attended the EuroSciPy 2010 conference in Paris, dedicated to scientific applications of the programming language Python. This was the third EuroSciPy conference, but the US-based SciPy conference has been a regular event for many years already, and recently SciPy India joined the crowd. It looks like Python is becoming ever more popular in scientific computing. Next year, EuroSciPy will take place in Paris again.
There were lots of interesting presentations and announcements, and the breaks provided a much appreciated opportunity for exchanges between the participants. I won't try to provide an exhaustive summary, but rather list my personal highlights. Obviously this choice reflects my personal interests more than the quality of the presentations, and I will even list things that were not presented but that I learned about from other participants during the breaks.
The opening keynote was given by Hans-Petter Langtangen, who is best known for his books about Python for scientific computing. His latest book is a textbook for a course on scientific programming for beginning science students, and the first part of his keynote was about this same course that he is teaching at the University of Oslo. As others have noted as well, he observed that the students have no problem at all with picking up Python and using it productively in science. The difficulties with using Python are elsewhere: it is hard to convince the university professors that Python is a good choice of programming language for such a course!
Another important aspect of his presentation was the observation that teaching scientific programming to beginning science students provides more than just training in some useful technique. Converting equations into programs and running them also provides a much better insight into the structure and applicability of the equations. Computational science thus helps to better educate future scientists.
The reproducible research movement has the goal of improving the standards in computational science. At the moment, it is almost always impossible to reproduce published computational results from the information provided by the authors. Making these results reproducible requires a careful recording of what was calculated using which version of which software running on which machine, and of course making this information available along with the publication.
At EuroSciPy, Andrew Davison presented Sumatra, a Python library for tracking this information (and more) for computational procedures written in Python. The library is in an early stage, with more functionality to come, but those interested in reproducible research should check it out now and contribute to its development.
Jarrod Millman addressed the same topic in his presentation of the plans for creating a Foundation for Mathematical and Scientific Computing, whose goal is to fund development of tools and techniques that improve computational science.
NumPy and Python 3
As a couple of active contributors to the NumPy project were attending the conference, I asked about the state of the porting effort to Python 3. The good news is that the port is done and will soon be released. Those who have been waiting for NumPy to be ported before starting to port their own libraries can go to work right now: check out the NumPy Subversion repository, install, and use!
Useful maths libraries
Three new maths libraries that were presented caught my attention: Sebastian Walter's talk about algorithmic differentiation contained demos of algopy, a rather complete library for algorithmic differentiation in Python. During the Lightning talks on the last day, two apparently similar libraries for working with uncertain numbers (numbers with error bars) were shown: uncertainties, by Eric Lebigot, and upy, by Friedrich Romstedt. Both do error propagation and take correlations into account. Those of us working with experimental data or simulation results will appreciate this.
There was a lot more interesting stuff, of course, and I hope others will write more about it. I'll just point out that the slides for my own keynote about the future of Python in science are available from my Web site. And of course express my thanks to the organizing committee who invested a lot of effort to make this conference a big success!
The question if living beings, in particular those of our own species, possess "free will", and how it works if it exists, has recently become fashionable again. The new idea that brought the topic back into discussion was that our sense of free will might just be an illusion. According to this idea, we would be machines whose fate is entirely determined by the laws of physics (which might themselves be deterministic or not), even though we perceive ourselves as actors who pursue goals and take decisions that are not even in principle predictable by a physical analysis of our bodies, no matter at what level of detail.
The topic itself is an old one, perhaps as old as humanity. I won't go into its philosophical and religious aspects, but limit myself to the scientist's point of view: is free will compatible with scientific descriptions of our world? Perhaps even necessary for such descriptions? Or, on the contrary, in contradiction to the scientific approach? Can the scientific method be used to understand free will or show that it's a useless concept from the past?
What prompted me to write this post is a recent article by Anthony Cashmore in PNAS. In summary, Cashmore says that the majority of scientists do not believe in the existence of free will any more, and that society should draw conclusions from this, in particular concerning the judicial system, whose concept of responsibility for one's acts is based on a view of free will that the author no longer considers defendable. But don't take my word for it, read the article yourself. It's well written and covers many interesting points.
First of all, let me say that I don't agree at all with Cashmore's view that the judicial system should be reformed based on the prevailing view of today's scientists. I do believe that a modern society should take into account scientific findings, i.e. scientific hypotheses that have withstood a number of attempts at falsification. But mere beliefs of a small subpopulation, even if they are scientists, are not sufficient to justify a radical change of anything. As I will explain below, the question "do human beings possess free will" does not even deserve the label "scientific hypothesis" at this moment, because we have no idea of how we could answer it based on observation and experiment. We cannot claim either to be able to fully understand human behavior in terms of the laws of physics, which would allow us to call free will an unnecessary concept and invoke Occam's razor to get rid of it. Therefore, at this time, the existence of free will remains the subject of beliefs and scientists' beliefs are worth no more than anyone else's.
There is also a peculiar circularity to any argument about what "should" be done as a consequence of the non-existence of free will: if that hypothesis is true, nobody can decide anything! If humans have no free will, then societies don't have it either, and our judicial system is just as much a consequence of the laws of nature as my perceived decision to take coffee rather than tea for breakfast this morning.
Back to the main topic of this post: the relation between science and free will. It starts with the observation of a clear conflict. Science is about identifying regularities in the world that surrounds us, which permit the construction of detailed and testable theories. The first scientific theories were all about deterministic phenomena: given the initial state of some well-defined physical system (think of a clockwork, for example), the state of the system at any time in the future can be predicted with certainty. Later, stochastic phenomena entered the scientific world view. With stochasticity, the detailed behavior of a system is no longer predictable, but certain average properties still are. For example, we can predict how the temperature and pressure of water will change when we heat it, even though we cannot predict how each individual molecule will move. It is still a subject of debate whether stochastic elements exist in the fundamental laws of nature (quantum physics being the most popular candidate), or if they are merely a way of describing complex systems whose state we cannot analyze in detail due to insufficient resources. But scientists agree that a scientific theory may contain two forms of causality: determinism and stochasticity.
Free will, if it exists, would have to be added as a third form of causality. But it is hard to see how this could be done. The scientific method is based on identifying conditions from which exact predictions can be made. The decisions of an agent that possesses free will are by definition unpredictable, and therefore any theory about a system containing such an agent would be impossible to verify. Therefore the scientific method as we know it today cannot possibly take into consideration the existence of free will. Obviously this makes it impossible to examine the existence of free will as a scientific hypothesis. It also means that a hard-core scientist, who considers the scientific method as the only way to establish truth, has to deny the existence of free will, or else accept that some important aspects of our universe are forever inaccessible to scientific investigation.
However, there is another aspect to the relation between science and free will, which I haven't seen discussed yet anywhere: the existence of free will is in fact a requirement for the scientific method! Not as part of a system under scientific scrutiny, but as part of the scientist who runs an investigation. Testing a scientific hypothesis requires at the very least observing a specific phenomenon, but in most cases also preparing a well-defined initial state for some system that will then become the subject of observation. A scientist decides to create an experimental setup to verify some hypothesis. If the scientist were just a complex machine whose behavior is governed by the very same laws that he believes to be studying, then his carefully thought-out experiment is nothing but a particularly probable outcome of the laws of nature. We could still draw conclusions from observing it, of course, but these observations then only provide anecdotical evidence that is no more relevant than what we get from passively watching things happen around us.
In summary, our current scientific method supposes the existence of free will as an attribute of scientists, but also its absence from any system subjected to scientific scrutiny. This poses limits to what scientific investigation can yield when applied to humans.
Tags: computational science, computer-aided research, emacs, mmtk, mobile computing, programming, proteins, python, rants, reproducible research, science, scientific computing, scientific software, social networks, software, source code repositories, sustainable software
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