What is the difference between math, science and philsophy?

I’ve been listening to the Philosophy Bites podcast recently. One from a few years ago consisted of answers from philosopher’s to the question posed on the spot and without time for deep reflection: What is Philosophy? Some managed to give precise answers, but many struggled. I think one source of conflict they faced as they answered was that they didn’t know how to separate the question of what philosophers actually do from they should be doing. However, I think that a clear distinction between science, math and philosophy as methodologies can be specified precisely. I also think that this is important because practitioner’s in each subject should be aware of what methodology they are actually using and what is appropriate for whatever problem they are working on.

Here are my definitions: Math explores the consequences of rules or assumptions, science is the empirical study of measurable things, and philosophy examines things that cannot be resolved by mathematics or empiricism. With these definitions, practitioner’s of any discipline may use either math, science, or philosophy to help answer whatever question they may be addressing. Scientists need mathematics to work out the consequences of their assumptions and philosophy to help delineate phenomena. Mathematicians need science and philosophy to provide assumptions or rules to analyze. Philosophers need mathematics to sort out arguments and science to test hypotheses experimentally.

Those skeptical of philosophy may suggest that anything that cannot be addressed by math or science has no practical value. However, with these definitions, even the most hardened mathematician or scientist may be practicing philosophy without even knowing it. Atheists like Richard Dawkins should realize that part of their position is based on philosophy and not science. The only truly logical position to take with respect to God is agnosticism. It may be probable that there is not a God that intervenes directly in our lives and that probability may be high but it is not a provable fact. To be an atheist is to put some cutoff on the posterior probability for the existence of God and that cutoff is based on philosophy not science.

While most scientists and mathematicians are cognizant that moral issues may be pertinent to their work (e.g. animal experimentation), they may be less cognizant of what I believe is an equally important philosophical issue , which is the ontological question. Ontology is a philosophical term for the study of what exists. To many pragmatically minded people, this may sound like an ethereal topic (or worse adjective) that has no place in the hard sciences. However, as I pointed out in an earlier post, we can put labels on at most a countably infinite number of things out of an uncountable number of possibilities and for most purposes, our ontological list of things is finite. We thus have to choose and although some of these choices are guided by how we as human agents interact with the world, others will be arbitrary. Determining ontology will involve aspects of philosophy, science and math.

Mathematicians face the ontological problem daily when they decide on what areas to work in and what theorems to prove. The possibilities in mathematics are infinite so it is almost certain that if we were to rerun history some if not many fields would not be reinvented. While scientists may have fewer degrees of freedom to choose from they are also making choices and these choices tend to be confined by history. The ontological problem shows up anytime we try to define a phenomenon. The classification of cognitive disorders is a pure exercise in ontology. Authors of the DSM IV have attempted to be as empirical and objective as possible but there is still plenty of philosophy in their designations of psychiatric conditions. While most string theorists accept that their discipline is mostly mathematical, they should also realize that it is very philosophical. A theory of everything includes the ontology by definition.

Subjects traditionally within the realm of philosophy also have mathematical and scientific aspects. Our morals and values have certainly been shaped by evolution and biological constraints. We should completely rethink our legal philosophy based on what we now know about neuroscience (e.g. see here). The same goes for any discussion of consciousness, the mind-body problem, and free will. To me the real problem with free will isn’t whether or not it exists but rather who or what exactly is exercising that free will and this can be looked at empirically.

So next time when you sit down to solve a problem, think about whether it is one of mathematics, science or philosophy.

We can all be above average

I was listening to physicist and science writer Leonard Mlodinow on an All in the Mind podcast this morning. He was talking about his new book, Subliminal, which is about recent neuroscience results on neural processes that operate in the absence of conscious awareness. During the podcast, which was quite good, Mlodinow quoted a result that said 95% of all professors think they are above average, then he went on to say that we all know that only %50 can be. It’s unfortunate that Mlodninow, who wrote an excellent book on probability theory, would make such a statement. I am  sure that he knows that 50% of all professors are better than the median but any number greater than one could be greater than the average (i.e. mean). He used average in the colloquial sense but knowing the difference between median and mean  is crucial for the average or should I say median person to make informed decisions.

It could be that on a professor performance scale,  5% of all professors are phenomenally bad, while the rest are better but clumped together. In this case, it would be absolutely true that 95% of all professors are better than the mean. Also, if the professors actually obeyed such a distribution then comparing to the mean would be more informative than the median because what every student should do is to simply avoid the really bad professors. However, for something like income, which is broad with a fat tail,  comparing yourself to the median is probably more informative because it will tell you where you place in society.  The mean salary of a lecture hall filled with mathematicians would increase perhaps a hundred fold if James Simons (of Chern-Simons theory as well as the CEO of  one of the most successful hedge funds, Renaissance Technologies) were to suddenly walk into the room. However, the median would hardly budge. (Almost) All the children in Lake Woebegon could really be above average.

Jun 18, 2013: I adjusted the last sentence to avoid confusion.

Double dose

I highly recommend listening to this Radiolab short podcast on the story of Tsutomo Yamaguchi who worked in Hiroshima and lived in Nagasaki in August of 1945.  He survived both blasts and lived to tell about it.  A remarkable fact is that there seems to be no statistically significant increase in birth defects or cancer rates of the children of Japanese atomic bomb survivors.

We need Google genome

I listened to two Long Now Foundation talks on my way to Newark, Delaware and back yesterday for my colloquium talk.  These podcasts tend to be quite long, so they were perfect for the drive.  The first was by environmental activist and journalist Mark Lynas and the second by National Geographic photographer Jim Anderson.  Both were much more interesting than I expected.  Lynas, who originated the anti-genetically modified organism (GMO) food movement in Europe in the 1990s, has since changed  his mind and become more pragmatic.  He now advocates for a more rational environmental movement that embraces technological solutions such as GMO foods and nuclear energy.  He argues that many more people are killed by particulate matter from coal-fired generating plants in a year than over the entire history of nuclear use.  I have always felt that nuclear power is the only viable technology to reduce carbon emissions.  I have also argued previously that  I’m more worried about the acidification of the ocean due to CO2 than an increase temperature.  I think we should start building CANDU reactors now and head towards fast breeder reactors.

Jim Anderson talked about the loss of diversity of domesticated plants and animals and how they are essential for the survival of humans.  For the first 9,900 years of agriculture, we increased the diversity of our food stuff.  For the last hundred, we have gone in the other direction. We used to have hundreds to thousands of varieties of fruits and vegetables and now we’re down to a handful.  There are at most 5 varieties of apples I can buy at my local supermarket, yet a hundred years ago, each orchard would produce its own variety.  This leaves us extremely vulnerable to diseases.  The world’s banana supply is dominated by one variety (the Cavendish) and it is under siege by a fungus that threatens to wipe it out.  The Irish potato famine was so severe because they relied on only two varieties that were both susceptible to the same blight. Our fire wall against future blights are seed banks, where we try to preserve as many varieties as we can.  However, not all seeds can remain viable forever.  Many have to be planted every few years from which new seeds are harvested.  This replanting is often done by amateur horticulturists.  The podcast made me think that with the cost of genome sequencing dropping so rapidly, what we need now is for someone, like Google, to start sequencing every living being and making it publicly available, like Google Books.  In fact, if sequencers become cheap enough, this could be done by amateurs.  You would find some plant or animal, document it as well as you can, and upload the sequence to the virtual seed bank.  This can be a record of both wild and domesticated species.  We can then always resurrect one if we need to.  There could also be potential for mischief with highly dangerous species like small pox or anthrax, so we would need to have a public discussion over what should be available.