Re: Why did Richard P. Feynman say, "I love only nature, and I hate mathematicians"?

On Thu, 14 Aug 2008, Jonathan Thiessen wrote:

Timo A. Nieminen wrote:
On Thu, 14 Aug 2008, PD wrote:

On Aug 13, 10:13 pm, "Timo A. Nieminen" <t...@xxxxxxxxxxxxxxxxx>
wrote:
On Wed, 13 Aug 2008, Edward Green wrote:
On Aug 13, 5:02 pm, "Timo A. Nieminen" <t...@xxxxxxxxxxxxxxxxx> wrote:
On Wed, 13 Aug 2008, PD wrote:
In my experience, if you want to know what science is, you ask a
scientist. It is unwise for an accountant to tell a carpenter that
what the carpenter does is not really carpentry, and that carpentry
should be defined according to what the accountant believes it should
be.

Unless you're a fan of Bacon!

Heh, despite Bacon's opinion of it, Gilbert's "The magnet" is still in
print. These days, perhaps more often read than Bacon.

I've read Bacon. I thought it was the greatest stuff ever, in
college.

Bacon only has half the story. Yes, he points out the value of experiment,
over and over. But he appears to have had no idea about what theory is
for. Experiment (i.e., bees collecting Baconian honey - is this more than
stamp collecting?) without theory is rather undirected and unfruitful.

Half of the scientific method is not the scientific method. Recording
observations of 3x5 index cards isn't complete science any more than
airy theorising is complete science.

But do tell, what impressed you about Bacon? Maybe I've read too many
critical secondary sources or suchlike, but I wasn't impressed. New
Atlantis is somewhat painful, with Salomon's House and all as his
exposition of the scientific method. (And for the Utopian genre in
general, More did better, along with some wry amusement to be had: people
speak of utopian ideals for dealing with, e.g., people with mental or
physical disabilities. What did they do with them in Utopia? Gave them
pensions and laughed at them in public, as state-paid public fools. Very
Utopian!)

That said, writers of 100 years ago were often very fond of Bacon.

PD brings up an essential tension, though: is X what X'ers are doing,
or is it something we can define ideally, which the X'ers can either
conform to or fall short of. It's like asking whether words mean
what's in the dictionary, or the way they are used in current speech.
We will always have both poles.

Science isn't what scientists do. Producing scientific results, doing
scientific research is what scientists do. Science is more than that
(although a large part of it is what scientists have done). As such,
science is not the scientific method, but is, in part, one of the outcomes
of the scientific method. The scientific method is not the only way to
produce science, and science is not exculsively the product of the
scientific method.

Given that, how can we usefully define scientific research as different
from what is done by scientists (including amateurs)? Now, if we want to
talk about an ideal method for doing scientific research - THE Scientific
Method, we might say - this isn't necessarily what scientists do. But who
is best placed to make statements about what the best methods are?
Accountants/lawyers, or researchers? A whole bunch of stuff of what is
written and taught about the scientific method is crap. The role of
creativity and imagination is often completely ignored, luck is officially
non-existent, and the complex feedback between theory and experiment is
reduced to the formulaic observation->hypothesis->test->theory. Ah well,
the usual oversimplification. Although I did like Dirac on what theory is
for - I've used his quote in a couple talks.

Excellent fodder for discussion.

I tend to view science as the activity rather than the product of the
activity. (One could also fret over the same distinction with
architecture, art, medicine, or plumbing.)

But I entirely agree with you that the common presentations of the
scientific method do over-distill a highly complex, variable, and
essentially human process. Hunch and pure insight play an essential
role, as does a rather poorly grasped esthetic sense that is used to
gauge or inspire ideas at the germination point. Also completely under-
represented are the various rules, workflows, and metrics by which
experimental results are collected and judged -- this is perhaps one
of the squishier areas in science. And it is also true that purely
humanistic aspects do influence science, even over longer periods of
time than the "scientific method" promises a cure -- these include
moral imperatives and collegial reputation.

But, and this is a big "but", the distilled "scientific method" as it
is taught to high school students everywhere, represents the
*essential* components that must be there for it to be recognizable as
science.

It depends on which version of the distilled "scientific method". The version, which is a common one, focussing entirely on hypothesis -> experimental test -> accept/reject theory is far too narrow. For starters, this would exclude much observational astronomy, geology, biology from being science. It would certainly rule out almost all mathematics (but then, some people are happy to call mathematics a non-science).

I do not wish to start or continue any sort of inter-discipline wars, however, I feel obliged to share my _opinion_ [feel free to disregard it].

I would argue that mathematics is the foundation of science [or at least scientific formalism]. One must accept a very narrow view of experimental tests in order to exclude _any_ mathematics from science.

That science uses mathematics as a tool does not make mathematics the foundation of science. Science uses language as a tool, and this is more fundamental. Science, as a collective body of knowledge, could not even exist without language. One of the important contributions of mathematics is to provide a precise and exact language for many of the technical details (and it does more than that). But does that make it _the_ foundation of science?

If there is a foundation of science, it must be philosophy and logic.

A scientific experiment is merely conducting a finite number of tests in order to disprove or not disprove the self-consistency of a particular set of statements given an initial set of axioms/postulates/assumptions [based on one's perception of physical reality].

That's a narrow definition of "experiment". But a common "scientific method" definition of experiment :)

The difference in math [or any sort of thought experiment] is that in addition to being able to disprove or not disprove a general hypothesis, one can possibly prove it, it need not be directly physical, and one may use a non-finite process to do so [eg mathematical induction].

The claim [not specifically claimed here, but I can't remember where it was] that science must be externally verifiable would necessarily exclude everything from science. All fields of science [including mathematics] depend on several base assumptions. The first of these is the assumption that we aren't [or at least one's self isn't] systematically deluded. If we were, it would be impossible to conclude anything. The very fact that we can't actually know if we are systematically deluded or not leaves us to believe everything that we "know", and to know nothing. This is were we make the leap of faith that maintains our sanity. This is not to say that science is baseless, but rather that mathematics [and thus science] is the best we have if we wish to say anything about anything.

The fundamental difference between mathematics and other fields of science [as I see it] is that mathematics assumes very little [thus making it completely general and concrete, but lacking the necessity of direct physical realisations of all things mathematical [all things physical must still be mathematically sound]]. Other fields of science greatly extend the base assumptions of mathematics leading to very specific physical results. It is for this reason that I deem all areas of science as partially overlapping subsets of mathematics.

Spoken like a mathematician! But I agree very much with your "leap of faith" paragraph. But this is needed to do anything useful in science. Sure, there are schools of talking about science where they claim that scientific knowledge is a mere social construct, essentially that the charge on an electron is e because that's what we've decided. Fooey to them; e is worth measuring because it objectively exists, and it's interesting, and perhaps useful, to know more about it.

But does this leap of faith, that there is an objective reality that we can learn things about, apply to mathematics?

Mathematics is clearly useful, even essential, to science. Is it science? I must confess to being uncertain. (I'll blame the fuzziness of definitions of science; with some definitions, it is science, and with others, not.) Well, it's traditional to award BSc degrees in maths, so it's at least socially acceptable to math "science".

--
Timo

.

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