Welcome back, this week we are looking at
the second of three books by Henri Poincaré, great French mathematician and philosopher of
science. Usually I start these out by giving a very brief overview of the writer and some of the
more interesting details of their life. This week, for the first time on this podcast, I'm looking
at a second book by a writer. A book by a writer, another of whose books we've already looked at,
and so I've already done that brief overview. If you'd like to hear
a little bit about
Poincaré's life, I recommend you check out last week's episode in which we looked at science
and hypothesis. At the beginning of that, I went into his life a little bit. This week, looking at
another book of his called The Value of Science. We don't need to do that again. And while I have
some notes about what he talks about generally, I'm now thinking that it will be better if we
instead dive right into the text. The first passage that we're going to read from The Value
of
Science is the very beginning of the introduction of the book. And the first words in the first
sentence of the introduction of this book are the search for truth. And grammatically, that's how
it fell out in English. Maybe it's not literally the first words in French. Maybe those words show
up later in the sentence. But he puts the search for truth at the very beginning of everything
he's talking about. And that may have only been a coincidence, but if so, it's a characteristic
one bec
ause he comes back to this topic throughout the book. And in this passage, he's talking
about the value of the search for truth, which is what science is, basically. And he says,
well, isn't it important also to alleviate human suffering? But he says that human suffering is
unavoidable, that to really get rid of suffering, you'd have to annihilate the world, which also is
kind of a Zen idea that at some level to live is to suffer. And I say also because in looking at
Jonathan Swift a month
ago or whenever that was, out of nowhere, this very Zen idea popped up in
the writing of this early 18th century Anglo-Irish writer. So it's interesting to see something
similar here, though, of course, this idea is prevalent throughout European philosophy as well.
It's not unique to Zen, but he says that suffering is unavoidable. And more importantly, the point
of overcoming suffering, of easing man's material cares is to make time to seek the truth, that
easing suffering is at best a prel
iminary step in that process. He says that the truth can be
scary, it can be cruel, that it's like a phantom, you have to chase it, it's always running away
from you. He says that illusion is more consoling, it's more comforting. And he says that to seek
the truth, you have to be independent. You can't be attached to a certain ideology or to a certain
party. And Heisenberg might have been a little bit better on this when he said that scientists cannot
be entirely unbiased and independent. T
hey're part of a particular community, they've had a certain
upbringing, it's not reasonable to expect them to be completely isolated in their thinking. It
might be a bit more realistic to acknowledge that and then to try to overcome it in your thinking,
to acknowledge that you have certain allegiances, certain communities that you're part of, and
then do your best to not let that unduly skew your thinking. But here, Poincaré lays out the
ideal, which is that to seek the truth requires inde
pendence, which means a kind of individual
weakness. You're weaker as an individual than you would be as part of a group, so a lot of
people don't try to seek the truth for that reason because it often leaves you alone. And
he goes a bit further and says that what he's talking about applies to both scientific and to
moral truth. And he acknowledges that in doing so, he's taking a step on which not everybody is going
to follow him, but he connects those two things, scientific and moral truth
. And he says that
to find both, you have to be dispassionate, you have to be sincere, you have to really only
be seeking the truth. And he finishes by saying people who fear one generally fear the other,
and that's because it's a type of person who is most concerned with consequences, and that person
doesn't like either kind of truth. They don't like scientific truth and they don't like moral truth
because what they care about is consequences, and these two things might obstruct them from
getting to the consequences that they want, whatever the truth might be. So Poincaré opens the
introduction of the value of science by writing, quote, The search for truth should be the goal of
our activities. It is the soul and worthy of them. Doubtless, we should first bend our efforts
to assuage human suffering. But why? Not to suffer is a negative ideal more surely attained
by the annihilation of the world. If we wish more and more to free man from material cares, it
is that he may be
able to employ the liberty obtained in the study and contemplation of truth.
But sometimes truth frightens us, and in fact we know that it is sometimes deceptive, that it is a
phantom never showing itself for a moment except to ceaselessly flee, that it must be pursued
further and ever further without ever being attained.Skipping ahead, we also know how cruel
the truth often is, and we wonder whether illusion is not more consoling. Yes, even more bracing, for
illusion it is which gives us c
onfidence. When it shall have vanished, will hope remain, and shall
we have the courage to achieve? Skipping ahead again, and then to seek truth it is necessary
to be independent, wholly independent. If on the contrary we wish to act, to be strong, we should
be united. This is why many of us fear truth. We consider it a cause of weakness. Yet truth should
not be feared, for it alone is beautiful. When I speak here of truth, assuredly I refer first to
scientific truth, but I also mean moral
truth, of which what we call justice is only one
aspect. It may seem that I'm misusing words, that I combine thus under the same name two things
having nothing in common, that scientific truth, which is demonstrated, can in no way be likened
to moral truth, which is felt, and yet I cannot separate them, and whosoever loves the one cannot
help loving the other. To find the one, as well as to find the other, it is necessary to free the
soul completely from prejudice and from passion. It is ne
cessary to attain absolute sincerity.
These two sorts of truth, when discovered, give the same joy. Each, when perceived, beams
with the same splendor, so that we must see it, or close our eyes. Lastly, both attract us and
flee from us. They are never fixed. When we think we have reached them, we find that we have still
to advance, and he who pursues them is condemned never to know repose. It must be added that those
who fear the one will also fear the other, for they are the ones who in ev
erything are concerned
above all with consequences." End quote. And I'm not religious, but if I were, I would use the
argument in this next passage to defend my faith. Not because it's a perfect argument, but it's a
strong one that isn't brought up as often anymore, and today we view science and religion as being
in competition, and there are certainly points on which they disagree pretty starkly, or they can
be interpreted to disagree. But for a long time, people who we now call scientists
viewed what
they were doing as an extension of their religion, and that they were studying God's creation. And
so the two don't necessarily have to be opposed, and we've talked on this podcast about how, on
the one hand, the church persecuted people who we now call scientists, most notably Copernicus and
Galileo, but there were many other scientists or natural philosophers who not only were religious,
but held some rank in the church. But anyway, before wandering too far, let's hear what P
oincaré
wrote about this. And from what I could tell, though sometimes in his writing, it seems
that he was religious. If you look it up, the consensus seems to be that he wasn't. But
he might have been thinking something similar, which is, I'm not religious, but if I were,
here's how I would defend it. But he wrote, quote, Men demand of their gods to prove their
existence by miracles, but the eternal marvel is that there are not miracles without cease. The
world is divine because it is a
harmony. If it were ruled by caprice, what could prove to us it
was not ruled by chance, end quote. And that's an interesting argument from a different angle,
that people often ask God for miracles, or they've asked the prophets to have God show them a miracle
so that they can believe. And in a physical sense, a miracle is a suspension or a violation of a
law that is otherwise maintained in the universe, a pattern of behavior. And if you take that
natural order and harmony for granted, then
a suspension of that order would seem miraculous,
would be very amazing. It would amaze the viewer, the spectator. But if you don't take that order
for granted, and Poincaré comes back to this point in different ways, if there weren't
many iterations of the same type of thing, if we couldn't find that there are many rocks that
fit a similar pattern, they are a type of rock, or there are many clouds that fit a similar
pattern, or plant cells resemble each other in certain ways, or all the d
ifferent ways that
there are patterns in nature that we can study, making science possible. If you didn't have
that order, that might suggest a lack of a designer. But instead, what we have is a lot of
consistency. The universe, as far as we can tell, is not flipping in and out of order. It's not
blinking in and out of existence. The laws that Newton established and other guys have added to
them hum along day in and day out without rest, and that by itself doesn't suggest a creator. But
th
is angle that Poincaré brings up is interesting. Why are you asking for miracles? What's really
miraculous is that there is an order in which a miracle could appear. That every single thing
that happens is not a sparkler going off, changing everything else that had happened before.
That's miraculous. And again, I'm not making a theological argument here. I just think his
thought is interesting, and we can appreciate the wonder and beauty of nature in that way, whether
we are religious or no
t. In this next passage, he starts by talking about the relationship
between old and new scientific thought. And he says that it's not that new scientific thought
replaces old thought the way that you would tear down a building and build a new building in
its place, but rather it evolves from it, like an animal takes on a new shape gradually
over a very long period of time by evolution. And in looking at the earlier book of Poincaré's
Science and Hypothesis, we saw that he is very familiar
with the crisis that was going on
in mathematics at the time and, for example, the way that non-Euclidean geometries were
disrupting, in that case, millennia-old ideas. And so he's clearly very familiar with revolutionary
shifts in science. He's not only talking about the accretion of knowledge over time within a single
paradigm, but the relatively sudden shifts in which our best way to explain something changes
more dramatically. But I think he would say that even those kinds of changes re
semble this organic
growth more than the demolition and reconstruction of a building, because even the new explanation is
somehow related to the old one, if nothing else, by the awareness of its negation. The people who
develop the new explanation are discarding the old explanation, and that negation, the awareness
that the old explanation is invalid in some way, is present in the new explanation. And he brings
this up in part to answer people who say, how can I believe science? A hundred y
ears ago, scientists
were telling us this. Everything that scientists have ever believed, except for the very most
recent set of explanations, has been discarded and disproven. Someday these will be also, so
I shouldn't trust them. I think he wants to answer those people by saying that it's not that
those explanations were discarded, it's that they were improved upon. And that's not to say that we
should unquestioningly trust whatever can disguise itself as science. We can and should questi
on
anything that we want to, but in doing that, you are actually doing the better science. If
someone comes along and says, science says this, and you do your own independent investigation
and present your findings and say, no, in fact, what you said is wrong, this is what's true, you
haven't disproven science. What you've done is do better science than that first person did. And
by the way, that's what every great scientist ever has done. So the point is not that we have to
perform our ge
nuflections to whatever can pilfer this mantle, but Poincaré is in part calling on
us to trust the process of science as a means of getting to ever improving explanations. And he
goes on to say that scientific thought is not the creation of the scientist. A scientist is not
making a scientific fact the way that a painter makes a painting. That fact is somehow in nature.
And he acknowledges that our sense of that thing is limited to our senses, and we don't have access
to absolute reality ou
tside of the filter of our senses. We can only take it through that filter.
But that observed fact, though it exists in the senses of the scientist, it is not purely his
creation. And he overcomes what seems like it may be a contradiction there by giving what I think is
a very nice definition of objective reality, which is that it is what is common to many thinking
beings and could be common to all. And that one takes a little thought because that's not the same
as ultimate reality. Reality
as it is seen by God, not by a human being with five or however many
fallible senses. He doesn't say objective reality is congruent with ultimate reality, but that it
is what many thinking beings have in common and what all could have in common. And he says the
only thing that fits that latter description that it could be common to all is he says the harmony
expressed by mathematical laws. And he winds up by saying that the harmony in the world is the
source of all beauty. And for that rea
son, it is worth doing the slow, deliberate work required
by science to try to understand that harmony. Poincaré writes, quote, the advance of science
is not comparable to the changes of a city where old edifices are pitilessly torn down to give
place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end
by becoming unrecognizable to the common sight, but where an expert eye finds always traces of
the prior work of the centuries past. One must not think
then that the old fashioned theories
have been sterile and vain. Were we to stop there, we should find in these pages some reasons for
confidence in the value of science, but many more for distrusting it. An impression of doubt
would remain. It is needful now to set things to rights. Some people have exaggerated the role
of convention in science. They have gone so far as to say that law, that science,The scientific
fact itself was created by the scientist. This is going much too far in the
direction of nominalism.
No, scientific laws are not artificial creations. We have no reason to regard them as accidental,
though it would be impossible to prove they are not. Does the harmony the human intelligence
thinks it discovers in nature exist outside of this intelligence? No. Beyond doubt, a reality
completely independent of the mind which conceives it, sees it, or feels it, is an impossibility.
A world as exterior as that, even if it existed, would for us be forever inaccessible.
But what we
call objective reality is, in the last analysis, what is common to many thinking beings, and could
be common to all. This common part, we shall see, can only be the harmony expressed by mathematical
laws. It is this harmony, then, which is the sole objective reality, the only truth we can attain,
and when I add that the universal harmony of the world is the source of all beauty, it will
be understood what price we should attach to the slow and difficult progress which little by
little enables us to know it better." In this next section, he's talking about two different types
of mathematicians or thinkers, and he describes one as being slow and logical, and he calls them
analysts, and he describes the other as being more daring and intuitive, and sometimes sallying out
toward conclusions that they can't hold or defend right away. He calls those geometers, and he
uses a military analogy, and the first group he compares to somebody named Vauban, who is the
Marquis
de Vauban, a 17th century French military engineer and marshal of France who worked for
Louis XIV. He did a lot of things in military engineering, and also the current northern and
eastern borders of France are, to a great extent, unchanged from what he suggested they should be
based on trying to establish a defensible border over 400 years ago. But here, Poincaré compares
the analysts that he mentions to this kind of guy, somebody very slow and methodical besieging
a castle in a very solid
but patient way, and he compares the geometers to cavalrymen
who charge out and gain a bunch of ground, but sometimes they have to give it up quickly. And
he's saying neither that one is better than the other, nor that it depends on the kind of work
that they're doing, that if they do geometry, they do it this way, and if they do analysis,
they do it that way. They say it's a matter of the nature of the mind of the person. Different great
and lesser mathematicians approach problems in diff
erent ways. He writes, quote, it is impossible
to study the works of the great mathematicians or even those of the lesser without noticing
and distinguishing two opposite tendencies, or rather two entirely different kinds of minds.
The one sort are above all preoccupied with logic. To read their works, one is tempted to believe
they advanced only step by step, after the manner of a Vauban who pushes on his trenches against
the place besieged, leaving nothing to chance. The other sort are gu
ided by intuition and at the
first stroke make quick but sometimes precarious conquests, like bold cavalrymen of the advance
guard. The method is not imposed by the matter treated, though one often says of the first that
they are analysts and calls the other geometers. That does not prevent the one sort from remaining
analysts even when they work at geometry, while the others are still geometers even when
they occupy themselves with pure analysis. It is the very nature of their mind which m
akes them
logicians or intuitionalists, and they cannot lay it aside when they approach a new subject. Nor
is it education which has developed in them one of the two tendencies and stifled the other. The
two sorts of minds are equally necessary for the progress of science. Both the logicians and the
intuitionalists have achieved great things that others could not have done." In this next section,
he's talking about how or whether we know that mathematical reasoning is sound, and he says
th
at all the past generations also thought that they had achieved absolute rigor. Maybe we think
that, but we're mistaken. And he continues talking about this division between logic and intuition,
and we talked about this a little bit last week, but he says that logic, and I think he
means deductive logic, syllogistic logic, is by itself not creative. It can at best get
you to a tautology, and that something else is needed. And he acknowledges that the word is not
perfect, but he says we can
call it intuition, but there are lots of different ideas under it.
And then he tries to categorize the different mental actions that take place outside of logic
under the umbrella of what he's calling intuition. We might also call it imagination, but this
slightly more free movement. So now he's creating a little taxonomy of those processes, and
he says you can appeal to the senses. You can use your imagination.You can generalize using the kind
of induction that's used in experimental scien
ce that if this is true under these circumstances,
maybe it's true under all similar circumstances or all situations in which the circumstances are
the same as this. And then he uses a phrase that's interesting but a little unclear. He talks about
the intuition of pure number. And unfortunately, he doesn't lay out exactly what he means by
this, but he later uses the word arithmetic interchangeably with it. And he also says it's
from this intuition of pure number that we get the second axiom
above. And I skipped over that part.
But that second axiom is a theorem is true of the number one. And if we prove that it's true of n
plus one, if true for n, then will it be true for all whole numbers? And this is the demonstration
by recurrence that he talks about in the first book. But we might take this phrase intuition of
pure number to mean either arithmetic or this very clear mathematical demonstration. And he closes
out by saying, with nothing but the syllogism and pure number, it
's possible that we have now
achieved absolute rigor. Poincaré writes, quote, have we finally attained absolute rigor? At each
stage of the evolution, our fathers also thought they had reached it. If they deceive themselves,
do we not likewise cheat ourselves? We believe that in our reasonings, we no longer appeal to
intuition. The philosophers will tell us this is an illusion. Pure logic could never lead us to
anything but tautologies. It could create nothing new. Not from it alone can any
science issue. In
one sense, these philosophers are right. To make arithmetic, as to make geometry, or to make
any science, something else than pure logic is necessary. To designate this something else,
we have no word other than intuition. But how many different ideas are hidden under this same
word? Skipping ahead. We have then many kinds of intuition. First, the appeal to the senses and the
imagination. Next, generalization by induction, copied, so to speak, from the procedures
of the
experimental sciences. Finally, we have the intuition of pure number, whence
arose the second of the axioms just enunciated, which is able to create the real mathematical
reasoning. I have shown above by examples that the first two cannot give us certainty, but who
will seriously doubt the third? Who will doubt arithmetic? Now, in the analysis of today, when
one cares to take the trouble to be rigorous, there can be nothing but syllogisms or
appeals to this intuition of pure number, the onl
y intuition which cannot deceive us. It may
be said that today, absolute rigor is attained, end quote. In this next passage, he's talking
more about how these two methods of thinking, practices of thinking, logic and intuition move
together. They have to be applied in tandem. Not at the same time, but next to each other. You move
a bit logically, then you use your intuition or your creativity or whatever you wanna call that
other part to connect it to something somewhere else. And by talkin
g so much about this topic,
Poincaré is showing that he has spent some time trying to examine how he thinks, as well as how
other scientists and mathematicians think. And he sees these two parts as being indispensable.
And in this section, he uses the word logomachy, which is an argument about words. Poincaré writes,
quote, this shows us that logic is not enough, that the science of demonstration is not all
science and that intuition must retain its role as complement, I was about to say, c
ounterpoise or
antidote of logic. I have already had occasion to insist on the place intuition should hold in the
teaching of the mathematical sciences. Without it, young minds could not make a beginning in the
understanding of mathematics. They could not learn to love it and would see in it only a
vain logomachy. Above all, without intuition, they would never become capable of applying
mathematics. But now I wish before all to speak of the role of intuition in science itself. If it is
use
ful to the student, it is still more so to the creative scientist, end quote. And later there was
a short line that caught my attention. He writes, quote, should a naturalist who had never studied
the elephant except by means of the microscope think himself sufficiently acquainted with that
animal, end quote. If there were a biologist who had only ever studied elephants under a
microscope, he never looked at the whole animal, would you think that that biologist knew about
elephants? No, pro
bably not. You would say that that biologist knew a lot about the cells in the
elephant and what those cells are doing, but not about the whole system. And that's an interesting
thought to look at for any topic. This is another way of illustrating this metaphor of losing the
forest for the trees, but it seems somehow more stark here. And the example of this that comes
to my mind is the study of history. This metaphor applies readily to that.The study of history is
often the study of the sto
ry of individuals this or that political or military or thought leader
and that's in part because the Data that we have about history if it can be called that is largely
written records often by and about Individuals there may be large armies but these sources are
still by definition written by a single person a letter a record a Contemporary history and
history is also Written and studied in that way because that is the level at which we intuitively
Understand it in our daily lives We are
individual people walking around doing stuff and we interact
with other people who are the same And so then our understanding of history is often a narrative
of many individuals now the way that we would take this elephant metaphor a step forward is by
talking about the history of a nation and The word nation in English is often conflated with Country
or even government, but the word has the same etymological root as the word for natal Natio
has to do with birth in Latin and a nation is bet
ter Defined as being a group of people with a
number of shared features usually a shared history language Ethnicity culture probably a territory
and when we define the word nation properly in this way and don't conflate it with Government or
country or these other concepts for which there are already perfectly suitable words and we don't
need another one we see that certain countries and governments can overlap more and less with certain
nations and also that more importantly nations and Co
untries are not the same a nation can outlast
a government or a government can outlast a nation but if we were to carry this Elephant metaphor
that Poincaré is using onto the study of history. We might notice that you can understand a lot
about individuals that are part of a nation without seeing the larger story of the nation
to study the group of people in the Aggregate is a different kind of study than studying the
individual stories of the people in it And it is in a way comparable to S
tudying the cells of
an elephant versus studying the behavior of the whole elephant now the trouble with studying
Nations in this way is that we don't have that many examples and we don't have that much data You
could say for example well there's something about the English the anglo-saxon that makes him get on
boats and set up colonies in other places and For some reason there's something in the slav in the
Russian that doesn't do that but that particular example might be better explained
by the fact that
the anglo-saxons were on a little island and the Russians had and have more land than they know
what to do with and Nations are so big that you can't move them around and put them in a different
environment To see how they would act the way that you could with an elephant So it's not a perfect
metaphor But that line of Poincaré made me think of this aspect or difficulty in studying history
though It could readily be applied to many other contexts as well another short one h
e later points
out quote scientific conquest is to be made only by generalization and quote and Generalizing when
the word comes up is something that is generally used to say that argument isn't valid You started
at this point and now you're applying it over here or you're applying a rule to More subjects than
it should be applied to you're generalizing. Don't do that but ironically the only way that we can
figure out anything in science is by doing exactly that is by Figuring out how somet
hing behaves in
a particular context whether it be an abstraction like numbers or something Concrete like the retina
reacting to light or something that we can now only explain as being somewhere in between Like an
atomic particle by establishing some behavior and then making a statement that all Similar phenomena
will behave in the same way under the same Circumstances and the trouble is you have to do
that very carefully because it's very easy to do it wrong You can extrapolate out in a w
ay that's
not valid But when we do generalize in a valid way that according to Poincaré is the only means to
scientific Conquest in another section that I'm not going to read from he points out how we do
not have a direct intuition of the equality of Two intervals of time that we use devices Clocks
or chronometers to say that this amount of time and that amount of time are the same They're both
an hour or a minute but our subjective perception would not be able to tell us that if you had
s
omebody wait for One minute and then you had them wait for a minute and five seconds or a minute
and ten seconds they wouldn't be able to tell you which one was a minute and which was aa minute and
10 seconds, though they could certainly tell you which was a minute and which was an hour. And he
also points out that if there are two clocks that are showing different times, we don't have any
way of knowing which one is the correct one, or if there is such a thing as the correct one, because
i
n a certain sense, timekeeping is something that we made up. But we decide which one is correct
based on what's convenient. If there are two clocks in your house and they're 10 minutes apart,
and you're living in 1904 when this book was published, then maybe you look out the window and
see what the town clock says, and whatever that says, you make sure both clocks in your house show
that time. But that's a matter of convenience. He says you pick one over the other because it's
convenient, n
ot because it's true or correct. And I don't know the story of the connection between
all of this physics and the atomic clock. We now take it for granted and have for, I guess, over
two decades. I remember when the atomic clock was established. And I'm sure there's a relatively
straight line between Poincaré and his friends worrying about how we don't know what time it is
really, and the development of the atomic clock. But we'll have to learn about that another day.
There's another sectio
n later, again, that I'm not going to quote from where he's talking about
how it's not clear if you have a set of events, which one is the antecedent and which is the
consequence of the other, which is the cause, which is the effect. And he says we sort of assume
this based on experience and our perception of the events that are happening. But he points out that
our perception is not always reliable. If we were to rely only on our senses in trying to understand
thunder and lightning, we wou
ld say the light comes first and then the sound comes. Or maybe
that the light causes the sound even. But we now know that they happen simultaneously and they have
the same cause. But that's not immediately obvious to our senses. So he says we have to be careful
about our sensed perception of cause and effect. If there are a few things going on apparently in
sequence, it cannot be taken for granted which is the cause and which is the effect. And a bit later
when he's talking more about caus
e and effect, he writes, quote, Have we really the right
to speak of the cause of a phenomenon? If all the parts of the universe are interchained in a
certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of
causes infinitely numerous. It is, one often says, the consequence of the state of the universe a
moment before. How enunciate rules applicable to circumstances so complex? And yet it is only
thus that these rules can be general and rigorous, en
d quote. And this was encouraging to me because
when you're trying to look at cause and effect in politics and in sociology, never mind the
fact that there are many potential causes of a thing. In fact, there are often many causes, not
just potential causes. If you look at the cause of a certain war or the cause of a certain
economic depression, and you say, what are the causes of it? More often than not, there
are more than one. There might be a main one, but there are often other contribu
ting factors as
well. And so then you try to develop a model that accommodates all of this. And as you do, you're
trying to cut out what doesn't matter and keep what does to try to account for and simulate those
main causes at least. And it becomes complex. And you come to this conclusion that he's talking
about is that the cause of this event is the state of the entire universe a moment before. And
that might seem like an exaggeration. You say, what could the solar system, much less the
u
niverse, possibly have to do with human events? And you start to sound like an astrologer, except
that you don't have to go too far to find examples like the battle of the eclipse in the 6th century
BC, in which the Medes were fighting the Lydians near Pateria, which is outside of what is today
Yozgat in Turkey. And an eclipse took place during the battle, which led the two parties to stop
fighting and agree on a peace for a while. So if you had developed your very sophisticated model of
As
ia Minor in the 6th century BC, and you failed to account for the position of the moon, then
your model would have blown it on that one. So to repeat the challenge that Poincaré writes out,
he says, quote, how enunciate rules applicable to circumstances so complex. And yet it is only thus
that these rules can be general and rigorous. And he's not even talking about history. He's talking
about math and physics, which, as he points out relatively early in science and method, which
we'll be lo
oking at next week, lend themselves more readily to this kind of investigation than
history and sociology do. And now, see, I did mark off some passages about him talking about our
flawed perception of time. So we can get into that a little bit. He writes, quote, it is difficult to
separate the qualitative problem of simultaneity from the quantitative problem of the measurement
of time.No matter whether a chronometer is used or whether a count must be taken of a velocity
of transmission as
that of light Because such a velocity could not be measured without measuring
a time to conclude We have not a direct intuition of simultaneity nor of the equality of two
durations If we think we have this intuition, this is an illusion We've replaced it by the aid
of certain rules, which we apply almost always without taking count of them But what is the
nature of these rules? No general rule No rigorous rule. A multitude of little rules applicable to
each particular case These rules are n
ot imposed upon us and we might amuse ourselves in inventing
others But they could not be cast aside without greatly complicating the enunciation of the laws
of physics, mechanics and astronomy We therefore choose these rules not because they are true But
because they are the most convenient and we may recapitulate them as follows The simultaneity
of two events or the order of their succession, the equality of two durations are to be so defined
that the Enunciation of the natural laws may b
e as simple as possible In other words, all these
rules, all these definitions are only the fruit of an unconscious opportunism End quote. So he's
saying we cannot tell intuitively whether two or more events are Simultaneous nor whether two
or more durations of time are the same and even if you look at our rules for dealing with this
there are many different rules for many different contexts and the real overarching rule is that we
choose the explanation either simultaneous or not or the sa
me duration or not which will make the
Explanation of the natural laws supposedly causing the phenomenon as simple as possible So in such
situations, it's a kind of opportunism that gets us to our explanation. We look for the simplest
explanation though we're not aware that that's what we're doing later. He starts talking about
absolute space and Location and position and this is related to the difficulty in Defining a point
and this passage is only one of the difficulties that he brings up
, but it's an interesting one He
writes quote I'm seated in my room an object is placed on my table during a second I do not move.
No one touches the object I'm tempted to say that the point a which this object occupied at the
beginning of this second is Identical with the point B which it occupies at its end Not at all
from point A to point B is 30 Kilometers because the object has been carried along in the motion
of the earth We cannot know whether an object be it large or small has not c
hanged its absolute
position in space and not only can we not Affirm it, but this affirmation has no meaning and in
any case cannot correspond to any representation end quote And I look this up the numbers that he
used are still accurate for the speed of the earth in its orbit They say 67,000 miles an hour, which
is about 18 miles or 30 kilometers per second And so it's interesting to think that on one level
if there's something sitting perfectly still on your desk that object is Actually m
oving 18 miles
per second But the larger argument that Poincare makes is that we can't know in absolute space How
something is moving and he doesn't point this out But I've read this somewhere else if you zoom
out and include the earth's motion around the Sun then there's this extra motion that you
don't think of initially but also the solar system itself is moving in a certain way as Is the
entire Milky Way and I think that's as far as they know I don't know if they think the universe is
moving or something So in terms of absolute space the whole universe put into a kind of coordinate
grid, how is a particular object? Moving related to a fixed point in that grid. We can't know
so it's not even necessarily Accurate to say that your morning coffee is moving at 18 miles
per second So you don't have to hold on to it. So tightly don't worry the point that he builds
toward about Localization and position and points is the following quote in a word the system of
coordinate axes to
which we Naturally refer all exterior objects is a system of axes Invariably
bound to our body and carried around with us It is impossible to represent to oneself absolute space
when I try to represent to myself Simultaneously objects and myself in motion in absolute space
in reality I represent to myself my own self motionless and seeing move around me different
objects and a man that is Exterior to me, but that I convened to call me end quote and he's even
going a bit further there He's
not only saying we can't do the calculation about how something is
moving because we don't have enough information yet That's part of the point that he makes earlier
But now he's saying we can't even imagine it because if you imagine Yourself on the earth,
which is rotating and orbiting the Sun which is in thisSolar System, which is going around in the
Milky Way, which is apparently moving in some way also, you are still looking at that imaginary
picture from the fixed point of your vision,
your imaginary vision. And he's saying that's not
what absolute space is even. That's still another demonstration of this point that he makes there,
which is that our concept of localization is a kind of coordinate grid that we carry around with
us. And somewhere he defines localization saying that it is a perception of the physical motions
that you would have to make to get to a thing. So if you localize a chair in your room, it means
you have some conception that to get to the chair, you
'd have to stand up, walk a few paces,
and you'd be at it. Or to localize the sun, you'd have to get in a spaceship, fly for eight
minutes at the speed of light or whatever it is, and then you could get there. And he says our
system for localizing is this thing that we carry around with us, and the nexus of it is ourselves.
And that's not a concept of absolute space. Unfortunately, I couldn't see that he somewhere
said absolute space is instead X, Y, and Z, but maybe he'll talk about that s
ome in Science
and Method, because there's certainly a little bit of overlap between what he talks about in the
value of science and in science and hypothesis, though there's still a tremendous amount of new
material, and it's certainly worth reading both books. And in a closing thought about space, he
says, quote, all we can say is that experience has taught us that it is convenient to attribute three
dimensions to space, end quote. So our assertion that we live in three dimensional space
is purely
based on the convenience of using that thought. And we should be troubled or possibly excited by
this, because as he's pointed out earlier, we have bad intuitions about time. We have bad intuitions
about space generally. That's a separate section that I didn't really go into. And when we
use devices to measure time, we come out with something that is different from our perceptions.
And so the foundation of our perception of space being in three dimensions as only a matter of
conv
enience leaves wide open the possibility that there are other dimensions that we're not
really aware of, because they are somehow outside of our perception. In this next passage, he's
talking about the value of mathematics. And first, he addresses people that he calls practitioners.
And we might say people who are practical or they think of themselves as practical. And they're
asking, what's the use of math? How does it help us make money? And he says that the question
needs to be flipped a
round. And we should ask, what's the use of making money if we have
to sacrifice art and science and our reasons for living in the process? But in terms of its
practical value, he says there are all kinds of people who criticize theory and have no idea that
that's how they get their daily bread. And what he means is that this kind of math is obviously
everywhere in daily life. And we probably have more respect culturally for math than they did
a hundred years ago. And maybe we understand it
s value a bit better, even at the popular level.
But he points out later, not in this passage, but in one we're going to be looking at a bit
later, that even Tolstoy questions or rejects the notion of math or science for its own sake. And
even when I was reading that, it comes up in What is Art? I was thinking that the only way that you
have the information that you need to make more significant connections later is you have people
tinkering with things, the use of which is not yet clear. A
nd then at some point, it gets used as a
piece of a larger puzzle. So even math or science, whose use is not immediately obvious, has benefit
and is worth doing. Now, the argument against this is we could all think of research that we've seen
done, particularly in fields outside of math and physics and astronomy, really hard sciences,
that is funded by taxes. And you wonder, why the heck are they spending money on that? And for
me personally, I would never say this of actual, sincere, genui
ne scientific research. But you
occasionally see something that is clearly ideologically driven. And more importantly, when
you look into it, the science behind it seems very shaky. But anyway, that's not what Poincaré is
talking about. And that's not what Tolstoy was talking about either. But Poincaré would say
to Tolstoy that you need the science or math for its own sake, because that's how you get all
the intermediate discoveries, all of the necessary connections in order to form somethi
ng larger
later. Then after the practitioners, the so-called practical people, he talks about people who
would ask about the connection of math to nature, particularly to very high-flown theoretical math,
whose application is not immediately obvious. And he says that math in particular has two prime
values. One is philosophical, and the other is aesthetic. And he says, philosophical function
is to help the philosopher to understand number, space, and time, these very difficult concepts.
Bu
t along with that is the aesthetic value of math, and he talks about that for a bit. And
he closes by saying that if math had only one of these two, either only its physical or its
aesthetic value, it would still be worthwhile, but in fact it has both of these together. Poincaré
writes, quote, you have doubtless often been asked of what good is mathematics and whether these
delicate constructions entirely mind-made are not artificial and born of our caprice. Among those
who put this questio
n I should make a distinction. Practical people ask of us only the means of
money-making. These merit no reply. Rather, would it be proper to ask of them what is the
good of accumulating so much wealth and whether, to get time to acquire it, we are to neglect art
and science, which alone give us souls capable of enjoying it and for life's sake to sacrifice
all reasons for living. Besides, a science made solely in view of applications is impossible.
Truths are fecund only if bound together.
If we devote ourselves solely to those truths whence we
expect an immediate result, the intermediary links are wanting and there will no longer be a chain.
The men most disdainful of theory get from it, without suspecting it, their daily bread. Deprived
of this food, progress would quickly cease and we should soon congeal into the immobility of old
China. But enough of uncompromising practitioners. Besides these, there are those who are only
interested in nature and who ask us if we can ena
ble them to know it better. To answer these, we
have only to show them the two monuments already rough-hewn, celestial mechanics and mathematical
physics. They would doubtless concede that these structures are well worth the trouble they have
cost us. But this is not enough. Mathematics has a triple aim. It must furnish an instrument
for the study of nature. But that is not all. It has a philosophic aim and, I dare maintain,
an aesthetic aim. It must aid the philosopher to fathom the notion
s of number, of space, of time.
And above all, its adepts find therein delights analogous to those given by painting and music.
They admire the delicate harmony of numbers and forms. They marvel when a new discovery opens to
them an unexpected perspective and has not the joy they thus feel the aesthetic character, even
though the senses take no part therein. Only a privileged few are called to enjoy it fully. It is
true. But is not this the case for all the noblest arts? This is why I do no
t hesitate to say that
mathematics deserves to be cultivated for its own sake and the theories inapplicable to physics as
well as the others. Even if the physical aim and the aesthetic aim were not united, we ought not
to sacrifice either." In this next passage he's talking about the relationship between physics
and math. And he says on the one hand it's been a long time since science was just theories. And
I think he's thinking both of the ancient Greeks and their theories about what matte
r comprises.
But he might have been expanding it to some of the metaphysics of the 18th century. But he says
that experiment now says the final word on what is true. That without a demonstrating experiment
you can't claim anything. But he says in order to articulate those laws that physicists demonstrate
by experiment, they need a very subtle language. They need a language more precise, more rich, more
deep than ordinary everyday language. Or more rich and precise in a particular way. And h
e says that
language is mathematics. And I've said before I was not a very good math student in high school.
But I've been really enjoying revisiting math as an adult. And when I was in middle school and
high school math seemed like a strange game that I didn't quite know the rules to. And I never really
knew what to do with it. But in the intervening years from high school to my late 20s I had done
a bunch of thinking on other topics. And I'd read a bunch of philosophy. And I'd thought abo
ut
logic. And so then when I revisited math it clicked for me that a lot of math is a sequence
of if-then statements. And this is an example of the kind of deduction that Poincaré talks about
sometimes. That when you're trying to solve for X in algebra. Or if you're doing integration in
calculus. And you write out the problem. And then you rewrite it. And then you rewrite it again.
Each time slightly adjusting what's there. You could put in between each of those lines if the
above then bel
ow. If the above is true then the following must be true. And then you write it
out again. And then you go if that is true then the following must be true. Which it might seem
like sort of a simple thought. But I was able to put it in this context that I understood better.
That in philosophy or in law.logic using words, you make a claim, and if that's true, you make
a claim based on that, and if you can show that that's true, and so on. And math is that,
essentially, or a large part of the
beginning of math is that. The induction and generalization
that Poincaré sometimes talks about is, of course, separate, but the deductive syllogistic part of
math is like that. And for me, that helped a lot, and this is part of thinking of math as
a language in which you're making claims, and you can have flaws in your logic at any step,
because each time you update that equation, you simplify it one more step somehow, you're doing
that based on established principles that someone else fig
ured out, and now you're using them. In
the case of calculus, a lot of it is Newton and Leibniz, but not all of it, but you're using these
quantitative logical principles, you could say, and in making those logical inferences, you could
make a mistake, and then you would end up all the way down at the bottom with the wrong answer
because somewhere in the third step, you missed something. And for me, it helped me to think
about it as somehow analogous to verbal logic, though ironically, the
origin of the concept of
proof is geometry, so it's really more that verbal logic has taken this from math, but however
it went historically, I personally had more experience dealing with words, so it was easier
for me to think about it as moving from that side to that one. And that was my first thought about
what Poincaré says in this next passage about math as a language. And my second thought had more to
do with calculus in particular, which I've been working on recently, which is that a
s you slowly
get higher in math, you're describing more subtle relationships more precisely, and this is best
expressed by connecting it back to the real world. When you're talking about algebra, you often have
a question about things like two trains moving at different speeds, and that kind of calculation is
still interesting. This train is going that speed, this train is going that speed, they're this far
apart, when do they cross? Those are interesting, but they are constant. Everything
is fixed.
There's a fixed distance, there's fixed speeds, and then they just start moving and they cross
at some point. When you get into calculus, you get into these questions like if you have
a cone-shaped container and you're filling it up with water, so it's shaped like an ice cream
cone, the point is at the bottom and there's water coming into the top, how fast does the water rise
or how long does it take the water to get three inches up the cone or whatever? And what makes
this compl
icated is that it's not a cylinder, it's a cone, so that as the water goes in, the
speed at which the water is rising slows down. And that's a more subtle relationship, but math
can also describe that very precisely. And I'm sure that as you get up higher in math, there
are even more and better examples of these kinds of extremely precise descriptions. And I value
writing in words and description a lot. Clearly, I have a podcast like this. So words are cool in
a different way and they can d
escribe things that math can't describe. You couldn't imagine having
a novel written in math that told any kind of story about what it's like subjectively to be
a person. But math can describe certain kinds of relationships much better than words can. And
I think all of that is part of what Poincaré is getting at in this next passage. He writes, quote,
"'The physicist cannot ask of the analyst "'to reveal to him a new truth. "'The latter could
at most only aid him to foresee it. "'It is a l
ong time since one still dreamt "'of forestalling
experiment "'or of constructing the entire world "'on certain premature hypotheses. "'Since all
those constructions "'in which one yet took a naive delight, "'it is an age. "'Today, only
their ruins remain. "'All laws are therefore deduced from experiment, "'but to enunciate them,
a special language is needful. "'Ordinary language is too poor. "'It is besides too vague to express
relations "'so delicate, so rich, and so precise. "'This there
fore is one reason "'why the physicist
cannot do without mathematics. "'It furnishes him the only language he can speak.'" End quote.
And this next one is a bit shorter, but he's saying a little bit more about the role of the
mathematician. And he compares it to that of an artist, that a mathematician should be permitted
to work in an open-ended way, the way that an artist is. And of course, Tolstoy would say he
has very particular constraints on what an artist should be doing too. And he s
uggests toward the
end of his book that somebody besides him ought to write a similar kind of book about the role of
science that he wrote about art. So Tolstoy would probably say, "'I don't only constrain science
in this way, "'I constrain art in the same way, perhaps more strictly.'" But anyway, Poincaré says
that the mathematician should be allowed to work the way that an artist does. He writes, quote,
"'Such are the services "'the physicist should expect of analysis, "'but for this scie
nce to be
able to render them, "'it must be.'"cultivated in the broadest fashion without immediate expectation
of utility. The mathematician must have worked as artists. What we ask of him is to help us to see,
to discern our way in the labyrinth which opens before us." End quote. So he's been talking about
what math has provided to physics. Among other things, it's given at this very precise language.
And in this next passage, he's talking about what has provided to math or to analysis. An
d he says
that math without physics is like art without subjects. That just as the world gives a painter
something to try to paint, to depict, physics gives math something to try to articulate in its
language. It gives it something to try to math. And he says in doing so, it keeps math from going
around in circles because nature, he says, is more varied than the human imagination. That without
connecting back to nature and trying to solve problems presented by nature, math would probably
g
et twisted around itself and people would be going around in circles trying to solve the same
problems forever. And in thinking about this relationship between mathematics, which doesn't
have a very clear definition, we all know what we're talking about when we say mathematics, but
the way that we say biology is the study of life, we don't have such a clear definition of what
math is. But it's some kind of manipulation of abstractions. In thinking about the relationship
between that human a
ctivity and the rest of human life, it's worthwhile to remember that math began
as applied math. When you talk about pure math and applied math, it's easy to think that pure math
is the more sacred of the two. It's untainted by all the messiness of the world. It's somehow
perfectly rigorous and it's done for its own sake. There's something almost numinous about it,
whereas when you compare that to applied math, math in engineering and technology and all of
the sciences that it's applied in,
that is, while simultaneously practical and awe-inspiring,
pure math people might be tempted to say that that's somehow lower. And it's hard not to see
the parallel with the Christian tradition in which the most religious people went and lived in
monasteries and kept themselves away from worldly life, and in doing so they were closer to God.
It's hard not to suspect that there might be a parallel perception there, that whatever gets
mixed up in worldly life must by definition be more munda
ne and less sacred. And pure math has
that whole appeal for me. I don't know very much about it, but it's easy to imagine that it's one
of the pinnacles of what humans are capable of, but it would still be worthwhile to remember
that the oldest math was applied math. Math emerged whenever it did, likely as a way of doing
business, probably. Figuring out how much money was going to be transacted for something, and then
thereafter it was probably used in construction. I've read about this in
the past, but I can't
remember the details of it. But if you're trying to build a nice building, it doesn't take too
long to figure out that it's useful if you try to measure it in certain ways, though it might have
taken humans 50,000 years to figure that out. But math first emerged as a means of understanding the
world, and then pure math came later. It grew out of that practice. Poincaré writes, quote, let us
now see what analysis owes to physics. It would be necessary to have completely
forgotten the history
of science, not to remember that the desire to understand nature has had on the development
of mathematics the most constant and happiest influence. In the first place, the physicist sets
us problems whose solution he expects of us. But in proposing them to us, he has largely paid us
in advance for the service we shall render him, if we solve them. If I may be allowed to continue
my comparison with the fine arts, the pure mathematician who should forget the existence
of the exterior world would be like a painter who knew how to harmoniously combine colors and
forms, but who lacked models. His creative power would soon be exhausted. The combinations which
numbers and symbols may form are an infinite multitude. In this multitude, how shall we choose
those which are worthy to fix our attention? Shall we let ourselves be guided solely by our caprice?
This caprice, which itself would beside soon tire, would doubtless carry us very far apart, and we
should q
uickly cease to understand each other. But this is only the smaller side of the question.
Physics will doubtless prevent our straying, but it will also preserve us from a danger much more
formidable. It will prevent our ceaselessly going around in the same circle. History proves that
physics has not only forced us to choose among problems which came in a crowd, it has imposed
upon us such as we should without it never have dreamed of. However varied may be the imagination
of man, nature is
still a thousand times richer. To follow her we must take wayWe have neglected
and these paths lead us often to summits whence we discover new countries What could be more useful
it is with mathematical symbols as with physical realities? It is in comparing the different
aspects of things that we are able to comprehend their inner harmony Which alone is beautiful and
consequently worthy of our efforts and quote and so part of his overall message here Is that math
and physics have a kind of
symbiotic relationship? They support each other. They help each other.
It's not that one is better than the other in this next passage He's talking about astronomy and
its value and how it should be best promoted to governments and ultimately to the public so that
it can be funded and this conversation is a little bit dated because at the time the practical value
of Astronomy for governments was still mostly centered on navigation on having very precise
Star catalogs and tables so that ship
s at sea could most effectively know where they are and
find the best routes to where they were Trying to get to and now we use space for Satellites
and ICBMs and all kinds of things so it's easier to make the argument for astronomy But but
astronomers still have to justify their expense. So it remains a relevant conversation But Poincaré
says we should make this argument not from the practical angle or not only from that angle but
by saying that astronomy makes us grand it gives us a sense
of our place in the universe and how
great our minds are Because we can try to study this enormous thing, but he says more importantly
astronomy Facilitated the other sciences which have a more obvious Practical value and he says
that astronomy is what gave us a soul capable of comprehending nature It made us believe that we
could study nature and we were talking about old math a few minutes ago One of the most important
examples is in astronomy for the purpose of trying to make a calendar
in order to do agriculture This
is after the Neolithic Revolution People figured out that you can plant seeds in the ground and the
food will just come up and this is another way of getting food rather than hunting and gathering
it foraging for it and they must have figured out that the crops don't grow when it's cold and
The weather is sometimes cold and sometimes hot and it changes in some kind of regular pattern but
what is that pattern and the pattern is measurable by astronomy and Fig
uring out that what they put
in the ground is somehow connected to those lights way up in the firmament Realizing that there was
some connection between those things must have been awe-inspiring for the first human to imagine
it But this is a very early application of math perhaps earlier than the trade and construction
purposes that we talked about before because both of those Trading in large amounts and building
elaborate structures were a consequence of agriculture You have agriculture
then you have a
surplus harvest Then you have a silo to store the surplus and then you have people trying to steal
it and so you need to protect it before long you have a large settled group and eventually they're
building buildings and participating in commerce but I imagine though I'd be open to a different
view that agriculture would have come before those things in some sense of the Calendar year would
have been required to do that and that would have required some proto astronomy So I'
m thinking that
that use came first But anyway in this passage Poincaré invites us to imagine that the earth had
Clouds like Jupiter does that made it so that we could never see the heavens. We could never see
the stars We could never see the other planets and he says, okay, don't trip me up on a technicality
I know that we need sunlight So let's imagine that the sunlight can still come through the clouds so
we can still have organic life But we still can't see the stars and he says how wou
ld humanity be
different? Maybe we'd never would have figured out that we can study comprehend Manipulate nature
even in the primitive way that we do to this day if it weren't for those initial steps Taken by
the first astronomers this allowed us to go from being the permanent Prey and victim of nature
to a being that under certain circumstances can stand up to its force or get out of the way
and that bit about imagining that the earth had this layer of clouds is Interesting because the
hi
story of the universe maybe could have turned out differently so that that was the case and we
would have said That's ridiculous to think that the universe goes on forever or something We would
have had a totally different Understanding of the universe simply because we couldn't see through
it and so we would assume that there's nothing out there It reminds me of HG Wells country of the
blind if you're interested, you can go check out that episode We looked at that a month or so ago
Poincar
e writes quote astronomy is useful because it raises us above ourselves It is useful because
it is grand that is what we should say It shows us how small is man's body how great his mind since
his intelligence can embrace thatthe whole of this dazzling immensity, where his body is only
an obscure point, and enjoy its silent harmony. Thus we attain the consciousness of our power,
and this is something which cannot cost too dear, since this consciousness makes us mightier. But
what I should w
ish before all to show is to what point astronomy has facilitated the work of the
other sciences, more directly useful, since it has given us a soul capable of comprehending nature.
Think of how diminished humanity would be if under heavens constantly overclouded, as Jupiter's must
be, it had forever remained ignorant of the stars. Do you think that in such a world we should be
what we are? I know well that under this somber vault we should have been deprived of the light
of the sun necessa
ry to organisms like those which inhabit the earth. But, if you please, we shall
assume that these clouds are phosphorescent and emit a soft and constant light. Since we are
making hypotheses, another will cost no more. Well, I repeat my question. Do you think that in
such a world we should be what we are? The stars send us not only that visible and gross light
which strikes our bodily eyes, but from them also comes to us a light far more subtle, which
illuminates our minds and whose effect
s I shall try to show you. You know what man was on the
earth some thousands of years ago, and what he is today, isolated amid a nature where everything
was a mystery to him. Terrified at each unexpected manifestation of incomprehensible forces, he was
incapable of seeing in the conduct of the universe anything but caprice. He attributed all phenomena
to the action of a multitude of little genii, fantastic and exacting, and to act on the world
he sought to conciliate them by means analogous
to those employed to gain the good graces of
a minister or a deputy. Skipping ahead. What a change must our souls have undergone to pass from
the one state to the other. Does anyone believe that without the lessons of the stars under the
heavens perpetually overclouded that I have just supposed, they would have changed so quickly?
Would the metamorphosis have been possible, or at least would it not have been much slower? End
quote. And later he talks about the philosopher Auguste Comte, an
d he criticizes him for saying
that we don't need to know the composition of the sun because it doesn't have any application
for sociology. And I don't know the context there. I don't know if Comte was saying that if
we are sociologists trying to understand society, we don't need to know about the composition of
the sun. Or did he mean humanity never needs to know the composition of the sun because it's not
relevant. All we need to do is figure out how to best manage society because that's
where we live.
Poincaré would say that he's wrong either way, but they are slightly different statements. But
Poincaré references this example about clouds circling the earth and how that has affected
society. And if we sat and tried to think of them, we could find a dozen other examples like the
battle of the eclipse, but others in which things that seemed to be unrelated to society affected it
significantly. And that's what Poincaré is talking about here. He writes, quote, Auguste Comte h
as
said somewhere that it would be idle to seek to know the composition of the sun since this
knowledge would be of no use to sociology. How could he be so short-sighted? Have we not just
seen that it is by astronomy that to speak his language, humanity has passed from the theological
to the positive state? He found an explanation for that because it had happened. But how has he not
understood that what remained to do was not less considerable and would be not less profitable?
Physical ast
ronomy, which he seems to condemn, has already begun to bear fruit and it will give
us much more for it only dates from yesterday. End quote. And as is often the case, there is a
lot of other material that I wanted to show you, but I've already gone a bit long. So I'm going
to close off with this one. And in this passage, he mentions a Mr. Leroy, which I think is
a reference to Edward Leroy, or in French, it's probably Leroy, who was a mathematician
and philosopher from that period. And he
also addresses Tolstoy. And though he doesn't mention
the book by name, I think he must be talking about what is art because Tolstoy talks about
this topic in there. But Poincaré is defending science for its own sake. And he talks about
how scientists choose the facts to try to know, because we can't know all of them. How do we
decide which things to try to know? And he says, Tolstoy says that scientists do this at random.
And he says, no scientists do it in order to complete an unfinished
harmony or to find what
will open up broader vistas of other facts. He talks here about the value of civilization and
what makes it valuable. And in defending science for its own sake, he has said earlier that
investigating what doesn't have an immediate practical application may well someday have one,
even though it's not clear what it is now. It will help to answer some other questions. So it's worth
it to accumulate this information because someday it'll be useful if it's not immediately
useful.
But here he goes further than that and says, even beyond the long-term practicalof science for
its own sake, the spiritual value of trying to know just for the sake of knowing, of making
life be not just about drinking alcohol, but about something higher, about higher and better
thought." And then he closes with a few lines about thought. Poincaré writes, quote, "...not
against Mr. Leroy do I wish to defend science for its own sake. Maybe this is what he condemns,
but this is what
he cultivates, since he loves and seeks truth and could not live without it. But I
have some thoughts to express. We cannot know all facts, and it is necessary to choose those which
are worthy of being known. According to Tolstoy, scientists make this choice at random, instead of
making it which would be reasonable with a view to practical applications. On the contrary,
scientists think that certain facts are more interesting than others because they complete
an unfinished harmony, or beca
use they make one foresee a great number of other facts. If they
are wrong, if this hierarchy of facts that they implicitly postulate is only an idle illusion,
there could be no science for its own sake, and consequently, there could be no science. As
for me, I believe they're right. And for example, I have shown above what is the high value
of astronomical facts. Not because they are capable of practical applications, but because
they are the most instructive of all. It is only through sci
ence and art that civilization is
of value. Some have wondered at the formula, science for its own sake, and yet it is as good
as life for its own sake, if life is only misery, and even as happiness for its own sake, if we do
not believe that all pleasures are of the same quality, if we do not wish to admit that the
goal of civilization is to furnish alcohol to people who love to drink. Every act should
have a name. We must suffer, we must work, we must pay for our place at the game, but th
is
is for seeing's sake, or at the very least, that others may one day see. All that is not
thought is pure nothingness. Since we can think only thoughts, and all the words we use to speak
of things can express only thoughts, to say there is something other than thought is, therefore, an
affirmation which can have no meaning. And yet, strange contradiction for those who believe in
time, geologic history shows us that life is only a short episode between two eternities of death,
and that, e
ven in this episode, conscious thought has lasted, and will last, only a moment. Thought
is only a gleam in the midst of a long night, but it is this gleam which is everything." End
quote. And that's what I've got for you from The Value of Science by Henri Poincaré. If you
enjoyed this podcast, I hope you will send it to a friend who you think will benefit from it as well,
and go over to my website vollrathpublishing.com and get yourself some books there. Farewell
until next time. Take care
, and happy reading.
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