What are explanations worth in science?

Minao Kukita, Grad. School of Informatics, Nagoya University
June 19-20, 2021
This research is supported by JSPS KAKENHI Grant No. 19H00518 and JST CREST Grant No. JPMJCR20D2.

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What are explanations worth in science?
What are explanations worth in science?

Minao Kukita, Grad. School of Informatics, Nagoya University
June 19-20, 2021
This research is supported by JSPS KAKENHI Grant No. 19H00518 and JST CREST Grant No. JPMJCR20D2.

AI

is an ambiguous term that refers to a great variety of technologies. In this talk, I will

use the term to mean the kind of AI currently most widely used and most proﬁtable: machinelearning systems based on big data. Such AI is becoming a mundane tool for doing science.
Against this background, I would like to consider the value of explanation in science. In general,
explanation is considered to be of central importance in science. However, as is often pointed
out, machine learning systems based on big data are opaque, that is, the process of how theycame to their decisions is unknown to humans who use it, making it a black box. In the future,
will AI science without explanation replace conventional science? Should such a practice becalled science? I would like to explore these issues in view of the value of explanation in science.

Science according to Steven Weinberg

Steven Weinberg, To Explain the World“Newton had given to the future a model of what a physical theory can be: a set ofsimple mathematical principles that precisely govern a vast range of diﬀerent
phenomena.”2

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What are explanations worth in science?

Science according to Steven Weinberg

Steven Weinberg, To Explain the World“Newton had given to the future a model of what a physical theory can be: a set ofsimple mathematical principles that precisely govern a vast range of diﬀerent
phenomena.”

Science according to Steven Weinberg
In his book To Explain the World, physicist and Nobel laureate Steven Weinberg states that themodel of science is a simple set of mathematical principles that precisely govern a wide varietyof phenomena. He has a rather unique and extreme view of science, going so far as to say thatanything that does not ﬁt this model is not science, and that therefore science did not exist
before Newton, who was the ﬁrst to practice such a form of science.

Science according to Steven Weinberg

Steven Weinberg, “Sokal’s Hoax”, The New York Review of Books, Volume XLIII, No.
13, pp 11-15, August 8, 1996
“if we ever discover intelligent creatures on some distant planet and translate theirscientiﬁc works, we will ﬁnd that we and they have discovered the same laws.”

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What are explanations worth in science?

Science according to Steven Weinberg

Steven Weinberg, “Sokal’s Hoax”, The New York Review of Books, Volume XLIII, No.
13, pp 11-15, August 8, 1996
“if we ever discover intelligent creatures on some distant planet and translate theirscientiﬁc works, we will ﬁnd that we and they have discovered the same laws.”

Science according to Steven Weinberg
He says that if there were intelligent life forms on distant planets, we would ﬁnd the same lawsof nature as we have in the sciences by these alien intelligences. Thus, Weinberg takes a very
narrow view of science.

Science according to Robin Dunbar

Robin Dunbar, Trouble with Science“The important point to emerge from all this is that science is a methodologicalprescription rather than a particular body of theory. It is a method for ﬁnding out
about the world based on the generation of hypotheses in the testing of theprediction derived from those hypotheses. Social anthropologists among othersargue that this approach is unique to modern Western culture. But is this really true?
In the next two chapters I should try to show that the methods of empirical science
are in fact genuine universals characteristic of all higher forms of life.”

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What are explanations worth in science?

Science according to Robin Dunbar

Robin Dunbar, Trouble with Science

Science according to Robin Dunbar“The important point to emerge from all this is that science is a methodologicalprescription rather than a particular body of theory. It is a method for ﬁnding out
about the world based on the generation of hypotheses in the testing of theprediction derived from those hypotheses. Social anthropologists among othersargue that this approach is unique to modern Western culture. But is this really true?
In the next two chapters I should try to show that the methods of empirical science
are in fact genuine universals characteristic of all higher forms of life.”

On the other hand, Robin Dunbar, a primatologist, oﬀers a view of science that is in sharp
contrast to Weinberg. According to Dunbar, science is a method of revealing various things
about the world by repeatedly formulating hypotheses and testing the predictions derived fromthem with facts. Dunbar believes that this method is not conﬁned to the modern West, but iscommon to people of all times and places, and indeed to all higher forms of life. In this way,
Dunbar takes a very broad view of science.

Modern AI

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What are explanations worth in science?

Modern AI

Modern AI
If we view science as Weinberg does, then the knowledge generated by AI cannot be called
scientiﬁc knowledge. On the other hand, if we take Dunbar’s view, we could say that AI scienceis also a kind of scientiﬁc activity. Leaving aside the issue of deﬁnitions, it seems certain that AIs role in science will continue to grow in the future. This is because there is useful informationthat cannot be reached without using AI which processes the vast and diverse data obtained
from various observation instruments. It is unlikely that all scientists will reject such information,saying that it is not science.

Values in science• Simplicity: Theories, formulas, or models should be simple.
• Precision: They should precisely conform to phenomena.
• Generality: They should be applicable to a wide range of things.

But, why?

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What are explanations worth in science?

Values in science• Simplicity: Theories, formulas, or models should be simple.
• Precision: They should precisely conform to phenomena.
• Generality: They should be applicable to a wide range of things.

But, why?

Values in science
Let us look back at Weinberg’s view. It emphasizes the following values: simplicity, precision,and generality. The emphasis on precision seems obvious. It is understandable that it is more
useful to be able to predict where a bomb will hit with an error of one meter than with an errorof one kilometer. However, the simplicity and generality is not so obvious. Why should science
conform to these values?

Fluidity of information

Cognitive ﬂuidity (Cf. Steven Mithen, The Prehistory of the Mind: The Cognitive
Origins of Art, Religion and Science)
Intra-group ﬂuidity (Cf. Joseph Henrich, The Secret of Our Success: How Culture is
Driving Human Evolution, Domesticating our Species, and Making us Smarter ; Alex
Pentland, Social Physics: How Good Ideas Spread)Inter-group ﬂuidity (Cf. Jared Diamond, Guns, Germs, and Steel: The Fates of
Human Societies)7

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What are explanations worth in science?

Fluidity of information

Cognitive ﬂuidity (Cf. Steven Mithen, The Prehistory of the Mind: The Cognitive
Origins of Art, Religion and Science)
Intra-group ﬂuidity (Cf. Joseph Henrich, The Secret of Our Success: How Culture is
Driving Human Evolution, Domesticating our Species, and Making us Smarter ; Alex
Pentland, Social Physics: How Good Ideas Spread)

Fluidity of information

Inter-group ﬂuidity (Cf. Jared Diamond, Guns, Germs, and Steel: The Fates of
Human Societies)

To think about this, I would like to focus on the importance of ”information ﬂuidity” in science(not Weinberg’s narrow science, but Dunbar’s broad science). Here I will consider the ﬂuidityof information in three diﬀerent situations. These are cognitive ﬂuidity, intra-group ﬂuidity, andinter-group ﬂuidity.

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What are explanations worth in science?

Cognitive ﬂuidity

Cognitive ﬂuidity
Cognitive ﬂuidity is an idea proposed by Steven Mithen, a cognitive archaeologist. Mithenconsidered it an important intellectual trait that separates Homo sapiens from other hominids.
Hominids close to Homo sapiens (say, Homo neanderthalensis) have several domain-speciﬁc
intelligences, such as social intelligence, natural history intelligence, and technical intelligence.
However, what is unique about Homo sapiens is the ability to export and apply knowledge andideas from one domain to another. Only Homo sapiens is able to apply the knowledge and ideas
gained in one domain to things in another domain by using abstraction, metaphors and so on.
Mithen insists that this is what makes Homo sapiens so diﬀerent from other hominids.

Intra-group ﬂuidity

Henrich, The Secret of Our
Success
Human toddlers (2.5 years old)
are not so diﬀerent from
chimpanzees and orangutans in
cognitive capacities except social
learning (learning by observing
others’ behaviours).

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What are explanations worth in science?

Intra-group ﬂuidity

Intra-group ﬂuidity

Henrich, The Secret of Our
Success
Human toddlers (2.5 years old)
are not so diﬀerent from
chimpanzees and orangutans in
cognitive capacities except social
learning (learning by observing
others’ behaviours).

Another ﬂuidity is the sharing and inheritance of information within a group. This is emphasized,
for example, by the anthropologist Joseph Henrich. He draws attention to research that showsthat when comparing the cognitive abilities of humans and other primates, the most prominent
advantage of humans lies in social learning. Humans are very good at watching and imitating
the behavior of others, and thereby acquiring knowledge and skills. The word ”to ape” is often
used to mean ”to imitate,” but in fact, humans are the ones who do the aping. This is how
useful knowledge and skills are accumulated in a group over generations.

Intra-group ﬂuidity

Henrich, The Secret of Our SuccessFigure 7.1. Eﬀects of each major step in
the Tukanoan manioc processing
technique. Percentages are relative tothe raw tuber.

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What are explanations worth in science?

Intra-group ﬂuidity

Henrich, The Secret of Our SuccessFigure 7.1. Eﬀects of each major step in
the Tukanoan manioc processing
technique. Percentages are relative tothe raw tuber.

Intra-group ﬂuidity
One of Henrich’s favorite examples is the processing of cassava, an easy-to-grow and nutrientrich food source that, however, is poisonous and cannot be eaten unprocessed. The poisonous
ingredient is removed through a rather complicated and extensive process. Such knowledge andskills are acquired and passed on within a group through social learning. No one single person,
however smart, cannot come up with how to eat cassava. This is why Henrich refers to thecommunity or society as “our collective brains.

Intra-group ﬂuidity

Alex Pentland, Social Physics: How Good
Ideas Spread
Figure 17. The model of idea ﬂow alongsocial ties accurately predicts GDP per
square mile.

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What are explanations worth in science?

Intra-group ﬂuidity

Alex Pentland, Social Physics: How Good
Ideas Spread
Figure 17. The model of idea ﬂow alongsocial ties accurately predicts GDP per
square mile.

Intra-group ﬂuidity
Alex Pentland is another researcher who focuses on the importance of information ﬂow within agroup. He has empirically (using big data analysis about people s social interactions) shown thatsocial network interactions and idea ﬂow are major drivers of creative outputs and productivity
in groups of various sizes. For example, Pentland et al. shows that the ﬂow of ideas along asocial network in a city accounts for statistical economic indicators such as GDP per square mile.

Inter-group ﬂuidity

Factors that determined the advantage of Eurasian people over others. Reproduced from
Figure 4.1 of Jared Diamond, Guns, Germs and Steel12

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What are explanations worth in science?

Inter-group ﬂuidity

Inter-group ﬂuidity
Factors that determined the advantage of Eurasian people over others. Reproduced from
Figure 4.1 of Jared Diamond, Guns, Germs and SteelFor the ﬂow of information between groups, let us see the work of Jared Diamond, who insiststhat the ultimate cause of the advantage of Eurasia over other continents was the continent’s
width along the latitude. The east-west spread means that there is a large area of land in thesame climatic zone, which makes it easier for cultivars discovered in one region to spread toother regions. Thus, from early on in the Eurasian continent, exchange between distant regions
has been taking place. This encouraged the exchange of ideas and products, leading to thedevelopment of science and technology earlier than other continents.

Why simplicity and generality matter in science
The key to new discoveries and inventions is how ﬂuently (and without noises) information andideas are conveyed from one place to another. For this purpose, simple and generally
applicable mathematical theory, formulas and models are ideally suited.

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What are explanations worth in science?

Why simplicity and generality matter in science
The key to new discoveries and inventions is how ﬂuently (and without noises) information andideas are conveyed from one place to another. For this purpose, simple and generally
applicable mathematical theory, formulas and models are ideally suited.

Why simplicity and generality matter in science
The lesson to be learned from these examples is that the key to new discoveries and inventions
is how to ensure that information and ideas ﬂow seamlessly from one place to another. With
this in mind, it is easy to understand why simplicity and generality are so important in science.
A person develops some theory, model, or formula to explain an observation or experiment. It
only makes sense when it is applied to other new cases. And for this purpose, simple and generalmathematical theories, formulas, and models are ideally suited. This point is related to thebreadth and speed of the explanation algorithms in Professor Dowek’s talk.

Feferman on the value of axioms

Solomon Feferman, “Does mathematics need new axioms?”“When the working mathematician speaks of axioms, he or she usually means those forsome particular part of mathematics such as groups, rings, vector spaces, topologicalspaces, Hilbert spaces, etc. These axioms have nothing to do with self-evident
propositions, nor are they arbitrary starting points. They are simply deﬁnitions of kindsof structures that have been recognized to recur in various mathematical situations.
But they act as axioms in the sense that they provide a framework in which certain
kinds of operations and lines of reasoning are appropriate whereas others are not.
(cont.)

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What are explanations worth in science?

Feferman on the value of axioms

Solomon Feferman, “Does mathematics need new axioms?”

Feferman on the value of axioms“When the working mathematician speaks of axioms, he or she usually means those forsome particular part of mathematics such as groups, rings, vector spaces, topologicalspaces, Hilbert spaces, etc. These axioms have nothing to do with self-evident
propositions, nor are they arbitrary starting points. They are simply deﬁnitions of kindsof structures that have been recognized to recur in various mathematical situations.
But they act as axioms in the sense that they provide a framework in which certain
kinds of operations and lines of reasoning are appropriate whereas others are not.
(cont.)

I would like to refer to the words of the logician Solomon Feferman. He says that axioms inalgebra, topological spaces, and so on are not expressions of self-evident truths (unlike those inarithmetic or set theory), but rather deﬁnitions of more general structures that become salientby extracting features that are common to certain mathematical structures.

Feferman on the value of axioms

And once we run into a structure meeting one of these axiom systems—for example, agroup associated with some equation or with a topological space—we can call on avast body of previously established consequences for our further work. Without trying
to argue this further, I take it that the value of these kinds of structural axioms for theorganization of mathematical work is now indisputable. Moreover, we seem to keep
coming up with new axioms of this sort, and I think the case can be made that theycome up due to a continuing need to package and communicate our knowledge
in digestible ways.”15

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Feferman on the value of axioms

What are explanations worth in science?

Feferman on the value of axioms
He calls such axioms “structural axioms

And once we run into a structure meeting one of these axiom systems—for example, agroup associated with some equation or with a topological space—we can call on avast body of previously established consequences for our further work. Without trying
to argue this further, I take it that the value of these kinds of structural axioms for theorganization of mathematical work is now indisputable. Moreover, we seem to keep
coming up with new axioms of this sort, and I think the case can be made that theycome up due to a continuing need to package and communicate our knowledge
in digestible ways.”and says that their value lies in their ability to organize

mathematical work. He says that mathematicians keep coming up with such axioms in order tomeet ”a continuing need to package and communicate our knowledge in digestible ways.

Information Communication in Mathematics[x ∈ A]..
.
B(x) true(∀x ∈ A)B(x) true

Group axioms oa∈Asatisfyentail(∀x ∈ A)B(x) true
B(a) true

Integers
entail

Inverses are unique

apply


/ -x are unique16

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What are explanations worth in science?

Information Communication in Mathematics[x ∈ A]..
.
B(x) true(∀x ∈ A)B(x) true

Group axioms oInformation Communication in Mathematicsa∈A

satisfyentail(∀x ∈ A)B(x) true
B(a) true

Integers
entail

Inverses are unique

apply


/ -x are unique

From a logic point of view, the proof containing the application of an introduction rule immediately followed by the correspondent elimination rule is called ”non-canonical”, but suchnon-canonicality is an essential part of mathematics as a collective intellectual activity. Such
proofs are also valuable in the sense that they create new abstract concepts and extend the worldof mathematics (and the world of science for that matter).

Earthly intelligence vs. alien intelligence

Metaphors, symbols, language, and mathematics are
instruments which our earthly intelligence contrived inorder to grasp and communicate how thisoverwhelmingly complex world works.
In contrast, Modern AI is becoming more and morecapable of dealing directly with the complexity of theworld, so that it has gone beyond humanunderstanding.

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What are explanations worth in science?

Earthly intelligence vs. alien intelligence

Metaphors, symbols, language, and mathematics are
instruments which our earthly intelligence contrived inorder to grasp and communicate how thisoverwhelmingly complex world works.
In contrast, Modern AI is becoming more and morecapable of dealing directly with the complexity of theworld, so that it has gone beyond humanunderstanding.

Earthly intelligence vs. alien intelligence
Metaphors, symbols, language, and mathematics are all tools devised by humans, who possess
limited intelligence, in order to grasp and communicate how the extremely complex world works,
and thereby survive in it. On the other hand, modern artiﬁcial intelligence is able to deal withthe complexities of the world in ways that humans cannot handle or understand. Thus, artiﬁcial
intelligence today can provide us with decisions that we don’t understand, but from which we
can proﬁt and avoid risks in an eﬃcient way.

It’s not what explanation is all about.

Steven Weinberg, To Explain the World“So the world acts on us like a teaching machine, reinforcing our good ideas with
moments of satisfaction. After centuries we learn what kinds of understanding are
possible, and how to ﬁnd them. We lean not to worry about purpose, because such
worries never lead to the sort of delight we seek. We learn to abandon the search forcertainty, because the explanations that make us happy never are certain. We learn
to do experiments, not worrying about the artiﬁciality of our arrangements. We develop
an aesthetic sense that gives us clues to what theories will work, and that adds toour pleasure when they do work. Our understandings accumulate. It is all unplanned
and unpredictable, but it leads to reliable knowledge, and gives us joy along the way.”18

2021-06-08

What are explanations worth in science?

It’s not what explanation is all about.

Steven Weinberg, To Explain the World

It’s not what explanation is all about.

“So the world acts on us like a teaching machine, reinforcing our good ideas with
moments of satisfaction. After centuries we learn what kinds of understanding are
possible, and how to ﬁnd them. We lean not to worry about purpose, because such
worries never lead to the sort of delight we seek. We learn to abandon the search forcertainty, because the explanations that make us happy never are certain. We learn
to do experiments, not worrying about the artiﬁciality of our arrangements. We develop
an aesthetic sense that gives us clues to what theories will work, and that adds toour pleasure when they do work. Our understandings accumulate. It is all unplanned
and unpredictable, but it leads to reliable knowledge, and gives us joy along the way.”

But addressing such beneﬁts and risks will not be the whole story of science. Let us refer to
Weinberg’s words again: at the end of To Explain the World, Weinberg mentions the joy thatscience brings. Over the centuries, we have learned what kind of understanding we can acquireand how to acquire it. At the same time, we have gradually developed an aesthetic sense thatﬁnds satisfaction and pleasure in understanding or in explanation itself.

Joy of understanding“The noblest pleasure is the joy of understanding.”
Leonardo da Vinci
https://www.brainyquote.com/quotes/leonardo_
da_vinci_154285

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What are explanations worth in science?

Joy of understanding“The noblest pleasure is the joy of understanding.”
Leonardo da Vinci
https://www.brainyquote.com/quotes/leonardo_
da_vinci_154285

Joy of understanding
Weinberg is referring only to modern science, but the sensibility to the pleasure of understanding
must have existed much earlier. In fact, Leonardo da Vinci is said to have said, “The noblest
pleasure is the joy of understanding.” Archimedes of ancient Greece is said to have run naked
through the city in his joy, when he discovered how to measure the volume of a complexly shaped
object while taking a bath. Will the rise of AI science mean fewer opportunities for this kind ofjoy?

Computer-generated proof

George Szpiro, Kepler’s Conjecture: How Some of theGreatest Minds in History Helped Solve One of the Oldest
Math Problems in the World“After examining the proof of the Kepler conjecture, one
cannot help asking: ‘What have I learned from this proof?,‘Did I get any deeper insight about mathematics?”, or ‘Am I
any smarter because I learned the proof?’ The answer is,unfortunately, ‘No’.”(My translation back from Japanese translation)20

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Computer-generated proof

What are explanations worth in science?

George Szpiro, Kepler’s Conjecture: How Some of theGreatest Minds in History Helped Solve One of the Oldest
Math Problems in the World“After examining the proof of the Kepler conjecture, one
cannot help asking: ‘What have I learned from this proof?,‘Did I get any deeper insight about mathematics?”, or ‘Am I
any smarter because I learned the proof?’ The answer is,unfortunately, ‘No’.”

Computer-generated proof(My translation back from Japanese translation)

A computer-generated proof of a mathematical theorem will provide hints for thinking about
AI science. On the computer proof of the Kepler conjecture, George Szpiro writes: “After
examining the proof of the Kepler conjecture, one cannot help asking: ‘What have I learned
from this proof? , ‘Did I get any deeper insight about mathematics? , or ‘Am I any smarterbecause I learned the proof?

The answer is,unfortunately,No .

Computer-generated proof

Thomas Tymoczko, “The four-color problem and its philosophical signicance”, The
Journal of Philosophy, Vol. 76, No. 2. (Feb., 1979), pp. 57-83.
“I will suggest, however, that, if we accept the 4CT as a theorem, we are committed tochanging the sense of ’theorem’, or, more to the point, to changing the sense of theunderlying concept of ‘proof’.”“Whether or not we choose to regard the 4CT as proved, we must admit that thecurrent proof is no traditional proof, no a priori deduction of a statement frompremises.”

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What are explanations worth in science?

Computer-generated proof

Thomas Tymoczko, “The four-color problem and its philosophical signicance”, The
Journal of Philosophy, Vol. 76, No. 2. (Feb., 1979), pp. 57-83.
“I will suggest, however, that, if we accept the 4CT as a theorem, we are committed tochanging the sense of ’theorem’, or, more to the point, to changing the sense of theunderlying concept of ‘proof’.”Computer-generated proof“Whether or not we choose to regard the 4CT as proved, we must admit that thecurrent proof is no traditional proof, no a priori deduction of a statement frompremises.”

Regarding the proof of the Four Color Theorem, another famous example of computer theorem
proving, philosopher Thomas Tymoczko argues that it is not a proof in the traditional sense, andthat if we accept it as a proof, we must change the way we think about theorems and proofs inmathematics.

Computer-generated proof

Historically, the concept of proof had in fact been extended. For example, at the endof the 19th century, non-constructive proof appealing to inﬁnite sets became popularwhen the set theory was invented. Despite some objections, mathematicians accepted
it because of its productivity (i.e., it enabled more theorems and publications).
Kazushige Terui writes in Can Computers Become Mathematicians? (in Japanese)that the day may come when the veriﬁcation by computers will be established as thestandard for mathematical rigour.

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What are explanations worth in science?

Computer-generated proof

Historically, the concept of proof had in fact been extended. For example, at the endof the 19th century, non-constructive proof appealing to inﬁnite sets became popularwhen the set theory was invented. Despite some objections, mathematicians accepted
it because of its productivity (i.e., it enabled more theorems and publications).

Computer-generated proof

Kazushige Terui writes in Can Computers Become Mathematicians? (in Japanese)that the day may come when the veriﬁcation by computers will be established as thestandard for mathematical rigour.

Historically, the expansion of the notion of ”proof” in mathematics has happened before: atthe end of the 19th century, when set theory was invented and non-constructive proofs using
inﬁnite sets were used, there was some opposition, but because of its productivity (in the sensethat it allow mathematicians to prove more theorems and therefore to publish more articles),non-constructive methods were accepted by mathematicians. Mathematician Kazushige Teruisays that computer proofs may eventually be accepted as the standard for mathematical rigor.

Meaning in computation

Masao Morita, Life That Computes
Computation is not just a matter of moving tokens andsymbols according to a set of rules and outputting theresults. Morita argues that it is a process in whichhuman beings creates new meaning in the world andexpands his own mind.

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What are explanations worth in science?

Meaning in computation

Masao Morita, Life That Computes
Computation is not just a matter of moving tokens andsymbols according to a set of rules and outputting theresults. Morita argues that it is a process in whichhuman beings creates new meaning in the world andexpands his own mind.

Meaning in computation
Masao Morita, in his recent book, Life That Computes, describes the intellectual history of
mankind in terms of “computation.

He argues that computation or manipulation of formal

systems is not just a process of moving tokens and symbols according to a set of rules to get
desired outputs. It is a process in which a human, who cannot help seek for meaning, creates
new meanings and enriches the world and herself with these meanings. Relying too much on
computers may deprive us of the opportunities for enrichment.

Alienation of Science

Since the industrial revolution, a large partof work has been mechanised at the cost of
joy of working.
The same will apply to the mechanisationof science.
Its ethical implications include the loss of
our awe toward the nature, andresponsibility for it.

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What are explanations worth in science?

Alienation of Science

Since the industrial revolution, a large partof work has been mechanised at the cost of
joy of working.
The same will apply to the mechanisationof science.
Its ethical implications include the loss of
our awe toward the nature, andresponsibility for it.

Alienation of Science
The use of AI will surely spread and gain weight in science because of its productivity. Then,the value and meaning that science has for humans may change. This is similar to the way
the nature of labor has changed dramatically since the Industrial Revolution, and the value andmeaning of labor has changed. Perhaps it does not only mean the loss of joy from science, butalso the loss of awe of the natural world and the responsibility of humans for it.