The Interplay of Science and Metaphor

Structured by AI 

Science, much like poetry, thrives on the use of metaphors. These figurative expressions can sometimes obscure meaning, leading to confusion or misinterpretation. At the heart of scientific inquiry lies the deployment of multiple metaphors, as exemplified by Pythagoras’s assertion that “All things are number.” This statement is often accompanied by another metaphor that helps frame the significance of those numbers, typically conveyed through models or tools.E. O. Wilson suggests that scientists should “think like poets and work like accountants.” This dual approach emphasizes that while precise calculations are essential, the true artistry of science lies in crafting effective metaphors. The ability to create compelling metaphors can elevate thinkers to genius status. For instance, Joule likened energy conservation to balancing a ledger, while Darwin drew parallels between natural selection and economic competition.However, the misuse of metaphors can lead entire disciplines astray. For example, equating people to “biological billiard balls” or economies to gases can result in significant misunderstandings. The economic poet Gary Becker’s metaphors—such as viewing families as “little firms” and children as “durable goods”—illustrate how poor metaphorical choices can distort reality.

The Dangers of Data-Driven Thinking

The mantra of letting “data do the talking,” popularized by proponents of Freakonomics, can be misleading. Alfred Marshall warned that relying solely on numerical data can be “treacherous.” Many concepts in fields like biology, economics, and social sciences—such as fitness, utility, and happiness—lack the measurable properties of physical quantities like mass or length. This limitation diminishes the effectiveness of mathematical approaches in these areas.There is often confusion regarding the relationship between quantitative and qualitative data. Nate Silver cautions that those who are not “quantitatively inclined” may inadvertently produce misleading conclusions. Effective quantification requires a solid foundation of qualitative understanding; otherwise, it risks generating nonsensical results. For instance, stating that the average human possesses one ovary and one testicle exemplifies the pitfalls of mixing different types of data.Statistical methods, while powerful, can be particularly slippery. They rely on the assumption that underlying phenomena exhibit stable patterns, which is often true for physical traits but not for behavioral data. This leads to logical fallacies, such as the fallacy of composition—where properties of parts are incorrectly assumed to apply to the whole—and its counterpart, the fallacy of division.

Missteps in Statistical Interpretation

Consider the contentious issue of police shootings. Sendhil Mullainathan’s assertion that racial bias in policing has “little effect” exemplifies the fallacy of division, as he assumes that national data accurately reflect local realities. Conversely, Rajiv Sethi highlights the fallacy of composition when questioning whether statistics from one city can be generalized to another with a different demographic makeup.Even leading researchers can mishandle statistical analysis, often engaging in practices like p-value cherry-picking or misapplying multiple regression techniques. Moreover, standard statistical methods may not always provide clarity; for example, randomization fails to address average testicle counts, and simply increasing data volume does not resolve inherent variability.

The Limitations of Quantification

Diane Coyle critiques GDP as a flawed measure, arguing that it fails to differentiate between harmful and beneficial economic activities and overlooks non-market contributions. The allure of data and calculation is strong, yet it is crucial to recognize that numbers do not hold exclusive rights to precision or truth. Words, metaphors, and qualitative insights can offer clarity and depth that numerical data sometimes cannot achieve.

Reference:

https://bigthink.com/hard-science/science-and-poetry-both-depend-on-metaphors/#link_time=1471092840

ABC proof

Mathematicians finally starting to understand epic ABC proof

By Jacob Aron

It has taken nearly four years, but mathematicians are finally starting to comprehend
a mammoth proof that could revolutionise our understanding of the deep nature of numbers.

The 500-page proof was published online by Shinichi Mochizuki of Kyoto University,
Japan in 2012 and offers a solution to a longstanding problem known as the ABC conjecture,
which explores the fundamental relationships between numbers, addition and multiplication
 beginning with the simple equation a + b = c.

Mathematicians were excited by the proof but struggled to get to grips with Mochizuki’s
“Inter-universal Teichmüller Theory” (IUT), an entirely new realm of mathematics
 he had developed over decades in order to solve the problem. A meeting held last year at
the University of Oxford, UK with the aim of studying IUT ended in failure, in part because
Mochizuki doesn’t want to streamline his work to make it easier to comprehend, and because
of a culture clash between Japanese and western ways of studying mathematics.

Now a second meeting, held last month at his home ground in Kyoto, has proved more successful.
“It definitely went better than expected,” says Ivan Fesenko of the University of Nottingham, UK,
who helped organise the meeting.

The breakthrough seems to have come from Mochizuki explaining his theory in person.
He refuses to travel abroad, only speaking via Skype at the Oxford meeting, which had made
it harder for mathematicians outside Japan to get to grips with his work. “It was the key part
of the meeting,” says Fesenko. “He was climbing the summit of his theory, and pulling
other participants with him, holding their hands.”

Glimmer of understanding

At least 10 people now understand the theory in detail, says Fesenko,
and the IUT papers have almost passed peer review so should be officially published 
in a journal in the next year or so. That will likely change the attitude of people 
who have previously been hostile towards Mochizuki’s work, says Fesenko. 
“Mathematicians are very conservative people, and they follow the traditions. 
When papers are published, that’s it.”

“There are definitely people who understand various crucial parts of the IUT,”
 says Jeffrey Lagarias of the University of Michigan, who attended the Kyoto meeting,
but was not able to absorb the entire theory in one go. “More people outside Japan have
 incentive to work to understand IUT as it is presented, all 500 pages of it, making use
of new materials at the various conferences.”

But many are still not willing devote the time Mochizuki demands to understand his work.
“The experts are still on the fence,” says Lagarias.
 “They are waiting for someone else to read the proof and asking why it cannot be made easier
to understand.”

It is likely that the IUT papers will be published in a Japanese journal, says Fesenko,
as Mochizuki’s previous work has been. That may affect its reception by the wider community.
“Certainly which journal they are published in will have something
to do with how the math community reacts,” says Lagarias.

The glimmer of understanding that has started to emerge is well worth the effort, says Fesenko.
“I expect that at least 100 of the most important open problems in number theory will
 be solved using Mochizuki’s theory and further development.”

But it will likely be many decades before the full impact of Mochizuki’s work on number theory
 can be felt. “The magnitude of the number of new structures and ideas in IUT will take years for
 the math community to absorb,” says Lagarias.

ABC proof

Mathematicians finally starting to understand epic ABC proof

By Jacob Aron

It has taken nearly four years, but mathematicians are finally starting to comprehend
a mammoth proof that could revolutionise our understanding of the deep nature of numbers.

The 500-page proof was published online by Shinichi Mochizuki of Kyoto University,
Japan in 2012 and offers a solution to a longstanding problem known as the ABC conjecture,
which explores the fundamental relationships between numbers, addition and multiplication
 beginning with the simple equation a + b = c.

Mathematicians were excited by the proof but struggled to get to grips with Mochizuki’s
“Inter-universal Teichmüller Theory” (IUT), an entirely new realm of mathematics
 he had developed over decades in order to solve the problem. A meeting held last year at
the University of Oxford, UK with the aim of studying IUT ended in failure, in part because
Mochizuki doesn’t want to streamline his work to make it easier to comprehend, and because
of a culture clash between Japanese and western ways of studying mathematics.

Now a second meeting, held last month at his home ground in Kyoto, has proved more successful.
“It definitely went better than expected,” says Ivan Fesenko of the University of Nottingham, UK,
who helped organise the meeting.

The breakthrough seems to have come from Mochizuki explaining his theory in person.
He refuses to travel abroad, only speaking via Skype at the Oxford meeting, which had made
it harder for mathematicians outside Japan to get to grips with his work. “It was the key part
of the meeting,” says Fesenko. “He was climbing the summit of his theory, and pulling
other participants with him, holding their hands.”

Glimmer of understanding

At least 10 people now understand the theory in detail, says Fesenko,
and the IUT papers have almost passed peer review so should be officially published 
in a journal in the next year or so. That will likely change the attitude of people 
who have previously been hostile towards Mochizuki’s work, says Fesenko. 
“Mathematicians are very conservative people, and they follow the traditions. 
When papers are published, that’s it.”

“There are definitely people who understand various crucial parts of the IUT,”
 says Jeffrey Lagarias of the University of Michigan, who attended the Kyoto meeting,
but was not able to absorb the entire theory in one go. “More people outside Japan have
 incentive to work to understand IUT as it is presented, all 500 pages of it, making use
of new materials at the various conferences.”

But many are still not willing devote the time Mochizuki demands to understand his work.
“The experts are still on the fence,” says Lagarias.
 “They are waiting for someone else to read the proof and asking why it cannot be made easier
to understand.”

It is likely that the IUT papers will be published in a Japanese journal, says Fesenko,
as Mochizuki’s previous work has been. That may affect its reception by the wider community.
“Certainly which journal they are published in will have something
to do with how the math community reacts,” says Lagarias.

The glimmer of understanding that has started to emerge is well worth the effort, says Fesenko.
“I expect that at least 100 of the most important open problems in number theory will
 be solved using Mochizuki’s theory and further development.”

But it will likely be many decades before the full impact of Mochizuki’s work on number theory
 can be felt. “The magnitude of the number of new structures and ideas in IUT will take years for
 the math community to absorb,” says Lagarias.