How to Convince Others

Source: Business Insider, Dec 2016

if you want to convince someone that your explanation for something is the best way to explain it, you might want to tack on some useless (though accurate) information from a tangentially related scientific field.

It turns out that when you tack on additional information from a respected field of study, people think that makes an explanation more credible.

We think longer explanations are better than short ones and we prefer explanations that point to a goal or a reason for things happening, even if these things don’t actually help us understand a phenomenon.

As the authors behind this most recent paper note, previous research has also shown that we prefer explanations of psychology when they contain “logically irrelevant neuroscience information,” something known as the “seductive lure effect.”

some interesting exceptions and additional takeaways here.

  • Good explanations matter, and were rated better than bad explanations (even if the bad explanations had reductive information).
  • Adding useless reductive information made the biggest difference when researchers added neuroscience to an explanation of psychological science.
  • Participants trusted psychology the least and — in the one exception to the general rule — didn’t think adding psychological explanations to social science made those explanations more credible (though these particular findings weren’t statistically significant).
  • Study participants actually considered neuroscience more rigorous and prestigious than the sciences considered more fundamental by researchers (biology, chemistry, and physics). This could explain the big effect that neuroscience explanation has when added to explanations of psychological science.
  • Mechanical Turk respondents thought the explanations with reductive information were better than undergraduates thought they were. That information made a big significant difference for them, but it was less of a big deal for undergraduates. Different groups of people are going to evaluate information in different ways, and neither of these groups of people can accurately represent the way the entire population evaluates information.
  • People who were better at logical reasoning were better at evaluating explanation accurately (they gave less credence to reductive information). The researchers think this could mean that philosophers who have studied logic are less susceptible to this cognitive bias.
  • People who knew more about science were also better at telling good explanations from bad explanations.

Larry Summers on Uncles Ken Arrow & Paul Samuelson

Source: Larry Summers website, Feb 2017

My mother’s brother, the Nobel economist Kenneth Arrow, died this week at the age of 95. He was a dear man and a hero to me and many others. No one else I have ever known so embodied the scholarly life well lived.

I remember like yesterday the moment when Kenneth won the Nobel Prize in 1972. Paul Samuelson—another Nobel economist and, as it happens, also my uncle—hosted a party in his honor, to which I, then a sophomore at MIT, was invited. It was a festive if slightly nerdy occasion.

As the night wore on, Paul and Kenneth were standing in a corner discussing various theorems in mathematical economics. People started leaving. Paul’s wife was looking impatient. Kenneth’s wife, my aunt Selma, put her coat on, buttoned it and started pacing at the door. Kenneth raised something known as the maximum principle and the writings of the Russian mathematician Pontryagin. Paul began a story about the great British mathematical economist and philosopher Frank Ramsey. My ride depended on this conversation ending, so I watched alertly without understanding a word.

But I did understand this: There were two people in the room who had won Nobel Prizes. They were the two people who, after everyone else was exhausted and heading home, talked on and on into the evening about the subject they loved. I learned that night about my uncles—about their passion for ideas and about the importance and excitement of what scholars do.

Paul Samuelson (1970 Nobel Laureate – economics)

Kenneth Arrow (Nobel Laureate 1972 – Economics)


Eastern and Western Thinking Styles

Source: BBC, Jan 2017
<great read>

From the broad differences between East and West, to subtle variation between US states, it is becoming increasingly clear that history, geography and culture can change how we all think in subtle and surprising ways – right down to our visual perception. Our thinking may have even been shaped by the kinds of crops our ancestors used to farm, and a single river may mark the boundaries between two different cognitive styles. 

Until recently, scientists had largely ignored the global diversity of thinking. In 2010, an influential article in the journal Behavioral and Brain Sciences reported that the vast majority of psychological subjects had been “western, educated, industrialised, rich and democratic”, or ‘Weird’ for short. Nearly 70% were American, and most were undergraduate students hoping to gain pocket money or course credits by giving up their time to take part in these experiments

the concepts of “individualism” and “collectivism”; whether you consider yourself to be independent and self-contained, or entwined and interconnected with the other people around you, valuing the group over the individual. Generally speaking – there are many exceptions – people in the West tend to be more individualist, and people from Asian countries like India, Japan or China tend to be more collectivist. 

When questioned about their attitudes and behaviours, people in more individualistic, Western societies tend to value personal success over group achievement, which in turn is also associated with the need for greater self-esteem and the pursuit of personal happiness. But this thirst for self-validation also manifests in overconfidence, with many experiments showing that Weird participants are likely to overestimate their abilities. When asked about their competence, for instance, 94% of American professors claimed they were “better than average”.

This tendency for self-inflation appears to be almost completely absent in a range of studies across East Asia; in fact, in some cases the participants were more likely to underestimate their abilities than to inflate their sense of self-worth. People living in individualistic societies may also put more emphasis on personal choice and freedom.

Crucially, our “social orientation” appears to spill over into more fundamental aspects of reasoning. People in more collectivist societies tend to be more ‘holistic’ in the way they think about problems, focusing more on the relationships and the context of the situation at hand, while people in individualistic societies tend to focus on separate elements, and to consider situations as fixed and unchanging.

this thinking style also extends to the way we categorise inanimate objects. Suppose you are asked to name the two related items in a list of words such as “train, bus, track”. What would you say? This is known as the “triad test”, and people in the West might pick “bus” and “train” because they are both types of vehicles. A holistic thinker, in contrast, would say “train” and “track”, since they are focusing on the functional relationship between the two – one item is essential for the other’s job.

Western philosophers emphasised freedom and independence, whereas Eastern traditions like Taoism tended to focus on concepts of unity.

Oppenheimer: on Math

Source: InfoProc, Jan 2017

Oppenheimer: Mathematics is “an immense enlargement of language, an ability to talk about things which in words would be simply inaccessible.”

Encouraging Spatial Reasoning for Children

Source: Mindshift, Jan 2017

  1. Spatial reasoning and mathematical thinking are intimately linked.
  2. Spatial reasoning can be improved. Education matters!
  3. Spatial thinking is an important predictor of achievement in STEM careers.
  4. Spatial reasoning is currently an underserved area of mathematics instruction.
  5. Spatial reasoning provides multiple entry points and equitable access to mathematics.


Quotes – Ramanujan

Source: WikiQuote, date indeterminate

Paul Erdős has passed on to us Hardy‘s personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.

  • Bruce C. Berndt in Ramanujan’s Notebooks : Part I (1994), “Introduction”, p. 14

The formulae (1.10) – (1.13) are on a different level and obviously both difficult and deep… (1.10) – (1.12) defeated me completely; I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him.

  • Michio Kaku, Hyperspace : A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), p. 172

The great advances in mathematics have not been made by logic but by creative imagination. The title of mathematician can scarcely be denied to Ramanajan who hardly gave any proofs of the many theorems which he enumerated.

A Perfect Voice – Jeremy Irons

Source: BBC, May 2008

Researchers say they have worked out a mathematical formula to find the perfect human voice.

The study, commissioned by Post Office Telecoms, asked people to rate 50 voices then analysed the results.

It found the best female voice to be a mixture of Mariella Frostrup, Dame Judi Dench and Honor Blackman. Alan Rickman and Jeremy Irons did best for the men.

the ideal voice should utter no more than 164 words per minute and pause for 0.48 seconds between sentences. Sentences themselves should fall rather than rise in intonation.

Actor Jeremy Irons came very close to the ideal voice model, speaking at 200 words per minute and pausing for 1.2 seconds between sentences.