Month: November 2010

Will a certain tritium atom decay by a certain time? According to our current science, this question concerning physical phenomena should be answered by sampling from a probability distribution, a process not unlike spinning a roulette wheel or rolling dice. However, a paper in Foundations of Physics suggests that the same could be true of a question concerning mathematical phenomena, even one as prosaic as “what is 2+2?

SFI Professor David Wolpert, a physicist, and former SFI Omidyar Fellow David Kinney, a philosopher and cognitive scientist, propose a unified, probabilistic framework to describe math, the physical universe, and even describe how humans reason about both.

In their framework, mathematics and science are both represented as a process of asking and answering questions. How a given mathematician or scientist answers a question will depend on the probabilities that they assign to different answers. In an extension of the basic formalism, these same probabilities also determine how correctly that mathematician or scientist answers those questions.

To illustrate, say you answer a mathematics question now, and in the faraway future, some mathematicians answer the same question. The correctness of your answer depends on how your probabilities match theirs. (In physics, your correctness would involve physical experiments, not future physicists.)

Randomness pervades every part of the question-answer process, from question selection to the answer given. This results in an important benefit of the proposed framework: a novel, formal justification for two common-sense shortcuts in science and math—believing more strongly in ideas supported by multiple lines of evidence, and believing more strongly in ideas that best explain something you already believe.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Santa Fe Institute

Researchers Jayne Spiller and Camilla Gilmore at the Center for Mathematical Cognition, University of Loughborough, U.K., have investigated the intersection of sleep and mathematical memory, finding that sleep after learning improves recall.

In their paper, “Positive impact of sleep on recall of multiplication facts,” published in Royal Society Open Science, the duo investigated whether learning complex multiplication problems before sleep would benefit recall compared to learning them during wakefulness to understand how sleep affects the memory of mathematical facts, specifically multiplication tables.

The study involved 77 adult participants aged 18 to 40 from the U.K. Each participant learned complex multiplication problems in two conditions: before sleep (sleep learning) and in the morning (wake learning). Participants completed online sessions where they learned new complex multiplication problems or were tested on previously learned material. Learning sessions included both untimed and timed trials.

Participants had better recall in the sleep learning condition than in the wake learning condition, with a moderate effect size. Even when participants had varying learning abilities, the sleep learning condition showed a beneficial effect on recall, with a smaller effect size.

Mathematical proficiency of the participants, as measured by accuracy in simple multiplication problems, was associated with learning scores but not with the extent of sleep-related benefit for recall.

The study highlights the potential educational implications of leveraging sleep-related benefits for learning. The positive impact of sleep on the recall of complex multiplication problems could be particularly useful for children learning multiplication tables or other math memorization skills, though it would be interesting to see how well a bedtime math lesson would be received.

While the authors suggest that sleep conferred the additional benefit on recall compared with learning during the daytime, the mechanisms by which encoding takes place are possibly enforced by a lack of continued external inputs. The authors point out this limitation of a lack of other comparative stimuli with a similar complexity of encoding to conclusively demonstrate in their study the specificity of sleep-related benefits on recall.

Asleep, the brain may be locking in the new learning because it has no other competition.

In contrast, an awake brain may be confronted with conversations, media reading or viewing and even other classes packed with learning material. This competition for memory encoding in the waking brain could be the cause of the memory differences seen in the study, though outside of recommending multi-hour meditation sessions between classes the likelihood of finding an alternative to sleep on memory may be limited.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to P by Justin Jackson, Phys.org