🎯 There’s a #law_of_large numbers, a #law_of_small_numbers, and a #law_of_medium_numbers in between.
1️⃣ The law of large numbers is a mathematical theorem. It describes what happens as you average more and more random variables. (goo.gl/9BFtxV)
2️⃣ The law of small numbers is a semi-serious statement about about how people underestimate the variability of the average of a small number of random variables. ( In general, people grossly underestimate the variability in small samples. This phenomenon comes up all the time)
3️⃣ The law of medium numbers is a term coined by Gerald Weinberg in his book An Introduction to General Systems Thinking. He states the law as follows.
"For medium number systems, we can expect that large fluctuations, irregularities, and discrepancy with any theory will occur more or less regularly."
The law of medium numbers applies to systems too large to study exactly and too small to study statistically. For example, it may be easier to understand the behavior of an individual or a nation than the dynamics of a small community. Atoms are simple, and so are stars, but medium-sized things like birds are complicated. Medium-sized systems are where you see chaos.
Weinberg warns that medium-sized systems challenge science because scientific disciplines define their boundaries by the set of problems they can handle. He says, for example, that
"Mechanics, then, is the study of those systems for which the approximations of mechanics work successfully."
He warns that we should not be mislead by a discipline’s “success with systems of its own choosing.”
Weinberg’s book was written in 1975. Since that time there has been much more interest in the emergent properties of medium-sized systems that are not explained by more basic sciences. We may not understand these systems well, but we may appreciate the limits of our understanding better than we did a few decades ago.
1️⃣ The law of large numbers is a mathematical theorem. It describes what happens as you average more and more random variables. (goo.gl/9BFtxV)
2️⃣ The law of small numbers is a semi-serious statement about about how people underestimate the variability of the average of a small number of random variables. ( In general, people grossly underestimate the variability in small samples. This phenomenon comes up all the time)
3️⃣ The law of medium numbers is a term coined by Gerald Weinberg in his book An Introduction to General Systems Thinking. He states the law as follows.
"For medium number systems, we can expect that large fluctuations, irregularities, and discrepancy with any theory will occur more or less regularly."
The law of medium numbers applies to systems too large to study exactly and too small to study statistically. For example, it may be easier to understand the behavior of an individual or a nation than the dynamics of a small community. Atoms are simple, and so are stars, but medium-sized things like birds are complicated. Medium-sized systems are where you see chaos.
Weinberg warns that medium-sized systems challenge science because scientific disciplines define their boundaries by the set of problems they can handle. He says, for example, that
"Mechanics, then, is the study of those systems for which the approximations of mechanics work successfully."
He warns that we should not be mislead by a discipline’s “success with systems of its own choosing.”
Weinberg’s book was written in 1975. Since that time there has been much more interest in the emergent properties of medium-sized systems that are not explained by more basic sciences. We may not understand these systems well, but we may appreciate the limits of our understanding better than we did a few decades ago.
Wikipedia
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close…
🎞 MIT #Machine_learning expert, Jonas Peters of the University of Copenhagen presents “Four Lectures on #Causality”.
1️⃣ https://www.aparat.com/v/hByIL
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3️⃣ https://www.aparat.com/v/qnONX
4️⃣ https://www.aparat.com/v/BeuES
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2️⃣ https://www.aparat.com/v/ID7n3
3️⃣ https://www.aparat.com/v/qnONX
4️⃣ https://www.aparat.com/v/BeuES
آپارات - سرویس اشتراک ویدیو
Lectures on Causality: Jonas Peters, Part 1
May 10, 2017
MIT
Machine learning expert Jonas Peters of the University of Copenhagen presents “Four Lectures on Causality”.
Produced by the Laboratory for Information
MIT
Machine learning expert Jonas Peters of the University of Copenhagen presents “Four Lectures on Causality”.
Produced by the Laboratory for Information
🔖 Network control principles predict neuron function in the Caenorhabditis elegans connectome
🔗 http://www.nature.com/nature/journal/vaop/ncurrent/full/nature24056.html
🔗 http://www.nature.com/nature/journal/vaop/ncurrent/full/nature24056.html
#سمینارهای_هفتگی گروه سیستمهای پیچیده و علم شبکه دانشگاه شهید بهشتی
🔹دوشنبه، ۱ آبان ماه، ساعت ۴:۰۰ - کلاس۱ دانشکده فیزیک دانشگاه شهید بهشتی.
@carimi
🔹دوشنبه، ۱ آبان ماه، ساعت ۴:۰۰ - کلاس۱ دانشکده فیزیک دانشگاه شهید بهشتی.
@carimi
💥 In physics, the Fermi–Pasta–Ulam–Tsingou problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou recurrence (or Fermi–Pasta–Ulam recurrence) – instead of ergodic behavior. One of the resolutions of the paradox includes the insight that many non-linear equations are exactly integrable. Another may be that ergodic behavior may depend on the initial energy of the system.
https://en.wikipedia.org/wiki/Fermi%E2%80%93Pasta%E2%80%93Ulam%E2%80%93Tsingou_problem
https://en.wikipedia.org/wiki/Fermi%E2%80%93Pasta%E2%80%93Ulam%E2%80%93Tsingou_problem
Complex Systems Studies
💥 In physics, the Fermi–Pasta–Ulam–Tsingou problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou…
"Fermi, Pasta, Ulam and the Birth of Experimental Mathematics"
http://people.maths.ox.ac.uk/porterm/papers/fpupop_final.pdf
A numerical experiment by Enrico Fermi, John Pasta, and Stanislaw Ulam
http://people.maths.ox.ac.uk/porterm/papers/fpupop_final.pdf
A numerical experiment by Enrico Fermi, John Pasta, and Stanislaw Ulam
رامین گلستانیان و محمدرضا اجتهادی اعضای جدید کمیسیون بیوفیزیک IUPAP
http://www.psi.ir/news2_fa.asp?id=2316
۲۹ امین مجمع عمومی کمیسیون بیوفیزیک انجمن بین المللی فیزیک محض و کاربردی International Union of Pure and Applied Physics(IUPAP) اعضای جدید مدیریتی این کمیسیون را انتخاب کرد.
http://www.psi.ir/news2_fa.asp?id=2316
۲۹ امین مجمع عمومی کمیسیون بیوفیزیک انجمن بین المللی فیزیک محض و کاربردی International Union of Pure and Applied Physics(IUPAP) اعضای جدید مدیریتی این کمیسیون را انتخاب کرد.