Fermi and the art of estimation
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73 RESONANCE January 2014 GENERAL ARTICLE Fermi and the Art of Estimation Rajaram Nityananda Keywords Fermi estimate, order of magni- tude, dimensional analysis. Rajaram Nityananda worked at the Raman Research Institute in Bangalore and the National Centre for Radio Astrophysics in Pune, and has now started teaching at the Indian Institute for Science Education and Research, Pune. He has worked on problems in optics, dynamics, and statistical physics, often applied to astronomy. The role of puzzles, paradoxes, physical arguments and connec- tions/analogies between different areas are a significant preoccupation.
Transcript of Fermi and the art of estimation
73RESONANCE � January 2014
GENERAL � ARTICLE
Fermi and the Art of Estimation
Rajaram Nityananda
KeywordsFermi estimate, order of magni-tude, dimensional analysis.
Rajaram Nityanandaworked at the RamanResearch Institute inBangalore and theNational Centre forRadio Astrophysics inPune, and has now
started teaching at theIndian Institute forScience Education andResearch, Pune. He hasworked on problems inoptics, dynamics, andstatistical physics, oftenapplied to astronomy. The
role of puzzles,paradoxes, physical
arguments and connec-tions/analogies betweendifferent areas are a
significant preoccupation.
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Howmanycoconut trees arethere in Kerala.
How manymolecules of
argon right now inyour lungshad passed
through the lungsof Akbar in his
lifetime?
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The balance wheelwill now shed someten percent of itsburden of air. Wecan then expectthe watch to run
faster, whencompared to sea
level, byabout ten secondsor less per day,
which is detectableby a carefulobserver.
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“I could observe verydistinctlyand actually measurethe displacement ofthe pieces ofpaper that were in theprocess of fallingwhile the blast waspassing. The shift wasabout 2.5 meters,which, at the time, Iestimated tocorrespond to theblast that would beproduced by tenthousand tons ofT.N.T.”
– Fermi
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Figure A (left). The distribution of density with distance at various times, as the fireball expands.Notice that it retains its shape, but changes in length scale (proportionally to time to the power of 2/5). This applies to the initial, so-called ‘Sedov’ phase of the explosion.Figure B (right). At a much later stage, we are dealing with a sound wave, whose profile – a sharpcompression followed by a longer rarefraction, is named after Friedlander.
1 Three famous scientists, von Neumann in the US, Taylor in the UK, and Sedov in the USSR arrived at thissolution, independently of each other because of World War II secrecy and lack of communication in thefollowing era.
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These methodswork best whenused by someone
with the sameintellect and insightinto all aspects ofphysics as Fermi
Within half a kilometreof the explosion
buildings are knockedover, temperaturesrise to thousands ofdegrees. It is filled
with blindingradiation and deadlyradioactivedebris
gradually spreadingfrom the bomb itself.
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Address for CorrespondenceRajaram NityanandaPhysics Group,HR-4, IISER
Pune 411 008, India.Email:
Suggested Reading
[1] Laura Fermi, Atoms in the Family: My Life with Enrico Fermi, TheUniversity of Chicago Press, Chicago, 1961.
[2] Enrico Fermi, Notes on Quantum Mechanics, The University of ChicagoPress, Chicago, 1961; Enrico Fermi, Thermodynamics, Dover Publica-tions, 1956, These two books are in Fermi’s own handwriting and reflecthis personal style.
[3] V F Weisskopf, Modern Physics from an Elementary Point of View,Geneva, European Organization for Nuclear Research, 1969.
[4] G Venkataraman,Why are Things the Way They Are?, Universities Press,1997.
The Fermi estimateis just the tip of aniceberg, a very smallpart of a totalphysicist – somewould say the last ofthis kind. However, itis this part of Fermiwhich we can allappreciate and learnfrom.
