Monday 26 November 2018

Statistics and Probability Effect Human Life in Every Way Imaginable


Statistics and Probability Effect Human Life in Every Way Imaginable

Someone on Quora asked me this, so I thought it was worth spending a few minutes on it.  I have worked in statistical analysis, or what is now called “data science” since my mid-20’s, so for over 30 years (for a non-profit, a government and a university). Naturally, I have also read a lot on the subject, with some focus on the history of the discipline.  I don’t claim to be a historian of science or mathematics, though, just an interested practitioner of the subject.


As someone who answered questions about Probability (statistics) before, can you help with this question?





Statistics and probability effect human life in every way imaginable, and always have.  From the earliest days, people have been estimating the odds of success versus failure, about small and large matters (note that the quotations are examples of what people might have said at the time, not actual historical quotes).

Prehistory (Instinct as expectation theory): “Is that motion of the grass a tiger or just the wind.  Most of the time its just the wind, but you never know.  I will come back to the waterhole a bit later, and check again, as I am not that thirsty yet.”


Biblical History (Early census and sampling theory): “How many people do we have and how much tax can we expect to raise from them?  We’d better do a census.”


Ancient history (Early informal probability theory): “Should we attack the Roman encampment?  It would be a fantastic victory, but the Romans win most of the time, so we had better not.”

 Cities founded by the Romans

Early Modern History (Early expectation theory profit/loss): “Columbus’s plan to cross the ocean to get to Cathay seems unlikely, but the prize is great, and the cost is bearable, so let’s fund him.”


Eighteenth Century (Formal development of probability theory): “I love to gamble but I am not doing so well at it.  Perhaps I will hire that Bernoulli fellow to study games more precisely, and get an edge that way.”


Nineteenth Century (Statistical physics): “Perhaps if we treated gases as a large collection of particles, we wouldn’t need to understand the motions of every one of them.  We will just compute the average behaviour of the collection, assuming a Gaussian distribution, and use that to derive the temperature and explain the concept of heat via kinetic-molecular theory.”


Twentieth Century 1 (Probability and weather forecasting): “The meteorologist says that there is an 80% chance of a gap in the stormy weather on June 6, based on past weather patterns, so there should be  fairly decent conditions for a landing.  So, lets go ahead with D-Day, and hope that his prediction comes to pass.”


Twentieth Century 2 (Evidence Based Medicine): “We really don’t know how well a lot of treatments actually work.  Many treatments have just been taught for generations, without rigorous testing.  Let’s come up with some standards for evidence and be sure that we know what really works.”



Twenty-first Century (Data science and the internet): “Perhaps I can use this clever data science algorithm to find just the right people to persuade to click through, and buy my book.”





So, now that you have read a bit about the effect of statistical theory on history, you could actually click through and buy my book. :)
How about a short story, also about interstellar interlopers.  It also features one possible scenario to explain why we haven’t met ET yet (as far as we know, anyway).  Only 99 cents on Amazon.

The Zoo Hypothesis or The News of the World: A Science Fiction Story

Summary
In the field known as Astrobiology, there is a research program called SETI, The Search for Extraterrestrial Intelligence.  At the heart of SETI, there is a mystery known as The Great Silence, or The Fermi Paradox, named after the famous physicist Enrico Fermi.  Essentially, he asked “If they exist, where are they?”.

Some quite cogent arguments maintain that if there was extraterrestrial intelligence, they should have visited the Earth by now. This story, a bit tongue in cheek, gives a fictional account of one explanation for The Great Silence, known as The Zoo Hypothesis.  Are we a protected species, in a Cosmic Zoo?  If so, how did this come about?  Read on, for one possible solution to The Fermi Paradox.

The short story is about 6300 words, or about half an hour at typical reading speeds.


Alternatively, consider another short invasion story, this one set in the Arctic.  Also 99 cents.

The Magnetic Anomaly

Summary
An attractive woman in a blue suit handed a dossier to an older man in a blue uniform.

“Give me a quick recap”, he said.

“A geophysical crew went into the Canadian north. There were some regrettable accidents among a few ex-military who had become geophysical contractors after their service in the forces. A young man and young woman went temporarily mad from the stress of seeing that. They imagined things, terrible things. But both are known to have vivid imaginations; we have childhood records to verify that. It was all very sad. That’s the official story.”

He raised an eyebrow. “And unofficially?”

“Unofficially,” she responded, “I think we just woke something up that had been asleep for a very long time.”



Saturday 10 November 2018

Interstellar Intruder ‘Oumuamua – Harvard Scientists Now Speculate about a Light Sail


Interstellar Intruder ‘Oumuamua – Harvard Scientists Now Speculate about a Light Sail

What We Know About ‘Oumuamua

In a paper published last year (Astrophysical Journal Letters: Interstellar Interloper 1I/2017 U1: Observations from the NOT and WIYN Telescopes, David Jewitt et al), researchers showed that a newly discovered object, since named ‘Oumuamua, must be of interstellar origin, due to its velocity (26 km per second) exceeding the escape velocity from the solar system. 


Furthermore, it was shown that its shape must be unusually elongated.  It must have at least a 5:1 ratio of length to width, possibly even much more.  That’s based on its light curve, or how the brightness changes over a short interval (about 7 hours).  The best explanation for that is a long, thin object that is tumbling with respect to the Earth, sometimes showing a shortened profile (and thus being less bright) and sometimes showing a longer profile (and thus being more bright).  If you spin a pencil around its long axis and observe how it apparent size changes, you can get the idea.
A following paper in Nature (Non-gravitational acceleration in the trajectory of 1I/2017 U1 (‘Oumuamua)) demonstrated that ‘Oumuamua has a non-gravitational component to its motion.  In other words, its trajectory has been influenced by some other push than the gravity of the major bodies of the solar system.  The effect is very small, so it took a lot of observational data to detect the anomalous motion. This was based on a comprehensive analysis of multiple observations, so the evidence is quite persuasive.  Plus, this paper was in Nature, so it no doubt had fairly intensive peer review.


That paper speculated that ‘Oumuamua is probably a comet that had been kicked out of another solar system long ago, and is slightly off-gassing as it goes through our solar system.  That produces a slight rocket-like effect, as the off-gassing is essentially reaction mass.  Its best fit velocity profile indicates that the acceleration is of a (1/R**2) form, as would be expected if the “driving force” was related to distance from the sun.

What the Latest Harvard Paper Says About ‘Oumuamua

The latest pre-print paper (COULD SOLAR RADIATION PRESSURE EXPLAIN ‘OUMUAMUA’S PECULIAR ACCELERATION? SHMUEL BIALY AND ABRAHAM LOEB, Harvard Smithsonian Center for Astrophysics), disagrees with the cometary explanation (it should be noted that this paper is by researchers from Harvard’s Smithsonian Astrophysics Center, so it has a credible pedigree).  Rather, it proposes that the non-gravitational acceleration that has been seen is more likely due to solar radiation pressure than off-gassing.  In other words, the light from the sun is doing the pushing, rather than it heating up material that off-gasses, thus producing a rocket-like effect.
This paper takes issue with the off-gassing comet theory for the simple reason that none of the usual features associated with a comet were observed in the ‘Oumuamua case.  There was no cometary trail, nor were gas emission/absorption lines seen in the observations.
In addition, a different paper that they cite (SPIN EVOLUTION AND COMETARY INTERPRETATION OF THE INTERSTELLAR MINOR OBJECT 1I/2017 ’OUMUAMUA Roman R. Rafikov) has argued from theoretical grounds that an outgassing comet would have evolved a much different spin than that actually observed.  These arguments are based on conservation of angular momentum considerations.  So, that is claimed to be supporting evidence that ‘Oumuamua is not a comet.
The Harvard paper goes through a chain of calculations to show that, if the object is not a comet, then a reasonable alternative explanation is a very thin object with a very small mass to area ratio (about 0.1 to 0.3 grams per square centimeter).  In other words, the object must be extremely thin, if radiation pressure is the driving force behind its non-gravitational acceleration, rather than off-gassing.
It also examines the probability that a very thin object could actually survive a long trip through the galaxy, rather than being destroyed (ablated or torn apart) or dramatically slowed down by collisions with matter in the interstellar medium such as gas or dust.  Again, a chain of theoretical reasoning is given to show that such an object could survive a long trip, as these collisions would not absorb much of the objects momentum, nor ablate much of its mass.  The interstellar medium is simply too sparse, and ‘Oumuamua’s velocity is too low to compromise its survival to a significant degree.
As indicated in the attached graph, an object of this type could travel many kiloparsecs before being appreciably slowed down or vaporized (for context, the distance from Earth to the center of the galaxy is on the order of a kiloparsec).


The possibility that a very thin object might also be torn apart by rotational torques or tidal forces is also examined.  Their calculations indicate that those would only be a problem if such an object passed very close to a star, much closer than is likely.  Presumably if it passed that close, it would be captured by the star, anyway.
Given the unusual physical constraints that these calculations give for such an object (very thin and elongated), what could it be?  There are no known solar system objects like this, but that doesn’t mean some natural astrophysical process might not produce such thin objects.  We just don’t know of any such process, and can’t think of one at the moment, but we also know that the universe has produced many unexpected surprises for us, as revealed by recent observations (e.g. hot Jupiters, planets around neutron stars).
Then, of course, there is always the possibility of the object having a non-natural genesis.  As the paper notes, a solar sail is an obvious possibility.  It would fit the possible geometry, and we know they exist, because we have built them ourselves.  Debris from some other sort of craft is also possible – perhaps it’s a quarter panel from a broken-up spaceship?
The paper also notes that an artificial source would have a bit of Occam’s razor on its side (my wording, not theirs).  Some earlier calculations about the probability of us observing a natural interstellar object that had been ejected randomly from another solar system, resulted in the conclusion that there must be a surprisingly large amount of these things produced during stellar evolution, just floating around in interstellar space (maybe a thousand trillion per cubic parsec).  If the object was artificial, and directed to our solar system on purpose, that surprising conclusion wouldn’t be necessary, though it would be replaced by the even more surprising conclusion that aliens sent a probe to our solar system.
Oh, and for what its worth, I actually included the idea of a solar sail in my last blog on the subject of ‘Oumuamua, as reproduced below.

Other Possible Explanations    

Some other physical models that might produce a non-gravitational acceleration were discussed.  For fun, I have included a Science Fiction possibility, which I have called SF response, where possible:
·        1.   Solar Radiation Pressure, such as that which drives a light-sail spacecraft.  This was rejected on the basis that the object would have to have an unrealistically low density, three or four orders of magnitude lower than natural solar system objects.
·        SF response – what if actually was a solar sail?


It’s nice to see that these Harvard researchers went to the trouble of looking into that possibility :). 

Sources:
1.     (Astrophysical Journal Letters: Interstellar Interloper 1I/2017 U1: Observations from the NOT and WIYN Telescopes, David Jewitt et al)
2.     (Non-gravitational acceleration in the trajectory of 1I/2017 U1 (‘Oumuamua))
3.     (COULD SOLAR RADIATION PRESSURE EXPLAIN ‘OUMUAMUA’S PECULIAR ACCELERATION? SHMUEL BIALY? AND ABRAHAM LOEB, Harvard Smithsonian Center for Astrophysics
4.     (SPIN EVOLUTION AND COMETARY INTERPRETATION OF THE INTERSTELLAR MINOR OBJECT 1I/2017 ’OUMUAMUA Roman R. Rafikov)



Now that you have read about a real interstellar interloper (natural or not), you should consider reading some Science Fiction.  How about a short story, also about interstellar interlopers.  It also features one possible scenario to explain why we haven’t met ET yet (as far as we know, anyway).  Only 99 cents on Amazon.

The Zoo Hypothesis or The News of the World: A Science Fiction Story

Summary

In the field known as Astrobiology, there is a research program called SETI, The Search for Extraterrestrial Intelligence.  At the heart of SETI, there is a mystery known as The Great Silence, or The Fermi Paradox, named after the famous physicist Enrico Fermi.  Essentially, he asked “If they exist, where are they?”.

Some quite cogent arguments maintain that if there was extraterrestrial intelligence, they should have visited the Earth by now. This story, a bit tongue in cheek, gives a fictional account of one explanation for The Great Silence, known as The Zoo Hypothesis.  Are we a protected species, in a Cosmic Zoo?  If so, how did this come about?  Read on, for one possible solution to The Fermi Paradox.

The short story is about 6300 words, or about half an hour at typical reading speeds.






Alternatively, consider another short invasion story, this one set in the Arctic.  Also 99 cents.

The Magnetic Anomaly

Summary

An attractive woman in a blue suit handed a dossier to an older man in a blue uniform.

“Give me a quick recap”, he said.

“A geophysical crew went into the Canadian north. There were some regrettable accidents among a few ex-military who had become geophysical contractors after their service in the forces. A young man and young woman went temporarily mad from the stress of seeing that. They imagined things, terrible things. But both are known to have vivid imaginations; we have childhood records to verify that. It was all very sad. That’s the official story.”

He raised an eyebrow. “And unofficially?”

“Unofficially,” she responded, “I think we just woke something up that had been asleep for a very long time.”