May 18, 2007
From the desk of Jane Galt:Good things come to those who wait
My recent rather startling run of bad luck has generated a couple of interesting emails. One asks "Is there anything we (the blogosphere) can do for you?" Alas no; sometimes life's a little rough, that's all.
Then there is Tyler Cowen, who mailed that "Very likely something very good will happen to you soon. At the very least you will get an extra serving of dessert."
The specifics of this theory are faulty, since the first thing that happens to me when I get stressed is that I lose my appetite and drop ten or twenty pounds. (Eight down, ? to go, according to the scale this morning . . . but some of that was winter weight that would have come off anyway, since I also lose my appetite when it gets warm. I'm a cyclical creature, I am.)
But what about the general theory? Intuitively, this is what we expect to happen, even those of us who are agnotheists and do not expect the universe to respond to us in any volitional way. We expect it in the same way that we expect a coin to turn tails after a long run of heads.
Of course, any statistician will tell you that this is nonsense. Provided the coin is honest, your probability of flipping a head for the 100th time is exactly the same as your probability of flipping a head the first time: 50%. We tend to confuse the probability of flipping the 100th head with the probability of flipping 100 heads in a row, which is indeed very low; it's (.5)100--a number so small that I can't give it to you, because my calculator only goes out to 30 decimal places. But our intuition is wrong. Once you have flipped 99 heads in a row, it is not particularly unlikely that you will flip the 100th.
So probabilistically, the chances that something good will happen to me right now are, I assume, about the same as they always were.
Do you believe that luck exhibits conditional probabilities? I asked Tyler.
"Regression to the mean", he replied. Fair enough. As I understand it, regression to the mean expresses the fact that highly improbable events are unlikely to be repeated. It's seen, for example, in the heritability of talent; the child of an Einstein or a Mozart is almost never* the genius his father was. In this case, it's reinforced by the fact that I'm rapidly running out of stuff to run out of, except for the aforementioned relatives and health.
So Howard Jones was almost right . . . there's a high probability that things can only get better. But no higher than it ever was. I just have to figure out what the general probability is that something very good will happen to me . . . if I can remember that far back.
* I'm tempted to say actually never . . . can anyone thing of counterexamples?
Posted by Jane Galt at May 18, 2007 6:01 PM | TrackBack | Technorati inbound linksIf you consider events relative to your current situation then you should get regression to the mean even if luck has unconditional probabilities. Bad luck makes your situation worse, so new events have an increasing chance of seeming like good luck.
If you consider events relative to your current situation then you should get regression to the mean even if luck has unconditional probabilities. Bad luck makes your situation worse, so new events have an increasing chance of seeming like good luck.
"a number so small that I can't give it to you, because my calculator only goes out to 30 decimal places."
/g
Actually at 30 digits it resolves to ....0001 .
with more digits it resolves to ....7889, but excel is notorious for being unreliable at high exponents.
/g
My guess is that you will find something you misplaced and felt lost long ago, which would be well better than seconds of dessert, even cheesecake.
how about J.S.Bach? CPE Bach Had a much higher regard than his father, who was then held higher later on. What is it to mean genius, when the fashions of the ages are the only thing that decide?
D
As I understand it, regression to the mean expresses the fact that highly improbable events are unlikely to be repeated.
Well, that's not exactly the way I'd put it. That might well be the shortest best explanation, though. A closer explanation (still incomplete) is that it expresses the fact that:
1) Most events and measurements have a deterministic component (something fairly easily measurable in repeatable experiments) and a random, or luck, component (something not easily measurable).
2) Most deterministic components tend towards zero monotonically as the deterministic component becomes more extreme away from the mean.
3) Due to 2), given a result, more likely than not the deterministic component is closer to the mean than the result.
For example, someone who bats .350 in his rookie year could be a .300 hitter who was lucky, a .350 hitter who bat average, or a .400 hitter who had an off year. There are so many more .300 hitters than .350 or .400 hitters that it's likely that he was lucky, and our expectation of his batting next year should be closer to the mean.
A 6'4" person is much more likely to be a person who grew taller than his 6' genes would predict than someone who was shorter than his 6'8" genes would predict, because there are a lot more people with 6' tall genes than 6'8" genes.
Einstein and Mozart are much more likely to be people who worked hard/got somewhat lucky than people whose genius was even greater than they expressed but were lazy/unlucky.
To the degree that this is bad luck, it's likely to turn around.
Of course, sexual reproduction adds a different, non-mathematical, effect of mixing genes with someone likely to be less impressive.
Insert joke re Presidents Bush here.
On another note, I join those who have commiserated with you over the loss of your dog. I lost a truly special and splendid one very suddenly in January (she was seven and in good health, but suddenly had a seizure and died). I still grieve for her daily. Hugs.
Amadeus Mozart's father - Leopold - was exceptionally talented, tho not as imaginative as Amadeus. there are also plenty of examples of children-besting-parents in professional sports, and a few in the arts. i can't think of many in the sciences, however.
The Bragg or Huxley families in physics are decent examples of exceptional ability passed between generations.
To add to the sciences list, there is the Bernoulli family, which was crammed full of geniuses responsible for major breakthroughs in mathematics, probability, and physics.
Niels Bohr is the better known, but his son Aage also won a Nobel prize in physics.
Continuing the family tradition, Marie and Pierre Curie's daughter, Irene Joliet-Curie, also won a Nobel with her husband.
For genius moving in different directions, there is the Mendelssohn family, although they are separated by a generation. Felix Mendelssohn is the better known of the two, but his grandfather was philosopher Moses Mendelssohn.
Along similar lines, Olivia Newton-John is the granddaughter of Max Born.
It's seen, for example, in the heritability of talent; the child of an Einstein or a Mozart is almost never* the genius his father was.
What about John Adams and his son, John Quincy Adams?
James
Great men with even greater children? Rare, but there are some: Philip of Macedon, Henry VIII, William Collins Whitney, Prescott Bush, I could go on. (Maybe even George H.W. Bush, whose son is a TWO-TERM president.) Indeed, probability dictates that, although most great men have children who are less successful, most really great people did not come from nothing, but had successful fathers.
Three highly accomplished children of accomplished parents:
1. Irene Joliot-Curie, who won a Nobel Prize in Chemistry. (Admittedly, she failed to completely equal her mother Marie Curie, who won two in Physics and Chemistry -- but, hey!)
2. Sir William Lawrence Bragg, who shared a Nobel Prize in Physics with his father Sir William Henry Bragg.
3. Bill Gates, world's richest man, son of an already rich but not ultra-rich man (William H. Gates, Sr.).
If you are thinking about luck, you should read Taleb's The Black Swan.
1/2 of the increase in value of the stock market over the last 50 years comes from the 10 days with largest movements :-)
It's not exactly like flipping a coin. Don't forget the upward time trend (few smart people peak at 35), at least until fatal illness and death.
Also, it is related to debates over business cycles in the late 80s and early 90s, namely if a developed economy is underperforming, can you expect a bump upwards again or not?
Under one view there is a "unit root" and on average you can expect your current situation to continue.
Under another view, successive "draws" are not independent and you can expect to make up lost ground. This is related also to "catch up" theories of economic growth, recovery from war, etc.
This debate has not yet been settled, so you are now a data point in macroeconomic debates.
on THIS blog no one mentions Milton & David Friedman!??!
Or Patri?
But glad you mentioned that you were referring to the Howard Jones version of that song. There's another (different tune and lyrics, same title "Things Can Only Get Better") by D:Ream which was used as the Labour Party campaign song in 1997, thus neatly disproving the contention.
"few smart people peak at 35"
That is of course unless they play chess for a living ;)
Jane, while I did and do sympathize overall with your travails, my offer (on behalf of the blogosphere, whose permission I neglected to ask) was primarily to address the server problem (whose cause was at that time unknown) just in case it was something that cash donations could fix. I thought it unlikely that that was the problem, but wanted to be sure you understood that people would be willing to help on the long shot that it was.
I mean, mighty is the blogosphere, but obviously even it can't bring back the dog, or bring back together your parents. For that all we can offer is sympathy, and hope for a better year going forward.
Wittgenstein and Hayek were cousins, and there is also the Darwin family. From the world of politics there is the Cecil family who first rose to prominence in the 16th century, when William Cecil was chief advisor to Elizabeth I, and have been prominent in British politics ever since, including one Prime Minister in the late 19th century.
y81 mentioned Henry VIII and Elizabeth I, to which could be added Henry VII giving a grandfather - father - daughter triple of great, greater, greatest.
John Stuart Mill came to my mind, but after that it's all sports stars:
Barry Bonds
Ken Griffey Jr.
Peyton Manning
How great does the parent have to be? How great an economist was John Neville Keynes, for instance? (I don't actually even think that Bobby Bonds, Ken Griffey Sr. or Archie Manning really count for this purpose, either, but I'm just throwing them out there.)
Flynn: I like David Friedman, but I don't think he's eclipsed his dad, yet.
* Oliver Wendell Holmes Sr. (the poet), Oliver Wendell Holmes Jr. (the jurist)
* As James mentioned: John Adams, John Quincy Adams, Henry Adams (grandson of John Q.)
* SCOTUS Justices John Marshall Harlan and John M. Harlan II (grandfather-grandson)
* The Gracchus brothers in ancient Rome
BTW, very sorry to hear about your dog. My condolences.
I always believe good things(opportunities)would make time to come,but the fact is we shouldn't wait for the opportunity rather we should create it.The long we practice the same thing the more we can get from it..
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One example that was missed is the famous sociologist Robert K. Merton, one of the most influential modern sociologists, and his son Robert C. Merton, one of the most influential financial economists of modern times and a Nobel winner in 1997 (for his work on Black-Scholes).
Since Einstein discarded a child, fate unknown, how can we be sure?
"the child of an Einstein or a Mozart is almost never* ...
* I'm tempted to say actually never . . . can anyone thing of counterexamples?"
Well, Colin Mozart probably was a genius. He is "a Mozart". I think there is a psychological factor at work here. Anyone who outshines his father, diminishes his father. If a genius has a greater genius for progeny, the elder is relegated by history to normalcy.
D'oh!
Make that Leopold Mozart above. Damn Monty Python skits are corrupting my memory of real events.
Years ago, as I was about to go through the Army's Ranger School, an older man gave me some very good advice: whenever something very bad or very good happens, he said, remind yourself, "this, too, shall pass." And it does. That was, on points, the worst time of my life: I lost thirty pounds (almost a fifth of my body weight), and went for almost five months with no more than four or five hours' sleep a day, sometimes less. It was the purest misery short of war, but there were still good and bad moments, happiness and despair; they never reached the cyclic level of predictability, but one was always waiting to follow the other.
So if it's bad; it will get better; if it's good, enjoy it while it's here.
Bernoulli family (several generations and includes cousins)
Max Noether (father) and Emmy Noether (daughter)
Neils Bohr (father), Aage Bohr (son)
Neils and Harald Bohr (brothers)
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I think most of you are missing the point about the geniuses. For example Milton and David Friedman. While David is a reasonably prominnent economist he is not his father. He will not likely win the nobel prize. Similarly Leopold and W.A. Mozart. Leopold was a good muscian but we would probably not remember (or at least only specialists would) but for his son. Even considering Henry VIII and Elizabeth I, I think you are considering one or both geniuses. They were both very talented but geniuses not so much. The only one that possibly compells me is JS BAch and CPE Bach but again I think history shows CPE was not quite on ar with JS.
The impressionist painter Pierre-Auguste Renoir was the father of filmmaker Jean Renoir.
Provided the coin is honest, your probability of flipping a head for the 100th time is exactly the same as your probability of flipping a head the first time: 50%.
And we all know that events in the real world are perfectly independent ;-)
The commenter who mentioned The Black Swan has it right on. Applying too much statistical thinking to real life is hazardous to your health.
Douglas Hofstadter (Pulitzer for Godel Escher Bach) is the son of Nobel physicist Robert Hofstadter.
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