Friday, July 19, 2024
Different Differences
Monday, July 15, 2024
A New Americanism
Friday, July 12, 2024
A Tale of Survival
Sunday, July 7, 2024
Ancient Rome lasted nearly Twenty-one Centuries
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Tom Kando
Thursday, July 4, 2024
Kamala Harris for President
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Sunday, June 23, 2024
Should we Fear Death?
Wednesday, June 19, 2024
Beautiful Kauai
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Of the many places I've traveled to in my long life, Kauai remains my favorite. I've had a decades-long love affair with this beautiful island. The moment the plane lands on this tiny speck of land in the vast Pacific Ocean, I feel at home. Every night, the soothing surf lulls me to sleep, and during the day, the trade winds caress my skin like a silken glove. The lush green of Kauai’s mountains and valleys contrasts perfectly with the red ochre of its soil. As the oldest of five sisters, Kauai, in my opinion, is also the most beautiful.
Monday, June 10, 2024
Gambler's Fallacy vs. Law of Large Numbers
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Here is a baffling mathematical problem which I have pondered for years:
The "Gambler’s Fallacy” and the “Law of Large Numbers" seem to contradict each other:
Consider two statements: (1) “Previous outcomes do not affect the probabilities of the next (similar) event.” Take coin tosses for example, each having a fifty-fifty probability of head or tail, right?
(2) The larger the number of coin tosses, the more likely you are to approach a fifty-fifty distribution of heads and tails, right?
Statement number #2 implies that if you have just tossed a coin twelve times, and ALL twelve of those have resulted in heads (a probability of 1 in 4,096) as you proceed to toss the coin for the thirteenth time, you expect it to come out a tail, and you bet accordingly, as some gamblers sometimes do.
But actually, the smart gambler might be better off betting on head because, given the outcome of the first twelve tosses, there is a chance that the coin was tampered with and is loaded towards “head.”
Statisticians try to explain the irreconcilability of the two statements above by quoting the “law of large numbers.”
In probability theory, the law of large numbers (LLN) is a mathematical theorem which states that the average of the results obtained from a large number of independent and identical random samples converges to the true value, if it exists.
More formally, the LLN states that given a sample of independent and identically distributed values, the sample mean converges to the true mean (Wikipedia).
Read more...
Friday, May 17, 2024
Who to Vote for President?
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Tom Kando
The presidential election is coming up. We will have four more years of the same president we had before - either a good and decent octogenarian who is doing his best, who is a normal human being, who is overseeing a country that is doing quite well despite turbulence overseas and a general domestic malaise, Or an unpredictable weirdo who is likely to steer the country deeper into right-wing chaos and extremism.
The president of the US matters. So I Googled this topic once again. Who were our good and successful presidents, and the bad ones? One Wikipedia website offers this in the form of metadata:
Twenty-one separate rankings
obtained throughout the second half of the 20th century and the
first decades of the 21st.
I summarize the combined results below:
Read more...Thursday, May 9, 2024
Israel's Mistake
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