Paul the Psychic Octopus

[Ernest]

Paul predicted 3 group games and 5 knock out games in a row. A group game can be a draw but Paul did not get a draw box. What's the chance of a group game being a draw? Unknown. If it's a third then the chance of Paul picking a group game winner correctly is 2/3 x 1/3 = 2/9. Obviously the chance of him picking a knockout game winner by chance is 1/2. So the chance of him picking all of the results by chance is

2/9 cubed x 1/2 to the 5 =

8/729 x 1/32 =

8/23328 =

1/2916

As a decimal my calculator gives

3.43e-4 (3sf)

What does this look like written normally?

Wiki says the odds, if the chance of a draw is a third, are 0.0039. Is that correct?

[La Cosa Blanca]

Octopus... psychic... world cup... :deadhorse:

[Mike]

Speaking of predictions, prior to the World Cup hosted in South Africa, one might have reasonably predicted that the news to be covering TNB. One could not have predicted that it would be covering vuvuzelas and psychic octopuses*.


*Note the correct plural. Please use it.

[mladikov]

*Note the correct plural. Please use it.
No. Octopi.

[La Cosa Blanca]

No. Octopi.

Oh no you didn't...

[Julian Curtis Lee]

I love this thread title.

[Niccolo and Donkey]

I think it's a tremendous and interesting political situation.

[Felix the Cat]

It's not pure chance because on all but one occasion he chose the box with a yellow/red flag on it.

[La Cosa Blanca]

It's not pure chance because on all but one occasion he chose the box with a yellow/red flag on it.

You too? :confused:

[Mike]

No. Octopi.You are wrong, sir.

Only certain (not all) English nouns taken from Latin with the ending -us properly form their plurals by changing the -us to -i. "Octopus" is from the Greek and the -us is not an inflection; it's part of the stem. "Pus" means foot and its athematic plural is "podes". Adding the prefix "octo-" meaning eight gives "octopus/octopodes" in Greek. Obviously in English, no one is going to say "octopodes" so the correct plural is "octopuses".

The hypercorrection "octopi" however is barbaric and unacceptable.

[Ahknaton]

It's not pure chance because on all but one occasion he chose the box with a yellow/red flag on it.
Octopuses are colour-blind.

[mladikov]

You are wrong, sir.

Only certain (not all) English nouns taken from Latin with the ending -us properly form their plurals by changing the -us to -i. "Octopus" is from the Greek and the -us is not an inflection; it's part of the stem. "Pus" means foot and its athematic plural is "podes". Adding the prefix "octo-" meaning eight gives "octopus/octopodes" in Greek. Obviously in English, no one is going to say "octopodes" so the correct plural is "octopuses".

The hypercorrection "octopi" however is barbaric and unacceptable.

You're wrong. The word is in Merriam-Webster (http://www.merriam-webster.com/dictionary/octopi) so it has to be a correct word. Incorrect words are never found in dictionaries! Unless you think you're better than Merriam-Webster...

[Mike]

You're wrong. The word is in Merriam-Webster (http://www.merriam-webster.com/dictionary/octopi) so it has to be a correct word. Incorrect words are never found in dictionaries! Unless you think you're better than Merriam-Webster...Some dictionaries list it. Those dictionaries are wrong. I am better than Merriam-Webster, at least in this instance.

[mladikov]

Some dictionaries list it. Those dictionaries are wrong. I am better than Merriam-Webster, at least in this instance.
No. A word wouldn't be in a dictionary if it wasn't a word. You're being silly.







Octopi.

[Felix the Cat]

Octopuses are colour-blind.He's clearly responding to some pattern. Creatures with monochrome vision may be better able to differentiate different shades of grey than we can.

[La Cosa Blanca]

He's clearly responding to some pattern. Creatures with monochrome vision may be better able to differentiate different shades of grey than we can.

He's clearly responding to being hungry and doesn't give an oyster's ass about flags, patterns, boxes, or prophecy.

[Mike]

Octopi.There is no etymological justification for that barbarism, and it should be redacted from dictionaries & dropped from usage.

[Ahknaton]

Mike is correct, "octopus" of Greek origin, so should not be pluralized as "octopi", which is the Latin form. However, "bus" is Latin (being an abbreviation of omnibus), so the plural should not be "buses", but bi.

[Felix the Cat]

Whatever sounds more natural should be used, and that would be octopuses in this case.

Octopi is "wrong" not because it breaks some grammatical rule but because it sounds bizarre to native English speakers.

[Mike]

Mike is correct, "octopus" of Greek origin, so should not be pluralized as "octopi", which is the Latin form. However, "bus" is Latin (being an abbreviation of omnibus), so the plural should not be "buses", but bi.:) I almost think I am being trolled. Please do not confuse the people. Be that as it may, I'll respond in the hopes that some may find this edifying.

Latin grammar has some complications, and so does the English plural noun in its wake. Only some Latin nouns ending in -us justifiably have -i as a plural. These are the masculine (and rarely feminine) Latin nouns of the second declension, such as focus/foci or alumnus/alumni. Other nouns with -us take different plurals, such as corpus/corpora (certainly not "corpi", ugh), or in the case of "virus", none at all, thus necessitating the innovative English plural form "viruses". All of these forms, by the way, are Latin nouns in the nominative case.

Adding to this complexity are the English nouns that were taken from Latin words that were not nouns in the nominative case. "Omnibus" is a plural noun in the dative case that means 'for all', but is given a singular meaning in English. Therefore it cannot justifiably take the -i ending anymore than "corpus" can. Likewise with the English noun "ignoramus" which is a plural verb in Latin.

In short, justifiable -us/-i nouns have to be rote-memorized as such.

[Macrobius]

As a decimal my calculator gives

3.43e-4 (3sf)

What does this look like written normally?

Wiki says the odds, if the chance of a draw is a third, are 0.0039. Is that correct?

3.43e-4 looks like 0.000343 in decimal notation.

The wiki article you are citing gives 0.0039 for 8 successes out of 8 'Bernoulli trials'.

A Binomial distribution for m successes in n trials looks like

(n choose m) * (0.5)^p * (0.5)^q

There is only one way to choose 8 things out of 8 (choose them all), so the prefactor "n choose m" is just 1.

p+q = 8 and the number of successes is p=8 and the number of failures is q=0, so the expression becomes

1* (0.5)^8 * (0.5)^0

The last factor is raised to the zeroth power, and any number to that power is a factor of 1, so it falls out too. The whole thing is just 1/2^8 = 1/256 = 0.00390625.

So the 0.0039 in the article had nothing to do with 1/3 or draws. It was figured on a straight even odds coin toss model with 8 correct calls. It has the same odds as 8 heads in a row with a fair coin.

The article doesn't tell you how to handle the three outcome case, but using a similar approach would require a Multinomial distribution:

http://en.wikipedia.org/wiki/Multinomial_distribution

The problem would have to be phrased carefully -- for example, are you looking for 'how surprising the result is' (predictive power), or odds of the exact thing that happened -- usually very small even for commonplace events. It doesn't matter in the 8 out of 8 case, because nothing more surprising can happen than that. But with draws, you have to decide whether fluffing one prediction about a draw is more surprising than fluffing a win/loss, and whether to weight wins and losses as equally surprising, if the prediction fails altogether. After all, the Octopus failed to predict a draw, and that amounts to censoring the data [there was a model failure]. This sort of thing ends up as part of Survival Analysis in Statistics, and is used for pharma trials and life insurance, say.

Also, the assumption that if there are three outcomes then the odds of each at 1/3 assumes you have no knowledge at all about the distribution. In fact, surely draws are less common, so you do know something after all. The 'prior distribution' should likely be based on past wins and losses in the sport or by the specific teams, or some similar predictive model.

Advanced section:

A more sophisticated analysis would consider the entropy encoded in the 'prior' assumptions, compared to the entropy in the predictions.

http://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence

(Notice the section on Bayesian updating and definition of 'surprisals').

[Felix the Cat]

Just rewatched The Future is Wild series from a few years back. One of the speakers, a biologist, uses both "octopuses" and "octopi" in the same 5-minute discourse.

[PseudoCop]

http://imgur.com/ToUpi.jpg