Main:
A British 2 pence coin (steel core with copper plating)(1). Was tossed 100 times the data was collected and statistically analysed. This was conducted to test the hypothesis: “Tails never fails, it rhymes ergo, it’s true”.
Also goes on to the P vs NP debate
‘The statistical distribution of tossing a coin and it rhymes it must be true!.
By Wolfmankurd.
Abstract:
A British 2 pence coin (steel core with copper plating)(1). Was tossed 100 times the data was collected and statistically analysed. This was conducted to test the hypothesis: “Tails never fails, it rhymes ergo, it’s true”.
Null hypothesis:
There is no statistical difference between the number of times a head and tail (2) was on top.
Method:
The coin was flipped with the right (flicking) hand kept still, this was done by placing the fist on a desk and making sure it did not leave the surface. The flick was made with the thumb, and the coin was caught with the flicking hand on return and flipped on to the left palm and viewed. This technique was used because it’s the participants were most familiar with, and to control the coin spin. (3).The coin was always flipped heads up.
Results:
Heads Tails
48 52
Graphs:
[img=http://img513.imageshack.us/img513/4849/tossnz1.th.png] (4)
Analysis:
The graph showed similar results, the values were taken to be the mean percentage chance of getting each result (5). The student’s t test was applied to these means and it was found to be un-significant at the p=0.05 level (6). In effect in 100 attempts at this experiment more than 95 would have this result.
Conclusions:
We must accept the null hypothesis and conclude that tails doesn’t always win. The further reaching consequence of this ground breaking paper is that it seems “It rhymes ergo, it’s true” is a fallacy, for the future we must find new and if possible even more logical inductions at least in this un-adapted form. I have offered a sketch proof in the appendix.
Evaluation:
This work had a number of limitations it was done by one person, using only one example of a coin. Further it used an English rhyme.
A topic for further research for the direct topic of this paper would be using different sized coins, also coins of different composition, possibly the post 1992 “whole copper” 2-pences.
Further research into the in-direct topic would be the evaluation of a number of testable situations which rhyme for example; “Step on a crack break your mothers back”, “Beans, beans, they’re good for you heart, the more you eat the more you fart” (N.B. This has two lines of pursuit.) And the equivalents. Possibly reaching into different languages.
Appendix:
Disproof of “It rhymes it must be true.”. This is a proof constructed by “Reductio ad absurdum” (7)
Let p be “It rhymes it must be true”
Assume p to be true.
Consider np, where np is a rhyming sentence which opposes p.
Applying p to np,
np must be true,
p is therefore false,
This is a logical contradiction, a search for the holy grail of modern logic “np” is on going as the np VS p debate rages. And a $1,000,000 prize awaits it’s proof.
For further reading consider http://en.wikipedia.org/wiki/P_vs_np.
References:
1. http://www.royalmint.com/RoyalMint/web/site/Corporate/Corp_british_coinage/CoinDesign/2pCoin.asp
It was magnetic therefore post 1992 (not including 1998), this change was due to the increase of the price of copper. I forgot to check the date.
2. http://en.wikipedia.org/wiki/Coin#Features_of_modern_coinage
Heads was defined as the side featuring the Queen’s profile.
3. It was felt that this technique applied the majority of the momentum directly to the centre of mass reducing moments and causing the coin to move upwards with the least rotation.
4. Http://img513.imageshack.us/img513/4849/tossnz1.th.png The graph was formed using Microsoft Excel, the copy-cut-pasted with Microsoft Paint.
5. This means P(heads)=0.48 and P(tails)=0.52 This was done to allow ease with Student’s T-Test.
6. The t value was 0.5633 and it was assed with 198 degrees of freedom. Full results from Graph pad 4:
Parameter Value
Unpaired t test
P value 0.5739
P value summary ns
Are means signif. different? (P < 0.05) No
One- or two-tailed P value? Two-tailed
t, df t=0.5633 df=198
How big is the difference?
Mean ± SEM of column A 0.4800 ± 0.05021 N=100
Mean ± SEM of column B 0.5200 ± 0.05021 N=100
Difference between means -0.04000 ± 0.07101
50% confidence interval -0.08799 to 0.007985
R squared 0.0016
F test to compare variances
F,DFn, Dfd 1.000, 99, 99
P value 0.5
P value summary ns
Are variances significantly different? No
7. An assumption is made and then shown to lead to a logical contradiction. http://en.wikipedia.org/wiki/Reductio_ad_absurdum
8. Of course I could not come up with the correct p, since trained mathematical poets are working on it day and night and have had no success.
By Wolfmankurd.
Abstract:
A British 2 pence coin (steel core with copper plating)(1). Was tossed 100 times the data was collected and statistically analysed. This was conducted to test the hypothesis: “Tails never fails, it rhymes ergo, it’s true”.
Null hypothesis:
There is no statistical difference between the number of times a head and tail (2) was on top.
Method:
The coin was flipped with the right (flicking) hand kept still, this was done by placing the fist on a desk and making sure it did not leave the surface. The flick was made with the thumb, and the coin was caught with the flicking hand on return and flipped on to the left palm and viewed. This technique was used because it’s the participants were most familiar with, and to control the coin spin. (3).The coin was always flipped heads up.
Results:
Heads Tails
48 52
Graphs:
[img=http://img513.imageshack.us/img513/4849/tossnz1.th.png] (4)
Analysis:
The graph showed similar results, the values were taken to be the mean percentage chance of getting each result (5). The student’s t test was applied to these means and it was found to be un-significant at the p=0.05 level (6). In effect in 100 attempts at this experiment more than 95 would have this result.
Conclusions:
We must accept the null hypothesis and conclude that tails doesn’t always win. The further reaching consequence of this ground breaking paper is that it seems “It rhymes ergo, it’s true” is a fallacy, for the future we must find new and if possible even more logical inductions at least in this un-adapted form. I have offered a sketch proof in the appendix.
Evaluation:
This work had a number of limitations it was done by one person, using only one example of a coin. Further it used an English rhyme.
A topic for further research for the direct topic of this paper would be using different sized coins, also coins of different composition, possibly the post 1992 “whole copper” 2-pences.
Further research into the in-direct topic would be the evaluation of a number of testable situations which rhyme for example; “Step on a crack break your mothers back”, “Beans, beans, they’re good for you heart, the more you eat the more you fart” (N.B. This has two lines of pursuit.) And the equivalents. Possibly reaching into different languages.
Appendix:
Disproof of “It rhymes it must be true.”. This is a proof constructed by “Reductio ad absurdum” (7)
Let p be “It rhymes it must be true”
Assume p to be true.
Consider np, where np is a rhyming sentence which opposes p.
Applying p to np,
np must be true,
p is therefore false,
This is a logical contradiction, a search for the holy grail of modern logic “np” is on going as the np VS p debate rages. And a $1,000,000 prize awaits it’s proof.
For further reading consider http://en.wikipedia.org/wiki/P_vs_np.
References:
1. http://www.royalmint.com/RoyalMint/web/site/Corporate/Corp_british_coinage/CoinDesign/2pCoin.asp
It was magnetic therefore post 1992 (not including 1998), this change was due to the increase of the price of copper. I forgot to check the date.
2. http://en.wikipedia.org/wiki/Coin#Features_of_modern_coinage
Heads was defined as the side featuring the Queen’s profile.
3. It was felt that this technique applied the majority of the momentum directly to the centre of mass reducing moments and causing the coin to move upwards with the least rotation.
4. Http://img513.imageshack.us/img513/4849/tossnz1.th.png The graph was formed using Microsoft Excel, the copy-cut-pasted with Microsoft Paint.
5. This means P(heads)=0.48 and P(tails)=0.52 This was done to allow ease with Student’s T-Test.
6. The t value was 0.5633 and it was assed with 198 degrees of freedom. Full results from Graph pad 4:
Parameter Value
Unpaired t test
P value 0.5739
P value summary ns
Are means signif. different? (P < 0.05) No
One- or two-tailed P value? Two-tailed
t, df t=0.5633 df=198
How big is the difference?
Mean ± SEM of column A 0.4800 ± 0.05021 N=100
Mean ± SEM of column B 0.5200 ± 0.05021 N=100
Difference between means -0.04000 ± 0.07101
50% confidence interval -0.08799 to 0.007985
R squared 0.0016
F test to compare variances
F,DFn, Dfd 1.000, 99, 99
P value 0.5
P value summary ns
Are variances significantly different? No
7. An assumption is made and then shown to lead to a logical contradiction. http://en.wikipedia.org/wiki/Reductio_ad_absurdum
8. Of course I could not come up with the correct p, since trained mathematical poets are working on it day and night and have had no success.
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