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CodeWarriorz Thoughts: Sunday, October 12, 2008 CodeWarriorZ BlueZ

CodeWarriorz Thoughts

Day to day musings of free speech activist CodeWarrior.

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Sunday, October 12, 2008

 

Intuitive Statistics, Mathematical Sstatistics, Real World events, and Bull Shit

Mathematicians believe that mathematics is a real thing in the sense it actually has validity. They believe two plus two will ALWAYS equal four (and yet, two black holes plus two more black holes, actually equal ONE big ass black hole).

In undergraduate studies I took and passed TWO statistics courses. I passed them by spewing back the same bullshit they wanted to hear, but in my experience, was just that, bullshit.

For example, what I told the teacher was that chances were ALWAYS 50/50. An event either happens or it doesn't happen, like snow in the Sahara. Folks would say that the chance that would happen was ZERO, but in fact, it did happen. For the only time in recorded weather history, snow fell in the Sahara desert in southern Algeria on February 18, 1979.

So, the chances were 50/50 every day, and on that day, the 50 percent chance it would snow, overtook the 50 percent chance it would NOT snow.

But, more to the point, how about the statistician's favorite endeavor, i.e. the "coin toss". More often in the real world, it is more a coin flip than a coin toss, because tossing would be more a translation event, whereas a coin flip is both translation and rotational. The physical means by which the coin is flipped is of consequence in the real world. Some more adept folks who place the coin with a head and tail side, a certain way on the top of the medial edge of the curve index finger, and then placing the thumb underneath the coin with an upward thumping motion, can often make it come up heads more than tails, defying the 50/50 probability that statisticians maintain will be borne out over large numbers of coin flips.

So, usually, when they are using a coin toss (actually a coin flip) they will say,
"Call it, heads or tails". Actually, this leaves out one important event that CAN happen. In other words, there are three possible outcomes to a coin flip or coin toss.
Heads, tails, and landing on the edge.

Now, when people are faced with this, their INTUITIVE mind says that coins hardly ever, IF EVER , land on edge. In fact, an entire Twilight Zone episode, starring the guy who played the witch Samantha's first husband Darren (or was it Darrin) Stephens, had a coin land on edge and somehow, this resulted in him being able to read other people's thoughts (or hear their thoughts in real time in his mind), until the coin went from its edge on position to a face down position.

One problem is that statisticians are often, like most people who worship at the alter of "Science", arrogant assholes who think they know it all, but don't.

For example, let's talk about this coin toss/ flip deal.

They treat whatever coin they use as if it represents all coins. Intuitive thinking tells you no. Coins vary widely on side, composition, weight, etc. A silver dollar from the 1800s in the US is different from a coin from ancient Rome. Furthermore, "science" says that objects traveling through the air, have their path changed by surface characteristics. The relief or raised face on a coin, may be quite different from the "tails" face. Just look at the lowly penny. Certainly , Lincoln's face is different from the facade on the opposite. But, statisticians treat the coin being tossed as if it had two blank faces with an "H" in black marker on one face , and a "T" for tails on the other. Now, before someone tells me that there are computer programs which will "toss" the coins randomly, i.e. virtual coins, that argument is even worse, but it carries the experiment farther away from real world analysis. The problem as I see it is that there are already far too many modeling programs trying to simulate the real world, however; as we know from the present financial debacle, the analog world is far too complex, has far many unique aspects to it to be properly predicted by a digital model.

Now, more to the point of the "land on the edge" aspect of the coin toss/ flip,
from http://www.fortunecity.com/emachines/e11/86/spinning.html
"In his paper in the European Journal of Physics, Sir Hermann attempted to calculate the probability that a coin dropped on to the floor will land on its edge, After five pages of tightly-argued mathematics, he arrived at a formula which predicts that the chances of a 2p coin landing on its edge must be less than 1 in 2,000.
And a lot less, by all accounts - for we don't hear of many accounts of referees having to re-toss coins that landed on their edge the first time. Sir Hermann wasn't able to put a much tighter limit on the probability because the maths involved is so tricky that he had to assume the coin just tumbled to the ground from a random starting position. Predicting the fate of a coin tossed high in the air is quite another proposition - and the way we toss coins may militate against on-edge landings.
It doesn't entirely rule them out, though - as I discovered recently after receiving a first.hand account of perhaps the only well- attested case of tossed coin landing on its edge.
On October 9, 1972, the mathematician Dr Jeffrey Hamilton from Warwick University wanted to show his students the effect of chance by tossing a coin. Taking a 2p coin out of his pocket, he tossed it, then watched as it hit the floor, spun round and came to rest on its edge.
Prof Hamilton tells me that dozens of students witnessed the amazing event, and after a stunned silence they all broke into wild applause. As well they might, for you don't need to be a distinguished Cambridge mathematician to postulate that none of them will see such an event again."

Now, we can all speculate on various variables that can affect coins landing, or not landing on their edge. One thing to consider is the effect(s) of "milling". Milling on a coin is the ribbed edge that one sees on dimes and quarters, but not pennies or nickels. The reason for milling is that back when coins actually contained precious metals like gold or silver, unscrupulous people would scrape or "shave" off bits of the edge of the coin, thereby, not giving the recipient the full measure of the coin, and also, it decreased the real value as it got passed along. To stop this, milling was instituted such that at a glance, one could tell whether the coin was tampered with. Pennies and nickels, being of lesser value, are not milled, and thus have smooth edges.

I would argue that a smooth edged coin, flat as it is, would be more apt to land and stay on edge, than a milled coined, which has a tendency to rock back and forth, and ultimately fall over because of the uneven nature of the edge as a result of the milling.

Also, a very slow, deliberate flip of a coin, with the thumb chambered against the inner aspect of the thumb and released in a flicking fashion, will generate less revolutions of the coin, and greater control can be exerted, especially if it is caught in the other palm, as opposed to being flipped in the air, such that it can end up on the ground. In those instances, there is more opportunity for a coin to change position and land more unpredictably. By that I mean that if one wants it to land heads or tails, it only takes a bit of practice and a deliberate attempt to restrict rotations of the coin, to end up generating the desired outcome. On top of this, there is the method in which the coin is caught in the palm of the hand that flipped it, and quickly turned over, placing the palm of the flipping hand on the back of the hand of the non-flipping hand, with the flipping hand being pulled away to reveal the heads or tails nature of the coin flip.

We have not even discussed the effects of slight air currents, humidity, or gone into depth about the angle the hand is held in when a coin is flipped. Of course, as in the "landing on the edge scenario" in the calculations previously referenced. if we were on the "Mythbusters" program,
a device could be rigged to drop a coin or flip a coin from a measured height, over and over.

Now, that kind of experiment could start with the coin in a perpendicular or horizonal orientation, and measure which orientation, i.e. on the edge at the beginning, with "heads" up or "face up" predominated in the final outcome, or a mechanical flipping device could be created to mechanically flip the coins. If this was carried out, with temperature, barometric pressure, wind currents, humidity held constant, and the coin allowed to land on a smooth, flat surface, then, we must not ignore the reslience of the landing material. For example, a smooth soft rubber mat would be different than a hard rubber mat, which would be different from smooth hard wood, which would be different from concrete, which would be different from steel.

And, we haven't even touched on how far the experiment is from the equator, time of day or night, or any of the other variables.

Here's another quote from another page on this landing on the edge issue:
"
The coin could land on its side, but just because 10% of its area is on the edge doesn't mean it has a 10% chance of landing on the edge - you need to take into account the surface, friction, spin of the coin, gravity etc.

In fact, a coin doesn't have a 50:50 chance of landing heads or tails - it is more likely to land tails as the heads side is slightly heavier. You'd need to toss it a lot of times to see the difference though.:

And another 0ne :
http://prola.aps.org/abstract/PRE/v48/i4/p2547_1
"

Phys. Rev. E 48, 2547 - 2552 (1993)

Probability of a tossed coin landing on edge

" Daniel B. Murray

Department of Physics, Okanagan University College, Kelowna, British Columbia, Canada V1Y 4X8

Scott W. Teare
Department of Physics, University of Guelph, Guelph, Ontario, Canada N1G 2W1

Received 9 March 1993

An experiment is reported in which an object which can rest in multiple stable configurations is dropped with randomized initial conditions from a height onto a flat surface. The effect of varying the object’s shape on the probability of landing in the less stable configuration is measured. A dynamical model of the experiment is introduced and solved by numerical simulations. Results of the experiments and simulations are in good agreement, confirming that the model incorporates the essential features of the dynamics of the tossing experiment. Extrapolations based on the model suggest that the probability of an American nickel landing on edge is approximately 1 in 6000 tosses.

URL: http://link.aps.org/abstract/PRE/v48/p2547

DOI: 10.1103/PhysRevE.48.2547
PACS: 05.45.+b, 46.10.+z"

More...
http://www.jimloy.com/math/probabil.htm
"The probability of flipping heads (with a theoretically perfect coin) is 0.5 (50%). We pretend that the coin is perfect, and the flip will be fair, and the coin can't land on its edge. These are assumptions that are pretty close to reality."

That's the kind of bullshit a skeptic would come up with...i.e. just to dismiss out of hand an event that the person making the bullshit rules has never seen or doesn't think possible to exist.

http://en.wikibooks.org/wiki/Applicable_Mathematics/Probability
"For instance, if the coin is thick enough, the possibility that the coin can land stablely on its edge should not be ignored. When tossing TWO coins, many people think there are three equally likely outcomes (two heads, two tails, one of each) and that therefore the chance of getting "one of each" is 1/3: but actually there are two different ways of getting a head and a tail, so the chance of getting "one of each" is actually 2/4 = 50%."

Now, the above source made an assinine comment, saying that it is "silly" to say that the chance an event happens is "1" and that it will not happen is "not 1", which the reader will remember is basically my assertion to the teacher when I took statistics.
Just to quote correctly, the author said "(To be silly, one might say "there are two possible outcomes ; 1 or not 1, therefore the chance of rolling a 1 is 1/2")."

I myself have tossed / flipped a coin and had it land on its edge, so, no matter how improbable the land on the edge phenomenon is, not only is it possible, it DOES occasionally happen, and thus, in any calculation of the possible outcomes of a coin toss, head cannot be .5 and tails cannot be .5 (50 percent respectively) because that would leave ZERO chance of an edge landing, making the edge landing impossible, but since it is known to happen, the null hypothesis is wrong based on practical, real world outcomes. Thus, heads and tails, by definition, must have less than 50 percent chances.

Now, I believe that the notion that one cannot have an edge landing outcome, may often be based upon folks using the "flip the coin in the air, catch it in the same palm of the hand that flipped it, and turn it over onto the back of the other hand, with the hand that flipped it, temporarily acting as a cover until it is pulled away to reveal heads or tails. In this scenario, there is ZERO chance of an edge landing, because the flipper actually FORCES the coin into a landing as heads or tails.

This is perhaps the most common use of the coin , i.e. as an informal decision making procedure to determine who goes first in some event.

The point to all this is that much of statistics has been based on things like coin tosses (again, coin flips). If they start from a fundamentally flawed principle, such as the probability of head/tail toss outcomes is ONLY heads or tails, then the foundation is faulty, since they are ignoring the edge landing, which as we have seen, is a distinct possibility, and one that is infinitely more likely than say, winning the lottery, although in the real world, despite 12 million or 20 million to one odds, people actually DO win lotteries!

So,screw you skeptics !

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