The Naked Scientists

The Naked Scientists Forum

Author Topic: Could a coin really land tail-side up 1000 times in a row?  (Read 9145 times)

Offline Xin

  • Jr. Member
  • **
  • Posts: 23
    • View Profile
    • http://xin1575.blogspot.com/
I know this isn't a math forum, but I've been thinking about how math works (or doesn't work) in reality. For example, math states that there is a possibility that I can flip a coin a thousand, or even a million times and have the coin land tails every time (assuming that the coin and flipper are NOT in a perfectly controlled and finely tuned environment where physics would cause the coin to land on tail every time). But is it REALLY possible to have this kind of outcome in reality? Does this mean that using math to predict something in science is invalid?

[mod edit - subject reformatted as a question - please try to do this in future as it helps other forum users to find information and relevant posts more quickly.]
« Last Edit: 05/08/2008 13:05:03 by chris »


 

Offline TheHerbaholic

  • Full Member
  • ***
  • Posts: 67
    • View Profile
I'm no good at maths at all. But what your saying about flipping a coin doesn't relate to the way scientists predict something in reality, its fact based rather guess work. Flipping a coin and it landing on heads or tails is 50/50, a pure guess. You can't give us this and then apply that to every time a scientists uses mathematics it must be wrong.

Take 2 + 1 = 3. We both know this to be correct.

You must of heard of H20? Water.

Hydrogen 2, oxygen 1. Put them together = H20 (water)

But because you flipped a coin thats now wrong? lololololol
 

lyner

  • Guest
The probability of an event happening is DEFINED as:
(the number of ways that event can occur/total possible number of outcomes)

For a coin, it's not really 1/2 for heads; it's 180/360 (if you measure the angle it can fall at, to 1o).
For a 'real' coin, with a slight curve in it and with the surface pattern of each side being different, you may find that the probability of a head could be 179/360 - not 1/2 exactly.
If you did thousands and thousands of throws, the 179/360 figure might reveal itself.
The Maths of '1/2' isn't wrong - it's the model that was used.
The problem is in how people interpret the theories involved with probability and statistics. It would be EXTREMELY unlikely to find 179000 heads turning up after 360000 tosses but the result would, almost certainly, be 'near' that value.

In Science, it's not 'guesswork' that tells you how the electrons will behave when they go through a lattice of atoms and what pattern they will form on the other side. The Physics of the situation predicts the most likely result. That's no more 'guessing' than going down the road and expecting your regular train to take you to work. In fact, it's probably a lot more accurate because all the variables have been considered (unlike the vagaries of the rail service).
« Last Edit: 05/08/2008 09:08:15 by sophiecentaur »
 

Offline graham.d

  • Neilep Level Member
  • ******
  • Posts: 2208
    • View Profile
50/50 is statistically the most likely outcome when tossing a coin. If you flipped a perfect coin (in a truly random way) 1,000 times, this does not mean you will get 500 heads and 500 tails. In fact the more times you flip, the less likely an exact 50/50 split becomes i.e. if you flip 1,000,000 times, the chances of 500,000 heads and 500,000 tails are a very unlikely result. However, the more times you flip, the closer you will get to 50% heads and 50% tails. For 1,000,000 flips, the chances of being within the range 499,500/500,500 are just over 68% and the chances of being within the range 498,500/501,500 are better than 99.7%.

Statistics, like these, are often used in science to check the validity of experimental results which, by their nature, involve measurement and some uncertainty. The statistics are used to verify that the experimental results are consistant with a theoretical prediction. It is in the nature of science that everything we know as "laws" are based on theory that can only ever be consistant with experiment. If any experiment shows that the theory's predictions are outside the statistical range that can be accounted for by experimental errors, then the theory is wrong and the science has to be re-thought through. An example is in showing Newton to be wrong and Einstein to be right in prediction of the decay of mu-mesons. The fact that Newton was wrong is not really to do with statistics but due to not having a full understanding of the underlying physics. While Einstein may also be wrong, this is not because of any inability to measure with perfect precision. The statistics are an aid in knowing the precision of measurements and then adjudging the validity of the data used in experiments, and not at all something that invalidates the science itself.

Quantum mechanics blurs this distinction somewhat because the statistics involved in measurements are part of the physics itself. But this does not make the physics any less valid or correct; it is just that we have to deal with probabilities of a predicted outcome more than within classical physics.

 

lyner

  • Guest
btw, is the initial post a question or just a complaint about how Science deals with things?
A bit of reasonable punctuation could reveal what was meant!?!
 

Offline RD

  • Neilep Level Member
  • ******
  • Posts: 8134
  • Thanked: 53 times
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #5 on: 05/08/2008 13:27:04 »
The coin does not have a memory.
Each time it is flipped there is a equal chance of heads or tails, even if the preceding ten flips were all tails.
 

Offline graham.d

  • Neilep Level Member
  • ******
  • Posts: 2208
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #6 on: 05/08/2008 13:29:03 »
To answer the question...

"Could a coin really land tail-side up 1000 times in a row? "

Yes, but the chances are 1 in 10.72 x 10^300.

That is 1 chance in

107200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000

so I wouldn't bet on it.

Please don't anyone tell me I have got the number of zeroes wrong by one or two :-) It is the principle I'm rying to get over.
 

lyner

  • Guest
Could a coin really land tail-side up 1000 times in a row?
« Reply #7 on: 05/08/2008 14:09:28 »
Yes - but you're only correct to four sig figs!
You'll have to do better than that next time.
 

Offline graham.d

  • Neilep Level Member
  • ******
  • Posts: 2208
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #8 on: 05/08/2008 14:32:18 »
OK. 1071508597... My calculator has no more significant bits. At least it's better :-)
 

Offline Xin

  • Jr. Member
  • **
  • Posts: 23
    • View Profile
    • http://xin1575.blogspot.com/
Could a coin really land tail-side up 1000 times in a row?
« Reply #9 on: 05/08/2008 17:20:43 »
Sorry for the confusion. It was rather late at night. I should explain myself a bit better as I certainly didn't mean to offend anyone, if I did.

I guess what I am getting at is based on an argument between a friend and myself. She believes that life, matter, and reality all occurred by pure chance, while I do not. My argument was that in order for life to just occur would involve a lot of precise events all happening at the right time and space to produce life. Since neither of us knew what the actual probability of that happening, I equated it to being similar to tossing a coin thousands of times and having it land tail every time. Or shuffling a deck of cards and having the result being a completed ordered deck.

Her rebuttal was simple: Probability shows that there IS a chance of that happening although minute. But this seems like a leap of faith to me and made me actually question the use of math in that fashion. Of course, I'd be taking a leap of faith as well if I say that life was created by a higher power.

I remember reading somewhere that Einstein or Hawkings predicted that time travel could be possible using a mathematical formula as it relates to gravitational fields near a black hole. And I recall reading other science articles about a variety of predictions based off a math equation. I certainly don't mean that they are wrong because math is not concrete proof, but it did make me wonder just how valid it is to use math to predict or prove things in science.
 

Offline techmind

  • Hero Member
  • *****
  • Posts: 934
  • Un-obfuscated
    • View Profile
    • techmind.org
Could a coin really land tail-side up 1000 times in a row?
« Reply #10 on: 06/08/2008 00:41:23 »
Last night, a friend of mine produced a coin and tossed it neatly a few times. I idlely commented that I'd be impressed if he got the same result several times in a row... he proceeded to toss 7 heads straight off. Then got a tail. I don't think there was any foul-play, but there's only a 1 in 128 chance of getting 7 heads in 7 tosses...
 

Offline Madidus_Scientia

  • Neilep Level Member
  • ******
  • Posts: 1451
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #11 on: 06/08/2008 08:32:39 »
What a tosser :P
 

Offline RD

  • Neilep Level Member
  • ******
  • Posts: 8134
  • Thanked: 53 times
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #12 on: 06/08/2008 08:48:01 »
Last night, a friend of mine produced a coin and tossed it neatly a few times. I idlely commented that I'd be impressed if he got the same result several times in a row... he proceeded to toss 7 heads straight off. Then got a tail. I don't think there was any foul-play, but there's only a 1 in 128 chance of getting 7 heads in 7 tosses...

The sequence produced by any seven tosses will be 1:128, not just when they are all the same outcome, e.g.
THTTTHT, HTHTTTH, THTHTHH, HHTHTHH, are also 1:128 possibilities.
Think of the sequence as a seven digit binary number, say Head=1 Tail=0, each seven digit sequence is one of the 128 possible.
All of these sequences are equally likely, (1:128), including when the outcomes are all the same (HHHHHHH, TTTTTTT).
« Last Edit: 06/08/2008 08:58:15 by RD »
 

Offline graham.d

  • Neilep Level Member
  • ******
  • Posts: 2208
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #13 on: 06/08/2008 13:24:16 »
Xin, have you heard about the "Anthropic Principle". This would dictate that we can only be in a position to debate the likleyhood of life occurring because life had occurred and developed to a point where we had the intelligence to debate it. It is like debating the chance of getting a thousand heads after the event but not being able to debate it (because we would not exist) if it had not occurred.

However, this is a matter of much philosophical debate. I think many scientists are uncomfortable with the thought that we, life, our planet, or the galaxy occupy any "preferred" or special place within the universe. But when it comes to the existence of the universe as a whole, including the laws of physics itself, then maybe the anthropic principle has a point. Afterall maybe there are an infinite number of universes (in space and time) of which we are one of only a few that has a sustainable structure. I don't think this is a question that we will have any answer to anytime soon, if ever.

As for using maths, it is based on logic and the initial assumptions only. It is hard to see that this, in itself, is refutable. Statistics can be problematic because the question being asked has to be interpreted correctly and the resulting answers are further open to interpretation, even though the calculations themselves are precise. Saying the chance of getting 7 heads in a row from 7 flips is 1 in 128 is absolutely correct and is fairly easy to understand. There are some uses of statistics that are not easy though, and when these are applied to complex subjects, the outcomes can be presented to support a particular view. This is not the maths at fault, but those who choose to selectively employ the results to support their views.
 

lyner

  • Guest
Could a coin really land tail-side up 1000 times in a row?
« Reply #14 on: 06/08/2008 22:27:40 »
The problem with trying to argue for or against there being more to it than mere chance that we are where we are now is that the numbers involved are so enormous. Your brain just trips out when trying to have a sensible opinion about really big numbers.

The theory behind the probabilities of tossing coins (and all the other scenarios) assumes that the system has no memory. This means that, whatever happened in the past has no bearing on what will happen next; each new throw is a brand new situation. Not all situations follow this simple rule; if the chances of you biting your tongue during the next meal (I just did this so it's a good example at the moment) is 1/100 then you couldn't say that the chances of biting your tongue in two successive meals would be 1/10000 because your tongue has a 'memory' and swells up, making it more vulnerable for the next few hours.

When considering the probability of life getting to the stage it has reached you are not dealing with a memoryless system. Once a simple organism has arrived (by 'chance') then the organism's structure and the way it lives is not memoryless. Probabilities of more complex organisms developing can become much much greater than a simple calculation might suggest.

Looking at the numbers involved, I am staggered at how FEW genes we have in our DNA. Most estimates put the number at well less than 100 thousand. Just imagine how big an instruction book you'd need  if you wanted to describe how to build a person in the same way as you describe building a car. Life has, I believe, arrived - by chance - but it wasn't just the structure that arrived, it's the dynamics and methodology of the 'life system' which was the really lucky bit.

If your coin tossing gave you 1000 heads in a row, you might start to look at the system to see whether someone had tinkered in some way or whether the system was not as simple as you thought. You'd look for magnets, glue, asymmetry etc. (or even that your tossing machine was so precise that there was no random element involved at all). If you could find nothing to explain the statistics, then the next throw would be equally likely to give you heads as tails. If you could find some 'intervention' you might not be surprised at another 1000 heads. I, personally, would assume, if I had not found any explanation when I got 1000 heads in a row, that I had missed something and not that 'someone else was involved'. In many ways, the 'someone else' idea  is a bit of a cop-out but I realise that this is dismissing the idea of God in a very glib way.
« Last Edit: 06/08/2008 22:30:45 by sophiecentaur »
 

Offline livingod101

  • Jr. Member
  • **
  • Posts: 15
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #15 on: 21/08/2008 19:44:34 »
I know this isn't a math forum, but I've been thinking about how math works (or doesn't work) in reality. For example, math states that there is a possibility that I can flip a coin a thousand, or even a million times and have the coin land tails every time (assuming that the coin and flipper are NOT in a perfectly controlled and finely tuned environment where physics would cause the coin to land on tail every time). But is it REALLY possible to have this kind of outcome in reality? Does this mean that using math to predict something in science is invalid?

I loved this discussion.  Don't know about mathematics or probabilities (not saying I don't know), but I used love tossing coins.  To the point I got so good, I realized there is a timing and power behind the flip.  So based on that I was (not anymore) able to predict the side of the coin landing, perfectly (American quarter is the best).  So at that time with my skills if someone asked me to flip 1000 tails (or heads) I may have been able to do it (over some time).

Now does that mean anything, no, it's just a story :)
 

lyner

  • Guest
Could a coin really land tail-side up 1000 times in a row?
« Reply #16 on: 25/08/2008 23:29:45 »
This is now into the realm of skills and not probability of random events. People with high skill at some games (small bore rifle shooting, for instance) are incredibly consistent and can repeat maximum scores again and again. The range of the variation of their results is very small and only a minority of shots may be worse than 10 as a consequence.
 

Offline Alan McDougall

  • Neilep Level Member
  • ******
  • Posts: 1285
  • Thanked: 14 times
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #17 on: 27/08/2008 13:19:38 »
Nearly impossible but given an eternity anything that can happen will happen.

Of course one could design a coin to do this, Weighted on one side

Regards

Alan
 

Offline neilep

  • Withdrawnmist
  • Naked Science Forum GOD!
  • *******
  • Posts: 20602
  • Thanked: 8 times
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #18 on: 27/08/2008 13:35:51 »
Would the way the coin is tossed repeatedly and the facing side help to equate a 50/50 chance over a thousand tosses ?

ie: alternate between starting with heads and tails facing upwards ?
« Last Edit: 27/08/2008 13:47:27 by neilep »
 

Offline TheHerbaholic

  • Full Member
  • ***
  • Posts: 67
    • View Profile
Could a coin really land tail-side up 1000 times in a row?
« Reply #19 on: 31/08/2008 06:51:32 »
Xin, I understand what you're getting at and life and the universe will in time, be explained by science.

I'm sorry to say this but, if god did create the universe, and us.. then who made god?

Rather than believing in god creating the universe, then having the problem of explaining who made god, I'd rather just have the problem of explaining how the universe came to be.

Many people believe in god for their own personal reasons, maybe you find strength from god. But how could anybody ever seriously use god as a FACT of creation for the universe. It's like a very old fairy tale passed through generations. Peoples belief in god is faiding, hardly anybody goes to church on a Sunday anymore. More so, if for not believing in god I'm going to go to hell, then great. I just hope I can take some kebabs to cook on the flames.

Now back to the point you're making of basically saying maths in science does not work. If you believe life was created by god for the reason scientists can't make a mathematical model of the chances that were taken to take us to this point - existence, please put a little more thought into it. If you want to keep this simple, and look at it as flipping as a coin which was how you started your theory of incorrect science. Then think about this, think of the coin being flipped, it has to land on heads a thousand times in a row before life is created. The coin will, eventually, given billions of years of being flipped, produce a thousand heads in a row.

But if you still disbelieve Science and maths, if we had more people like you in the world, we would of never left the gravitational pull of the earth. And possibly still believe in a real kingdom in the clouds.
 

Offline _Stefan_

  • Hero Member
  • *****
  • Posts: 814
    • View Profile
    • My Photobucket Album
Could a coin really land tail-side up 1000 times in a row?
« Reply #20 on: 31/08/2008 12:42:20 »
It is a mistake to think that life is here by chance. The molecular precursors of life and the very first microbes arose as a result of the chemistry and physics of this universe. There is chance involved in this. But once there are replicators (RNA, DNA, and later, early cells), natural selection can act. Natural selection works by favoring the replicators that are good at surviving and reproducing, over those that are less able. Over time, there is a build up of function. There is some chance involved also in the variation of a population of replicators, but natural selection is the non-random determiner of which variations survive and which do not.

As others here have said, however unlikely it is that we are here, we must be one of the rare instances where life has happened, otherwise there would be no-one here to talk about it.
 

lyner

  • Guest
Could a coin really land tail-side up 1000 times in a row?
« Reply #21 on: 31/08/2008 18:00:16 »
Would the way the coin is tossed repeatedly and the facing side help to equate a 50/50 chance over a thousand tosses ?

ie: alternate between starting with heads and tails facing upwards ?
Exactly half and half is very unlikely. About half and half is very likely.
 

The Naked Scientists Forum

Could a coin really land tail-side up 1000 times in a row?
« Reply #21 on: 31/08/2008 18:00:16 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums