Estimating the age of the Universe, and getting it all wrong (1 Viewer)

Jon

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After watching the James Webb telescope launch the other day, I had a revelation that came to me as a bright white light. It came from the heavens.

The experts say the Universe is 13.8 billion years old. Yet many believe the Universe may have the potential to last for an infinite amount of time. Given that, probability would suggest to get the best estimate of the average age of something, you would choose the half way point, which would be the items age divided by 2. Let me give an example.

A human lifespan in the UK averages out to about 80. So, to get the best estimate of a human age, the most accurate prediction with the minimum error, given no other information, would be 80/2, or 40. If you were placing bets, and you said someone was 20, with no other information, and I said 40, I am more likely to be closer to the true age than you are, since more of the population would be closer to my estimate. Make sense?

The same applies with the Universe. But in this case, the potential age of the Universe is unending, so infinity/2 is still infinity. Accordingly, the most likely age of the Universe is inifinity, with infinite confidence. Therefore, the maths would suggest that to say it was 13.8 billion years old would be infinitely improbable. Or, in laymans terms, 100% wrong!

Your thoughts? :geek:
 
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AccessBlaster

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Still wrapping my head around this. :p

Telescopes as time machines​

How can we see the birth of stars and galaxies that happened billions of years ago.

“A telescope is really a time machine because light travels at a finite speed through the universe,” said Klaus Pontoppidan, an astronomer with the Space Telescope Science Institute in an interview with the Associated Press. “We see the universe as it existed when that light is emitted.”

For instance, it takes eight minutes for light to travel from the sun to the earth. So when you’re looking at the sun, you’re actually looking at the sun eight minutes in the past.
 

Steve R.

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It's the modeling. The modeling may not be correct. The modeling for estimating the age of the universe is based on the "Big Bang" theory being correct. I don't think that the "Big Bang" theory is correct, but then I'm a bit short on credentials since I'm not an astrophysicist.

There was a website devoted to disputing the "Big Bang" theory. The owner of the website died and the website appears to have subsequently disappeared. Had a lot of interesting articles documenting how the "Big Bang" theory was flawed.
 
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The_Doc_Man

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Given the current state of cosmological physics, the universe's estimated age is 13.8 billion years based the red-shift numbers that tell us how fast everything is moving away from us. The assumptions in deriving that number are the basis for some of the "Big Bang" controversy. However, the fact remains that if you have things moving away from you and you use math to "reverse time" via simulation, you get the "big crunch" at the indicated time.

Of course, Jon, if you try to use the "half-age" estimation, you run into the problem that when you say "at age 40" you have no idea whether that is 50% of your subject's life, or 90% or 30% - because using half-ages is a two-pass algorithm. Playing the odds works for populations but not for individual people.

And then there is trying to base this on mental age, and there you will find me to be totally aberrant anyway. I have absolutely NO intention of ever growing up.
 

Jon

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if you try to use the "half-age" estimation, you run into the problem that when you say "at age 40" you have no idea whether that is 50% of your subject's life, or 90% or 30%
Agreed. But choosing the half-way point gives the minimum error, on average. Imagine this...

Something has an average life of 10 million years. If someone then guesses the current age is 1 year, they may be correct. But the probability is that my guess would be closer to the true age if I chose 5 million years than 1 year. Why? Because there is a 50% chance that the item has an age of over 5 million years. That means my guess is closer to the truth than someone guessing 1 year for the 5 million+ group. And closer for the halfway point between 5 million years and 1 year. I hope this makes some sense to others. It does in my head!

Playing the odds works for populations but not for individual people.
If you throw a coin, you have a 50% chance of it landing heads. You don't have to have (a population of) multiple coins or multiple throws for those odds to exist. It is inherent in the coins design. Same for people. Same for the Universe?
 
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Minty

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@Jon - Without looking it up what do you think the odds are of someone in a room having the same birthday as you?
To be more specific how many people do you need in a room on average to get a match.

I think you'll be surprised at the answer.
 

Jon

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Intuitively, it would be 1 in 365. So I would say 365. But then again, it depends on if the distribution of birthdays is evenly spread throughout the year. i.e. the population has the same number of birthdays on Jan 1st, Jan 2nd etc. That is unlikely, since folks might be getting more randy during breeding season etc. :geek:

It is similar to the explanation about guessing someones age. Choosing the half age as an estimate is simplistic, because it depends on the population distribution. By this I mean that you are likely to get less people over 70 than under 10, because people die off more when older than when younger.

So, to answer the question what do I think the odds are, I think it would depend on when your birthday was, with some dates being more probable than others.

Unless this is a trick question! Or you are referring to DOB, instead of the day of the year.

Edit: Wait! 1 in 730! The reason is that I have to include myself in the numbers. Or 1 in 366. Trying to work out which it is. The latter. You would need 366 people. Final answer! Or is it! Probability can give you meltdowns! I think 366, since your birthday is already known. So you need yourself plus 365 other people in the room, ignoring leap years.

My answer above is ignoring uneven distribution of birthdays throughout the year.
 
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Steve R.

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Red shift, is it "real"?
Everything ages. Additionally, we do not live in a frictionless world.
This raises a possibility light, as it ages and/or interacts with other "stuff", becomes "tired" (slows down) and looks increasingly red.
Science is always evolving, maybe we have not yet uncovered all the effects that could be interacting with light, causing it to shift red as it traverses billions of light years.
 

Jon

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Forgive me @Minty if I disagree for a moment. Let me explain.

You said this:

Without looking it up what do you think the odds are of someone in a room having the same birthday as you?
To be more specific how many people do you need in a room on average to get a match.

Those two questions you asked in context above are actually different questions to that presented in the article you linked to. The article is asking about the odds of two people having a matching birthday. Your question was about the odds of someone matching MY birthday, given that I am already in the room too. The difference is, my birthday is known, while the articles case is two unknown birthdays.

Your second question in isolation would be an accurate representation of the articles question, but the first sentence modifies the meaning of the second question, since it states it is about my birthday, which is know.

Let us use dice as an example.

If I throw a six, you already have a known result. Then the chances of throwing another six are 1 in 6. So, although you have two sixes as the total outcome, since you already knew you had a six already, you are only calculating the odds of rolling a six on one die.

If I have not yet thrown any dice, the odds of getting two sixes are 1/6 x 1/6 = 1/36.

Both outcomes have two sixes thrown, but the odds are very different: 1/6 vs 1/36

Likewise, since your question was about having the same birthday as ME, I already know what my birthday is. So, it is like the "one roll of the dice" example given above. This question is different to the one in the article.

Nevertheless, the article shows just how unintuitive some of these paradoxes can be. Probability can be very complicated and it can twist your thinking into all sorts of contortions.

Edit: To add, I would not have guessed the answer to the articles question!
 
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NauticalGent

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NauticalGent

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My father in law and I have had a few conversations about this. He is a devout Pentecostal and a former pastor. He believes in the science yet also believes the "In the beginning" story.

My argument that is that one disproves the other. His is that God can do anything. It's always been a short conversation....
 

Minty

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@Jon I realised after I posted that I had messed up the question slightly, and you being an accurate chap, spotted it straight away.
My wife and Mum share the same birthday, and that article always springs to mind when it's that time of year.
 
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Jon

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There are many probability paradoxes that are so hard to understand. I think I mentioned one of them at AWF's, unless it was at The Mind Tavern. Can't remember which one. But here it is: The Monty Hall problem.

 

NauticalGent

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There are many probability paradoxes that are so hard to understand. I think I mentioned one of them at AWF's, unless it was at The Mind Tavern. Can't remember which one. But here it is: The Monty Hall problem.

Not bad, I like the way she explained it. Here was my first exposure to the "Game Show Problem":
 
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The_Doc_Man

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I know what everyone says and I know that Mythbusters did an experiment on this. But the explanation is wrong.

Follow this carefully:

1. Monty shows 3 doors, gives his usual "car & 2 goats" spiel. Contestant picks a door. For discussion, call it door number 1. (In fact, 3-fold symmetry of the problem allows door #1 to represent any of the doors.) So at this point we all agree that any door would have 1/n chance (for 3 doors, 1/3 chance) of hiding the car. All three doors are equal. EVEN AFTER THE PICK, the probabilities remain equal, because making a pick does not change the location of the car or YOUR knowledge of where it is located.

2. Monty shows one of the other doors. For discussion, call it door number 2. (Again, discussions of symmetry allow #2 to represent either choice.) It's a goat. Monty now gives the option to switch doors to #3. Everyone says "best odds are to switch."

This is the point where everyone mis-analyzes the problem.

In the earlier video (numberphile) there is a little scene where the three doors have 1/3 probability each. Then open one door, the goat steps out, and probability shifts to have 0 under door 2 and 2/3 under door 3. But if door number 1 has not been opened yet, this shift is INCORRECT. The probability shift SHOULD be that door 1 gets half of the probability from door 2, and door 3 gets the other half. Stated another way, from the raw probability viewpoint, since door 1 is not yet revealed, there is no reason to asymmetrically split the probabilities. So 1/6 probability shifts each way. That means you should have a 50/50 shot at the car, equal probability between the two doors. Granted, you would NOT shift to the known donkey door. Its odds are zero. But revealing the donkey cannot change the odds of only one door. It must affect all remaining closed doors.

Doing this the other direction, look at the chances to be wrong: The chance that you picked the WRONG door is (n-1)/n so for 3 doors, 2/3 chance each. Note that probabilities considered this way don't have to add up to 100%.

So you picked a door. The odds are 2/3 that you were wrong. But that is (momentarily) the same for each door. Now Monty shows door #2 and the donkey kicks up his heels. We now KNOW that door #2 has probability of 0/3 of holding the car. But what of the other two doors? The new information is that the car can only be behind 1 of 2 doors. So the odds of picking (or having picked) the wrong door are (n-1)/n - which is 1/2. You now have a 50-50 shot at either door being right.

Here is why the numbers come out like they do when you run the simulation ... the game is slightly rigged. Read this article


The reason the numbers come out like they do when you make any simulation is because the odds are skewed by the "hidden" rules that are listed in this article. The common description of the problem is incomplete.
 
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Jon

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Doc, are you saying that you should adopt the strategy to switch or to not switch?
 

The_Doc_Man

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Actually, I was modifying my post slightly and got whacked by a network glitch.

To switch or not to switch? That is the question. - Whether 'tis better in the mind to agonize over the chance of being zonked, or agonize over the pain of a wrong choice, and by choosing, end the debate....
 
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Jon

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Actually, I was modifying my post slightly and got whacked by a network glitch.
So, if I read your post correctly, you say there is no benefit to switching?
 

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