What is the Threshold of Intolerable Miraculousness?

[Eugene Shubert]

For the sake of argument, let's define a miracle to be something fantastically improbable.

Suppose that we have a biased coin that, if flipped, would almost always land tails-side up with a mathematical probability of (1-p); otherwise, it would land heads-side up with a mathematical probability of p.

By the threshold of intolerable improbability, I mean the largest mathematical probability p such that if we flipped our biased coin just once and it lands heads-side up, then there's nothing miraculous about that at all, but if we flipped that coin a second time and it lands heads-side up for a second time in a row, then we know that we have violated a known law of physics.

 

[danshawen]

For the sake of argument, let's define a miracle to be something fantastically improbable.

Suppose that we have a biased coin that, if flipped, would almost always land tails-side up with a mathematical probability of (1-p); otherwise, it would land heads-side up with a mathematical probability of p.

By the threshold of intolerable improbability, I mean the largest mathematical probability p such that if we flipped our biased coin just once and it lands heads-side up, then there's nothing miraculous about that at all, but if we flipped that coin a second time and it lands heads-side up for a second time in a row, then we know that we have violated a known law of physics.

A coin having two heads does not violate a known law of physics. Neither does a loaded pair of dice, or for that matter, the scientific discovery that different kinds of statistics apply to different kinds of fundamental subatomic particles.

Statistics is math, which is both a symbolic language in its own right and a tool of science, not subject to the same range of falsifiabilty as other science knowledge is. You can have good science supported by bad math (defined as math with mistakes), just as you can have bad science supported by good math (defined as consistent math that is not a complete physical description or model of the science).

No math is ever both consistent or complete, nor an accurate reflection of nature to the last arbitrary decimal place, and the science it supports suffers from many of the same shortcomings for the same reason(s).

Welcome back Eugene. You haven't posted in a while.

The world is full of miracles, every minute of every day, everywhere. Most people, who are miracles themselves, are just too jaded to notice.

You're certain you wanted this posted in "Physics and Math" and not "General Philosophy"? The natives here are a little touchy about what is science lately.

 

[spidergoat]

but if we flipped that coin a second time and it lands heads-side up for a second time in a row, then we know that we have violated a known law of physics.

No, not at all. Improbable things aren't impossible things, just unlikely. Unlikely things happen all the time.

 

[Eugene Shubert]

A coin having two heads does not violate a known law of physics.

No, not at all. Improbable things aren't impossible things, just unlikely.

Apparently, no one recalls that the probability for heads on the second toss, after the first toss resulted in heads, is still p. As all students of mathematical probability theory known, coins have no memory.

Nevertheless, I'm still serious about the opening question. Suppose now that we have two biased coins, where, for each coin, the probability for heads is p. What would be the threshold of intolerable improbability for getting two heads when flipping both coins independently?

 

[danshawen]

Nevertheless, I'm still serious about the opening question. Suppose now that we have two biased coins, where, for each coin, the probability for heads is p. What would be the threshold of intolerable improbability for getting two heads when flipping both coins independently?

Then you would have to deal with the probabilities of four cases to consider, assuming they are flipped together:

1. heads + heads
2. heads + tails
3. tails + heads
4. tails + tails

Also, you didn't specify HOW the two coins are individually biased. Is one biased heads and the other biased tails, or any of the other possibilities from the table? Not trying to be obtuse, Eugene; I just hate badly or ambiguously specified problems. We get enough of them here.

The "miracle", or unlikely outcome, if there is one, would then be if a coin biased heads comes up tails more than half of the time, or verse vicea.

Expectation values can be added, by the way.

It is well known that a U.S. Linoln penny is already biased 51/49 percent heads/tails because the side with Lincoln's face is heavier than the obverse.

At 51/49, the humble penny commemorates the bias in almost all recent U.S. general elections. In view of this convenient bias, I propose we forget voting, designate "heads" as "Democrat" and flip for the next presidential election. Just as fair, or actually, fairer than letting Putin bias our elections, I'll be bound. I would even support a constitutional ammendment along those lines. No more gerrymandering, no more electoral college. Pure statistics.

I want all political candidates to pass a civil service exam and an approved official application to purchase a firearm as a minimal sanity check, however. See how easy it is to make things oh so much better? Beats vetting candidates on reality TV. Now THAT would be a miracle.

http://www.smithsonianmag.com/scien...ds-in-a-coin-flip-arent-quite-5050-145465423/

 

[Eugene Shubert]

You didn't specify HOW the two coins are individually biased. Is one biased heads and the other biased tails?

How could I have stated it any clearer? I wrote: "Suppose now that we have two biased coins, where, for each coin, the probability for heads is p." Bias in coin-flipping simply means that p doesn't equal 1/2.

 

[danshawen]

How could I have stated it any clearer? I wrote: "Suppose now that we have two biased coins, where, for each coin, the probability for heads is p." Bias in coin-flipping simply means that p doesn't equal 1/2.

Because the probabilites for the outcomes is different depending on whether both coins are biased heads, both coins are biased tails, or a mixture of heads/tails or tails/heads.

Or to put it another way, 51/49 <> 49/51. Call them p1 and p2.

You could also just specify whether you are using real pennies or not. If they are, the bias is already 51/49 for heads/tails. That would clear it up in a hurry.

Everyone seems to be on my case about mathematical modeling of reality today. I am quite sane, and feel pretty good, and have more than enough advanced math instruction through vector calculus and linear algebra to do this. I know you do too, Eugene.

 

[danshawen]

Okay then. The "threshold of miraculousness" is a probability between 0<p< 1, exactly the same range as the answer to any other probability problem. Only values of 0 or 1 would be absolute certainty that something either will or will not occur, and the rest of the range would be eligible as "miraculous. Not really a threshold, but there you are.

Not an impressive answer, but then, it wasn't really a very impressive question, was it? That's because you failed to adequately define either your terms or the problem you were trying to solve.

As I originally suggested, "miraculous" should encompass a much wider range of experience than it typically does, all day, every day.

 

[Michael 345]

The threshold of miraculousness would be if

the coin (or coins)

land balanced on their edges

 

[Eugene Shubert]

You failed to adequately define either your terms or the problem you were trying to solve.

My definition of the threshold of intolerable improbability is clear enough. My purpose in creating that definition was to refute a mighty world religion. Undeniably, I overthrew that world religion by asking an unanswerable question that expertly eviscerates the common descent postulate:

If two or more distinct life forms developed on earth, far from each other, such that each of those life forms could eventually have descendants strikingly similar to the descendants of the other original life forms, then how could we determine the original number of distinct life forms?

Here is my summary of the non-answers I received:

"Indisputably, believing in one instance of the creation of life is the only conceptualization of miraculousness they can muster. And they insist that there wasn't anything miraculous about that event at all. On the other hand, if they had the courage to answer honestly, having to believe in two or more spontaneous creation events is going too far, since that level of miraculousness defies the second law of thermodynamics.

1 creation event is not miraculous.
2 or more creation events is inconceivably miraculous."

Their inanity is what I was attempting to model mathematically.

 

[Michael 345]

Undeniably, I overthrew that world religion by asking an unanswerable question that expertly eviscerates the common descent postulate:

You fell at the first moment out of the gate

Common descent is NOT a religion

If

You lost your jockey

Speculation no evidence

two or more distinct life forms developed on earth, far from each other, such that each of those life forms could eventually have descendants strikingly similar to the descendants of the other original life forms, then how could we determine the original number of distinct life forms?

Both horse and jockey have broken legs

Wild speculation and again no evidence

Indisputably, believing in one instance of the creation of life is the only conceptualization of miraculousness they can muster. And they insist that there wasn't anything miraculous about that event at all.

And broken arms

There is evidence it occurred and can be demonstrated

As has been shown on this thread it may have been a long shot none the less it happened

On the other hand, if they had the courage to answer honestly, having to believe in two or more spontaneous creation events is going too far, since that level of miraculousness defies the second law of thermodynamics.

A even longer shot which happened NOT to happen

1 creation event is not miraculous.
2 or more creation events is inconceivably miraculous."

1 long shot

2 even longer shot

Close enough to a matmatical representation

Incidentally one of the general theories about life in general is that it may have occurred more than once and both forms are still around today

Symbiogenesis, or endosymbiotic theory, is an evolutionary theory of the origin of eukaryotic cells from prokaryotic organisms, first articulated in 1905 and 1910 by the Russian botanist Konstantin Mereschkowski, and advanced and substantiated with microbiological evidence by Lynn Margulis in 1967. It holds that the organelles distinguishing eukaryote cells evolved through symbiosis of individual single-celled prokaryotes (bacteria and archaea)

The theory holds that mitochondria, plastids such as chloroplasts, and possibly other organelles of eukaryotic cells represent formerly free-living prokaryotes taken one inside the other in endosymbiosis, around 1.5 billion years ago. In more detail, mitochondria appear to be related to Rickettsiales proteobacteria, and chloroplasts to nitrogen-fixing filamentous cyanobacteria.

https://en.m.wikipedia.org/wiki/Symbiogenesis

In very simple terms two different types of cells became one when one swallowed the other and found each could give the other some thing they needed (arr soul mates )

And even that seems to have happened twice

Konstantin Mereschkowski's 1905 tree of life diagram, showing the origin of complex life-forms by two episodes of symbiogenesis, the incorporation of symbioticbacteria, to form nuclei and chloroplasts respectively.[1]

https://en.m.wikipedia.org/wiki/Symbiogenesis

 

[Eugene Shubert]

Common descent is NOT a religion

religion
noun
1. a set of beliefs concerning the cause, nature, and purpose of the universe, especially when considered as the creation of a superhuman agency or agencies, usually involving devotional and ritual observances, and often containing a moral code governing the conduct of human affairs.
2. a specific fundamental set of beliefs and practices generally agreed upon by a number of persons or sects.
3. the body of persons adhering to a particular set of beliefs and practices.

ipso facto
A body of believers pretending that two or more strikingly similar spontaneous creation events on earth exceeds a scientifically acceptable level of miraculousness is a religion.

 

[exchemist]

For the sake of argument, let's define a miracle to be something fantastically improbable.

Suppose that we have a biased coin that, if flipped, would almost always land tails-side up with a mathematical probability of (1-p); otherwise, it would land heads-side up with a mathematical probability of p.

By the threshold of intolerable improbability, I mean the largest mathematical probability p such that if we flipped our biased coin just once and it lands heads-side up, then there's nothing miraculous about that at all, but if we flipped that coin a second time and it lands heads-side up for a second time in a row, then we know that we have violated a known law of physics.

OK let's take you off Ignore and answer this, as there is a general point of possible interest to other readers.

There is no "threshold of intolerable improbability". This seems to be a term of your own invention.

There is a non-zero probability of a tossed coin, even a biased one, turning up heads 10 times in succession or even 100 times in succession. If the probability is not zero it can in principle happen. Of course one combination of outcomes may be a lot less likely than another, but then you are talking about which would be more likely, not whether one was actually impossible.

This is a discussion of probability. This is a branch of mathematics and as such has nothing to do with physics.

A miracle, however, is generally taken to be not just an improbable event, but one that is said to be inexplicable by natural causes and is thus said - by religious believers - to be due to divine intervention. Of course to non-believers, an event that seems inexplicable by natural causes suggests that maybe our model of natural causes may be incomplete.

 

[iceaura]

Incidentally one of the general theories about life in general is that it may have occurred more than once and both forms are still around today

The body of evidence still points to one surviving origin or original "pool" of all living cells, in the single remaining code and other shared chemistry. The multiple symbiotic events would have been made possible by their common basic code, strings of which could therefore merge over time within a shared translation machinery - the remnants of that joining are after all major pieces of evidence for that symbiosis.

There was once, in a yard off of a side street from West River Road in Minneapolis, a large bur oak that had grown a triangle: two major branches forking from the trunk itself shared a large side branch, which had truly and solidly joined one after growing from the other.

The bark covering was continuous - the triangle was not a contact point or overlapping but a solid, melded, heartwood to heartwood, bark enclosed join. It was difficult to tell which trunk branch was the origin of the cross branch. The cross branch was well over a foot diameter, and had the classic bur oak trunk and main branch bark as the other two did. The entire triangle was about twenty feet in the air.

 

[Michael 345]

religion
noun
1. a set of beliefs concerning the cause, nature, and purpose of the universe, especially when considered as the creation of a superhuman agency or agencies, usually involving devotional and ritual observances, and often containing a moral code governing the conduct of human affairs.
2. a specific fundamental set of beliefs and practices generally agreed upon by a number of persons or sects.
3. the body of persons adhering to a particular set of beliefs and practices.

ipso facto
A body of believers pretending that two or more strikingly similar spontaneous creation events on earth exceeds a scientifically acceptable level of miraculousness is a religion.

About the ONLY part of that definetion which relates to Darwinians (as a group) is that they are a group believing in common desent

Your particular definetion adds numerous extra beliefs

as well as a extra belief you have added

...... pretending that two or more strikingly similar spontaneous creation events on earth ........

How you decide they are pretending I have no idea

As for happening twice or more times that claim is backed up by evidence as detailed here

Konstantin Mereschkowski's 1905 tree of life diagram, showing the origin of complex life-forms by two episodes of symbiogenesis, the incorporation of symbioticbacteria, to form nuclei and chloroplasts respectively.[1]

https://en.m.wikipedia.org/wiki/Symbiogenesis

Since your definetion of religion contains by my count at least 12 aspects pertaining to religion of which only 1 pertains to Darwinians

ipso facto

belief in a common decendant is not a religion

Show proof of god creating life and

ipso facto

no more Darwinians

 

[Michael 345]

The body of evidence still points to one surviving origin or original "pool" of all living cells, in the single remaining code and other shared chemistry. The multiple symbiotic events would have been made possible by their common basic code, strings of which could therefore merge over time within a shared translation machinery - the remnants of that joining are after all major pieces of evidence for that symbiosis.

There was once, in a yard off of a side street from West River Road in Minneapolis, a large bur oak that had grown a triangle: two major branches forking from the trunk itself shared a large side branch, which had truly and solidly joined one after growing from the other.

The bark covering was continuous - the triangle was not a contact point or overlapping but a solid, melded, heartwood to heartwood, bark enclosed join. It was difficult to tell which trunk branch was the origin of the cross branch. The cross branch was well over a foot diameter, and had the classic bur oak trunk and main branch bark as the other two did. The entire triangle was about twenty feet in the air.

The triangle seems to be more a case of one branch rubbing together before blending

Konstantin Mereschkowski's 1905 tree of life diagram, showing the origin of complex life-forms by two episodes of symbiogenesis, the incorporation of symbioticbacteria, to form nuclei and chloroplasts respectively.[1]

https://en.m.wikipedia.org/wiki/Symbiogenesis

This is more a case of two distinct forms with seperate properties mixing

I guess thinking a little deeper the question could be asked

Were the two forms capable of becoming life in their seperate forms?

OR

Was their mixing one of requirements to life's originating?

 

[iceaura]

The triangle seems to be more a case of one branch rubbing together before blending

Exactly. The metaphor of the tree of life is pretty good.

Were the two forms capable of becoming life in their seperate forms?

They already were - they were each specific and fully developed living organisms. That's what symbiosis involves.

 

[danshawen]

1 creation event is not miraculous.
2 or more creation events is inconceivably miraculous."

You mean like, for instance, the creation of separate evolutionary tracks for PLANTS and ANIMALS would be two events that are inconceivably miraculous, Eugene?

I would agree with your premise, but I honestly wouldn't know how to model that mathematically; let me think about it a while. I'll get back to this thead. Good one, Eugene!

I keep telling folks, lots of things are miraculous o this planet alone. They don't believe me.

 

[Michael 345]

You mean like, for instance, the creation of separate evolutionary tracks for PLANTS and ANIMALS would be two events that are inconceivably miraculous, Eugene?

The division of life into two branches

Plant and

Animal

is ONE event

Mathematically you might try

1 = 1 + 1

equals

Common ancestor 1 equals = Plants 1 plus + Animals 1

Your on your own now

I keep telling folks, lots of things are miraculous o this planet alone. They don't believe me.

I'm sure many do believe you

Only the pesky ones who want evidence don't believe

 

[danshawen]

Plant and

Animal

is ONE event

I see your point. Still thinking...