# re: "Finite" For "Greater Than Zero"page 22

•  197
Speaking of airlines and their symbols: . I can't wait to meet some of their flight attendants.

Aren't they famous for their wings?

Their rudders aren't too shabby either.

dg (domain=ccwebster)
If you and I each privately write down a 5l-digit ... this? That's the magnitude of odds Borel is talking about.

That's not the meaning I take out of Borel's 'specified', although those events might be included in the class specified. ... in a vacuum, say, one could in principle measure that to an accuracy of greater than one part in 10[/nq]^50.
Borel would apparently say that this specified quantity couldn't have this value by chance since it is too improbable that it should have precisely this value.

Honey lamb, you specify it, then we'll talk.
What he said is closer to: if you did name (that's specifying) the precise speed of light (or any other thing) to fifty decimal places (of some unit) and then, somehow, it turned out you were right to the penny was that by chance? Borel would say, no. You don't get to be that extremely right by a lucky guess. You had to have known what you were doing.
Smaller numbers, you might get lucky and guess right; people do win the lottery. Incomprehensibly large numbers, no. (For a value to "no" that means "near enough to No as makes no difference.")

If I open my mouth and make noises, and what comes out is a famous poem, nearly word-perfect is that because I randomly generated bits of noise and got extraordinarily lucky, or because I once learned the poem and still know it? Some things don't happen by chance. Most things.

So no, Borel isn't saying whether light "got" its speed "by chance" or some "divine creator," any more than he's talking about who wrote that poem I just described, or who is buried in Grant's Tomb. He's not talking about causation of events or their nature. What he's talking about is the mathematics of "Probability," of predicting events.

I wish you could get that what you think he says is not what he said, and I wish his fuller text was on-line so that you wouldn't have to take my word for it, which you appear reluctant to do (and rightly so).

Another illustration (which I'm slightly reluctant to bring up because everyone and his brother feels they know something abut flipping coins) would be - suppose you flip a coin over and over and over and it keeps coming up heads. Most of us know that that theoretically can happen, given the nature of probability. Yet, at what point do you or I or anyone become totally convinced that the coin is loaded, that we are not seeing a truly random series of events, but a false coin? Borel would suggest a cutoff point a number of flips that essentially could not have happened by random chance...
By my reckoning, the odds of getting N heads in a row is l out of 2^N. Since 2^10 is roughly 10^3, that means 10^51 is approximately equal to 2^170. Borel's test would say that if you get 170 heads in a row, you can be sure this isn't chance. The odds against flipping that many heads in a row, with a fair coin, are simply astronomical. It's far, far more likely that someone tinkered with the weight of a coin that came into your possession.
I suspect most of us would be suspicious long before 170 trials, actually.
OTOH, unless one posits divine intervention, then it is difficult to see that c has this value, except by chance, or because it is determined by other constants that themselves have values determined by chance.

That's a different subject. He's not talking about why the speed of light *is* what it is.
Essentially this is my problem with Borel's statement, it invites one to seek a first cause.

Try thinking about middle causes. I think Borel would probably point out there is a huge region between pure random chance on one hand, and divine intervention on the other. Maybe scientists and mathematicians don't think a lot about what it means for any event to happen "on purpose" instead of "by accident," but even a small child knows there's a difference. And it's not about God.
Some people, of course, see the existence of a universe that depends for its stability on certain physical constants having narrowly constrained values as proof of the existence of God.

Yeah, I know. This is not about God.

Best Donna Richoux
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That's not the meaning I take out of Borel's 'specified', ... to an accuracy of greater than one part in 10[/nq]^50.
Borel would apparently say that this specified quantity couldn't have ... is too improbable that it should have precisely this value.

Honey lamb, you specify it, then we'll talk. What he said is closer to: if you did name (that's specifying) ... by chance. Most things. So no, Borel isn't saying whether light "got" its speed "by chance" or some "divine creator,"

But, my little chickadee, it appears Dembski is. I tried, but failed, to follow the link you gave. But a little googling took me to Dembski's personal website which is a list of articles attempting to prove the existence of the creator from 'Borel's Law'. Strange that I divined without knowing anything about Dembski.
any more than he's talking about who wrote that
poem I just described, or who is buried in Grant's Tomb. He's not talking about causation of events or their nature. What he's talking about is the mathematics of "Probability," of predicting events.

Try http://quaker.org/clq/2005/TQE118-EN-BorelsLaw.html for a less tendentious view of Borel's law.
I wish you could get that what you think he says is not what he said, and I wish his fuller text was on-line so that you wouldn't have to take my word for it, which you appear reluctant to do (and rightly so).

I'm happy with using significance levels of much lower than 10^50 for every day hypothesis testing - what I worry about is that people think the fact that low probability events happen allows other kinds of inferences.
Another illustration (which I'm slightly reluctant to bring up because everyone and his brother feels they know something abut flipping ... by random chance... By my reckoning, the odds of getting N heads in a row is l out of 2[/nq]^N.
Since 2[/nq]^10 is roughly 10^3, that means 10^51 is approximately equal to
2[/nq]^170. Borel's test would say that if you get 170 heads in a row, you
can be sure this isn't chance. The odds against flipping that many heads in a row, with a fair coin, ... a coin that came into your possession. I suspect most of us would be suspicious long before 170 trials, actually.

But that run of trials is no more unlikely than any other sequence. Your ascription of a special significance to this particular sequence is dependent on your theory of the process that generates the returns.
OTOH, unless one posits divine intervention, then it is difficult ... by other constants that themselves have values determined by chance.

That's a different subject. He's not talking about why the speed of light *is* what it is.

I don't think there's anything deep about Borel's Law. He was writing a popular book at the time and simplifying for a lay audience. The problem lies with the 'Intelligent Design' lobby who have taken up his work.
Essentially this is my problem with Borel's statement, it invites one to seek a first cause.

Try thinking about middle causes. I think Borel would probably point out there is a huge region between pure random ... "on purpose" instead of "by accident," but even a small child knows there's a difference. And it's not about God.

It's the asymmetry of the thing. You can't infer purpose just because unlikely things happen, but if things happen that shouldn't on the basis of your espoused theories the it may be time to look for a new theory.
There's nothing very deep or interesting about Borel's law, it's just standard theory of hypothesis testing that you can find in any introductory statistics textbook.
Some people, of course, see the existence of a universe ... narrowly constrained values as proof of the existence of God.

Yeah, I know. This is not about God.

Good, but a lot of people aren't clear on that.
Mike Page
(snip) You start with diploid cells and end with haploid gametes, each of which has half the genetic material.

But you end up with twice as many of them (actually, four times as many for the complete process)

Oh come on now. If you tear down your house and use the material to build a smaller house for yourself and another smaller house for your ex-spouse, you don't say "we both live in houses that are the same size as our old house", do you?
In the same way, these early cell biologists were interested in the amount of chromosomal material per cell, not the total amount in the world. And the amount per cell decreases in meiosis.
^50.

Sorry to break in on all this happy chirping,
but did you notice there actually is a FAQ on Borel and creationism?

Jan
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Honey lamb, you specify it, then we'll talk. What he said is closer to: if you did name (that's specifying) ... don't get to be that extremely right by a lucky guess. You had to have known what you were doing.

No problem at all for a big bad wolf:
the speed of light equals 1 (exactly of course)
to no less than infintely many decimal places.
Now if that isn't proof of divine creation,
Jan

"Tout est pour le mieux dans nĂ´tre monde, le meilleur des mondes possibles" (Pangloss)
...>>
Try http://quaker.org/clq/2005/TQE118-EN-BorelsLaw.html for a less tendentious view of Borel's law.

Sorry to break in on all this happy chirping, but did you notice there actually is a FAQ on Borel and creationism?

Thanks, says much the same as the URL I quoted, but adds some authoritative detail, AFAICS.
Mike
Mike Page
If you mean "odd" in the sense of "unusual" then ... way with other things for the purpose of a singletheorem.

I'm sorry you weren't here, Se=E1n, in the days of the endless discussion I started by claiming zero wasn't odd ... abused and misused. I'm still getting over it. Charles Riggs There are no accented letters in my email address

Sorry for the slow reply and my apologies also because I was not offering any mathematical support for your point of view.

I was only saying that using the popular non-mathematical meaning of "odd", many of the things discussed in this thread are odd. For example, I would be happy with this statement: "Zero is odd because you cannot divide by it". This is not formal mathematics just an informal comment with the everyday meaning of "odd" as "unusual".

However, I would not forbid you from redefining "odd" and "even" in anyway that suits you. As I have said many times, mathematics is not subject to any formal standard (e.g. ISO) and it does vary from mathematician to mathematician. The closest it gets to a standard is that most mathematicians happen to agree on something. We discussed whether or not zero is positive recently. The answer was that pretty all English speaking mathematicians today would say zero is not positive but a few foreigners say that it is both positive and negative.
Since "zero is even" is even (sic) more well agreed on than "zero is neither positive nor negative", you will need to clearly warn people that you are using a different definition of "even". And, if you want others to not think that you are a crank, you will need to show that something interesting results from your unusual usage. If you change the terminology but show no interesting consequence, you will be just as much a crank as the spelling reformists that appear in this group occasionally.
For me, a strong intuitive reason to call zero even is that the alternating odd / even pattern continues undisturbed past zero: 3, 2, 1, 0, -1, -2, -3. =20

Se=E1n O'Leathl=F3bhair
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