Free Will and an Infallible God

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Cain
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Post by Cain »

No, it won't. Marius is right. The overall result depends on the totality of the unpredictable factors. Your equation is merely an approximation.
Actually, it's not; and I can prove it by using the example as a whole.

Let's take one liter of water, and add 3.00 mol NaCl at point X. At time Y+ (any time after the net movement has exceeded the distances availiable) I can take the whole sample, and demonstratably show that we now have 3.00M NaCl(Aq). It cannotbe more or less, due to the conservation principle.

What you're forgetting is that molarity is merely a statement of concentration, and not position. As I stated, the math to describe the exact positions of each Na+ ion does not exist today. However, we can predict the overall concentration *without* having to calculate the exact positions. The exact positions of the particles don't really matter.

Let's use blood as an example. Marius will gleefully pounce on any errors I make, so we'll use him for a fact checker. Okay, so when O2 enters the bloodstream at the pulmonary capillaries, the diffusion gradient causes O2 to be exchanged with CO2, saturating our blood with oxygen. This is pretty basic stuff, so far.

However, that amount of O2 isn't sufficient for our needs. What happens is that the O2 binds to Hemoglobin, which effectively takes it out of the gradient. So, more O2 diffuses in, gets bonded to hemoglobin, etc, etc. Given standard conditions, I can then predict how much O2 is being absorbed by the capillaries at any given moment. (The Starling equasion, basically.)

Now, it doesn't matter where in the alveoli the O2 happens to be during this exchange. If you stop and think about it, though, it should be highest at the points furthest away from the epithelium, where gas exchange does not occur. But even with a mismatch like that, I can still correctly predict the rate of exchange.

See what I'm getting at? I don't need to know the exact number and position of molecules to provide some very exacting results. In fact, it will be exact; you should be aware of the principle of significant figures.
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Marius
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Post by Marius »

Let's take one liter of water, and add 3.00 mol NaCl at point X. At time Y+ (any time after the net movement has exceeded the distances availiable) I can take the whole sample, and demonstratably show that we now have 3.00M NaCl(Aq). It cannot be more or less, due to the conservation principle.

What you're forgetting is that molarity is merely a statement of concentration, and not position. As I stated, the math to describe the exact positions of each Na+ ion does not exist today. However, we can predict the overall concentration *without* having to calculate the exact positions. The exact positions of the particles don't really matter.
That's not what you said, though. You didn't say you could calculate the "overal concentration." You said you could "predict the exact salinity at any given point in the vial..." You will, of course, know definitively what the overall concentration is, however local concentrations will vary, due to vagaries in the positions of Na+ ions.
There is then a need to guard against a temptation to overstate the economic evils of our own age, and to ignore the existence of similar, or worse, evils in earlier ages. Even though some exaggeration may, for the time, stimulate others, as well as ourselves, to a more intense resolve that the present evils should no longer exist, but it is not less wrong and generally it is much more foolish to palter with truth for good than for a selfish cause. The pessimistic descriptions of our own age, combined with the romantic exaggeration of the happiness of past ages must tend to setting aside the methods of progress, the work of which, if slow, is yet solid, and lead to the hasty adoption of others of greater promise, but which resemble the potent medicines of a charlatan, and while quickly effecting a little good sow the seeds of widespread and lasting decay. This impatient insincerity is an evil only less great than the moral torpor which can endure, that we with our modern resources and knowledge should look contentedly at the continued destruction of all that is worth having. There is an evil and an extreme impatience as well as an extreme patience with social ills.
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FlameBlade
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Post by FlameBlade »

and using mathematician's definition of point. At that the point, it's either: empty space, or an atom. An single atom :)
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3278
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Post by 3278 »

Marius and Flame are both correct, although Marius is less nitpicky. :)
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Cain
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Post by Cain »

That's not what you said, though. You didn't say you could calculate the "overal concentration." You said you could "predict the exact salinity at any given point in the vial..." You will, of course, know definitively what the overall concentration is, however local concentrations will vary, due to vagaries in the positions of Na+ ions.
If that were true, then at some point random forces would produce net movement of Na+ ions against the gradient. Random forces would eventually cause crystal formation to occur. That doesn't happen.

What you're saying is that at some point when I reach for that 3.00M bottle of medication, at some point the first dose will randomly make itself into 6.25M. Has that ever happened? More importantly, does it happen often enough to ruin your experiment or kill a patient?

The overall point, however, is that free will may not matter at all. If a supreme being exists, then he/she/it/they may have simply accounted for free will in the same way that we account for the random movement of particles. Individual movements may be unpredictable, but overall patterns are very easily detected.
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Marius
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Post by Marius »

If that were true, then at some point random forces would produce net movement of Na+ ions against the gradient. Random forces would eventually cause crystal formation to occur. That doesn't happen.
Yes it does. If you haven't seen it yet, then you haven't waited long enough.
There is then a need to guard against a temptation to overstate the economic evils of our own age, and to ignore the existence of similar, or worse, evils in earlier ages. Even though some exaggeration may, for the time, stimulate others, as well as ourselves, to a more intense resolve that the present evils should no longer exist, but it is not less wrong and generally it is much more foolish to palter with truth for good than for a selfish cause. The pessimistic descriptions of our own age, combined with the romantic exaggeration of the happiness of past ages must tend to setting aside the methods of progress, the work of which, if slow, is yet solid, and lead to the hasty adoption of others of greater promise, but which resemble the potent medicines of a charlatan, and while quickly effecting a little good sow the seeds of widespread and lasting decay. This impatient insincerity is an evil only less great than the moral torpor which can endure, that we with our modern resources and knowledge should look contentedly at the continued destruction of all that is worth having. There is an evil and an extreme impatience as well as an extreme patience with social ills.
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3278
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Post by 3278 »

You can even compute the exact odds. They're not good - Dawkins has done similar calculations - but they're quite possible.
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Cain
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Post by Cain »

You can even compute the exact odds.
Out of curiosity, what are they? I have no idea how to even begin setting up the equasion.
Yes it does. If you haven't seen it yet, then you haven't waited long enough.
I've seen crystal formations due to evaporation and other factors, but not due to randome movement alone. Generally, the water evaporates first.
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