Calculus junkies

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For the calculus junkies:

The longer an inevitable occurrence does not happen, the higher the probability of it happening becomes.

Furthermore, I fail to see what your post has to do with calculus.

That is untrue. If the occurrence is inevitable, then the probability of its occurrence is 100%. A probability cannot be higher than 100%, so the probability of the occurrence of this event cannot possibly increase.

2. She might mean that calculus is needed to determine such probabilities. In this problem we would create a distribution function to represent the per day probability of the Sun going out,

then integrate that function to determine probabilities.

For the calculus junkies:

The longer an inevitable occurrence does not happen, the higher the probability of it happening becomes.
Ok
While the existing pattern may cause complacency.*
All humans may comprehend this.
The sun may rise in the morning, but it will not rise every day forever. The Earth will not support life forever. (See LaPlace')
This is not a probability, but a certainty.

How would we know the probability per day without knowing how much time is left before the event occurs?

For example, if we know that the event will occur sometime within the next week, the probability of it occurring today would be 1/7, the next day, 1/6, and so on. Using the OP's example, no one has a precise idea of how many days are left until the sun "stops rising," so we'd have nothing on which to base our probabilities. ?

Integration is only meaningful for continuous functions. If we are to represent probabilities per day, then wouldn't we have a discrete function, and be obliged to use summation?

1. I believe she is saying the *probability per day* increases, since it is inevitable. For example, some astronomers say the Sun will inevitably die, and the life on Earth will consequently die thereafter, however, the probability it will happen tomorrow is not 100%.

If any astronomers say that, then they should be summarily fired from their jobs for being incompetent.

All life on Earth will die long of years before the sun dies.

But, astronomers not being specialists in biology, would lack of that knowledge really imply incompetence?

And, now that I've noticed it, what do we even mean by "die" in reference to the sun?

Yes it would imply incompetence. I can't imagine any legitimate astronomer not being at least aware of the events that will happen as the Sun runs out of hydrogen to use to fuel its nuclear fusion.

When the Sun runs out of hydrogen,

The astronomical events, sure, but the biological events? For all life, even viruses and bacteria?


This is what you mean by "die"?

I would say the the Sun dies when it cools off and no longer shines.

How many viruses and bacteria will be able to survive billions of years of heat near or higher than that of boiling water?

About 1.2 billion years from now, the sun will begin to change. As the hydrogen fuel in its core is used up, the burning will spread outward toward the surface. This will make the sun grow brighter. This increased radiation will have a devastating effect on our planet. ...

The mean surface temperature of the earth will rise from about 68°F to 167°F. The earth’s oceans will evaporate. The planet will become a stark, lifeless desert.

...

Finally, as it approaches the age of 5-8 billion years, the sun will run out of hydrogen almost entirely. When the sun uses hydrogen to create energy, it changes it to helium. After all these years, the core of the sun will be filled with left-over helium. This helium will become unstable as it begins to collapse under its own weight. The core of the sun will become even denser and hotter. As this happens, the sun will swell one-and-a-half times its normal size and grow more than twice as bright as it is now.

...

At the age of about 11-12 billion years the sun will blow off more than a quarter of the mass of its outer surface. With a less massive sun to attract them, the planets’ orbits will change. Venus will become as distant as the earth is now, and the earth will move even farther away. Eventually, the ever-swelling sun will become a red giant. It will become 166 times larger than the sun we knew. This is almost as large as the orbit of the earth today. The planets Mercury and Venus will be devoured in the flames of the giant star. The mountains of the earth will melt and flow like red-hot molasses into vast, flat seas of lava. A bloated red sun will fill more than half the sky.

...

When the sun reaches its maximum size as a red giant, the helium core will reach a temperature of 100 million degrees. This is hot enough to trigger helium fusion. When this happens, helium atoms are crushed together, releasing huge amounts of energy in the process. At first it will seem as though the sun has gotten a new lease on life. It will shrink in size, though it will never get less than ten times its present size. It will begin a period lasting for the next 110 million years during which little change will occur.

...

Out of fuel, the sun will approach the beginning of the end. It will grow to an enormous size as the last gasps of helium and hydrogen are blown away. It will become 180 times larger than the sun we know and thousands of times brighter. Huge quantities of its atmosphere will be thrown off into space, until nearly half its mass is lost. The loss of mass will cause the planets Venus and the earth—-now little more than burned-out cinders—-to move even farther away.