The dumb questions thread

[Bomb#20]

Most practical applications of pretty much anything would consider plus or minus 5% an excellent degree of accuracy.

Obviously there are some applications that require much greater precision. But I would estimate* that that's fewer than five percent of real world applications.

95% of statistics are made up on the spot.

 

[barbos]

Well, I remember Pi to 3.1415926536 and e to 2.718282

 

[Swammerdami]

Well, I remember Pi to 3.1415926536 and e to 2.718282

I find it easier to remember Euler's Number as 2.718281828. Almost poetry.
If you want a rational approximation to compete with pi's 355 / 113, your best bet may be 2721 / 1001.

 

[Loren Pechtel]

All this talk of pi.

 

[Gun Nut]

Finding meaning in Base 10? what, still counting on our fingers and toes, kids?

 

[Keith&Co.]

Finding meaning in Base 10? what, still counting on our fingers and toes, kids?

Um, i can count to 1023 on my fingers...

 

[bilby]

Finding meaning in Base 10? what, still counting on our fingers and toes, kids?

EVERY base is base 10. You're going to need to be more specific.

 

[Jimmy Higgins]

Can the spacetime fabric exist without matter? IE, when the last particle that has mass withers into the dustbin of time, is there any significance to that? Or as mass withers away into energy, does this impact the universe's expansion? I realize this is 10^40ish years (I think) into the future.

 

[bilby]

Can the spacetime fabric exist without matter? IE, when the last particle that has mass withers into the dustbin of time, is there any significance to that? Or as mass withers away into energy, does this impact the universe's expansion? I realize this is 10^40ish years (I think) into the future.

The spacetime fabric is a roiling seething soup of particles, some with rest mass, constantly popping into existence with their anti-particle partners and re-annihilating each other. There's always going to be particles, as long as there's space. A vacuum isn't empty. Although, on average, it is. So it depends how closely you look.

Black holes evaporate over time because of this - every so often, a particle anti-particle pair arises near, but outside, the event horizon, and only one of the pair is captured, with the other escaping. The first law tells us that this reduces the mass of the black hole, as it is equivalent to the black hole radiating the escaping particles. This is called Hawking Radiation, because it was theorised by Stephen Hawking as part of his work on Black Holes. The smaller a Black Hole gets, the more rapidly it radiates away its mass, until eventually it evaporates completely.

 

[Wiploc]

Can the spacetime fabric exist without matter? IE, when the last particle that has mass withers into the dustbin of time, is there any significance to that? Or as mass withers away into energy, does this impact the universe's expansion? I realize this is 10^40ish years (I think) into the future.

Space exists anywhere there is energy.

Photons, for instance: Space exists anywhere there is electromagnetic radiation.

 

[George S]

Can the spacetime fabric exist without matter? IE, when the last particle that has mass withers into the dustbin of time, is there any significance to that? Or as mass withers away into energy, does this impact the universe's expansion? I realize this is 10^40ish years (I think) into the future.

Space exists anywhere there is energy.

Photons, for instance: Space exists anywhere there is electromagnetic radiation.

Each point in space is a white hole from which spacetime grows at 1 light-second/second. Energy is constant. The net effect is spacetime becoming more dilute -- "expanding" -- going through phase changes.
Photons are nature's way of moving energy from (x,y,z,t) to (x',y',z',t'). The photon's clock cannot move when traveling at c as a particle. It is as it was in the beginning at its ending. Then, again, photons are not particles exactly. The wave of energy can have a higher frequency when received than when created (blue shift). This behavior is characteristic of waves. Yet a photon delivers its energy particle-like to exactly one electron in some atom.
Particles define the "downhills" of space affecting the paths energy can travel probabilistically. The speed of light in a non-vacuum is less than c.
To answer the original question -- without matter time stops for all the remaining energy moving at c. A literal end of time.
That's my dumb answer which raises a new dumb question.
Given some matter, somewhere (absolute vacuum does not exist in a real universe) doesn't that mean that no light actually travels at the speed of light -- c?

 

[Shadowy Man]

That's my dumb answer which raises a new dumb question.
Given some matter, somewhere (absolute vacuum does not exist in a real universe) doesn't that mean that no light actually travels at the speed of light -- c?

Since c is now a defined quantity that means that the vacuum permeability is a measured quantity now, so I expect that one can in principle measure this for various levels of vacuum. My guess is the differences between most outer space vacuums and “pure” vacuum are negligible, but you’re technically correct that there’s a non-zero difference.

 

[George S]

For what it's worth I now doubt my favorite origin theory (which was an anti-universe collapsing into ours.) I just watched https://youtu.be/1zXC51o3EfI. I now like Penrose's theory. Quite compelling.

 

[steve_bank]

Space is an arbitrary concept for visualizing reality.

A vacuum like space has a measured impedance of about 377 ohms. The ratio of E/H in an EM wave, electric to magnetic fields. Antennas serve as an impedance match to free space.

What does it all mean? I have no idea. All we know is the model works to design antennas and predict how EM waves act.

I like the white hole idea. The Pimple Theory.

 

[Angry Floof]

Dumb question about battery life, the kind of batteries you buy in bubble packs and such, not laptop or phone batteries, although the answer probably applies to those, too.

How precise is battery life? Say a few batteries are created and charged all at the same time, and then they all end up in the same consumer package, and they are purchased and used in all the smoke alarms in a house (say 3 alarms).

So here's the question: What are the odds that all three batteries will die at precisely the same time down to only a second or two difference?

 

[Bomb#20]

So here's the question: What are the odds that all three batteries will die at precisely the same time down to only a second or two difference?

One in a trillion, near enough.

 

[Angry Floof]

So here's the question: What are the odds that all three batteries will die at precisely the same time down to only a second or two difference?

One in a trillion, near enough.

Can you explain for a layperson why that is?

 

[steve_bank]

A real example.

In the 90s a twin engine commercial jet flying in Florida first first the ekctrical generator on one negine, then the generator on the other engine.

Some jets have a backup turbine generator, you can see the exhaust pipe on the tail. The pilots tried to start the generator using the backup batteries and the batteries failed leaving the plane without electrical power.

The odds of that are low, it was triple redundancy. Low probabilities can and do happen.

Fortunately the plane was not fly by wire, the controls were connected to the control surfaces with cables. The throttles were connected to the engines with cables. They landed successfully.

My company built the battery charger but we were not at fault.

You have to know the failure distributions for the batteries.

You have two batteries each with a 80% probability of lasting 100 hours. What is the probability of both failing by 100hours?

I have not heard of greater than triple redundancy. The Space Scuttle had three redundant computers.

 

[bilby]

So here's the question: What are the odds that all three batteries will die at precisely the same time down to only a second or two difference?

One in a trillion, near enough.

Can you explain for a layperson why that is?

I think the odds are MUCH shorter than that.

It's going to depend on a lot of factors, but the manufacturer likely has a target capacity that they hit fairly closely; If you are selling 300mAh batteries, then you don't want to have many leaving your factory with an actual capacity of 350mAh, because that implies a wasteful production process; And you don't want any below the specification, if you're ethical and/or concerned about being sued or fined for selling products not fit for purpose.

The other major variable is the current draw of the smoke detectors, which for similar units will again be unlikely to vary very much.

If the variation in battery capacity is 5mAh, and the current draw is exactly 1mA (numbers ex ano for illustrative purposes only), then the odds of failure within plus or minus 2.5 seconds are very crudely one in the number of 5 second intervals in 5 hours, or 1:3600

However, this assumes that the distribution of actual capacities is random. More plausible is that they are normally distributed, with far more batteries having capacity close to the central value than have capacity at the extremes of the distribution (or even outside it).

This could easily bring the odds down to one in a few hundred - and that's for each pair of smoke alarms, on each occasion that the batteries are simultaneously replaced. Replace the batteries simultaneously every six months for a decade on a half dozen smoke alarms, and the odds of two simultaneously running out could be very high indeed - certainly high enough to be fairly unremarkable if it happens.

But the number of variables is very high, so any odds you calculate are going to be very woolly indeed.

 

[Angry Floof]

Can you explain for a layperson why that is?

I think the odds are MUCH shorter than that.

It's going to depend on a lot of factors, but the manufacturer likely has a target capacity that they hit fairly closely; If you are selling 300mAh batteries, then you don't want to have many leaving your factory with an actual capacity of 350mAh, because that implies a wasteful production process; And you don't want any below the specification, if you're ethical and/or concerned about being sued or fined for selling products not fit for purpose.

The other major variable is the current draw of the smoke detectors, which for similar units will again be unlikely to vary very much.

If the variation in battery capacity is 5mAh, and the current draw is exactly 1mA (numbers ex ano for illustrative purposes only), then the odds of failure within plus or minus 2.5 seconds are very crudely one in the number of 5 second intervals in 5 hours, or 1:3600

However, this assumes that the distribution of actual capacities is random. More plausible is that they are normally distributed, with far more batteries having capacity close to the central value than have capacity at the extremes of the distribution (or even outside it).

This could easily bring the odds down to one in a few hundred - and that's for each pair of smoke alarms, on each occasion that the batteries are simultaneously replaced. Replace the batteries simultaneously every six months for a decade on a half dozen smoke alarms, and the odds of two simultaneously running out could be very high indeed - certainly high enough to be fairly unremarkable if it happens.

But the number of variables is very high, so any odds you calculate are going to be very woolly indeed.

And if the number of smoke alarms is 3 or more, the odds be much higher still. Thanks!