Could the universe be collapsing?

[caveman1917]

I'm not sure this is what you meant to say. I see no reason for an expanding universe to have to go through a singularity to start contracting, though a contracting universe might have to do so to start expanding again.

You're right, using a negative cosmological constant would work (or more general potentials that can be negative). From contraction to expansion does still require a singularity though, as we will always have (assuming the null energy condition).

Flatness isn't even a factor.

It is when disregarding the cosmological constant as i was doing, since we then have

and setting and having implies which in turn implies that the turning point cannot happen in finite time.

[neilzero]

Likely Newton's shell theorem assumed uniform density and a true sphere, otherwise there would be a net gravity at most locations in the interior. Neil

[Grey]

It is when disregarding the cosmological constant as i was doing...

Something that I've always thought was interesting is that back in the days when we assumed the cosmological constant was zero, the fate of the universe was tied to the flatness. So a closed universe would eventually stop expanding and begin to collapse, an open universe would expand forever, and a flat universe would continue to expand, but at a rate that approaches zero. But with a cosmological constant in the mix, that's no longer true. Depending on the values (and whether the "cosmological constant" is really constant; it could vary over time), you can have a closed universe that expands forever, or an open universe that eventually collapses. There are all sort of other interesting possibilities, like "loitering universes" that expand to a certain point and then stay at roughly the same scale for a long period of time before beginning to expand again. Even though many of those alternatives don't fit the universe we live in, I just always was intrigued by the increase in possibility.

[caveman1917]

Something that I've always thought was interesting is that back in the days when we assumed the cosmological constant was zero, the fate of the universe was tied to the flatness. So a closed universe would eventually stop expanding and begin to collapse, an open universe would expand forever, and a flat universe would continue to expand, but at a rate that approaches zero. But with a cosmological constant in the mix, that's no longer true. Depending on the values (and whether the "cosmological constant" is really constant; it could vary over time), you can have a closed universe that expands forever, or an open universe that eventually collapses. There are all sort of other interesting possibilities, like "loitering universes" that expand to a certain point and then stay at roughly the same scale for a long period of time before beginning to expand again. Even though many of those alternatives don't fit the universe we live in, I just always was intrigued by the increase in possibility.

Indeed. Though at some point i wonder whether this is going to do us much good, since by having so much free parameter space to play in we could find ourselves in a situation where no matter what experimental constraints we have, we will always have a bunch of equally predictive models that fit it.

Oh and thank you cjameshuff for pointing out the mistake in my thinking there, it was quite a silly mistake for ignoring the cosmological constant. I thought that an accelerating expansion would never get me anywhere so i just ignored the cosmological constant term without considering it could be made negative.

[Grey]

Indeed. Though at some point i wonder whether this is going to do us much good, since by having so much free parameter space to play in we could find ourselves in a situation where no matter what experimental constraints we have, we will always have a bunch of equally predictive models that fit it.

Yep, it's true. If we could just fast forward a quick billion years or two to grab a couple extra data points, it would be great. :)

[caveman1917]

Yep, it's true. If we could just fast forward a quick billion years or two to grab a couple extra data points, it would be great. :)

I wonder if given a set of equally predictive models we should favor the cyclic class? We already have the cosmological principle with respect to space, but the cyclic models include time, so would seem to have a bit of a philosophical edge (everything else equal). On large enough scales we'd also have isotropy and homogeneity with respect to the time dimension, this iteration is as good as any other in that case.

[RandyD123]

A couple of immediate problems occur to me.

This idea assumes that there is a centre and an edge to the universe. That doesn't seem to be the case.

Secondly, and more importantly, the mass on the outside of a sphere does not pull on the material inside. This was proved by Isaac Newton some time ago and is known as the Shell Theorem.

This is exactly why I say the Big Bang theory has seen its days. With no center and no edge there can be no Big Bang.

[cjameshuff]

This is exactly why I say the Big Bang theory has seen its days. With no center and no edge there can be no Big Bang.

Why not?

[Noclevername]

This is exactly why I say the Big Bang theory has seen its days. With no center and no edge there can be no Big Bang.

The evidence for the BB is universal expansion (observed) and residual heat in the form of the CMB (observed). What observations lead to think otherwise?

[RandyD123]

When people try to explain the Big Bang to people who think of it as an "explosion" they talk about how the Big Bang doesn't have a point of origin like an explosion and that it happened "everywhere"....

If the Big Bang happened everwhere then by default there is no "edge"..... an edge implies that there is a center, a center implies there is an edge.....if there is no center, there is no edge.....no center, no edge....NO BIG BANG. Everywhere is just another term for "infinity"....did the Big Bang happen "Everywhere" or did it not??? If it did then then the universe is by default infinite. You can't have it both ways, it's one or the other.

I'm amazed how such a common sense approach has not retired the Big Bang Theory long ago. The Big Bang is dead and is outdated. Time to explore more plausible theorys...

[cjameshuff]

When people try to explain the Big Bang to people who think of it as an "explosion" they talk about how the Big Bang doesn't have a point of origin like an explosion and that it happened "everywhere"....

Right.

If the Big Bang happened everwhere then by default there is no "edge"..... an edge implies that there is a center, a center implies there is an edge.....if there is no center, there is no edge.....no center, no edge....NO BIG BANG.

This is just a repetition of the claim, not support for it.

Everywhere is just another term for "infinity"....

No, it isn't. It could just as easily mean every point in a finite universe as every point in an infinite one.

did the Big Bang happen "Everywhere" or did it not??? If it did then then the universe is by default infinite. You can't have it both ways, it's one or the other.

Why not?

I'm amazed how such a common sense approach has not retired the Big Bang Theory long ago. The Big Bang is dead and is outdated. Time to explore more plausible theorys...

Common sense has a notably poor track record in even basic mechanics. You need to justify your position with more than just your personal incredulity that things could be a certain way...and you need to provide a better alternative. Do you have one?

[RandyD123]

The original post asked a specific question, it is not my intent to hijack this thread. I will ask my question in a new thread.

[Jeff Root]

When people try to explain the Big Bang to people who
think of it as an "explosion" they talk about how the Big
Bang doesn't have a point of origin like an explosion
and that it happened "everywhere"....

If the Big Bang happened everwhere then by default
there is no "edge"..... an edge implies that there is a
center, a center implies there is an edge.....if there is
no center, there is no edge.....no center, no edge....
NO BIG BANG.

The expansion of the Universe, which is what the Big
Bang theory describes, was first derived from general
relativity by Alexander Friedmann in 1922, a few years
before the redshift of distant galaxies was discovered.
This expansion does not have a center or edge.

Everywhere is just another term for "infinity"....did the
Big Bang happen "Everywhere" or did it not???

There might be parts of the Universe (or other universes)
which were not involved in the Big Bang. That is what
"multiverse" theory is about. But all we can see, and
all we know anything about, is what came out of the
Big Bang. That could be all there is. In that case, the
Big Bang happened everywhere.

If it did then then the universe is by default infinite.
You can't have it both ways, it's one or the other.

On the contrary, if the Big Bang happened everywhere,
then -- I contend -- the Universe must be finite.
However, there is no observational evidence yet that
can distinguish between a finite or an infinite Universe.
And others disagree with me about this logical inference.
They say that the Universe could be infinite even if the
Big Bang involved the entire Universe. That makes no
sense to me, but apparently it does to some people.

I'm amazed how such a common sense approach has
not retired the Big Bang Theory long ago.

It is interesting that your commonsense approach and
my commonsense approach, both rejected by the BAUT
mainstream police, give exactly opposite conclusions.

The Big Bang is dead and is outdated. Time to explore
more plausible theorys...

It looks fine to me. It needs a lot more work, but in
general it fits observations very well. What problem
do you see that I don't?

-- Jeff, in Minneapolis

[Shaula]

It is interesting that your commonsense approach and
my commonsense approach, both rejected by the BAUT
mainstream police, give exactly opposite conclusions.

Yes, it highlights nicely why you should not rely on 'common sense' and should instead rely on the predictions of the theory.

[Strange]

It is interesting that your commonsense approach and
my commonsense approach, both rejected by the BAUT
mainstream police, give exactly opposite conclusions.

Which is exactly why common sense is pretty much useless in science.

[tusenfem]

The original post asked a specific question, it is not my intent to hijack this thread. I will ask my question in a new thread.

But if your question in going to lead you to your conclusions in post #40, then take it to ATM.

[Jeff Root]

It is interesting that your commonsense approach and
my commonsense approach, both rejected by the BAUT
mainstream police, give exactly opposite conclusions.

Yes, it highlights nicely why you should not rely on
'common sense' and should instead rely on the
predictions of the theory.

There is no reason that common sense and predictions
of theory should not be in complete accord. Common
sense is relied on to develop every theory. Common
sense is relied on to make predictions from any theory.
Good common sense should generally be in accord with
good predictions made with good theory.

The problem is not with common sense. The problem
is with your assumption that common sense must be
uneducated. Good common sense depends on good
understanding, which depends on learning.

-- Jeff, in Minneapolis

[Jeff Root]

It is interesting that your commonsense approach and
my commonsense approach, both rejected by the BAUT
mainstream police, give exactly opposite conclusions.

Which is exactly why common sense is pretty much
useless in science.

All of science is the application of common sense to
observations and measurements.

-- Jeff, in Minneapolis

[caveman1917]

All of science is the application of common sense to
observations and measurements.

-- Jeff, in Minneapolis

I'd agree if you leave out the word "common".

Here's a simple experiment to test your statement, ask many random members of the public the following question:
Suppose you're stuck on the middle of a frozen lake on perfectly frictionless ice with nothing to grab onto. How do you get out?
The answer of course is that you throw something away in the opposite direction you want to go and use conservation of momentum.

How many people got that right? And that's just simple newtonian mechanics, not big-bangs and infinite universes.

[Jeff Root]

All of science is the application of common sense to
observations and measurements.

I'd agree if you leave out the word "common".

Webster's New World Dictionary of the American
Language, College Edition (1964):

common sense, 1. originally, the faculty which supposedly
united and interpreted impressions of the five senses; hence,
2. practical judgement or intelligence; ordinary good sense.

I think "common sense" is apt.

Here's a simple experiment to test your statement, ask
many random members of the public the following question:
Suppose you're stuck on the middle of a frozen lake on
perfectly frictionless ice with nothing to grab onto.
How do you get out?

Perfectly frictionless ice is an idea that might take a bit of
mental effort to comprehend.

The answer of course is that you throw something away in
the opposite direction you want to go and use conservation
of momentum.

I'd try swimming first. Use my hands to push against the air.
That might violate your "nothing to grab onto". If you put me
in space instead of on ice, to ensure that there is nothing for
me to grab onto, then making a little hole in my spacesuit to
throw air away would be more obvious, although directional
control would be more difficult than on a surface where motion
is constrained to two dimensions. I'd be sure to sit down on
the ice before throwing anything backward, over my head, or
lie down and throw it forward. Throwing anything with one
arm wouldn't do much good.

How many people got that right?

I don't know. There was a magazine on the subject of
misconceptions of physics, how they are learned, and how
they can be unlearned. I didn't see that particular scenario
presented, but it is exactly the kind of thing they did a lot.
It has been too long since I last saw it for me to recall the
title, but it may have been something like "The Physics
Educator" or simply "Physics Education". It was in the
U of M Science & Engineering Library.

-- Jeff, in Minneapolis

[WayneFrancis]

This is exactly why I say the Big Bang theory has seen its days. With no center and no edge there can be no Big Bang.

That is about on par with saying "With no planets made of chocolate and vanilla there can be no Big Bang" if you understand that the "Big Bang" is not an explosion within space time but an expansion of space time. The only centre of the big bang you'll find is a centre in time as far as the main stream model goes.

[caveman1917]

"With no planets made of chocolate and vanilla there can be no Big Bang"

Said the head of a student's club of highly advanced aliens during a brainstorming session for finding a name for their yearly gastronomic festivity.

[WayneFrancis]

When people try to explain the Big Bang to people who think of it as an "explosion" they talk about how the Big Bang doesn't have a point of origin like an explosion and that it happened "everywhere"....

If the Big Bang happened everwhere then by default there is no "edge"..... an edge implies that there is a center, a center implies there is an edge.....if there is no center, there is no edge.....no center, no edge....NO BIG BANG. Everywhere is just another term for "infinity"....did the Big Bang happen "Everywhere" or did it not??? If it did then then the universe is by default infinite. You can't have it both ways, it's one or the other.

I'm amazed how such a common sense approach has not retired the Big Bang Theory long ago. The Big Bang is dead and is outdated. Time to explore more plausible theorys...

Because your "common sense approach" is logically flawed.

We are talking about "space-time" not just "space". There is a centre in that the big bang occurred at point in time but every where in space.

The amount of space may or may not be finite and regardless of the universe being infinite or finite in spatial extent GR suggests that the universe is unbounded in that it has "No edge". If finite the manifold loops back on itself and "common sense" might lead you to think space can't be "flat" if it loops back on itself but "common sense" would not serve you well in this topic.

Next the extent of the universe may or may not be infinite with respect to time. Even with a starting point there may or may not be an ending point with respect to time. That depends on the particulars of how the universe evolves.

But lets go with your statement of

If the Big Bang happened everwhere then by default there is no "edge"

correct, it happened everywhere spatially.

an edge implies that there is a center, a center implies there is an edge

Correct and since the big bang theory doesn't claim there is a centre in a spatial sense and there is no edge this isn't a problem..

.if there is no center, there is no edge.....no center, no edge

Ok, you've just said the same thing 3 times all of which the BBT agrees with.

....NO BIG BANG

WHAT?!?!

This is the equivalent of saying
"Sugar makes a cake sweet. You need sugar for a sweet cake. Sweet cake needs sugar....NO CHOCOLATE CAKE!"

The reason the BBT is mainstream is because it is the most plausible theory regardless of your misunderstandings.

[WayneFrancis]

Webster's New World Dictionary of the American
Language, College Edition (1964):

common sense, 1. originally, the faculty which supposedly
united and interpreted impressions of the five senses; hence,
2. practical judgement or intelligence; ordinary good sense.

I think "common sense" is apt.

And I'd say to our 5 senses and practical judgement and intelligence is not enough to get correct results on the macro and micro scales. This is why GR is so hard for so many to grasp and even when you've been exposed to it for a while and accept it as fact you can still mess up explanations, like I have on numerous occasions, because of instead of using the model I tried to use "common sense" mixed with my knowledge of the subject matter and produced a thought experiment that was flawed.

I don't know. There was a magazine on the subject of
misconceptions of physics, how they are learned, and how
they can be unlearned. I didn't see that particular scenario
presented, but it is exactly the kind of thing they did a lot.
It has been too long since I last saw it for me to recall the
title, but it may have been something like "The Physics
Educator" or simply "Physics Education". It was in the
U of M Science & Engineering Library.

-- Jeff, in Minneapolis

And common sense doesn't imply advanced training. That is why it is common to many people untrained in the specific area of interest.

I'll say someone can make an informed judgement on something but I believe this is very different then "Common Sense"

I've used this example many times in the past on various forums about how "common sense" is often not the best coarse of action.

In urban warfare if your point man goes through a door and and explosion takes them out "common sense" would have you retreat while training will tell you that the safest direction to travel in is now forward through that point for the following reasons.
1) That explosion has a high probability of disabling any other traps in that area
2) Traps like this are normally put in place to force a change in direction, often into other traps and away from your objective.

Once I know the actual situation my decisions stop being "common sense" and become "informed"

[Tobin Dax]

I'd try swimming first. Use my hands to push against the air.
That might violate your "nothing to grab onto". If you put me
in space instead of on ice, to ensure that there is nothing for
me to grab onto, then making a little hole in my spacesuit to
throw air away would be more obvious, although directional
control would be more difficult than on a surface where motion
is constrained to two dimensions. I'd be sure to sit down on
the ice before throwing anything backward, over my head, or
lie down and throw it forward. Throwing anything with one
arm wouldn't do much good.

That is an excellent example of how common sense (or practical judgement or whatever else) should not be relied on to solve such a problem.

I have to ask about your extension of the situation: How, exactly, would making a hole in a space suit and releasing air qualify at "ordinary good sense"?

[Jeff Root]

Webster's New World Dictionary of the American
Language, College Edition (1964):

common sense, 1. originally, the faculty which supposedly
united and interpreted impressions of the five senses; hence,
2. practical judgement or intelligence; ordinary good sense.

I think "common sense" is apt.

And I'd say to our 5 senses and practical judgement and
intelligence is not enough to get correct results on the
macro and micro scales.

So humans are incapable of coming up with correct
descriptions of things on "macro and micro scales"?

Or are you saying that we need to use intuition as well as
common sense?

Or are you merely saying that we need knowledge in
addition to common sense? That's where "observations
and measurements" come in. Already covered.

This is why GR is so hard for so many to grasp and even
when you've been exposed to it for a while and accept it
as fact you can still mess up explanations, ...

General relativity is described by math which I suspect
nobody understands. Most of the physics, however, is
not particularly hard to understand. If it seems hard to
understand, it likely is because you don't understand it.
Once you understand it, it is pretty common-sense.

Once I know the actual situation my decisions stop
being "common sense" and become "informed"

You stop using your intelligence and substitute rote
recital. Everyone does that. It's an animal thing.

-- Jeff, in Minneapolis

[Jeff Root]

I'd try swimming first. Use my hands to push against the air.
That might violate your "nothing to grab onto". If you put me
in space instead of on ice, to ensure that there is nothing for
me to grab onto, then making a little hole in my spacesuit to
throw air away would be more obvious, although directional
control would be more difficult than on a surface where motion
is constrained to two dimensions. I'd be sure to sit down on
the ice before throwing anything backward, over my head, or
lie down and throw it forward. Throwing anything with one
arm wouldn't do much good.

That is an excellent example of how common sense
(or practical judgement or whatever else) should not be
relied on to solve such a problem.

If one does not rely on common sense in such a situation,
then one must rely either on luck or a cell phone. Using
common sense would definitely be my first choice. I don't
own a cell phone. A person in a spacesuit would have the
equivalent of a cell phone, but being stranded in mid-space
could be a sign of other problems, which might include the
communication equipment not working, so common sense
is a really good starting point. Good luck is better than
intelligence, but only when you get it. You can't depend
on getting it. If you're stranded in mid-space, you probably
haven't been getting it recently.

I have to ask about your extension of the situation: How,
exactly, would making a hole in a space suit and releasing
air qualify at "ordinary good sense"?

Because it would be, as I said, obvious. Anyone in a
spacesuit, stranded in space, would think of it almost
immediately. It is just common sense. They would know
that even if they have a supply of items to throw away,
which they are willing to throw away (stuff taken on EVA
tends to be expensive), they are very unlikely to be able
to throw it in the right direction to make them get where
they want to go, rather than just tumble. A small jet of
air coming out of the spacesuit would allow more time
to fine-tune the direction of the thrust, by changing the
configuration of the body in response to the observed
direction of motion. Of course this means you'll run out
of air a lot sooner, so if you're also already low on air,
common sense might say to try something else instead.

I can think of two movies that involved being pushed in
space by an air jet: 'Destination Moon' (1950), in which an
astronaut who is stranded in mid-space is rescued by another
using an oxygen tank for propulsion, and 'Marooned' (1969),
in which a confused astronaut blows the Apollo command
module hatch open, and the resulting expelled air pushes
the spacecraft out of reach of a would-be rescuer.

-- Jeff, in Minneapolis

[Tobin Dax]

If one does not rely on common sense in such a situation,
then one must rely either on luck or a cell phone. Using
common sense would definitely be my first choice. I don't
own a cell phone. A person in a spacesuit would have the
equivalent of a cell phone, but being stranded in mid-space
could be a sign of other problems, which might include the
communication equipment not working, so common sense
is a really good starting point. Good luck is better than
intelligence, but only when you get it. You can't depend
on getting it. If you're stranded in mid-space, you probably
haven't been getting it recently.

So instead of responding to the original comment, you have made up your own situation and brought superstition into it. Can you respond to the original example of being stranded on the ice? If the common sense answer is "swimming," then the common sense answer is incorrect, being a waste of time and energy.

Because it would be, as I said, obvious. Anyone in a
spacesuit, stranded in space, would think of it almost
immediately. It is just common sense. They would know
that even if they have a supply of items to throw away,
which they are willing to throw away (stuff taken on EVA
tends to be expensive), they are very unlikely to be able
to throw it in the right direction to make them get where
they want to go, rather than just tumble. A small jet of
air coming out of the spacesuit would allow more time
to fine-tune the direction of the thrust, by changing the
configuration of the body in response to the observed
direction of motion. Of course this means you'll run out
of air a lot sooner, so if you're also already low on air,
common sense might say to try something else instead.

So your answer to how depleting your air supply is good sense is that: (a) tools are expensive, and apparently worth more than you and the suit, so you should risk sacrificing yourself first instead of leaving that as a last resort, and (b) that an off-center jet of air will not cause you to tumble?

[RandyD123]

I'd agree if you leave out the word "common".

Here's a simple experiment to test your statement, ask many random members of the public the following question:
Suppose you're stuck on the middle of a frozen lake on perfectly frictionless ice with nothing to grab onto. How do you get out?
The answer of course is that you throw something away in the opposite direction you want to go and use conservation of momentum.

How many people got that right? And that's just simple newtonian mechanics, not big-bangs and infinite universes.

I would force myself to sneeze and off I go!!!

[Jeff Root]

If one does not rely on common sense in such a situation,
then one must rely either on luck or a cell phone. Using
common sense would definitely be my first choice. I don't
own a cell phone. A person in a spacesuit would have the
equivalent of a cell phone, but being stranded in mid-space
could be a sign of other problems, which might include the
communication equipment not working, so common sense
is a really good starting point. Good luck is better than
intelligence, but only when you get it. You can't depend
on getting it. If you're stranded in mid-space, you probably
haven't been getting it recently.

So instead of responding to the original comment, you
have made up your own situation and brought superstition
into it. Can you respond to the original example of being
stranded on the ice?

I did respond to the original question, and added the case
of being stranded in space because the original scenario
didn't perfectly fit caveman's original intent of not having
anything to grab onto. Being surrounded by air, I could
"grab" onto the air by "swimming" through it. I can't do
that in space.

If the common sense answer is "swimming," ...

What on nine planets gives you the idea that there is only
one commonsense answer? "Swimming" in the air is just
what I would try first, as I said.

... then the common sense answer is incorrect, being a
waste of time and energy.

Huh? Why would it be incorrect? Why would it be a waste
of time and energy?

Caveman suggested that "the" correct answer is to throw
something away in the opposite direction you want to go.
That might work if you have something to throw, and you
are able to throw it in the right direction. To give an object
as much speed as possible, a person almost always revolves
the object around them. Even in shotput, where pushing
the heavy shot straight away from the body is the final step,
rotation is extremely important for giving the shot additional
speed. The muscles can work over a much greater distance
than if they just pushed the object in a straight line.

That rotation does no good in pushing you across the ice
or through space. It just makes you fall over or spin. So on
the ice, you need to either be sitting down and throw the
object backward over your head with both hands (your legs
prevent you from rotating forward), or lie down on your back
and throw the object forward over your body with both hands
(your entire body prevents you from rotating backward).
Either way is pretty clumsy and inefficient. You do get to
rotate your arms, but only through a limited range, so you
can't transfer as much momentum to the object as you
could if you could swing them all the way around.

So although paddling through the air with my hands would
be inefficient, so would throwing something. And it is a
method I could use even if I had nothing to throw, or the
only thing I had to throw was valuable to me. And it is a
method I would definitely choose over throwing something
because I have such poor control over the timing of when I
let go. I can control the time to maybe a tenth of a second.
I want the object to fly off horizontally to give me the
maximum momentum. If my arms swing through an arc of
90 degrees in two tenths of a second, then the object could
go up at at a 45-degree angle, or down at a 45-degree
angle. I would be worse than useless on a baseball field.

So "swimming" through the air with my hands would be my
first choice.

Because it would be, as I said, obvious. Anyone in a
spacesuit, stranded in space, would think of it almost
immediately. It is just common sense. They would know
that even if they have a supply of items to throw away,
which they are willing to throw away (stuff taken on EVA
tends to be expensive), they are very unlikely to be able
to throw it in the right direction to make them get where
they want to go, rather than just tumble. A small jet of
air coming out of the spacesuit would allow more time
to fine-tune the direction of the thrust, by changing the
configuration of the body in response to the observed
direction of motion. Of course this means you'll run out
of air a lot sooner, so if you're also already low on air,
common sense might say to try something else instead.

So your answer to how depleting your air supply is good
sense is that: (a) tools are expensive, and apparently worth
more than you and the suit, so you should risk sacrificing
yourself first instead of leaving that as a last resort, and
(b) that an off-center jet of air will not cause you to tumble?

Anyone in a spacesuit in space would know how much air
he has left and roughly how long it would take to lose the
rest of it if the leakage rate increases. He would also have
a rough idea of how long it would take to reach safety by
propelling himself with a jet of air from the suit. He would
also have some idea of the relative value of the suit and of
whatever -- if anything -- he might be carrying. He would
also know that the chances of throwing a single object in
exactly the right direction to send him back to safety would
be very small. In my case, virtually zero. He would also
know that he could continuously adjust the direction of a
jet of air escaping from a hole in his suit by changing the
orientation of his body, in response to his observations of
what happens to his motion once he makes the hole. He
would have way more control over tumbling than if he were
to throw an object, and he would have way more control
over his linear motion.

You suggest that I would risk sacrificing myself first rather
than leaving that as a last resort. I know that my air is
limited. I know it is constantly being depleted. I know I
have only a limited time to save myself. I cannot wait until
it is too late. I cannot throw something if I have nothing
to throw. I will not throw something if I expect that doing
so will set me tumbling without pushing me to safety. Not
making a hole in my suit would be the bigger risk. I would
be depending on luck instead of common sense.

-- Jeff, in Minneapolis