Let's move on to mutual time dilation. It is often said that moving clocks run slow. This may be a misleading statement, or at the least, incomplete. — FreeEmotion

Incomplete I'd say. You can say that clocks run slow in frames in which they are not stationary. That's almost the same thing. Sans frame, a clock has no velocity.

What I think it means is that when transforming measurements between moving frames, we can no longer use Galilean transformations when the relative velocity (speed?) of the frames is comparable to the speed of light. This is because of the constancy of the speed of light within each frame, no matter which frame the origin of the light.

Sounds good. Frames don't move since they don't have a position, but they have velocity relative to each other and I think that's what you mean.

Does it mean that in inertial frames moving relative to each other, that mutual time dilation occurs? Is it just an illusion?

It's quite real. Not sure what you would consider an illusion, but none of it is fake and the clocks are not being inaccurate. It really is possible to get to a place 1000 light years away and not die of old age en-route or require cryonics. But alas, my car seems to be a bit underpowered for the task.

There are fast particles that get created in the upper atmosphere (60000 m up) that have a lifespan long enough for light to travel about 600 meters before decaying. Almost none should reach the ground, but a vast percentage of them do because their decay is delayed by the time dilation from moving at about 99.5% of light. They age slow enough to reach a destination well beyond their life expectancy of about 2 microseconds. They could not do this if the dilation was but an illusion.

The question only asked how to get to base the quickest. Maybe home base has a circular magnet that slows you down as you go through it. :) Or you can shoot the alien with the fifth projectile at lower energy. — Joseph

Then the answer provided is wrong.
Quickest was is to not do this perpendicular sidetrack. Blow all 5 ejections immediately straight towards home, which gets you there 14x pronto. Stopping once you get there can not be done by the rules, but you seem to have springy bumpers, so crashing is an option.

Oh wait. Just smack into the alien. Let the springs do their work. Never mind then.

Thought of all that, but wouldn't you want to stop once you arrived at base? Absolutely no way to do that by these rules. So you just blast on by at some preposterous speed, no use to anybody except as a battering ram to one alien ship.

Let's face it, the Good Samaritan was "good" because he was able to help some guy struggling in the gutter on the other side of the road. How else could he be "good"? — Jake Tarragon

By being distinct from all the other passers-by that did nothing. If anybody would have helped, it would just be what people do, and not notably 'good'.

The sun is not the origin of Earth or other planets. They're all from a different star, which is what it means to be a second generation system.
The probe falling into the sun puts a bit of heavy metals into it to trivially add to the collection it already has. I can't see how this is offensive no matter the spin put on it.

That's a weak advantage. It takes more instructions (calculator key presses) to code with FPN.
RPN 3,15+ (where comma is <enter>)
FPN +3,15, <-- extra comma

Either one requires a stack, but an operation consumes less space than a number, so the FPN stack takes fewer resources to implement the worst case stack.

I could be wrong about this.

The point is choice-making is programmable. That nullifies the discriminating power of human ability to choose to make the distinction free will as opposed to no free will.

That effectively makes free will an impossible concept to even think of. ''Free will'' can't be defined and is meaningless 4 ÷ 0. — TheMadFool

This is one of those areas where the philosophy of mind matters.
Your example that choice-making is programmable only works under physical monism. A dualistic view has a different definitions of 'agent of choice', which is defined as the immaterial mind. The computer may or may not have one of those, but if it does, it is apparently not capable of altering the determined course made by the program, and therefore is not free.

Will is neither free nor does it have control of outcome. One can only try to make the choice. There are all manner of constraints and influences that affect outcomes. One can only attempt to move in a particular direction. Two football lineman exhibit this type of tug-of-war.

Insofar as responsibility is concerned, that is a issue of human condition. Since outcomes are unpredictable, responsibility is purely subjective which is why we have courts to adjudicate. — Rich

You seem to be under the impression that I'm asserting something. I'm just putting out a set of premises that I think works. If you disagree, tell me where my definitions run into conflict.

If you have a different set of premises, that's great. But your descriptions have been confined only to personal experience of the thing, and that doesn't tell me what the thing might be.

Will is a feeling that the body generates. That is how we know it and observe it. Sometimes its effects can be observed by others as one exerts themselves. It is strange that feelings are made subservient to words or other symbols. Will is directly experienced. — Rich

Again, you are describing human will. I have no way of applying that elsewhere. If humans are special, then that's a premise, and you have to tell me why. If they're not, then the introspection is useless in determining what else has will.

If x > 1 then 4/x else goto line 10

If choice is programmable then free will becomes nonsense. — TheMadFool

Only if you use inconsistent definitions. If going to line 10 is the right thing to do in this case, and there is no inhibition to the PC going there (such as there is no line 10), then this is an example of free will in my view.
If going to line 10 is the wrong thing to do, the will is still free, but the program must now bear whatever responsibility it holds for going to the wrong place. Perhaps it will malfunction and crash.

This is very similar to the responsibility relationship between my toes and my brain. The brain evolved partly to bear responsibility to keep the toes safe. If the brain (the agent) doesn't do its job and notice the rock, the toe is injured and the brain bears the responsibility. The pain is experienced upstairs, not by the toe. There is no evolutionary advantage to the toe experiencing pain for choices it did not make. The pain is in the correct place and serves as a deterrent to future toe stubbage.
Yes, that's a word.

I feel will as a force being generated from within me which creates the impetus to move in a particular direction, together fulfilling the choice. It can be imagined as a directed wave. — Rich

Not really asking how it makes you feel. That road leads to solipsism since even I don't have choice since I don't make you feel that way when I pick vanilla. You can presume I have similar feelings, but there is no way to apply the rule to anything nonhuman. I want a definition of will, not of human will.

I would think that at its core, 'will' is what an 'agent of choice' wants to do. It is the output of the choice, the volition. This definition seems to work regardless of one's view, even if we differ on what constitutes an agent of choice.
The will is free if the desired choice can be effected, and thus the agent can bear responsibility. So if I will to help a choking person but I'm inhibited by a barrier between us, the will is not free to perform the act, and thus is not responsible in any way for not helping the other person in need.

Anyway, that's sort of the basics in my view. None of the above presumes a particular philosophy, although 'bear responsibility' was not touched on at all.

The butterfly flapping its tiny wings represents the small changes in weather variables. — TheMadFool

In two worlds with the only difference being the butterfly flap or not, the weather in these two worlds after some months will bear no resemblance to each other (except for that storm in 430 days). One butterfly does not constitute a difference. Two do. 'Changes' is not part of it.
Any small difference amplifies, which is characteristic of a chaotic system.

It doesn't mean that a butterfly can actually affect the weather.

Unless the butterfly is outside the light cone of some event, or in Schrodinger's box (yes, these exist but not ones that hold a butterfly), the butterfly affects that event. But many dynamic systems are not chaotic. Some small meteor slated to hit Earth in 2 years is going to do that no matter what the butterfly or the weather is like. The Earth's rotational orientation will not be significantly different in a century.

One example they used a lot to develop chaos theory is that of a dripping faucet. The drips are completely predictable at low flow, but become unpredictable at a fixed pace, but then become predicable again at a slightly higher pace, but with more complex drip patterns with different size drops.

OK, I think you might not ascribe choice to the thermostat because the purpose it serves is that of it's installer (the house occupant), not its own. If so, I think I can drive that definition to contradiction, but perhaps we first need to figure out what we mean by 'will', and the distinction between free and not free.

A machine doesn't make choices. The choices are made by the human that programs the machine. Just like a hammer doesn't make choices. The choices are being made by the human that is using it. Similarly, a piano don't make choices. The pianist is making the choices. Tools used by humans are not human. — Rich

No, I may set the threshold but don't actually tell the thermostat when to turn on the heat. I simply design the thing to make its own choice based on a comparison between the temperature and the setting . I arrange it so it is capable of making that choice, but if the choice is mine, I would have no need of the thermostat, and there would just be a manual toggle on the wall.

So I disagree, but that is my definition I'm working from. You can define choice any way you want of course. The idea is to find a set of definitions/premises that don't contradict.
So what is choice that a machine doesn't have it but a human does? I'm not (yet) asserting it has free will. Just trying to get the terms straight.

Well, I'm working at this problem indirectly. Free will is central to morality, which in turn, necessitates the choice to do good rather than bad. — TheMadFool

Excellent way to approach it.

I feel as if the free will problem is nonexistent because I take this approach. First of all, various philosophy of the mind interpretations have completely different premises about what really is a person, morals, choice, volition, etc. So the confusion only exists if you take the premises of one view and apply them to a different view.

Computers don't make choices. They are programmed by humans who do make choices when writing the programs. — Rich

You have not stated your premises for this assertion, but I'm guessing a dualistic set of premises, in which case you're right.
A physical monist says choice is a purposeful selection of action, which is what a machine (thermostat say) does and a rock doesn't. It senses a specific condition and acts on that condition and not just a fatalistic random effect of prior causes, which is how a rock does not choose when to break in half.

I think I understand now. Small differences in initial states have vastly different outcomes. For example, the temperature may differ by 0.000007 degrees but this tiny difference can mean the difference between fair weather and storms. The butterfly is simply a metaphor for this small difference in a variable. — TheMadFool

Much better. The difference has no lower limit of triviality. One atom doing a radioactive decay or not is such a difference. The butterfly is an example, not just a metaphor.

I see. So, you do agree that a blink of an eye can cause weather changes. — TheMadFool

The weather will change, and there is no way, lack of eye blink included, to prevent that. So no, I don't agree with that statement.

What would distinguish this practical utopia from modern society? — Reformed Nihilist

Sustainability for one. Going for greater happiness is a lower priority than something that can last.

But you said small changes can magnify as the causal chain moves forward in time. Isn't an eye-blink a small change? Can you absolutely rule out the possibility that it won't magnify its effects down the causal web? — TheMadFool

An eye blink is a small difference from a not-blink. That difference (there is no change here) amplifies. and in the two divergent paths, the weather is totally different in a matter of months, and a different list of people have died from accidents. Accidental death is quite chaotic, but slow death not so much.

The difference magnifies only if in a chaotic dynamic system not tuned to a strange attractor, and the weather for the most part doesn't have strange attractors, but orbiting things can. So difference yes, but certain storms are predicable well in advance. It will rain on Colorado Springs at 3:30 PM on Sept 7, 2018. You heard it here first folks.

Well in the golden rule tradition that is supposedly the core of what are purported to be objective (not just for humans) morals, "do unto others as you would have them do unto you" or some variant of that.

Point is, the aliens come down and do you want them to grant us rights under objective moral code, or do we go by the more natural human moral of: "It's not like me, so its OK to do whatever to it".

So, can I change the fate of the universe by blinking my eye? — TheMadFool

Wouldn't be fate if you could.
You are part of the causal chain of local events, blink of eye or not. What you are labeling 'change' is not change by any usual definition. Change is what happens to a candle over an hour once it has been lit. Change is not what happens to the candle given the alternate choice to leave it on the dash of your car instead.

Also, the Butterfly Effect is a scientific theory. I just want to explore its logical implications, one of which seems to allow for superstitions to be true. — TheMadFool

Superstition would assert that the magic words get to choose the desired weather. Butterfly effect helps you not at all on that account. You are indeed wielding the tool incorrectly.

While the escape velocity is unlikely, the subject has been of some interest since the Newtonian 'wobble' effect along the axis caused by possible changes to the internal motions of the crust relative to earth' spin from events like earthquakes, environmental depletion and even nuclear testing that all impacts on polar shifts. — TimeLine

Those things have more effect on the rotation of Earth (nonchaotic and more predictable) and not so much the orbit, and all of them are negligible compared to tides. Not sure what you mean by polar shifts. Magnetic or physical? There's clear evidence only for the former.

If you think of something like orbital resonance, gravitational interactions and any possible deceleration of earth there could possibly bump us into a higher or lower orbit, or at the very least would have some lunar impact that would devastate the internal planetary dynamics.

Orbital resonance is a gravitational interaction, and only a close passing object would alter the moon orbit more than (again) the tides. The moon is slated to eventually collide with Earth, but that is not a chaotic event. They can predict the time pretty accurately, and it turns out to be moot. The sun will swallow both first.

A lot of the examples being given are not the 'butterfly effect', a popular term for chaotic systems.
Gene mutations, spread of disease, a flame in a grain elevator. All examples of things whose effect can grow exponentially, but not really chaotic systems. Even the planet example I gave is a poor one since the imbalance of relative masses lends more stability to our solar system than a small meteor is likely to disrupt. But the effect is still strong enough that it is impossible to say where Earth will be in its orbit a million years from now,. Those chaotic effects are the same ones that occasionally dislodge comets into the inner solar system.

'Back to the Future' is an example of how it doesn't work. Marty working to restore his future existence after he disrupts the meeting of his parents. Nonsense. Alter one atom of the past and there is no future Marty

Hard to say with Hitler. Sure, the saving of the child resulted in the way WWII was played out, but I think it would probably have happened regardless. The world was playing a game of 'Risk', and needed to take its natural progression from isolated countries to superpowers. The war was inevitable, but it ending with a cold war was not. Despite USSR being as bad as Germany, I'm not sure what sort of hell hole the world would have become if the USA or anyone else had finished the war instead of letting it go cold.

The perturbance from one slow sand-grain meteor can make the difference between a planet remaining in orbit or being ejected permanently into deep space.
— noAxioms

That's scary. Are you serious? — TheMadFool

Orbital mechanics are unstable beyond two objects. Look up three-body problem. The sun is massive enough to dominate our solar system, and the planets sufficiently distant from each other that their mutual interaction is not likely to throw one away soon. Nevertheless, prior positions of planets are known only so far into the past because of this unpredictability.
I have a screen saver that simulates three or more similar size bodies in perfect orbit, and it takes very little time for all but two of them to achieve escape velocity. A tiny difference in initial conditions (the sand grain) might result in two different remaining ones.

Weather is far more chaotic than that. Any difference at all (say one radioactive decay) is likely to utter alter the weather a few months hence compared to the weather without that decay.

I think the most important question is how to stop it. — Pollywalls

I've never seen a viable suggestion. All the treaties seem to attempt to slow it, but none will admit to what needs to be done to reverse it. The Holocene extinction event is predicted to eliminate over 90% of all species, including us. Delaying that is not a plan. Humans by nature do not plan for long term.

The current plan to go out in spectacular fashion is arguably a better one than what is proposed in international treaties. I think there are few humans left that know how to live without the infrastructure. I certainly am not one of them.

Chaos theory was developed to study such dynamic systems.

Small events may cascade and cause larger events. However, the strength of effects also dissipate. — Bitter Crank

Not so for chaotic functions, and weather is very much such a function.

The butterfly-causing-a-hurricane is a figure of speech -- not to be taken literally.

It is meant literally. One wave of a butterfly wing, sufficiently prior to said chaotic event, is the difference between a hurricane and not that hurricane. This is not to be confused with the wing being the sole cause, but for any storm in history, the storm would not have ever existed given any seeming trivial difference in the distant past. Instead, other storms would happen.
This is why weather cannot be predicted even given perfect information. Any trivial difference anywhere grows into a completely unpredictable difference. Planetary orbits are similarly chaotic, despite the appearance of stability mostly due to one of the objects being so much larger than the others. One planet orbiting a star is stable, but a third object makes the system chaotic, hence the three body problem. The perturbance from one slow sand-grain meteor can make the difference between a planet remaining in orbit or being ejected permanently into deep space.

Don't think you'll keep it to 60 lines. Is multiple calls to isPrime(x) function cheating?

Side note: The language requires the empty else { } clauses? Not used to that as a C person.
I have a harder time thinking in C anymore since I'm pure C++ now.

I know. I was admiring it.
I think it can be done with no loops at all.

Anyway. After you guys were talking about writing the 10001st prime code without nested loops, I just couldn't resist. This code is mortifying (I got bored/tired by the time I got it working) and completely impractical, but satisfies the condition of having 'just one loop'. :P — Efram

Technically one loop. Still 0(n squared), but implemented as a state machine instead of loops.

Awesome. I fixed it.

Best prime finding program I ever saw was an algorithm that would solve your problem above (10001st prime) with instant runtime. The code included itself and all the work (Sieve of Eratosthenes) took place in the preprocessor. The code compiled to one line that printed the answer, but it took hours to compile on some compilers.

C code. Only two conditionals, not four.

Mirrors do reverse things, else the image would not be left handed.
It reverses front to back.

That said, I think my mirror image would be antimatter possibly? Don't know enough physics to say one way or the other.

I'd like to discuss the importance of emotion and intuition over the importance of logic and pure reason. I feel that as biological beings our views will constantly be skewed by biological and evolutionary impulses (emotion and intuition). — Zoonlogikon

Maybe being fit was a better survival strategy than being rational. Rational thinking only came about once there was an advantage to it, and it still takes second seat if the more established side vetoes what it learns.

This situation is equivalent to the spaceship sending out particles at the speed of light throughout its journey. — FreeEmotion

Photons, yes, and ships often show lights. It is actually sending them out, not just the equivalent.

The ship takes 13 months to travel here. That is not in question. What of the particles emitted from the ship? The first one will take 12 months or one year to reach us. The last one will take zero time to reach us.

Yes, the first one has 12 light-months distance to go, and the last one has zero distance to go. All this is in the frame of the planets.

1 year of travel is compressed into 1 month of images?

No, the image is as viewed by the observer on the destination side, who does not travel at all. He just observes the 13 month trip, and that observation takes only a month since he doesn't see the beginning until 12 months after the trip actually started and the ship is already almost at its destination.

Any time you see something, you are observing the past, not the present. The further away something is, the further back you are seeing. Things on Earth are so close that this effect doesn't matter, but even the sun actually sets 9 minutes before the image of it disappears.

Again, none of this is relativity or has relevance to Einstein's thought experiment. This stuff was known in the 18th century when they first started adjusting actual positions of planets due to measured light speed.

Perhaps because if everything is possible then it must exist. — Jake Tarragon

That conflicts with the meaning of possible. If it must exist, it is necessary, not just possible.

I am reviewing my prior thread since this came up a lot. Studying up on my modal logic since the field seems indispensable for these sorts of questions.

As to chance and why this world:
The question should be viewed in objective terms. So no "why is this world actual?", but "what would be the experience of something actual in this world?" It seems that the experience would be that of a world where experience is possible. No surprise that we're in such an improbable one then.

Well, you could believe that the Earth was created 6,000 years ago, and that the rocks were created with a ratio of carbon-12 to carbon-14 such that the carbon dating formula outputs a result of 4,000. — Michael

This is last-Tuesdayism, and I never understood why the flood geologists didn't just take that stance, that the universe was created with memory of nonexistent times, such as dinosaur bones and light en-route from stars more than 6000 light years away. It would hold up to falsification far better than what they propose now. How do they explain galaxies? They're really just tiny things much closer by? Did Adam see no stars at all, but they all winked on over the course of 6000 years?
The last-Tuesday approach is far more air-tight, unless the god is insufficiently omnipotent to set that up.