Science speculation

[kamui]

this debate is exactly the same thing as Achille and the tortoise : we never going to see the end xD Ironic

But it takes proportionally less time than a larger displacement! So, the total sum of all of the times it takes to perform each step is finite.

Again we agree that this implies that an infinity of steps can take a finite amount of time. So when I moved at 1m/s from my position to 1 meter further, it takes me 1s to pass through an infinity of steps/states… (1/2m in 1/2s + 1/4m in 1/4s + 1/8m in 1/8s + … goes to 1m in 1s) <= So I am able to pass through an infinity of steps/states where it is mathematically/conceptually impossible, but where it seems possible in reality

[ThornEel]

Look at it that way:
You move through x steps, each step takes y time, so the total move time is xy
So you move once in 1s (x=1, y=1). You moved during a total of 1s.
Next, you move twice, each time during a half-second (x=2, y=1/2). You moved during a total of 2(1/2) = 1s
Next, you move four times, each time during a quarter-second (x=4, y=1/4). You moved during a total of 4*(1/4) = 1s
…
We can continue like that as much as we want. If we keep x=n and y=1/n, then the end result will always be n*(1/n) = 1
As you can see, the result is always 1 and is actually independent from n.

Now what happens if n=+∞ ?
The result is independent of n, so it will still be 1.
We can talk about it as a function, with f(n) = n*(1/n). That’s the same thing that we did above, with n=1, n=2, n+4 and n=+∞ respectively.
The result at +∞ is called a limit. it is where the function tends toward when we get closer to infinity. This case is pretty simple as it is always equal to 1, so of course it tends toward 1. But for example, 1/x tends toward 0, as the bigger x, the closer to zero is 1/x

Limits are what Zeno didn’t have, hence the (apparent) paradox. Without limit, you would try to calculate +∞* (1/+∞) but that would be +∞/0, which is undetermined. The trick with limits is that you can rewrite the same function in different manners (as did here with n* (1/n) = 1) where you won’t actually have an undetermined.
This is of course not always possible for all functions, but in this particular case, it is.

Limits were discovered only a few centuries ago, and opened whole new fields in mathematics.
To start with, it enabled movement. A little known fact is that nothing could move before the nineteen century. Which was a good thing, as gravity didn’t exist before Newton, everything would have just floated away.()
() may not be entirely exact

In a more intuitive manner, as your number of steps rises, the size of each step drops. When you tends toward an infinite number of steps, each step tends toward zero. So you have an infinite number multiplied by a size of zero.
Every finite number (bar zero) times infinity equals to infinity. After all, if you have an infinity of something, you have any quantity of the something an infinity of times.
Every finite number time zero equals zero. After all, if you have zero something, you have zero anything.
So what happens when you have an infinity of zero, or put another way, zero infinity? Well, it could literally be anything. It depends on what zero and what infinity, if you want.
In this particular case, it happens to be 1.

[thelazyjaguar]

So I am able to pass through an infinity of steps/states where it is mathematically/conceptually impossible, but where it seems possible in reality

There’s no “seems” about it. Go outside and walk 1 meter. Was it possible?

The impossibility comes from a self-imposed restraint. If you try to do anything to infinity, by the very definition of infinity, you will fail. If you do succeed, then it wasn’t infinite.

A reasonable person would, at some point, realize that dividing what is essentially zero in half is still essentially zero, and would therefore stop trying to subdivide it.

On the mathematical side of the house, your procedure for solving it is infinite. It takes a logical conclusion to step back and say “Hey! I’m moving zero distance now.” It’s a tolerance involved in the calculations. At what decimal point in your calculations do you say that zero is in fact zero? Blindly following a procedure leads to infinity. Just ask any computer program stuck in an infinite loop.

[Argopeilacos]

For some reason, physicists have concluded that the particles are influencing each other at the time of measurement. I’m having difficulty wrapping my head around why that would be true. They already influenced each other at the beginning of the experiment.

I have exactly the same issue. What we expect is a hidden state to exist independently from our knowledge. The “local hidden variable” flavour has been experimentally disproven by Alain Aspect experiments. See https://en.wikipedia.org/wiki/Hidden_variable_theory.

[Kichae]

A reasonable person would, at some point, realize that dividing what is essentially zero in half is still essentially zero, and would therefore stop trying to subdivide it.

The universe isn’t a reasonable person, though, and if space is smooth and non-discrete, then anything that moves must move through an infinite number of points, and so it’s an issue worth discussing. Either space is quantized, or it’s possible to move through an infinite number of steps in a finite amount of time. Or, as it turns out, both.

Because it turns out that it’s possible, both mathematically and physically, to perform a task in an infinite number of steps in a finite amount of time, so long as the mathematical series that describes those steps and the series that describes the timing of those steps converge in the right way.

Again we agree that this implies that an infinity of steps can take a finite amount of time.

If you agree that an infinite number of steps can be completed in a finite amount of time, what’s the problem?

[kamui]

I agree with the implication not the conclusion. The problem is that there is a paradox !! And I don’t know how reality solves it ! To solve it implies to choose between a discrete and a non-discrete etc…

I think I understand your point, but I think you make an approximation in your reasoning when you play with infinity (we see at this moment you are a physicist ;)). You solve it by assuming something like 0.99999999… = 1. For me, in physics, it is like assuming universe is discrete

And you just explained all what it can imply so I am happy to see you understand well what is my problem

[ThornEel]

If I remember correctly, 0.99999999… = 1, mathematically speaking.
Or at least, it is according to the repository of all and only truth, so it must be true (unless a student modified the page to avoid a bad grade, or a teacher modified it to catch sloppy students(*))

(*) No really, I’ve known of people doing each of those

[kamui]

for me this just shows limitations on representation of fractions in a digit form.

this is the “…” part of the representation that permits such absurd equalities, because it is not well defined, and so not rigorous.

[Kichae]

The problem is that there is a paradox !!

There isn’t. There’s simply the very common assumption that it can’t be done, which makes it appear that there is a paradox.

You solve it by assuming something like 0.99999999… = 1

That’s not an assumption, any more than 1+1=2 is an assumption, or that 1 metre = 1000 millimetres is an assumption.

Let’s see if I can’t explain this in a different way. I’ve been focusing on the time it takes to complete a step getting smaller. Maybe that’s the wrong approach.

Let’s talk about the rate, or speed if you will, at which these steps are being completed. We’ll stretch out the jumps in distance so that they’re all the same. Since there are an infinite number of steps, the distance between A and B is now infinite, right?

But the time it takes us to cover each step gets progressively smaller and smaller. In effect, our speed is getting faster and faster. As we keep going, our speed increases at an ever quickening pace, and does so in such a way that when we “hit” the “last” step (an infinite distance away) we are traveling at an infinite speed!

If speed = distance / time, then time = distance / speed. That means we have infinity / infinity. When you divide an infinity by another infinity, the answer can be infinite, finite, or zero, depending on what “kind” of infinities we’re talking about. If the distance infinity is larger than the speed infinity, then the time to reach the end is, in fact, infinite, and we end up with the situation you keep picturing in your head: You can never reach Point B.

If the speed infinity is significantly larger than the distance infinity, it takes 0 time to reach the end, and you’re moving at an infinite speed in real life (or, more physically, you’re moving at the speed of light). All of distance becomes meaningless.

But if the distance infinity and the speed infinity are comparable, then they collapse into a regular, finite number, as ThornEel describes above.

So, you can complete an infinite number of steps, because the rate at which you perform those steps increases to infinity as well.

[thelazyjaguar]

The universe isn’t a reasonable person, though, and if space is smooth and non-discrete, then anything that moves must move through an infinite number of points, and so it’s an issue worth discussing.

The universe didn’t define an infinite number of points, the person did by assuming that space was smooth and non-discrete.

Either space is quantized, or it’s possible to move through an infinite number of steps in a finite amount of time. Or, as it turns out, both.

If space is quantized, then space takes on discrete values and therefore cannot be defined with an infinite number of points.

The problem is that there is a paradox !! And I don’t know how reality solves it !

Again, reality didn’t create this paradox. A person did. It’s all down to how they setup the problem. They took no consideration for time in it. See everyone else’s explanations for details.

[Crayfish]

Why are the two particles with entangled state not the same as a meter rule broken into two?

Because the particles don’t actually exist until they are measured.

Einstein also thought that the truth was of the form of a broken meter rule. Then a guy called John Bell came up with a theory that predicted a difference between measured results if the ruler existed all along and if it came into existence at the point of measurement. The difference between the predicted measured results is known as Bell’s inequality. If you want to understand the details then there’s a super little write up here that requires only simple mathematics so even I can understand it.

People found ways to test Bell’s theorem (eg. Alain Aspect ref’d above) and in every case the measured results align with the predictions of quantum mechanics. The ruler only exists as a probability until it is measured. At the point of being measured it is as if the ruler goes back in time and breaks at a certain point which is then propagated to the other (entangled) part of the ruler.

There are still some loopholes that could allow hidden variables but the weight of evidence is firmly in the camp of quantum mechanical behaviour. By the way it is conceived, Bell’s inequality also rules out the possibility that the probability waveform holds the hidden state of the particle. The state can’t be anything apart from “undefined” until measured, at which point all entangled particles assume an appropriate state.

[Kichae]

The universe didn’t define an infinite number of points, the person did by assuming that space was smooth and non-discrete.

And you could just as easily say the same thing about space being quantized. We don’t know the structure of space. All we can talk about are ideas, and whether our ideas approximate reality or not.

If space is quantized, then space takes on discrete values and therefore cannot be defined with an infinite number of points

And yet, it would still be true that quantized space wouldn’t be a requirement for resolving the issue. So, in that case it would be both.

[thelazyjaguar]

And you could just as easily say the same thing about space being quantized.

Yes, but I’m not the one who picked one of those two assumptions. You did. I simply addressed the ones brought up.

All we can talk about are ideas, and whether our ideas approximate reality or not.

That’s basically what I’m saying. When does our approximation of zero sufficiently match reality? That does require a reasonable person and not invocations of the universe does it not?

And yet, it would still be true that quantized space wouldn’t be a requirement for resolving the issue. So, in that case it would be both.

I took your original reply to mean that both were simultaneously possible instead of each being uniquely distinct. I don’t believe you can take a finite distance and divide it a finite number of times and arrive at an infinite number of steps. If you mean they are both distinct and valid, but mutually exclusive possibilities then we have no argument.

[Bentware]

The mission to demonstrate technologies needed to detect gravitational waves in space has been a stunning success.

There is currently enormous excitement around gravitational waves - the ripples in space-time generated in cataclysmic cosmic events, such as the merger of black holes and the explosion of giant stars.

The existence of these phenomena was first confirmed last year at the Advanced Ligo facilities in the US.

So Kichae, is this true?

Gravity space mission passes big test

[Kichae]

So Kichae, is this true?

Which? That LIGO found strong evidence for gravitational waves? Or that the satellite mission was successful?

The LIGO team definitely presented some interesting and compelling, if unconfirmed, early evidence for gravitational waves. I’ve never heard of the satellite mission, but I haven’t really had my ear to the ground these past few months.

[Bentware]

Thanks, and this part: [quote=“Bentware, post:74, topic:3186”]
The existence of these phenomena was first confirmed last year
[/quote]

[Bentware]

" ‘Harmful’ robot aims to spark AI debate "
“The First Law” after a set of rules devised by sci-fi author Isaac Asimov. What this artical is about.

[Skyentist]

I think you forgot to link it @bentware

[Bentware]

This has been a classroom assignment, everyone failed.

The correct answer is:

'Harmful' robot aims to spark AI debate

One Browne point for Skyentist.

[Kindred]

as someone who is working with A.I. as a bit of a hobby, i’m just going to add my commentary on the link:

there seems to be a trend about the definition of “artificial intelligence”, and this one kind of hits a propaganda mark against it. similarly to google’s proposed “kill switch.”

as it stands, there is no possibility of that the robot could: “it could decide to do something harmful”.

the truer statement reflecting programming (and algorithmic neural networking): “it could do what it was programmed to do”.

the facts as it stands is that the robot in question didn’t decide to do anything harmful. the creator behind it made those decisions. this is as if saying if a go algorithm (not artificial intelligence) eventually evolved and became self-aware and decided it wanted to forgo the game of go. it doesn’t work like that.

robots are programmed for a specific function and are programmed specifically within those parameters. artificial intelligence can be reprogrammed, but only to the degree of its parameters regardless. in essence, this robot isn’t artificial intelligence. it is merely a robot that commands a random number generator between 0 and 1. then just happens to prick your finger your finger if its a 1. this was not, at all, any kind of turing test. the mentioning of asimov’s laws is just more of the same attention seeking, as in theory they are implementable but computationally they’re not a problem we will face for a long, long time, if we ever do.

(p.s. i hope i answered your question and thank you for posting the link!)