A frog jumps towards a pond.

Every time it jumps, it jumps half the remaining distance.

How many hops does it take before it reaches the pond?

Lincoln Torres

A frog jumps towards a pond.

Every time it jumps, it jumps half the remaining distance.

How many hops does it take before it reaches the pond?

Nicholas Adams

It'll never get there

Thomas Ward

What he said. Learned this from Stone Ocean.

Asher Brown

Correct.

That how one loses their virginity.

Justin Lee

Fuck you ori

Parker Adams

Eventually it will be exactly one atom's jump away from the pond. Next it jumps on the atom and the second jump is in the pond.

Ian Martinez

Wrong.

You don't understand atoms.

Jonathan Morgan

There's an infinite number between 0.000001 and 0.000002

Caleb Howard

It's a magical thing when it happens.

(but it's not likely to occur)

Easton Allen

shit unrelated topic thread, this has ruined this shit board. thanks op, now kys.

Chase Edwards

Have you seen the tranny threads on this board?

Jonathan Ross

YOU don't understand atoms. Atom literally means something that can't be divided. You can't jump half the distance of something that can't be divided.

There's nothing infinite in nature.

Lincoln Gomez

>You can't jump half the distance of something that can't be divided.

So he never arrives since he only jumps half the remaining distance.

Anthony Diaz

There's an infinite number of air molecules

Gabriel Rivera

"atom" (indivisible) is from ancient Greek.

We've progressed since then.

Look up subatomic particles.

Camden Sanders

But if it MUST jump, it can only jump the full length of the atom, landing in the pond.

No, there's a limited number of everything, especially on Earth, which is a self-contained system.

I was using it in the original greek definition, yes. Atoms are made of smaller particles, but there is an end to how much more these particles can be divided. At the bottom is the smallest measure of length in nature and that can't be divided.

Joseph Lopez

no theres a finite amount of air molecules, if there were infinite there wouldn't be climate change bullshit pushed on us today.

Joseph Baker

Half is still half.

Nicholas Baker

>Frog jumps .9584 atomic units

>Frog jumps .4792 atomic units

everyone in this thread btfo

Jaxon Parker

There can't be a jump at half the smallest length that can be jumped. You can imagine it, but it can't happen in nature.

Jordan White

The half is zero.

Jeremiah Thompson

Real life is analog, not digital. An atom is not a pixel. You can move half the distance of an atom, and half of that, and so on infinitely. You seem to believe atoms line up perfectly between different objects, but that is not the case.

Oliver Gomez

>it can only jump the full length of the atom, landing in the pond.

It jumps in place

Jordan Perez

This isn't true. It is possible to move "half an atom" or half of that, etc.

If spacetime was in terms of atoms, then we would just teleport through (empty) space which obviously makes no sense.

It's impossible with a finite number of jumps, but what's kinda cool is that (1/2+1/4+1/8+...) converges absolutely, so with infinite jumps, you would land exactly where you wanted to be.

Logan Cruz

It jumps in peace

Jaxon Hernandez

Your dick is half an atom, nigger.

Thomas Butler

lol

wjnvkmrjnem bdk;vn fd,lmk;e,sv dfndmvkf ,gnfv

Jaxon Gomez

Atoms are massive and composed of a multitude of sub-atomic particles, some of which are also compositions.

The shortest possible length is the Plank length.

You all are massive brainlets.

Camden Russell

Give me a moment to pond-er asymptotically.

Connor Watson

>Real life is analog, not digital.

Care to present evidence supporting your hypothesis? In fact what you think of as "digital" is represented by sampling (quantizing) analog values to begin with. So "digital" is merely emergent from "analog"...

More importantly however in quantum mechanics as far as I'm aware a vector is discrete rather than continuous. In fact it can be said that the very concept of a vector isn't particularly valid. I wish I could check back 500+ years from now and see if we finally figure out how we've fucked all this up.

Regardless, the ENERGY used to transport the "frog" quantum through space whether continuous or not IS DISCRETE, so our particle can not change state to a mid-way point between its two minimum quantum states. This means that the travel of the frog will eventually end where its momentum is quantized to ZERO, at a dead stop.

Posters have also assumed that the step between where the "pond" is defined would inherently be the next step before this effort occurs. That's clearly an obnoxious assumption - the minimum quantum state of the frog may occur at some far more significant distance from the "pond" which would make it impossible to reach the pond: ever.

This is similar in some ways to being outside the "light cone". **en.wikipedia.org**

... but rather than due to expansion of space vs. the speed of light, we're dealing with the distance vs. minimum quantization state of the momentum of our quantum frog.

You can find discussion of this concept as it relates to the "butterfly effect" which is in fact impossible on larger scales (the effect of the butterfly's wing is quantized to zero past some limiting "window".) **en.wikipedia.org**

Jaxon Wood

The frog itself is not infinitesimal, nor is an infinitesimal movement a "jump." This formulation fucks up the paradox in a few ways, but the most important is that it poses the subdivision as a discrete action, rather than an analytical approach.

Cameron Hernandez

BTW; this is all nano-bot level stuff. If you can figure out how to avoid the decay of energy on such scales you'll solve countless problems in modern technology... if you can force the quantization upward to increase the energy rather than decay to zero, you'll have invented the perpetual energy machine.

Sodium Chloride.

Ethan Wilson

Unless it is stolen.

Jeremiah Wilson

The very low-level (simple) version of the math is:

apow(n,r) = log(n) / log(r)

steps to minimum quantum = apow(quantum, 1/2)

So assuming our initial step size = 1 and our minimum quantum is 1e-24:

steps = 79.726274277296696348887666307745364220755953432589934689314153499582434638607005180403353840624883722391776921046006043843778327622324645318607266551967729452446832463780133647432422620560597400006594400976285674980497002633180795220964300551739361659938712522385421198599820538773657205439434017459310272234546160472531469635681881388301234726505014109463333631790966929968884597833881227019319632400574107051536144674577361533077796424170279709399813139951732675363039157575822348681611358818808808081621953696

So the 80th "hop" would be null (dead stop.)

Nathan Sanders

>The shortest possible length is the Plank length.

Actually that's not true which I knew intuitively as I've tried to find evidence for a "digital reality" in the sense of hard quantization of quanta like position.

In reality (ha ha ha ha ha) what we understand so far is more leaning toward "position is not valid. it's only our interpretation of things on a meta level."

Think in terms of relativity. We can only measure position relative to, not absolutely. Does it terrify you to realize you already know there is no such thing as absolute position?

Ryder James

Wherever you go; there you are. Have you grown when you own what you've already known?

Camden Garcia

What the fuck are you rambling about?

Length and a coordinant system position are completely different topics. There is no meaningful distance in our universe less then the Plank length which is fixed by the speed of light. All of which are intrinsic values relating to the specific geometry of our space-time.

This was determined even before your parents were born, and you have the Internet. Try actually reading shit instead of making up nonsense in your bedroom.

Gavin Torres

>Plank length

Actually, you mean Planck.**en.wikipedia.org**

Everything you said is nonsense you made up on the spot.

Blake Parker

Atoms can be divided tho

Adrian Taylor

For example consider light that travels less than c. This is very common, light never travels c outside a total vacuum and unaffected by gravitational lensing, which does not exist within the universe.

The planck length is merely the space over which a photon would travel if it's assumed to be a particle (it's not) and c is assumed to be a fixed constant speed (c is, but the velocity of a photon is not.)

So you're making assumptions that the absolute position of a particle (which doesn't exist) is quantized to planck lengths based upon ... ? What exactly?

You're just pulling this assumption out your ass. Any particle can travel less than c and can have a relative position that is not quantized.

Carter Long

"The Planck length is sometimes misconceived as the minimum length of space-time, but this is not accepted by conventional physics, as this would require violation or modification of Lorentz symmetry.[7] However, certain theories of loop quantum gravity do attempt to establish a minimum length on the scale of the Planck length, though not necessarily the Planck length itself,[7] or attempt to establish the Planck length as observer-invariant, known as doubly special relativity."

Also nice job telling someone intimately familiar with the material to read something you yourself have clearly no knowledge about.

Parker Perez

find half of zero thread.

Elijah Cooper

> spelling matters

Classic

Light always travels at, wait for it.... The speed of light. When anyone mentions a deprecated speed of light though a medium they are implicity mentioning delays due to absorption and reemition. This has nothing to do with the Plank equation.

I never said space had a minimum length and for that reason specifically stated that distances less than Plank length have no meaning.

The only material you are intimately familiar with is yo-gi-oh.

Camden Robinson

>The only material you are intimately familiar with is yo-gi-oh.

I put some of that in your mother and you emerged.

Carson King

How does it feel to actually be a brainlet

Eli Howard

this question is unanswerable

why? you haven't told us how long the first hop was