Recent comments in /f/explainlikeimfive

Antman013 t1_jec925g wrote

Small, modular, nuclear reactors would be ideal for this, I would think.

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As to the salts, truck them to locations with "winter" in order to clear roads. Also, aren't the oceans becoming less "salty" due to polar ice cap loss?

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Parking-Guest545 t1_jec8ybq wrote

Zeno argues that motion is impossible because in order to get from one point to another, an object must first travel half the distance, then half the remaining distance, and so on, ad infinitum. Since there are an infinite number of distances to be traveled, the object can never actually reach its destination.

In reality, Achilles will eventually catch up to the tortoise, despite the paradox's argument that he cannot. Zeno's paradox is based on the assumption that an infinite number of smaller and smaller distances must be covered in order to reach a destination, but in reality, there is a smallest possible distance that can be traveled, such as the Planck length in physics.

Furthermore, the paradox assumes that time is infinitely divisible, which is also not true according to modern physics. When the actual physical laws are taken into account, the paradox can be resolved, and it becomes clear that Achilles can indeed catch the tortoise, given enough time.

Zeno's paradoxes continue to be interesting philosophical puzzles that raise questions about the nature of space, time, and motion, but their solutions lie in our understanding of modern science and mathematics, which provides a more accurate and realistic description of the world around us.

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DavidRFZ t1_jec8wfj wrote

Achilles definitely catches the tortoise.

The way the story is told, they keep describing snapshots in time that are closer and closer to the time the tortoise is caught without telling you about that moment.

Like if he catches him at noon and you tell a story describing 11:59, then 11:59:30, then 11:59:45, then 11:59:52.5, etc.

You can certainly tell a story like that where you never get to noon. But we all know how time works. Eventually noon will come.

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Mental_Cut8290 t1_jec73wh wrote

Tortoise has a head start, but moves slow.

Achilles will overtake and win despite starting behind.

The problem is an infinite series.

Achilles will run, for some amount of time, and eventually reach the tortoise's starting point. But the tortoise has also advanced during that time and Achilles is still behind.

The race continues a lesser amount of time and Achilles reaches the tortoise's last checkpoint, but again the tortoise has moved on.

EVERY time Achilles reaches where the tortoise was, the tortoise has moved a little bit farther. This will be true for infinite points.

How can Achilles reach the infinite number of checkpoints and ever pass the tortoise if the tortoise is always a little bit further away for infinite points?

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TheDefected t1_jec6x8q wrote

Another cause/fix to it is to do with quantisation, and quantum physics.
This lead to a similar paradox called the UV catastrophe.

The premise was you could infinitely divide things, time and distance, so half of whatever measurement there is, but it turns out you can only get so far, and then it blends together in the Planck length and Planck-time.
It's not a case of just being the smallest thing currently measurable, it's more the limit on the granularity of the universe.

The UV catastrophe is what started quantum physics, the maths said that a black body (in simple words, something that radiates heat perfectly) would radiate energy at all different frequencies in differing levels. The maths divided these frequencies infinitely, and they all had at least some energy, at that would mean it would radiate infinite energy too.
It was figured out that you couldn't just divide everything infinitely, it got down to discrete quantised steps, eg mini packets or "quanta" in these levels.

The Planck length is the smallest possible division of space and distance, and you can't halve it, and the Planck time is the time it takes light to cover the Planck distance, eg the fastest possible thing covering the smallest possible distance, and it can't get smaller.

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mkstot t1_jec6nxy wrote

Your alternator may not produce enough voltage to power your electrical system fully. In older cars this was ok because you didn’t have such a high demand for power unlike todays cars with power windows, steering, heated seats, cameras, etc. best err in the side of caution, and have the battery and the alternator tested at a parts store.

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cocompact t1_jec5aml wrote

Let's give some formulas for Achilles and the Tortoise, to see how the times when Achilles reaches a point where the Tortoise was previously at keeps shrinking and stays below a definite time (when their positions are tied) rather than getting big.

Say Achilles has position A(t) = t at time t and the Tortoise has position T(t) = 4 + t/100 at time t, so A(0) = 0 and T(0) = 4: at time 0, the tortoise is 4 units ahead (meters, feet, whatever).

Achilles reaches position 4 at time 4: A(4) = 4. And at that time T(4) = 4.04 > 4, so the tortoise is still ahead at time 4.

Achilles reaches position 4.04 at time 4.04: A(4.04) = 4.04. And at that time T(4.04) = 4.0404 > 4.04, so the tortoise is still ahead at time 4.04.

Achilles reaches position 4.0404 at time 4.0404: A(4.0404) = 4.0404. And at that time T(4.0404) = 4.040404 > 4.0404, so the tortoise is still ahead.

Achilles reaches position 4.040404 at time 4.040404: A(4.040404) = 4.040404. And at that time T(4.040404) = 4.04040404 > 4.040404, so the tortoise is still ahead.

Despite the tortoise always being ahead of Achilles at these times, notice the times we are working with are always remaining below 4.040404040404... < 4.05. So it's simply false that Achilles "never" catches the tortoise because such reasoning is just ignoring the actual passage of time by focusing on ever vanishingly small units of time. Once the time reaches 400/99 = 4.040404040404..., Achilles and the tortoise are at the same position: their positions are tied. And after this time Achilles gets ahead of the tortoise and remains ahead. Notice the time when Achilles and the tortoise are tied is the value of an infinite decimal 4.0404040404..., which can be thought of as a convergent infinite series 4 + .04 + .0004 + .000004 + ..., which is related to the answer by u/EquinoctialPie saying that the resolution of the paradox is the fact that infinite series can have finite values. One does not need other tools from calculus (like integrals), but perhaps the series can be viewed in different ways related to those other tools.

You can graph this: plot y = t and y = 4 + t/100. For very small positive t, we have t < 4 + t/100 (Achilles is behind the tortoise), but when t = 400/99 the two lines cross, and when t > 400/99 the first line is higher than the second line (Achilles is ahead of the tortoise).

In summary, there is no actual paradox if you pay attention to all times instead of getting fixated only on quite small times. The error here is analogous to people who mistakenly think an unending decimal like pi = 3.141592653589... is an "infinite number" because it has infinitely many digits: this confuses the number of digits with the numerical value of the decimal.

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redditfejs t1_jec4r8g wrote

The part of Siberia where the tigers live isn't the stereotypical taiga you are probably imagining. Google "Ussuri broadleaf and mixed forests", "Sikhote-Alin Nature Reserve" or "Ussurisky Nature Reserve". It's very far south, far enough that the boreal taiga is replaced by a temperate forest, not unlike those in China, Korea or Japan.

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Bthejerk t1_jec3fjh wrote

Substandard insurance companies do this all the time. I’m sure they know that for every minute that people sit on hold, so many people will hang up. If you have minor damage to your car and their insured hit you, you might give up in frustration and forget about it.

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