Random things
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- เผยแพร่เมื่อ 27 ก.ย. 2024
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Hope you guys enjoy! As stated at the end I'll taking a little holiday break so will return in the New Year (possibly with a new skit video). You can check out the second channel th-cam.com/users/zachstarhimself for exclusively skit videos and as always check out STEMerch.com to get the floating globe, meme shirts, and more.
Have a nice holiday!
Hey can you do a video on the dream Minecraft speed running statistics and why he got banned
Hey Zach, can you plz do a video on mechatronics engineering. Please I would really appreciate that thanks.
The fog boat is just the chase of the Bismarck
That was awesome but the first one is utterly counterintuitive and I think needs a video of its own...really...shouldn't it travel fast enough in the forward direction due to the same velocity of wind taking it in the first direction to make up for the slowing caused in the second direction...the first direction might almost be instantaneous whereas second one takes the amount of time taken by the no wind plane to go back and forth?...please explain...thanks a lot.
How does a mathematician capture all lions in Africa? He builds a cage, steps into the cage and defines: "This is outside."
That's hilarious.
He’s thinking outside the box
And then he gets eaten by a lion that was outside the cage.
@Butch (the black cat from tom and Jerry) He missed that a lion had snuck into the cage
@@Etazoz *out of
*Physics strategy of taking things to the extreme*
"Now, assuming this cow is perfect sphere,"
@@AmmoGus1 and the sun doesnt exist too, so photons wont push it in any direction and no energy is being added to the system
And pretend the cosmic microwave background doesn't exist, and neither does heat transfer by radiation.
Oh yes, and all collisions are perfectly elastic
don't forget to Assume all gasses are ideal and the system is isolated
Everybody gangsta until the cop car chase goes into a logarithmic spiral...
lmao
Doesn't really work with cars unless it's in a city with logarithmic spiral streets :,D
just change direction 2 times
Or just drive slower at a different velocity.
Or just don't commit crimes :D
Faster method for the 'fog-boat' thing: start the spiral when you would have encountered the boat if it turned 180*
Which boat as shown in the animation of the video would u go for 1st tho?
@@bamb8s436 the one which goes straight to the left. It was for some reason omitted from the visualization.
David.
Interesting thought!
Why do you think this? It's certainly an attractive idea because you start your spiraling earlier. but the spiraling isn't the essence of what you're about, surely. You want to find the other boat earlier and since 50% 0f the time the spiral is away from the target, no matter which way it chose to flee, therefore 50% of the time your early spiral is giving the target extra time in which to get more distant, surely?
A thought which may or may not be equivalent, I'm not sure, in 50% of all cases starting early to veer away from your path straight ahead on known information is adding to the time the target has to add to its distance from the last place you saw it, don't you think?
@@lordfnord5768 if one thinks in worst cases, my method is better. Once you start spiraling, you have to max do one round. Since I both use less distance to where I start and have a smaller spiral (the chased boat haven't gotten as far when I reach it) it will be faster.
@@lordfnord5768 also, in the case in the video the 50% who turn backwards make that spiral longer. So it is the same either case, but i travel less before starting spiraling.
Joke of the day:
Did you hear about the claustrophobic astronaut?
*He needs a lot of space.*
*pokerface*
Get your hands off my face bro
th-cam.com/video/KZFcYK2VzkI/w-d-xo.html
YOOO brother
6:55 : I have discovered a truly remarkable proof of the irrationality of pi plus e, but the margin of this TH-cam comment is too small to contain Fermat's last theorem.
Go up 🔝🚀
Lmao, nice historic math reference!
I thought he said it hasn't been proven whether or not it's irrational?
@@anshumanagrawal346 It's a joke referencing Fermat's Last Theorem.
See: en.wikipedia.org/wiki/Fermat's_Last_Theorem
Wouldn't be the first time I escaped from a balloon when I wasn't supposed to.
damn
damn
damn
"I don't need any math, I can think." -- Joan Robinson, English economist.
The wind is going to slow you down one way. Going slower you will be slowed down for a long time.
The wind is going to speed you up going the other way. Speeded up you are going to be speeded up for a short time.
You're speeded up by the same speed as you're slowed down by -- but there's more slowing down than speeding up going on, so you'd rather have neither, QED
What a paradoxical statement.
“I don’t need Maths because I can think”,
Obviously, you might be smart but lack intelligence.
Mental calculations are included in mathematics.
So please find the area under the graph of x^x from 0 to 1 using language
@@gammarayneutrino8413 that seems like an unfair test, since you didn't state the problem using natural language
Savethiscomment
@@BlaqRaq
🤣
Maybe google up "affirmation of the consequent" and then take it from there, Albert.
And when you use quotation marks to imply that you are quoting something, please try to get the quotation accurate, OK? Not to do so is, well, dishonest.
That boat scenario was super relatable, thank you I no longer feel alone
No shit.
Me a physics boi: wouldn’t the limiting case be the plane takes infinite time when W=V.
Zach 0.2 nano second after: 2:15
YO im also a physics boi
Edit for clarity: 200 ps
Suppose wind flowing in direction a to b now at first plane will reach twice fast but when returning as wind speed against plane is same , the plane velocity will be 0 and plane won't move which ultimately makes time infinite 🥱.
If W >V, the divisor becomes negative and so the time becomes negative. I just invented a time machine.
Unless the boat in the mist actually stops and changes direction several times knowing the seeker will try to use this sort of predictable pattern to find it
The idea of the Wind Puzzle (A round trip always takes more time in the presence of wind) was used to disprove the existence of ether.
Ether was a proposed medium that surrounds everything, and was supposed to be the medium light uses for travelling from the sun to the earth. Just like sound travels through air, ether was proposed to be a medium in which light travels. The experiment was to measure the round trip taken by light in two perpendicular directions - One in the direction of ether and the other perpendicular to ether. The light beam in one of the directions (perpendicular) was supposed to be faster, but such a difference was never recorded even though this experiment was performed in multiple orientations in multiple locations.
At last, it was concluded that light is a wave that can travel in vaccuum.
This was really interesting. Merry Christmas!
As a student of Piratical Engineering the second example was super relevant to me
This guy sounds just like those two guys that kidnapped the wrong girl
Wut
Go watch his second channel
Interesting how things turn out to go when you consider many factors!
You know, we can just HEAR the other boat
the oily-macaroni constant lmaoo
I just wanna get a reply from Zach. I have never gotten a reply from him. It's my last chance this year.
Here you go!
@@zachstar omg
Lmao what
@@ViratKohli-jj3wj What a mad lad
You should follow up by asking to be an extra in an upcoming video or something.
Winds add necessary maneuvering for take off and landings if there's a tailwind.
1) The case with tailwinds on the first leg (as shown), the plane needs to take off INTO the wind so it must take off in the opposite direction of travel -- and when it lands, it must overshoot the airport and turn to land, again INTO the wind. Then on the way back, it just has headwinds; it can take off and land in the same direction of travel.
2) With headwinds on the first leg, it can just take off and land in the same direction as travel, but on the return it must oppose the direction of travel to take off and land.
With no wind, no extra maneuvering, needed, thus no extra distance and time needed.
All of that is assumed to take a negligible amount of time, compared to the essence of the problem.
“How does this first one affect my life”
Me, a CFI: “ummmmmm”
1:46 Fly against wind that is faster than your airplane, time becomes negative, go there before you started. I just invented the time machine. Patent pending.
Cranks on that imaginary wind to get a faster flight than I would with no wind.
For the first one, using extreme provides a really good example. Say the planes travel at 350 mph, and the wind blows at 350. From A to B is 350 miles. The plane with no wind travels the total 700 miles in two hours. The plane with wind gets a 2x speed boost and travels the first 350 miles in half the time and twice the speed of the first plane. However, on the way back, if we were to reverse the 2x speed boost the plane got on the way out, we would have to cut its speed by half, which would mean a wind speed of 175 mph. Since the wind speed is constant, it is too fast, and slows the plane down
The headwind slowing you down means you spend more time in headwind.
Additionally,
1+1
The still air vs constant wind journey scenario can be asnswered much more simply using common sense. With a wind, any tailwind acts to improve groundspeed for less time and the headwing acts to reduce groundspeed for longer.
That still isn't enough to tell the difference between a still wind and a round trip with and against a constant/uniform headwind/tailwind. You need to set up the problem mathematically to tell the difference. A general common sense statement that tailwinds improve ground speed and headwinds reduce ground speed, isn't enough reasoning to conclude that it is any different from the case with no wind.
My answer to thumnail: the same should they not be? Unless the plane is designed to catch back wind and not be affected by head wind, in which case constant wind is superior.
There is something like the trawler problem that had real world consequences.
In the 1980s a Cessna on a delivery flight to Australia lost its compass and couldn’t find its heading.
A passenger plane (DC-10, IIRC) was asked to help and agreed try to find the Cessna. Passengers also agreed (and delay the flight) by looking out the windows.
However to find the lost plane they first noted when and where they first made direct contact with the Cessna and then had to fly until they lost radio contact. The radio range was well known and they calculated a rendezvous point then guided the plane to safety.
It is thought they flew passed the smaller plane but it was so small that it wasn’t spotted.
I can’t remember the book I read this in.
The Wikipedia entry has a slightly different (and probably more accurate) version.
en.wikipedia.org/wiki/Cessna_188_Pacific_rescue?wprov=sfti1
Fun fact: Even though we don't know for sure if pi+e and pi*e are irrational, we know that at least one of them is. Otherwise, if pi+e and pi*e were both rational, then the solutions (namely pi and e) to the equation x^2 - (pi+e)x + pi*e = 0 would be quadratic irrationals, but we know this is not the case.
Imagine wind speed approaching speed of plane in 2nd case
It's out of my *limits*
For someone : w²/v approaches v (from LH) v-w²/v approaches 0, 1/(v-w²/v) approaches ______
I think you've greatly oversimplified the wind problem here, Zach.
How?
@@axelnils Apologies for taking so long to reply to this. I actually found that Zach was "right" but you have to make assumptions that he himself did not state he was making. Let me start by using the assumption that I imagine most would use: no thrust force is applied to the plane. With this assumption in play, the planes would never move at a constant velocity as even in the no wind scenario, air resistance is still a thing. In fact, even with a tailwind, the second plane would move slower than in a vacuum until the wind matched or was faster than the plane's own speed. Furthermore, there is not a chance that the second plane's velocity would be impacted that much by w (assuming w is the wind speed). Imagine you are jumping around in gale force winds for science or whatever. You will certainly be affected by the winds but not nearly enough to fling you around at twice the speed of Usain Bolt. Conversely, a 1 m/s wind is not going to do anything to you walking at 1 m/s. In fact, you will barely feel it. To work out this problem, you would have to deal with some differential equations that I'm just far to lazy to solve.
All that being said, Zach can be completely right if
a) Thrust forces are applied such that the velocities are as Zach said.
b) The drag is directly proportional to the the plane's relative speed to the air. (The standard model of using the square of the plane's relative speed also works for Zach but the logic differs a bit).
Assumptions a and b allow for the planes to have the same resultant thrust force applied. Of course, you could allow the planes to have different thrusts but that kind of defeats the purpose of the problem.
Imagine the wind speed w is greater than the velocity of the plane. Then the plane would never be able to travel from B to A, hence the time is infinite. (You can also observe this in the equation as well, if w>v, then t
Simple reckoning, flying into wind time will be longer so negative effect of wind is greater than positive effect on ‘with wind’ leg.
4:55 Spock: "Mr. Star is intelligent, but not experienced. His pattern exhibits two-dimensional thinking".
baloon 4d sphere thing means that every point in closed universe would have it's antipode. Never thought about that
The Euler-Mascheroni constant looks suspiciously close to 1/ sqrt(3).
You can take your first question to an even further extreme (and funnily enough, even stay within what can really happen). Get the headwind to be faster than the airspeed, and then you're going the wrong direction to cover the required distance. I've known people who have used this extreme case to land a Cesna going backwards. They didn't describe how taxiing was after landing, though
Actually the spiral would be more complex as the boat didn’t turn directly into you so you wouldn’t need to recheck water you just crossed. So perhaps a
For the plane and wind problem, I would say that with the wind, the plane will stay longer at low speed than at high speed so the mean will be more affected by the low speed flight and then this case will be the slower
5:34 oily macaroni constant
My guess is that it will take longer with wind because you are going faster for less time and slower for more time, so your average speed per minute is slower.
Before it starts spiraling, the chase boat is traveling twice as fast as the target, but as soon as it starts to spiral it's traveling about 9 times faster. Would have been interesting to see how big the spiral would need to be if the chase boat was "only" twice as fast (or less).
wow its good to know that i could become outside of an infinitely stretchy ball in a 4d hyperspherical universe
The plane result is counterintuitive.
I was binge watching your skits. I genuinely watched 8 minutes of this before i was like, wait, this one isnt a a joke.
π+e=6
π-e=0
πe=9
π^e=27
Here you go, in your face Euler- mascheroni constant
More like I massacred your only constant😂
Well if
π=e
And
π^2=10
=> π=√10
e=√10
Thus,
π+e=2√10. So
6=2×√10
The plane problem is similar to the doppler effect with a moving source.
Worth mentioning is that it is known that at least one of π + e and π x e is irrational.
This comes directly from the fact that pi and e are both transcendental. Actually only one of them has to be transcendental.
exept that in the prosses of exiting the baloon, you would put everything that was outside of it inside it
OBJECTION !!! *ace attorney music starts * But what if the boat turns and stops and you whooosh past it?
Also, for the first problem, the opposing force seen by going opposite the wind is greater than the supportive force from the tailwind. Hence, the time is further lengthened by the presence of wind. And, the stronger the wind, the larger the difference.
I'd love to see more unsolved maths problems in future videos
The wind senario doesn't make sense though, headwind gives a plane lift which can make said plane faster! And there is no limit set on the question to how complex the answer can be which means the answer can be either faster or slower.
At 5:12, the radial component of your velocity must equal the speed of the target for this to be true. Since your velocity is mostly tangential once the spiral begins, this places a high constraint on your boat's capability vs. the target's capability. Additionally, if the target changes direction for a short time and then changes direction again, your strategy will fail because the target is always between your search paths. At 9:10, 4D space-time is hyperbolic instead of spherical; one might yet suppose, but this is unrealistic.
As a random thing I can confirm these are random things
for the first one
how i got this intuitively was thinking about "how much time do i spend with time in one direction" instead of thinking about total time directly. you can somewhat see that way of thinking in the extreme case
moving forward, i don't spend much time in the wind, as i already reach my destination
moving backward, i get slowed down for longer.
it's a classic "i move half the way at 30 and the other half at 20, what's the average speed?" question
Thanks, good holiday!
for the first problem, it would be equal if the times spent under both velocities were equal.
but here, you make the distances equal, resulting in more time for the deceleration to act and less time for the boost to help.
At 2:22, if the plane is at a stand still, it would stall and fall and never arrive so the answer is A
For the wind problem there's something I dont understand. Since the wind is a velocity, lets make it a vector that follows the direction of the movement. When its going in one way, the Work would be |AB| x |v| x cos(x), when its going back, the angle is now opposite so the work would be |AB| x |v| x -cos(x). Thus, the total work should equal 0, so the wind shouldnt make a difference in the airplane's speed. What's wrong in my reasoning?
8:33 - but you're only drawing the fence. Colour in the circle and you'd have a clear definition of "inside" and "outside". Defining the "inside" as automatically being smaller than the "outside" is just arbitrary, isn't it?
You can start with the endstate of the circle, color it in and reverse the process. Now what is colored in - the "inside"- has flipped again.
@@lunkel8108 It seems to me that "inside" vs. "outside" is relative. The balloon creates a partition, and whether or not something is "inside" the balloon depends on whether the observer starts on the same side or the opposite side of the partition from that something.
If a cage separates me from the rest of the universe, in some sense the rest of the universe could be said to be "inside" the cage from my reference point.
I don't think there's a really good way to define "inside" vs. "outside" from a reference point which is not itself on the sphere, but I also don't think there really needs to be.
@@tissuepaper9962 Neither me nor Zack is saying there "needs to be" anything, the point was just to point out that, as you said yourself, defining a general notion of "inside" doesn't really work. That's it.
Which side would you colour when the sphere is at its maximum volume?
For the first one an easy way to think about it is that when something is inversely related to another (like time and velocity) subtracting something from the denominator will always have a bigger affect than adding to it. This is visualized in the graph y=1/x where the slope is a lot steeper as x approaches 0.
The wind example is effectively why the Michelson and Morley experiment could show no aether wind for the speed of light.
The wind example is what they were searching for, if there was an aether wind as the medium of light. The theory behind their experiment, is based on that wind example. The experiment found no results, because Galilean relativity is not applicable for speeds that are significant fractions of the speed of light, or the speed of light itself.
Make a video about how to enter the space industry, like whether should we get a degree in aerospace or get a degree in mechanical engineering. Ohh and whether is it possible to get a master in aerospace by having a mechanical degree?
When transcendental numbers were first proven to exist, nobody knew of a single example for years. There was a conjecture that pi was one, but it wasn't proven. So that number that might or might not be rational is a reminder of that flavor of historical uncertainty.
first puzzle: a decrease is more significant than an increase, so wind slowing you down makes sense
This should be a series
I thought the first one would have wind resistance modeled as a force with acceleration
The solution to the second one is just cool as f*ck.
If the wind problem is posed as an absolute, like there's always wind that's constant and I am asked which trip is faster, I have always solved this problem with setting wind speed equal to jet speed. Infinite time. No wind is faster. Similar logic applies of you set it 1 mph under. If the problem says there's one answer use the extreme example.
Well, if points A and B are on opposite sides of the earth the wind could help in both directions.
My intuition about the wind problem was that drag forces are cubic with velocity, so gains going with the wind are not compensated for by gains going against it.
Drag is irrelevant. Groundspeed is everything. The headwind acts on the aircraft for longer than the tailwind.
He forgot about aerodynamics and on the second the boat would make ripples in water and if careful you can detect where to go
The first airplane doesn't have wind, so it falls
Dream be like
the trawler problem: how fast must the second boat go (more than 3 times the original speed?) and what shold the helmsman do to the rudder? the latter can be figuered out, but are patrol craft 3 times faster than cocaine runners
For the first puzzle it would be quite interesting to see if the consumed energy is larger, assuming that you always want to travel at the same speed, no matter if there's wind or not.
As friction exponentially increases with speed and the relative speed is higher with wind coming from the front it would need more energy to overcome than could be saved by the savings of energy with wind from the back over the same time, right?
Assumption of winds effect of adding and decreasing of speed to the plane is wrong so the answer you given.
I think aerodinamically back wind speeds up the plane more than
nose wind speeds down the plane,
so in some cases it is possible the wind assisted trip is faster than no wind trip.
ah yes oily macaroni
Shouldn't you factor in aerodynamics, which could actually make the 2nd plane faster?
No
The last one is either mind boggling or trivial. Depending on how one looks at it. Wouldn't the balloon (if we move to the 3D example) turn inside out so the inner skin would be outside when it "flips"?
I have things to ask.
What would happen if you activate a vaccum cleaner in space?
What would happen if you built a very long straw that can reach space from earth's ground and you suck on it?
If gravity bents the space to create that thing that i forgot the name, does space an element/matter itself?
So the hypersphere thing. Does that mean it's possible for us to go outside of this universe?
The thing I tend to get curious about for the 2nd one is HOW much faster does the faster boat have to be to be able to catch the slower boat using the spiral? What's the slowest the faster boat can be in relation to the slower boat and still be able to catch it? Also couldn't you just change the base of the logarithm to potentially catch the slower boat with a slower and slower fast boat? Just as long as it IS faster.
One of my friends looks exactly like you, so whenever I see him, I say "Holy shit, it's the man, the myth, the legend... Zach Star himself"
I know, random, but i really gotta get a refresher.
@Zach Star or anyone:
Which video was it, where he talked about likely choosing the best (canidate) for a job or whatever, (something about forget the first 3rd of the elements of the set, then sift through the ones from 1/3 into the pile and pick the first great option you see) im not sure what the actual context was for the example, but yeah, that whole idea
I might need force sensors on my bike pedals. I need data on how wind affects my rides.
I watched too many aviation videos, because my thought process was a entirely different one. Starting with factors like relative airspeeds, friction, engine power, lift...
This affected my life.
i mean for the circle on the sphere, it may look like you're outside of the encircled region but would it not technically still be inside? If you colored the inside of the circle red, the person would still be standing over red meaning they're "inside" the region still? kinda confused idk
The trawler one was very cool
These are my favourites, thanks for this video❤❤
Thank you Santa!🎅
9:00 inside or outside?!?!?!?! GOOOD Question.
That t-shirt LOL
I'm studying physics and I really wanna wear that shirt in the university .. I'll be hired
With the plane I would talk about turbulence. The trawler problem is interesting, I missed that Numb3rs.
All hail the great circle
this was really interesting and fun to watch, thanks
without wind is faster, at least at high wind speeds
if the wind is 99.9% the speed of the plane, A to B takes half as long, but B to A would feel like forever