I first became aware of advertising on TV in the 1960s. I remember ads for laundry detergent, for example, that had a box with the lettering "Brand X", but the colors and designs were clearly a box of Tide. I was so clever because I saw through their shenanigans and recognized the box of Tide my mom used.

>Thanks, I think this is starting to make sense. So when the car changes speed, it's applying work against the ground/earth and that's the frame of reference? I think that's what I was missing

The frame of reference is just what you define as being stationary for your calculations. It is something that just exists in the model you use for the calculation.

The speedometer of the car measures the speed of the car relative to what is rolling on. Let's assume that it is a day with no wind. let's say the speedometer shows 120, the unit does not matter, that is the relative speed between the car and the ground.

So you can use the ground as the frame of reference then the car moves forward at 120 or you can use the car then the ground and the air move backward at 120. So any calculation you do need to include both parts

So the situation is like if you drive a remote-controlled toy car on a treadmill and add a fan to get the air moving. Compare that car to a remote-controlled car on the floor beside it. From the behavior, it is quite clear that the moment of the treadmill has an effect on the behavior of the car.

So if you use a car that is more relative to the earth as the frame of reference you need to include that earth is moving backward just like if you drive on a treadmill and the frame of reference is the ground you need to include the motion of the band on the treadmill

For spacecraft or any other rocket engine, the propellant is moving at the same speed as it. They will both have the same speed regardless of what frame of reference is used. What speed at both moves depends on the frame of reference you use but it will always be the same.

The result is it works out the same regardless of what framer of reference you use, what can change it how hard the calculation is

In very simple terms, overfitting is when a model appears to work very well on one datatset, but it completely breaks down on another one. Usually this means that it performs well on the training and validation sets used during development, but it doesn't actually work when it's given data that it's actually supposed to process in practice. That's why it's bad: it ends up being useless.

What overfitting actually is depends on the model, but in general it means that the model has learned to exploit some peculiarity of the training dataset that is not present "in the wild". For example, if you were training a model to look at pictures of people and tell you wether they have blue eyes or not, and every single blue eyed person in your training datatset had blonde hair, the model could learn to actually recognize blond hair. Then if you gave it a picture of a brown haired, blue eyed person, it would tell you that they don't have blue eyes.

That's plausible, although I'd say it would be very careless of a doctor to use that terminology. I get not wanting to use the phrase "severe sore throat" which sounds a bit childish, but there are perfectly good alternatives like pharyngitis (or tonsillitis, as the case may be), which describe the symptoms rather than the cause (strep throat is one cause of pharyngitis, but more commonly it the cause is a viral infection, which can still be very nasty). Or just "inflammation of the throat" if you prefer plain English over Latin & Greek.

Let’s chose as reference the a point on a road. And let’s accelerate a car. I assume you know the equations. Let them assume we use the car’s engine to generate the force, and this engine is a combustion one, and we never shift gear, fix gear ratio.

We start the reasoning with: Speed = time * force / mass.

It happens that the car will travel faster and faster while accelerating, covering more and more distance per second. Distance=time squared * force / mass.

I will keep using force/mass as a substitute for acceleration.

Now, let’s say you push ed the car with 1000force, for 1000 distance, it will get to 10speed. To get the same car to the speed of 20, it will take twice the time.

But how much distance it took? To get to 20 speed instead of 10 speed, we will need twice the time. Again, distance=time squared*force/mass. So we will cover 4 times more distance as 2time squared is gives 4time as a result.

Breaking it down to the combustion in the engine, while the car gets faster and faster, the engine spins faster and faster, burning fuel faster and faster. There will be a fix ratio between engine and wheel, for each revolution of the wheel there will be a fix number of combustion cycles, all burning the same fuel. Pause it at any point of the travel: you can see for each meter of road, you burn a fix amount of fuel.

If getting to twice the speed covers four time more road, therefore burning four time more fuel.

This means the car has received 4 times more energy to get to 20speed compared to the energy it takes to get to 10speed.

From energy pov, the time it took doesn’t matter, what matters is what you burn to get there and for how much distance you had to burn.

The car’s kinetic energy is nothing else that the burned fuel energy. And the amount is determined by how much force for how many meters It traveled under that force.

To recap: kinetic energy=“fuel used” to get the object to that speed.

(speed=force * time /mass, transform this you have:

force= speed * mass / time.

Distance= speed * time)

SO HERE WE ARE: Kinetic energy = “fuel used” = force * distance = (speed * mass / time) * (speed * time) = speed * speed * mass / time / time= mass * speed squared

Hope this example helped visualize it. The rest of your question is answered just by changing the reference point. Law applies the same.

I am no animal expert, so consult an expert if you do need to do that for any reason.

If it's only as a food for thought, depending on the mammal you'd probably be fine unless whatever animal has a very prominent feature you need to worry about. Farm animals have prominent features (cow produce lots of milk, sheep produce lots of wool) that most likely unbalance things a lot compared to us. Other mammal like cats and dogs probably have a balance close enough that the variation between their RDA and ours should be fine.

If you look at anything other than mammals, things change drastically. Hollow bones and feathers in birds, cold blood and scales in lizards, etc... are probably much further away from us.

Again, not expert on this subject, consult an expert if you're planning on putting your dog on the same diet as yourself.

good explanation! Thank you!

So applying the RDA for vitamins and minerals to mammals would make no sense? (After modifying for body weight of course)

Every vitamin is used by bodies for some purpose. Depending on what a certain species has or do, you'll need more or less of certain vitamin.

Animals with "bigger" brain will usually require more energy to make it work. Animals with large, constantly growing claws/teeths will need certain vitamin to keep growing them. Animals with hot blood will need more food for their heat.

Everything has a use, and what your body can do decide how much of each you need in average.

Say you sample a sine function, but your data points have some noise. Now say you attempt to fit a polynomial of degree N to those data points i.e. a + bx + cx^2 +... zx^N, assigning values to the coefficients to minimize your error.

If you let N=1 then you can only make a line, so not a good fit. Let N=2 and you can make a parabola, which is closer. If you continue to increase N you get a more and more complicated curve which gets closer and closer to every data point. Eventually N becomes large enough that your function exactly matches all data points with errors of zero, but the problem is that you now have a crazy looking squiggly line that no longer reassembles the smooth sine function which generated the data. Thats because you gave your function so many degrees of freedom that it was able to exactly fit the noise rather than average the data like it would have if it had fewer parameters to work with.

It really depends on the dataset and model. In general, the smallest model that meets your requirements is a good idea but that size could range wildly depending on the data format, richness, and required performance.

Cheers

If it was overfitted like discussed before it wouldn't recognice those 1000 pictures, because it wouldn't actually know what a cat is but just know exactly the 100 pictures you first gave it. This is exactly overfitting you are fitting the data into 100 pictures and not into detecting Cats, so any new data that you give doesn't work.

That is why you take 80 pictures from the 100 and test the algorithm with the remaining 20 to make sure it detects cats and doesn't overfit into those 80 pictures

thanks for the answer! it covers the follow-up question to the first commentator. Just one last question in your example what is the rule of thump to avoid very few variables and too much? like is there an accepted level of accuracy?

It would not recognize those and that's exactly overfitting, learning ONLY it's dataset, but not the pattern within the dataset that is general and can be applied to new data.

If this happens does also depend on how complex your ML model is though (compared to the amount of input data). The simpler it is, the more resistant it is to overfitting (but also the less complex the pattern is allowed to be).

There is a scientist joke: "If you want to perfectly fit a linear regression just give it 2 datapoints". The linear regression is pretty much the simplest model, but giving it a too small dataset makes even that useless.

So if I gave it the 100 pics without stopping criteria and then tested it on a much larger data set, say, 1000 pics, will the detection error increase or is this not considered overfitting since it trained on a dataset and then used on a completely different set?

It's not just for machine learning, it's a general problem with any models that try to simplify anything. Overfitting is basically when you make the model so "big" (enough values that it can adjust) that it can perfectly fit *any* training data you feed it. So your model will look *amazing* in terms of performance, but it may totally fail when you finish training and try to do something useful with it because it's too hyperspecialized to the training data.

As a trivial/over-simplified example, suppose I want a machine learning widget to recognize pictures of traffic lights so I can automate those stupid captchas (yes, I know that's not how they actually work). I get training data of 10,000 pictures of traffic lights and 10,000 pictures of non-traffic lights and use that to train the model. Except I give the model 10,000 different variables to work with (far too many). The model can "learn" to recognize each of the 10,000 pictures because it can use one variable to match each photo of a traffic light. The results on the training data will be perfect...it recognizes every one of my 10,000 traffic lights and ignores anything that isn't those. 100% success!!! But now I feed it a new picture of a traffic light...and that doesn't match any of the 10,000 I trained it on before. The model will say "not a traffic light" because it got too specific...I overfitted the model so much that it can *only* recognize the training data. It was never forced to figure out how to efficiently recognize traffic lights with a much smaller number of variables that would learn "traffic-light-ness" but still be general enough to recognize other traffic lights.

You can do the same trick in Excel with polynomial fits to data points...if you give the polynomial enough free variables it can match basically anything to a pretty high accuracy. That doesn't mean you've discovered some amazing 70th degree polynomial that magically predicts your data, you've just (grossly) overfitted the model.

Other mammals, unlike humans, don’t even need to eat vitamin C at all.

So humans need to eat more vitamin C than other mammals ?

Overfitting means the system learned not the pattern you want it to learn, but rather just knows it's training data completely.

If you give it 100 pics with 50 cats and let it learn wich ones are cats without any stop criteria it will overlearn that exactly those 50 pictures are cats, but not by what the pictures have in common. It will learn stuff like "oh yeah the one with the dark blue background is a cat pic"

To prevent that you use some part of your data not for training but for quality control. You feed it only 80 pics to learn from, and use 20 only to check if they are also recognized without ever being shown to it during training.

[deleted]

In short, no, it varies. Most mammals can produce their own vitamin C, for example, so they don’t need to take it in with food. Humans (and other primates from the same group as humans, and also bats and guinea pigs) can’t make their own vitamin C, and therefore require to have it in their diet. In humans it’s due to a certain mutation that have broken our vitamin-C-making gene a long, long time ago.

It'll all work out *as long as the frames aren't accelerating*. If you're in accelerating reference frames all bets are off.

> So it shouldn't matter at what speed the spacecraft is traveling since the thing it's doing work against (propellant) is always traveling at the same speed as the spacecraft?

That is exactly right.

From the spaceship, when I expel some exhaust, I gain some constant amount of energy. So, it makes sense to me that me acceleration is steady.

From the ground, for a spaceship to have steady acceleration, it must be gaining more and more energy per second. The faster I am going, the more energy I need to gain a little bit more speed. This extra energy comes from the fact that the fuel is moving along with the spaceship - from the ground, the fact that it's moving means it has extra kinetic energy to expend on propelling the spaceship. If you do the algebra, you'll find that the extra quadratic terms on the spaceship's energy and the fuel's energy exactly cancel out.

So the actual effect (constant acceleration of the spaceship) looks the same, but the accounting of which object has how much kinetic energy looks completely different.

I also had this problem. It seems unintuitive that somehow going from 50 to 60 mph adds a different amount of oomph to an object than going from 60 to 70 mph.

I'm going to base my answer on this physics stackexchange answer. I'll rephrase it to make the mathematical steps more clear, but I recommend reading that answer as well if you know high school algebra well.

Hopefully you have the intuition that energy is some property that objects have which can cause internal transformations in matter. Whenever an object collides and as a result deforms or heats up, that's kinetic energy acting on the object.

So let's look at a situation that makes it easy to account for all the kinetic energy - a clay ball hits a wall. It will splatter, and the size of this deformation can be used to calculate the energy. If two clay balls of equal size hit a wall and splatter to the same extent, they had the same amount of energy. Let's say the balls were moving with speed v, and had an amount of energy E.

Our first step is to change this experiment. Instead of throwing the balls at the wall, we throw them at each other. They splatter in the air instead of on the wall, coming to a complete stop. They were both still moving with speed v, but in opposite directions. When we do this experiment, we find that the amount of deformation each ball undergoes in this collision is the same as when they hit a wall. This makes sense - each ball has energy E, so the entire collision has energy 2E, but it's spread out through twice as much mass. Each ball undergoes an E's worth of explosion, the same as if they each hit a wall.

Our second step is to change this experiment once again. Throw the balls a each other, but now observe them from a car moving forward at speed v. The ball we're following looks like it's hanging in the air, while the other ball is moving toward it at speed 2v. Now to see what happens when they collide, you'll need to keep track carefully. To a person standing on the ground, the two balls stopped moving completely, and fell straight down. But since we're in a car moving forward at speed v, the collided balls are now moving backward at speed v. From the car, it looks like the 2v ball came in, collided, and knocked the combined system backwards.

Now the crucial step - other than this change in relative speeds, the collision looks identical. Us being in the car doesn't change the events. The splatter of each ball is the same size. So the moving ball went from 2v to v, and yet it delivered 2E's worth of energy. Going from 0 to v grants an object E worth of energy, and yet going from v to 2v grants at least 2E (in reality more, since the two-ball system is still moving, so it didn't lose all its kinetic energy to the splatter). We got here not by assuming any kind of mechanics, but by assuming that the laws of physics work the same when we're moving as when we're stationary - if we do all our math from a moving car, we should still observe the same things happening, even if we observe them happening at different speeds.

To get the exact quadratic relationship, we have to account for the fact that the two balls are now moving backwards with velocity v, which means there is an extra 2E's worth of energy stored in their motions. That's a total of 4E. If velocity v has energy E, while velocity 2v has energy 4E, that means doubling the velocity quadruples the energy, which is only possible if E(v) ~ v^(2). Then E(2v) ~ (2v)^2 ~ 4 v^2.

This argument suggests that this relationship does not come from the inherent properties of objects, the way electromagnetic energy does. That energy is somehow stored in the bonds between nuclei and electrons. Kinetic energy is some kind of property of the geometry of space and time, so just thinking about the symmetries of motion can tell us what the relationship between motion and energy must be.