First, we need to start with the calculus discuss from before. Specifically projectile motion.
The projectile motion equations are first given in high school physics but you also derive them in calculus for the first time (using the derivatives and integrals mentioned above). Then, finally in differential equations class above you go and solve projectile motion to include things like wind resistance.
Here's an image of any projectile motion...remember, projectile motion covers everything basically moving in the air under no external force other than gravity (it has no engine running). So any thrown ball, anything dropped, a skydiver, a rocket once it runs out of fuel, etc...
The equations are (where y=height, x=distants, t=time, theta=angle of intial release)
The only issue with this equation is that the y (height) equation assumes initial release from the ground. To fix this just had an "h" for initial release point (if its 5 feet off the ground then h would be 5).
These equations are, again true for baseballs, golf balls, tennis balls, rockets (once out of fuel), bullets shot from a gun, etc.
Now, these equations eliminate one important factor, which becomes more important the faster the speed/velocity of the projectile...wind resistance.
These equations are the once you first learn because wind resistance makes it more complicated to solve.
For instance...something that is moving pretty fast in the air, the motion curve could be vastly different if you include air resistance. If it is moving slow then the curve is relatively the same.
A curve for an object moving fast..
Ok, so how does all this relate to a curveball?
Have you EVER heard someone say that a curveball is an illusion, it is physically impossible to throw a ball with enough spin to actually make it curve inside of 60 ft 6 in (distance from pitching rubber to home plate).
These people who say this understand physics of a baseball through high school and first year college physics as well as the differential equations level of math (2 full years of calculus in college). The first couple years you ignore wind resistance. You can't make a ball curve AT ALL without wind resistance.
Secondly, even with wind resistance, the mechanism of why a ball curves (will cover below) would require such HUGE amounts of spin on a sphere that it is humanly impossible to make a sphere curve based on spinning in the air.
So, let's cover that physics first, how does spinning a ball help a ball curve?
It's called the "Magnus effect". Its a physical phenomenon that a spinning ball in air/water/whatever will cause it to move one direction.
The friction caused by the rotation actually causes more friction on the side that is spinning into the direction of flight (against the wind resistance) than the side that is rotating away from the direction of flight (with the wind resistance).
This difference in wind resistance on 2 different sides of the same object will create MORE resistance on the left side of the ball in the picture than on the right side of the ball. This will create a high pressure "air" on the left side of the ball and a "low" pressure air on the right side of the ball.
The problem with the math on this is, in order to spin a ball fast enough to make it curve, according to the equations, the spin rate would have to be astronomical (read breaking your wrist/elbow on every successful curve). This is why some people say the curveball "is an illusion".
The problem with this statement is that the equations have to assume that the ball is a sphere, and the equations are "right" that if the ball were a perfect sphere a curveball would be impossible to throw as a human.
However, the stitches on the ball, that have been there since baseball was created, creates EXTRA resistance as it spins. The stitches on a ball are exactly what makes a curve ball possible.
This is also why good pitchers know how to grab/hold the ball in different positions of the ball to get different "spin rates" which allows the ball to curve more or less even with the same arm motion/velocity.
Along the same lines, the "hair" on a tennis ball and the white "lines" where hair is not is why a tennis ball will curve. The dimples on a golf ball help add distance, but they are also the reason a golf ball will curve (slice or hook).
This same reason is why if you followed the flight of a baseball thrown as a normal fastball or any normal throw from the outfield, etc and tracked it against the projectile motion equations. The flight would look very "flat" meaning it wouldn't curve "down" after a peak like the graph above. You also hear the phrase in baseball about pitchers that throw in the high 90s/low 100s that their fastball looks like it "rises".
A normal throw/fastball has "backspin" by the way it releases off the fingers. This "backspin" makes the Magnus Effect want to curve the ball upwards. However, gravity wants the ball to curve down. The low 100s fastball doesn't REALLY "rise", but our brain/eyes are so used to seeing the ball start to "fall" near the end of its flight that when it doesn't "fall", we think it is rising. A very hard thrown fastball or ball from the outfield absolutely wants to "rise" by the Magnus Effect, but the Magnus Effect is not quite strong enough to overcome gravity. The ball will "flatten" out and then eventually fall to the ground anyway.
I wish it wasn’t true, but it was hilarious when he said it.
I am definitely a weird nerd. Was/am athletic (played 3 sports in HS, was all state in baseball and played it at Akron U until I hurt my shoulder), and love watching sports...just also really “geek out” on math/science stuff.
I was used to talking sports with family and friends in HS, I get into engineering classes in college and the kids looked at me like I had 3 heads when I tried to talk Indians or Browns or Ohio State football.
The famous physics experiment known as the double slit experiment was originally done with water waves to show how waves interfere with each other and create amplifying and cancelling wave frequencies.
Later on, in 1801, it was done for the first time with light. At the time scientists weren't sure if light was particles or waves. The double slit experiment, when done with light showed the same interference patterns that a water wave does.
This led them to conclude that light was a wave...not a particle.
Fast forward to 1927 and it was done for the first time specifically with subatomic particles, this time electrons. Electrons, and protons for that matter, were assumed to be particles, and therefore the double slit experiment should not show interference patterns, but simply two "exit" markers on the "reading" filament (think if you threw baseballs repeatedly through 2 different slits and marked where they hit the backstop). That's what they assumed electrons, and later protons) would do. However, it showed interference patterns like waves?
So how can something that we can measure its mass (at this time we knew how much electrons and protons weighed) be a wave?
This led to the understanding that subatomic particles sometimes behaved as particles and sometimes as waves, which also made them reconsider light from the 1801 experiment. Light also shows wave and particle characteristics (hense a photon was discovered as the subatomic particle of light).
So, what in the world does this have to do with alternate dimensions/multiverse? Ok, before we jump that far ahead we need to simplify subatomic physics a little bit, because it gets really SCREWY when we get down that small...
Ok, first the Heisenberg Uncertainty Principle says that the more precisely we measure the position of a subatomic particle the less precisely its speed can be known/predicted and vice versa. In the subatomic world, specifically for an electron to make sense, you can not possibly know where the electron is located at a given time AND its velocity at that time. It's impossible. For this reason all subatomic physics (mostly called molecular dynamics) is expressed in statistical probabilities.
For instance, the simplest atom, a hydrogen atom does not REALLY look like what we learned in high school chemistry:
No, it looks more like this...
Where all the black dots are probable electron locations, and it is more like an electron "probability cloud". And it only gets crazier (the electron clouds) from there as we get to larger and larger atoms.
So, now that we understand that in subatomic particles we can only talk about probabilities lets talk about the next step in the electron double slit experiment...
They then decided to slow down the electron beam flow to the point where only a SINGLE electron was shooting out at a time and therefore only one electron was going through the 2 slits at a time. the electron would have to either go through the left or right slit. They just had to run this experiment a LOT longer to see how the pattern would develop on the collector filament.
They FULLY expected it to show its "particle" behaviour at this point (like if it were baseballs) and just have 2 spots where the electrons hit on the other side. 1 behind the left slit, and 1 behind the right slit.
The results utterly floored them, so much that they didn't believe it and ran the experiment over and over again....the same exact interference pattern showed up on the filament as if they were shooting millions of electrons at a time.
How in the WORLD is this possible? There was no other electron going through the slits for the electron to "interfere" with!
There are two prevailing theories to this day, and both are equally weird/unbelievable....
The first one uses the probability nature of an electron listed above to explain that the electron actually goes through BOTH slits and interferes WITH ITSELF!
Ok, if that doesn't flip your mind...the next one will...
The other prevailing theory is that the electron actually interferes with electrons FROM ANOTHER UNIVERSE. Yes, look up quantum foam, its an "out there" idea that on the quantum levels alternate universes can not only interact with each other, but subatomic particles can travel back and forth between universes.
So, that's how a water wave double slit experiment eventually leads to a multiverse/alternate universe theory being REAL in physics, and not just in Marvel movies/comic books.
For an AMAZING science fiction book that covers this exact theory of the double slit experiment and multi-verse, read Michael Crichton's (yes, same guy that wrote Jurassic Park) book Timeline.
The movie truly sucked, they butchered the book, but the book was truly Crichton's best in my opinion, even better than Jurassic Park.
Will do that one tonight or tomorrow. I always found theoretical physics fascinating.
Along with all my other classes while in undergrad, for "fun" I took a junior level "Modern Physics" class which is the study of Einstein's theory of relativity as well as other theoretical topics on space-time over the last 75 years or so.
I was the only "volunteer" in the class, meaning I was the only one that signed up for the class for "fun", everyone else in the class (about 12) had it required by their major (some physics variation). They all looked at me like I was an alien when they found out I was not required to be in the class.
So yes, Laley's post on the last page is absolutely true...NERD!
Well, only 2 votes, so calculus wins by being the first...
Ok, I will start with something we all remember doing in middle school and high school. We remember graphing fuctions.
First you would have graphed straight lines with the formula y=mx+b where "m" is the slope of the line and b is the "y-intercept" (where it crosses the y-axis). Then, if we took algebra 1 and especially algebra 2, we started graphing more complex functions like parabolas (y=mx^2+b) and hyperbolas (y=a/(bx-c))
Let's start with a basic hyperbola, y=1/x. It's graph looks like this...
I kind of promise last graph...
So, in late pre-calculs and early calculus 1 you learn about "limits". Basically the limit of a function as "x" approaches something. Its easy for say the limit as x approaches say 1 in this hyperbola above. The answer is just what you get when you plug in 1. (side note, at this time you start using f(x) instead of y, that means a function of x). So limit of f(x)=1/x as x approaches 1 is 1/1=1.
However, what is the limit as x approaches infinity? or as x approaches 0? Well, as x approaches infinity you can see by the graph that f(x) approaches 0. It NEVER hits 0 but it gets infinitely close to 0. I am going to ignore as x approaches 0 for this discussion basically because you get into approaches from the right or left and it has nothing to do with the next part.
So, limits are important if we go back to the original graph we all drew, y=mx+b. The "m" is the slope of the line. Well, for functions that are not a straight line it is still very interesting to know (more in a bit) what the slope of the curve is at any given point. Well, if we remember from our lines, m=(y2-y1)/(x2-x1) or "rise over run".
Ok, for a function that isn't a line, that can and does look like [f(x2)-f(x1)]/(x2-x1). However, this just gives us the slope of a line between two different points on the curve, now the instantaneous slope at one point. So, if we take the limit of [f(x2)-f(x1)]/(x2-x1) as x2 approaches x1...then we get an instantaneous slope. Also, this instantaneous slope is also a function of x...in calculus we call it f'(x) (there is an apostrophe between the f and parenthesis). This allows us to plug in any x and know the slope of the original function at that point.
So we have a slope function...in calculus 1 we learn that this is called the derivative.
You spend most of a semester in calculus 1 learning how to find the derivative of all different types of functions...until at the end of calculus 1 you get asked...what if I want to go backwards, find the original function if I have the derivative?
You start off learning that this is called an "anti-derivative", which makes sense to you, you later learn this is called an integral function.
I told you the derivative is the slope of the original function. The integral of the function also has a physical meaning as well. It is the area under the curve of the original function. See below..
You spend all of calculus 2 learning how to integrate 1000s of different types of functions and other various uses of integrals other than areas, like volumes of 3D objects which leads right into the 3rd semester, calculus 3...
Calculus 3 repeats EVERYTHING you did in Calc 1 and Calc 2...except now in 3 dimensions. No new concept here.
Ok, so how does this apply in the real world?
Well, for math majors and engineers the next class after 3 semesters of calculus is called Differential Equations.
In physics, if I have a function of the distance traveled by any object from a train, to a jet, to a bungee cord jumper, to a sky diver, to a weight on a spring...then the derivative of the distance function is the velocity of the object. Think about it "backwards". Area of a 2d graph is the sum of all the 1d "lines" under the graph, so if I summed up all of the velocities of the object over time, I would have how far the object traveled, or distance.
Along the same lines, the derivative of the velocity function is the objects acceleration. So, if I can write an equation based on an objects velocity and acceleration I can possibly solve for the objects distance/location at any given point.
Let's take the most simple version of this, acceleration by gravity, or free fall. My acceleration is directly affected by gravity, my velocity can be affected by wind resistance (but for simplicity we will neglect wind resistance...as it doesn't come really into play until the object gets close to terminal velocity).
if "y" is your location, then y' is velocity and y'' is acceleration.
so we know from physics that acceleration due to gravity is 9.8 meters per second per second and I set my reference point at the top of the building as "0" and that toward the ground is "positive" distance then..., y''=9.8.
If we set our initial conditions to the position is "0" and our velocity is "0" (I dropped the ball, I didn't throw it down) then the solution for the position of the ball is y=4.9x^2 where x is time in seconds and y is distance in meters. So you would be say 4.9 meters down in 1 second, 19.6 meters down in 2 seconds, and 44.1 meters down in 3 seconds.
So, think back to algebra when you had a quadratic equation like x^2+2x+1=0 and you had to solve for x. In differential equations instead of powers of "x" you have different derivatives of "y". So it would be like y''+2y'+1=0. Again, where each apostrophe is a derivative of the original function, and you have to solve the original function.
Now, these simple (yes, so far we are in the simple range) differential equations can explain things like any object in motion (projectile motion like shooting a bullet, throwing a baseball, falling with a parachute, a leaf falling from a tree, shocks/spring motion like in a car, etc).
Once we get to more complicated real world problems like fluid flow, heat transfer, modeling chemical reactions, modeling of infectious diseases (COVID-19) we start to get into what is called Partial Differential Equations...think back to what I said about Calculus 3 where it was all you learned in Calc 1 and Calc 2 but in 3 dimensions? Well, PDE is just Diff Eq in 3 dimensions...
Partial Diff Eq can be used to explain simple things like heat transfer in 1 dimension like if you stick your fork in boiling water how long does it take for the heat to reach your hand holding the fork.
These differential and partial differential equations are what is used to model and design everything from industrial furnaces, to bridges, to fluid pumping systems, etc. Now, most of the common systems we see/use now were modeled 50-100 years ago and the parameters are set by those that solved the PDE and DE equations to begin with.
However, in buildings, especially newer/taller skyscrapers, the wind loads are STILL modeled by differential equations.
I will leave you with one video, if you have ever seen the Tacoma Bridge collapse. At one point right before the collapse you can see the bridge literally oscillating up and down like a wave in the ocean (sine wave if you remember high school algebra and pre-calc).
This happened because the original designer of the bridge ignored a VERY important part of the differential equation that goes into bridge design, the wind load "forcing function" as it is called in differential equations.
This video was shown by my differential equations professor in class when we were doing forcing functions specifically for this type of differential equation and why not ignoring the forcing function even if it appears to be "small".
Unfortunately, that sounds like serial killer behavior, not engineer behavior. 🙃
You are not that far off. The unabomber was insanely smart with like a 167 IQ, that’s Einstein level IQ.
My version of no empathy goes like this...
Person A is crying or upset about something bad going on in their life.
A normal person sits with them, listens to their problem, lets them “cry on their shoulder”.
jmog either immediately gives a 5 step logic and reason response on what they need to do in order to get out of their situation...
OR jmog literally has to walk away because it starts to fill me with anxiety.
My logical list of what they should do may technically be correct, but obviously the wrong place and time to give it.
If my lack of empathy went way further than it is, it most definitely heads toward the path you are referring.
The best explanation I can ever give for my version of it is if you ever watched the TV show Scorpion from a few years ago, think about the main character. Good guy, extremely smart, socially awkward, and no understanding how to process his own or other’s emotions.
Ok....nice resume brah......but seriously....you work on furnaces with all that paper hanging on your wall?
I am not an HVAC repairman if that’s what you think.
When I say furnace, I am talking about huge industrial furnaces for steel, glass, etc. Furnaces that are 2-7 stories tall, a football field long, burn like 100 million BTU/hr (same as 1000 house furnaces).
I have done everything from R&D on the burners that go into these furnaces (sometimes 200+ burners per furnace) to design the whole combustion and emission abatement system on the furnace.
Mostly I now work on helping our customers with either emission lowering or what type and how much of a specialty gas to put in their furnace to do special surface treatments to their product.
I am not fixing your mom’s home furnace.
Side note:no paper on the wall, couldn’t even tell you where my degrees are located. I bet my wife knows though.
People are just like that with math. Clicks for them. I'm terrible. I lived in the tutor room when I took a higher level business calc class.
I have a friend he makes 250k. Ridiculous at math, I can't put into words how good. Downside...his level of social awkwardness equals that of his math skills.
Look up what EQ (emotional quotient) is and it’s inverse relationship with IQ.
I am not that social awkward, compared to other engineers, but I have near zero ability to empathize with anyone and their struggles. It’s my biggest negative trait, especially as a father. Honestly tried therapy to help and my therapist literally told me “fake it, fake empathy, you don’t have the ability so fake it. The other person will get the same benefit if you fake it well enough.”
My oldest son just started working as an electrician for the same company I do, he is 18. After a couple weeks he comes home and says “mom, dad is not near as weird as we thought he was. Holy crap, he is the most normal engineer in the company.”
Thanks. Next step is the FE test for mechanical. Training course was supposed to start last week, obviously not happening. Not sure if it's worth it or not. I said fuck it, just do it. Her employer is paying.
FE/PE is essential for civil engineers.
It is desirable and can help electrical and mechanical engineers.
It isn’t important for chemical engineers.
If she is going to continue doing MechE work then it is worth the time/effort, especially since her work is paying for it.
I do not have my PE. I took the FE exam as a senior in college, passed it, and never cared about it again.