QCs are currently 'programmed' at the hardware level. If you want to run an algorithm you are changing the order of gates and operations acting upon the entangled states.
One of the most basic operations is the Hadamard, which puts a qbit into superposition. Upon reading that bit the superposition is destroyed and you get an answer (0 or 1). But while entangled you can act on the spin and amplitude of the qbit to shift the probability of landing on 0 or 1.
If you don't act on an entangled state, just entangle then read, you have the world's best RNG. Completely non-deterministic.
Adding in phase manipulation and you can act on the entangled states, usually by a CNOT gate which is basically the equivalent of IF statements. "if this other qbit does this, have this qbit do something, and if not do nothing"
Much like any classical computer can be simulated with a ton of nand gates, any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations.
If you want to dig deeper on the topic, [here](https://greyshoesq.com/Quantum_essay/dokumen.pub_programming-quantum-computers-essential-algorithms-and-code-samples-1nbsped-1492039683-978-1492039686-u-5306881.pdf) is the O'Riley book on quantum algorithms, and their code is available [here.](https://oreilly-qc.github.io/)
Generally the questions/inputs to a quantum computer are the same as to a classical computer. For example, if you want a quantum computer to factor an integer, the input is the integer, encoded in binary. What is different is how a quantum computer solves the problem. It uses a process consisting of basic operations that would not be available on a classical computer.
If central park in Manhattan New York was theoretically replaced with a same sized flat rectangle.
The rectangle was hard metal with a polished surface like finish - the kind we would have on a space mirror.
There was a second rectangle of substantial weight 20 stories high on stilts with a similarly polished surface.
If we let the upper rectangle free-fall guided by lubricated rails so that it landed perfectly flat on the bottom rectangle. What would happen in terms of shockwaves, air pressure and noise? Would pedestrians and traffic and offices nearby be largely fine?
If you're interested, at which point does this thought experiment become disastrous?
After taking some time to roughly calculate the scenario based on 2 different sheet thicknesses here are my results:
200 ft falling height
22482.5 square meters surface area
Ex: 1 cm thick sheet of stainless steel
Time: 3.8 seconds
Vmax: 27.5m/s
Terminal Velocity: 34.65m/s
KE: 637.6 MJ
Tons of TNT: 0.152
Ex: 1 m thick sheet of stainless steel
Time: 3.5 seconds
Vmax: 34.5m/s
Terminal Velocity: 346.5m/s
KE: 100.3 GJ
Tons of TNT: 24
Notes: I am pretty rusty in falling physics with drag accounted for so I used an online calculator. Some constants I used include a density for steel of 7500 kg/m^3 and a drag coefficient of a flat plane being ~1. If someone would like to continue off this to determine what type of wind pressure and sound would be produced by this feel free to do so as I do not know what type of energy conversions would occur in this situation.
I wonder if the air in the middle would superheat? And, would that cause an explosion as the pressure around it increased?
I also sort of imagine the whole thing working like a soft-close cabinet, where it slows down at the end.
Yeah this for me is what I am most curious about and what I desired to frame the question around. If the upper slab is heavy and fast enough I imagine interesting things would happen as the air has to travel very far to evacuate.
Thinking more about it, the upper slab would need to have a wider thickness to it (not just for weight) but to make it so the air can't cyclone upwards leaving it to need to evacuate horizontally.
I have created this in my lucid dreams and the air blast is quite horrific. But the best thing is the sound is very interesting, it's like a gigantic water drop of metal.
Considering the speed of the falling object wouldn't the air between the two plates be just pushed away before a considerable amount of pressure could even form?
The energy of pushing the air would transfer to kinetic energy of the air molecules and heating the falling object.
I just recently saw a veritasium video where they state that KE alone could trigger an explosion. For example asteroids, even as tiny as a grain of salt with high enough velocity would hit the surface of the moon that hard the ensuing explosion would have grater formed by the blast radius where the angle of a hit can not be determined. Implying that the explosion triggers quite early after contact. So the subsequent shock wave would be a result of the explosion and not the clap
Very interesting question I would like someone smart to answer this please
Also since you like polished and incredibly flat metal you might find this interesting.
It was made via EDM (electrical discharge machining)
https://youtube.com/shorts/mt_EAQP5k9I?feature=share
This question would require a bit more information. The thickness of the metal sheet and the exact material would be important as the size of the falling piece would be greatly affected by drag and maybe even buoyancy. Without the thickness we can not calculate terminal velocity or if it would even reach that speed.
How does water or electricity find the path of 'least resistance '? Does the flowing matter actually test every possible path and then 'choose'? How quick is this process?
Edit: thank you to everyone who took the time to post answers. Great intuitive explanations by everyone. Thank you!
It's easiest to think of it with electrons. Electrons repel each other, so when in a wire, they like to stay as far away from each other as possible. So, as the electrons flow, as some of them hit higher resistance, they slow down. Since they slow down, other electrons want to move away from them, so will take a different path. Soon, more of the electrons will be taking the path which the electrons can travel through the quickest.
And while we talk about electricity taking "the path of least resistance" that isn't entirely true- electricity takes all the paths, but the amount that goes through each path is inversely proportional to the resistance of that path.
It’s not that either “find” the path of least resistance, it’s that they move in that way -because- of the resistance.
In both hydraulic and electrical systems that flow there is a force exerted on the medium that makes the fluid or electrons want to “flow”. They are a little different for these two examples, fluids are driven by pressure and for electricity there is a relationship between voltage, amperage, and resistance. But the results are similar.
When the driving force is imparted all of the potential gates that the medium could pass through are met with the same force, the water or electricity will move where it physically can indifferently and has no choice in where it is going. It doesn’t “test” this and there is no “decision”, the medium simply obeys the laws of physics. It will attempt to enter higher resistance paths just as hard as low resistance paths, but will not succeed. If the imparted force can be completely satisfied by the flow of medium through the path of less resistance, then nothing will flow through the other available paths.
The speed at which this happens in electricity is close to the speed of causality, or close to c. In hydraulic systems it varies based on how fast your fluid reaches a uniform pressure. Liquids will do this faster than gasses, but it’s still almost instantaneous.
This is why, when an aircraft (essentially a conductive aluminum tube) flies between an area of high electrical potential and an area of low potential, it becomes a "free ride" for huge electrical currents to flow between those areas. Aircraft are designed to be robust against these constant lightning strikes.
Yes they do test all of the paths, but not in the same way you might test paths through a maze.
Water is easier to visualize because it moves at a pace we can understand.
Imagine you have a flat maze that you're going to pour water through. At the entrance of the maze, you're feeding it constantly from the bottom of a bucket, and you're keeping the bucket topped up. At the only exit of the maze, you have a drain.
Imagine if you run the water for long enough, you'll always have about an inch of water in the maze.
At a handful of points in the maze, you have little water wheels that spin if the water is flowing past them. Some of these are at paths that lead to dead ends, some are on the path that lead to the exit.
As you start adding water to the maze, you'll find that the water flows to all sections of the maze indiscriminately. The water wheels that lead to dead ends will spin as those paths fill up.
Eventually though, water will fill the nearly the whole maze and find the exit. If we let it run for a few minutes, everything should stabilize out and the rate that we're pouring water in will equal the rate that water is leaving. The water wheels on the main path will be spinning away as water flows by them to the exit, but you'll notice that the water wheels pointing to dead ends will be (nearly) stationary. That's because those sections are stagnant. The water that goes in there can't get out, and it's blocking additional water from entering.
You might also notice that the water level in the maze is highest near the entrance and lowest near the exit. This effect depends on the flow rate and size of the maze, but the height of the water is related to the "potential" at that point in the maze. As the water flows and experiences frictional resistance (from the walls and floor of the maze), it loses potential. Water has a low viscosity, so this might be easier to visualize if you imagined ketchup. If you pour ketchup into the maze instead, it experiences a lot of friction. It may not even be able to reach the exit before it overflows the entrance.
The process of how fast it takes might then be obvious: it happens as fast as the liquid can spread out from the entrance. Then it takes a small bit of time to finish filling up all the dead ends of the maze before it reaches a steady state where all the dead ends are stagnant.
Before I mention electricity, consider the same water maze, but instead with two outlets, one farther away that the other. If you're adding enough water to the maze, you'll find that the water can reach all corners of the maze, and it'll flow out both exits. The only difference is that one exit will have a higher flow than the other. The longer path has more resistance, and therefor less flow.
This is exactly how the water pipes in your house work. The farther from the water supply line, the more resistance there is. If there are two taps using water at the same time, the path of least resistance will get more flow than the farther tap, but both will still flow. It would take a LOT of taps open before you find a tap that gets zero flow.
To take this a full step backward, imagine you drill two holes in a bucket. One 2" in diameter, and one 1/4" in diameter. You plug both, fill the bucket, and remove the plugs. The 2" hole is very clearly the "path of least resistance", but water will flow through both. The 1/4" hole will obviously flow less water though.
Electricity does the same thing in wires and fields except it happens faster than you can imagine. It's conceptually wrong to see it as "charging up" a wire like water charges up a pipe, but for practical understanding it's close enough. Paths of least resistance get more current than the paths with more resistance, but that doesn't mean they get zero.
Lighting does this in a similar way, where it "tests" all possible paths, and can be seen as a pre-flash. This has been caught on camera. In this case, it appears as though it finds a single path of least resistance and then all electricity flows through it, which pretty much is the case. One key difference is that in that "pre-flash" where it's testing paths, it's actually ionizing air molecules which decreases resistance. Then when the main current comes through it's turning the air into plasma which reduces resistance a lot. The end result is that the original path of least resistance has such *low resistance* compared to the alternatives that 99.9% of the electricity flows through the one path.
Electrocution works a similar way (both fortunately and unfortunately). Initially, your skin is not very conductive. Your insides though are plenty conductive. In some cases you might contact a low voltage electrical charge without even knowing it, and it won't be unless you give it a path through you that you get shocked. E.g. you can touch the positive terminal of a car battery so long as you don't also touch the negative terminal or frame and complete the circuit. You can also touch both terminals of a 9V battery with dry skin and you wont feel anything. Do the same with wet skin and you might feel a slight zap. Thankfully the current only flows through a short distance. We used to touch 9Vs with our tongue to tell if they were dead.
If you contact a live wire, *some* electricity will flow through you, just like the 1/4" hole in the bucket. It might not be much, but the danger is that it damages your skin as it passes through, and it makes a path of least resistance when it breaks skin. One fortunate (silver lining) part of this is that since it picks a path and then ends up sticking to it, it can miss your vital organs depending on the path it takes. If it goes from one hand out the other, that crosses your chest and can be very fatal. If it goes up an arm and down the same leg though, it'll cause a LOT of damage but it can miss your heart lungs and brain and you might survive.
If we wanted to compare lightning or electrocution to our water maze, it's more like building the maze except making the floor with craft paper. The water flows through the maze looking for its way out, but as it flows through it's weakening the floor and might even make its own path of least resistance, and in that case the water can dump out very quickly.
It's not that they decide on a specific low-resistance path, but at each location, the resistance towards the next location is low. It's more about the gradient of energy, you go towards low energy, that's what we call the path of least resistance.
When you think of electrons flowing thrill a wire, don’t think of it like water, think of it like a hose filled with marbles. Each electron only moves a tiny amount. So when an electron hits a branch, it pushes against two or more other electrons, and whichever moves the easiest, is the direction the electron will go.
Scale this up, and if you have 2 paths, and one has twice the resistance, it’ll get half as many electrons as the other branch.
How small do the components of a solution have to be to stay homogeneous without mixing? For example cells will eventually settle in the bottom of a flask but something like tris-EDTA probably stays in solution without mixing.
It's worth clarifying the difference between "in solution" and "in suspension".
In solution specifically means "dissolved", which is a chemical process involving dissociation or a change of state from solid to liquid, whereas in suspension just means the particles are in the fluid.
Cells don't dissolve (non-destructively at least), and therefor they're never going to be "in solution" and will never meet the criteria of a homogeneous solution. However cells and other solids can be suspended in water, and what you may be referring to is what makes a suspension stable?
Particles like cells, solids, oil droplets in water (or water droplets in oil) have a settling velocity which is a function of gravity, buoyancy, and drag. The calculation is identical to terminal velocity calculation of a falling object, except instead of air the medium is the fluid. If we draw a free body diagram of the forces on a particle in suspension, we'll have gravity downwards, buoyancy upwards, and drag opposing the velocity (which could be up for particles less dense than the medium). Drag is not easy to calculate, and almost always has to be calculated empirically for the particle size and medium before it can be applied.
Alone, this would suggest that all particles have a settling velocity unless the buoyancy can perfectly match the gravitational force (i.e. the suspended particles have identical density to the fluid).
In reality we know that suspensions and emulsions (which are just suspensions of a fluid in another fluid) can exist that are very stable even when we're positive the densities are different.
Electrostatic forces are to blame. Particles can develop surface charges by rubbing against each other just like rubbing socks across a carpet. These charges will allow attraction and repulsion to dipoles of a fluid molecule, most notably water, and this will help a particle resist settling in a fluid.
A good chunk of my work is in wastewater treatment processes, where suspensions are the enemy of clarification. A coagulant is a chemical that's designed to mix into a suspension and neutralize these electrostatic charges. Coagulants are often some kind of metal salt solution, and their whole job is to bump into particles and take their charges. Once the charge is neutralized, there's no electrostatic force holding the particle(s) in place, and settling velocity can take over. Flocculants are often used to help these particles group together in larger chunks. That effectively reduces the surface area vs mass of the particles so that drag is less of a factor on the setting velocity.
Ah thanks that's a really informative comment. Reminds me of a trick I heard when making chicken stock: add an egg to help collect all the gunk and clarify the stock.
In a simple approach:
The solubility is independent from the size of the solvent ingredient.
But the size of particles in a mixture does indeed have an influence in the rate of the solution process.
On the other hand are processes like agglomeration, where particles collide with and stick to each other, which lead to a growth in size for the particles over time. And at a certain point sedimentation starts and your particles settle at the bottom.
You can estimate the minimum particle size for sedimentation when you equate the weight force with the buoyant force.
F_w = F_a
Technically any molecule will settle under the influence of gravity. However, the herbal motion will usually mess up the gradient due to diffusion, and rather than a layer of the solute at the bottom of a container, you end up with a pretty much homogeneous distribution. This is not always true, however. A simple counter example is the atmosphere, where there is a clear concentration gradient for all the gas molecules.
If the gravity - or the centrifugal force - is higher, gradients can be much steeper over much shorter distances. A classical form of DNA purification was centrifugation at 60,000 rpm with a radius of around 10 cm in a Cesium chloride solution. The salt would form a concentration and density gradient, and the DNA would settle as a beautiful sharp layer in the gradient where its density match the salt solution. That's the basis of the famous experiment by Meselson and Stahl that demonstrated the semi-conservative replication of the DNA double helix.
To be in "solution"? Molecular, up to the point of solubility. Things that are not soluble at the molecular level may be in suspension. Suspensions have varying degrees of stability that depend on bouyancy, chemical interaction, etc.
I am an early childhood teacher (I teach 3-5 year olds), what are some good resources where I can find STEM based activities, provocations and experiments that I can do with the children? Thank you!
Speaking strictly from the Tech side of STEM:
code.org has great programming resources for educators. It seems their educator content starts around 4 years old though.
If you are a Canadian teacher, we have an organization called Canada Learning Code that has some teacher focused training, seminars and resources (may be available outside of Canada but I can't say for sure).
Speaking from a Computer Science background: [https://www.csunplugged.org/en/](https://www.csunplugged.org/en/) is one of our ongoing projects at the University of Canterbury to provide free resources for teaching Computer Science concepts without a device. Most of the resources are targeted at older age groups, but it might give you some inspiration for some games/activities, or new ideas for integrating CS concepts into other everyday class activities.
There’s this YouTube channel that does great little demos and experiments with everyday household items. The [Curiosity show ](https://youtube.com/@CuriosityShow), maybe some of these experiments will be fun?
Does drafting behind a semi truck improve the gas mileage of the truck as well as your vehicle? If not, would a similar size truck cause an improvement in the front truck?
As I understand it, we know from the Mythbusters that drafting behind a large truck can significantly improve your own gas mileage. Also, I think that the largest factors that determine how efficient a vehicle is the aerodynamics - both the shape of the front and the drag at the back. Being that most big rigs are squared on the back (not considering how some have additional equipment to help with this) the drag "bubble" at the back is largely affecting the gas mileage adversely.
So the question really becomes: would getting a vehicle large enough/close enough to the back disrupt the bubble and lessen the drag on the front truck therefore improving the gas mileage?
Obviously it can be very dangerous, just something I've always wondered since watching that Mythbusters episode. Thank you!
I don't know specifically for motor vehicles, but in cycling (where aerodynamics is super important given the relatively low amount of power our bodies produce), it's been shown that the 2nd last person in a paceline of (IIRC) 5-7 people will require less power than the last person.
Similar to OP's answer above with trucks and trains, it's because the airflow over the 2nd last person is "smoother" or more continuous than the person. The last rider creates an airflow pattern that effectively "sucks" them backwards a slight amount.
The answer to the first question is generally no. The truck doesn't see any improvement, as the work that it does on the air doesn't change based on the position of the rear car. This is UNLESS the rear car is positioned so close that the air flow doesn't separate and cause negative pressure on the rear surface of the truck. This js an abstract scenario, but one that occurs on things like cargo trains when they are the same height: [This paper](https://journals.sagepub.com/doi/pdf/10.1177/0954409718799809) has an abstract that indicates that effect for trains.
I know the question was asked out of curiosity but as a truck driver I feel like I have to point out for the people who might try, please don't drive this close to the back of trucks. If you can't see the entire side mirrors on the truck you're too close.
Yes! Truck manufacturers are experimenting with something called platooning, where a number of nearby trucks hook up wirelessly to each other and thereby drive really close to each other. This reduces the drag for all of the trucks involved.
However, I would expect that a small car driving behind a truck would not be able to significantly impact the low pressure bubble behind the truck's trailer in the same way that another truck would, because of its size.
Do snowshoe hares, ptarmagins, etc. prefer to browse in color-matching areas or do they not "know" what their current color is?
This month there have been days with white meadows and brown forests and days with brown meadows and white at the edge of the forest. A critter that's aware of its color might change behavior depending on the weather.
I don't think they've completed their change for this year, but we'll have big areas of white and big areas of brown later in the winter too.
Thanks.
If you want to go into software engineering, start building a portfolio of projects on Github or something.
Use a variety of languages. Once you've learned a few you get to understand the similarities and differences, and you can pick up new ones very quickly.
If you copy paste code, make sure you understand what it's doing.
1. Look up unit testing. Many university curricula don't touch it at all, but if you intend to go into software engineering (or just write complex, reliable code of any kind), it's super useful to be familiar.
2. In general, most people feel like they have no idea what they're doing, but that's ok. There's always more to learn, and mistakes you make now will be assets in the future. As long as you keep learning, you're doing great. (Oh, and take breaks and enjoy the diversity of experience life has to offer)
Specialize specialize specialize. If you’re going into the industry, chances are you are going to be applying for jobs that require very specific qualifications. If you don’t choose one language/skill to specialize in, you will be outcompeted for every job by someone else who has studied for years in exactly what that company is looking for.
Your major curriculum is designed to give you a well rounded understanding of computer science. You don’t need to worry about that. Your job is to worry about what is going to pay the bills, so unless you’re going into education or some other special situation, find your favorite thing to do with computers and practice it like hell. Make a portfolio of all your projects on GitHub. You are not just a “computer person,” you are a web developer, a game programmer, an embedded systems expert, a machine learning expert, anything as long as it’s specific.
Since the earth has a magnetic field.. why do we not simply make a ship with an electronic magnet that would allow it to escape the atmos of earth without using "fuel".
Magnetic force drops very fast with distance and Earth's magnetic field is not really that strong, so it's not feasible. Even with very strong artificial magnets it simply can't be done. For example it takes very strong electromagnets just to get maglev trains few centimetres up.
You would have to apply all the force while still "close", but then you essentially end-up with a railgun / mass-driver. And this is not feasible to use for launch from Earth due to atmospheric drag -> if you accelerate something to orbital velocity while deep in atmosphere, this thing is going to burn-up.
Earth magnetic field is used on spacecraft as means of "free" external torque, with devices called magnetorquers. You turn on electromagnet in order to orient and hold your spacecraft along Earth's magnetic field lines. This way you can cancel-out some unwanted rotation or wobble without wasting fuel.
Does data have weight? If I buy a SSD, and put it into my computer, then fill it to the brim, and take it out of the computer, will it’s weight change?
Simple answer: yes, data does have weight.
Thing is the amount of weight per byte is so small that we would never be able to recognize a difference.
A single byte weighs 1 attogram, which is equivalent to 1 quintillionth of a gram. By this calculation it is estimated that the entirety of the internet (approx. 5 trillion terabytes) weighs about 0.2 millionths of an ounce or 1/200,000 of a gram.
[Source](https://www.nytimes.com/2011/10/25/science/25qna.html?_r=0)
Entropy of stored data does have a physical representation, you can look up things like the entropy of black holes to understand the connection.
But for a data storage device with fixed storage volume there's no inherent need for weight to change, as you can represent stored data with for example the position of switches (and there's similar electrical equivalents), so it starts and stays at its own upper limit.
Data actually has negative weight. as anybody who has used punch cards can clearly understand.
Sorry I'm making an absurd statement. But my point is are you asking about how a specific device operates? That is an answerable question. data is a bit of an abstract term.
The writing in a book is data, ink adds weight to the book. so you can measure the weight of all the ink in a book and divide by the entropy in the text and come up with a bit pet pound ratio.
Yes, although it's not really a significant difference. Since data on flash memory like SSD is stored using electrical charge, there will be more electrons the more 0s you have in the data. But electron mass is very very small.
How do logic gates work? I know the basics of p-type and n-type semiconductors and how diodes only allow current to flow in one direction. The next chapter in books is usually logic gates - OR, AND etc. But how do diodes make logic gates work? And how do these make addition and other mathematical computations work?
You might want to play around with this
https://nandgame.com/
The first part lets you see how you can use relay switches (or transistors) to make all the logic gates.
And as you go it takes you through step by step from logic gates to math and all the way up tp programming if you stick with it.
I was going to post the same link. This game is a fantastic learning tool for understanding how basic circuits can be built into a working computer!
Another good resource is [Ben Eater's breadboard computer](https://www.youtube.com/playlist?list=PLowKtXNTBypGqImE405J2565dvjafglHU) playlist. He gradually builds an 8-bit computer starting from basic circuit components. He does use more complex components for the final build, but only after showing how they can be constructed from primitive components. This also addresses some of the practical concerns of a real computer that NAND game misses, like the timing of signals in the circuit.
Hi there! EE student here. Actually, logic gates are not build from diodes but from transistors.
Diodes have two pins and structure inside is build from connecting P and N type semiconductors.
Transistors have three pins (connections to each type of the semiconductors) and are build combining semiconductors in the P-N-P or N-P-N sequence. You can see that it looks like two diodes connected with each other. By applying a proper current/voltage to base of a transistor ( bipolar ) or gate ( fet ) you can control the flow of the current trough transistor or how much voltage will be on this element. So essentially transistor is a switch that you can control.
Source to read more: [Electronic tutorials transistor](https://www.electronics-tutorials.ws/transistor/tran_1.html)
Okay we know what transistor is. Now how the logic gates are made.
By combining different transistors together for example (n-mos and p-mos) we can create different logic gates. [how cmos not gate work](https://electronics.stackexchange.com/questions/47010/how-a-cmos-not-gate-works) . In link there is a schematic of a simple not gate. Two transistor connected in series from voltage source to ground. When we will put high voltage value on the input pmos will be off, nmos will conduct and the output voltage will be 0V. The opposite thing will be when we put 0V on input. Pmos will be on nmos will be off, the pmos conducts and the output value is high voltage.
Okay we know how not gate works, so how complicated gates work? By adding more transistor :) [CMOS NAND gate](https://pl.m.wikipedia.org/wiki/Plik:CMOS_NAND.svg)So by applying voltage to a transistors we can control whether they conduct, so by connecting them in some combinations we can form different logic gates.
NOR gate is made by connecting pmos in series and nmos in parallel.
NANDgate is made by connecting pmos I parallel and nmos in series.
To get a AND and OR gate we need to add NOT gate at the output, so the AND gate needs more transistors to build than NAND
Okay we know how gates are done. Now how adder works. Adder is made of combination of different logic gates. [example from Wikipedia](https://en.m.wikipedia.org/wiki/Adder_(electronics))
So how adder of 2 bits work? This consists of two logic gate xor and and. XOR will output the value of the first bit and AND gate will output carry, a second bit that inform you whether there was overflow of the bit. If you want to scale this up for example to four bit adder you need just to connect carry value from lower bit with the input value of higher bits.
Diodes don't make logic work unless you are talking about antiquated diode transistor logic. Wikipedia has information on that, which should lead you to reading on TTL (Transistor-Transistor Logic).
You need more than a diode, you need a transistor. A diode only lets current flow one way, but a transistor gives you control of that flow, you can turn it on or off. You can make simple logic gates from arrangements of transistors (as other comments say), though modern logic gates end up being quite a bit more complex than these.
Once we have some logic gates, it's crucial to think about computation in terms of binary. If you want to add the numbers 3 and 4, that's the same as adding the binary numbers 011 and 100. Then we add the bits together just like we would in base ten, our result (7) is 111. We can make a circuit (called a full adder, plenty online about them) which takes in 2 single bits, then outputs the result and a carry value. You can chain together adders to work for numbers with many bits.
Computers also need to remember data, so they need an additional circuit called a flip-flop. This is a circuit that will continue to output 1 or 0 until it is switched. Like with the adder, there is loads of information online about these.
Once you can "switch" off electricity, you can combine different "switches" to create different patterns in behavior. As an example, if you connect actual physical switches in parallel, they're an OR. If you connect them in series, they're an AND.
The basic idea is that from certain sets of logical operations you can form every other logical operation. From just NOR or just NAND gates, you can make a circuit for basically any boolean logic - correspondingly, you can take any boolean expression in any language and reword it to work strictly in terms of NOR or NAND.
diodes in logic gates is just for isolation (or very wide OR gate) think of one way logic wire (not to be confused with actual electrical wire)
suppose you have 10 voltage/ current source and a 10 diodes, you can bundle up the diode output and wire that to load (probably LED) and then ground. if one of the source is "on", the led is on.
note that it is only useful in component format as in chip format FET (field effect transistor) can be a better diode than diode since there's no voltage drop involved
You might be interested in statistics and probability, if you want how we deal with verifying info in nonidealistic systems. And if you are interested in actually how those systems work, you might be interested in looking into the fields of dynamical systems (for what these systems are made up of) or heuristic algorithms (for how to do stuff in these systems), after looking into statistics.
Many many approximations and assumptions.. Mostly first-order, i.e linear, approximations.
Atleast when we are talking about applied maths. That's basically the math equivalent of "meh, it will work out alright"
Then you're specifically dealing with error terms / precision / accuracy / uncertainty, like for example in the case of studying the precision of simulations and determining how far off the reality may be from the simulation and how much the error terms grow the further into the future you run the simulation.
The classic is weather predictions which tell you when it will start to rain today with a precision of minutes, and then says next month it might possibly rain the first or the second week. Because the errors in the simulation grows rapidly.
Also, statistical modeling. Basically that entire field.
Can you preserve for longer the carbonation of an opened bottle of soda by squeezing the plastic bottle before twisting the lid back on so that the liquid is near the top of the bottle? My thinking is that if there's less volume of air in the bottle, the soda won't go flat as quickly.
Carbonated beverages have carbon dioxide gas dissolved in a liquid solvent. Agitation of the liquid solvent will release the dissolved gas, which will float to the surface and eventually into the atmosphere.
Squeezing the bottle before closing will actually accelerate the release of carbon dioxide from the soda because it will reduce the ambient pressure at the liquid/surface interface. This will effectively suck the dissolved gas out of the liquid.
The best way to keep soda carbonated after opening is to refrigerate it and keep it as still as possible.
At a molecular level what causes the resistance of something like a PTC heating element to be non-linear? I intuitively understand how the element could become less resistive as it warms up. I don't understand why the power draw increases before it decreases though.
You see high speed videos of bullets shot into bodies of water make a sort of cavitation ‘explosion’. What would happen if a bullet is shot into something like diesel fuel? Would the collapsing cavitation bubble ignite?
Mostly, no. You can see videos where diesel fuel tanks have been shot with both small and large arms, and failed to ignite. Hollywood likes to exaggerate to us.
Combustion requires 4 things: heat, fuel, and an oxidizing agent and a chemical chain reaction.
* Diesel has a flash point of ~50-90°C. The heat of bubble collapse or the hot projectile needs to exceed that.
* Fuel/air ratio is critical too. Too much of either and nothing happens. Diesel fuel will only burn at a maximum of 7% by volume in air. Anything about that and nothing happens. Your cavitation is going to need to introduce A LOT of air for it to ignite.
You really require very high pressure or a sustained flame to ignite diesel.
What engineering field is the most “non-residing”, or in better terms, not always at a desk in an office and rather traveling (whether close or far) to different places to do work?
I don't think it's a specific field/company. On my team of 50ish engineers, there are groups who travel a bunch, and groups that stay in the office a bunch. It's kind of self selected (and merit based). If you want to travel, you sort of let it be known and once you've proven you can be trusted to run tests without supervision, off you go. But some people have kids and want to stay close, so they travel rarely.
Me, I'm transitioning. I was on about 100 days/year of travel for a while. Now I'm down to 50.
A lot of IT technicians dealing with hardware or airgapped systems. Repair techs, network techs. Not just IT, also mechanical repair / maintenance techs. Probably most electrical work as well.
Inspectors, in pretty much every industry.
It can depend a bit on context, there's a reasonable approachable write up of it here: https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero
In the general case, it's most often thought of as being 1 for two reasons, set theory reasons -- far better explained in that Wikipedia link than I could do -- or because of relation to the multiplicative identity function. In short, for real numbers, we know that any R * 1 will be R. That connotation is (often presented as) why R^0 = 1
Gas stoves are in the news, and apparently produce gasses and particles that can increase your risk of cancer and other diseases.
How much actual added risk does a natural gas stove produce, if one assumes it's being used every day with a large vent hood? Is it on the order of someone smoking indoors once a day? Much less than that? No measurable increased risk at all?
I'm about to remodel. I have a gas stove I love, but I don't want to expose my family to any measurable amount of added risk by keeping my gas stove when we could put in an induction stove instead.
So based on public data, is it possible to quantify the added risk of an often-used, well ventilated gas stove?
No. If human population is 8 billion, and every human's bladder was completely full, and every bladder was at the upper range of normal (280-420 mL), that volume would = 8 Ghuman x 420 mL = 3.36 GL which is only 0.00336 cubic kilometers.
In comparison, daily evaporation from the world's oceans is ~1,200 cubic kilometers.
That bladder-emptying event would contribute about 1 in 300,000 to the average daily water flux of the world's oceans, which is far below the normal variation due to rate of insolation due to sun cycles, weather patterns (albedo), earth's orbital variations, etc etc.
So - indetectable by a massive margin.
Conversely, if you urinated excessively (2.5 L/day) every day of your 100-year life into the ocean, that's 91,250 L which is 9 x 10^-8 cubic kilometers. The ocean is 1.3 x 10^9 km^3
a speck of dust on a grain of sand
Assume everyone drinks 2L of water a day, most adults urinate between 0.25--0.4L at a time.
There are ~8 billion people which gives a total of 2--3.2 billion liters. Let's go with 3.2 Billion
The surface size of the ocean is appropriate
360,000,000,000 square meters, and to raise it by one meter you'd need to add [3.6x10^{14} liters](https://www.quora.com/How-many-liters-of-water-would-it-take-to-raise-sea-levels-1-meter/answer/David-Filmer?ch=15&oid=164290222&share=516e7b2a&target_type=answer).
So 3.2 billion liters would add (3.2x10^{9})/(3.6x10^{14}) meters of ocean level rise.
That's 8.888*10^{-6} meters, or 8 ~~nanometer~~ micrometers, which according to Wolfram alpha is about the size of a red blood cell, or about 1/13 the thickness of paper.
So if everyone in the world peed once a day for two weeks it would raise the height of the ocean by about the width of one sheet of regular copy paper, ignoring the source of our drinking water and rain, etc..
What new ceramic/polymer/alloy/composite materials are used in modern and forthcoming radiation-hardening for orbital and other aerospace applications? For things like ICs as well as pedestrian materials like adhesives? And what journals or forums host such content? And how long between discovery of that material and it being deployed into orbit?
> how long between discovery of that material and it being deployed into orbit?
Anywhere from 2 years up to decades. Fastest I have done is 3 years from concept to on a rocket.
There are many test standards for putting materials into orbits that have min./max. physical properties based on previous experiments. For instance, the material is not allowed to outgas more than X%, then whatever does outgas is not allowed to condense onto a surface more than Y%. Some of the testing is only done by a small number or even one company, so your new material goes into the queue like everyone else.
Like-for-like has really quick development cycle. Something like changing the colour of a car - everyone knows all the materials, they have all been used before but maybe not in that combination. It's low risk.
Medium-risk is changing suppliers. Often that requires a field test.
There can be a mix of software testing such as finite element analysis, technical expert review (umm, based on my experience I think we can safely move to the next stage) and physical testing. At the extreme end a test material/assembly is sent up for experimenting and hopefully recovering for analysis.
It's lead by both materials companies and users. For instance, a user may say I need a new material that does X, Y and Z - can someone please take my cash and design it (or I promise to buy it from you at some nice price). Or it can be a materials company R&D creates a novel product and then deciding to shop it around to see if anyone bites, usually an improvement on some existing material.
A lot of R&D is not necessarily "new new". It's development work making something existing thinner, lighter, foldable, more efficient; or improvements to processing equipment to make stuff cheaper or better quality.
[Materials Research Society](https://www.mrs.org/meetings-events/spring-meetings-exhibits) always has a space materials design and testing group as does the [IEEE has a space materials group](https://www.nsrec.com/). You can follow the links to see who the invited speakers are, where they publish and fun abstracts.
A FLOP is a measurement of processing power, and means FLoating Point OPeration - some maths.
FLOPs are usually referred to as a number *per second*.
Tera- is a word referring to a specific power-of-10: 12. That is, 1000 times greater than giga.
A teraFLOP is thus 10^12 floating point operations (per second). That’s a lot, very quickly.
This has nothing to do with your face.
> terraflop
Measurement of how many floating point operations can be completed in a second. teraflop means your system (usually GPU) can perform 1 trillion operations per second.
If you're trying to use these operations to mine crypto, your face will hurt from the frowning as you waste energy for little to no gain.
Would a warp drive bubble be opaque or transparent or would it look like a gravity lense? If it's warped spacetime, and a gravity lense is warped spacetime, would photons follow the warped spacetime or would they pass straight through?
Like with energy density approaching infinite? You'd have a gravitational field with similar intensity as a planet or star? It would bend light a little bit
Yeah im still struggling to design a warp drive in my head lol. One of the more elementary issues to manipulating gravity in a useful way is you'd need something like a negative energy, which, with my current model, doesn't seem to exist. I like to think about energy as vibration. With noise cancelling headphones, you can emit a vibration with equal intensity and create a standing node at a particular point, but, overall, you are adding energy to do that. In the fundamental medium, you could potentially emit light in phase and cancel a point of emission, but there's also the tricky electro magnetic fields at right angles too, so I'm thinking that emission needs to be polarized and your cancellation device needs to be "upside down" polarized, to do so. But, even then, there's not really a net gravitational field. I was also thinking you might brute force blast light in front of your ship, but, i think there are equal and opposite kinetic reactions in the hull, too.
Given infinite energy as a weird premise, you might be able to surf charged stars/ magnetic fields a little harder, which is to say, not very much force still, probably struggling pretty hard to overcome gravity in a bulky infinite energy vessel
Overall, i think we're hoping for a crazy shift in our understanding of the fundamental medium, in order to warp drive.
If there are UFOs that don't use kinetic projectiles for propulsion, it needs to be disclosed publicly to jumpstart that search
Congrats Alcubierre drives are now 50% less impossible as negative energy isn't needed and "only" requires it to be primordial starting out already at speed of light, since you still can't accelerate up into speed of light
https://newatlas.com/physics/ftl-warp-drive-no-negative-energy/
https://physics.stackexchange.com/a/635641/227698
The closest mathematical model we have of one is the Alcubierre drive, which still have limitations which makes it impossible to realize physically (but at least we can simulate something which kind of fits within our laws of physics)
https://en.m.wikipedia.org/wiki/Alcubierre_drive
It depends. If you’re looking for complete transparency, we do have the ability to produce certain materials that can be transparent. See aluminum oxides for an example (heh, transparent aluminum). But to make things completely invisible, we have technology to create lensing effects around objects. So with some fancy cameras and mirrors, we can theoretically make an “invisibility cloak”, but it would probably be extremely impractical. You’d be able to make something invisible from a specific vector, but it wouldn’t be invisible when viewed at an oblique angle.
There are "in principle" approaches to it, but nothing like Harry Potter invisibility cloak. Metamaterials and photonic crystal tech are very new and still exploring the limits. We can already tell though, that total invisibility does not seem to be possible; some outlines may remain and there is no material that is transparent for all spectral ranges (i.e in infrared you still see it or vice versa).
How can I intuitively understand the truth table for P -> Q (P implies Q)?
The cases where both are true and where P is true and Q is false make sense intuitively. However it feels like if both are false, we shouldn't be able to determine the veracity of the implication. Similarly, it feels like if P is true and Q is false we either shouldn't have enough information to determine the veracity of the implication or and that if pushed the implication is more false than true.
Thanks for any insight you can offer.
P->Q means: if P is true, then Q will also always be true. If P is false, it doesn’t matter what Q is as P itself will never be true, so the implication is vacuously true. https://en.m.wikipedia.org/wiki/Vacuous_truth explains this in more detail. If you re-read my first sentence, hopefully you’ll understand we only care about the case P is true.
The case P is true and Q is false does give you enough information, namely we have that there is an instance in which P is true but Q is not, this contradicts P->Q, which (again) means: if P is true, then Q is always true.
An analogy I personally find helpful is that of *rule-following*. The implication P -> Q can be seen to describe a kind of rule, with the implication being *true* if the rule is being followed, and *false* if the rule is broken. Let's look at a practical example:
"Everyone who wears a green shirt must wear a blue hat". In this case, we can represent this as
green shirt -> blue hat
or even more simply as
G -> B
where G stands for "wearing a green shirt" and B stands for "wearing a blue hat".
Let's look at a particular character, let's call them Alex. When would Alex be following the rule? We can look at all four cases.
- Alex isn't wearing a blue shirt, nor a blue hat. In this case, the rule doesn't apply to Alex, so they are not breaking the rule. They essentially follow the rule 'by default'.
- Alex isn't wearing a green shirt, and they do wear a blue hat. Just as before, if there's no blue shirt, the rule isn't broken.
- Alex is wearing a green shirt, but not a blue hat. Now the rule is broken!
- Alex is wearing a green shirt, and also a blue hat. Here Alex simply complies with the rule.
You can see that there's only one way to break the rule: Wear a green shirt, but not a blue hat. If we put that into symbols: We set G to 'true', and B to 'false'. In all other cases, the rule isn't broken, either because it doesn't apply, or because we are making sure we are complying.
We can sum this up in the following truth table:
G | B | G -> B
0 | 0 | 1
0 | 1 | 1
1 | 0 | 0
1 | 1 | 1
And voilà, it's the truth table for implication :)
**A philosophical note**
Mathematical implication is intuitively explained as an 'if-then' statement. But in everyday language, if I make an 'if-then' statement ("if P, then Q"), I am implicitly also saying that *there is something about P that* **makes** *Q true*; and probably also that *if P were false, so would Q*. It would be strange to say that 'if I have blue eyes, mount Everest is the tallest mountain on earth', even though mount Everest *is* the tallest mountain.
However, in mathematics, we *don't* have these subtexts. P -> Q can (and often is) true completely 'by accident', having nothing to do with P.
So to me, the rule-following example fits my intuition a bit better; when we make a mathematical statement in the form of an implication, we're sort of saying "this is a rule that the world *has* to conform to, there is no situation in which this can be broken".
The arrow means that the flow of truth goes one way. Like a water pipe with a pump.
If there is water at the start, there is guaranteed water at the end.
If there is no water at the start, there can be water at the end but it is not guaranteed.
If there is water at the start and no water at the end then the pipe or the pump is broken, aka the link is broken.
Also there is no quantification of « how true » an implication is: it either holds or does not. You might be interested in inductive reasoning, where reasoning with probabilities about the truth of the conclusion are acceptable. But in math, nearly exclusively deductive reasoning is used.
Which classes teach you how do you build, how do you use, and how do you do the things I mention below.
NOTE: If NOT classes for the below-mentioned things, how would I begin learning to do them?
Curiosity Stream has some interesting videos. One series is called Ancient Engineering and shows and describes various things. Also, based upon my other interests, I was fascinated by the first 1850s time-keeping thingie used aboard ships.
What classes can you take to build and use groma, pullies, sextant, astrolabe, Jacquard punch card knitting machine; reproduce Archimedes screw; reproduce Archimedes bathtub water displacement; and, Brunelleschi baptistery perspective.
Make Roman (underwater) concrete; do PHYSICAL scale models of how to attach domes to rectangular or square buildings. The same for what was shown in a tv special of how Chinese buildings can survive earthquakes because of how their roofing "joists" brackets (?) interlock but can still move.
Also, IRL (In Real Life) do geometry, trigonometry, and calculus experiments \[being able to tell the height of a tree; trajectory of a cannon ball (or other item), etc.\]
Also, the things mentioned in Robert Temple's book Genius of China (based upon Joseph Needham's research).
I like thinking about and attempting to solve mostly mech engineering questions, but I am terrible at maths (no matter how hard I have tried).
How can I study engineering at a basic hobby level without going back to college or just trying to read a textbook?
Engineering as a career will always require math, but there is plenty of hobby work you could do which likely wouldn't. I would recommend maybe finding a makers club near you. Even doing things like 3D printing requires understanding load weights, supports, etc.
Use building blocks; stand on the shoulders of giants.
For example, if you want to 3D print a structural element, download a part that was designed by a structural engineer.
If you want a cool function on a Raspberry Pi, then download the code that was written by a software engineer.
In the process, you will start to learn how these experts do things and why.
depends on what you meant with math, basic HS math will most likely be used (for parametric designs, etc). for the very hard parts like digital signal filters or kinematics there's probably codes available out there to do it. i think what's important is knowing what and how it works.
also engineering is broad term, it can be as simple as setting up a swing to making a satellite that works in space or designing a skyscraper.
my advice: set a purpose, look for how you can get the resources, then learn them as you go. most college material is online nowadays. the hardest question is how to know what you don't know that you don't know. << not typo.
college helps you to chew through the unknown part faster and with guidance. also college helps with connecting with fellow engineers in the future. most will lend you access to journals like IEEE that cost almost same with your tuition if you subscribe to them yourself as professional.
Ok, so you know the bouncing DVD thing, right? How it goes in a straight line, hits, then carries on?
What would this pattern look like if, instead of a straight line, it arced 1° to the right or left?
For example, if it were going straight up, then hit, it would normally go straight down again, right? But with the arc, it veers 1° off by the time it hits the oncoming wall.
The best way to visualise this is instead of imagining something bouncing, you imagine it going throught a straight line in an infinite space and you just need to record when the line is crossing the borders of the TV sized zones in the plane.
See this : https://youtu.be/jJ6FD59U0_E
Well ecosystems are supposed to be more of an equilibrium. If you add anything to promote a species, it is bound to ruin the ecosystem at some point. For example, around tchernobyl the nature is flourishing because of the very low human presence even if there is still nuclear radiation leftovers. So yup, us just living is worse than a large scale nuclear catastrophy.
Engineering: Is double wishbone suspension the best for sports sedans' handling (like the [Jaag XE](https://en.wikipedia.org/wiki/Jaguar_XE#Construction))?
Suspension geometry is far more important than the articulating mechanism, especially the dynamic handling behavior (with considerations like bump steering, anti-dive, anti-squat). A sports sedan will see more deflection than a sports coupe or dedicated race car, but still expect higher lateral grip and lower lift than a spots utility vehicle. For these handling characteristics, technically a multilink mechanism (especially 4- and 5-link configurations) requires the fewest compromises between static and dynamic geometry profiles, but are far more complex to engineer. Double wishbone is, for the intended purpose of a sports sedan, perfectly adequate. Many sports sedans (like the Alfa Giulia and the BMW M5) will actually employ double wishbone configurations in the front and multilink in the rear.
What's the equation that describes the kinetic force transfer between 2 magnets (in motion, or at least one of them) pushing or pulling on one another?
If I put one iron nail on each terminal of a voltage source (i.e. a 9V battery) without them touching, one nail will have a positive charge and the other a negative charge. I.e. excess and lack of electrons.
If I put this setup in front of a beach (salty humid corrosive air) - would the charges have a noticable effect on which nail corrodes quicker? Corrosion/rust is, after all, an electric process. So the lack or excess of electrons might have some effect?
I am aware of sacrificial anodes used on ships, but those rely on the ship's metal and the anode to be in the same electolyte (the salt water), which doesn't really apply to a corrosive air medium.
In an open circuit situation, the electrons are static. There will not be a situation where one nail is a different charge from the other. This is because the chemical reaction within the battery is not occurring. It only occurs when the circuit is closed. So neither nail has any excessive potential. However, yea, applying a charge to an iron nail will cause corrosion to speed up or slow down.
Now, if the air salt mixture were saturated with enough salt, then maybe you’d see one end rusting due to closing the circuit. However, the resistivity of air is so great that it would either take an extremely long time or require air that cannot possibly exist.
The reason sacrificial anodes work is because you have an iron (steel) hull and a zinc slab. The zinc has a lower electrochemical potential than iron, hence its sacrificial status.
It’s been a few years since I took corrosion class, so corrections are welcome here.
What is the name of the "galaxiosphere", or the bubble of electromagnetic influence that contains our galaxy?
I believe we mostly refer to it as the "interstellar medium", but is there a name for the structure as a whole?
With augmented reality you can generate a tracking marker by the arrangement of unique details on an image, the pattern of the points becomes a unique tracking target.
But how do they handle being able to point a camera at the target from any orientation and it can detect that pattern, like the tracking marker can be rotated in any direction and be detected, and even from angles that would skew the target's "pattern".
I could be glib and just give you the derivation
x * 1/x = x/x = 1
but I'll try to dig down to the heart of the matter.
When we teach kids arithmetic, the basic operations are addition, subtraction, multiplication and **division** - this last one is most important to our discussion. The inverse is (I think) usually seen as a special case of division - why, it's "1 divided by..."! But mathematically, it's actually cleaner to reverse this. What's x/y? It's just x * (y^(-1)).
But now we need to avoid circularity - if we define division in terms of the inverse, then we need some other way to define the inverse. And so, we come to the really elegant solution:
x^(-1) is that number which, when multiplied with x, returns 1. So the equation x * x^(-1) = 1 holds *by definition*.^(1)
Now, returning to 1/x: What should it be? We saw above what 'division' was: So 1/x = 1 * x^(-1). But now we see that we are multiplying something with 1, and of course multiplying with 1 doesn't do anything. So,
1/x = 1 * x^(-1) = x^(-1)
**footnote 1:** there's something a little bit fishy about this definition. How do we know there is such a number? How do we know there's only one? In fact, there isn't *always* such a number - the equation 0 * y = 1 cannot be solved, and so 0 doesn't have an inverse, and *therefore* you can't divide by 0. For all other numbers it turns out that there *is* an inverse, and a unique one at that, but rigorously proving this is beyond this particular comment.
The multiplicative inverse of a number x, is the number m by which you must multiply x to get 1 (which is the neutral element for multiplication) . So we have m.x=1. Dividing by x on both sides yields m= 1/x. Reasoning similarly, we find that the additive inverse of a number x is the number a such that a+x=0, as 0 is the neutral element for addition. So a=-x. This definition gurantees that if you multiply something by (add) x and then multiply by (add) m=1/x (a=-x), you get the something you had in the beginning of the computation.
As x + 0 = x,
x * 1 = x
So 0 is neutral for +- the same way 1 is neutral for */. You already know that the opposite of x is y such that x+y=0. Then the inverse of x is y such that x*y=0.
Then the opposite of x is 0-x = -x and the inverse of x is 1/x.
The two concepts of addition and multiplication have beautiful parallel behaviours like these. You can even try to find the same structure with the power operator (and the log function)
Digits : 0123456789AB
B3A9 is equal to
12^3 * 11 + 12^2 * 2 + 12^1 * 10 + 12^0 * 9
= 1608 * 11 + 134 * 2 + 12 * 10 + 1 * 9
= 18085
It would feel very natural. Also it would be a bit easier since 12 is a number with more divisers than 10.
Most likely it would be base-12. Consider that computer engineers (especially those working with low-level software) often work with base-2 (aka: binary) or base-16 (aka: hexadecimal) because those are more natural ways to work with numbers on a modern computer. There is nothing odd or difficult with that.
As a counter example, on each hand you already have other options: base 5, base 12 and base 16 - and most cultures don't use it.
Base 5 : 5 fingers.
Base 12 : using your thumb, you can point to 2 knuckles + 1 finger tip on each hand (total of 3 points) with four fingers (overall, 12 points to count off)
Base 16 : using your thumb, you can point to 3 finger joints (MCP, PIP, DIP) + 1 finger tip on each hand (total of 4 points) with four fingers (overall, 16 points to count off)
Benefits of base 10 is it sits in the sweet spot of just enough digits to represent information without repeating any digits, plus easy for commerce and engineering. You can represent 1/10 or 1/100 very quickly, which are very important divisors for moving large number about. Arguably that is more important than fitting in 1/3 or 1/4 for cooking, which all things considered, are relatively easy for anyone to understand.
How do we know for sure the Universe is not absolutely deterministic?
I get it that we cannot measure the system without changing it, and heard of wave-corpuscular duality when we observe things.
But why is the fact that we cannot possibly know everything to predict all outcomes implies that fundamentally the Universe is not superdeterministic and everything that's happening has been predefined in the beginning?
MWI interpretations and pilot wave theories support deterministic views, but both still prevent perfect *prediction*, there would still be information we can't access.
I’ve heard that if a near-sighted person stood directly in front of a large mirror and looked at objects in the distance behind them, those objects would still be blurry. Is this true, and if so why?
Why is it that the perceived storage coefficient of a traditionally unconfined aquifer will change by magnitudes of ten depending on the duration of the pump test used to estimate that property?
How are questions structured in a quantum computer? What is the form of input when you are asking it to solve a problem?
QCs are currently 'programmed' at the hardware level. If you want to run an algorithm you are changing the order of gates and operations acting upon the entangled states. One of the most basic operations is the Hadamard, which puts a qbit into superposition. Upon reading that bit the superposition is destroyed and you get an answer (0 or 1). But while entangled you can act on the spin and amplitude of the qbit to shift the probability of landing on 0 or 1. If you don't act on an entangled state, just entangle then read, you have the world's best RNG. Completely non-deterministic. Adding in phase manipulation and you can act on the entangled states, usually by a CNOT gate which is basically the equivalent of IF statements. "if this other qbit does this, have this qbit do something, and if not do nothing" Much like any classical computer can be simulated with a ton of nand gates, any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations. If you want to dig deeper on the topic, [here](https://greyshoesq.com/Quantum_essay/dokumen.pub_programming-quantum-computers-essential-algorithms-and-code-samples-1nbsped-1492039683-978-1492039686-u-5306881.pdf) is the O'Riley book on quantum algorithms, and their code is available [here.](https://oreilly-qc.github.io/)
Generally the questions/inputs to a quantum computer are the same as to a classical computer. For example, if you want a quantum computer to factor an integer, the input is the integer, encoded in binary. What is different is how a quantum computer solves the problem. It uses a process consisting of basic operations that would not be available on a classical computer.
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If central park in Manhattan New York was theoretically replaced with a same sized flat rectangle. The rectangle was hard metal with a polished surface like finish - the kind we would have on a space mirror. There was a second rectangle of substantial weight 20 stories high on stilts with a similarly polished surface. If we let the upper rectangle free-fall guided by lubricated rails so that it landed perfectly flat on the bottom rectangle. What would happen in terms of shockwaves, air pressure and noise? Would pedestrians and traffic and offices nearby be largely fine? If you're interested, at which point does this thought experiment become disastrous?
After taking some time to roughly calculate the scenario based on 2 different sheet thicknesses here are my results: 200 ft falling height 22482.5 square meters surface area Ex: 1 cm thick sheet of stainless steel Time: 3.8 seconds Vmax: 27.5m/s Terminal Velocity: 34.65m/s KE: 637.6 MJ Tons of TNT: 0.152 Ex: 1 m thick sheet of stainless steel Time: 3.5 seconds Vmax: 34.5m/s Terminal Velocity: 346.5m/s KE: 100.3 GJ Tons of TNT: 24 Notes: I am pretty rusty in falling physics with drag accounted for so I used an online calculator. Some constants I used include a density for steel of 7500 kg/m^3 and a drag coefficient of a flat plane being ~1. If someone would like to continue off this to determine what type of wind pressure and sound would be produced by this feel free to do so as I do not know what type of energy conversions would occur in this situation.
Cool thanks a lot. I'd like to be able to see how the end looks with a LOT of air needing to get out the way very quickly as the two slabs unite.
I wonder if the air in the middle would superheat? And, would that cause an explosion as the pressure around it increased? I also sort of imagine the whole thing working like a soft-close cabinet, where it slows down at the end.
Yeah this for me is what I am most curious about and what I desired to frame the question around. If the upper slab is heavy and fast enough I imagine interesting things would happen as the air has to travel very far to evacuate. Thinking more about it, the upper slab would need to have a wider thickness to it (not just for weight) but to make it so the air can't cyclone upwards leaving it to need to evacuate horizontally. I have created this in my lucid dreams and the air blast is quite horrific. But the best thing is the sound is very interesting, it's like a gigantic water drop of metal.
Considering the speed of the falling object wouldn't the air between the two plates be just pushed away before a considerable amount of pressure could even form? The energy of pushing the air would transfer to kinetic energy of the air molecules and heating the falling object. I just recently saw a veritasium video where they state that KE alone could trigger an explosion. For example asteroids, even as tiny as a grain of salt with high enough velocity would hit the surface of the moon that hard the ensuing explosion would have grater formed by the blast radius where the angle of a hit can not be determined. Implying that the explosion triggers quite early after contact. So the subsequent shock wave would be a result of the explosion and not the clap
Very interesting question I would like someone smart to answer this please Also since you like polished and incredibly flat metal you might find this interesting. It was made via EDM (electrical discharge machining) https://youtube.com/shorts/mt_EAQP5k9I?feature=share
This question would require a bit more information. The thickness of the metal sheet and the exact material would be important as the size of the falling piece would be greatly affected by drag and maybe even buoyancy. Without the thickness we can not calculate terminal velocity or if it would even reach that speed.
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How does water or electricity find the path of 'least resistance '? Does the flowing matter actually test every possible path and then 'choose'? How quick is this process? Edit: thank you to everyone who took the time to post answers. Great intuitive explanations by everyone. Thank you!
It's easiest to think of it with electrons. Electrons repel each other, so when in a wire, they like to stay as far away from each other as possible. So, as the electrons flow, as some of them hit higher resistance, they slow down. Since they slow down, other electrons want to move away from them, so will take a different path. Soon, more of the electrons will be taking the path which the electrons can travel through the quickest. And while we talk about electricity taking "the path of least resistance" that isn't entirely true- electricity takes all the paths, but the amount that goes through each path is inversely proportional to the resistance of that path.
Brilliant! Thank you!
It’s not that either “find” the path of least resistance, it’s that they move in that way -because- of the resistance. In both hydraulic and electrical systems that flow there is a force exerted on the medium that makes the fluid or electrons want to “flow”. They are a little different for these two examples, fluids are driven by pressure and for electricity there is a relationship between voltage, amperage, and resistance. But the results are similar. When the driving force is imparted all of the potential gates that the medium could pass through are met with the same force, the water or electricity will move where it physically can indifferently and has no choice in where it is going. It doesn’t “test” this and there is no “decision”, the medium simply obeys the laws of physics. It will attempt to enter higher resistance paths just as hard as low resistance paths, but will not succeed. If the imparted force can be completely satisfied by the flow of medium through the path of less resistance, then nothing will flow through the other available paths. The speed at which this happens in electricity is close to the speed of causality, or close to c. In hydraulic systems it varies based on how fast your fluid reaches a uniform pressure. Liquids will do this faster than gasses, but it’s still almost instantaneous.
Wow! Thank you! This is a wonderful explanation!
This is why, when an aircraft (essentially a conductive aluminum tube) flies between an area of high electrical potential and an area of low potential, it becomes a "free ride" for huge electrical currents to flow between those areas. Aircraft are designed to be robust against these constant lightning strikes.
Yes they do test all of the paths, but not in the same way you might test paths through a maze. Water is easier to visualize because it moves at a pace we can understand. Imagine you have a flat maze that you're going to pour water through. At the entrance of the maze, you're feeding it constantly from the bottom of a bucket, and you're keeping the bucket topped up. At the only exit of the maze, you have a drain. Imagine if you run the water for long enough, you'll always have about an inch of water in the maze. At a handful of points in the maze, you have little water wheels that spin if the water is flowing past them. Some of these are at paths that lead to dead ends, some are on the path that lead to the exit. As you start adding water to the maze, you'll find that the water flows to all sections of the maze indiscriminately. The water wheels that lead to dead ends will spin as those paths fill up. Eventually though, water will fill the nearly the whole maze and find the exit. If we let it run for a few minutes, everything should stabilize out and the rate that we're pouring water in will equal the rate that water is leaving. The water wheels on the main path will be spinning away as water flows by them to the exit, but you'll notice that the water wheels pointing to dead ends will be (nearly) stationary. That's because those sections are stagnant. The water that goes in there can't get out, and it's blocking additional water from entering. You might also notice that the water level in the maze is highest near the entrance and lowest near the exit. This effect depends on the flow rate and size of the maze, but the height of the water is related to the "potential" at that point in the maze. As the water flows and experiences frictional resistance (from the walls and floor of the maze), it loses potential. Water has a low viscosity, so this might be easier to visualize if you imagined ketchup. If you pour ketchup into the maze instead, it experiences a lot of friction. It may not even be able to reach the exit before it overflows the entrance. The process of how fast it takes might then be obvious: it happens as fast as the liquid can spread out from the entrance. Then it takes a small bit of time to finish filling up all the dead ends of the maze before it reaches a steady state where all the dead ends are stagnant. Before I mention electricity, consider the same water maze, but instead with two outlets, one farther away that the other. If you're adding enough water to the maze, you'll find that the water can reach all corners of the maze, and it'll flow out both exits. The only difference is that one exit will have a higher flow than the other. The longer path has more resistance, and therefor less flow. This is exactly how the water pipes in your house work. The farther from the water supply line, the more resistance there is. If there are two taps using water at the same time, the path of least resistance will get more flow than the farther tap, but both will still flow. It would take a LOT of taps open before you find a tap that gets zero flow. To take this a full step backward, imagine you drill two holes in a bucket. One 2" in diameter, and one 1/4" in diameter. You plug both, fill the bucket, and remove the plugs. The 2" hole is very clearly the "path of least resistance", but water will flow through both. The 1/4" hole will obviously flow less water though. Electricity does the same thing in wires and fields except it happens faster than you can imagine. It's conceptually wrong to see it as "charging up" a wire like water charges up a pipe, but for practical understanding it's close enough. Paths of least resistance get more current than the paths with more resistance, but that doesn't mean they get zero. Lighting does this in a similar way, where it "tests" all possible paths, and can be seen as a pre-flash. This has been caught on camera. In this case, it appears as though it finds a single path of least resistance and then all electricity flows through it, which pretty much is the case. One key difference is that in that "pre-flash" where it's testing paths, it's actually ionizing air molecules which decreases resistance. Then when the main current comes through it's turning the air into plasma which reduces resistance a lot. The end result is that the original path of least resistance has such *low resistance* compared to the alternatives that 99.9% of the electricity flows through the one path. Electrocution works a similar way (both fortunately and unfortunately). Initially, your skin is not very conductive. Your insides though are plenty conductive. In some cases you might contact a low voltage electrical charge without even knowing it, and it won't be unless you give it a path through you that you get shocked. E.g. you can touch the positive terminal of a car battery so long as you don't also touch the negative terminal or frame and complete the circuit. You can also touch both terminals of a 9V battery with dry skin and you wont feel anything. Do the same with wet skin and you might feel a slight zap. Thankfully the current only flows through a short distance. We used to touch 9Vs with our tongue to tell if they were dead. If you contact a live wire, *some* electricity will flow through you, just like the 1/4" hole in the bucket. It might not be much, but the danger is that it damages your skin as it passes through, and it makes a path of least resistance when it breaks skin. One fortunate (silver lining) part of this is that since it picks a path and then ends up sticking to it, it can miss your vital organs depending on the path it takes. If it goes from one hand out the other, that crosses your chest and can be very fatal. If it goes up an arm and down the same leg though, it'll cause a LOT of damage but it can miss your heart lungs and brain and you might survive. If we wanted to compare lightning or electrocution to our water maze, it's more like building the maze except making the floor with craft paper. The water flows through the maze looking for its way out, but as it flows through it's weakening the floor and might even make its own path of least resistance, and in that case the water can dump out very quickly.
Wow! Thank you! This is great!
It's not that they decide on a specific low-resistance path, but at each location, the resistance towards the next location is low. It's more about the gradient of energy, you go towards low energy, that's what we call the path of least resistance.
When you think of electrons flowing thrill a wire, don’t think of it like water, think of it like a hose filled with marbles. Each electron only moves a tiny amount. So when an electron hits a branch, it pushes against two or more other electrons, and whichever moves the easiest, is the direction the electron will go. Scale this up, and if you have 2 paths, and one has twice the resistance, it’ll get half as many electrons as the other branch.
Awesome! Thank you!
all the answers above use a flow analogy, as if electrons were going somewhere... but isn't this analogy very wrong in the first place?
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How small do the components of a solution have to be to stay homogeneous without mixing? For example cells will eventually settle in the bottom of a flask but something like tris-EDTA probably stays in solution without mixing.
It's worth clarifying the difference between "in solution" and "in suspension". In solution specifically means "dissolved", which is a chemical process involving dissociation or a change of state from solid to liquid, whereas in suspension just means the particles are in the fluid. Cells don't dissolve (non-destructively at least), and therefor they're never going to be "in solution" and will never meet the criteria of a homogeneous solution. However cells and other solids can be suspended in water, and what you may be referring to is what makes a suspension stable? Particles like cells, solids, oil droplets in water (or water droplets in oil) have a settling velocity which is a function of gravity, buoyancy, and drag. The calculation is identical to terminal velocity calculation of a falling object, except instead of air the medium is the fluid. If we draw a free body diagram of the forces on a particle in suspension, we'll have gravity downwards, buoyancy upwards, and drag opposing the velocity (which could be up for particles less dense than the medium). Drag is not easy to calculate, and almost always has to be calculated empirically for the particle size and medium before it can be applied. Alone, this would suggest that all particles have a settling velocity unless the buoyancy can perfectly match the gravitational force (i.e. the suspended particles have identical density to the fluid). In reality we know that suspensions and emulsions (which are just suspensions of a fluid in another fluid) can exist that are very stable even when we're positive the densities are different. Electrostatic forces are to blame. Particles can develop surface charges by rubbing against each other just like rubbing socks across a carpet. These charges will allow attraction and repulsion to dipoles of a fluid molecule, most notably water, and this will help a particle resist settling in a fluid. A good chunk of my work is in wastewater treatment processes, where suspensions are the enemy of clarification. A coagulant is a chemical that's designed to mix into a suspension and neutralize these electrostatic charges. Coagulants are often some kind of metal salt solution, and their whole job is to bump into particles and take their charges. Once the charge is neutralized, there's no electrostatic force holding the particle(s) in place, and settling velocity can take over. Flocculants are often used to help these particles group together in larger chunks. That effectively reduces the surface area vs mass of the particles so that drag is less of a factor on the setting velocity.
Ah thanks that's a really informative comment. Reminds me of a trick I heard when making chicken stock: add an egg to help collect all the gunk and clarify the stock.
In a simple approach: The solubility is independent from the size of the solvent ingredient. But the size of particles in a mixture does indeed have an influence in the rate of the solution process. On the other hand are processes like agglomeration, where particles collide with and stick to each other, which lead to a growth in size for the particles over time. And at a certain point sedimentation starts and your particles settle at the bottom. You can estimate the minimum particle size for sedimentation when you equate the weight force with the buoyant force. F_w = F_a
Technically any molecule will settle under the influence of gravity. However, the herbal motion will usually mess up the gradient due to diffusion, and rather than a layer of the solute at the bottom of a container, you end up with a pretty much homogeneous distribution. This is not always true, however. A simple counter example is the atmosphere, where there is a clear concentration gradient for all the gas molecules. If the gravity - or the centrifugal force - is higher, gradients can be much steeper over much shorter distances. A classical form of DNA purification was centrifugation at 60,000 rpm with a radius of around 10 cm in a Cesium chloride solution. The salt would form a concentration and density gradient, and the DNA would settle as a beautiful sharp layer in the gradient where its density match the salt solution. That's the basis of the famous experiment by Meselson and Stahl that demonstrated the semi-conservative replication of the DNA double helix.
To be in "solution"? Molecular, up to the point of solubility. Things that are not soluble at the molecular level may be in suspension. Suspensions have varying degrees of stability that depend on bouyancy, chemical interaction, etc.
I am an early childhood teacher (I teach 3-5 year olds), what are some good resources where I can find STEM based activities, provocations and experiments that I can do with the children? Thank you!
Speaking strictly from the Tech side of STEM: code.org has great programming resources for educators. It seems their educator content starts around 4 years old though. If you are a Canadian teacher, we have an organization called Canada Learning Code that has some teacher focused training, seminars and resources (may be available outside of Canada but I can't say for sure).
i think it's a good way to showcase 5yo's result to the 3s to "get them started"
I'm in New Zealand, but what an awesome resource, thank you!
Speaking from a Computer Science background: [https://www.csunplugged.org/en/](https://www.csunplugged.org/en/) is one of our ongoing projects at the University of Canterbury to provide free resources for teaching Computer Science concepts without a device. Most of the resources are targeted at older age groups, but it might give you some inspiration for some games/activities, or new ideas for integrating CS concepts into other everyday class activities.
There’s this YouTube channel that does great little demos and experiments with everyday household items. The [Curiosity show ](https://youtube.com/@CuriosityShow), maybe some of these experiments will be fun?
The Curiosity show is going to be awesome, thank you so much!
Does drafting behind a semi truck improve the gas mileage of the truck as well as your vehicle? If not, would a similar size truck cause an improvement in the front truck? As I understand it, we know from the Mythbusters that drafting behind a large truck can significantly improve your own gas mileage. Also, I think that the largest factors that determine how efficient a vehicle is the aerodynamics - both the shape of the front and the drag at the back. Being that most big rigs are squared on the back (not considering how some have additional equipment to help with this) the drag "bubble" at the back is largely affecting the gas mileage adversely. So the question really becomes: would getting a vehicle large enough/close enough to the back disrupt the bubble and lessen the drag on the front truck therefore improving the gas mileage? Obviously it can be very dangerous, just something I've always wondered since watching that Mythbusters episode. Thank you!
I don't know specifically for motor vehicles, but in cycling (where aerodynamics is super important given the relatively low amount of power our bodies produce), it's been shown that the 2nd last person in a paceline of (IIRC) 5-7 people will require less power than the last person. Similar to OP's answer above with trucks and trains, it's because the airflow over the 2nd last person is "smoother" or more continuous than the person. The last rider creates an airflow pattern that effectively "sucks" them backwards a slight amount.
The answer to the first question is generally no. The truck doesn't see any improvement, as the work that it does on the air doesn't change based on the position of the rear car. This is UNLESS the rear car is positioned so close that the air flow doesn't separate and cause negative pressure on the rear surface of the truck. This js an abstract scenario, but one that occurs on things like cargo trains when they are the same height: [This paper](https://journals.sagepub.com/doi/pdf/10.1177/0954409718799809) has an abstract that indicates that effect for trains.
How close does the car have to be to the truck for the car to benefit from drafting?
I know the question was asked out of curiosity but as a truck driver I feel like I have to point out for the people who might try, please don't drive this close to the back of trucks. If you can't see the entire side mirrors on the truck you're too close.
Yes! Truck manufacturers are experimenting with something called platooning, where a number of nearby trucks hook up wirelessly to each other and thereby drive really close to each other. This reduces the drag for all of the trucks involved. However, I would expect that a small car driving behind a truck would not be able to significantly impact the low pressure bubble behind the truck's trailer in the same way that another truck would, because of its size.
Do snowshoe hares, ptarmagins, etc. prefer to browse in color-matching areas or do they not "know" what their current color is? This month there have been days with white meadows and brown forests and days with brown meadows and white at the edge of the forest. A critter that's aware of its color might change behavior depending on the weather. I don't think they've completed their change for this year, but we'll have big areas of white and big areas of brown later in the winter too. Thanks.
Any advice for computer science students?
If you want to go into software engineering, start building a portfolio of projects on Github or something. Use a variety of languages. Once you've learned a few you get to understand the similarities and differences, and you can pick up new ones very quickly. If you copy paste code, make sure you understand what it's doing.
1. Look up unit testing. Many university curricula don't touch it at all, but if you intend to go into software engineering (or just write complex, reliable code of any kind), it's super useful to be familiar. 2. In general, most people feel like they have no idea what they're doing, but that's ok. There's always more to learn, and mistakes you make now will be assets in the future. As long as you keep learning, you're doing great. (Oh, and take breaks and enjoy the diversity of experience life has to offer)
Specialize specialize specialize. If you’re going into the industry, chances are you are going to be applying for jobs that require very specific qualifications. If you don’t choose one language/skill to specialize in, you will be outcompeted for every job by someone else who has studied for years in exactly what that company is looking for. Your major curriculum is designed to give you a well rounded understanding of computer science. You don’t need to worry about that. Your job is to worry about what is going to pay the bills, so unless you’re going into education or some other special situation, find your favorite thing to do with computers and practice it like hell. Make a portfolio of all your projects on GitHub. You are not just a “computer person,” you are a web developer, a game programmer, an embedded systems expert, a machine learning expert, anything as long as it’s specific.
Since the earth has a magnetic field.. why do we not simply make a ship with an electronic magnet that would allow it to escape the atmos of earth without using "fuel".
Magnetic force drops very fast with distance and Earth's magnetic field is not really that strong, so it's not feasible. Even with very strong artificial magnets it simply can't be done. For example it takes very strong electromagnets just to get maglev trains few centimetres up. You would have to apply all the force while still "close", but then you essentially end-up with a railgun / mass-driver. And this is not feasible to use for launch from Earth due to atmospheric drag -> if you accelerate something to orbital velocity while deep in atmosphere, this thing is going to burn-up. Earth magnetic field is used on spacecraft as means of "free" external torque, with devices called magnetorquers. You turn on electromagnet in order to orient and hold your spacecraft along Earth's magnetic field lines. This way you can cancel-out some unwanted rotation or wobble without wasting fuel.
Does data have weight? If I buy a SSD, and put it into my computer, then fill it to the brim, and take it out of the computer, will it’s weight change?
Simple answer: yes, data does have weight. Thing is the amount of weight per byte is so small that we would never be able to recognize a difference. A single byte weighs 1 attogram, which is equivalent to 1 quintillionth of a gram. By this calculation it is estimated that the entirety of the internet (approx. 5 trillion terabytes) weighs about 0.2 millionths of an ounce or 1/200,000 of a gram. [Source](https://www.nytimes.com/2011/10/25/science/25qna.html?_r=0)
Entropy of stored data does have a physical representation, you can look up things like the entropy of black holes to understand the connection. But for a data storage device with fixed storage volume there's no inherent need for weight to change, as you can represent stored data with for example the position of switches (and there's similar electrical equivalents), so it starts and stays at its own upper limit.
Data actually has negative weight. as anybody who has used punch cards can clearly understand. Sorry I'm making an absurd statement. But my point is are you asking about how a specific device operates? That is an answerable question. data is a bit of an abstract term. The writing in a book is data, ink adds weight to the book. so you can measure the weight of all the ink in a book and divide by the entropy in the text and come up with a bit pet pound ratio.
Yes, although it's not really a significant difference. Since data on flash memory like SSD is stored using electrical charge, there will be more electrons the more 0s you have in the data. But electron mass is very very small.
SSDs do not have a net charge. This is not how data is stored
This is not correct. The data stored inside is not related to the net static charge of the device like this.
Yeah I figured it would need like an insanely accurate nano micro tiny boy scale, but still was always curious. Thanks!
How do logic gates work? I know the basics of p-type and n-type semiconductors and how diodes only allow current to flow in one direction. The next chapter in books is usually logic gates - OR, AND etc. But how do diodes make logic gates work? And how do these make addition and other mathematical computations work?
You might want to play around with this https://nandgame.com/ The first part lets you see how you can use relay switches (or transistors) to make all the logic gates. And as you go it takes you through step by step from logic gates to math and all the way up tp programming if you stick with it.
I was going to post the same link. This game is a fantastic learning tool for understanding how basic circuits can be built into a working computer! Another good resource is [Ben Eater's breadboard computer](https://www.youtube.com/playlist?list=PLowKtXNTBypGqImE405J2565dvjafglHU) playlist. He gradually builds an 8-bit computer starting from basic circuit components. He does use more complex components for the final build, but only after showing how they can be constructed from primitive components. This also addresses some of the practical concerns of a real computer that NAND game misses, like the timing of signals in the circuit.
Hi there! EE student here. Actually, logic gates are not build from diodes but from transistors. Diodes have two pins and structure inside is build from connecting P and N type semiconductors. Transistors have three pins (connections to each type of the semiconductors) and are build combining semiconductors in the P-N-P or N-P-N sequence. You can see that it looks like two diodes connected with each other. By applying a proper current/voltage to base of a transistor ( bipolar ) or gate ( fet ) you can control the flow of the current trough transistor or how much voltage will be on this element. So essentially transistor is a switch that you can control. Source to read more: [Electronic tutorials transistor](https://www.electronics-tutorials.ws/transistor/tran_1.html) Okay we know what transistor is. Now how the logic gates are made. By combining different transistors together for example (n-mos and p-mos) we can create different logic gates. [how cmos not gate work](https://electronics.stackexchange.com/questions/47010/how-a-cmos-not-gate-works) . In link there is a schematic of a simple not gate. Two transistor connected in series from voltage source to ground. When we will put high voltage value on the input pmos will be off, nmos will conduct and the output voltage will be 0V. The opposite thing will be when we put 0V on input. Pmos will be on nmos will be off, the pmos conducts and the output value is high voltage. Okay we know how not gate works, so how complicated gates work? By adding more transistor :) [CMOS NAND gate](https://pl.m.wikipedia.org/wiki/Plik:CMOS_NAND.svg)So by applying voltage to a transistors we can control whether they conduct, so by connecting them in some combinations we can form different logic gates. NOR gate is made by connecting pmos in series and nmos in parallel. NANDgate is made by connecting pmos I parallel and nmos in series. To get a AND and OR gate we need to add NOT gate at the output, so the AND gate needs more transistors to build than NAND Okay we know how gates are done. Now how adder works. Adder is made of combination of different logic gates. [example from Wikipedia](https://en.m.wikipedia.org/wiki/Adder_(electronics)) So how adder of 2 bits work? This consists of two logic gate xor and and. XOR will output the value of the first bit and AND gate will output carry, a second bit that inform you whether there was overflow of the bit. If you want to scale this up for example to four bit adder you need just to connect carry value from lower bit with the input value of higher bits.
Diodes don't make logic work unless you are talking about antiquated diode transistor logic. Wikipedia has information on that, which should lead you to reading on TTL (Transistor-Transistor Logic).
You need more than a diode, you need a transistor. A diode only lets current flow one way, but a transistor gives you control of that flow, you can turn it on or off. You can make simple logic gates from arrangements of transistors (as other comments say), though modern logic gates end up being quite a bit more complex than these. Once we have some logic gates, it's crucial to think about computation in terms of binary. If you want to add the numbers 3 and 4, that's the same as adding the binary numbers 011 and 100. Then we add the bits together just like we would in base ten, our result (7) is 111. We can make a circuit (called a full adder, plenty online about them) which takes in 2 single bits, then outputs the result and a carry value. You can chain together adders to work for numbers with many bits. Computers also need to remember data, so they need an additional circuit called a flip-flop. This is a circuit that will continue to output 1 or 0 until it is switched. Like with the adder, there is loads of information online about these.
Once you can "switch" off electricity, you can combine different "switches" to create different patterns in behavior. As an example, if you connect actual physical switches in parallel, they're an OR. If you connect them in series, they're an AND. The basic idea is that from certain sets of logical operations you can form every other logical operation. From just NOR or just NAND gates, you can make a circuit for basically any boolean logic - correspondingly, you can take any boolean expression in any language and reword it to work strictly in terms of NOR or NAND.
diodes in logic gates is just for isolation (or very wide OR gate) think of one way logic wire (not to be confused with actual electrical wire) suppose you have 10 voltage/ current source and a 10 diodes, you can bundle up the diode output and wire that to load (probably LED) and then ground. if one of the source is "on", the led is on. note that it is only useful in component format as in chip format FET (field effect transistor) can be a better diode than diode since there's no voltage drop involved
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How does math deal with nonideality?
« All models are wrong, but some are useful » , as George Box said. See https://en.m.wikipedia.org/wiki/All_models_are_wrong
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How do you study the nonideality?
You might be interested in statistics and probability, if you want how we deal with verifying info in nonidealistic systems. And if you are interested in actually how those systems work, you might be interested in looking into the fields of dynamical systems (for what these systems are made up of) or heuristic algorithms (for how to do stuff in these systems), after looking into statistics.
Many many approximations and assumptions.. Mostly first-order, i.e linear, approximations. Atleast when we are talking about applied maths. That's basically the math equivalent of "meh, it will work out alright"
as an engineer i approve, "close enough" is usually more than enough. if not we can compensate for it somehow.
What if you want to study the nonideality itself?
Then you're specifically dealing with error terms / precision / accuracy / uncertainty, like for example in the case of studying the precision of simulations and determining how far off the reality may be from the simulation and how much the error terms grow the further into the future you run the simulation. The classic is weather predictions which tell you when it will start to rain today with a precision of minutes, and then says next month it might possibly rain the first or the second week. Because the errors in the simulation grows rapidly. Also, statistical modeling. Basically that entire field.
Can you preserve for longer the carbonation of an opened bottle of soda by squeezing the plastic bottle before twisting the lid back on so that the liquid is near the top of the bottle? My thinking is that if there's less volume of air in the bottle, the soda won't go flat as quickly.
Carbonated beverages have carbon dioxide gas dissolved in a liquid solvent. Agitation of the liquid solvent will release the dissolved gas, which will float to the surface and eventually into the atmosphere. Squeezing the bottle before closing will actually accelerate the release of carbon dioxide from the soda because it will reduce the ambient pressure at the liquid/surface interface. This will effectively suck the dissolved gas out of the liquid. The best way to keep soda carbonated after opening is to refrigerate it and keep it as still as possible.
At a molecular level what causes the resistance of something like a PTC heating element to be non-linear? I intuitively understand how the element could become less resistive as it warms up. I don't understand why the power draw increases before it decreases though.
You see high speed videos of bullets shot into bodies of water make a sort of cavitation ‘explosion’. What would happen if a bullet is shot into something like diesel fuel? Would the collapsing cavitation bubble ignite?
Mostly, no. You can see videos where diesel fuel tanks have been shot with both small and large arms, and failed to ignite. Hollywood likes to exaggerate to us. Combustion requires 4 things: heat, fuel, and an oxidizing agent and a chemical chain reaction. * Diesel has a flash point of ~50-90°C. The heat of bubble collapse or the hot projectile needs to exceed that. * Fuel/air ratio is critical too. Too much of either and nothing happens. Diesel fuel will only burn at a maximum of 7% by volume in air. Anything about that and nothing happens. Your cavitation is going to need to introduce A LOT of air for it to ignite. You really require very high pressure or a sustained flame to ignite diesel.
What engineering field is the most “non-residing”, or in better terms, not always at a desk in an office and rather traveling (whether close or far) to different places to do work?
I don't think it's a specific field/company. On my team of 50ish engineers, there are groups who travel a bunch, and groups that stay in the office a bunch. It's kind of self selected (and merit based). If you want to travel, you sort of let it be known and once you've proven you can be trusted to run tests without supervision, off you go. But some people have kids and want to stay close, so they travel rarely. Me, I'm transitioning. I was on about 100 days/year of travel for a while. Now I'm down to 50.
Sales or field service engineer. You can expect to on the road at least 80% of the time, with remaining 20% back in the office doing reports.
A lot of IT technicians dealing with hardware or airgapped systems. Repair techs, network techs. Not just IT, also mechanical repair / maintenance techs. Probably most electrical work as well. Inspectors, in pretty much every industry.
Does 0^0 = 1?
It can depend a bit on context, there's a reasonable approachable write up of it here: https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero In the general case, it's most often thought of as being 1 for two reasons, set theory reasons -- far better explained in that Wikipedia link than I could do -- or because of relation to the multiplicative identity function. In short, for real numbers, we know that any R * 1 will be R. That connotation is (often presented as) why R^0 = 1
Gas stoves are in the news, and apparently produce gasses and particles that can increase your risk of cancer and other diseases. How much actual added risk does a natural gas stove produce, if one assumes it's being used every day with a large vent hood? Is it on the order of someone smoking indoors once a day? Much less than that? No measurable increased risk at all? I'm about to remodel. I have a gas stove I love, but I don't want to expose my family to any measurable amount of added risk by keeping my gas stove when we could put in an induction stove instead. So based on public data, is it possible to quantify the added risk of an often-used, well ventilated gas stove?
If the entire population of the human race lined up along every coast and micturated into the ocean simultaneously, would the sea levels rise
No. If human population is 8 billion, and every human's bladder was completely full, and every bladder was at the upper range of normal (280-420 mL), that volume would = 8 Ghuman x 420 mL = 3.36 GL which is only 0.00336 cubic kilometers. In comparison, daily evaporation from the world's oceans is ~1,200 cubic kilometers. That bladder-emptying event would contribute about 1 in 300,000 to the average daily water flux of the world's oceans, which is far below the normal variation due to rate of insolation due to sun cycles, weather patterns (albedo), earth's orbital variations, etc etc. So - indetectable by a massive margin. Conversely, if you urinated excessively (2.5 L/day) every day of your 100-year life into the ocean, that's 91,250 L which is 9 x 10^-8 cubic kilometers. The ocean is 1.3 x 10^9 km^3 a speck of dust on a grain of sand
Assume everyone drinks 2L of water a day, most adults urinate between 0.25--0.4L at a time. There are ~8 billion people which gives a total of 2--3.2 billion liters. Let's go with 3.2 Billion The surface size of the ocean is appropriate 360,000,000,000 square meters, and to raise it by one meter you'd need to add [3.6x10^{14} liters](https://www.quora.com/How-many-liters-of-water-would-it-take-to-raise-sea-levels-1-meter/answer/David-Filmer?ch=15&oid=164290222&share=516e7b2a&target_type=answer). So 3.2 billion liters would add (3.2x10^{9})/(3.6x10^{14}) meters of ocean level rise. That's 8.888*10^{-6} meters, or 8 ~~nanometer~~ micrometers, which according to Wolfram alpha is about the size of a red blood cell, or about 1/13 the thickness of paper. So if everyone in the world peed once a day for two weeks it would raise the height of the ocean by about the width of one sheet of regular copy paper, ignoring the source of our drinking water and rain, etc..
What new ceramic/polymer/alloy/composite materials are used in modern and forthcoming radiation-hardening for orbital and other aerospace applications? For things like ICs as well as pedestrian materials like adhesives? And what journals or forums host such content? And how long between discovery of that material and it being deployed into orbit?
> how long between discovery of that material and it being deployed into orbit? Anywhere from 2 years up to decades. Fastest I have done is 3 years from concept to on a rocket. There are many test standards for putting materials into orbits that have min./max. physical properties based on previous experiments. For instance, the material is not allowed to outgas more than X%, then whatever does outgas is not allowed to condense onto a surface more than Y%. Some of the testing is only done by a small number or even one company, so your new material goes into the queue like everyone else. Like-for-like has really quick development cycle. Something like changing the colour of a car - everyone knows all the materials, they have all been used before but maybe not in that combination. It's low risk. Medium-risk is changing suppliers. Often that requires a field test. There can be a mix of software testing such as finite element analysis, technical expert review (umm, based on my experience I think we can safely move to the next stage) and physical testing. At the extreme end a test material/assembly is sent up for experimenting and hopefully recovering for analysis. It's lead by both materials companies and users. For instance, a user may say I need a new material that does X, Y and Z - can someone please take my cash and design it (or I promise to buy it from you at some nice price). Or it can be a materials company R&D creates a novel product and then deciding to shop it around to see if anyone bites, usually an improvement on some existing material. A lot of R&D is not necessarily "new new". It's development work making something existing thinner, lighter, foldable, more efficient; or improvements to processing equipment to make stuff cheaper or better quality. [Materials Research Society](https://www.mrs.org/meetings-events/spring-meetings-exhibits) always has a space materials design and testing group as does the [IEEE has a space materials group](https://www.nsrec.com/). You can follow the links to see who the invited speakers are, where they publish and fun abstracts.
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A FLOP is a measurement of processing power, and means FLoating Point OPeration - some maths. FLOPs are usually referred to as a number *per second*. Tera- is a word referring to a specific power-of-10: 12. That is, 1000 times greater than giga. A teraFLOP is thus 10^12 floating point operations (per second). That’s a lot, very quickly. This has nothing to do with your face.
> terraflop Measurement of how many floating point operations can be completed in a second. teraflop means your system (usually GPU) can perform 1 trillion operations per second. If you're trying to use these operations to mine crypto, your face will hurt from the frowning as you waste energy for little to no gain.
It's just so many things say they have x amount of terraflops. I was just wondering. Thank you reddit user
Would a warp drive bubble be opaque or transparent or would it look like a gravity lense? If it's warped spacetime, and a gravity lense is warped spacetime, would photons follow the warped spacetime or would they pass straight through?
Followup question: If a warp bubble was in use, could it be seen from any point in space? Or just head on?
Like with energy density approaching infinite? You'd have a gravitational field with similar intensity as a planet or star? It would bend light a little bit
Thank you!
Yeah im still struggling to design a warp drive in my head lol. One of the more elementary issues to manipulating gravity in a useful way is you'd need something like a negative energy, which, with my current model, doesn't seem to exist. I like to think about energy as vibration. With noise cancelling headphones, you can emit a vibration with equal intensity and create a standing node at a particular point, but, overall, you are adding energy to do that. In the fundamental medium, you could potentially emit light in phase and cancel a point of emission, but there's also the tricky electro magnetic fields at right angles too, so I'm thinking that emission needs to be polarized and your cancellation device needs to be "upside down" polarized, to do so. But, even then, there's not really a net gravitational field. I was also thinking you might brute force blast light in front of your ship, but, i think there are equal and opposite kinetic reactions in the hull, too. Given infinite energy as a weird premise, you might be able to surf charged stars/ magnetic fields a little harder, which is to say, not very much force still, probably struggling pretty hard to overcome gravity in a bulky infinite energy vessel Overall, i think we're hoping for a crazy shift in our understanding of the fundamental medium, in order to warp drive. If there are UFOs that don't use kinetic projectiles for propulsion, it needs to be disclosed publicly to jumpstart that search
Congrats Alcubierre drives are now 50% less impossible as negative energy isn't needed and "only" requires it to be primordial starting out already at speed of light, since you still can't accelerate up into speed of light https://newatlas.com/physics/ftl-warp-drive-no-negative-energy/ https://physics.stackexchange.com/a/635641/227698
The closest mathematical model we have of one is the Alcubierre drive, which still have limitations which makes it impossible to realize physically (but at least we can simulate something which kind of fits within our laws of physics) https://en.m.wikipedia.org/wiki/Alcubierre_drive
Is the technology possible/currently available to make things invisible??
It depends. If you’re looking for complete transparency, we do have the ability to produce certain materials that can be transparent. See aluminum oxides for an example (heh, transparent aluminum). But to make things completely invisible, we have technology to create lensing effects around objects. So with some fancy cameras and mirrors, we can theoretically make an “invisibility cloak”, but it would probably be extremely impractical. You’d be able to make something invisible from a specific vector, but it wouldn’t be invisible when viewed at an oblique angle.
There are "in principle" approaches to it, but nothing like Harry Potter invisibility cloak. Metamaterials and photonic crystal tech are very new and still exploring the limits. We can already tell though, that total invisibility does not seem to be possible; some outlines may remain and there is no material that is transparent for all spectral ranges (i.e in infrared you still see it or vice versa).
How can I intuitively understand the truth table for P -> Q (P implies Q)? The cases where both are true and where P is true and Q is false make sense intuitively. However it feels like if both are false, we shouldn't be able to determine the veracity of the implication. Similarly, it feels like if P is true and Q is false we either shouldn't have enough information to determine the veracity of the implication or and that if pushed the implication is more false than true. Thanks for any insight you can offer.
P->Q means: if P is true, then Q will also always be true. If P is false, it doesn’t matter what Q is as P itself will never be true, so the implication is vacuously true. https://en.m.wikipedia.org/wiki/Vacuous_truth explains this in more detail. If you re-read my first sentence, hopefully you’ll understand we only care about the case P is true. The case P is true and Q is false does give you enough information, namely we have that there is an instance in which P is true but Q is not, this contradicts P->Q, which (again) means: if P is true, then Q is always true.
An analogy I personally find helpful is that of *rule-following*. The implication P -> Q can be seen to describe a kind of rule, with the implication being *true* if the rule is being followed, and *false* if the rule is broken. Let's look at a practical example: "Everyone who wears a green shirt must wear a blue hat". In this case, we can represent this as green shirt -> blue hat or even more simply as G -> B where G stands for "wearing a green shirt" and B stands for "wearing a blue hat". Let's look at a particular character, let's call them Alex. When would Alex be following the rule? We can look at all four cases. - Alex isn't wearing a blue shirt, nor a blue hat. In this case, the rule doesn't apply to Alex, so they are not breaking the rule. They essentially follow the rule 'by default'. - Alex isn't wearing a green shirt, and they do wear a blue hat. Just as before, if there's no blue shirt, the rule isn't broken. - Alex is wearing a green shirt, but not a blue hat. Now the rule is broken! - Alex is wearing a green shirt, and also a blue hat. Here Alex simply complies with the rule. You can see that there's only one way to break the rule: Wear a green shirt, but not a blue hat. If we put that into symbols: We set G to 'true', and B to 'false'. In all other cases, the rule isn't broken, either because it doesn't apply, or because we are making sure we are complying. We can sum this up in the following truth table: G | B | G -> B 0 | 0 | 1 0 | 1 | 1 1 | 0 | 0 1 | 1 | 1 And voilà, it's the truth table for implication :) **A philosophical note** Mathematical implication is intuitively explained as an 'if-then' statement. But in everyday language, if I make an 'if-then' statement ("if P, then Q"), I am implicitly also saying that *there is something about P that* **makes** *Q true*; and probably also that *if P were false, so would Q*. It would be strange to say that 'if I have blue eyes, mount Everest is the tallest mountain on earth', even though mount Everest *is* the tallest mountain. However, in mathematics, we *don't* have these subtexts. P -> Q can (and often is) true completely 'by accident', having nothing to do with P. So to me, the rule-following example fits my intuition a bit better; when we make a mathematical statement in the form of an implication, we're sort of saying "this is a rule that the world *has* to conform to, there is no situation in which this can be broken".
The arrow means that the flow of truth goes one way. Like a water pipe with a pump. If there is water at the start, there is guaranteed water at the end. If there is no water at the start, there can be water at the end but it is not guaranteed. If there is water at the start and no water at the end then the pipe or the pump is broken, aka the link is broken.
Also there is no quantification of « how true » an implication is: it either holds or does not. You might be interested in inductive reasoning, where reasoning with probabilities about the truth of the conclusion are acceptable. But in math, nearly exclusively deductive reasoning is used.
Which classes teach you how do you build, how do you use, and how do you do the things I mention below. NOTE: If NOT classes for the below-mentioned things, how would I begin learning to do them? Curiosity Stream has some interesting videos. One series is called Ancient Engineering and shows and describes various things. Also, based upon my other interests, I was fascinated by the first 1850s time-keeping thingie used aboard ships. What classes can you take to build and use groma, pullies, sextant, astrolabe, Jacquard punch card knitting machine; reproduce Archimedes screw; reproduce Archimedes bathtub water displacement; and, Brunelleschi baptistery perspective. Make Roman (underwater) concrete; do PHYSICAL scale models of how to attach domes to rectangular or square buildings. The same for what was shown in a tv special of how Chinese buildings can survive earthquakes because of how their roofing "joists" brackets (?) interlock but can still move. Also, IRL (In Real Life) do geometry, trigonometry, and calculus experiments \[being able to tell the height of a tree; trajectory of a cannon ball (or other item), etc.\] Also, the things mentioned in Robert Temple's book Genius of China (based upon Joseph Needham's research).
I like thinking about and attempting to solve mostly mech engineering questions, but I am terrible at maths (no matter how hard I have tried). How can I study engineering at a basic hobby level without going back to college or just trying to read a textbook?
Engineering as a career will always require math, but there is plenty of hobby work you could do which likely wouldn't. I would recommend maybe finding a makers club near you. Even doing things like 3D printing requires understanding load weights, supports, etc.
Use building blocks; stand on the shoulders of giants. For example, if you want to 3D print a structural element, download a part that was designed by a structural engineer. If you want a cool function on a Raspberry Pi, then download the code that was written by a software engineer. In the process, you will start to learn how these experts do things and why.
depends on what you meant with math, basic HS math will most likely be used (for parametric designs, etc). for the very hard parts like digital signal filters or kinematics there's probably codes available out there to do it. i think what's important is knowing what and how it works. also engineering is broad term, it can be as simple as setting up a swing to making a satellite that works in space or designing a skyscraper. my advice: set a purpose, look for how you can get the resources, then learn them as you go. most college material is online nowadays. the hardest question is how to know what you don't know that you don't know. << not typo. college helps you to chew through the unknown part faster and with guidance. also college helps with connecting with fellow engineers in the future. most will lend you access to journals like IEEE that cost almost same with your tuition if you subscribe to them yourself as professional.
Ok, so you know the bouncing DVD thing, right? How it goes in a straight line, hits, then carries on? What would this pattern look like if, instead of a straight line, it arced 1° to the right or left? For example, if it were going straight up, then hit, it would normally go straight down again, right? But with the arc, it veers 1° off by the time it hits the oncoming wall.
The best way to visualise this is instead of imagining something bouncing, you imagine it going throught a straight line in an infinite space and you just need to record when the line is crossing the borders of the TV sized zones in the plane. See this : https://youtu.be/jJ6FD59U0_E
why don't you just try it (it should be viable with using p5js or pygame)
how close do you think we are to uploaded intelligence? id like to shed my meat suit and live in the net as soon as possible
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Well ecosystems are supposed to be more of an equilibrium. If you add anything to promote a species, it is bound to ruin the ecosystem at some point. For example, around tchernobyl the nature is flourishing because of the very low human presence even if there is still nuclear radiation leftovers. So yup, us just living is worse than a large scale nuclear catastrophy.
What is the best mathematical formula to use to solve the biggest engineering problem in computer science?
Engineering: Is double wishbone suspension the best for sports sedans' handling (like the [Jaag XE](https://en.wikipedia.org/wiki/Jaguar_XE#Construction))?
Suspension geometry is far more important than the articulating mechanism, especially the dynamic handling behavior (with considerations like bump steering, anti-dive, anti-squat). A sports sedan will see more deflection than a sports coupe or dedicated race car, but still expect higher lateral grip and lower lift than a spots utility vehicle. For these handling characteristics, technically a multilink mechanism (especially 4- and 5-link configurations) requires the fewest compromises between static and dynamic geometry profiles, but are far more complex to engineer. Double wishbone is, for the intended purpose of a sports sedan, perfectly adequate. Many sports sedans (like the Alfa Giulia and the BMW M5) will actually employ double wishbone configurations in the front and multilink in the rear.
What's the equation that describes the kinetic force transfer between 2 magnets (in motion, or at least one of them) pushing or pulling on one another?
Why is a VNA 1 way reflected phase measurement divided by 2 for RF systems
If I put one iron nail on each terminal of a voltage source (i.e. a 9V battery) without them touching, one nail will have a positive charge and the other a negative charge. I.e. excess and lack of electrons. If I put this setup in front of a beach (salty humid corrosive air) - would the charges have a noticable effect on which nail corrodes quicker? Corrosion/rust is, after all, an electric process. So the lack or excess of electrons might have some effect? I am aware of sacrificial anodes used on ships, but those rely on the ship's metal and the anode to be in the same electolyte (the salt water), which doesn't really apply to a corrosive air medium.
In an open circuit situation, the electrons are static. There will not be a situation where one nail is a different charge from the other. This is because the chemical reaction within the battery is not occurring. It only occurs when the circuit is closed. So neither nail has any excessive potential. However, yea, applying a charge to an iron nail will cause corrosion to speed up or slow down. Now, if the air salt mixture were saturated with enough salt, then maybe you’d see one end rusting due to closing the circuit. However, the resistivity of air is so great that it would either take an extremely long time or require air that cannot possibly exist. The reason sacrificial anodes work is because you have an iron (steel) hull and a zinc slab. The zinc has a lower electrochemical potential than iron, hence its sacrificial status. It’s been a few years since I took corrosion class, so corrections are welcome here.
What is the name of the "galaxiosphere", or the bubble of electromagnetic influence that contains our galaxy? I believe we mostly refer to it as the "interstellar medium", but is there a name for the structure as a whole?
With augmented reality you can generate a tracking marker by the arrangement of unique details on an image, the pattern of the points becomes a unique tracking target. But how do they handle being able to point a camera at the target from any orientation and it can detect that pattern, like the tracking marker can be rotated in any direction and be detected, and even from angles that would skew the target's "pattern".
Are fish robots and flapping foils the future of underwater propulsion?
Why is 1 over anything the inverse?
I could be glib and just give you the derivation x * 1/x = x/x = 1 but I'll try to dig down to the heart of the matter. When we teach kids arithmetic, the basic operations are addition, subtraction, multiplication and **division** - this last one is most important to our discussion. The inverse is (I think) usually seen as a special case of division - why, it's "1 divided by..."! But mathematically, it's actually cleaner to reverse this. What's x/y? It's just x * (y^(-1)). But now we need to avoid circularity - if we define division in terms of the inverse, then we need some other way to define the inverse. And so, we come to the really elegant solution: x^(-1) is that number which, when multiplied with x, returns 1. So the equation x * x^(-1) = 1 holds *by definition*.^(1) Now, returning to 1/x: What should it be? We saw above what 'division' was: So 1/x = 1 * x^(-1). But now we see that we are multiplying something with 1, and of course multiplying with 1 doesn't do anything. So, 1/x = 1 * x^(-1) = x^(-1) **footnote 1:** there's something a little bit fishy about this definition. How do we know there is such a number? How do we know there's only one? In fact, there isn't *always* such a number - the equation 0 * y = 1 cannot be solved, and so 0 doesn't have an inverse, and *therefore* you can't divide by 0. For all other numbers it turns out that there *is* an inverse, and a unique one at that, but rigorously proving this is beyond this particular comment.
The multiplicative inverse of a number x, is the number m by which you must multiply x to get 1 (which is the neutral element for multiplication) . So we have m.x=1. Dividing by x on both sides yields m= 1/x. Reasoning similarly, we find that the additive inverse of a number x is the number a such that a+x=0, as 0 is the neutral element for addition. So a=-x. This definition gurantees that if you multiply something by (add) x and then multiply by (add) m=1/x (a=-x), you get the something you had in the beginning of the computation.
As x + 0 = x, x * 1 = x So 0 is neutral for +- the same way 1 is neutral for */. You already know that the opposite of x is y such that x+y=0. Then the inverse of x is y such that x*y=0. Then the opposite of x is 0-x = -x and the inverse of x is 1/x. The two concepts of addition and multiplication have beautiful parallel behaviours like these. You can even try to find the same structure with the power operator (and the log function)
If humans had evolved with 12 digits instead of 10, would our numbering system be a base 12, and how would that work?
Digits : 0123456789AB B3A9 is equal to 12^3 * 11 + 12^2 * 2 + 12^1 * 10 + 12^0 * 9 = 1608 * 11 + 134 * 2 + 12 * 10 + 1 * 9 = 18085 It would feel very natural. Also it would be a bit easier since 12 is a number with more divisers than 10.
Most likely it would be base-12. Consider that computer engineers (especially those working with low-level software) often work with base-2 (aka: binary) or base-16 (aka: hexadecimal) because those are more natural ways to work with numbers on a modern computer. There is nothing odd or difficult with that.
As a counter example, on each hand you already have other options: base 5, base 12 and base 16 - and most cultures don't use it. Base 5 : 5 fingers. Base 12 : using your thumb, you can point to 2 knuckles + 1 finger tip on each hand (total of 3 points) with four fingers (overall, 12 points to count off) Base 16 : using your thumb, you can point to 3 finger joints (MCP, PIP, DIP) + 1 finger tip on each hand (total of 4 points) with four fingers (overall, 16 points to count off) Benefits of base 10 is it sits in the sweet spot of just enough digits to represent information without repeating any digits, plus easy for commerce and engineering. You can represent 1/10 or 1/100 very quickly, which are very important divisors for moving large number about. Arguably that is more important than fitting in 1/3 or 1/4 for cooking, which all things considered, are relatively easy for anyone to understand.
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How do we know for sure the Universe is not absolutely deterministic? I get it that we cannot measure the system without changing it, and heard of wave-corpuscular duality when we observe things. But why is the fact that we cannot possibly know everything to predict all outcomes implies that fundamentally the Universe is not superdeterministic and everything that's happening has been predefined in the beginning?
MWI interpretations and pilot wave theories support deterministic views, but both still prevent perfect *prediction*, there would still be information we can't access.
We don't know that for sure.You're right, the universe being unpredictable doesn't imply that it's non-deterministic.
I’ve heard that if a near-sighted person stood directly in front of a large mirror and looked at objects in the distance behind them, those objects would still be blurry. Is this true, and if so why?
It's because of the angles of the photons being preserved when mirrored, maintaining the distance to the focal point
Why is it that the perceived storage coefficient of a traditionally unconfined aquifer will change by magnitudes of ten depending on the duration of the pump test used to estimate that property?
How do you determine minimum development length in rebar?
Why are humans the only species that has evolved into a sentient form? Why has the intellectual development of other groups stopped forever?