Let's say I were to design a low level language, just for example. What is the actual smallest datatype for a variable I can have? Let's say for example the primitive boolean in java only needs 1 bit, what is the actual memory footprint (memory size) that it uses?
My prefix is food, my suffix is rude
My prefix is food.
My suffix is rude.
My infix comes in rounds.
I keep you off the ground.
What am I?
This is the first "Riley riddle", created by Riley. Riddles of this sort has become a trend in the Puzzling SE. Let us do a code-golf challenge equivalent o...
@mousetail I only just learned how a radian is defined yesterday! I always just thought radians and degrees were two equally arbitrarily designed units of measure that we just had to tediously convert in math class.
So that's why there are 2 pi radians in a circle-- precisely because there the circumference is 2 pi r. So if a radian is the angle subtended by one r, then the full circle is 2 pi of them.
Also made me realize that the circumference is the derivative of the area, which I'm sure can't be a coincidence, but I don't really remember anything about that. It would've been so much clearer if we expressed area as 1/2 tau r^2!
That looks properly integral-y.
@mousetail Wait, that's really funny. I never thought about that.
When you move up a straight line one unit your Y position obviously moves up one unit. When you move up a curved line, as the curved line approaches straight your direction approaches straight up. The sine of a angle is the distance you move along Y when moving around the circle. The right edge of a circle approaches a straight vertical line as you zoom in on it. Thus, we can conclude that the derivative of sin(x)=1 if x=0
and that sin(x) approximately equals x for small x
Huh, I'm pretty sure I avoided them at all costs/just thought of them as trivial pi/180° conversion, without actually understanding the inherent meaning.
@mousetail Whelp. So are degrees just the Fahrenheit of angular measures? Why do we still use them in mathematical lingo like "90 degree angle" and "sum of the angles in a triangle is 180 degrees" and "alternate interior angles...".
I tutor some middle school math students, and degrees are most definitely introduced and used a lot in their homework, long before radians make an appearance.
@AviFS Degrees are convenient, since for humans it's much easier to tell what is 45 degrees vs what is 0.24522 radians. I think they have their place, unlike Farenheit
radians are mostly nice in more advanced trigonometry and calculus, when you are actually using the identities that require them
I'm not fresh enough on series and expansions to challenge the calc claim, and I'll believe it. But why did we do the unit circle with radians, instead of degrees?
How can anything only work in radians? Both are units of angular measure.
Sine and cosine etc. are all defined in terms of the radius between the circumference and the radius. Fundamentally that's how they work. There is no unit involved
But I'm still really interested in what you're saying, because it sounds like you're saying that it's the most "mathematically pure" unit we could have (in that it equals 1).
@mousetail Funny you should say that... cuz moles are also units.
We think of things like speed and mass and energy as different things, but relativity and quantum theory tells us they are all really the same, and can be converted into eachother. They are all fundamentally different types of the same thing, and there is a smallest possible quantity of that. Which is the plank units. There is just one of them really
@AviFS I disagree but that's just a question of different definitions for the word "unit" and impossible to argue about
And further, if we defined different base units, eg CGS instead of MKS, we'd have different "non-units" by your definition.
@mousetail In common understanding of "units" and dimension analysis, there are multiple dimensions of base units-- seven according to the current SI. You certainly have at least MKS/CGS.
@AviFS No, those wouldn't work as base units since they are subdividable. I beleive there is one fundamental unit defined by physics. Not just by opinion
It might not be plank units, we might find a even more fundamental unit system. The concern here is not what that unit system is just that there exists one, thus all "units" are just multiples of this single universal unit
That sounds really interesting, but it's not what is conventionally understood to be meant by units. If you say "base units," a linear basis of eg 7 SI units, is understood, not one super-unit.
I still find it frustrating that somehow base units aren't units to you, but I'm curious about the bit where "sine and cosine ... [are] defined in terms of the ratio (?) between the circumference and the radius."
I’m starting to think of radians as the ratio between circumference and radian— a useful concept in some mathematics. And of degrees as the “percent” measure. That is, a highly divisible convenience number of which we can take fractions. So that eg 1/4 circle becomes 90°, and 1/6 circle becomes 60°.
Esp. since we (humans) tend to be better at thinking about, and comparing, whole numbers than fractions.
So that, eg an 80% off sale is better than a 75% off sale, and a 20° angle is smaller than a 30° angle. (The comparison is easier to understand for most than 4/5 vs 3/4 or 1/12 vs 1/18.)
@mousetail Well that was all new to me, so thanks!
Disclaimer: Of course, it doesn't really "work" to backwards-justify contemporary mathematical conventions that have evolved over centuries, as though they were designed with intent. Just as that's foolish to do for any other natural process (or complex system) that has evolved over the ages.
But it's certainly a useful exercise to better understand their respective benefits & drawbacks, and why those two systems might have, so far, stood until the present day. Or, at minimum, what their use cases would be for someone working today.
Random late-night thought: What's the 1d analogue of angular measure?
(Is it the same as distance?)
Oh wait, I guess it's just a constant of 1 at all points.
Reasoning: 'Cuz if in 3-space, steradians are d^2/d^2 = 1; in 2-space, radians are d^1/d^1 = 1; then in 1-space, the analogue must be d^0/d^0=1.
A sphere is 3D and any direction from its centre to a point on it needs 2 parameters. A circle is 2D and any direction from its centre to a point on it needs 1 parameter. A line is 1D and any direction from its centre to a point on it needs 0 parameters.
I'm not sure if that actually makes sense, but I'm sure if I change that to "the trivial angle," and add a few more 'trivial's in there, it'd sound legit.
@Adám Woah, that's really cool. I love that visual, and that intuition. Gotta admit, it's really taking me a sec here to picture 3-space from 2 parameters. It's like a spherical Etch-a-Sketch!
I'm pretty sure they have like those balls, right, that have two axes of rotation?-- A globe. Maybe I'm thinking of a globe, lolol
@mousetail Rotationally, you have just have n-1 axes of rotation in n-space, right?
@AviFS Right, you need longitude and latitude, whereas on a flat map (picture squeezing the globe down to a plane), you just need a compass heading. On a line (picture squeezing the plane down to a line), you just need a ←→ directional indicator to pinpoint one of the two "surface" points.
Yes, but a point is not a rotation. In 3d it's the same. Even i you are pointing at the same place you could rotate your hand around your wrist and create a different angle
Aside: I couldn't quickly find the generalized version. Evidently, I'm told perimeter/circumference are for 2d and surface area is 3d. What about n-d?!
as I said earlier, they're a system for loading arbitrary Rabbit code at runtime
basically, you use a schema block to create a schema, and then load modules that comply with it
suppose I had this schema:
schema TestSchema:
function foo(int n) -> int
I could then use that schema to load a schema module containing a function foo with that signature
the same system also works for structs, constants, and traits
schema modules have a few restrictions:
first, only the functions specified by the schema will be visible to anything loading the module
second, the module can't import anything that isn't available to the calling module
that's it I think
the Rabbit Script Host is a tool that can load and run Rabbit schema modules, which in this case can be arbitrary files (although these scripts can only access the standard library)
the most scary thing is the vast amount of power that is used to train and use these models
that alone might destroy the planet because the AI gets round to it
"OpenAI will release GPT-4 next week and the generative AI program will allow users to turn text into video, according to Microsoft Germany Chief Technical Officer Andreas Braun."
"It turns out that one type of gluon chain behaves in the four-dimensional spacetime as the graviton, the fundamental quantum particle of gravity. In this description, gravity in four dimensions is an emergent phenomenon arising from particle interactions in a gravityless, three-dimensional world."
Hm, two appropriately spaced sticks or tight strings are enough guidance for a ball to roll down. I assume that two appropriately spaced planes are enough to control a 4D sphere's roll…
"In the Flat Earth model, 'gravity', rather than being a force, is the upward acceleration of the Earth. The Earth always accelerates upward at 1g, which is equivalent to the gravitational acceleration in the Round Earth model. Like the force of gravity, the Earth's acceleration causes several commonly observed phenomena in our daily lives."
I suppose an appropriate flat Earth model is theoretically impossible to refute, although you do get an interesting singularity (plurality?) at the south pole.
Every integer can be expressed in powers of 2. You know this as the binary system
Assume you are given a set of k numbers >0 <2^n.
You want to decide for this set whether every integer power of 2 up to 2^(n-1) occurs at least m times
One example:
n = 7 (2^n = 128, )
k = 5
set =
{100,
91,
88,
63,...
"The figure of 24,900 miles is the diameter of the known world; the area which the light from the sun affects. Along the edge of our local area exists a massive 150 foot Ice Wall. The 150 foot Ice Wall is on the coast of Antarctica. It is widely known and widely studied. The Ice Wall is a massive wall of ice that surrounds Antarctica. The shelf of ice is several hundred meters thick. This nearly vertical ice front to the open sea is more than 50 meters high above the water's surface.
The Ice Wall was discovered by Sir James Clark Ross, a polar explorer who was among the first to venture to…
I want to drop of 10 flat earthers regularly spaces around the perimeter of antarctica, with snowmobiles and other proper equipment, and thell them all to go south
Let's say I were to design a low level language, just for example. What is the actual smallest datatype for a variable I can have? Let's say for example the primitive boolean in java only needs 1 bit, what is the actual memory footprint (memory size) that it uses?
My prefix is food, my suffix is rude
My prefix is food.
My suffix is rude.
My infix comes in rounds.
I keep you off the ground.
What am I?
This is the first "Riley riddle", created by Riley. Riddles of this sort has become a trend in the Puzzling SE. Let us do a code-golf challenge equivalent o...
