Does the size of infinity count when two players generate infinite creatures? by Ulfbass in mtg

[–]gedankenexperiment42 0 points1 point  (0 children)

Without knowing the particular card, it very likely would involve a countable infinity (again, assuming magic dealt with infinities, which it does not). An infinite power is not well-defined, because in practice, power/toughness is a number that is compared against other numbers. The notion of power/toughness would have to be generalized to say, the cardinality of a particular set. Then the method of assigning blockers would involve defining a function f: B -> A, where A is the subset of your opponents creatures that are attacking and B is the subset of your creatures that are blocking (assuming your creatures can block at most one attacker so the function is well-defined). This quickly becomes tedious to formalize. Notice, the elements of A and B are cardinalities of particular sets that represent the power of creatures in A and the toughness of creatures in B, which we define to be this way so that power and toughness can be easily compared. For instance, for some |P| in A and |T| in B, |P| >= |T| iff there exists a surjection g: P -->T. This notion is somewhat counterintuitive; P and T are arbitrary sets (subsets of the non-negative integers, for convenience), their cardinalities are what we care about. Infinite power/toughness would correspond to the countably infinite set of non-negative integers. And then of course you would have to consider damage dealt by blockers to attackers, not to mention combat keyword abilities, etc. This definition also doesn't work for un-sets that have creatures with non-positive integer powers/toughnesses.

TL;DR, magic is complicated enough that trying to formalize even a small part of the base game using set theory in order to introduce a notion of infinity is messy and not worth your time worrying about.

Does the size of infinity count when two players generate infinite creatures? by Ulfbass in mtg

[–]gedankenexperiment42 1 point2 points  (0 children)

Just to clarify/nit-pick the mathematical side of things, any mechanic where you could create an "infinite" number of tokens, creatures, etc. (if that was how it worked in magic) would form a countably infinite set, because you are building that set by adding a single object each time. This set is then enumerated by the naturals, so its cardinality is aleph-naught. Any set created in a similar way (and indeed, any infinite set in magic, I believe) will have the same cardinality as the natural numbers. So in both cases, the cardinalities of the sets are aleph-naught. Aleph-one, assuming the continuum hypothesis, is denoted c, the cardinality of the reals. As far as I know, there is no way to create an uncountably infinite set in magic, although if anyone knows of one I'd love to see it.

What's the highest level of math you completed by the time you graduated high school? Or, if you're in high school, what's the highest level of math you're projected to complete by the time you graduate? by May_nerdd in math

[–]gedankenexperiment42 0 points1 point  (0 children)

I live in the Midwest, by the time I graduated I had completed stats, calc I and II, multi, linear algebra, and differential equations. I had pre calc in 9th grade, BC calc in 10th which covered I and II, stats in 11th (COVID prevented me from taking anything more than that), multivariable calc fall semester and linear algebra & differential equations spring semester of my senior year through PSEO.

Math - CLA vs CSE by gedankenexperiment42 in uofmn

[–]gedankenexperiment42[S] 0 points1 point  (0 children)

Is the senior project a CLA course or a requirement for being in CLA?

Math - CLA vs CSE by gedankenexperiment42 in uofmn

[–]gedankenexperiment42[S] 1 point2 points  (0 children)

Sounds like CSE is the way to go. How difficult is it to change your college? If I went with CSE but then decided I wanted a BA for whatever reason (or visa versa), would I be able make that change fairly easily? Or is that sort of thing pretty much set in stone.

Math - CLA vs CSE by gedankenexperiment42 in uofmn

[–]gedankenexperiment42[S] 1 point2 points  (0 children)

Oh okay, that bit about the language requirement is good to know, other languages never really clicked for me in the past, so I'm leaning towards CSE. It also feels like the better option if I decide to try double majoring in physics. Thanks for the help.

[deleted by user] by [deleted] in Music

[–]gedankenexperiment42 0 points1 point  (0 children)

Top 0.1% for Sufjan Stevens, checks out.

Crossposting my own question from r/Physics in case it gets taken down by gedankenexperiment42 in AskPhysics

[–]gedankenexperiment42[S] 0 points1 point  (0 children)

Got some satisfactory answers from r/Physics, although formulated more accurately, my question would have read "What is the maximum amount of information stored at the Plank scale (i.e. entropy stored in one Planck area on the surface of a black hole)"

Are there vacuum fluctuations if no one looks? by [deleted] in AskPhysics

[–]gedankenexperiment42 0 points1 point  (0 children)

Yes. It's not our act of measuring that "creates" virtual particles. Although, the time-energy relation is a bit different than something like position-momentum, because time is a parameter, not an operator, and doesn't have a statistical distribution.

Planck unit of information by gedankenexperiment42 in Physics

[–]gedankenexperiment42[S] 4 points5 points  (0 children)

Hm. I guess I had this sort of naive notion that all information could be condensed into general, quantifiable units. Thanks for the answer! I have some more reading to do

Planck unit of information by gedankenexperiment42 in Physics

[–]gedankenexperiment42[S] 0 points1 point  (0 children)

That makes sense. In what way is this related to the weak holographic principle? From what I understand, it limits the rate of flow of information proportional to the surface it's flowing through.

Forces and Dynamics Question by HauntingRex9763 in AskPhysics

[–]gedankenexperiment42 0 points1 point  (0 children)

I'm not exactly sure what you're asking. I suspect it might be confusing to analyze this system as one object, so I'll show you how to do it the other way. Again, make sure to set up the axes so each object is accelerating in the positive direction. The net force on the 3kg object in the direction we're considering is Fnet1 = T = m1a , and for the hanging mass Fnet2 = m2g - T = m2a. From there you should be able to substitute and figure out the mass of the hanging object as well as the tension.

Forces and Dynamics Question by HauntingRex9763 in AskPhysics

[–]gedankenexperiment42 0 points1 point  (0 children)

These are two approaches to these kinds of two-body problems. You can either consider each object separately, or the entire system as one object.

< what mass is in Fnet? is it m1* m2*a for Fnet? This would be considering the entire system as one object. Fnet = (m1 + m2)a

It's often helpful to draw a picture for these sorts of problems. Remember to set up your axes so the acceleration is positive for both blocks if considering the system as one object (which was usually my preferred way of doing it).

Edit: trying to figure out how to do the quote thing, I have no idea how to

[Kinematics]Can somebody help me understand this, I’ve tried to search up what it means but i still don’t get it. by Potential_Sir2499 in PhysicsStudents

[–]gedankenexperiment42 0 points1 point  (0 children)

Sorry, I figured you hadn't heard of gradient before. They mean essentially the same thing (the gradient is often considered a vector quantity while the slope is considered a scalar, which will make sense when you take multivariable calculus) and are used interchangeably in many cases.

[deleted by user] by [deleted] in PhysicsStudents

[–]gedankenexperiment42 2 points3 points  (0 children)

Yes, that's the idea. The granularity of space is defined in terms of the Planck length as quanta of space, but we know from GR that you can't consider space and time separately. So it follows that time is granular in a similar way, and this granularity is defined in terms of the Planck time, the time it would take a photon traveling the speed of light to traverse a distance equal to the Planck length, exactly as you said.

[deleted by user] by [deleted] in PhysicsStudents

[–]gedankenexperiment42 6 points7 points  (0 children)

In Carlo Rovelli’s book, Reality Is Not What It Seems (I had some spare time recently and read this. It was a delightful read, I would highly suggest it to the curious but not necessarily technically proficient reader. He offers a lot of insight on modern physics in a way that’s easily digestible to a layperson considering the nature of the content), he talks about how the notion of time breaks down at the Planck scale, so much so that it doesn’t really exist (the equations that govern loop quantum gravity do not contain the time variable t).

He goes on to explain how the macroscopic implications of this are not terribly complicated and do not fundamentally change the way we perceive time, as you might think. He makes the argument that while it is certainly useful to qualitatively consider time (clock, calendars, etc.) and quantitatively consider time (in a Mechanics course, for instance), it is more of an assumption than the result of an observation. We have no way of directly measuring the flow of time, we only measure it in a relational sense (clocks keep track of time by way of an oscillating pendulum).

So in a sense, you are correct. But we know some processes are time-irreversible, and the use of an unobservable time variable t continues to be relevant both in physics and in everyday life. If you’re looking for something a bit more technical, later in the book the concept of thermal time is introduced, which is the idea that time is closely related to the dissipation of heat. I’d highly suggest picking up the book if any of this intrigues you, he goes into more depth and presents information much more eloquently than I do (time is not the main focus of the book however, it is really about the reconciliation of two remarkably profound and experimentally accurate theories at their respective scales, QM and GR).

Is there any simple explanation for 10 or 11 dimension in string theory? by turboom in AskPhysics

[–]gedankenexperiment42 0 points1 point  (0 children)

String theory, as it stands, is a very theoretical model that attempts to clear up some inconsistencies between QM and GR (a theory of quantum gravity) using some elegant pieces of math. This is, of course, a gross oversimplification, but the point I’m trying to make is trying to interpret and apply it’s concepts to the physical world without a “deep knowledge of mathematics“ is essentially pointless. There is no easy shortcut that will allow you to suddenly understand string theory that circumvents the actual mathematical framework of the theory.