
Posts
10567 
Joined

Last visited

Days Won
2
Content Type
Profiles
Forums
Calendar
Posts posted by ydoaPs


It depends on the kind of classical physics and the complexity. If you want to understand basic toy kinematics and dynamics at the high school level, you could get away with going up to the first order differential equations.
You'll be doing stuff like taking the derivative of a displacement equation to get a velocity equation.
If you want to understand more complex problems with more modern paradigms, then you'll need multivariable calculus.
You'll be doing things like solving the EulerLagrange equations and integrating Lagrangians to find the least action.
With waves, electromagnetism, and "Modern Physics", that table of contents specifically tells me you'll likely need the multivariable parts of the calculus text as well.
But it might be simplified for like an introductory course. You'll have to look at the physics book. If it has [math]\partial[/math] or an upsidedown triangle,you know you'll need the multivariable parts.
TL;DR:
That physics book's topics suggest you'll need the entirety of the calculus book
Edit:
!Moderator Note
Topic moved from Lounge to Classical Physics
1 
On 9/29/2021 at 6:14 PM, swansont said:
You have an infinite number of points in any finite, onedimensional line segment. So this is incorrect.
It should be pointed out that this is an uncountabe infinity. It is waaaaaaaaaaaaaaay bigger than the infinite cardinality of the natural numbers
Infinities come in different sizes
0 
3 minutes ago, studiot said:
That's a somewhat spectacular return ydoaPs +1
Well thank you. It took some doing to fix my bbtex mistakes on the phone with autorendering
1 
On 5/9/2021 at 11:04 PM, neonwarrior said:
Hello everyone,
Why 2 .(3) = 6
Why is it positive?
Why we accept that (minus sign) times (minus sign) is positive ? What is its origin?
Thanks in advance
It's good that you asked in Linear Algebra And Group Theory, because we're going to need some algebra you likely have never seen (unless you went to college) to answer it.
Multiplication isn't one thing. What multiplication is depends on what you're multiplying. Algebra is how we define this.
In Algebra, there are a handful of different kinds of structures. Here, we're interested in Groups, Rings, and Fields. Rings and Fields are kind of made of Groups, so we'll start there.
Say we have a set (the lay concept of set will work fine for our purposes), and we'll call it S.
On this set, we need to define a rule called a "binary relation" that takes any two things in the set and gives some output. We want this set to be closed under this relation, so the relation can only give us things that are already in the set. For this combination of set and relation (for now, we'll use ? to denote the relation) to be a Group, they need to have the following properties:
1) Associativity: for any three things a, b, and c in the set, the relation doesn't care about where the parentheses go. a?(b?c)=(a?b)?c
2) Identity: there is a special thing in the set (traditionally denoted by e when talking abstractly) where, for any other thing a in the set, a?e=e?a=a
3) Invertability: for any thing a in the set, there is another thing in the set a^{*} where a?a^{*}=e=a^{*}
That's enough to be a Group. But we want a special kind of Group, called an Abelian Group. That's just a regular Group that has an extra property:
4) Commutativity: for any two things a and b in the set, a?b=b?a
Tradition dictates that for Abelian Groups, + is used in place of ? and 0 is used in place of e and a in place of a^{*}. If a Group is not Abelian, we often use × (or nothing at all) in place of ? and 1 in place of e and 1/a in place of a^{*}.
If S is the set, we write (S, +) or (S, ×) for the group, but we often just write S if it is clear from the context that we're talking about a group.
This is enough to let us build a Ring.
With Rings, we still have a set S, but we have two relations. (S, +) is an Abelian Group, but × is a bit more lax. × only has to satisfy two properties:
1) Identity, and
2) Distributivity: for any three things a, b, and c in S, a×(b+c)=(a×b)+(a×c)
Like how (S, ?) is a Group, (S, +, ×) is a Ring.
If a Ring is commutative and has inverses for each relation, then the Ring is called a Field.
There are four particularly important facts mentioned above that are important to why a negative times a negative is a positive:
1) a+(a)=0,
2) a+0=a,
3) a×0=0 (not mentioned above, but still important), and
4) a×(b+c)=(a×b)+(a×c)
Proof a×b = a×b:
Let a and b be positive numbers in our field (S, +, ×).
0=b+(b)=a(b+(b))
a×b = (a×b) + a(b+(b)) = a×b + a×b + a×b = a×b + a×b + a×b = b×a + b×a +a×b = b(a+(a)) + a×b = a×b
TL;DR:
It's because Fields are commutative, have identities, and are distributive
3 
On 11/19/2019 at 7:08 AM, justqwer said:
There is a concept of "irreducible complexity". Meaning that some biological systems could not be produced by incremental steps. Evolutionists really can't explain an evolution for almost any of internal organs.
Go look for yourself. How 2 chamber heart evolves into 3 chamber heart, how lungs evolved, how bactrium evolved a flagellum. This is very simple stuff, and yet evolutionists can't provide an evolutionery path to any of that. And yet they manage to live in small illusion that they got it all figured out.
Actually evolutionists have nothing. They can't explain anything really.
The Muller Two Step was a prediction of evolution before Behe was even born, let alone before he decided it was somehow a problem for evolution.
0 
5 hours ago, studiot said:
No I don't think our terminology is different but my point was that 'equivalence' hides more levels of meaning.
Consider the set of positive integers, n.
This may be partitioned into two subsets, which form equivalence classes.
n is odd
n is even
No two members of either subset are numerically equal.
No two members of either subset are identical.
Yet any even (or odd) number is equivalent to any other even or odd number.
You can also demonstrate this with functions and mappings if you please.
So in that case there are three levels of meaning to the word "equivalence"
And before I was only describing two.
And that's not even counting all of the other forms of sameness like adjoint situations. There's so many different forms of "eh, that's sort of the same as this other thing in certain ways".
1 
What LaTeX packages can we use in blogs? If the one we need (say, for commutative diagrams) isn't installed, is there a way to get it installed?
0 
17 minutes ago, studiot said:
Thank you ydoaPs
But we should be careful using the word 'equivalence' as it does not mean 'equal', and of course certainly not identity.
Mathematical Equivalence is a very specialised way of using partitions of sets, as I'm sure you know.
If I'm understanding you correctly, I think you're using different terminology. It might be a geographic thing.
As far as I learned, an Equivalence Relation has the properties you detailed in your post, and, by the process I discussed, partitions a set into Equivalence Classes resulting in the quotient set (or monoid or group or category etc). I'm not sure what there is to gain by using "equivalence" only in terms of equivalence classes rather than for either equivalence relations and equivalence classes. If we had to pick, I'd probably make the relation "Equivalence", but that's probably just the categorial bias I have.0 
On 3/24/2020 at 9:43 PM, MigL said:
Books like the Bible, which are meant for moral guidance ( not historical account ) usually reflect the morals of the times they were written.
The Old Testament part is much more violent than the New Testament, wherein the only time Jesus gets mad is when he upsets the moneylender's tables in the temple, and, he asks his Father to forgive his crucifiers.
This reflects the change in moral values that had occurred.I would expect a 'Modern Testament' ( if one were written ) to have much different messages/guidance, especially in relation to the treatment of women, homosexuality, certain 'sins', treatment of the poor, etc.
Jesus also got mad when a fig tree didn't produce figs when it was not fig season.
0 
On 3/25/2020 at 6:09 AM, studiot said:
To amplify Mordred's statement ( +1 )
Mathematically and logically a relation is a particular conncetion between pairs of (mathematical) objects.
Equality as represented by the equals sign = is characterised by three properties.
Where A B and C are three mathematical objects
1) Reflexivity
A = A
2) Symmmetry
If A = B then B = A
3) Transitivity
If A = B and B = C then A = C
These may seem obvious but they are fundamnetal and very important.
Another stronger reelation is identity. This is different from equality and should be carefully distinguished.
All identities are also equalities, but not all equalities are identities.An easy way to see this is to compare the following
x2−1≡(x+1)(x−1)
This is an identity. Note the different symbol.It is true for all x or each and every possible value of x.
But
x2−1=0
is only an equality. It is only true for certain values of x and not true for many more.To pick up on the remark about chemical equations.
You noted that chemical reactions represent a process as well as an equality (mass balance charge balance etc)
These are more properly shown with various arrows for this reason
→
etcThat's a great post.
Yeah, equivalence relations are much looser than identity. Any bivalent relation will give you an equivalence relation. You can actually even define an equivalence relation out of any function.
Take a function f, and you can define the equivalence relation ~ such that a~b iff f(a)~f(b). This is part of a process of decomposing a function. If the domain (what the function is taking as an argument) is A, and the the codomain (what the function points to) is B, then you can decompose a function via ~ in the following way.
Make a function f^{* }that takes A and maps each element to the set of other elements of A that it is equivalent to under ~. So, an a in A maps under f^{*} to all of the other a's that map to the same thing under f. For example, take the rule for f to be f(x) = x^{2}. f^{*}, then, will map 1 to {1, 1}, 2 to {2, 2}, 3 to {3, 3} etc, because 1 and 1 both go to the same place under f. We typically write the codomain of f^{*} as A/~.
You can then go from A/~ to what is called the "image" of f. And that's just the collection of things in B that actually get pointed to from things in A by f. Often you'll see this just imf.
So we have A > A/~ > imf. But there's something neat here. Since we have in essence collapsed A into things that don't map to the same thing in imf and all of the things in imf get mapped to, this function is reversible. So we have A > A/~ <> imf. Since it goes back and forth like that (assuming the function is structure preserving), A/~ and imf are isomorphic. That's a big word for "for all current intents and purposes, they're the same structurally". A nice fact about isomorphisms is that they are all equivalence relations.
We can go further into canonical decomposition and go from imf to B, but, for our purposes, we've gotten what we need for this discussion.
Any function gives us two different equivalence relations. So in our example of f(x) = x^{2 }from the Real numbers to the Real numbers, we get the Real numbers being equivalent to sets of Real numbers that have the same absolute value. Those clearly aren't the same thing, in terms of identity. We also get this set of sets of numbers with the same absolute value being equivalent to the set of the squares of the absolute values of the previously mentioned set. Clearly sets containing things like {2, 2} and sets containing things like 4 aren't identical, but they are equivalent.
Any nice back and forth will satisfy the axioms for the equivalence relation. Identity, on the other hand, has extra cool stuff like substitution. Identity is much stronger than equivalence.0 
On 12/15/2019 at 8:34 PM, NonScientist said:
Okay, so I’m new here. Hi everyone.
So I’m not sure why this is affecting me this severely, but I recently discovered the whole “free will vs. determinism” question, and I’ve realized quickly that I should’ve never been introduced to this idea, because I’m finding it almost impossible to deal with the notion of not having free will. It has sent my mind into this state of extreme shock, agony, and despair that almost seems insurmountable. It’s like my whole world and everything I believed has been flipped on its head. I’m serious in saying that this has sent me into a straight panic and shock. I feel like I’m having this nervous breakdown. It’s an overwhelming feeling.
I’m trying to keep myself calm and just relax, but this has really messed me up.
Does anyone here believe in free will? Or can offer any good defenses or arguments for free will? I feel like I need to be reassured that there is free will or else I won’t be able to deal with it. The idea that everything is predetermined, and I’m just robot with no agency or ability to do otherwise is more than my psyche can handle. I’m sort of in this crisis.
How many coin flips does it take to make a free choice?
0 
On 10/6/2019 at 11:15 PM, Mahalo_22 said:
Write a Python program that prompts the user for the length and width of a rectangular field (in feet, allowing a fractional part), then calculates and prints the area of the field in acres. Area = length times width, there are 43,560 square feet in an acre.
You'll need to define a function; do you know how?
You'll need to take an input from the user; Do you know how?
You'll need to make sure the data type of the input is a certain type; do you know what type that is and how to check that the input is that type?
Then you'll need to perform the calculation and print the result; Do you know how?
Give it a shot, and if you can't figure out how to do any of the above steps, let us know. We won't do your homework for you, but we'll help you figure it out.1 
That's kind of the definition of UFO.
3 
You could map the wavelengths of visible light to [0,1], map [0,1] to some continuous subset of your time variable, then do a graph for different colors (points in time) for any "granularity" of colors (moments) that you'd like.
0 
8 hours ago, koti said:
If you find a minute, could you rephrase that?
Throwing a ball up has it start with a velocity v coming out of your hand. There is no force causing it to accelerate upward, but there is a force causing it to accelerate downward: gravity.
So, from v, the velocity slows with the acceleration due to gravity until it stops. But, then, it starts going down, still accelerating due to gravity. This trajectory is symmetric about the point at the top where the velocity is zero. So, for any other point, there is a partner where the ball has the same speed. But for each speed, the ball has that velocity for 0 seconds.
There must be a time or two that the ball is at each speed, but it is at each speed for no time at all.8 hours ago, Strange said:The velocity is constantly changing and so the ball has any specific velocity for 0 seconds.
(I disagree with the last part. The ball may have the same speed twice (for zero seconds each time) but will never have the same velocity.)
Indeed, speed, not velocity. You've earned yet another cookie for catching my mistakes.
0 
9 hours ago, zapatos said:
Sorry, but a quick offtopic question:
If the extent of time that the ball has zero velocity is zero seconds, does this mean that that the ball is always moving in its flight, even at the top of its path when it has a velocity of zero?
For any velocity the ball has along its trajectory, it has it for precisely 0 seconds, and for all but v_y = 0, it has said velocity twice for 0 seconds.
2 
4 hours ago, swansont said:
What is the duration over which it has zero velocity?
Precisely 0. There must be a time where v_y=0, but the amount of time v_y=0 is precisely 0. This is honestly very unintuitive for a lot of people (Iirc, this might explicitly be a motivating example in the intro to Frames and Locales). Tbh, this is a big part of why I'm not a fan of pointy space. Localic space ftw.
0 
!
Moderator Note
Topic moved to General Philosophy
0 
!
Moderator Note
Topic moved to General Philosophy
0 
6 hours ago, Strange said:
Yes. So maybe I am asking why those specific pairs are related via Fourier transforms.
No, there isn't. Which is interesting.
Then I'm inclined to think it's just a coincidence.
0 
2 hours ago, Strange said:
Someone asked a question the other day that made me realise that there seems to be a parallel between the Heisenberg uncertainty principle (HUP) and Noether's theorem.
For example, one conjugate pair of variables in the HUP is energy and time. While in Noether's theorem, the conservation of energy is related to time symmetry.
Another conjugate pair is momentum and position. And the conservation of momentum is related to spatial translation symmetry.
I assume this is not just a coincidence. So is there a deeper reason? Is Noether's theorem the reason why these are conjugate pairs?
IIRC, the HUP is just a consequence of position and momentum being related via fourier transform.
So, global gauge invariance of the EM field gives us conservation of charge via Noether; is there a corresponding uncertainty pairing?0 
10 hours ago, wtf said:
Also note that you meant that A is an element of the power set. It's a subset of the integers, but an element of the power set.
That's a good point. This is an important distinction and one that technically makes the proof incorrect. A is an element of P(Z), not a subset. A is a subset of Z. The elements of P(Z) are the subsets of Z.
1 
0

Reflexivity and transitivity look good, but "obviously" won't cut it for symmetry. You should cite that set intersection is commutative for (b).
0
How big is a point? (Can be that the Natural Numbers are Finite?)
in Linear Algebra and Group Theory
Posted
When you're talking about volumes and hypervolumes, your set needs to be equipped with a measure function. The technicalities are too much to go into in a single post, but see the wiki link if you're interested.
The standard measure used on the Reals is the Lebesgue measure where the length (in one dimension) is just the difference of the endpoints.
So, if we're looking at the length of a point p, we need to just take pp, which is, of course, 0.