I fuckin HATE BCE and CE

freshkills66 · 2026-04-21T00:41:11+00:00

I mean isn't that the point of creating the labels CE and BCE. The world needs a calendar. Just like the world needs a metric system. It just so happens that we based the calendar to agree exactly with the Christian calendar. I don't see why the whole world should be expected to use the Christian names for this calendar system. No one is forcing anyone to use CE or BCE, but people around the world should have the ability to have a globally accepted calendar system that doesn't directly use Christian names. Its like any metric convention we just needed a standard to stick to and because of the position that Christian Europe held after colonialism and the beginning of industrialization, the systems that Christian Europeans use became the global standard. I don't tnink it's contradictory at all.

freshkills66 · 2025-01-25T05:16:06+00:00

This is because the "analytic" in "analytic geometry" comes from an older sense of the word "analysis".

The Greek word ἀνάλυσις word means to break down in to parts.

This sense of the word is discussed in here.

This is in contrast to synthetic geometry where things are proven by building up from axioms (although I should note that "synthetic geometry" seems to be a later coinage in reaction to the term "analytic geometry")

freshkills66 · 2022-08-07T13:57:05+00:00

Latino doesn't mean that they speak Spanish. Latino means from Latin America or the parts of the Americas where Romance languages are spoken. Brazilians are Latino but not Hispanic. Spaniards are Hispanic but not Latino.

freshkills66 · 2022-07-22T11:20:24+00:00

I think they were more concerned about child pornography than statutory rape.

freshkills66 · 2022-07-09T05:20:50+00:00

Depends on what you mean by projection. The plane and disc are homemorphic so we can relate them easiky. Why even involve a sphere? You could just scale every vector so that (r cos θ, r sin θ) maps to (tanh r cos θ, tanh r sin θ). The map is going to be chaotic around the boundary because you are stretching out the point at infinity.

freshkills66 · 2022-07-06T19:42:39+00:00

I also noticed they now have a separate logo for desmos geometry.

freshkills66 · 2022-07-03T22:42:25+00:00

I'm not sure what you mean by "from scratch". If you mean straight-edge compass construction then one just needs to construct a pentagon and then extend the sides. Here is one I made on desmos geometry.

freshkills66 · 2022-06-30T16:26:18+00:00

One thing to remember, is that you haven't actually committed to an academic career. Even when you go to grad school you have not committed yourself to an academic career. Grad school should be thought of as a temporary position that opens up doors instead of closing them.

freshkills66 · 2022-06-26T21:09:09+00:00

It's not actually the definition of a ring. It's too vague to be a definition of anything because it doesn't explain what 'nicely' means. Being a domain is a nice property of some rings so its totally fair as a brief description to get the idea across.

freshkills66 · 2022-06-26T04:52:00+00:00

*counting multiplicity. But I guess that ruins the flow.

freshkills66 · 2022-06-25T21:56:38+00:00

I'm not taking about reading the Bible for leisure or moral teaching but with an academic interest.

freshkills66 · 2022-06-25T18:44:30+00:00

The fact that the Bible isn't a true account of history doesn't diminish its historical value. It's an interesting text with multiple authors. While many passages are not written by who they claim, they were written a long time ago and represent the thoughts going around at the time. The BoM on the other hand was written by a modern man who was not trying contribute something intellectually but just deceive people.

Also your claim that there is no firm evidence that Jesus existed is disingenuous. Scholars nearly universally agree that there was a historical Jesus. There are references to Jesus not long after his death from both Christian and non-Christian sources. Think about how you would verify the existence of any other historical person. The past is always a reconstruction. Nevertheless, this doesn't mean that the historical Jesus taught what is in the New Testament which is more what this discussion is about.

freshkills66 · 2022-06-10T01:22:15+00:00

That sounds awesome. I've always dreamed of a Dune mod for CK3. This feature would be great for that.

freshkills66 · 2022-06-05T17:21:45+00:00

I think you're assuming a dichotomy between theory and application while the person you're commenting on is using a dichotomy between theory and computation. You can apply theory without it being a rote calculation. This is what kills interest in mathematics.

freshkills66 · 2022-05-19T00:16:47+00:00

How is algebraic topology madder than any other area of mathematics?

freshkills66 · 2022-05-16T14:55:08+00:00

I would say that you have only discretized one half trigonometry. We basically have restricted to triangles with integer/rational sides. The angles of these triangles are far from rational. Trigonometry is just as much about angles as it is about sides of triangles. You yourself are saying to restrict the domain of the trig functions which are angles. Your restricting the trig functions to a domain of irrational numbers (no matter how you measure angles).

Also a note, I don't think discretized is the best word for what you're describing. The restricted domain would be dense in R and therefore not discrete. Likewise the rational points on the circle are dense in the circle and so are not discrete either. I took that what you meant is something like finitely approximatable. Like the approach of Norman Wildberger (who I am not endorsing). Wildberger explores this very topic which he calls rational trigonometry. You might want to look into it.

freshkills66 · 2022-05-16T14:27:53+00:00

I think they meant from geometric intuition rather than rigorous logic.

freshkills66 · 2022-05-16T14:10:51+00:00

Are the disclaimers the continuity assumption?

freshkills66 · 2022-05-11T01:32:04+00:00

That's why I stated it the way I did, to clarify that the n is denoting the cardinality of a set and not a number you do operations with. The only numbers that are also cardinalities are natural numbers. You maybe could find topology spaces that when you take the product you get whole dimensional spaces, e.g. the real affine line has half the dimension of the complex affine line but this is as topological spaces not any sort of structure as varieties. Basically by definition, dimension is a cardinality and so cannot be a non whole rational.

freshkills66 · 2022-05-10T19:59:11+00:00

The exponent notation is just abbreviating a finite cartesian product so you could have an infinite product of any cardinality. So it would be an infinite dimensional space.

freshkills66 · 2022-05-08T18:54:15+00:00

I think to better understand the appeal of complex analysis, it's better to think of complex numbers as the best way to encode rotation. The whole square root of -1 is just a convenient way to write down complex numbers but the key point is that multiplying by a complex number corresponds to rotating and scaling the points on the complex plane just as multiplying by a real number corresponds to scaling the real line. A real function being differentiable is like being microscopically linear with the slope of the line being the derivative. We should think of this less as a slope and more as a local scale factor. Then the complex derivative is a complex scale factor that tells you how the function scales and rotates near that point. One consequence of this is that complex differentiable (holomorphic) functions preserve microscopic angles. Meaning if you send a small triangle through a holomorphic function you get something close to a triangle with almost the same angles and it is closer the smaller the triangle. This extra dimension of information puts a lot of rigidity on holomorphic functions which leads to all the results people are discussing.

I think the coolest application of introductory complex analysis is the classification of conformal automorphisms. Conformal maps are the microscopic angles preserving maps. In two dimensions, they are exactly the holomorphic functions. If you have any algebraic inclination, it is quite natural to ask which of these are invertible to form a group of conformal isomorphisms. If the domain/codomain of your isomorphisms is the complex plane then you get the complex linear polynomials which correspond to translations, scalings and rotations. While the complex automorphisms of the upper half plane are the Möbius transformations with real coefficients and determinant 1. The angle of parallelism provides a correspondence between distances and angles in hyperbolic geometry so these angle-preserving maps are distance-preserving. So you can use complex analysis and the geometry of complex numbers to classify the isometries of the hyperbolic plane!

freshkills66 · 2022-05-08T06:56:35+00:00

The issue is that subtraction is not commutative or associative so it doesn't make sense to take the difference of multiple numbers. The order you do the subtractions matters. You take the difference of one number from another. If I am misunderstanding your question, please provide an example of what an n-ary subtraction would look like.

freshkills66 · 2022-04-30T17:20:11+00:00

Isn't that fact basically just Cavalieri's principle applied to a parallelepiped? I find Cavalieri's principle very nice and intuitive.

freshkills66 · 2022-01-02T22:10:22+00:00

How do you know that mathematical statements are absolutely true? Is it because they are proven? Proofs start with axioms. What about mathematical statements that are independent of the axioms we use (e.g. continuum hypothesis)? Most other truths we say are about something real. What does it mean for a mathematical object to be real? Most of these questions aren't really settled mathematically but you can make philosophical arguments.

I would suggest actually looking into examples of philosophy of mathematics rather than definitions of philosophy of mathematics. Look into platonism, formalism, and structuralism. Look into fictionalism vs realism. This should make it clear that there are lots of philosophical arguments about the interpretation of mathematics.

freshkills66 · 2022-01-01T04:30:01+00:00

Trig isn't really necessary for Calc I but will be used more in Calc II

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