u/future_sponJ

2 eyes makes sense for depth-perception. 0 eyes also makes sense for animals in complete darkness to not waste energy on eyes. But what about the advantages of 5 eyes (insects), 8 eyes (spiders), & other eye numbers like 3 or 6 over simply 2 eyes?

If entropy depends on what properties we choose to describe our macrostate (e.g. temperature, volume) & microstate (e.g. position, velocity) then is it subjective?

Another question: Is the k in the formula redundant & if it is would temperature & energy have the same units with heat capacity being dimensionless?

I always see people saying things like "there are 20 quadrillion ants on Earth" or something similar with other extremely large diverse groups like fish. But all of these are groups with thousands of species. If not by individuals then it's by biomass instead.

So which single species in the animal kingdom has the most individuals?

I have seen the claim that |x| is elementary because it's √x², but then:

• sgn(x) = x/√x² (x≠0)
• floor(x) = x-½+arctan(cot πx)/π
• & many other non-elementary functions should be considered elementary too if |x| is elementary.

What about tanh(1/x) which has an non-asymptomatic discontinuity at x=0?

After reading about axiomatic definitions in maths like equivelance relations I tried to define a very vague idea which is an average. The term "average" is commonly used to refer to many variadic functions so I chose to create an axiomatic definition for them (like reflexivity, symmetry, transitivity for equality):

1. avg(a)=a (idempotency or reflexivity)
2. Commutativity
3. avg(a1,a2,...,a_n) a) =avg(a1,a2,...,a_n,t) for t=avg b) ≥avg(a1,a2,...,a_n,t) if avg>t c) ≤avg(a1,a2,...,a_n,t) if avg<t
4. Replacing kth lowest/highest with kth highest/lowest in the definition keeps the final value unchanged

Using these you can prove other rules such as min<avg<max.

(While these do work for almost all averages such as the median, the arithmetic mean, & the positive geometric mean, the mode breaks most of these)

I also didn't know whether to flair this as arithmetic, logic, or statistics.

I've seen a lot of people/sites saying that scientists at the BEPC in China have found a particle confirmed to be a glueball & I want to make sure that their claim is true. Is there any truth to it?

I've seen a lot of people/sites saying that scientists at the BEPC in China have found a particle confirmed to be a glueball & I want to make sure that their claim is true. Is there any truth to it?

What about being an INTP parent with an INTP partner?

I'm 14 living in the UAE (Egyptian nationality). It's summer & I just finished year 9 (eighth grade). I have completed the full school curriculum for mathematics (up to calc 2 & introductory linear algebra) & am currently studying physics & later hopefully coding too.

I feel like I'd be wasting time at school next year & am wondering if there's a way to apply early & enter college at 14. Unfortunately colleges here do not accept anyone without a HS diploma so it's unlikely for me to enter without traveling to another country or doing online college.

So.. do you have any advice for entering college/university at 14? I want to major in either Physics or Mathematics but possibly engineering or CS if I can't.

I started self-learning calc around 2 years ago but gave up at integration because I felt like integrals were too hard. I came back to it like last week & it was way easier than I expected. IBP & u-sub were also easy & unchallenging but then I hit a wall at trig-sub.

I watched a couple of videos on the topic but couldn't understand or comprehend anything & we're not taking it in school until at least after 3 years. It's the last thing in calc 2. What do I do?

Thank you for you help!

Also, isn't sqrt(x^2-a^2) just i*sqrt(a^2-x^2) ?

Functions like Re(z), Im(z), |z|, arg(z), sgn(z), & z̄.

They're all very basic continuous but non-elementary non-differentiable functions ℂ->ℝ or ℂ->ℂ but are elementary & differentiable almost everywhere in ℝ. If you have any of them along with z, you can derive all of the others using elementary operations. They seem special but I haven't ever seen a term for them? Does one exist?

I'm 14 & have already learned linear algebra & calculus on my own. I sometimes read about particle physics & other things but I want to build a foundation & start studying HS-level physics online now. Where do I start?

A robot will only do something if it is commanded to do it & it is physically able to. So, assuming it wasn't specifically created for this purpose, it will only "take over the world" (or attempt to rise on humans) if the instructions were vague & it had the resources to do so. Otherwise, I don't see the problem.

Why would an electron bounded to an atom & a free electron have the same rest mass? Why does a down quark have the same fundamental rest mass whether it's in a proton, neutron, or any other hadron?

The same question could also be applied to the electromagnetic field too not just the Higgs Field.