Help me get 5$

!!!SUMMONING ALL BRUTE BRILLIANT MUSCLE!!!

Ok so... Got myself into a hole.

In my AP Bio lab, got into an argument with my lab partner. Made a 5$ bet that by tomorrow I'll model the brain function of a fruit fly (Drosophila_melanogaster) that will explain the vector motion of the fruit fly through space.

Any ideas?

Here's what I've come up with:

Gonna use a bunch of equations describing motion and four fundamental forces and spacetime to be as general as possible. Also gonna throw in some totally random equations about brain and neurons from random articles. Gonna add a brief description (help me on that) to explain the relevance of each equation. [actually what we currently have makes some very good sense. Didn't expect that.]

Combining, we get:

First, let us define the fundamental relations of space-time-energy composition of the fruity fly and its physical interactions with external matter:

$UNCERTAINTY$ UNCERTAINTY-No process may be defined with a certain precision about all of its parameters (i.e. position and momentum).

$GRAVITY$ GRAVITY

-Gravitational force interactions (need something better than this)

$Nucelar$ Nucelar

-Nuclear energy interactions

$sa$ sa

-Fundamental behavior of physical systems with respect to time

$a=\frac{F_{net}}{m}$

Motion due to external forces

$motion 3d space$ motion 3d space

-Vector motion properties through 3D space and 1D time

$ke$ ke

Motion-energy relations

$tim$ tim

Definition of time via observation

Now to the brain:

sad sad

Neuron computation function

sadsa sadsa

Fruit fly's multilayer perception of information in 3D space, including input, hidden and output layer.

From this article, will copy all equations and some doodles from pages 13, 16 and 17. Am going to explain as: The set of relations describing dynamic models of temporal basis functions of neural brain regions. I scribbled some terms together from page 13 below Dynamic Modeling.

$Schrodinger$ Schrodinger

Diffusion process in complex space, describing wave mechanics of the fly's molecular structures.

I dunno what to say about this

Michael Michael

Majorana-Weyl spinors accounting for the influence of solar neutrinos on the brain function of a fruit fly during its flight through 4D spacetime.

$sad$ sad

Mathematical decomposition of spinor rotators into counter-symmetric parts in an even dimensional space, and their representation of the spin tensor product in terms of the alternating representations of the orthogonal group for 4D Space-Time-Energy interactions.

$staff$ staff

Fruit fly temperature comfort boundary in 3 dimensional vector space, where $T_1=12°C$ , $T_2=29°C$

Alright I kinda gotta run now lol but TELL ME HOW IM DOING SO FAR!!!

Production:

John Muradeli (complex jargon and forgery coordinator)

Michael Mendrin (Mr. Mathopedia)

Daniel Liu (confused bystander)

Josh Silverman (party pooper)

You (if you add something) (appropriate nick)

...

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold


- bulleted
- list

bulleted
list


1. numbered
2. list

numbered
list

Note: you must add a full line of space before and after lists for them to show up correctly

paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

example link

> This is a quote

This is a quote

    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"

# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"

Math

Appears as

Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

\sin \theta

\boxed{123}

\boxed{123}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

And I'm just sitting here like "what did I just read?"

Daniel Liu - 6 years, 9 months ago

And all that stuff for just 5 dollars!

Bogdan Simeonov - 6 years, 9 months ago

Read below. I did not get paid.

John M. - 6 years, 9 months ago

Hahha me too!!

Hasan Kassim - 6 years, 9 months ago

Exactly! Same here! -_-

Pranjal Jain - 6 years, 7 months ago

I’m surprised that you haven’t included mention of Majorana-Weyl spinors, which can be expressed, for instance, either

${ \psi }_{ \eta }=\quad \left( \begin{matrix} i{ \sigma }_{ 2 }{ \eta }^{ * } \\ \eta \end{matrix} \right) \quad or\quad { \psi }_{ \xi }=\left( \begin{matrix} \xi \\ -i{ \sigma }_{ 2 }{ \xi }^{ * } \end{matrix} \right)$

making use of two component Weyl spinors. How else are we going to account for the influence of solar neutrinos on the brain function of a fruit fly as it goes vectoring through space? As we all know, there's a lot of neutrinos coming here from the sun every day.

Michael Mendrin - 6 years, 9 months ago

Hm I found this one fancy-looking equation when looking through "spinors":

$s$ s

Can you briefly describe what it is or what it does or how it is relevant? It's from this Wiki article

It's ok if you don't have time, I think I've accumulated enough toys already. Thanks again

I can try to start somewhere. First of all, we're familiar with doing operations on numbers. Then we learn that we can do operations on something a bit more complicated, called "complex numbers", which is really a kind of a constructed entity composed of two parts, which have defined properties which are different from, say, 2D vectors, which is another constructed entity. Then we have quaternions, which are even more complicated "constructions", which, again, are different from 3D vectors. It doesn't stop there. We also have octonions and sedenions, which are increasingly more complicated constructs (but far from arbitrary!), along with still more other constructs in vector space, which includes matrices, tensors, etc. And then we get into Clifford Algebras, which sort of generalizes it all, a grand overview of these kinds of things and what sort of properties they can have and only have. Spinors, like tensors having certain properties under transformations, are such objects that have certain properties under "continuous rotations", and they do often end up being solutions to certain equations in physics, such as the Dirac Equation, hence "Dirac Matrices", etc. Okay, now we're getting somewhat close to this staggeringly ugly equation you've posted here. In mathematics, it's always a nice thing to be able to decompose objects, such as functions into a symmetric and an anti-symmetric part, because breaking things into parts make things easier to manipulate and analyze. The Clebsch-Gordon decomposition is one such decomposition process, and if the dimension is even, then THIS decomposition becomes possible. Now, aren't you happy that, now that we know this can be decomposed, your life will be made so much more convenient in dealing with this kind of thing?

@Michael Mendrin – U...uum... uuh... Ok let me try:

Mathematical decomposition of spinor rotators into counter-symmetric parts in an even dimensional space.

Good? And what about the tall tale I wrote under it for what I thought it was? I'm gonna add this. Also, one more thing:

Now I'm not sure how familiar you are with Physics, but this is a Heat Equation and it's equal to zero. So what if I wanted to write that $12<T<29$ , where $T$ is temperature? Or is this the wrong equation? But it looks damn fancy.

Oh and I think I found an answer to that, see if you're interested: Paul's Notes

So I think I'd just have to plug in those two values for $T_1$ and $T_2$ .

Btw congratz on solving my 100 follower problem without ANY HINT STEPS! Lol I have a trouble reading the solution itself and you just bashed it head on. #EXPERIENCE

@John M. – You should note the similarity between this Heat Equation with the Diffusion Equation (after all, heat does behave like a diffiusion). But what's especially interesting is that with a change of "scale" introducing the imaginary number $i$ to the diffusion equation, out pops none other than the famous Schrodinger Equation that you have posted here here! This is the reason why Richard Feynman proposed that perhaps quantum physics is like a diffusion process in complex space, i.e. a random walk on the complex line, instead of a real one. Unfortuantely, he soon afterwards realized that the only realistic way to try to simulate this process using a computer was to use a QUANTUM computer! This is fun stuff, really.

Speaking of physicists, though, I think Ettore Majorana is one of the most underrated, virtually unknown physicist there is in the popular media. Emily Noether was another such "underrated, virtually unknown physicist", but since the word got out that she's a woman, she's gathered a bit of notoriety by now. So I thought I'd include a little of his work in here, in the fascinating study of what fruit flies think to do.

@Michael Mendrin – Oh-oh man what are those WORDS!!! It's like the classmates I speak to when I mention quantum mechanics, but now it's me who's like the students LOL (nah not really I almost get everything you're saying). Ok so what do you mean "change of "scale"" and where do I introduce $i$ to... "get" the Schrodinger Equation? And what do you mean "get"? Like, you plug in $i$ and all of a sudden you have the whole thing?

Alright I'll stop here lol don't wanna bust your head with question xD

If you were to describe the Schrodinger Equation in one sentence in the style I've described the above equation, what would it be? (make it as confusing as possible ;))

@John M. – In one sentence, the Schrodinger Equation really describes a diffusion process in complex space. But it's not taught that way in college undergrad physics. It's taught as "wave mechanics", where complex numbers are introduced to "represent wave motion". Given a function, like the exponential $y={ e }^{ x }$ , what happens when $x$ is scaled using the imaginary $i$ ? Yes, you get sinusoidal waves. Get it now?

@Michael Mendrin – oh whoa so that's why sinh is in terms of $e^{ix}$ ! no I had no idea they just dumped the concept in my face :O

Ok so:

SOUND GOOD? I"M GOIN WITH THAT! thanks!

@John M. – there you go, you are now making excellent progress, you're sure to win that $5

@Michael Mendrin – wait WHAT? Quantum Computer?? how did he know? Didn't Feymnman live like in the caveman era? them 1900s

@John M. – Feynman was is in his young 20s when he worked on the Manhattan Project, something that probably contributed to his relatively early death from a "rare cancer". He was already thinking about the possibility of quantum computers in the 60s and 70s, one of the first to do so, and one of the motivations was to come up with an "universal quantum simulator". You might think it ought to be possible to use regular computers to "just do the quantum math", but the idea is to simulate quantum behavior using methods similar to "finite element methods" used to stimulate physical behavior using conventional computers. Turns out it can't be done using conventional computers, it needs quantum computers!

@Michael Mendrin – Seriously when quantum computers come out I'm getting one into my head. Wolfram Alpha will be a poop compared to me... IMAGINE THE LEARNING CAPABILITIES??? Download Wikipedia into your brain! Read all books ever written in days! And ANALYZE ALL THE INFORMATION!!! MAKE 10D GRAPHS IN YOUR HEAD! PREDICT STOCKS! SEE PARTICLES! Don't even get me started LOL...

But okie briefly how did you solve the 100 followers problem? Did it take many steps (like in my book), or did you use some chaos math and solve the whole thing with one equation? It was supposed to be solved using differential equations, but I'm sure there are more ways. Just for insight, thx :)

@John M. – This happens to be the classic "straight line pursuit" problem, and so it was a matter of figuring out how far the rabbit went before the dog catches up to him. Then we know the dog went twice as far.

Yeah. He didn't get it. He said it's irrelevant (even though I solved the 100 followers problem (replacing dog with fruit fly and rabbit with scent) and created (forged) a parametric curve to make it look realistic. He did laugh though, like a LOT, when he saw "space time energy constitutents matter properties interactions eletromagnetic gravity particles dimensions" lol. I'll screenshot exactly what I wrote if ya'll want, it came out pretty cool.

And I would't say this is irrelevant. I wrote the most fundamental equations of the universe, encompassing force, spacetime, and motion. Plus some brain models. This should be good enough (but obviously not as good as a professional paper).

He said he'd give me 2$ cause I made him laugh. Well, guess what. Next time he needs help with algebra or science he ain't getting it.

I don't understand why you aren't proceeding straight from the underlying structure of the universe, and seemingly wasting your time with all of these disproven theories such as GR and QFT. Why not just recognize that the fly is a really a pinned D-brane?

Josh Silverman Staff - 6 years, 9 months ago

a wha brane now? gr qft? huuu?

Yes, I'm afraid your only shot at the $5 are extended object embeddings in a string cosmology.

@Josh Silverman – LOL XD

Don't worry I'll probably demand $20 instead (not that this isn't worth way more). But the Brilliant experience is what makes it worthwhile, even if it is just pesky 5$ ;)

Okie so I seem to have almost the complete model. Now I need some equations for brain cells and brain parts (FRUITFLY), those that induce motion, and I'll be done.

And D membranes may be much of a stretch. This isn't the Theory of Everything, for 42's sakes. This is a fruit fly lab rat experiment... or a mathematical model of the brain vector space of ... stuff ... functions... omg poor neurologists.

@John M. – This is beyond me. I can't tell if you two are joking or not.

@John M. – If we want to simulate the brain and all that stuff accurately we need to at least go into string theory. Not Super string theory. Thats crazy (26D) and it isnt proven or even widely accepted. But physicist dont truely understand this and thus the entire probability collapse concept of anything and so we can not yet even dream of simulating the brain of a fruitfly.

Julian Poon - 6 years, 9 months ago

@Julian Poon – Yes it is supposed to be complex, but I doubt THAT complex. I mean, they could create a faily good model of the universe with supercomputers, what's a fruit fly's brain compared to that?

It's just that there's not enough funding for such things.

Oh and what the heck are you implying with 26D? Those are different dimensions, mathematical dimensions, not physical. We're talking Space-Time-Energy (or... if you go above 7 there are new parameters introduced). String Theory takes place in 11D (but my understanding only stretches till 10th - I haven't spent time with 11th). Don't mix the two.

A 26D physical dimension... oooh... My mind could collapse into a black hole trying to think about that.

@John M. – There were actually about 5 different versions of string theory that were all 10D models. It was physicist Witten who realized that by introducing an extra dimension, he was able to devise a "more universal" string theory, dubbed M-theory, by which each of the other 5 earlier 10D string theory models could be seen as subsets. Well, but in mathematics, there's a thing called "equivalent representation", which is a kind of a more generalized concept of duality, and it happens that for the 10D models, there is a mathematical equivalent "bosonic" model that requires 26D. That is to say, one type of 10D string theory model "works essentially the same as" as another type of 26D string theory model. A lot of this is explained in Group Theory, and many physicists today are hoping that the "giant" group called E8 may be the appropriate framework for an unified field theory. E8 has a "complex dimension" of 248!

Because of this thing called "equivalent representation" in mathematics, the idea that we "necessarily" exist in some particular number of dimension, such as 3D, or 3D-T, or 4D, or 10D, or 11D, or 26D, or 248D, is meaningless. What matters is the actual mathematics, and one thing you have to understand is that there are often multiple ways to "represent" the exact same thing, and it cannot be argued that any one representation is "correct and true", while all the others are "false", because, mathematically speaking, any one of them can be converted to another. For example, Hamiltonian and Lagrangian mechanics in classical physics, while seemingly different from each other, are convertible either way using the Legendre transform., so they are equivalent.

@Michael Mendrin – 248D?

Yeah well dunno about all the bosonic and advanced stuff, but what I do know is that if one thing can be CONVERTED into another that does not imply it is the same thing. I don't know what kind of conversions you're referring to, but if it's something like $F_{net}=ma$ , then you can't say that $F_{net}$ is equivalent to $ma$ . Those are two totally different things. $ma$ is the measure of how strong the force applied is, but not the force itself.

No?

Dunno. Oh an I have absolutely no clue on how matter can be converted to do energy. Isn't energy the property of matter that allows it to do work? How can matter be converted into a property of matter that allows it to do work?

Well, that's what I thought a few months ago. Now I think I could relate to it more, because I know that there are subatomic particles that transmit force, so I thought that maybe that's what happens when you break down matter to that level; maybe all the protons electrons and neutrons deconstruct to quarks and quarks deconstruct to whatever the heck they're made of and in the end they all turn into the form of matter that transmits force, and thus, work, and thus, energy. Dunno. I've never studied nuclear physics, and I don't even know what strong and weak forces are. But I will. I will...

But 248D? What kind of a stretch is that? Don't tell me that 1D is equivalent to 4D cause it's not. in 1D you can't go left and right if you're going back and forth. And THAT's a fact.

@John M. – I was referring to "mathematical equivalence", not physical conversion. For example, in geometrical duality, any theorem or proof in one representation would have a counterpart in the other that's also a fact. This is a huge and very interesting subject, and all the disparate models in physics start to make more sense once one understands the concept of "mathematical equivalence". As an easy [or maybe not so easy] example, if you look yourself in a mirror, do you see yourself reversed right from left, or top from bottom? It's likely you'll say, "right from left, obviously", but in fact, it's just as correct to say, "top from bottom"!.

@Michael Mendrin – Well, mathematical means logical. It's like 1+2=2+1. No problem here. But if you're going to equate 10D to 248D, I have big problems with that. There better be proofs for this seemingly hogwash theory.

@John M. – Okay, let's be more precise here. First of all, understand that "String Theory" is not a single model, there's several. Some of the 10d versions can be shown to be mathematically equivalent to a 26d version. That is not the same as saying "10 dimensions is the same as 26 dimensions". As an analogy, an icosahedron and a dodecahedron are duals, but the first has 12 vertices and 20 faces, while the second has 12 faces and 20 vertices. They are considered to be duals.

@Michael Mendrin – oah ok no the way i read it it sounded like you said 10d=248d. yes i know about string theory i watched brian greene explain it and animate it in pbs nova (the playlist ive been trying to make you watch). sorry, havent slept in 48 hrs. and i ran 1 mile in 5 mins 6 secs today even though i told the teacher im tired. yesterday i did beep test for 153 beeps - beat em all. and now im typing this with my face; but the week ain't over. i still have some work from the 7 ap classes i take. freakin sciences are over the head with their goddam labs. hate school labs. so much imprecision.

okie ima go now

@John M. – Yeah, no way you can think clearly in the condition you're in now. Get some rest.

@Josh Silverman – 7D? Thats a lot of calculus. Im not into it.

8.5 more hours from NOW. Then I'll be cashing in. You can still post, but it won't count towards the 5$.

Thanks for all the support.

Are there any predictions you want to attempt with your model? For example, how often does the fly change its direction by more than $\theta$ , the curvature of its path, etc?

Well, it's AP Bio, so you could just say it will fly to the nearest female then start mating. That's what all the labs involved lol

Justin Wong - 6 years, 9 months ago

And you should add the tag #biology @John Muradeli

I didnt get anything except 5$ bet!

and I didn't get the 5$.

John M. - 6 years, 7 months ago

Bad luck! I wont be gonna bet again! :-|

@Pranjal Jain – Hheh this is worth way more than 5$. At least I could save this for the future, for a more intelligent and less arrogant audience.

Cheers

@John M. – Did I sound arrogant? Sorry for that! But I could not understand a bit!! Although seems impressive!

@Pranjal Jain – Oh no I didn't mean you! I meant the person I've made the bet with; a real a-hole.

And thanks! I hope to find someone like you in the future who'll show some respect.

Cheers ^.^

@John M. – :) Cheers! I hope ill be learning all this stuff soon in my near future!

BOOYAH! /(+o+)/

Albert Liu - 5 years, 4 months ago

nerub inebfgiu

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$