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This thread is an attempt to quantify the methods used to communicate a mathematical concept to another person for the purpose of applying the concept. Each response should ideally contain: A single math concept, as you would present it to an inexperienced colleague in your field, who asks for help. Any additions that you would include for the average person. Optional comments. Provide as many examples as you like, including historical examples, but please send each as its own post for ease of evaluating responses. There are no restrictions on field or complexity. The only restrictions on length and format are the practical limitations of this forum. You may provide links to external resources. Any document over 10 pages provided as a link or attachment should call out the most relevant page numbers in the body of the post. We specifically request examples that include unconventional, obsolete, historical, experimental, graphical, scanned handwritten, 3 dimensional, or otherwise odd notation provided it is useful to explain a math related practical concept. Computer code from any language is welcome. Please note if you would use computer code exclusively, or coupled with traditional notation. Please identify the notation type or language if it is not obvious to an English speaking C/C++ coder. We understand there is ambiguity in the question, such as "What is a single math concept?" Use your personal judgement. Disambiguation is another feature of the thread. Thank you. I hope the results are interesting.

Hi everyone, im a beginner to study the knowledge of science.

! Moderator Note This is in the mainstream science sections, so time is part of a coordinate system, and extremely useful, not an illusion at all. If you want to post philosophy, or wild guesswork, don't do it in mainstream, OK? Thanks for understanding. Oh my gosh, read a book, please.

Hi, Do you rather tend to philosophy of science or to applied science?

If light and dark energies were paired as you suggest, they'd be exactly equal to each other, like a yin/yang situation, or like matter and anti-matter, almost exactly equal, right? Except there's a lot more dark energy than light, so that falls down rather quickly. "Plane" is the wrong word for time. Time is a dimension, a temporal one, and together with the three spatial dimensions, they make up the continuum we call spacetime. Movement in three dimensions of space and one of time can be expressed as a coordinate system we can use to plot the when and where of any event. We don't actually "watch" our pasts, do we? We gain experience, and use that experience to predict what will work best in future situations. We don't "chase" our futures, we do our best to figure them out ahead of time. Prediction is one of science's strongest abilities, since by experiment and observation we learn to expect what happens when we mix A with B and heat that up by a certain amount. It allows us to trust the knowledge we have to the greatest degree possible.

They should not short sell in the first place! It is not constructive financial tool (in the case of stock market, in commodity exchanges it is completely different story). Doesn't build, but ruins businesses. If somebody thinks company is a bad business or eventually it will collapse should not buy their stocks. But if you short sale their stocks, that is evil! You are causing collapse of the company in shorter time. Hedge fund managers got what they deserved for and they were punished..

I find the notion of shortselling rather distasteful because influential shortsellers can, at a whim, decide if a struggling company is going to fail or not, simply by shorting its stock. Images of vultures comes to mind. The hive mind can overwhelm institutionalised questionable practices like this. They need to get used to it. This is a new form of regulation they are probably going to have to adapt to. I remember Elon Musk going off his head because some were trying to short Tesla a couple years ago. It can be used as a tactical maneuver, which just stinks.

I definitely prefer "Distance is proportional to time" over s = ut, but introduce an additional concept like constant acceleration and one requires equations and units to relate to other concepts like average speed. Wouldn't it be nice if there were an intuitive ubiquitous system to quickly sketch free body diagrams with the limited information you have and the system generates all the standard equations and allows you to cherry pick the output information you require in terms of whatever variables you failed to specify? v^2 = u^2 + 2fs, s = (u + v)t/2 are filled in just in case you need them. DistanceAtoB(m, LinearPath) = Velocity@A(m/s) * DurationAtoB(s, LinearPath) + AccelerationAtoB(m/s^2, LinearPath) * DurationAtoB(s, LinearPath)^2 / 2 is how I would express your example in code I'm working on that lets you define a label such as DistanceAtoB in several explicit ways, while the system implicitly defines other relationships by recognizing the type of quantity and the points from the name and other info like units or path integration from passed in parameters. A specific path defined by several points with velocity at each point could be substituted for the LinearPath parameter. You can select undefined labels and the system will suggest candidate definitions like Intellisense for math. If the system does not have enough information to solve a system of equations it will tell you the minimum number of additional equations required and the variables that should be included in them. It allows aliases to be used for expressing one set of relations with relationships defined by another set. Example: Pressure, Restriction, and Flow substituted for Voltage, Resistance, and Current. It will keep track of all operations and units so they can be simplified or unwound on demand. Division in particular works much better when you just store the dividend and divisor for use in future calculations and only calculate the quotient and units when called upon to display an answer. It isn't a complete or consistent system by any measure. It just doesn't work. And the notation is way too long and complex. But it convinced me there is something there worth exploring further. "obscure and impenetrable" I fear I may have made that worse with this explanation. Whether I try to be verbose or concise, it seems to end up that way. I could blame the head injury. Ever since, I hear things extremely literal and tend to express things by sloppy analogy. After over a decade struggling to be understood, applying various edits to my habits, this is what I am capable of. I appreciate any honest critique of my writing style. It is how I improve. Honestly, I think my mental delay gives me a helpful perspective on some problems with an answer so obvious that it was selected before exploring other answers. When everyone else has heard the problem, processed immediately and moved on, I am still processing... and before reaching the obvious conclusion my mind drifts to something seemingly unrelated. When I snap back to what I was processing, the unrelated stuff gets mixed in and considered as well. It isn't very efficient, but it allows me to see connections I would have missed before the injury. Or maybe those aren't insights at all and just mental illness. Maybe. I choose to explore it anyway. I don't know what the result of this study will be. That is why it is being made. Yes, ML = Machine Learning. This is not associated in any way with Microsoft's Lean or work done at Imperial College, London. I was completely ignorant of that.work, but looks like I have some reading to do. The this link just pointed to specific content on the page explicitly linked further down the post. You didn't miss anything. It was such a long address I just didn't want it to interrupt the flow. If you are ever nervous about a link, just hover your mouse over it but don't click. Then look at the lower left of your browser window to see the URL it points too. Yours is a good general policy to avoid mischievous links. I'll keep that in mind for future posts. You can also hover over the link and invoke your context menu with a right click, or 2 finger tap on the touchpad. Select "Copy Link Address" to put it on your clipboard, then Ctrl V or paste into a text editor or browser address bar to see where it is they are trying to take you. Probably a wise choice to resist calling out examples of 'bad' forums. I retract that call to action. I'm glad you found value here! Take all the time you need to respond. I appreciate your engagement.

ML = Machine Learning ? Does this research have any connection with Microsoft's Lean? Is that the ML abbreviation? If not, you may have a passing interest anyway. I'm cautious about giving out links but you sound competent enough to make your own searches for what is being done at Imperial College, London, UK - where Lean is being used to try and develop a competent artificial mathematician. For whatever it is worth, I was very relunctant to click the links you provided, especially the hyperlinked word this you used in one earlier post. I prefer to be in direct control of navigation and not pass extra information through the URL string sent to a server - but then I am old and don't own a mobile phone. I wouldn't really want to comment or offend anyone or any organisation. On the other hand, listing some positive points seems less problematic: Studiot, the other person replying to you seemed very pleasant and I probably wouldn't have bothered coming back to this forum for a second day if there hadn't been a few like that on here. Physics Stack Exchange is also another good site. I promised you an example, I'm sorry, Real Life has got in the way and it took me half-an-hour to write this much text. Another day please.

There is quantum fluctuation, there is zero energy universe, there is M-theory and there is conformal cyclic cosmology. Take your pick. There are plenty of ways to come from nowhere. The universe is not necessarily limited by our need for logic.

You just need a thesaurus, some of my sentences are just the set up to, or just jokes. I wish I was special...

Surely the basic Physics comprises the 'invariants' of the Theory ? In SR the invariant intervals form a network that requires no coordinate system whatsoever. In fact the addition of any coordinate system adds restrictions that are not present in the physics, in the similar way that the introduction of coordinate geometry restricts the geometry of Euclid. For GR the invariants are different and still being worked on to this day. https://en.wikipedia.org/wiki/Curvature_invariant_(general_relativity) https://link.springer.com/article/10.1007/BF02726036

While tunneling has been postulated as a mechanism for Hawking Radiation ( along with some other mechanisms ), see here [hep-th/9907001] Hawking Radiation as Tunneling (arxiv.org) Hawking radiation will only come into play once a Black Hole is small enough that its 'temperature' exceeds the CMB temperature of 2.7o, otherwise the BH is an absorber of radiation, making it grow ( and get 'colder' ). As for 'White" Holes, you would think the 'tell tale' radiation from such an object would be readily detectable. And while GR may allow for their existence, it is not a guarantee of such, and none have ever been detected.

As soon as we happened our “happened in” time dimension, became our past, and the speed of light became our future. We can never attain our future, and we can never regain our past. We are the present. We are the light. We have a probability of 1. Therefore: We always had to be. / Past We have to be. / Present We always have to be. / Future We exist in a twined / mirrored, dark energy / light energy Universe, on a time plane we call the present: constantly watching our pasts: as we chase our futures. A “photon of light” is in fact a twinned dark energy / light energy couple, hence the wave.