Sensei

Why do you write such nonsense? Matrix operations are nothing more than operations on multiple variables simultaneously/parallely. If you have matrix 2x2, you have 4 equations. If you have matrix 3x3, you have 9 equations. If you have matrix 4x4, you have 16 equations. etc. The operation between vector with n-th element and matrix which has n-th x n-th element, can be expressed (for somebody reading it) as an array ("matrix") of equations. For example (the simplest case), the scale matrix will have a format such as: sx, 0, 0, 0, sy, 0, 0, 0, sz https://en.wikipedia.org/wiki/Scaling_(geometry) https://www.google.com/search?q=scale+matrix How to perform operation with a such matrix? Multiple columns by vector [x,y,z] element and add them together in the same row.. e.g. x' = sx * x + 0 * y + 0 * z; y' = 0 * x + sy * y + 0 * z; z' = 0 * x + 0 * y + sz * z; Because matrix had 0 in some columns and rows (most of them!), this can be much simplified without matrix multiplication to just: x' = sx * x y' = sy * y z' = sz * z From 9 equations (3x3 matrix with 3x vector elements, 9) we can have 3. From 16 equations (4x4 matrix with 4x vector elements, 16) we can have 4. For rotation it is not so simple. E.g. rotation in Y axis: Matrix 3x3 will have format e.g. cos( angle), 0, -sin( angle ), 0, 1, 0, sin( angle ), 0, cos( angle ), Or something like that (+/- sinuses and cosines) https://en.wikipedia.org/wiki/Rotation_matrix For translation you need 4x4 matrix with format: 1, 0, 0, tx, 0, 1, 0, ty, 0, 0, 1, tz, 0, 0, 0, 1, https://www.google.com/search?q=translation+matrix Matrix operations are 1) easy for computers to perform in parallel 2) slow down the whole process (during plain scaling and/or translation) 3) speed up operations if they were complex are they were merged together 4) make it more readable for humans who needs to review them. The matrices can be "multiplied" by other matrices, yielding matrices that can be used for the final vector transformation. Which can simplify the entire vector transformation process. https://www.google.com/search?q=matrix+combine https://www.google.com/search?q=matrix+merge MMX means Matrix Math Extensions or Multi Media eXtension. Pentium CPU ~ 26 years ago. SSE means Streaming SIMD Extensions. They are basically operations on matrices and vectors. Multiply 2, 3 or 4 elements in an array and/or add them together in the one CPU operation. If you write things the right way, MMX and/or SSE/SSE2, etc. will be automatically activated by the compiler and used, and you will be able to increase the performance of your code... or you can write your own MMX/SSE/SSE2+/AVX CPU code.. https://en.wikipedia.org/wiki/Advanced_Vector_Extensions (AVE = "Advanced Vector Extensions" > SSE > MMX) i.e. AVE is SSE on "steroids".. and SSE is MMX on steroids... ..now depreciated by GPUs..

..unfortunately those good times are over..

..I would guess without even bothering microscope.. I would just use my lie detector..

Does he have free will or is he predestined to utter such words..? Look at Swansont's minature - "resistance is futile"..

..and they never look the same as they did before, so every time you look at a nail like that, you are reminded of an accident from the past.. Accident, is the most common way to lose nails..

The number of bizarrenesses increases with each generation.. The apparent result of living too well..

Are you able to explain your thought path that led you to such extraordinary conclusions.. ?

..or you were predestined to say such words.. Philosophical discussions can be shortened to the statement "I know that I know nothing".. If one needs brain exercises, one should start creating algorithms, i.e. solving solvable problems, rather than wasting (precious human life) time on unsolvable ones..

Unwise. Used socks and shoes should not be given, exchanged, purchased or sold to other people - in this way it is very easy to get infected with onychomycosis and/or foot fungus. Onychomycosis ends with the old nail falling off and a new one growing in its place.. It takes many months..

I used to get $2 socks for Christmas. They had to last for the next year..

..the founders of philosophy were slave owners.. they raped the women and men which they just bought in the slave market.. occasionally killing them for fun.. Did they have free will and use it to rape them, or were they determined to rape them? (in between of thinking about "philosophy")

"philosophy can determine" something? Do you read what you write before you click the "Submit" button.. ? De-railed threads about nothing, just a thought.. Didn't I just say: ps. There are no participants in the discussion because people don't want to waste their time.. ..actually this sentence makes no logical sense....

Whether an object is in the plasma, gaseous, liquid or solid state depends on temperature and pressure. The same thing can be in several states of matter depending on the pressure or temperature used. Check the diagrams of molecules or elements to find out at what pressure and temperature they are in which phase. Scientists began condensing gases long before you were born. One can measure mass of gas before liquefy and after and get the idea that they are the same with different volume (therefor different density), and the same number of atoms. As the liquid cools further, it transforms into a solid and reduces its density again (with a few exceptions, such as water). Every engineer who works with trains and railroad workers knows that metals expand when exposed to heat and contract when exposed to cold. Railroad tracks can bend when exposed to too low or too high a temperature if welded too tightly, which can lead to disaster. Look online for charts of elemental density versus temperature. An increase in temperature above a certain threshold, which varies for each element, causes electrons to be released from the atom. This may allow a further reduction of volume. The whole idea of a hollow atom came from the gold foil experiment, in which alpha particles passed through the metal almost transparently: https://en.wikipedia.org/wiki/Geiger–Marsden_experiments ..except for some that were deflected (when they hit the heavy gold nucleus).. The use of the cloud chamber also shows how highly accelerated alpha (and other) particles accelerate and eject electrons from other elements in their path. https://en.wikipedia.org/wiki/Cloud_chamber

In the case of IPA, it evaporates: https://www.google.com/search?q=IPA+evaporation+time ..electronics engineers often use it to clean circuit boards, so it's pretty well measured.. there are YouTube videos that compare several different fluids.. This is not a single compound. Too ambiguous. Find the name of the compound, then review articles about it. ..I would use it without any serious doubts..

People fly because of their brain size, capacity and power, not because of their muscles.. ps. Muscles bigger than the brain are only needed by MMA fighters, boxers, etc.

The way you express your thoughts on the forum is cumbersome for people (too ambiguous), so don't have too high expectations for people to join and participate.. Any discussion with you is full of "what did you mean?" instead of a real discussion.. It is annoying and cumbersome.. Learn how to be non-ambiguous, and you will have more successful discussions.. ..what I see in this world is just: increase the time served in prison, increase the time served in prison.. I don't recall any politicians claiming that reducing prison time is desirable. Unless you meant "prisoners of free will" or "prisoners of determinism".. ? Of course, for society, the fewer people in prisons, the better, because these people simply waste everyone's time (except investors who bought shares in private prisons on the stock market, guards and prison management). Philosophical discussion belongs in the dustbin..

C'mon. That's not the speed of light anyone here knows.. ..it is true.. measurements taken in space may differ slightly from those taken on Earth. that's why scientists fly into space and repeat measurements to see how they differ.. ..what if you own emitter and detector? Is the laser rangefinder not working? ..do you know the ,meaning of exponential function.. ? https://en.wikipedia.org/wiki/Exponential_function

Depends on the people.. It doesn't work in the Middle East. If you think something "works", you are blatantly lying and/or you're an idiot. Generation after generation keeps the "secret" of who killed their father, mother, grandfather, grandmother, grandfather, grandmother, grandfather, grandmother, etc. etc. etc. Parents and grandparents share their hatred with younger generations.. Hatred is directed at people who have been dead for decades, centuries or thousands of years. Therefore, the hatred is directed at the living, who have no connection to the source of the hatred, and the cycle repeats itself. By killing them ("terrorists"), you create more of them ("terrorists")... You're terrorist, who created more terrorist.. I watched a documentary in Chinese. It was simple. A senior communist leader-teacher was training young workers how to deal with Western tourists on cruise ships, etc. They called tourists from Europe and the US "white devils".. This was not 50 years ago. Only 5.. Europeans or US citizens often think that "everything is fine".. because there is no war, etc. when hatred is growing all around them (directed against them) without their knowledge.. people are stupid.. Your grandfather murdered some grandfather/family member of theirs a few hundred years ago and they want/demand revenge and you are just a blatantly stupid tourist who just came to their country thinking only about your crap stuff and fun..

LOL. Your sense of humor. The wave interference can be constructive or destructive.. We will be in a destructive interference phase when all the madness in Gaza will also disappear..

https://www.google.com/search?q=the+victim+becomes+the+executioner "The victim becomes the executioner".. Mass murderers were often victims abused as children by family members, teachers, priests, acquaintances.. Whatever they do, they will create more "terrorists" and more people in the world who will want to kill him, his family, his nation and everyone else. "Terrorist-to-be" should be better informed so they know who to attack and who is responsible for their losses (i.e. who killed their family before they became "terrorist")..

..people have committed crimes.. not nations.. When you show their face, they are afraid of absolute justice.. .."the final judgement"..

Massless means having no rest mass, i.e. being stationary, i.e. having no rest-frame of reference. https://en.wikipedia.org/wiki/Rest_frame It about detection rather than the rest - photon which is stationary could not be detected as photon.

....which makes no sense actually..

This is how mass murderer killing children look like: @Anonymous

I share your point of view, but more chance of being hit by lightning.. (no more golf game? ) ps. If such a mortal is hit by lightning, some will say Zeus doesn't like him..