I have chronic migraine. It sounds worse than it is; I rarely suffer attacks anymore, and when I do, they're usually mostly harmless, as in the case I'll describe below.
Contrary to popular belief, migraine is not a headache. It's something a little more like an epileptic seizure. Intense headaches are one common symptom, but there are a lot of others.
One common symptom of migraine is called *scintillating scotoma*. A scotoma is a blind or blank spot in the visual field. A scintillating scotoma caused by migraine is an area of the visual field that is temporarily replaced by a vivid visual aura. Its appearance is commonly the first symptom of a migraine attack, and is often followed by more unpleasant symptoms.
I've seen scintillating scotoma many times over the years. A few years ago I was reading and enjoying a good book, and my scotoma appeared. It was a humdinger: roughly triangular prisms of white light with utterly black zebra stripes moving along them kaleidoscope-style. It took up the lower left middle of my visual field, pulsing and radiating and turning, covering the book in my hand.
I was disappointed. I didn't want to stop reading. I was enjoying the book. So I decided to keep reading until the scotoma made it impossible to continue.
It never did.
It became so vivid that I couldn't see my hand at all, but I still had no trouble reading the book. I even started reading it aloud without any difficulty.
After a few minutes the scotoma faded. In that instance, it was not followed by any other symptoms (that's happened more and more frequently over the years since probably my forties).
I could now see the book again, and could confirm that what I had been reading was indeed what was on the page.
I thought about how to explain my experience. The best hypothesis I've come up with so far is that the neurological process of seeing and the neurological process of being consciously aware of what I'm seeing are not the same thing. They're independent processes. The scotoma prevented me from subjectively experiencing seeing the book, but did not prevent me from actually seeing it, nor from correctly interpreting what I was seeing.
This experience (and one two other odd experiences) has led me to adopt the working hypothesis that many of our cognitive experiences are more complicated than we tend to assume, and that they're often made up of several more or less independent processes. We usually benefit if related processes pretty much work together, so they pretty much do. Because they do, we experience them all together as a single experience, but that's an illusion that unravels if circumstances screw up their synchronization.
I hope someone finds that as interesting as I do.
As these patterns were explored, they were found to be even more systematic and pervasive than they had appeared. In some cases, one sound would systematically change into another sound from language A to language B.
https://en.wikipedia.org/wiki/Grimm%27s_law
These patterns helped reveal historical connections between most languages of Europe, Central Asia, and South Asia, showing that those languages had descended from the same ancient sources. (Note that this isn't true of 100% of languages in this region -- there are other unrelated families that turned up -- but it's true of a significant majority.)
https://en.wikipedia.org/wiki/Indo-European_languages
The languages that turned out to be related this way included the Germanic family (like German, English, Dutch, and the Scandinavian languages), the Romance family (like French, Spanish, Portuguese, Romanian, and Catalan), the Celtic family (like Irish and Welsh), the Slavic family (like Russian, Bulgarian, and Ukrainian), and also Farsi and all the Central Asian languages related to it, and Hindi/Urdu and all the South Asian languages related to it. Oh, and Greek.
If I tried to list all the languages and language families that were linked up to this family tree, we would probably be here all day, because they go on and on. Just under half the people in the whole world have one or another of them as a native language today!
These languages changed quickly enough in history that most people no longer noticed, or remembered, that most of them were related to one another, yet slowly enough that it's been feasible to deduce an enormous amount of information about the history of particular languages and particular words, once many of the rules and patterns had been identified.
A Grimm's Law example is that the h sound in Germanic languages usually corresponds to the k sound in Romance languages (note that this can be stated much more technically and accurately). So, it turns out that "hundred" and "cent"/"cento"/"centum" actually share the same origin. And "heart" and "cœur"/"corazón"/"καρδία" (origin of "cardiac") (also "cordial"; the root in Latin sounds like "cord-"). And "who" and "que"/"quoi"/"qui" (and similarly for other wh- questions in English and qu- questions in Romance, which were originally hw- sounds in English and kw- sounds in Latin).
Some other examples are t to d ("ten" and "decem"/"diez"/"dez", plus some of the examples above that have a t in English), and f to p ("foot" and the Latin and Greek words from which we get "pedestrian" and "podiatrist", and Romance "pied"/"pie"/"pé"; and don't forget about "father" and "padre"/"pater"/...).
Those are just a couple of the phenomena that people noticed in the 1800s; while the exact development of these patterns gets much more complicated, they've proven to work over and over and over, for hundreds of languages and hundreds of thousands of words!
(... Also, the Grimm from Grimm's Law is one of the Brothers Grimm, from Grimm's Fairytales!)
For a pill that can be digested, often it will be the case that the pharmaceutical compound needs a lot of buffer space, sugar or something else to prevent it from being absorbed too quickly. So if a pill says "Do not break in half" or "Do not chew", this is because doing these things increased the pill's surface area and the rate that the drug gets absorbed, when optimal rate of absorption has already been calculated.
I knew very little about music when I decided to play the harmonica. I looked for an instrument that required little maintenance, were easy to transport and easy to play everywhere. So I decided to learn to play the harmonica by myself. It's easy to start with it, but it gets challenging when you try to learn those techniques mostly because you can't see inside people's mouths to see what they are doing and you aren't used to force your tongue to do those specific movements. When you see what people can do with it, it can be jaw dropping. I'm still a beginner at it but it's so rewarding after practising a lot to get your first bending, to reproduce songs you have learned just by muscle memory, to sound a little bit closer to those blues masters... definitely something worth to try in my opinion.
Only thing you need for this is:
1. An idea and some knowledge about electronics
2. An EDA software where you design the schematic and the PCB (Horizon EDA, KiCAD, Eagle, ...). This software will give you the Gerber files needed to manufacture the PCBs and the BOM (Bill of Materials) and a Pick-and-Place file which is basically just a CSV telling the manufacturer which part goes where and in which orientation.
3. Using the BOM you find corresponding parts the manufacturer has and put create a CSV that matches their format requirements
4. You order (e.g. I ordered at jcbpcb)
The electronics knowledge is the hardest part.
Most modern music chords patterns are easy to find out on piano.
Start on any of the white keys, and play 7 white keys left to right. That is called a mode: a series of notes separated by certain intervals to compose a song.
Different modes have different vibes. Atmosphere of the song ( sad or happy) is directly correlated by how "willing" the notes are to resolve to the mode root (the first key of 7 you hit).
Now, take a 1-3-5 grip on the white keys (press one key, skip one, press one, skip one, press one). That is called the first chord. Move one to the right, and do it again. That is the second chord. One more to the right is the third etc.
Most popular songs are composed by using mostly the same repeating chord patterns:
- 1-5-1-4 (first, fifth, first, fourth)
- 1-4-5
- 1-5-6-4
If you experiment a little bit with this, you will instantly recognize a lot of songs, although they might be pitched higher or lower.
One step further, is learning different chord fingerings: we started with 1-3-5 which mostly results in a major or minor chord in a mode.
- 5th chords are 1-5
- 7th chords are 1-3-5-7
- sus2 is 1-2-5
- sus4 is 1-4-5
- etc
Now, the next thing you need to learn is to transpose: move songs up or down one or more keys to the left or right, but also taking into account the black keys when moving up/down. This will allow you to play along with a song in the perfect key (starting note of a scale)
There's other things (like modulating modes in songs), but this should give you a headstart.
[1] https://youtu.be/g7oA1-y0EJE
Edit: layout and some extra clarification
Scale/size can seemingly be taught accessibly young... we just don't. Nor use size as an organizational frame to catalyze understanding of the physical world. Asking first-tier medical school graduate students how big red blood cells are... goes surprisingly poorly. But there seems lots of fun to be had.
Alpha, Bravo, Charlie, Delta, Echo, Foxtrot, Golf, Hotel, India, Juliet, Kilo, Lima, Mike, November, Oscar, Papa, Quebec, Romeo, Sierra, Tango, Uniform, Victor, Whiskey, X-ray, Yankee, Zulu
Gotta spell anything over a voice line? Use it. No more screwing around with "B.. like Bryan, and then U, like .... under". s-c-r-o-l-l-a-w-a-y: sierra charlie romeo oscar lima lima alpha whiskey alpha yankee.
I learned it when I was 14, and I genuinely used this a TON in the decade and half since.
This is why your manager believes that engineers are too conservative and always pad estimates, while projects are always late. Indeed, they can learn both these things from observation without realising that they are contradictory. Because humans learn by the most common observation, which is represented by the median, but outcomes can be dominated by the less common, which affect the mean but hardly affect the median.
In this physics thought experiment, a Boltzmann brain is a fully formed brain, complete with memories of a full human life in our universe, that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium. Theoretically, over an extremely large but not infinite amount of time, by sheer chance, atoms in a void could spontaneously come together in such a way as to assemble a functioning human brain. Like any brain in such circumstances (the hostile vacuum of space with no blood supply or body), it would almost immediately stop functioning and begin to deteriorate.
By one calculation, a Boltzmann brain would appear as a quantum fluctuation in the vacuum after a time interval of 10^10^50 years. This fluctuation can occur even in a true Minkowski vacuum (a flat spacetime vacuum lacking vacuum energy). Quantum mechanics heavily favors smaller fluctuations that "borrow" the least amount of energy from the vacuum. Typically, a quantum Boltzmann brain would suddenly appear from the vacuum (alongside an equivalent amount of virtual antimatter), remain only long enough to have a single coherent thought or observation, and then disappear into the vacuum as suddenly as it appeared. Such a brain is completely self-contained, and can never radiate energy out to infinity.
Sources:
https://en.wikipedia.org/wiki/Timeline_of_the_far_future https://en.wikipedia.org/wiki/Boltzmann_brain
Thanks for coming to my TED talk.
This is a legacy of the base 20 numerical system used by the Celtics thousands of years ago before the modern Romance language drove it out. The hybridization with our current base 10 system came with the Roman conquest of the Gaul.
Another example of the base 20 in use is the Quinze-Vingts National Ophthalmology Hospital in Paris, where Quinze-Vingts (fifteen twenties) refers to the original capacity of 15*20 = 300 beds available when built in the Middle Ages.
Example:
7-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1-4-2-1-4-2-1...
Any positive integer you take, you end up in a 1-4-2-1 loop.
It's not proved yet but there's no number found yet that satisfies otherwise. That's the Collatz Conjecture or the 3n+1 problem.
Probably the easiest conjecture to explain to someone.
Good day/night!
The cantata is a chorale cantata based on the Lutheran Hymn "Wachet auf, ruft uns die Stimme", the opening movement is a chorus that is based on this tune. The tune is in Bar form, the first 3 verses are repeated, followed by 6 verse which is sung once through (3x2 + 3x2), and Bach's chorus mirrors this structure. Bach decided to set the piece in E-flat, which is a key signature with 3 flats. He also decided to make the time signature 3/4, so each bar has 3 beats. There are 3 groups of musicians involved (not counting the obligatory basso continuo): 1) vocal forces, 3 parts (Soprano + Alto + Tenor, the bass mostly doubles the basso continuo and is not independent); 2) strings, 3 parts (violin 1 + violin 2 + viola); 3) winds, 3 parts (oboe 1 + oboe 2 + alto oboe). Also, the opening melody of the chorale outlines the 3 notes of the tonic triad of E-flat (E-flat, G, B-flat), while later on, Bach being Bach, there is a miniature fugato where the three lower voices open with the same 3 pitches in a different order (G, B-flat, E-flat).
I'm usual sceptical of most other numerological readings of Bach's music precisely because when Bach wished to make a point with numbers, he makes it damned obvious, as in this case.
$ mkdir hi
$ cd
https://www.hrw.org/reports/2001/prison/report.html
Caution: that’s hard, explicit, distressing reading.
Time is a straight arrow: call it t.
The guitarist plays, and their guitar pickup records a signal. At any time t, measure the value of this signal's waveform: call it x.
That signal can go into a pedal that maps each value to create an output signal. Call it f(x, t).
The pedal is a linear system when it satisfies f(x1 + x2, t) = f(x1, t) + f(x2, t). In English, you can blend two guitar signals going into a single linear pedal, and it will sound the same as if you used a separate pedal for each guitar.
The pedal is a time-invariant system when it satisfies f(x, t1) = f(x, t2). In English, a time-invariant pedal does not warble over time.
The magic happens when a system is both linear and time-invariant. These systems are so special, we call them "LTI" for short. Feed an LTI system a single, really loud, POP! Something like a clap, or a gunshot. Record the sound of this gunshot, and call it "impulse_response.wav". This file characterizes EVERYTHING about the system. If you know how the system responds to an impulse, you will know how the system responds to any other sound. All you have to do is convolve the sound with the impulse response, i.e. use the contents of impulse_response.wav as a set of weights and pass the sound through it.
The echoes you hear when you speak in a large room is a real-world example of an LTI system. People will go to a cathedral, an open field, or a large tunnel, set up a microphone, and fire a blank pistol. They can go home, convolve the sound of their guitar or voice or whatever with the impulse response, and it will sound exactly like they're in that space! There are whole communities of people making and sharing impulse responses out there, and I just think it's the coolest thing ever.
For any guitarists reading this, I'll bring this back to the pedalboard. Another cool thing about LTI systems is that when you chain multiple of them together, the order does not matter. Reverb, delay, EQ, and wah are all LTI effects. If you've ever wondered why pedal ordering sometimes matters and sometimes doesn't, this is why.
While many use "fact" and "factoid" interchangeably, they are (by original definition) inherently two entirely different things.
Did you know that time-travel is a modern concept but in the Indian scriptures, which dates back to thousands of years already mentioned about it. It is a story about King Kakudmi, who sought a husband for his beautiful daughter, Revati. They both had travel to Lord Bhrama's(Creator of the universe) place which was apparently very far from our planet to seek advice. Lord Bhrama then explains them that time moves very differently on his plane of existence and the people they knew on their planet are already dead as it's been 116 million years that has passed in last 20 minutes of Bhrama's time.
They then travel back to Earth after seeking the advice.
Hindu scriptures mentioned a lot of "modern-day concepts" thousands of years back. Isn't it fascinating?
Look at your choices and try to find an independent entity making a decision.
You will likely notice your conditioning and preferences, beliefs, emotions, thoughts, physiological and psychological state in the moment, your environment, habits, trauma patterns, all collaborating toward one thing or another.
“Free will” is a shortcut for all these forces we have mo control over. Even when we explicitly feel we’re in control - usually the goal this control serves is not in our control. We don’t choose our preferences, tastes, morality, desires, or thoughts.
Paradoxically, in this complete absence of “choice” as we understand it, lies freedom.
Double-clicking and dragging selects text word-by-word.
Triple-clicking selects the whole paragraph.
Middle-clicking a link opens it in a new tab.
Middle-clicking a tab closes it.
Middle-clicking in general often has useful functionality!
Nobody I've met even knows what they are. I came across them years ago in the shaving section, and was blown away by their utility.
They are solid pieces of some saltlike material that are super effective at stopping bleeding. We don't even have bandaids in our house anymore, the pencils are way more useful.
https://en.wikipedia.org/wiki/Molotov_bread_basket
In 1939, the Soviet Foreign Minister, Vyacheslav Molotov, claimed the Soviet Union was not dropping bombs on Finland, but merely airlifting food to starving Finns. The Finns sarcastically dubbed the RRAB-3 cluster bomb "Molotov's bread basket." Consequently, the improvised incendiary device that Finns used to counter Soviet tanks was named the "Molotov cocktail", "a drink to go with the food."
Oh, and neutron stars have mountains: height differences on their crust of a few centimeters or less. Scaling that height difference takes more energy than scaling Mount Everest. Gravity is weird.
(Armchair interest in astrophysics; this is roughly correct but I'm sure others can point out nuances better).
which actually converges because the norm has the negative of the exponent.
pari/gp has a native p-adic calculator, where you can type 1/2 + O(3^5) and get the first p-adic digits.
I don’t know why this impresses me, but it is probably because there are just two ways of extending the rationals, and the p-adic numbers are like the lesser known brothers of reals. I feel, I should have known this for ages. And no, I don’t know if there are known applications, outside number theory, but still, its cute.
Users with 100 or more followers can often be business owners, well known employees from FAANG companies and the like.
Users with 1000 or more followers tend to be specialists in lesser used technologies who have created open source technologies used widely in that specific domain.
Users with 10000 or more followers tend to be luminaries who have created technologies most people in the industry are familiar with, like say coffeescript.
[1]: https://github.com/andrewmcwattersandco/github-statistics
Solution:
- Bose QC 35
- Earplugs
Now the earplugs don't get pushed in and don't aggrevate the tinnitus. The bose QC 35 gets pushed onto whatever is directly outside your ear, which is a bit uncomfortable but fine.
This is my new earplugs setup and it works.
https://www.gillibrand.senate.gov/news/press/release/gillibr...
Soft disclosure has happened already via the USS Nimitz encounter. If UAPs are true, then the floodgates are open and will lead to a forced re-evaluation of other high strangeness phenomena (telepathy, ESP, etc).
(install with 'sudo install cw')
Extremely handy in rental cars.
Example: https://www.huffpost.com/entry/know-instantly-which-side-you...
https://planetary.s3.amazonaws.com/web/assets/pictures/20120...
Back in the 00's an Irish heritage group in Canada bought a chunk of land in Ontario and managed to get it designated as a Gaeltacht.
So officially, as of today, Irish is the common vernacular in several small-ish regions of Ireland and a .25km^2 chunk of Canada.
Bit more info here: https://en.m.wikipedia.org/wiki/Permanent_North_American_Gae...
This (particular type of broad) gauge is known as Irish gauge, and is also used in Ireland and Australia.
We can't simply just "move" to a different location like other animals.
Ctrl-T does the same in emacs, and also in readline based programs like bash, as well as everywhere on macOS.
Here is my favorite mental-model for problem solving (and my favorite analogy)
So I have this problem:
I love eating scramble eggs, I hate cleaning up the pan and have been trying over the years many different techniques to make sure the egg's doesn't stick to the pan. (No I don't want teflon thanks).
So I tried different oils, temperatures and techniques, all with the goal of getting those delicious eggs not to stick in my pot/pan afterwards.
Then one day it hit me, I'm solving the wrong problem. The problem to be solved is not "EGGS NOT STICKING TO PAN", it's "FINDING A BETTER WAY TO CLEAN" the pan !
And I have found it, it's using a different type of plastic-scrubber. It looks like steel-wool, but it's all plastic.
So whenever I'm stuck on a problem for too long, I try and model the problem as an "eggs-in-pan" problem statement.
sin(30) = sqrt(1)/2.
sin(45) = sqrt(2)/2.
sin(60) = sqrt(3)/2.
sin(90) = sqrt(4)/2.
You probably knew all of those, but may not have seen it set out in this fashion before.
I'm 40 and overlap with all of the 100 verified oldest women and 100 oldest men, save for one.
On Linux, you can usually left-click-drag-release to highlight some text, move your mouse cursor to a new location (in any window), and middle-click once to paste the text you highlighted there. No explicit keyboard or right-click copy and paste required.
At this point, AWS has updated the API to allow querying for the region as one would expect. See my answer on the afore-footnoted question[2].
[1] The number and variety of answers on the topic is both hilarious and terrifying: https://stackoverflow.com/q/4249488
I personally cannot deal with the alt tab style switching between all windows this app to app switch works much better for me and I use it constantly.
One workflow is to git clone mirror the main repo and use that as a shared read-only source of historical references when cloning a new repo. You can also hardlink or reference those objects to save disk space (though some file systems will do that transparently for you).
It feels like this could be done entirely transparently to the user, for a free speed boost but it's not quite there yet and still needs some thought and setup. Some big services use this behind the scenes though so it's presumably robust.
So worth looking into if you are spending time waiting for clones.
The word derives from the Venetian phrase "s-ciào vostro" or "s-ciào" (schiavo/sciavo) literally meaning "(I am) your slave"
This greeting is analogous to the medieval Latin servus which is still used colloquially in parts of Central/Eastern Europe or the antiquated English valediction "Your Obedient Servant." https://en.wikipedia.org/wiki/Ciao
In Italy you say ciao both when you meet somebody, and when you leave, while in other countries (e.g. Brazil), you say "Ciao" only when you go away: if you use it when you meet somebody sounds sooooo weird :) :)
It will relaunch the last command you used with sudo before. Example:
$ apt upgrade Could not open lock file ... $ sudo !! sudo apt upgrade [sudo] password for ...:
Betty White was born before Anne Frank.
These times we are living in are not the most important. Or, of they are, then everyone everywhere is at everytime living at the same importance.
Now, there is something called the hinge of history that some mathematicians have looked into the chance of "well right now is most important, people in the past and future are delusional". The chances are very very low.
Think of this the next time you hear someone appeal to urgency as political motivation.
A wonderful nostalgic way to play the game.
This means that we are not simply connected to the past by cause and effect -- we're also coupled to the future. For any specific end to come about, our experiences must be constrained.
In differential equations, we use the boundary conditions to solve for the dynamical behavior in the time interval between them.
In analysis, we use the existing conditions in a process called 'analytic continuation' to recover the whole process.
In fractals or the physical theories surrounding them (AdS/CFT correspondence), the boundary determines the bulk. So if you have only the frame/margins of an M.C Escher tesselation, the entire inside foreground (the bulk) can be recovered by gradually painting in what's missing.
So we are more of a continuation of both the past and the future than simply a remnant of the past.
While the past may have pushed us, the future attracts us.
We must recognize that war is common, strife is justice, and all things happen according to strife and necessity. War is father of all and king of all; and some he manifested as gods, some as men; some he made slaves, some free.
Conflicting powers of opposites, including those of elemental bodies, make possible the world and all its variety; without that conflict we would have only lifeless uniformity."
http://dtrace.org/blogs/wesolows/2014/04/10/libsunw_ssl-or-h...
Humans look symmetric on the outside but have stark asymmetries on the inside Thus, we have a spleen on the left but not the right. Our left lung has two lobes, but our right lung has three. Our heart and stomach are shifted left of center, our liver is shifted right of center, and our intestines meander throughout our abdominal cavity with no regard for the midline at all.
https://www.cambridge.org/core/books/abs/quirks-of-human-ana...
1. "cat foo.json | python -m json.tool" pretty print on console.
2. "cal" pretty prints current month on console. "cal 2022" pretty print current year.
> interesting to you
1. Bank of England one of the earliest banks to issue paper money was establish to finance war expenditure.
2. Federal reserve is holding (and hence funding) ~$2.7T worth of mortgage backed securities[1]. It started out as a stop gap measure to cushion 2008 crisis but they are yet to discontinue it.
1. Other than a gag mannequin or few.
This image is taken from the wikipedia article mentioned below. https://en.wikipedia.org/wiki/File:EarthsOrbit_en.png
$ awk 'BEGIN {srand(); t = srand() ; print t}'
1651247949
1. srand if not provided with a seed will use the current unix epoch as seed
2. srand will return its previous seed in a new initialization (and we assign it to t)
3. we print t
I learned this via a "Systems we love" talk (https://www.youtube.com/watch?v=IfhMUed9RSE)
I find this community very knowledgeable, smart and down to earth. It was impressive to see a 40+ year old body builder (he is no Arnold, but has impressive physique for an amateur) doing so well on this diet.
If someone is interested, spend some time googling this topic. It is well worth your time.
Addie Joss threw the fourth perfect game in MLB history, in 1908.
If you use Spotlight search to look up a word in dictionary, you need to hit down arrow repeatedly to select the word, or click on the word. Instead, you can:
- Command + L to jump to the word
- Command + D to open Dictionary app with that word
If you'd known this, you'd have given some idea of your background. Therefore, the above is the only thing that we can know is new to you. :P
https://www.unitedbsd.com/d/308-moritz-systems-bsd-tips-and-...
You often hear that it was next to impossible to calculate with Roman numerals. That's not true at all. People developed a very ingenious scheme to do additions and multiplications using pebbles. Since the word for pebble in Latin is calculus, we now call calculus calculus.
How did it go? You represented the digits of a number by a pebble. You drew some lines in the sand, some rows and columns. The rows represented the digit magnitude (I, V, X, etc). The columns were for the operands. Two columns for a number. Why two? Because Roman numerals sometimes use negative digits.
Let's see a concrete example. You want to do the addition 28+44. That is XXVIII + XLIV.
You first draw the lines and put the pebbles in the corresponding squares. Note that XLIV has two negative digits (44 = XLIV = -10 + 50 -1 + 5). So the pebble for 10 and the one for 1 are put on the left side.
The first number does not have any negative digits, so no pebbles in its left column.
———————————————————————————————
L | || | o
X | oo || o |
———————————————————————————————
V | o || | o
I | ooo || o |
———————————————————————————————
———————————————————————————————
L | || | o
X | o || |
———————————————————————————————
V | o || | o
I | oo || |
———————————————————————————————
Now we just move the pebbles from the fourth column to the second column.
———————————————————————————————
L | o || |
X | o || |
———————————————————————————————
V | oo || |
I | oo || |
———————————————————————————————
————————————————
L | o ||
X | oo ||
————————————————
V | ||
I | oo ||
————————————————
Multiplication can be also performed, and it's quite a lot of fun. I'll explain it in the post below.
Let me describe what I mean.
When we want to describe a structure, for example the natural numbers with their usual arithmetic (addition, multiplication and so on), we first decide on a language to use. Our language should contain the symbol 0 (so we can identify the first element) and symbols for the functions S (successor function), + and *. We also introduce variables such as x, y, etc.
Then we write down a list of axioms for the structure, i.e. logical statements that should characterise that structure. Such statements in first order logic are built out of the symbols we introduced, together with equality (e.g. 2+3=5 is a statement, where 2 is an abbreviation for S(S(0)) etc.), logical connectives such as "not", "and", "or", "implies", etc. (e.g. not(1 = 2), or "1 = 1 AND 2 = 2") and importantly quantifiers, "for all elements" and "there exists an element such that" (for example: "for all x, x = 0 OR there exists a y, such that x = S(y)").
A structure for a specific language is nothing more than a set of elements together with an interpretation for all the symbols. So, for our language we may just take the natural numbers with the usual interpretation of +, * etc. But we might just as well have chosen the single-element set {aardvark}, where 0 is interpreted as aardvark and all functions evaluate to aardvard no matter their arguments, i.e. aardvark + aardvark = aardvark. That's silly, but allowed. The natural numbers with their usual interpretation of symbols satisfy all the sentences I introduced above; we say that this structure is a model of that set of sentences. Our aardvark-structure is not a model of these sentences, since not(1 = 2) is not true in it (remember that this is just an abbrevation of not(S(0) = S(S(0))) and in this structure, this evaluates to not(aardvark = aardvark), which is false).
We can now take the set of all statements which are true in the natural numbers, a.k.a. the theory of natural numbers, Th(N). This set is clearly infinite (for example, it contains the statement "n = n" for all n), but that doesn't bother us. Clearly, the natural numbers are a model of Th(N). But are there other models of Th(N)?
Well, in a sense trivially. I can just define the structure {aardvark0, aardvark1, ...} where, for example, aardvark2 + aardvark3 = aardvark5, and so on. That's also a model for Th(N), but if that feels like cheating it's because it is: these structures are exactly the same except for the names of their elements. We therefore call them "isomorphic" and treat them as the same.
But are there models of Th(N) not isomorphic to the natural numbers? Yes, there are.
Let's introduce a new symbol to the language, call it c. Then add to Th(N) the infinitely many statements not(0 = c), not(1 = c), not(2 = c), etc. There is no way we can interpret this symbol c in the natural numbers and make all these statements true: eventually there has to be some natural number which c is equal to.
But now comes the kicker: By the compactness theorem of first order logic, whenever we have a set of sentences so that all finite subsets have a model, the original set has a model. Now, for any finite subset of Th(N) plus the infinitely many statements involving c, we have a model, namely the natural numbers (since the subset is finite, there is a biggest n for which not(n = c) is in the set of statements; then interpret c as n+1). But then, by compactness, the original set of sentences has a model.
So there must exist a structure that makes all statements true that are true for the natural languages (i.e. that is a model for Th(N)), but that also has some element c that is bigger than anything that can be "reached" by applying the successor function arbitrarily often to 0. What does such a structure look like? Well, it turns out that such an element must live in a so called Z-chain, a set of elements that "looks like the (positive and nonnegative) integers", but is totally disconnected from the natural numbers (this is because in Th(N) every number that is not zero has a successor and a predecessor); so in essence this structure contains the natural number and, disconnected from it, a copy of the integers. In fact, we may have more than one copy of the integers.
Compactness is a really powerful and weird theorem. It can be used to prove that any set of statements that allows for infinite models has infinite models of arbitrary cardinality (i.e. "as big as we want"). It can be used to construct an extension of the real numbers that contains "infinitesimal", non-zero elements (smaller than any positive real number), which is what motivated so-called nonstandard analysis (and makes Newton's and Leibniz's original intuition of "infinitesimally small quantities" precise). And so on.
If we want to actually describe the natural numbers uniquely, we have to turn to a stronger logic, such as second-order logic. In second-order logic we can't only quantify over elements, we can also quantify over sets (or, equivalently, properties). We may for example say "for any set, if it is not empty, it has a least element" (a statement that is true for the natural numbers if we introduce the usual ordering). We can then in second-order logic formulate the principle of induction, which suffices, with some other axioms, to describe the natural numbers uniquely (up to isomorphism, of course).
However, second-order logic has significant downsides. In particular, there exists no proof procedure in second-order logic that is both sound (it only proves true statements) and complete (it can prove all true statements). That means that, in practice, it's often not all that useful. We do have well-behaved proof procedures for first-order logic and that's why we usually stick to it.
Relatedly, in central and south America, _sapote_ is the native american term for (roughly) "edible fruit". The word has nothing to do with the taxonomy of these plants. European colonists made the mistake of adopting the word "sapote" for various different tree species ("what's this called?"; "sapote"), which has led to a lot of subsequent misunderstanding. If you google for "sapote" you'll find some results which naively attempt to give a latin classification to the unqualified "sapote". Now we have fairly useless english names for a variety of these regional fruits, such as (read "sapote" as "edible fruit" in these examples): "green sapote", "white sapote", "black sapote", "yellow sapote", "sun sapote", "south american sapote", and so on - although many of them also have more distinctive names (such as "canistel" or "chupa chupa"), which are much less ambiguous and should be preferred.
The company United Fruit was formed by the merger of two companies in 1899. One half of the merger was originally founded by an american railwayman, who obtained a 99 year lease of 800,000 acres of land from the Costa Rican government in exchange for constructing and operating a railway from the capital city to the carribean port of Limon (during the construction of which, thousands of laborers died from tropical disease). Once the railway started operating, usage was insufficient to pay back the debt on the loans that he'd taken out for construction, and so he pivoted to banana exports; the story goes that he had planted bananas along the tracks during construction as a cheap means of feeding his workers (which doesn't quite make sense given that bananas take 14+ months to fruit), and so he doubled down by increasing the density of planting over the area of the land that he owned, of course clearing more primary tropical forest to do so. The United Fruit company (today Chiquita) became heavily involved in politics in the countries that it was operating in, with the most famous example being its significant role in instigating the CIA backed coup in Guatamala in the 1950s that overturned the democratic government and installed a violent dictatorship, and led to 4 decades of civil war in which at least 140k people died, and which set Guatemalan economic development back by decades or more. So yeah, bananas.
Oh, and finally, there are dozens of varieties of bananas. The one that's exported most commonly (Cavendish) is relatively large and travels well, but is far from the most flavorful. There have been rumors of a killer fungus for many years, which hasn't had a significant impact on availability (yet); however, there are many varieties of bananas that aren't impacted by this fungus, so in the next decade or two we could see one of the other varieties replace Cavendish as the most widely consumed.
* your neurons are not in your "brain" 90% of your neurons are not in what you generally denote by brain. They are in your cerebellum. The cerebellum has a distinct neural architecture, that difference is in fact clearly visible with the najed eye. A very poor simplistification would be to call it our GPU.
* the spinal cord is huge and is structurally a contiguous extension of your brain.
* your brain is mostly not filled with blood but with the transparent cerebrospinal fluid Btw there is a liquid almost twice as much more present in the human body than blood, the white lymph. It's unclear to me why we don't see lymph on dissected bodies. (possibly because of microvascularisation?) also anyone know how is lymph pumped? I don't think the heart pump lymph so is it stagnant?
* opiods,nicotine, and cannabinoids are endogenous neuroreceptors. They have the name of exogenous drugs because it happens they bind on those ligands but that also means that the brain generate similar but slightly different analogues itself.
* in terms of neurotransmitter s, types of receptors and even patterns of activation of brain regions per stimulus, humans are not much different from rats or other mammals and this apply for surprisingly high levels cognitive tasks such as e.g ADHD.
* the problem of consciousness/qualias If qualias are supraphysical then how can it be created from a physical process? Moreover where are you?! Where are you qualias located in your brain? And more remarquably, how many are you? Our two hemispheres are highly (but not that much though) symmetric, we might have one consciousness per hemisphere. Or not? But then what about those people that have their hemispheres crosstalk surgically cut? They behave normally (mostly), and have two independent brains. However the best proof might be e.g dolphins, which have a mono-hemispheric alternating sleep. So if one hemisphere dream, the other day it's the other hemisphere. Hence two distinct qualiesque brain in one dolphin brain.
These are called Rydberg atoms and exist because the electon bound to the nucleus of the these atoms has climbed up to very high excitation levels, a state that is very unstable as any collision with another particle or interaction with electromagnetic fields will cause it to collapse down to lower energy levels. The extreme emptiness of interstellar space allows such atoms to persist for long periods.
The density of interstellar hydrogen clouds is much lower than what can be achieved with the best vacuum systems on Earth, but laser cooling techniques have now made the production and maintenance of such atoms possible, to the point where they can be used as delicate sensors, and have possible applications in quantum computing.
It was a picture of a tree, and it took eight hours to expose.
Cancer? PNC-27 + thymalin
Ageing? Skq1 + Epitalon
Quantum gravity? https://arxiv.org/pdf/gr-qc/9706055.pdf