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A one-of-a-kind oasis of intelligent, in-depth, productive, civil debate.

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Use this forum to discuss the philosophy of science. Philosophy of science deals with the assumptions, foundations, and implications of science.
By Cathal
#471330
"In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions... After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles and formally published in 1995."

I tried to analyse Fermat's Last Theorem in terms of visual perspective as if one big cube could perfectly block out both smaller cubes in the background much like you were observing cubed houses from a hilltop. I thought momentarily that you could somehow reshape one little cube into a rectangular cuboid to attach to another big cube to form an even bigger rectangular cuboid somehow equating to a huge cube. Then the semantics of the argument stung seeing as if a cube and a cube is equal to a rectangular cuboid then it couldn't sum to a cube much like a triangle and a triangle forming a square being largely unrelated to the initial triangular shapes. In other words the answer wasn't capable of being a precise cube value from many cube values if it wasn't even a cube to begin with! Needless to say I never fully read the mathematical small print in Fermat's Last Theorem to fully analyse the question when I first saw the numerical equation years ago! It'd be like you'd merely the wrong cube solution much like a decimal or fraction sized cube not equal to a full number as would've occurred with visual contraction from depth perception. Or perhaps if we use quantum planck lengths then could you derive two even shaped cubes matching an uneven cube but perhaps this might be cheating as if you could spread out a cube into surface area?! Maybe smoothing out a rectangular cuboid as much as possible to almost remould it into a cube might resemble a fake number 12 duodecimal scale! I thought it'd be easy enough to weld one cube superficially around another to make a second cube only that this might have a deficient quantity were we dealing with truly large numbers!

In a Vsauce spherical mirror youtube video it was mentioned how a mirror ironically halves the size of all objects in a way that appears invisible much like warping a horizontal landscape photo into a vertical portrait photo. Then to get even more mystifying would a mirror reflecting off a mirror much like an infinity mirror room present all objects as being 1/4 or an exponent less the size of the original mirror as a half-sized mirror of a half-sized mirror in spite of it still appearing the same size? Then it's not only your own visual depth perspective contracting a far away object in a recursive mirror in a mirror but also a recursive mirror in a mirror somehow mimicking the same process in itself. This might be spooky like those Russian dolls fitting inside of each other! So maybe is it your brain that enlarges your own reflection in the mirror instead of the mirror hiding your miniaturised reflection as if conscious visual perspective works by magnification rather than demagnification? In other words might a robot or an animal actually see a self-reflection off a mirror half their own size in external reality? Were we living in a mirror reality then if an object you see directly is half its actual size while a reflected image of the object is also half its size then what gives other than the perimeter of a small mirror itself contracting and expanding under depth perspective? So if you looked at an object moving back and forth with a monocular scope and ignored the background then the object might always be the same size under visual perspective. Then much like the quantum uncertainty principle the moment you look at the background then the foreground object has somehow reduced in size not in itself but in relation to the increasing amount of the background you can see in your near-peripheral vision as the object moves further away. An easier way to think of this might be if your vision were like a cinema projection in your brain with less resolution than your eyes as if the image is being dispersed thinner as it expands in such away that every object you see is actually magnified without a need for depth perspective being real. So if you look at your hand moving closer to the mirror with alternating and intermittent glances at the reflected image in the mirror you can focus on how the reflected image of your hand is apparently getting bigger instead of smaller.
Benny Benassi ft. Gary Go - Cinema

Does one equilateral pyramid and another equilateral pyramid equal the size of a larger equilateral pyramid or is the result just a cube or a diamond? The ancient Egyptians might never forgive us!
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3 Giza pyramids

Even if we ignored Christianity then America makes the argument that if everyone in ancient Rome had converted to bows and arrows and capitalism then they wouldn't have been evil. Yet with all other forms of amoral or immoral porn genres from bestiality to naturism then a limitation is we could stress test this line of logic further if ancient Egypt would've been less evil under such circumstances had we time travelled back to offer such advice to make everyone more blasé and less hostile with public sex acts! So if everyone were truly serious then we could possibly afford to indulge in such amoral porn genres but perhaps the clue with divine judgement is that we're not always self-aware enough to know where we lacked of intelligence such that a sexually frustrated society 1000 years in the future might not judge us as kindly as we thought were we as expendable as ancient Egypt! I'm sure I could comment more about the mathematics of Fermat's last theorem but my head is too dizzy either from the technicalities or from the temptations of amoral porn!
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Kissing sphinx perspective illusion
Attachments
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By Cathal
#471333
Reconciling quantum mechanics with general relativity might be helpful in reconciling short-sighted vision with far-sighted people! So a far sighted person would have blurrier central vision for closer magnified objects and more vivid peripheral vision for smaller and more compact distant objects oddly enough were it an intentional ailment! It’d be like your brain can’t concentrate hard enough in such a way that your eyes have better vision so to speak than your brain.
By Cathal
#471334
A dualistic way to think of a closer object being more sparse in light intensity in spite of being magnified against the background might be how looking at a star in the night sky with your naked eye can be unknowable in intensity as if you weren’t practiced enough to analyse how concentrated the light might have been.

Mr. Fox doesn’t think much of my science theories or my eyesight on my late night stroll!
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There’s no limit to how long you could spend looking at the night sky like the grey heron outside my tennis club!
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By Cathal
#471358
A dualistic way to view a refraction telescope is if the light ways reversed direction then the image of a planet is expanding and diluting rather than contracting inside a telescope.
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A probability argument for my rash maths argument in the opening post is if there were an infinite number of fractional cube sums then the chances of finding an integer cube sum becomes increasingly unlikely the larger the numbers involved. Yet this intuition might be insufficient for supercomputers needing perfect cubes!
By Cathal
#471367
Humility and the problem of evil can be paradoxically intertwined in the sense that you’ve already to be very skilled to better understand someone stronger than you or else you’d soon forget them in light of how unrelatable their superior strength is. Hence you’re not necessarily very proud to be very overconfident in a way that mimics the problem of evil in how sarcastic someone could appear! So as I’m approaching age 30 in May I can actually identify how fast certain serves are from lower ranked professionals on youtube in a way that was previously downplayed. Yet the way I’m now more humble can be very slight seeing as I’d have to consent that I’m almost capable of mimicking the lowest baseline standard of their serves to half make sense of them in a way that both creates and tames tantalisation. The painting mimicking the snowy summit of Mt Kilimanjaro below was hanging up in my parents sitting room for years without me paying much attention only for it recently to make more sense after I tried a few small paintings of my own in prior months. I noticed the light blue mirage under the mountain as if it were one simple stroke with a wide paint brush. By contrast in prior years I dismissed the height of the mountain as if they were merely abstract clouds as an abstract feature rather than focusing on the light blue underneath. Then I noticed the yellow huts seemed brighter than before as if there was lots of glare from the Sun. So unlike a song a painting can take years to make sense and become more immersive as if it were a stealthy exorcism against megalomania in your own visual perception when it could take months for a painter to create the painting without it being immediately apparent.
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By Cathal
#471378
A limitation of the problem of what its like to be a bat is that even if you explained to a lion exactly what it feels like to be a zebra than the lion would still hunt the zebra! That way the hard problem of consciousness is interconnected with the problem of evil.

[yid=FpekkNyDPcc&pp][\yid]
Madagascar (2005) - Alex Goes Crazy Scene (7/10) (bite)
By Cathal
#471385
The way I live in a large town of Ennis in Ireland is like being caught between a rock and a hard place whenever I travel to rural villages and big cities. One reason humility is hard to detect emotionally is that it can be circular as if a rural person was originally megalomaniacal but ended up so irrelevant that they immediately appear humble while a city person tried to be the most humble living among so many others only for them all to be more successful leading to a temptation for chauvinism in such a way a city can appear too proud in hating the countryside! As a child I always remember Dublin city appearing huge only for the city to appear slightly smaller these days as if there’s a risk that if no one actually cared about living in a city then there was a risk of there being no foundation such that each historical street is at risk of appearing dilapidated rather than self-deprecating! That way humility can be so stealthy that it can mostly be a spiritual rather than emotional quality. So I notice if I’m playing with a new tennis grip then when I travel to Limerick city then the background can feel more hectic as if the way I’m secretly defined as irrelevant by defensive pedestrians rather than just being ignored becomes almost paranormal in a relativistic fashion such that a new information learned is forced to justify itself or be consigned to the bin! Hence it’s as if a new tennis grip can fathom other strangers slightly differently where a new grip defines itself as irrelevant only if its learned off perfectly! So when it comes to studying academia in the third world then who knows whether we focus too much on how intelligent Shakespeare was and not enough on how nice he might have been to be less relevant in his own era to have spoken so seriously!
By Cathal
#471451
2^{3}+3^{3}=35
cubed root of 35= 3.27106631 (millimeters still relevant for an ant crawling along a multidimensional leaf like those string theorists!)

A limitation of communism during the Cold War was trying to accurately price goods without a competitive customer market. As such when it comes to pure maths we don't always know how valuable an arithmetic technique is when the likes of the number 0 in algebraic form truly took hold only in the 7th century AD after multiple people spent their lives investigating the concept of nothingness. As such the sentimental quality of a cubed root function might be unquantifiable were it not for the centuries long search for Fermat's Last Theorem were we ever bereft of a calculator in a desert!
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https://www. history. com/news/who-invented-the-zero (external links not allowed apparently)

"The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this and crediting it to himself instead of Pythagoras which was the norm in Pythagorean society." wiki
By Cathal
#471452
A potential application of Fermat's Last Theorem might be in virtual reality as if you could have a number line with an infinite sequence of cubed values and then another infinite sequence of square values in order to translate and foreshorten the third dimension into the second dimension.
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By Cathal
#471525
Over half a year after first suffering tinnitus in my right ear I can gently hallucinate visual imagery much like the shifting of the tinnitus from my inner to outer ear functioned like a photocopier scan. Were we to think of the brain like a holistic photocopier then perhaps each individual neuron could contain your entire psyche but with a different emphasis as if each neuron simply copied and pasted all the information from the afferent neutron which comes from the sense organ to the brain. It'd be like each neuron would be a rarefied genetic clone of you in the nucleus of the neuron that overlaps with other neurons serving to make your conscious mind denser like an infinity mirror room. The way in which the rare and brief hallucinations during the day aren't too jarring is not only because of prior focus on dreams but also because in the months immediately after an accidental knife scrape off a plate I was able to gradually pre-empt the onset of visual hallucinations by deflecting vivid waking imagery with educational information from new tennis techniques to new songs as a reference point for complexity as a contrast with my inner psyche. In other words if my subconscious ever went against my conscious desires then I could ignore any visual hallucination in the next few moments that failed to match a new technique I was practicing on as a form of re-enforcement and creativity. I could counteract one hallucinatory ear worm song in one genre with a completely different genre afterwards to limit my addiction. So much like a physical illness like cancer the earlier you detect a mental illness the more time you have to limit and guide chaos theory in your own thinking style. That way when I could vividly picturise bits and pieces of the Titanic movie after watching it earlier today I could collide it with failed attempts to intermittently hear the song "snakeblood" by leftfield in Leornado DiCaprio's other movie "The Beach". So the way I could only rhyme the beginning of the song in inner mind but not the ending verse served as a limit for how ingenious I could have been to have the Titanic sink in my photographic memory. A caveat is that were I actually God then perhaps I wouldn't even need to feel the cold when I hallucinated the water gush into the ship!
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Titanic - Jack and Rose hold barriers as ship sinks
By Cathal
#471551
"Pointillism is a technique of painting in which small, distinct dots of color are applied in patterns to form an image."
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GEORGES SEURAT, UN DIMANCHE APRÈS-MIDI À L'ÎLE DE LA GRANDE JATTE, 1884-86.

Pointillistic paintings tries to square the circle quite literally between realist and impressionist paintings that often both use straight or curved lines off a paintbrush. Pointillistic paintings often take years to paint and the apparent underachievement and lack of vividness of such paintings might be where the pun lies. Unlike impressionist paintings the pointillistic paintings are much more coercive in your visual attention in a way that might prove beneficial for artificial intelligence. As I watched the Titanic movie yesterday I was stunned by how much more vivid the colours appeared than more recent movies in spite of it being an old 90s movie simply by giving you more time to focus on the colours rather than the colours. literally being more graphic. It's as if the eyes of an artificially intelligent computer would need more diverse colour pixels not to make the visuals better but to actually make the visuals worse in artificially creating a blurrier peripheral vision as if to slow down light even further in their eye for analysis.

Maybe one reason I partially forget some of my lucid dreams isn't always that the dream is more extreme than me but the other way round too as if my own faith system is more extreme than a lucid dream in such a way that the lucid dream is a warning against me being more rather less extreme. In other words it can be all too easy consciously pick the most extreme reference points immediately such that a lucid dream can tell you to be more moderate when we're not fully self-aware of our own spiritual faith system. So the way I can't fully remember my lucid dream years back of the uncanny valley is that my own perception of consciousness being 2-dimensional is actually more extreme than tactile 3-dimensional colours with invisible 2 dimensional internal light in the uncanny valley dream. The way there was no apparent solar system or skyline in the shopping centre of the uncanny valley dream resembled a thought experiment to explain why few people have an intuitive understanding of Newtonian mechanics to fathom the chaos of Einstein's gravity imbuing less determinism in day to day life.
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Titanic exit off port

"Realism portrayed the cold truth of the world while Impressionism favored the more frivolous and ethereal elements of life. Impressionist art used unblended, fragmented, broad brushstrokes to depict contemporary scenes of modern life."
By Cathal
#471658
One way to compare a visual hallucination during the day with your dreams might be to think of a mental image as travelling at light speed way faster than the speed of sound for your own thinking mind to have little reaction time to deflect or emphasise a visual hallucination.
By Cathal
#471716
Years back in other threads I mentioned about trying to figure out the value of inverse Newtonian mechanics as if seconds per metre rather than metres per second were used. I figured that if there were ever going to be a theory of quantum gravity then not only would quantum mechanics be easier but so too would there be cheat codes at the back of the book for Newton’s laws of motion due to a mutual equivalence between classical mechanics and quantum mechanics. So this morning I was thinking a close analogy to a s/m would be bullet drop as if you focused more on the horizontal “i” direction and less on the vertical “j” direction for assessing displacements on ball throws. So one way to think of it is if the vertical j component was somehow super-deterministic much like the recoil of cannon repelling upwards and not just backwards. That way the speed of the ball is intrinsically connected to the diagonal height as if to hit further you actually had to hit upwards as if the height were an epiphenomenon. Somehow then you could theoretically ignore the accidental upward height trajectory and focus only on the forward “i” trajectory along with the downward gravity component. It’d be as if gravity decelerates the ball toss immediately rather than just after the peak height.
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“That upward launch angle can be accounted for, but a simpler case to analyze is when there is initially horizontal flight. If a bullet is fired horizontally (no upward angle), and another bullet is dropped at exactly the same time from the same height, they will both hit the ground at exactly the same time! Gravity is pulling on both at exactly the same rate, regardless of the initial launch angle, but the case where it’s fired horizontally is easier to understand and calculate.”
https:// selectfiretrainingcenter. com/bullet-drop/
By Cathal
#471717
Tom Hanks joked on Saving Private Ryan’s filming review how he suggested the camera be placed on the artillery shell falling down on the victims to see their faces before the explosion! This would mimic the quantum observer effect as if a bullet could be embodied by placing a camera on it in terms of s/m inverse mechanics. Bullet drop on an upward grenade throw would be like measuring the descending visual angle from the initial throwing point rather than the mathematical formulae. One example of determinism might be how the ball might keep bouncing an equal distance after the landing in terms of the co-efficient of restitution compared to a lower trajectory when we think of the conservation of energy were we to play catch on ice! When we throw a ball we might not be self-aware of how much harder it is to throw upwards rather than horizontally were our muscles not always under the pull of gravity.
By Cathal
#471718
There are limits to embodying large classical objects compared to quantum objects without playing God!
[\yid]
LOTR Gothmog versus large projectiles (Return of the King)

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