>Where are the physical limits? According to Bremermann (1982), a computer of 1 kg of mass and 1 liter of volume can execute at most 1051 operations per second on at most 1032 bits. The trend above will hit the Bremermann limit roughly 25 decades after Z3, circa 2200. However, since there are only 2 x 1030 kg of mass in the solar system, the trend is bound to break within a few centuries, since the speed of light will greatly limit the acquisition of additional mass
They shift from talking about the transistor density to somehow considering a supermassive construct. Reminds me of LLM mashups.
It's a natural extension of the ideas being discussed - the limit in computation per gram of mass has energetic bounds, as well, with configurations nearing the upper limit that start looking more like nuclear explosions than anything we'd regard as structured computation. The extremes are amazing to consider - things that look and act like stars, but are fantastically precise Turing machines, and so on.
It's a theme that sci-fi authors have explored deeply. Accelerando is a particularly fun and worthwhile read if you haven't already!
> The naive extrapolation of this exponential trend predicts that the 21st century will see cheap computers with a thousand times the raw computational power of all human brains combined
i.e. putting an upper bound on the exponential with solar system mass
Yeah at work I’m paid to own some components that I didn’t write and don’t entirely understand, so I figure my job is to help discover answers for the questions that arise.
I would not want to be a public maintainer though. I don’t have the patience or motivation to use my spare time for that.
Cipher and "Arabic" numerals are not just loan words, they are loan concepts - from India. They originated from ancient India, because the Arabs adopted and translated those ideas and texts from the original texts written by ancient Indians/Hindus.
Fact - Origin of Numerals and Mathematical Zero:
Mathematical zero and numerals were not discovered/invented by the Arabs. There is no such thing as "Arabic" numerals because the Arabs did NOT invent numerals or cipher (to represent emptiness and/or mathematical zero).
The Arabs learnt the concept & use of mathematical zero, numerals, decimal system, complex mathematical calculations (including the subjects we call today as Algebra, Calculus, Trignometry), etc. from the ancient Hindus/Indians. And from the Arabs, the Europeans learnt it all.
Persian scholar Al Khwarizmi translated and used the Hindu/Indian numerals (including concept of mathematical zero) and "Sulba Sutras" (Hindu/Indian methods of mathematical problem solving) into the text Al-Jabr, which the Europeans translated as "Algebra" (yup, that branch of mathematics that all schoolkids worldwide learn from kindergarten).
Origin trivia: Originating from the Sanskrit word for zero शून्य (śuṇya), via the Arabic word صفر (ṣifr), the word "cipher" spread to Europe as part of the Arabic numeral system during the Middle Ages.
https://www.etymonline.com/word/cipher
Fun fact: The Sanskrit word for mathematical zero and emptiness/voidness is the same: Shunya (शून्य). In fact, mathematicians are of the opinion that ancient Indians were among the first to understand the concept of mathematical zero because they understood the meaning of empty/void (Shunyata). Dhyana (meditation by focusing on voidness/stillness, away from random intrusive thoughts) is an aspect of Yoga (world's oldest active fitness discipline).
Another fun fact: The world's oldest recorded cipher (as an example of cryptography/ encryption) is the ancient Indian epic Ramayana by Maharshi Valmiki. It has 24000 verses (Sanskrit shlokas), and the first syllable (akshara) of each 1000th verse/shloka forms a series of 24 syllables that form the sacred Sri Gayatri Mantra.
Proofs of oldest records mathematical zero being of Indian origin, are available..
Bakhshali manuscript (stored in Oxford) from ancient India/Bharat - is the world's oldest text having Mathematical Zero and equations.
World should know the vital mathematical concepts & representations of numerals, decimal system, binary system, algebra, calculus, trigonometry, etc. we know and use today are originated from Indian/Hindu texts and scholars.
Both Isaac Newton and Gottfried Leibniz claimed to be The Father of Calculus, but reality is that they likely learnt it from maths-savvy Jesuit missionaries who themselves simply carried the knowledge of Calculus to Europe from its source: The Kerala School of Mathematics from Malabar, India.
Wikipedia used to mention that the "Arabic" numerals are originated from "Hindu" numerals, but I see that origin has been removed from Wikipedia. It is sad when historical truths are hidden from the world, and mistruths are propagated instead.
By the way, Tamil and Sanskrit are the oldest extant (active) languages in the world.
While the use of zero and of the positional writing system for numbers have become widespread in Europe after taking them from the Arabs, which had previously taken them from India, these were already known in the Ancient World, both in Ancient Greece and even earlier in Assyria and Babylonia.
However, in the Ancient World the use of zero and positional numbers was restricted to some special applications, e.g. in astronomical tables, and it was unknown for most of the people.
The most novel feature of the Indian system was the application of the positional principle to decimal numbers, instead of sexagesimal numbers, and not the use of zero, which did not differ much from how it was used earlier.
The most novel feature of the Indian numerals is the use of the rounded zero symbol for the mathematical zero, so we all know it so well.
The Indian numerals also covered all the basic numeral digits and fit perfectly into the decimal system (which was also invented by the ancient Indians - they primarily used it for measuring weights, especially for currency/trade). The word meter/metre (from Sanskrit "miti") is also of Indian origin. The mathematical zero also fits in perfectly with binary system, also an ancient Indian invention.
The ancient Babylonians did use a dot/period as symbol of zero, but there is no information on whether they also associated zero with voidness/emptiness which the ancient Indians certainly did.
It can be argued that the ancient Babylonians and Indians independently discovered the concept of mathematical zero, and rest of the world learnt such basic concepts from them gradually,
Interestingly, while even modern science+mathematics only uses big numbers to a certain extent, the ancient Indian Jain's & Hindus were doing computations of up to 10^32! Hindu cosmology even calculates time up to 10^15, and knows about multiverse, whereas modern science calculates Time only upto billions of years (10^9) and only recently started acknowledging the possibility of multiverse (as it is only explanation of what existed before the Big Bang), I
i.e. Time is cyclical, and universes are birthed (Big Bang), grow (expand), decay (collapse) and shrink back to the Infinitesimal Dot again).
So it is a shame that ancient India's contributions to mathematics and other fields (e.g., geography, surgeries, medical tools, metallurgy, etc.) are unknown and ignored by most of the world, and the credits for such knowledge were stolen.
Did you know?..
India built and managed the world's first universities, in Takshashila and Nalanda, which has lots of diverse subjects/disciplines being taught and researched. The Arabs/Turks later invaded, looted and destroyed these amazing universities and their priceless treasure trove of books (the libraries were so huge that the arson fires burnt for months). The ruins of these ancient pioneering repositories of knowledge still stand as mute witnesses to their glorious knowledge-sharing past.
The criticism is of the spin in these articles. The experience these kids get is great, it should happen more. The articles always spin to get your attention, and the subject matter is fascinating, but it can be presented with less spin.
And frankly any kid deserves praise for doing the unglamorous work that this takes. Very few can be arsed to put up with the extra work that it takes to do anything worthwhile, we are a nation getting lazier every day.
Making things, I made my daughters wooden practice swords, two-handed claymores.
Now for Christmas I always make something. This year was cross-body bags with elaborate patterns. Fun for me, I’m just glad they put up with the eccentric choices.
Yeah I’m dreading a change in Apple TV in this direction. I avoid the crappiness of smart tvs by not connecting them to wifi and just using Apple TV, but how long before that becomes crappy too?
Tldr: reconstruction of statue painting is based on residual pigments alone, and tend to look garish because the reconstruction is just an expression of the available data and fully saturated color.
But where we see wall frescoes and the like they are painted with what we would call artistic taste and not like the garish reconstructions.
>Where are the physical limits? According to Bremermann (1982), a computer of 1 kg of mass and 1 liter of volume can execute at most 1051 operations per second on at most 1032 bits. The trend above will hit the Bremermann limit roughly 25 decades after Z3, circa 2200. However, since there are only 2 x 1030 kg of mass in the solar system, the trend is bound to break within a few centuries, since the speed of light will greatly limit the acquisition of additional mass
They shift from talking about the transistor density to somehow considering a supermassive construct. Reminds me of LLM mashups.
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