Posts Tagged ‘limits’
“The world of reality has its limits; the world of imagination is boundless”*…
… and the digital world? Maybe, as Rob Beschizza reports, somewhere in between…
Alex set out to debunk the given wisdom that the maximum dimensions of a PDF are 381 km2, which is smaller than Germany. She presents her conclusions in an article titled “Making a PDF that’s larger than Germany,” so you know from the outset she succeeded. It’s a fascinating example of the disalignment of specifications, implementations, and reality. You can make one by hacking the postscript, and while Adobe Acrobat won’t like it, other apps will…
Borges would be delighted…
“On exactitude in PDFs“
Just how big was Alex [Chan] able to make her PDF?…
… unlike Acrobat, the Preview app doesn’t have an upper limit on what we can put in MediaBox. It’s perfectly happy for me to write a width which is a 1 followed by twelve 0s…
If you’re curious, that width is approximately the distance between the Earth and the Moon. I’d have to get my ruler to check, but I’m pretty sure that’s larger than Germany.
I could keep going. And I did. Eventually I ended up with a PDF that Preview claimed is larger than the entire universe – approximately 37 trillion light years square. Admittedly it’s mostly empty space, but so is the universe. If you’d like to play with that PDF, you can get it here.
Please don’t try to print it.
“Making a PDF that’s larger than Germany“
* Jean-Jacques Rousseau
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As we scale up, we might spare a thought for Émile Borel; he died on this date in 1956. A mathematician (and politician who served as French Minister of the Navy), he is remembered for his foundational work in measure theory and probability. He published a number of research papers on game theory and was the first to define games of strategy.
But Borel may be best remembered for a thought experiment he introduced in one of his books, proposing that a[n immortal] monkey hitting keys at random on a typewriter keyboard will – with absolute certainty – eventually type every book in France’s Bibliothèque Nationale de France. This is now popularly known as the infinite monkey theorem.
“The Universe is not only queerer than we suppose, but queerer than we can suppose”*…

Complex nature
Albert Einstein said that the “most incomprehensible thing about the Universe is that it is comprehensible.” He was right to be astonished. Human brains evolved to be adaptable, but our underlying neural architecture has barely changed since our ancestors roamed the savannah and coped with the challenges that life on it presented. It’s surely remarkable that these brains have allowed us to make sense of the quantum and the cosmos, notions far removed from the ‘commonsense’, everyday world in which we evolved.
But I think science will hit the buffers at some point. There are two reasons why this might happen. The optimistic one is that we clean up and codify certain areas (such as atomic physics) to the point that there’s no more to say. A second, more worrying possibility is that we’ll reach the limits of what our brains can grasp. There might be concepts, crucial to a full understanding of physical reality, that we aren’t aware of, any more than a monkey comprehends Darwinism or meteorology. Some insights might have to await a post-human intelligence…
Abstract thinking by biological brains has underpinned the emergence of all culture and science. But this activity, spanning tens of millennia at most, will probably be a brief precursor to the more powerful intellects of the post-human era – evolved not by Darwinian selection but via ‘intelligent design’. Whether the long-range future lies with organic post-humans or with electronic super-intelligent machines is a matter for debate. But we would be unduly anthropocentric to believe that a full understanding of physical reality is within humanity’s grasp, and that no enigmas will remain to challenge our remote descendants…
Martin Rees (Lord Rees of Ludlow), cosmologist and astrophysicist, Astronomer Royal since 1995, past Master of Trinity College, Cambridge, and former President of the Royal Society, on the limits of human understanding (and how we might transcend them): “Black holes are simpler than forests and science has its limits.”
For a “companionable” take on the character of the knowledge that we do (seem to) have, see “Is Quantum Theory About Reality or What We Know?“; and for an argument that we should stop worrying about the limits of human knowledge, and start worrying about wasting the knowledge we already have, see here.
* J. B. S. Haldane, Possible Worlds and Other Papers (1927)
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As we prepare to call (an artificially-intelligent) friend, we might send acutely observant birthday greetings to an astute student of the human animal, anthropologist Margaret Mead; she was born on this date in 1901. Best-known for her studies of the nonliterate peoples of Oceania, she was 23 when she first traveled to the South Pacific, to conduct research for her doctoral dissertation. The book that resulted, Coming of Age in Samoa, was– and remains– a best-seller.
“Gods do not limit men. Men limit men.”*…

Everything has a limit – or does it?…
Some maximums will never be surpassed, but as the author Arthur C Clarke once said, “the only way of discovering the limits of the possible is to venture a little way past them into the impossible.”
See a larger version of the graphic above at “Ultimate limits of nature and humanity.”
* Tom Robbins, Jitterbug Perfume
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As we bump up against boundaries, we might send compressed birthday greetings to Aaron “Bunny” Lapin; he was born on this date in 1914. In 1948, Lapin invented Reddi-Wip, the pioneering whipped cream dessert topping dispensed from a spray can. First sold by milkmen in St. Louis, the product rode the post-World War Two convenience craze to national success; in 1998, it was named by Time one of the century’s “100 great consumer items”– along with the pop-top can and Spam. Lapin became known as the Whipped Cream King; but his legacy is broader: in 1955, he patented a special valve to control the flow of Reddi-Wip from the can, and formed The Clayton Corporation to manufacture it. Reddi-Wip is now a Con-Agra brand; but Clayton goes strong, now making industrial valves, closures, caulk, adhesives and foamed plastic products (like insulation and cushioning materials).




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