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Category: mathematics – Page 83

There are two aspects to a computer’s power: the number of operations its hardware can execute per second and the efficiency of the algorithms it runs. The hardware speed is limited by the laws of physics. Algorithms—basically sets of instructions —are written by humans and translated into a sequence of operations that computer hardware can execute. Even if a computer’s speed could reach the physical limit, computational hurdles remain due to the limits of algorithms.

These hurdles include problems that are impossible for computers to solve and problems that are theoretically solvable but in practice are beyond the capabilities of even the most powerful versions of today’s computers imaginable. Mathematicians and computer scientists attempt to determine whether a problem is solvable by trying them out on an imaginary machine.

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Join the ORE community to learn about computational redstone like this at:

Mc.openredstone.org.

Instruction Set: https://1drv.ms/x/s!AkiZre7Tutskiw5SEwrIS90RQEK9?e=YhXXzR
Assembler: https://1drv.ms/u/s!AkiZre7TutskjCaMNSG6SuvbnN-B?e=kdPKtb.

Music used in this video:
Aria Math Space Remix: https://youtu.be/ajlXyZQp9N4
I do NOT own any of the music used in this video!

Links:

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‘Spin’ is a fundamental quality of fundamental particles like the electron, invoking images of a tiny sphere revolving rapidly on its axis like a planet in a shrunken solar system.

Only it isn’t. It can’t. For one thing, electrons aren’t spheres of matter but points described by the mathematics of probability.

But California Institute of Technology philosopher of physics Charles T. Sebens argues such a particle-based approach to one of the most accurate theories in physics might be misleading us.

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Year 2017 face_with_colon_three

A basic question [1] in the study of the gauge-gravity duality is this: which field theories have a gravity dual? In the case of applications to actual strongly coupled systems such as the Quark–Gluon Plasma [2], [3], [4], [5], [6], this question becomes: does every realistic strongly coupled system have such a dual? To settle this, one needs to examine the most extreme cases. The most extreme strongly-coupled systems currently accessible to experiment are probably (see below) the plasmas produced by collisions of heavy ions at the LHC [7], [8] ; so one needs to consider whether holography works in this case.

In [9] we adduced evidence suggesting that it does not. The problem is a very fundamental one: it appears that the purported gravity dual in some cases does not exist when one attempts to interpret it (as one ultimately must [10]) as a string-theoretic system.

The situation may be briefly explained as follows. Ferrari and co-workers have shown [11], [12], [13], [14] that, simply for reasons of internal mathematical consistency, a string-theoretic bulk spacetime with a holographic dual must satisfy certain fundamental relations between the Euclidean spacetime action and the action of probes (such as branes). This has been explicitly confirmed in a large number of concrete cases [14].

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A model for information storage in the brain reveals how memories decay with age.

Theoretical constructs called attractor networks provide a model for memory in the brain. A new study of such networks traces the route by which memories are stored and ultimately forgotten [1]. The mathematical model and simulations show that, as they age, memories recorded in patterns of neural activity become chaotic—impossible to predict—before disintegrating into random noise. Whether this behavior occurs in real brains remains to be seen, but the researchers propose looking for it by monitoring how neural activity changes over time in memory-retrieval tasks.

Memories in both artificial and biological neural networks are stored and retrieved as patterns in the way signals are passed among many nodes (neurons) in a network. In an artificial neural network, each node’s output value at any time is determined by the inputs it receives from the other nodes to which it’s connected. Analogously, the likelihood of a biological neuron “firing” (sending out an electrical pulse), as well as the frequency of firing, depends on its inputs. In another analogy with neurons, the links between nodes, which represent synapses, have “weights” that can amplify or reduce the signals they transmit. The weight of a given link is determined by the degree of synchronization of the two nodes that it connects and may be altered as new memories are stored.

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This video covers the timelapse of metaverse technologies from 2030 to 3000+. Watch this next video about the Future of Virtual Reality (2030 – 3000+): https://bit.ly/3zfjybO.
► Support This Channel: https://www.patreon.com/futurebusinesstech.
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► Brilliant: Learn Science And Math Interactively (20% Off): https://bit.ly/3HAznLL
► Jasper AI: Write 5x Faster With Artificial Intelligence: https://bit.ly/3MIPSYp.

SOURCES:
• https://www.futuretimeline.net.
• The Singularity Is Near: When Humans Transcend Biology (Ray Kurzweil): https://amzn.to/3ftOhXI

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• The connection between Science Fiction concepts and reality.

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Continue reading “Future of the Metaverse (2030 — 10,000 A.D.+)” | >

This video covers Mars in 2050 and 10 future technologies in the first Mars city. Watch this next video about the world in 2050: https://bit.ly/3J23hbQ.
► Support This Channel: https://www.patreon.com/futurebusinesstech.
► Udacity: Up To 75% Off All Courses (Biggest Discount Ever): https://bit.ly/3j9pIRZ
► Brilliant: Learn Science And Math Interactively (20% Off): https://bit.ly/3HAznLL
► Jasper AI: Write 5x Faster With Artificial Intelligence: https://bit.ly/3MIPSYp.

SOURCES:
• https://scitechdaily.com/mars-settlement-likely-by-2050-says…-elon-musk.
• https://www.news18.com/news/buzz/elon-musk-and-nasa-may-fina…79184.html.
• https://2050.earth/predictions/a-sustainable-civilization-of-humans-on-mars.
• https://www.businessinsider.com/elon-musk-plans-1-million-pe…2020-1
• https://www.inverse.com/innovation/spacex-mars-city-codex.
• https://www.inverse.com/article/54358-elon-musk-explains-how…rs-by-2050
• https://futurism.com/the-byte/elon-musk-million-people-mars-2050
• https://www.lpi.usra.edu/V2050/presentations/Tuesday/6_8236_Ehlmann.pdf.
• https://www.mars-one.com.
• https://en.wikipedia.org/wiki/Colonization_of_Mars.
• https://www.nationalgeographic.org/hires/human-settlement-mars/
• https://www.spacex.com/human-spaceflight/mars/
• https://ntrs.nasa.gov/api/citations/20070008279/downloads/20070008279.pdf.
• https://www.space.com/how-feed-one-million-mars-colonists.html.
• https://www.usatoday.com/in-depth/news/nation/2020/12/30/col…091010001/
• https://eatlikeamartian.org/

Official Discord Server: https://discord.gg/R8cYEWpCzK

💡 On this channel, I explain the following concepts:
• Future and emerging technologies.
• Future and emerging trends related to technology.
• The connection between Science Fiction concepts and reality.

SUBSCRIBE: https://bit.ly/3geLDGO

Disclaimer:

Continue reading “Mars in 2050: 10 Future Technologies In The First Mars City” | >

Cancer cells can shrink or super-size themselves to survive drug treatment or other challenges within their environment, researchers have discovered.

Scientists at The Institute of Cancer Research, London, combined biochemical profiling technologies with to reveal how lead to differences in the size of cancer cells—and how these changes could be exploited by new treatments.

The researchers believe smaller cells could be more vulnerable to DNA-damaging agents like chemotherapy combined with targeted drugs, while larger cancer cells might respond better to immunotherapy.

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Tech giants from Google to Amazon and Alibaba —not to mention nation-states vying for technological supremacy—are racing to dominate this space. The global quantum-computing industry is projected to grow from $412 million in 2020 to $8.6 billion in 2027, according to an International Data Corp. analysis.

Whereas traditional computers rely on binary “bits”—switches either on or off, denoted as 1s and 0s—to process information, the “qubits” that underpin quantum computing are tiny subatomic particles that can exist in some percentage of both states simultaneously, rather like a coin spinning in midair. This leap from dual to multivariate processing exponentially boosts computing power. Complex problems that currently take the most powerful supercomputer several years could potentially be solved in seconds. Future quantum computers could open hitherto unfathomable frontiers in mathematics and science, helping to solve existential challenges like climate change and food security. A flurry of recent breakthroughs and government investment means we now sit on the cusp of a quantum revolution. “I believe we will do more in the next five years in quantum innovation than we did in the last 30,” says Gambetta.

But any disrupter comes with risks, and quantum has become a national-security migraine. Its problem-solving capacity will soon render all existing cryptography obsolete, jeopardizing communications, financial transactions, and even military defenses. “People describe quantum as a new space race,” says Dan O’Shea, operations manager for Inside Quantum Technology, an industry publication. In October, U.S. President Joe Biden toured IBM’s quantum data center in Poughkeepsie, N.Y., calling quantum “vital to our economy and equally important to our national security.” In this new era of great-power competition, China and the U.S. are particularly hell-bent on conquering the technology lest they lose vital ground. “This technology is going to be the next industrial revolution,” says Tony Uttley, president and COO for Quantinuum, a Colorado-based firm that offers commercial quantum applications. “It’s like the beginning of the internet, or the beginning of classical computing.”

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Whether we realize it or not, cryptography is the fundamental building block on which our digital lives are based. Without sufficient cryptography and the inherent trust that it engenders, every aspect of the digital human condition we know and rely on today would never have come to fruition much less continue to evolve at its current staggering pace. The internet, digital signatures, critical infrastructure, financial systems and even the remote work that helped the world limp along during the recent global pandemic all rely on one critical assumption – that the current encryption employed today is unbreakable by even the most powerful computers in existence. But what if that assumption was not only challenged but realistically compromised?

This is exactly what happened when Peter Shor proposed his algorithm in 1995, dubbed Shor’s Algorithm. The key to unlocking the encryption on which today’s digital security relies is in finding the prime factors of large integers. While factoring is relatively simple with small integers that have only a few digits, factoring integers that have thousands of digits or more is another matter altogether. Shor proposed a polynomial-time quantum algorithm to solve this factoring problem. I’ll leave it to the more qualified mathematicians to explain the theory behind this algorithm but suffice it to say that when coupled with a quantum computer, Shor’s Algorithm drastically reduces the time it would take to factor these larger integers by multiple orders of magnitude.

Prior to Shor’s Algorithm, for example, the most powerful computer today would take millions of years to find the prime factors of a 2048-bit composite integer. Without Shor’s algorithm, even quantum computers would take such an inordinate amount of time to accomplish the task as to render it unusable by bad actors. With Shor’s Algorithm, this same factoring can potentially be accomplished in a matter of hours.

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