Infinity is Not Real
In our material, measurable world, infinity is never a real, physical quantity; it is only an abstraction.
This post originally appeared on the RealClearScience Newton blog. Read the original here.
Infinity is an invaluable abstract concept in mathematics, physics, and philosophy. Isaac Newton used the abstraction of infinitely small times and distances to formulate the calculus upon which all modern physics and much of mathematics relies. But, can we see infinity in the world around us? According to some, the answer is yes. I beg to differ.
The question centers on whether Infinity (∞) is a quantity, or amount. Amounts are sizes and distances and tallies -- and they are represented by numbers. Numbers only have importance relative to other numbers. Infinity, however, ruins all number comparisons.
Mathematically, number amounts are compared by division and addition:
6/2=3 and 6+2=8
3/2=1.5 and 3+2=5
2/2=1 and 2+2=4
All numbers have relative value compared to any other number (in this case the number two). How about comparing infinity?
Compared to infinity, every other number is nothing. Infinity should not exist in the world we see because it would rewrite the rules for numbers: we would have infinity, and every other number would be nothing (0) by comparison.
Can we measure infinity in our universe? Does it exist in the same way that death and taxes and sunsets exist, and what are some possible real incarnations of infinity?
Think about this: The time from when dinosaurs walked the earth to now feels like an eternity to our imagination, but it pales compared to infinity. The amount of time from this very moment until the sun burns out over our extinct civilization, until all the stars in the universe slowly disintegrate, until nothing large enough to see by eye is left in the universe... is all the blink of an eye compared to the vastness of infinity.
Is the universe infinitely large? We have no evidence that it is. As far as you could ever travel in the universe, you will have always traveled a certain number of miles (and you could never reach the edge anyway). Your spaceship's odometer would always show a finite number. No place is infinitely far from another place, just very, very, very far.
Does infinity exist in more common human endeavors?
In chess, losing your king means you lose the game. Does this make the king infinitely valuable relative to every other piece? No! If the king truly had infinite value, all positions featuring the living king would be equally good. (Remember, infinity plus any number is just infinity). The infinitely valuable king would make all of the pieces, in every possible position on the board, equal -- i.e., equally worthless.
Considering the king to be worth twice, or ten times, or one-hundred times the value of other pieces may work well. But numbers like two, ten, 100, and 1000 are nowhere close to infinity.
Some people say death is infinite. It is not. Death is a finite length of time. As long as you may be dead, it will have been some number of years. Lucy, an early evolutionary ancestor of ours, has been dead for 3.2 million years. But this large number is nothing compared to infinity.
By trying to describe the universe as we observe it, physics does not allow us to experience infinity. String theory may talk about infinity. (Anyway, String Theory is irrelevant: right now string theory is as real as magic or paranormal hauntings.) In physics or engineering, infinity is the numerical answer that the machinery of theory spits out when something is impossible, irrelevant, or broken. An event that takes infinitely long to occur simply never happens. Something at an infinite distance is simply not there. Infinitely small means 0.
A more interesting question, perhaps, would be: "Is God infinite?" In this discussion, the abstraction of infinity might have real relevance. It would be useful and philosophically fascinating to consider.
In our material, measurable world, though, infinity is never a real, physical quantity; it is only an abstraction. A mathematician can tell you about an infinite set of numbers, but as much as he wishes, he can't find you a cup of coffee with infinite joe. That "bottomless" cup of coffee eventually runs dry.
Why self-control makes your life better, and how to get more of it.
(Photo by Geem Drake/SOPA Images/LightRocket via Getty Images)
- Research demonstrates that people with higher levels of self-control are happier over both the short and long run.
- Higher levels of self-control are correlated with educational, occupational, and social success.
- It was found that the people with the greatest levels of self-control avoid temptation rather than resist it at every turn.
Ready your Schrödinger's Cat Jokes.
- For a time, quantum computing was more theory than fact.
- That's starting to change.
- New quantum computer designs look like they might be scalable.
Quantum computing has existed in theory since the 1980's. It's slowly making its way into fact, the latest of which can be seen in a paper published in Nature called, "Deterministic teleportation of a quantum gate between two logical qubits."
To ensure that we're all familiar with a few basic terms: in electronics, a 'logic gate' is something that takes in one or more than one binary inputs and produces a single binary output. To put it in reductive terms: if you produce information that goes into a chip in your computer as a '0,' the logic gate is what sends it out the other side as a '1.'
A quantum gate means that the '1' in question here can — roughly speaking — go back through the gate and become a '0' once again. But that's not quite the whole of it.
A qubit is a single unit of quantum information. To continue with our simple analogy: you don't have to think about computers producing a string of information that is either a zero or a one. A quantum computer can do both, simultaneously. But that can only happen if you build a functional quantum gate.
That's why the results of the study from the folks at The Yale Quantum Institute saying that they were able to create a quantum gate with a "process fidelity" of 79% is so striking. It could very well spell the beginning of the pathway towards realistic quantum computing.
The team went about doing this through using a superconducting microwave cavity to create a data qubit — that is, they used a device that operates a bit like a organ pipe or a music box but for microwave frequencies. They paired that data qubit with a transmon — that is, a superconducting qubit that isn't as sensitive to quantum noise as it otherwise could be, which is a good thing, because noise can destroy information stored in a quantum state. The two are then connected through a process called a 'quantum bus.'
That process translates into a quantum property being able to be sent from one location to the other without any interaction between the two through something called a teleported CNOT gate, which is the 'official' name for a quantum gate. Single qubits made the leap from one side of the gate to the other with a high degree of accuracy.
Above: encoded qubits and 'CNOT Truth table,' i.e., the read-out.
The team then entangled these bits of information as a way of further proving that they were literally transporting the qubit from one place to somewhere else. They then analyzed the space between the quantum points to determine that something that doesn't follow the classical definition of physics occurred.
They conclude by noting that "... the teleported gate … uses relatively modest elements, all of which are part of the standard toolbox for quantum computation in general. Therefore ... progress to improve any of the elements will directly increase gate performance."
In other words: they did something simple and did it well. And that the only forward here is up. And down. At the same time.
These modern-day hermits can sometimes spend decades without ever leaving their apartments.
- A hikikomori is a type of person in Japan who locks themselves away in their bedrooms, sometimes for years.
- This is a relatively new phenomenon in Japan, likely due to rigid social customs and high expectations for academic and business success.
- Many believe hikikomori to be a result of how Japan interprets and handles mental health issues.
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