![]() get_potential_energy () -31.492847800329216 Supported Calculators ¶ĪCE-Molecule amber DeePMD-kit DMol³ Gaussian Grimme DFT-D3 gulp Mopac qmmm tip3p ~deMon-NanoĪSE version 3.22.1 released (1 December 2021).ĪSE version 3.22.0 released (24 June 2021).ĪSE version 3.21.1 released (24 January 2021).ĪSE version 3.21.0 released (18 January 2021). calc = NWChem ( xc = 'PBE' ) > opt = BFGS ( h2 ) > opt. Abacus.> # Example: structure optimization of hydrogen molecule > from ase import Atoms > from ase.optimize import BFGS > from import NWChem > from ase.io import write > h2 = Atoms ( 'H2'. Sadly, there is no way to multiply or divide automatically on this device. We can also use the shifting trick to speed up the process. The basic idea is to count how many times we can subtract the denominator from the numerator. We just directly add subsequent numbers to it. Note that we do not need to clear the counter during the process, so there is no need to remember the result of 24*6. If we want to calculate 24*36, we can first calculate 24*6 by rolling the handle six times, then shift 24 to 240 and roll the handle three times to add 24*30 to the result! (24*30=240*3 24*30+24*6=24*36) Here is another trick: we can shift the counter, which is equivalent to shifting the control panel in reverse direction. ![]() If we want to multiply a number by 6, we add the number 6 times! There is another counter that records how many times we have rolled the handle, so we do not need to worry about forgetting it. It can also calculate multiplication, but the process is quite tricky. To subtract a number, the user can roll the handle in reverse direction so that the counter decreases. In this way, it can add numbers automatically. ![]() The counter will bring a carry to the next digit when a digit exceeds 9. The panel is connected to mechanical parts inside, and it will push the counter automatically when the user rolls a handle. The difference is that there is a huge control panel on top of the counter where the user can dial a second number. It seems that some ideas are brought from abacus: there is a counter at the bottom that records the current number, just like what people do on an abacus. This was the device that caught my interest when I visited one of my professors and inspired me to write on this topic. For example, Hamann Manus R is a cumbersome mechanical calculator that can add numbers without asking the user to remember math rules. (Scherphuis, 2016)Īs technology developed, people eventually developed devices that can not only store numbers but also calculate automatically. The advantage is that the interface is less obscure than abacus and it is cheap to produce. People still need to manually rotate the pointer based on math rules. There is a pointer on each plate that points to the current number. Its main interface is a set of dialing plates, with each of them representing a digit. (Wikipedia, 2019)Ī modern variant of the abacus is pocket adders. However, because the numbers are stored on a device instead of people’s brain, it is less likely to make errors after people learned it. ![]() Abacus is quite hard to learn because the device does not do any calculations itself and people need to learn the math rules to operate it. People can store digits on the device and manipulate the number to get the desired result. The device acts more like a memory than a computer. Although we cannot determine the exact origin of this device, we know that most merchants in China, Russia and Europe used it for accounting. (Wikipedia, 2018)Īnother mechanical computing device called abacus is much more common in ancient times. An improved version of this device can be driven automatically by water flow. In analogy, it is like an analogue computer. However, in contrast to a modern computer, all the results are shown by moving parts instead of numeric value. It can be used to predict the moon phase and relative direction of the sun from earth, which was then used to produce precise calendars. For example, the Chinese developed a device called the armillary sphere to simulate the earth’s and moon’s orbit. Long before electronic computers were invented, people have come up with ways to calculate without electricity.
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