Physical address extension.
With 32 bits, only 4GB RAM can be addressed.
This started becoming a limitation for large servers, so Intel introduced the PAE mechanism to Pentium Pro.
To relieve the problem, Intel added 4 new address lines, so that 64GB could be addressed.
Page table structure is also altered if PAE is on. The exact way in which it is altered depends on weather PSE is on or off.
PAE is turned on and off via the PAE bit of cr4.
Even if the total addressable memory is 64GB, individual process are still only able to use up to 4GB. The OS can however put different processes on different 4GB chunks.
Paging is done by the Memory Management Unit (MMU) part of the CPU.
Like many others (e.g. x87 co-processor, APIC), this used to be by separate chip on early days.
It was later integrated into the CPU, but the term MMU still used.
As of 2022:
The median household income at the time was 31k[ref]. Clearly, putting one child through university with that income would be basically impossible, you would pay 19 - 5 = 14k/year, almost half of your income. Two children would be impossible. Remember how each family needs to have two children minimum to perpetuate life?
Take the group of all Translation in .
Let's see how the generator of this group is the derivative operator:
The way to think about this is:
So let's take the exponential map:
and we notice that this is exactly the Taylor series of around the identity element of the translation group, which is 0! Therefore, if behaves nicely enough, within some radius of convergence around the origin we have for finite :
This example shows clearly how the exponential map applied to a (differential) operator can generate finite (non-infinitesimal) Translation!
SVG 1.2 by Ciro Santilli 37 Updated 2025-07-16
Dropped in favor of SVG 2.
Originally done with (neutral) silver atoms in 1921, but even clearer theoretically was the hydrogen reproduction in 1927 by T. E. Phipps and J. B. Taylor.
Video 1.
The Stern-Gerlach Experiment by Educational Services, Inc (1967)
Source. Featuring MIT Professor Jerrold R. Zacharias. Amazing experimental setup demonstration, he takes apart much of the experiment to show what's going on.

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