I have some legacy 32-bit software that I'd really like to keep running on my brand new MBP (odds and ends, but mainly Keynote 5.3 — i.e., from the iWork 2009 suite). On my (2015) iMac, I have two partitions: one for El Capitan and one for Catalina. I'd like to create the same setup on the MBP, but I believe that the IT folks at my organization have deployed the computer so that I can't create a new partition to give it a whirl. They tell me that it won't work anyway — the computer's too new, but it's not like the chips are that different. (Is Apple really crippling older OSes in this way?!) Anyway, before I ask them to create a second partition to let me try, I thought I'd double-check that it's in fact hopeless. Their view does get some support from the fact that when I attempt to boot from an external carbon-copy-cloner-cloned volume of ElCap, the boot halts with the message: &quot;A software update is required to use this startup disk&quot; (with options of choosing another disk or &quot;updating&quot;, which does nothing). Has anyone been down this road before. Any other ideas? I've tried Parallels and can finagle an installation of ElCap there, but Keynote's graphics are broken in it. It runs most of the other apps I need, though, so maybe I just cut bait and deal with the crappy new version of Keynote. Thanks much!
I need Mac OS X 10.6.8 (Snow Leopard) in order to work with some legacy software and I want to buy new Mac Mini computer.  Is it possible to install this OS on a new Mac Mini or it's not compatible with it?  If so, what is the latest model of Mac Mini that I can use in this scenario?
Decomposition of semisimple Lie algebra via its roots Exercise 14.33 in Fulton and Harris's Representation Theory claims that  If the roots of a semisimple Lie algebra lie in a collection of mutually orthogonal subsets, one sees that the Lie algebra decomposes into a direct sum accordingly.  Although intuitively I can see why this is true, could anybody direct me to a proof of this assertion, or outline how I should go about doing it? Bash prompt error when pressing up arrow I've written this nice and colorful prompt for my OS X terminal:   parse_git_branch() {     git branch 2&gt; /dev/null | sed -e '/^[^*]/d' -e 's/* \(.*\)/ [\1]/' }  export PS1="\e]2;\w\a\e[1;30;1m\][\u@\[\033[0;36m\]\h\e[1;30;1m\]:\[\033[0;35m\]\w\e[1;30;1m\]] \[\033[0;31m\](\t) \[\033[0;33m\]\$(parse_git_branch)\n\[\033[0m\]\e[1;30;1m\]\$\[\e[0m\]"   I source ~/.bash_profile it and it works fine. except when I use the arrow up to navigate the history I get a weird thing happening.   basically the beginning of the source ~/.bash_profile command in the history, becomes part of the prompt. when I ctrl+c or enter it returns to normal, but as soon as I see the history of the source command the prompt changes again.   Here's an example where I've seen the history and then ctrl+u and typed ls:   [user@host:~/Documents] (14:01:40)  [branch] $source ~/.ls   Any clue about this? The arithmetic - geometric mean inequality states that $$\frac{x_1+ \ldots + x_n}{n} \geq \sqrt[n]{x_1 \cdots x_n}$$ I'm looking for some original proofs of this inequality. I can find the usual proofs on the internet but I was wondering if someone knew a proof that is unexpected in some way. e.g. can you link the theorem to some famous theorem, can you find a non-trivial geometric proof (I can find some of those), proofs that use theory that doesn't link to this inequality at first sight (e.g. differential equations …)?  Induction, backward induction, use of Jensen inequality, swapping terms, use of Lagrange multiplier, proof using thermodynamics (yeah, I know, it's rather some physical argument that this theorem might be true, not really a proof), convexity, … are some of the proofs I know. Defining the Product of Ideals Where does the &quot;naive definition&quot; of the product of two ideals $I$ and $J$, $IJ = \{ ij \mid i \in I, j \in J \}$ fall apart? (The product of two ideals $I$ and $J$ is defined to be $IJ := \sum_i a_ib_i$, where each $a_i$ is in $I$ and each $b_i$ is in $J$.)  Note: This is a question from a problem set I'm working on. I am not expecting a full solution for the answers, but I'd like some help knowing where to look. It seems to work fine in $\mathbb{Z}$ and $\mathbb{C}[x]$. More Efficient Spatial join in Python without QGIS, ArcGIS, PostGIS, etc Is there a way to make rigid body interact with softbody physics? I'm trying to have a surface with soft body hold obects that are falling on it with rigid body physics, but for some reason, no what matter what mass I give it, the objects just fall trough the softbody enabled surface.  Is there a toggle or a value I need to change to make them stay there? Where did my default brushes go? I was working on a logo design for a client in Illustrator CS4 when suddenly the default brushes were no longer there. The brush files are still in place but they do not show up in the brushes panel. The options to show the brushes by type are checked but greyed out.   I tried a preference reset, that didn't fix it. I haven't tried any new brushes because the brush I needed was in the stock set. I know its bad form not to try everything but I needed one of the stock brushes to tweak an existing design. Is there a website listing the location of all the Windows 10 lock screens? Windows 10 has an extensive collection of lock screen photos, many of which have  here on Travel.SE.  Is there a website which lists the location of all of these photos? I imagine Microsoft has purchased an official license, so they should have a record about the photographer and the place where the photo was taken. Intertext vertical spacing How do I reduce the vertical spacing of \intertext? Irreducibility of $X^n - 2$ over $\mathbf Z[i]$. I was “playing” with Eisenstein's criterion and the polynomials $X^n-p$ ($p$ being a prime number).  Over $\mathbf Z$, the classical Eisenstein's criterion directly applies and shows that $X^n - p$ is an irreducible element of $\mathbf Z[X]$. The question was “what happens over $\mathbf Z[i]$?”  We know that in this new ring, a prime number $p$ has one of three different fates:   if $p \equiv -1\ (\mathrm{mod}\, 4)$, $p$ still is an irreducible element of $\mathbf Z[i]$, or equivalently $(p) \subset \mathbf Z[i]$ still is prime. (Unless I'm mistaken, number theorists say that $p$ is inert). Eisenstein's criterion still applies and the polynomial is irreducible over $\mathbf Z[i]$. if $p \equiv 1\ (\mathrm{mod}\, 4)$, $p$ can be written as a sum of two squares: $p = n^2 + m^2$ and is therefore reducible on $\mathbf Z[i]$: $p = (n+im)(n-im)$. These two factors aren't associated (the units in $\mathbf Z[i]$ being $\pm 1$ and $\pm i$) so $(p)$ splits: $(p) = (n+im)(n-im)$ is the product of two different prime ideals. One can still use Eisenstein's criterion with either of these prime ideals, and $X^n - p$ is irreducible over $\mathbf Z[i]$. if $p = 2$, the oddest of all primes, one still has a factorisation $p = (1+i)(1-i)$ but this time, $1+i$ and $1-i$ are associated. In NT slang, $(2)$ is ramified: $(2) = (1+i)(1-i) = (1+i)^2$ and one cannot directly use Eisenstein's criterion.   So here's my question: how do we prove (or disprove) the irreducibility of $X^n - 2$ over $\mathbf Z[i]$? We are using .Net to make web service calls the Salesforce API. Is there a way to know for sure that the calls are using TLS 1.2? Are there any API logs or records of the protocol is use in Salesforce we can review to be confident the change is working? I am looking for a story about the future of mankind, in which most people have been enslaved in a virtual reality. It ends with the revelation that the people are just lying there imagining their lives with their heads in a trough of feed.  It explains that chemists began to create compounds that could be released into the air to manipulate citizens - causing them to live, shop, think as desired by whoever was in charge. Eventually these tools got subtle enough that they could simulate reality using just these airborne compounds.  This was clearly a prescient view of what later became computer-based virtual reality fiction. How can we unlock an iPhone backup file if we don't know the password? For three days straight, I have connected to the public WiFi network at my local library. Each day, I have seen a different prompt in Terminal. Here are some of the prompts I've seen:  zp-pc:~ russell$ mary-pc:~ russell$ normob05:~ russell$   I have check under System Preferences -> Sharing, and my computer name is "Russell's Mac". Also, I set the DHCP Client ID to "RUSSMAC" under System Preferences -> Network -> Advanced -> TCP/IP, but I still see the random host names at the Terminal prompt.  Why is my computer name changing every day? How to unzip a zip file from the Terminal? Just downloaded a .zip file from the internet. I want to use the terminal to unzip the file. What is the correct way to do this? Whenever I try to do a fluid simulation, the fluid domain remains visible.  I have tried:ctrl+a-scale, turn on/off visibility for render/viewport  Here's a video demonstrating my problem:   Here's the blend file in case I have messed up some settings:   Thank you for any help! Best way to implement keyboard shortcuts in a Windows Forms application? Can a negative charge ionize air? Adding to this question, I have studied that positive charge ionizes air but never studied that negative charge ionize air. If possible, please explain how does it ionize air? UK visa: unsigned application form What is the intuition behind defining completeness in a statistic as being impossible to form an unbiased estimator of $0$ from it?