What is philosophical abstraction?
I’m assuming this question is “what is abstraction?” asked within the context of philosophy. It’s easier to forget the “philosophy” part for a second, but we’ll get to it.Abstraction is like addition or multiplication. It’s a logical operation like any other, and it’s this:x = y + zWhenever we say “let x” be something else, we are creating an abstraction. It’s simplification. X now abstracts whatever we let it be, by allowing us to only have to deal with x. Nothing goes away. We can say the contents of x are hidden, but they are still there as x. And we can always look them up. But the key is now we can work with just x. And in fact, we are introducing x, and now we have something we didn’t have before — an abstraction. Now we have everything that is x, and x. But we gain the capability to just deal with x.Linguistically, all words are abstractions. Just like with x, every word is used to represent something else. Again, it isn’t that the meaning of the word is hidden. To the contrary, the word is used to access that meaning, so nothing goes away. Abstractions help us create simpler patterns to reason with. Though long words sometimes seem harder to deal with or reason with, they are still always easier than not having that word. Imagine if we didn’t have the word “abstraction”. We’d have a lot more explaining to do.Computer programming is where mathematical and linguistic abstractions are put to immediate practice. Coding is the act of defining abstractions in logical and meaningful terms. We define values and processes and give them names, and then have computer processors run that code to make things like email and spreadsheets and Quora happen.Abstractions are real, they are useful, and they are ubiquitous already.Then what is abstraction philosophically?Philosophy is about putting words to our intuitions. Nothing actually has to be real or even concrete. It just has to make sense, and incredibly, we are capable of sensing and sharing this sense, which is sort of what is happening here hopefully.When an intuition reoccurs enough, we find ourselves looking for an easier way to refer to it, so we create words. Philosophical abstraction is the act of discovering new intuitions and inventing new words for them.
In Excel, how are percentages multiplied?
Not totally clear here on what you are asking but:Percentages are just numbers. 22% is the same as 0.22 which you can readily see in Excel by changing the cells number format.You can just multiply them directly. So if I want to know 10% of 25% I can enter=25%*10%into a cell. It shows 2.500% [if it shows something else look at the number format for the cell]You can replace those constants with cell references to cells containing a percentage.So if Cell A1 contains 10% and B1 has 25% and C1 has 100 (for more excitement)=A1*B1shows 25% of 10%=c1*A1Will show 10% of 100 or 10
How can I find the concentration of H+ ions in a solution given its pH?
The pH of a solution is equal to the base 10 logarithm of the H+ concentration, multiplied by -1. If you know the pH of a water solution, you can use this formula in reverse to find the antilogarithm and calculate the H+ concentration in that solution. Scientists use pH to measure how acidic or basic water is. A low pH value means water is acidic and a high value means it's basic, often referred to as alkaline. In acidic water, there is an increased concentration of positively charged hydrogen atoms, H+. This concentration determines the pH value.Enter into the calculator the pH value for which you intend to calculate the H+ concentration. For example, if the pH of your solution is 5, enter 5 into the calculator. pH values will almost always be between 0 and 14, so your number should be within this range.Multiply the value you just entered by -1. This is the first step toward calculating the concentration of H+ in the solution, based on the equation pH = (-1) log [H+], where "log" is short for base 10 logarithm and the square brackets around H+ stand for "concentration." Multiplying the pH by -1 puts this equation in the form log[H+] = - pH. In the example, you would multiply 5 by -1 to get -5.Take the base 10 antilogarithm (or "anti-log") of the value you just calculated. You can take the anti-log by using the 10^x key on the calculator. By doing this, you are changing the pH equation into the form anti-log (log[H+]) = anti-log (- pH). The two reverse operations (anti-log and log) on the left-hand side cancel each other out, leaving [H+] = anti-log (- pH). So the value you calculate in this step is the concentration of H+ in the solution. The units of this concentration are molarity, or moles H+ per liter of solution. The example with a pH of 5 would therefore have an H+ concentration equal to anti-log (-5) which equals 0.00001 moles/liter. (properties of anti-logs from ref 3)TipSome scientists prefer to use the formula H3O+ instead of H+, to show that the positive hydrogen atom typically combines with a neutral water molecule (H2O) to form H3O+, known as the hydronium ion.
How do you compute the remainder of [math]3^{20}[/math] divided by [math]2^{20}[/math] by hand only?
Well we have two options here, find 2^20 and 3^20 and then find the remainder or find the remainder from the fractional part of (3/2)^20, I’ll do the first since the second amounts to more of the same or calculating 1.5^20.A good place to start would be finding these large numbers, a simple way of doing this is using exponentiation by squaring. Notice that 20 (base 10) = 10100 (base 2), so in essence we have n^20 = n^16 * n^4, and we can proceed by calculating n, n^2, n^4, n^8, n^16. This will require 5 calculations rather than 20.2^2 = 4, 2^4 = 2^2 * 2^2 = 16, 2^8 = 2^4 * 2^4 = 256, 2^16 = 2^8 * 2^8 = 65536, 2^20 = 2^16 * 2^4 = 65536 * 16 = 10485763^2 = 9, 3^4 = 3^2 * 3^2 = 81, 3^8 = 3^4 * 3^4 = 6561, 3^16 = 3^8 * 3^8 = 43046721, 3^20 = 3^16 * 3^4 = 43046721 * 81 = 3486784401So now we could try and manually go through 3486784401 mod 1048576, or we could go back a step and notice that (3^16 * 3^4) mod 2^20 = (3^16 mod 1048576) * (3^4 mod 1048576) mod 2^20, which is likely simpler.We could do 3^16 - 2^20 until the result is less than 2^20, or we could do it a little more handily and notice 3^16 > 40 * 2^20 and start with 3^16 - 40*3^20 = 1103681. One more with 1103681 - 2^20 = 55105. So thus we have 55105 * 81 mod 2^20 = 4463505 mod 2^20 and, subtract down, 4463505 - 4*2^20 = 269201 which is the correct answer.Alternatively, we could calculate the first few terms of the series 3^n mod 2^n for n = 1,2,3,4,5… and see if we can search for the integer series. Searching 1,1,3,1,19 on the OEIS database gives us A002380 - OEIS, which is pretty cool. Sadly it doesn’t seem there’s a better way to calculate it by hand, darn.
Toshiba Satellite R850 or Toshiba Satellite A660?
Specs for R850: 500GB, 4GB RAM, Intel core i3 T2310M, Battery life 7 hours Specs for A660: 640GB, 4GB RAM, Intel Core i3 380M, Battery life 4 hours Which would you choose?
What is half of 1/3?
We can apply the law of multiplication of fractions.‘Half’ means ‘1/2’, ‘of’ means ‘multiplication’ and ‘exactly 1/3’ is only ‘1/3’.Thus, ‘half of exactly 1/3’ is equal to “1/2 × 1/3”.To multiply two or any number of fractions, we have to multiply the numerators together and the denominators together. The product of the numerators gives the numerator of the product and the product of the denominators gives the denominator of the product.Thus 1/2 × 1/3 = ((1×1)/(2×3)) = (1/6) = 1/6 .This was according to the laws of mathematics.But to understand this practically, there is an activity which I have been taught in school to understand the concepts and laws of mathematics.The activity is :-“ Take a square piece of marble paper (craft paper) and fold it into half (shown in image below).As we have folded the paper vertically 1 time, thus the paper has been divided into 2 parts vertically.Now, we have to multiply this 1/2 by 1/3, so we will have to fold this paper 2 times horizontally to get the paper divided into 3 parts horizontally (shown in image below).Now, we get 6 parts in total. If we take a part, the part is 1/6 of the total sheet (shown in image below).Thus, 1/3 × 1/2 = 1/6.”Now, we have proved both practically and theoritically that the ‘half of exactly 1/3’ is ((1/2)×(1/3)) is 1/6.Hope it helped…. :)
If GEM = NJZ, then what is KID =?
GEM = NJZG (7) MAPPED TO N(14) (i.e 7x2 =14)E (5) MAPPED TO J(10)M (13) MAPPED TO Z(26)SimilarlyK(11) 11X2 =22 (V)I(9) 9X2 =18 (R)D(4) 4X2=8 (H)KID = VRH