Poll: Asking for a friend – what do you understand by "6x4" | Hacker News Reader

Poll: Asking for a friend – what do you understand by "6x4"

17 pointsColinWright56 comments

Recently I've had an enlightening discussion with a colleague about notation in maths and computing. I don't want to "lead the witness" so I'm not going to repeat it here, but I'd like to ask about the internal understanding of individuals in this community.

What do you understand by the expression "6 x 4" ? I fully expect that I haven't covered all the possibilities, I know that self-selected polls are useless for proper statistics, I know that some people just click all the options, etc. All that not withstanding, I'd be interested to see what people think.

Thanks.

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The ordinary language expression "six times four" [and a wasted opportunity to use Polish notation]. After that "24" and I don't mean some picture of countable things but just the abstraction called "24".

Even after reading the poll answers none of the this-or-that options even prompt an image of a grouping. What makes algebraic notation useful is that it abstracts away the need to model the calculation further in most cases. There's no need to ponder "x lots of y or y lots of x". That's good because "lots" and "of" are more muddied. concepts than "times". My fourth grade teacher could explain "times" by giving examples of timesing. Examples of lotsing and ofing are harder to come by.

That is an interesting idea. It is the opposite of how my kid is learning math in the 4th grade today. They are taught to think about grouping and what the phrase represents in an attempt to make it more intuitive. Then if they don't know 7x4 then they can work it out by adding one more group of 4 to 6x4. Eventually the hope is that it will become rote memory. I learned it by memorizing the facts although I could have forgotten the other part of the lesson. I mostly remember times table quizzes.

In the US the increased use and then widespread adoption of Common Core over the past decade or so has changed mathematics pedagogy. There's much more attention to procedurall reasoning and its systematic content standards in the elementary grades has reduced the prevalence of ad hoc methods.

When my son started multiplying fractions, the instruction from the teacher was clear and to the point: Parents don't teach them the methods you learned.

I'll throw in another vote for the "six-by-four area" group, this time from communicating the sizes of lego pieces to my brother while we were building things. I also see a malformed attempt at typing in a hexademical number.

Those were quite literally the first two things to come into my mind after "6 times 4", right down to Lego's with my brother.

Before looking at the full question I started with a timber size. Then thought it might represent an area. Within the context of the full question I suppose it is:

a) An Area or b) Six, four copies of

but the little automated arithmetic unit at the back of my brain keeps "shouting" 24.

I may have done too much math to give a useful answer. 6 x 4 is the number which is the result of multiplying 6 and 4, here written with the 6 first, but probably not for any particular reason. It doesn't seem like any arrangement of lots or copies of anything, but all the listed arrangements of lots and copies are instances of it. Some other instances that are nothing like the suggested answers are "the area of a rectangle with dimensions 6 and 4" or "the amount of torque you get if you apply 6 Newtons to the end of a 4 meter arm"

There are two options for "six, four copies of".

I see this as an area with six units along one side and four units along the next side.

I'd read "6 x 4" as "multiply 6 by 4" which I'd see as "6 + 6 + 6 + 6" and the same as six x four.

I am not sure what you mean by "lots" or "copies".

A grid of 6x4 cells, or a generic thing of 6 units by 4 units.

First association - wood (mighty big as well)

Second association - 6 wheeled vehicle, 4 wheels driven (possibly because of the recent Top Gear with the Mercedes 6x6).

Wood for me too, I guess all those summer jobs at construction left something behind.

The context has to be very particular for me not to consider this to be exactly 24 (natural number, not real number) without intermediate representation. I assume we're working over the ring of integers here. In that case, 6x4 is only ever not instantly 24 when it's part of an expression of similar terms (say, 6x1 + 6x2 + 6x3 + 6x4) in which a pattern is being expressed.

If you're not working over the usual ring, though, intuition goes out the window and I think of it as "six-but-not-six blob four-but-not-four". That's because in a module sense, it is 6 (element of ring) times (arbitrary multiplication operation) 4 (element of module).

For me the multiplication is not all that obvious because I'm used to reading and writing "6*4" for multiplications within an ASCII context. 6x4 looks like a noun to me, a type of real-world object or maybe an area.

How about: "The multiplicative ring operation of ℤ on the elements (((((1+1)+1)+1)+1)+1) and (((1+1)+1)+1)."

As a mathematician with a slight focus on algebra when I see such terms the questions that come to my mind are rather: Which ring am I working on, has it finite characteristics, is one of these numbers a ring element and the other an Element of ℤ [1]? It is always funny to see how your focus changes your perception :)

[1] For example 4 could be an element of the finite field with 5 elements GF(5). Then I would interpret 6x4 as 4+4+4+4+4+4, because 6 is not an element of GF(5) and I thus cannot plug it into the multiplication operation of GF(5).

A big chunk of wood.

<fx: Grin> Thanks for that - really helpful. Reveals some of your background nicely. Related, I was seriously tempted the other day to apply a "Clue by four" to one of my customers. Hard to resist ...

Neat :) I have that temptation too sometimes, must. not. give. in.

Missed you on my tour of the UK, I really should have thought of you, that was stupid of me. Write-up is here: http://jacquesmattheij.com/journeyman-project-trip-1-united-...

First thought I had as well. In fact, it was the only one I had. I was thinking, "I know what a 2x4 is, and a 2x6 is, a 6x4 is probably a really large beam? But why didn't he call it a 4x6?"

I read through the possible poll answers and realize I was totally missing the question.

yep definitely wood.

Strangely, despite coming from South Africa, where I've never heard the terminology used in real life (maybe it is, but I don't do much woodwork), I've watched enough American crime series that the wood terminology came to mind immediately. I had to Google to confirm that the terminology refers to wood, and not, say, a large metal pole.

Google also tells me that it's actually a 2by4: "He took a 2x4 to the head".

When I saw "6x4", my immediate thought was a "six by four" matrix. So, by convention, this means 6 rows and 4 columns, corresponding to e.g. 6 observations of 4 variables each (from a statistician's perspective). The closest answer I could find here was "six lots of four."

Definitely a matrix... * is for multiplication ;)

Standard photo size (6 inches by 4 inches) - or at least some form of note card/postcard/paper size.

First I assumed it was related to timber (though I'm squarely from a metric culture).

I see the 6 and 4 as being equal and congruent, so I don't imagine one number as multiplier of a lot of some other thing or visually as groups of things. I guess my answer would be the dry mathematical 24. Maybe I'd be better at mathematics if I'd try to visualise things more...

Your question reminds me of the little experiment Feynman did where he tried counting to a minute while reading, and how people can see and do even simple tasks differently in their head.

Ways Of Thinking: http://www.bbc.co.uk/archive/feynman/

Another new IPv6 transition mechanism?

I find it really interesting that people instinctively say 24, which to me means they know the answer, but they don't actually compute it - it's just learnt, which is why if I asked 14*19, most people would reach for a calculator. It Reflects a lot of maths and education in general nowadays - it's more important to know the answer over why that is the answer. It should be the opposite - the latter is far more important.

It can mean any of the things on your poll, and many not on your poll, except for "Six lots of four", that one doesn't make sense to me.

But that term has MANY meanings - without the context (arithmetic? wood? cars? IPv6? matrix?) it's impossible to say.

Because it's not in an obviously maths context, I read it as "Six by Four", the first association in my mind for that is cars - 4 x 4 being four wheel drive, so I guess 6 x 4 would be a six wheeled vehicle with 4 driven wheels.

That's probably going too far...

Not a block of wood with a cross section the size of three two-by-fours?

Maybe this is the designer in me speaking, but I immediately thought of width x height.

Another possibility is a vacuum tube: http://www.radiomuseum.org/tubes/tube_6x4.html

This is the top hit when I Google for "6x4".

I see 6x4 either as the dimensions of a surface, or as some kinds of informal coordinate (like "the 4th episode of the 6th season of a tv show).

A two-dimensional raster/array/grid/matrix of six by four elements. Or a LEGO plate of those dimensions.

Six sets of four reps each. But that's a really weird routine. I recommend 3-4 sets of 8-12 reps for most people.

I have always found 5 sets of 8 to be best :)

Three sets of Five reps (except the deadlift which one set of five is good, and the power clean, which I can't do anyways.)

http://startingstrength.wikia.com/wiki/FAQ:The_Program

Thats more of a beginner program. Also its very strength focused. I started with something similar but later shifted to slightly higher reps and splits. More size for less work.

As others have mentioned, a grid of 6 columns by 4 rows, like the resolution of a display.

It's six wide and four tall.

A plank of wood? i.e. six by four

I thought of 4x6, the photo size.

6" by 4" photograph.

Me too. That's what 6x4 will always means to me -- standard sized prints.

As for the wording of the options, in maths terms, I never think in terms of 'so many lots of something' -- it's just 6 times 4 (well, I guess that's semantically the same as 4 lots of 6, but I'd never think of it in those words).

I read it as six by four, as in the size of a photograph in inches.

Standard dimensions for photographic prints, pre digital cameras.

6 inches wide by 4 inches tall.

Multiplication would be 6 * 4 or 6 × 4, not 6 x 4.

My first thought: a small rectangle (width: 6px, height:4px)

A 2-dimentional array with width = 6 and height = 4.

An unusual use of the 24x7; 6 hours for 4 days?

A 6 by 4 inch board of an undetermined length

6 wheels out of which 4 are driving wheels.

A box that is 6 units wide and 4 deep.

······ ······ ······ ······

A common photograph size

It reminds me of the 6to4 translation for IPv4 connectivity for IPv6 hosts.

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