#JIBC

[theohonohan]

The Creation of Quaternions

Growing up in Dublin, I was aware at an early age of talk of quaternions and pride in their discoverer William Rowan Hamilton. Unfortunately, this pride didn't translate into widely promulgated and accessible introductions to quaternions. There was instead a lot of insecure narcissistic celebration of the fame of quaternions (see this sort of thing). I can't blame Dubliners for feeling the need to bolster pride in Irish mathematical achievements, but it is all a bit empty without an insight into the mathematics itself.

I recently came across this introduction to the quaternion story in Stuart Hollingdale's Makers of Mathematics, a book I found on a reading list for prospective maths students. Here's the section about the discovery of quaternions. (Hollingdale does tell the Brougham Bridge part of the story, but I'm not including that.)

The Creation of Quaternions

The recognition that the real numbers can be interpreted as points along a line and the complex numbers as points in a plane led naturally to the search for ‘hypercomplex’ numbers that could be represented by points in three-dimensional space. In 1833 Hamilton read a paper to the Royal Irish Academy in which he pointed out that the plus sign in \(a + ib\) was a misnomer, as \(a\) and \(ib\) cannot be added arithmetically. Following Gauss, he proposed that a complex number should be regarded as an ordered pair of real numbers \((a, b)\) which obey certain operational rules, in particular \[ (a,b) + (c,d) = (a+c, b+d) \quad \text{(addition)} \] \[ (a,b).(c,d) = (ac - bd, ad + bc) \quad \text{(multiplication)} \] (Remember that \(i^2 = -1.\)) Hamilton then sought to extend this idea to ordered ‘number triples’, \((a, b, c)\), to be written as \(a + ib + jc\), where \(i\) and \(j\) are two distinct and independent square roots of \(-1\). The problem defeated him for many years: he could add and subtract his triples, but he could not multiply them. With hindsight, the source of the difficulty is not hard to pin down. The geometrical effect of multiplying one complex number by another is to change the length (or modulus) of the corresponding directed line (or vector) and to rotate it in the complex plane. In the polar coordinate representation of complex numbers, the ‘product’ of \((r_1 cos \theta, r_1 sin \theta)\) and \((r_2 cos \phi, r_2 sin \phi)\) is \[ (r_{1}r_{2}cos(\theta + \phi), r_{1}r_{2}sin(\theta + \phi)) \]

Since the direction of the axis of rotation is determined (it is normal to the complex plane), only one ‘length change’ and one rotational parameter are needed, i.e. two altogether. In three dimensions, however, we need two parameters to specify the direction of the axis of rotation, a third to determine the amount of rotation and a fourth to specify the change of length. The need to specify four parameters means that it is not possible to ‘multiply’ one ordered number triple by another. Hamilton knew, of course, that when a complex number \(a + ib\) is multiplied by its conjugate, \(a - ib\), the product is the positive real number \(a^2 + b^2\): the square of the modulus of either number. Let us consider the analogous operation for number triples. If we multiply \(a + ib + jc\) by \(a - ib - jc\), we find that most of the product terms cancel out and we are left with \[ a^2 + b^2 + c^2 - 2ijbc \]

Hamilton’s difficulty lay in the existence of the product term. Setting \(ij = 0\) will not do, because \(ij.ij = i^2.j^2 = (-1).(-1) = 1\), so we have a contradiction. After pondering the matter for many years, he noticed that the product term actually consists of two terms, namely \(-ijbc\) and \(-jibc\). If we assume that \(ij = -ji\), the unwanted term disappears. The crucial insight, which came to Hamilton in a sudden flash, as we shall see shortly, was the realization that he could break the commutative law of multiplication and still be left with a consistent mathematical structure. The next question is: what is \(ij\) itself? Now, \[ ij.ij = i(ji)j = - i(ij)j = -(i^2)(j^2) = -(-1)(-1) = -1 \] so it appears that \(ij\) is yet another independent square root of \(-1\); let us call it \(k\). As the product of two number triples will, in general, involve this new ‘imaginary’ number \(k\), we are led at once to the concept of ‘number quadruples’ \((a, b, c, d)\) of the form \(a + ib + jc + kd\), where \(i^2 = j^2 = k^2 = -1\). These three square roots of \(-1\) have a symmetrical relationship: \[ ij = k, jk = i, ki = j \quad \text{and} \quad ji = -k, kj = -i, ik = -j \] Since \(ij = k\), the result \(ijk = -1\) follows at once. Hamilton called these number quadruples quaternions. They obey all the fundamental laws of arithmetic with the single exception of the commutative law of multiplication. The operation of division can be defined by using the fact that \[(a + ib + jc + kd).(a - ib - jc - kd) = a^2 + b^2 + c^2 + d^2 \] A quaternion can be used as an operator to change any directed line from the origin in three-dimensional dimensional space into any other such line. The four numbers \(a, b, c\) and \(d\) are sufficient for the purpose, whereas number triples are not.

[bcfirearmsacademy]

Combination trigger locks are still on sale here at ours for Cabela’s. You always need trigger locks so why not get them when they’re 25% off 💥 🎯 Do you need your PAL or CORE? Visit www.bcfirearmsacademy.ca Online Study Guides Are Always free: Free online PAL tests & study material: https://bcfirearmsacademy.ca/product/firearms-safety-course-online-study-guide/ Free online CORE test & study material: https://bcfirearmsacademy.ca/product/online-core-hunter-education-course-study-guide/ #PAL #CFSC #CRFSC #Cabelas #JIBC #BCFirearmAcdemy #Firearms #Training#BC #Canada #Delta #Abbotsford #License #Gun #Course #PALcourse #UseofFore #ATC #CORE #exam #hunting #FWID BC Firearms Academy 604-592-2410 http://bcfirearmsacademy.ca https://www.facebook.com/BCFirearmsAcademy/ https://lc.chat/now/9783380/ (at Cabela's) https://www.instagram.com/p/B2R7N0UgOS_/?igshid=1n8tg0ol1xpna

[itsgarrylunn]

[shaziali]

#JIBC mark your calendars!! Looking forward to seeing y’all there. #DrShaziaAli #AestheticTreatments (at The Ritz-Carlton, Jeddah) https://www.instagram.com/p/BsS76-Olx6O/?utm_source=ig_tumblr_share&igshid=ajx6520f4kij

[mikedangeli]

A few weeks ago my buddy artist Jerry Whitehead posted a selfie with my pole at the JIBC, so I'm returning the favour with some of his beautiful work!! Keep on painting your works awesome buddy! #jerrywhiteheadpainting #jerrywhitehead #aboriginal #aboriginalart #firstnations #firstnationsart #jibc (at Justice Institute of British Columbia: JIBC)

[deansawthetvglow]

HE LIKES TOPPING OKAY I CANT DIG INTO THE IMPLICATIONS I CANT DO IT I AM THINKING ABOUT THE DOM BROW I AM THINKING ABOUT MISHA THIS IS ALL TOO CLOSE TO REAL LIFE I AM THINKING ABOUT JIBC-

[prospectiveparamedicblog]

The JIBC EMR course

What it is

EMR (emergency medical responder) is the lowest level of training one can have to work with BC Ambulance, and is a prerequisite to get into the PCP program. While most people who take this want to go down that path, it can also be used if you’re interested in going into fire, search and rescue, ski patrol etc. It is a three-week intense course similar to OFA 3 but with a pre-hospital focus rather than the workplace. You will be taught how to handle a variety of medical and trauma calls, get CPR-HCP (health care provider) certified, and even administer medications.

Weekly schedule

The first week we covered the equipment we will be using in our jump kits, how to operate the cot and load into the ambulance, emergency moves, how to perform a primary survey, CPR-HCP certification testing which includes a quiz, and began to cover cardiac and respiratory emergencies and the medications we are able to give.

The second week we wrote a quiz on the material from the first week, covered our diabetic protocol and medications, and dove head first into trauma. This included spinal management, some basic OFA skills, burn management, chest and abdominal trauma (flail chest, sucking chest wounds from stabbings or bullets), bowel eviscerations and protruding objects, and unstable fractures (pelvic and double femur fractures).

The third and final week was mainly spent practicing calls for our final practical exam, but there was still one more quiz covering week 2 material and a day talking about delivering babies, maintaining an IV line for paramedics, and stable fracture management (making arm splints and learning about the traction splint for legs).

The patient assessment model

We have a PAM (patient assessment model) we use for every single call scenario. It comprises of a scene survey, primary survey, and secondary survey. The first thing you must do is a scene survey to make sure the area is safe to enter. The acronym we were taught was HEMP BC:

H – hazards we rule out to make sure the scene is safe

E – environment. Is the patient outside in the freezing BC rain or safe in their beds indoors?

M – mechanism of injury or illness (MOI). Basically what caused the patient’s emergency

P – number of patients involved

B – body substance isolation (BSI) precautions. To remind you to put on gloves and think about glasses/masks/gowns if the situation calls for it.

C – condition of patient. What info you can gather just by looking at your patient (are they unconscious, obviously short of breath, grey and sick looking to indicate cardiac emergencies etc)

Once you determine the scene is safe to enter and you greet your patient, you’re going to want to do a primary survey. This is meant to be fast (2 minutes or less for EMR level) and to make sure you fix any life or limb threatening injuries. The faster you can memorize the order of your primary the faster you will be, and be sure to follow the order as it was made to tackle the most serious things first. This is just a brief overview, you will go through each step with more detail in the course, so don’t panic if you have no clue what any of this means.

D – Delicate spine, or D-spine. This is when you rule in/out spinal precautions

LOC – Level of Consciousness. We use the acronym AVPU (alert, verbal, pain, unresponsive)

A – airway. Examples of fixing an airway problem would be suctioning out fluids, placing the patient in a head tilt chin life/jaw thrust to lift the tongue out of the way, or inserting an airway adjunct (OPA or NPA).

B – breathing. Make sure patient breathing is adequate, if not you may need to ventilate for them with the use of a BVM

C – circulation. Assess the patient to see if they have a pulse or not, and the quality (ex. strong and regular). Obviously if there is no pulse you will want to start CPR

RBS – rapid body survey, meant to quickly feel the patient from head to toe for fractures or bleeds

S – skin assessment. This is meant to see how the patient is circulating

O – oxygen, this is when you determine if your patient needs O2 at all, and how much

A – another airway check. Mainly meant to remind you to go back and put an airway adjunct in if you haven’t already done so (for unconscious patients)

P – position. If your patient is unconscious and doesn’t require spinal precautions, you will roll them into recovery.

I – Interventions. If you find a bleed or a fracture etc this is when you go back and deal with them

RTC or Non RTC – Rapid Transport Criteria. Is this patient in critical condition and we need to transport ASAP to the hospital, or can we stay on scene a bit longer?

After your primary comes the secondary survey. This will be done in the back of the ambulance if you determined your patient was RTC, or on scene if you ruled in Non RTC. It involves critical history, vitals, head to toe examination, and a functional inquiry.

The first step in a secondary is to get a critical history from the patient, essentially we want to find out more about why we’re being called today and find out relevant patient medical history. The acronym for this is CHAMPLE:

C – chief complaint. What is the main reason the patient called 911 today

H – history of the chief complaint, a helpful acronym mainly used for pain but can be modified for any call is LOTTARRPS:

              L - location

              O - onset

              T - type

              T - timing

              A – associated symptoms

              R - radiation

              R - relief

              P - provocation

              S – severity

A – allergies (be sure to ask how the patient reacts to allergies)

M - medications

P – past medical history

L – last oral intake/last bowel movement

E – events leading up. Different than onset, this is asking how the patient has been feeling the past couple of days

The next step is taking vitals (if you’re on scene your partner can do these for you). The ones we want to know are GCS (measures level of consciousness and awareness), heart rate, pulse rate, blood pressure, skin assessment, pupils and their reactiveness, and blood oxygen percentage. If your patient is RTC you need to be taking vitals every 5 minutes, and every 15 minutes for not RTC.

Then comes your head to toe inspection. This is similar to the RBS but more thorough and you want to write down every bump and bruise you find on the patient. The final step is to do a functional inquiry. This is asking the patient 2-3 questions about every body system (neuro, cardio, respiratory, GI, GU, endocrine, and musculoskeletal).

Quizzes and Examinations

We had 3 quizzes (multiple choice), one final written exam (multiple choice as well), and two final practical examinations (one trauma, one medical). The passing grade for all of these was 71%, and we were given one remedial per quiz/exam. If you were not able to get 71% or higher on your remedial, unfortunately you would be withdrawn from the program.

The final practical exam remedials could be one of three things:

500 word essay (if you failed on something that wasn’t skill related)

Skill station (if you failed to do something technical that wasn’t life threatening such as the traction splint, arm splint, spinal collar application, vitals). You would not have to do a full call over again you would just need to demonstrate the skill

Full call remedial (if your overall mark was under 50%)

Tips for success

Read as much of your EMR textbook as you can before the course. While technically you are not required to pre-read, your days will be long and exhausting and you will probably not want to read 3 or more chapters a night before class

Take advantage of blackboard. This is the online access through JIBC and it has literally everything on there to make you successful. The practice quizzes were identical to the actual quizzes, you had access to call scenarios, and even links to web versions of your textbooks (so you don’t have to spend $35 on a CPR booklet that only has a page or two of necessary reading)

Practice practice practice! The more you run calls, the better you will be. Many of us would stay after class and come back on weekends to go over things we were struggling with but didn’t have time to cover in class.

Accept feedback. Not only from your instructor, but from your classmates as well. Odds are if you only have one instructor they will not see all of your calls but your classmates will and can give constructive feedback.

If you don’t know something, ask. It seems obvious but never be afraid to ask for more help. Everyone has strengths and weaknesses so if the medical calls aren’t your jam, ask help from those who love it. Can’t grasp spinal? Watch those who do and let them teach you. Can’t get a blood pressure reading? SAY SO and don’t make a number up!

Get a watch. Preferably one that does 24-hour clock and has a stop watch function as you will need these for vitals.

Don’t work on the weekends. Between weekend practice sessions, reviewing material for the upcoming quiz, and reading new material for the week there’s just too much on your plate to balance work.

Hopefully this has been helpful! As I said earlier, don’t worry if this looks overwhelming and you’re a complete beginner. Everything will make a little more sense as the course goes on, but I won’t deny it’s very fast paced and a lot to take in. If you’re willing to put in the effort of studying and practicing you’ll do just fine. The majority of my EMR class was beginners and we all passed in the end 😊

[breannebihari]

Second time at the gun range at school. Got to fire a semi automatic machine gun, a 34 revolver, a 44 revolver and a few other guns. Had a blast! @justiceinstitutebc #school #class #classess #socialenvy #PleaseForgiveMe #teacher #teachers #student #students #instagood #classmates #classmate #peer #work #homework #bored #books #book #photooftheday #textbook #textbooks #messingaround #JIBC #justiceInstituteofBritishColumbia #JIgunrange #gunrange

[thebusinesstips101-blog]

PRAXIS FEATURED ON-BOARD AMERICAN AIRLINES TALK BUSINESS 360

What is Praxis:

Praxis was made through research and development by the Justice Institute of British Columbia (JIBC) which is a leading North American public safety educator which gives dynamic justice and public safety education through its exceptional applied education, training and research. Number of leading companies and academic institutions is already using Praxis.

Praxis was featured on American Airlines on TALK BUSINESS 360 “Industry Innovators” on-board TV programming. The Industry Innovators TV program aired during the months of June and July 2017 reaching approximately 4.6 million business and leisure travelers on 27,000 flights worldwide. The TV show features one-on-one interviews and profiles of business leaders and innovators.

Source: https://www.praxissim.com/2017/07/13/praxis-featured-on-board-american-airlines-talk-business-360/

[nova0000scotia]

SWEET JESUS, MOTHER MARY AND JOSEPH... you shame all Canadians ... especially those who serve and save us and have continuously providing all the freedoms we hold so dear along with our individual liberty.... #SHAMEONCANADA  ... fix this... newspapers.... cause that where the real journalism lives in this day and age....

  quote:  “This is a country #China  – which the Chinese Communist Party has control of – this is the country that is detaining [Michael Kovrig and Michael Spavor] and we are training their police officers on Canadian soil? This makes absolutely no sense whatsoever. And for this not to be a significant issue in Canada, troubles me,” said Heed.

Former B.C. Solicitor General and retired municipal police chief Kash Heed says there is no need for a review; the program should be cancelled in its entirety, he said.“I am absolutely astonished by what is going on. I had no idea …and I cannot believe all three levels of government are allowing this to happen and the JIBC board is allowing this to happen,” Heed told Glacier Media.

Heed joins a chorus of other criminal justice and national security experts who think the program ought to be terminated.

“This is a country – which the Chinese Communist Party has control of – this is the country that is detaining [Michael Kovrig and Michael Spavor] and we are training their police officers on Canadian soil? This makes absolutely no sense whatsoever. And for this not to be a significant issue in Canada, troubles me,” said Heed.The review is not a clear rebuke of the program, unlike when the Canadian government issued statements to the public last December that a similar military training program with the People’s Liberation Army on Canadian soil had been cancelled.  #China #Canada #shame #2Michaels 

[bcfirearmsacademy]

Winchester thousand rounds 115 grain ammo it’s on sale for 60 bucks off. That’s 1000 rounds for two $39.99+ tax🎯 💥 Do you need your PAL or CORE? Visit www.bcfirearmsacademy.ca Online Study Guides Are Always free: Free online PAL tests & study material: https://bcfirearmsacademy.ca/product/firearms-safety-course-online-study-guide/ Free online CORE test & study material: https://bcfirearmsacademy.ca/product/online-core-hunter-education-course-study-guide/ #PAL #CFSC #CRFSC #Cabelas #JIBC #BCFirearmAcdemy #Firearms #Training#BC #Canada #Delta #Abbotsford #License #Gun #Course #PALcourse #UseofFore #ATC #CORE #exam #hunting #FWID BC Firearms Academy 604-592-2410 http://bcfirearmsacademy.ca https://www.facebook.com/BCFirearmsAcademy/ https://lc.chat/now/9783380/ https://www.instagram.com/p/B2FVlc0gRCq/?igshid=8v0gyaimx6q7

[itsgarrylunn]

[shaziali]

View this post on Instagram

A post shared by Shazia A Ali (@drshaziaali)

The teacher inside me needs to come & play from time to time. Sixteen lips, one full face along with a dozen #marionettelines plus #nasolabialfolds and #chins - It was sure fun yesterday!! #DrShaziaAli #JIBC (at The Ritz-Carlton, Jeddah) https://www.instagram.com/p/BsdJnQiFw3D/?utm_source=ig_tumblr_share&igshid=spd9vok1lgfp

[orangeandlester]

Hello! Your kindness and generosity has touched multiple lives in Cagayan through our donation drive! We've reached over 200 families with food packs and hygiene products. We have also included tracts in sharing the Gospel to provide not only nourishment for the body, but for the soul as well. Your support in our donation drive shows that no help is too big or too small from a heart that truly wants to help! We were able to reach people in Cagayan! However, our brothers and sisters in Christ in Butuwanan were also affected by the typhoon and our church building was heavily damaged. As part of JIBC Youth Fellowship initiative, we will be allocating 2nd batch of incoming donations to provide assistance in repairing our church building in Butuwanan, Siruma, Camarines Sur. We are still accepting  cash donations.  For donations: BDO Account - 004820183128 Gcash - 09771433321 Patricia Dequito Thank you for your support and for continuing to do what matters. May God bless your generous hearts.

[prospectiveparamedicblog]

First post!

Welcome to my blog! If you're like me, you're wanting to start a career as a paramedic but you're finding that information is lacking. You already binge read My Paramedic Blog which was beyond helpful but you're wanting more, especially after you found out it was written in 2009. I'm hoping that by sharing my own experiences I too can help inspire and help those who are curious about the process. Right now the route to becoming a paramedic (PCP) with BCAS (BC Ambulance Service) is still the same in 2017:

Complete an EMR (Emergency Medical Responder) course

Take the PCP course

Get licensed

Get hired

or

EMR course

Get licensed

Get hired

Take PCP course

Upgrade your license

As of now, I've just passed the EMR through JIBC course and am juggling the pros and cons of either path though I am leaning towards getting licensed and hired right away. I doubt this blog will be as personal as My Paramedic Blog and it certainly won't be as well written, but I will try and be as informative about the courses and process itself.

[breannebihari]

This is for international women's day which is tomorrow. We did this in our diversity class. #thiswomanmyhero #jibc #internationalwomensday2017 #internationalwomensday